Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
PLENARY INVITED PAPER
ON A VERY HIGH RATE SENSITIVITY OF CONCRETE FAILURE AT HIGH LOADING RATES AND IMPACT Janusz R. KLEPACZKO Laboratory of Physics and Mechanics of Materials Metz University, Ile du Saulcy, F-57045 Metz, France, e-mail:
[email protected] ABSTRACT During last decades, there has been increasing interest in the effect of high strain rates on mechanical behavior of materials including fracturing of rocks and rock-like materials such as different concretes. The subject of this contribution is on recent results of concrete testing at high strain rates in tension, compression and shear. The so-called pseudo-viscosity of compression failure discovered recently at high strain rates is analyzed. Special attention will be given to the recent results obtained in France, and in particular at Metz University, for dry and wet concrete loaded at different rates in tension. Experimental technique applying wave mechanics will be discussed anew to test brittle materials at high strain rates in tension. This technique is based on the phenomenon of spalling combined with the Hopkinson measuring bar. The results obtained in LPMM-Metz for the tension mode of failure will be compared with the recent results obtained in tension and shear modes at the University of Florida. It has been found that a high "anisotropy" of failure occurs for different modes of failure at high strain rates. The highest rate sensitivity is found in tension and the smallest in compression. The rate sensitivity in the shear mode is closer to the tension case. Clearly, the hydrostatic component of stress affects strongly the failure mechanisms of brittle materials. Finally, a model of failure applicable to short-time loading, which is based on the statistics of Weibul, will be mentioned.
Keywords Concrete, rate sensitivity, failure criteria, dynamic tension, spalling, dynamic compression. PRELIMINARIES Many concrete structures of special application like covers of nuclear reactors, off-shore units, shelters of strategic destination for personnel and equipment, are constructed with a thick reinforced concrete elements, for example slabs, shells, shear walls. Such constructions are susceptible to be subjected to accidents including earthquakes, collisions, impacts or explosions. It is clear that design and optimization of such structures, which are at high risk of being loaded by short time forces, must be accompanied by a precise data bank on dynamic behavior of concrete. During recent decades behavior of concrete in uniaxial compression has been studied at relatively wide range of strain rates, typically from quasi-static rate -lo4 I/s to high strain
2
Janusz R. KLEPACZKO
rate -lo3 11s. However, this is not the case when compared to dynamic behavior of concrete in tension where experimental data are very limited because existing experimental techniques will not allow for reaching in most cases the maximum strain rate of 30 Us. Indeed, very few experimental methods permitted to exceed the strain rate limit of 10 Us. Among those few experiments, the early one based on wave effects causing a spall failure, that can be also called the "Stress-Wave Technique", [l-31, can be mentioned. In those methods a compression longitudinal elastic wave generated on one side of relatively long bar is reflected at the free end as a tension one causing failure by spalling. The first publication on concrete spalling was reported in [2]. A compression incident wave is usually generated by explosives or by mechanical impact on to the incident side of the bar. This technique permits to attain a strain rate of about 20 Us, [4,5]. The range of strain rates of the same order as in the "Stress-Wave Techniques" can be obtained by different adaptations into tension the Kolsky apparatus more commonly called the Split Hopkinson Pressure Bar (SHPB), [ 6 ] .One of a more recent arrangement of the Kolsky apparatus to test concrete in tension is loading of the incident bar by impact tension using a falling mass, such setup has been constructed by the Delft University of Technology, [7]. Another direct adaptation of SHPB to tension is application of the Brasilian specimen placed between the incident and transmitter bars. Experimental programs on concrete by means of this technique, [8], were conducted recently at strain rate in tension of about 20 Us, [9]. Those low and high strain rate tests in tension on variety of concretes indicate true rate effects on failure for this material with two ranges of strain rate. The first one is characterized by a moderate increase of the failure stress from quasi static rates up to 1.O lls, for example the review published in [lo]. In the second one, the dynamic strength may increase even up to six times of the quasi-static value at strain rate of 20 l/s, [4,11]. For strain rates lower than about 1.O Us, several investigators attribute the rate effects observed to the presence of excess moisture in concrete, [12,13]. The higher strengths in the second region may be due to viscous-type and inertia forces acting on micro-cracks at the macro level or due to dynamic superposition of micro-cracks, [ 151. Nevertheless, the substantial increase of the rate sensitivity of failure in the second region, that is at strain rates higher than 1.O l/s still poses an open question as to physical reasons of this phenomenon. One of many reasons may be related to the inertia of micro-cracking, [ 141, or in parallel a multiple dynamic interaction of many micro-cracks, [ 151. More recently, a set of results has been presented in [ 161 on "mini concrete" failure (small size of aggregate) in tension and compression. Later new results for the same material tested at high strain rates in shear were published in [17]. In order to obtain the shear mode of loading a large diameter SHPB was applied with a special specimen configuration to convert compression into shear. Again, a high rate sensitivity of failure stress was found above strain rate approximately 10.0 Us. Experimental techniques, which are briefly mentioned in the previous part of this paper, have some limitations, specially in case of tension, as to measurements and precision of experimental conditions. Thus a new experimental technique to test dynamic tensile strength of brittle materials has been developed in the Laboratory of Physics and Mechanics of Materials at Metz University, [18]. This experimental technique combines in an efficient way all advantages of Hopkinson bar used as measuring instrument and as device to impose a wave loading onto specimen being in touch with the transmitted side of the bar. The arrangement is discussed briefly in the next part of this paper. The LPMM setup has permitted to conduct a series of spall tests on so called "mini-concrete" MB 50 due to small size of aggregate (maximum diameter 2.0 mm). Experiments were conducted on this concrete in dry (0 % of humidity) and wet conditions (100% humidity) at the range of strain rates very difficult to reach in tension by other experimental techniques, that is from 20 I/s to 120 Us.
-
3
On a v e y high rate sensitiviv of concrete failure at high loading rates and impact
The overall scope of this study is the characterization of mortar or concrete behavior at high strain rates in tension, shear and compression. Experimental results reported in the literature and discussed below indicate for a strong increase of the strength observed at high strain rates in tension shear and compression. The analysis of the relation between the failure stress and the loading time indicates for a delayed fracture. TENSION TEST - EXPERIMENTAL TECHNIQUE
An important limitation for experimental methods of dynamic tension for brittle or quasibrittle materials, which are also heterogeneous, is the effect of wave propagation and wave dispersion in specimens. As to problems related to measurements, a direct determination of small strains on a concrete specimen surface is not so precise. In both cases, like application of strain resistance gages and displacements gages to measure the mean deformation over all specimen length at the instant of failure is also difficult. For example, use of the linear voltage differential transducers (LVDTs), in order to measure the net specimen displacement, shows in addition to inertia effects, some difficulties associated with a band pass of signal conditioners, [7]. Concerning the experimental techniques of dynamic tension test of brittle materials, which are based on the split Hopkinson pressure bar (SHPB) arrangement, it is difficult to find a compromise between the diameter of Hopkinson bars and the specimen size. Both sizes are important because phenomenon of the wave dispersion in bars and specimen limits the maximum strain rate defined as the difference of the two velocities of two specimen faces, [6].A more detailed discussion of those problems obscuring measurements in tension SHB, including wave dispersion, is given in references [ 18,21-271. The principles of the arrangement based on only one Hopkinson bar, which are shown in Fig.1, are as follows: a striker bar which is accelerated by a gas launcher impacts coaxially an instrumented Hopkinson bar in tight contact with a concrete cylindrical specimen. The striker, the bar and the specimen are of the same diameter 40 mm. The lengths are respectively: 120 mm, 1000 mm and 120 mm. The striker and the measuring bar are made of the same hard aluminum alloy 6060-T5 having very close mechanical impedance in comparison to concrete.
ur VO
e
CT5 t.
3 2
y>ccitricii
Mcdwriiig bdr
plolcclllc
Fig. 1 Arrangement for dynamic tensile test by spalling, 51,52 and 53 are SR stations. After impact of the striker on the measuring bar an incident compression wave 01 (t) is generated, this wave propagates along this bar up to the interface bar/specimen. Because a slight difference in the mechanical impedances of the measuring bar and the specimen, the incident wave is partly reflected back as tension wave OR (t) and partly transmitted into the specimen as compressive wave OT (t). This transmitted compressive wave is refldcted from the free end of the specimen as a tension wave. A superposition of the transmitted
4
Janusz R. KLEPACZKO
compression wave into specimen with the reflected tension wave, which propagates in the opposite direction, generates a fast increasing tension stress causing fracture at the specific distance from the specimen free end. Possibility to use different striker lengths (80 mm, 120 mm, 160 mm) and to apply different impact velocities enables to achieve relatively high local loading rates of spalling. However, application of high amplitudes of the incident wave leads to a consecutive multiple spalling, for example Landon and Quiney [2]. In such situation the chronology of spalling is very important. When a multiple spalling occurs only the first one was analyzed (only the first spalling is recorded by the measuring bar). In order to find the chronology of spalling, as well as to observe development of failure, a coupled arrangement of six fast CCD cameras has been applied [ 191. It is important to note that the specimen wave history of loading can be exclusively controlled by the Hopkinson bar data. In order to determine the whole wave history the Hopkinson bar called also the measuring bar has been instrumented with three SR gage stations, Fig.1, with adequate potentiometric circuits and three wide band amplifiers. More details on measurements are given elsewhere [ 181. In order to analyze the experiment the principal objective is reconstitution, with maximum possible precision, the stress impulse CJT (t) transmitted into a concrete specimen. The reconstitution of the transmitted wave OT (t) is based on precise measurements of the incident q(t) and reflected oR(t) waves. The time of the specimen loading is determined by taking into account the geometrical wave dispersion analyzed theoretically elsewhere, [ 18,2 1-27]. On the other hand, it was assumed, because of the small length of the specimen (120 mm), that the theory of one-dimensional wave propagation is sufficiently exact for this case. Starting from the computer files of the compression wave transmitted into specimen in the form GT(t), all process of wave superposition up to failure, which is assumed instantaneous over entire specimen cross section, is simulated numerically by a special program written in the MappIeR framework. The numerical analysis permits for determination of the loading history aF(t) in the specimen cross-section where spalling occurred, the critical time to failure L,and also the local strain rate B =
4 where , ZC is the distance of the failure from the specimen free 4
end. The distance of the cross-section & from the specimen free end where spalling occurred was carefully measured after each experiment. TENSION TEST - EXPERIMENTAL RESULTS A review of experimental techniques applied in tensile testing of concrete and comparison of some results was published in [lo]. The experimental results of the last three decades of the XX Century were collected in the form of the DIF as a function of the logarithm of strain rate in one of the figures in that paper, where the DIF means the Dynamic Intensification factor, defined as the ratio of the current failure stress at specific strain rate to the quasi static failure stress at strain rate Us. It was shown that the rate sensitivity of the failure stress substantially increases as a function of strain rate. The rate effect intensifies at strain rates above approximately 0.1 Us. This review also shown that it is very difficult to test brittle materials, including concrete, at strain rates above -jO Us. Since that time no experimental data were available at strain rates above -10 11s. Strain rate effects in tension on various cementitious materials have been reported in several publications, [8,9,16,17,20,29]. Here, only two sources will be analyzed, that is the results reported in [17] and the data of LPMM-Metz, [18]. In general, it is of interest what kind of law governs the rate-sensitive failure at strain rates above -10 lls. Two
On a very high rate sensitivity of concrete failure at high loading rates and impact
5
approximations given below will be analyzed, the standard definition of the rate sensitivity p and the pseudo-viscosity q. Those two parameters are defined by the equations given below. The standard rate sensitivity p
OF
+ p log
= OFO
(
fo)
and
p=(*)
ai0g.i
when the DIF is introduced equation ( I ) is transformed into the form
)-!
D = 1 + pDlog( where D = a , / a , , and The pseudo-viscosity q
pD=p/O,,,,
and
pD= ( alog8 E)
&=1.0 11s.
when the DIF is introduced equation (3) is transformed into the form
D=1+qD8
and
r].=(%)
a0
(4)
where qD = r ] / a,, . Values of the rate sensitivity p and the pseudo-viscosity q has been analyzed for experimental data given for tension in [8,17]. The standard SHPB arrangement was used together with the specimen splitting technique. The large diameter SHPB loads a disk specimen rotated go", so the load is applied along the specimen diameter. This is so-called "Brasilian Test" applied in dynamics. However, in order to determine the failure stress in tension a hybrid approach must be used by applying numerical analysis along the specimen. It has been confirmed numerically that the stress distribution in the central part of specimen at failure is similar for both the dynamic and quasi-static loading [8]. But because of dense distribution of experimental points obscuring the trend of data the experimental points were reanalyzed by approximation of clusters of two to three points by one mean point. Such procedure resulted in more clear trends to be shown. The reanalyzed results are shown in Fig.2; a - in the form of D(log 8 ) and b - in the form of D( i ). After Fig. 2b the rate sensitivity can be determined only at strain rates higher than -5.0 11s. The same is for determination of the pseudo-viscosity qo after points of Fig.2b. Simply, the transition strain rate from the low strain rate behavior to the high strain rate behavior is estimated for those experiments as 8, =4.6 11s. Estimated values for both rate sensitivities are p0=2.15 and q~=3.28*10-~ s.
6
Janusz R. KLEPACZKO
FAILURE IN COMPRESSION FOR MORTAR
“ 1 6 0.5
o ! 1 2 3 Log (STRAIN RATE) [lk]
0
Fig.2a
4
FAILURE IN COMPRESSION FOR MORTAR
3 ,
o ! 0
200
400
600
800
1000
STRAIN RATE [lls]
Fig.2b Fig.2 Rate sensitivity of mortar in tension, [8,17], a- logarithmic scale, b- linear scale. The LPMM experimental data obtained up to much higher strain rates intension, -120 Us, for wet mini-concrete MB 50, [18], are shown in Fig.3 together with the data of Fig 2 for mortar, Fig.3a in the logarithmic scale of strain rate and Fig.3b in the linear scale of strain rate, The concrete that has been tested in LPMM (MB 50) had the maximum aggregate size 2.0 mm, relatively high cement dose CPA HP and the ratio of the watedcement was 0.5. The technology in preparation of the concrete was optimized to assure a high level of homogeneity of all components. All doses and mechanical characteristics of the concrete are given in [18]. The stress rates determined by the numerical analyses of the records vary between 800 GPa l/s up to 5000 GPa l/s, corresponding to strain rates varying from -20 l/s to -120 Us.
7
On a very high rate sensitivity of concrete failure at high loading rates and imact
FAILURE IN TENSION FOR MORTAR AND WET CONCRETE 14 m=
12
0
1
0.5
1.5
2
2.5
Log (STRAIN RRATE) [ l l s ]
Fig. 3a FAILURE IN TENSION FOR MORTAR AND WET CONCRETE 14
--
12
r
z
10
$ 8
z
F 6
z
! k 4 0
2
01
0
Fig.3b
100 STRAIN RATE (I/$] 50
150
Fig.3 Rate sensitivity in tension of mortar (shown in Fig.2) and wet concrete MB 50, a- logarithmic scale of strain rate, b- linear scale of strain rate. As shown in Fig. 3 a substantial increase of strength is observed as a function of strain rate. Remembering the quasi-static strength of the wet concrete as CTF = 4.0 MPa the relative increase of strength at high loading rates (DIF) is of the order from 4 to 10 times within that range of strain rates. Another conclusion obtained aAer experimental results reported in the literature, as well as the results reported in this paper, is that above strain rate 1.0 l/s the same trend of steep increase of the tensile strength is found without any sign of saturation at
-
8
Janusz R. KLEPACZKO
-
120 Us. In general, the results for the mortar obtained at much lower rates are fitting very well with the results for the MB 50 wet concrete. However the rate sensitivities PO and T ~ for MB 50 are higher than for the mortar, PD = 9.85 and T ~ = D 8.94*102 s . The same analysis of the test data has been applied for the MB 50 dry concrete. The results for dry MB 50 along with the mortar data are shown in Fig.4, Fig.4a as the logarithmic scale of strain rate and Fig.4b in the linear scale. FAILURE IN TENSION FOR MORTAR AND DRY CONCRETE
-7 -6-
gz 5 -
Pz 43 -LL
E 2 -
0
0.5
1
1.5
2
Log (STRAIN RRATE) [ U s ]
Fig.4a
FAILURE IN TENSION FOR MORTAR AND DRY CONCRETE 8
-7
C 6 2
Q 5 v)
Ez 34
k 2 1
0 0
Fig.4b
20
40
60
80
100
STRAIN RATE [l/s]
Fig.4 Rate sensitivity of mortar in tension (shown in Fig.2) and dry concrete MB 50, a- logarithmic scale of strain rate, b- linear scale of strain rate. As shown in Fig.4 a substantial increase of DIF in observed for the dry concrete. Since the quasi static failure stress is estimated as OF = 5.0 MPa at high strain rate 2 80 U s the DIF increases up to -7.5. Again, above the critical strain rate estimated for tension as 4.6 l/s the
D
9
On a very high rate sensitivity of concrete failure at high loading rates and irnact
rate sensitivities of the dry MB 50 are high, but slightly lower in comparison to the wet concrete, PD = 4.91 and V D = 8.31*10-2 s. Of course, in both cases, that is wet and dry concrete estimation of the rate sensitivities in tension is preliminary. No statistical methods were applied indicating which fit is better, logarithmic or linear. More detailed statistical analyses with higher number of tests should be performed in the future. SHEAR TEST - EXPERIMENTAL RESULTS The only shear tests reported relatively recently are those in [ 171. The same mortar was tested as in tension using the Brasilian specimen, Fig.2. This time the shear strength data were obtained by using a special geometry sp.ecimen loaded in compression by SHPB, [ 171. Those results have been reanalyzed using real experimental points provided by Dr. Ross [29]. The failure stress as a function of strain rate is shown in Fig.5. In FigSa is shown the shear strength as a function of the logarithm of strain rate, and in Fig 5b in the linear scale of strain rate. The rate effects in shear are equally strong as in tension. The transition point from the low rate sensitivity to the high rate sensitivity region is estimated as .kc = 10 l/s, see FigSa. Because of the limited number of tests performed in shear it is difficult to estimate the rate sensitivities. A rough estimation leads to the following values: PD =3.29 and T D =1.39*10-2 s. At strain rate -lo2 l / s the level of DIF is lower, DIF = 4.5 as compared to the tension data for the wet concrete MB 50 (Fig.3), at strain rate -lo2 l/s the DIF is approximately -10. Value of DIF at -lo2 l/s estimated by extrapolation (Fig.4a) for dry MB 50 is -7.5, still higher than for strength of mortar in shear.
FAILURE IN SHEAR FOR MORTAR
4.5 -
- 3.5 -
f
4-
L
0.5
transition point
0
0
FigSa
0.5
1
1.5
Log (STRAIN RATE) [l/s]
2
2.5
10
Janusz R.UEPACZKO
FAILURE IN SHEAR FOR MORTAR
I
o ! 0
Fig.Sb
50
100
150
STRAIN RATE [Ils]
Fig.5 DIF strength of mortar in shear, [ 17,291, a- logarithmic scale of strain rate, b- linear scale. Because of limited number of points, values of the rate sensitivities in shear are approximate. Similarly as for tension, more tests should be performed in shear to apply statistical approach to find which approximation is the most exact. It seems that for higher strain rates the pseudo-viscosity approach (linear approximation) to the rate sensitivity is slightly better. It is interesting to note that transition from low to high strain rate sensitivity occurs for shear at strain rate -10 l/s. This is higher value than for tension -4.6 Us.
COMPRESSION TEST - REVIEW OF EXPERIMENTAL RESULTS Compression test of concrete has been applied probably at the same time when this construction material has been put on the market. In spite of early applications, for very long time compression tests were carried out only in quasi-static conditions. Development of new experimental techniques like fast hydraulic machines and SHPB, with specimen confined or not, make it possible to advance compression testing to high strain rates. Availability of those new devices caused more research and publications in compression testing of mortar, variety of concrete and geologic materials. Typical range of strain rates applied in compression l/s to -lo3 Us, that is nine decimal orders. testing is from In this paper only the high strain rate region will be discussed. The main task is to demonstrate variations in the rate sensitivity of concrete when the loading path (hydrostatic component of stress tensor) changes fi-om tension via shear to compression. Only one paper reports those three paths of loading for the same concrete, [17], so the results reported for compression have been reanalyzed in the same way as for tension and the final result is shown in Fig.6, in Fig.6a in the logarithmic scale of strain rate and in Fig.6b the linear scale is used.
11
C,, .v e y high rate sensitivity of concrete failure at high loading rates and impact FAILURE IN COMPRESSION FOR MORTAR
0
1
2
4
3
Log (STRAIN RATE) [l/s]
Fig.6a FAILURE IN COMPRESSION FOR MORTAR
-=
32.5 -
A
1
I 0.5 - transition point
'
I
0 0
200
400
600
800
1000
STRAIN RATE [Ws]
Fig.6b Fig.6 Rate sensitivity of mortar, reanalyzed after [ 171, a- logarithmic scale, b- linear scale of strain rate. Although the scatter of data is substantial it can be concluded that linear approximations in both cases is acceptable. However, in order to show which fit is the best more tests should be needed to apply statistical analyses. Here a preliminary estimations of the rate sensitivities D 3.28*102 s. It is interesting to note that both yield the following numbers: PO = 2.15 and T ~ = rate sensitivities are much lower than those obtained in tension and shear. On the other hand the transition strain rate to the high rate sensitivity regime is much higher, i.c = 49 l/s. Also the MB 50 wet and dry concrete was tested in compression in LPMM-Metz (fast hydraulic machine) and in Ecole Polytechnique-Palaiseau (SHPB and direct impact). The results for the complete spectrum of strain rate from lo4 11s to -lo3 l/s are published elsewhere [30], here the results has been transformed into DIF and limited only to the high strain rate region. Such transformed data for MB 50 are shown in Fig.7 for the wet state and
12
Janusz R. KLEPACZKO
in Fig.8 for the dry. For the wet and dry MB 50 the quasi-static failure stress was respectively OF = 42 MPa and (TF = 52 MPa. FAILURE IN COMPRESSION WET CONCRETE MB 50
-
- 3.5 = . 3
z
9 2.5
v) v)
$
a
2
2 1.5
8
z 1 U
5 0.5
1
1.5
2
2.5
,
3
Log (STRAIN RATE) [lk]
Fig.7a FAILURE IN COMPRESSION WET CONCRETE MB 50
-
3.5 2 3 G5 2.5 v) 0
E
2
8
1.5
E
l
z
LL
0.5 0
0
Fig.7b
200 400 STRAIN RATE [l/s]
600
Fig.7 Rate sensitivity of wet MB 50 concrete in compression, a- logarithmic scale, b- linear scale of strain rate, the lowest three points - hydraulic machine, squares - direct impact, diamonds - SHPB . In this case the linear fit to the data seem to be slightly better for the logarithmic scale of strain rate, but the limited number of points eliminates statistical approach to show the best fit. The rate sensitivities obtained for this wet MB 50 are as follows: PD = 2.74 and q D = 6.46*10” s. Again those rate sensitivities are much lower than obtained for the same material in tension, see Figs.3 and 4.The transition strain rate is estimated for MB 50 as -90 Us. The same analysis has been performed for the dry MB 5 and the results are shown in Fig.8, in both logarithmic and linear scales of strain rate.
13
On a very high rate sensitivity of concretefailure at high loading rates arid impact FAILURE IN COMPRESSION DRY CONCRETE MB 50
-
2.5
Y
z
2-
2
1.5 -
=8
1-
Q rn
. . =. ... . #
E
8
4
.=e
z
I.0.5 0
01 I
1.5
2
2.5
3
Log (STRAIN RATE) [lls]
Fig.8a
FAILURE IN COMPRESSION DRY CONCRETE MB 50
-- 2.5 :2
E! rn
8
1.5
f8 l
t
z
5 0.5
[transition]
0
0 0
Fig.8b
200
400
600
800
STRAIN RATE [ l l s ]
Fig.8 Rate sensitivity of dry MB 50 in compression, a - logarithmic scale, b - linear scale od strain rate, the lowest points (diamonds) - direct impact, squares - SHPB. The results for the dry MB 50 are very similar as for the wet concrete. The linear approximations are equally possible for both cases. The rate sensitivities for the dry MB 5 are: PO = 1.63 and T ~ =D 2.4*10-3s. As expected those values are lower than obtained for the wet concrete. An enhanced rate sensitivity of failure by the water content in concrete is relatively well documented in the low strain rate range. The result reported here is relatively new. The effect of the water content can be measured by the ratio of the rate sensitivities for wet and dry concretes, Rp = POW/ POD and R,= ~ D /W~ D ,D in the case of MB 50 those ratios are: Rp = 1.68 and R, = 2.69. The effect of the water content is quite substantial in compression. On the other hand the same ratios can be obtained for MB 50 tested in tension. After values of the rate sensitivities given for tension failure by spalling in the previous part of this paper the
14
Janusz R.KLEPACZKO
ratios of the rate sensitivities are: Rp = 2.01 and R,,= 1.08. The effect of the water content is also present in tension failure. Because availability of experimental data for mortars and concrete from different sources some of those results are shown and discussed in the next part of this paper. The main reason is to gather more results in order to find a range of rate sensitivities for different materials from different sources. The absolute values of the pseudo-viscosity q will be only analyzed here. The first example is estimation of the pseudo-viscosity for mortar of different maturity, 28 days and 6 months [14]. The failure stress of mortar versus strain rate in the linear scale of strain rate is shown in
Fig.9 Rate effects and pseudo-viscosity for mortar of two maturity periods, [14]. Another example is shown in Fig.10 in the form of reanalyzed data obtained in compression (SHPB) and reported in [31]. The chart shown in Fig.10 is in the form GF (i). MAXIMUM STRESS VS STRAIN RATE
180
z
I6O 140 -
::120 Y
5
3
9
-
-
100-
806040-
20
Mortar (Giorgia Tech.)
0
200
400
600
800
1000
1200
1400
1600
STRAIN RATE [lh]
Fig.10 Reanalyzed data for mortar reported in [3 11.
1800
On a very high rate sensitivity of concretefailure at high loading rates and impact
15
For both cases shown in Figs.9 and 10 relatively good fit to the points is obtained in the linear scales of failure stress and strain rate, indicating that for this wide range of strain rates the absolute value of the pseudo-viscosity q is a reliable measure of the rate sensitivity of mortars and concrete in compression. These data, and also other sources, were used to compare the pseudo-viscosity for different materials (coal, mortar and concrete), this comparison is given in Table 1 .
Coal Coal
3.03 4/29
ofo- z***
Mortar Mortar Mortar
4.52 4.39 3.35
ofm- 28 days
Mortar Mortar
4.27 5.95
of,,,- 28 days of,,,- 6 months
Mortar
8.63
of,,,- no maturity
Concrete (dry) 12.48 Concrete (wet) 21.14
ofm
Klepaczko (1982)
-Z Tianxi et al. (1983)
of,,,- 2 months of,,,- 3 months Klepaczko ( 1990)
Zhou (1 999)
ofm- more than 28 days Gary and of,,,- more than 28 days, Klepaczko (1996)
of,,,- more than 28 days Brara and Concrete (wet) 87.1 (spa11 tension) Klepaczko (1999) * Note qo = 3 q a . ** I direction parallel to the bedding plane. 45' direction inclined 45' to the bedding plane. *** Z - direction is perpendicular to the bedding plane.
I
Table 1 shows that the order'of the pseudo-viscosity q is comparable for di ferent rock-like .values l of q. materials, including coal. In general the MB 50 concrete shows relatively hi $ Also a substantial increase of q for tension in comparison to compression is obvious. An interesting effect of aggregate on the rate sensitivity in compression has been reported in [Malvern]. The compression test data reported in [Malvern] (SHPB) has been reannlyzed
16
Janusz R. KLEPACZKO
for four different concretes and the results are shown in Figs.11 and 12. Although number of points was limited the statistical analyses by linear regression were performed in order to more precisely compare the differences of the rate sensitivity q for those concretes. The regression coefficients are given in figures as well as in Table 2. It is clear that the rate sensitivity to failure may vary when the strength parameters of aggregate change. The correlation coefficient is found to be around 0.9. This is not the value indicating for a perfect MAXIMUM STRESS VS STRAIN RATE
-0.95031 Andesite aggregate
E
Seattle gravel aggregate
04 0
20
60
40
80
120
100
140
STRAIN RATE [ l l s ]
Fig. 1 1 Rate sensitivity of two concretes with different aggregates, reanalyzed data after [ 111, triangles represent the best fit. MAXIMUM STRESS VS STRAIN RATE 300
-P
250
)-l
Limestone aggregate
200 v) v)
Lu
g
150
5
9
E
lcon.0.90161 Solite Lightweight aggregate
loo
50
04 0
20
40
60
80
loo
120
STRAIN RATE [lls]
Fig. 12 Rate sensitivity of two concretes with different aggregates, reanalyzed after [ 1 I], extreme triangles represent the best fit. fit when the correlation coefficient should be close to 1.0. However, for relatively small range
On a very high rate sensitivity of concretefailure at high loading rates and impact
17
of strain rates applied, maximum strain rate -120 l/s, the correlations indicate that the linear approximation is acceptable for the purpose of comparison. The figures as well as Table 2 indicate that different kinds of aggregates may change not only the stress level of failure but also the rate sensitivity. It is interesting to note that a stronger aggregate increases the rate sensitivity. Since it is believed that the main source of the rate sensitivity in concrete, rocks and ceramics are processes related to micro-cracking inertia and its mutual interaction a stronger aggregate will slower those processes. The rate sensitivities found for those concretes are much higher, 35.0 [Pa*s]*104 < q < 116 [Pa*s]*104 that those obtained for mortars, 3.4 [Pa*s]*104 < q < 6.0 [Pa*s]*IO4 . Mortars have larger contact surface per unit volume between quartz grains and matrix so the probability of cracking on the meso-level is higher. TABLE 2 VALUES OF PSEUDO-VISCOSITY q DETERMINED FROM EXPERIMENTAL RESULTS, DATA AFTER [ 111
7 = (--)aT U f m
as
Material
Pseudo-Viscosity
[MPU * s]
T - constant temperature
Conditions
Correlation
Seattle Gravel
44.46
13.0
0.9291
Limestone
115.50
13.0
0.9203
34.3 1
9.5
0.9016
Solite Lightweight
The review of the concrete behavior at high strain rates in tension, compression and shear confirmed occurrence of very high rate sensitivities for all types of loading. Although transition from the region of low rate sensitivity to the high rate sensitivity is not abrupt, in general the transition strain rate can be specified practically for all experimental data. It is interesting to note that this transition increases at least one decimal order for compression. GENERAL DISCUSSION AND REMARKS ON MODELING
It is well known that concrete is a multiphase complex material consisting aggregate of various sizes and irregular shape. The aggregate is dispersed and embedded in hardened cement paste. Different imperfections like small voids, interfacial cracks between aggregates and cement matrix, micro-cracks inside the cement paste and small water bubbles are usually
18
Janusz R. KLEPACZKO
found due to manufacturing procedures. In addition, during the hardening period variety of physical and chemical processes occur. This is the main reason why mechanical behavior of concrete is so complex. The multiplicity of factors affecting the mechanical behavior in general, and at high loading rates in particular, may explain many difficulties encountered in attempts to formulate general constitutive models for this material. Variety approaches may be already found in the open literature. It is out of scope of this paper to review all formulations, the most common is application of the framework of rate-dependent plasticity theories with account for compressibility. A promising direction in modelirig of failure end fragmentation of brittle solids is a multiscale approach, [15]. Such models have been developed for ceramics, however, there is no limitation in application of the multi-scale approach to concrete. Here, one model that seems to be applicable to concrete failure in dynamic conditions of loading will be briefly discussed. Since the population of flaws that lead to crack nucleation may be different in tension and in compression the model discussed is limited to damage in tension. The main factor leading to structural failure is assumed to be crack nucleation and growth. Cracks are supposed to emanate from defects and relax the local stress of their surroundings and next to propagate. This process leads finally to formulation of damage in larger volumes and kinetics law. The model predicts transition between single and multiple fragmentation. The nucleation of a crack in brittle materials subjected to quasi-static tension is assumed to be due to existing micro-defects defined by the local failure strength a, (n,). When the equivalent stress a(x,), that is the maximum principal stress, is greater than a,(x,) a crack emanating from the defect leads to the failure of entire structure. The local failure strength is a random function related to the defect spatial distribution within the material. Therefore, the ultimate strength in the model is not deterministic and the failure probability PF can be defined by the Weibull distribution, [32], leading to the "weakest link model". The distribution PF can be represented by the following relations
where ht is the defect density, m is the Weibull modulus, QO and ho are respectively the reference stress and the reference defect density, (SF is the failure stress, that is the maximum equivalent stress in the considered domain, Z,r is the effective volume, surface or length. The microstructure of the undamaged material is approximated in the model by the defect density ht with random spacing. The mean failure stress ow and corresponding standard deviation q d are given by
Note that in the present discussion all relations are given in general form the explicit relations are given in the original publication [ 15). In order to take into account crack nucleation the interaction of nucleated defects and other defects that would nucleate must be analyzed. When a crack nucleates it creates obscuration zone with time where the local stress normal to the crack is decreasing. The defects inside this zone are shielded and do not nucleate. Thus, the total density ht can be split into two parts: the density of broken ht, flaws and the .density of shielded (obscured) flaws h, . The distribution of total flaws within the zone of measure Z is assumed to be modeled by i Poisson point process of intensity ht [o(t)]. New cracks will initiate only if the defect exists inside the considered zone and if does not belonging to the relaxed zone. The time evolutiori
On a very high rate sensitivity of concretefailure at high loading rates and impact
19
of the broken flaws is given by
with hb(0)= h,(O)= 0. For a very high stress or strain rate most of the initial defects nucleate before any significant development of the shield zones, that is
On the contrary, when a very low stress or strain rate is applied, the shielded zone occupies the whole volume and then
z,(t)=, Z
(9)
where n is the space dimension (n = 1 for a line, n = 2 for a surface and n = 3 for a volume). It means that after the first crack nucleation (weakest defect) the further nucleation is stopped due to shielding and the shield zone &(t) occupies the whole volume Z. The initial defect population hl defines both the quasi-static and dynamic failure. The fraction of relaxed zone (9) defines also the rate-dependent damage D(t). Because of those two extreme cases a transition must be assumed between those two processes of failure: the low rate failure and the high rate failure. When the dynamic proportional loading is considered with a constant stress rate d- = d D~i d t the characteristic stress CT,= d-tc can be defined by the characteristic zone of measure Z, containing one flaw that may break at the characteristic time . Consequently, two failure criteria were derived in [15], one in the form of Eq.(6) , for quasi-static cases (one defect triggers failure) and the second given below for dynamic loadings where the ultimate applied stress Ci is related to the local critical stress ccand the Weibull statistics P
The ultimate stress in tension id defined by standard relation
Those closed form solutions were analyzed numerically in [ 15,331 using Monte-Carlo simulations. The result of the simulation for a ceramic is shown in Fig.13. It is interesting to note that the closed form solutions for quasi-static or dynamic regimes, as it is observed in the experiments discussed in this paper, permit to find the point of transition kc = E i., . The transition between single and multiple failures can be estimated as the intersection between the weakest link and the multiple fragmentations, the condition is given by, [ 151
20
Janusz R. KLEPACZKO
---- Weibull law
Multi-scale
Dimensionless volume, Z/Z, 10-5 10-4 10-3 10-2 10-1 1
10’
102
1o3
10
1o4
102
103
1o5
Stress rate (MPdps) Fig.13 Ultimate macroscopic failure stress vs. stress rate predicted by the multi-scale model [15] and Monte-Carlo simulation [33] for a ceramic. The transition does not only depend upon Weibull parameters characteristic of a material but also involves the size of the considered element Z and the applied stress rate & , [15]. It can be concluded after analysis of the multi-sale model that the fragmentation of brittle materials at different rates is a combination of material parameters, size and rate or strain rate. Fig.13 shows that when Z / Z , 2 1 the scatter of the ultimate strength becomes very small. In other words, when the loading rate increases the characteristic scale of fragmentation decreases. In extreme conditions, for example loading by high explosives, high loading rates lead to fragmentation in the form of powder. The model discussed here has not yet been applied for a concrete loaded at different rates but it seems to cover all features observed in experiment. At present stage of development the multi-scale model is derived for tension. It is clear that the hydrostatic component of the stress tensor will change the model variables. HYDROSTATIC COMPONENT AND RATE SENSITIVITY
It is well known that hydrostatic pressure changes mechanical responses of rocks and concrete to different paths of loading. However, it is reported here for the first time that pressure component of the stress tensor changes strain rate sensitivity. This is clearly demonstrated by comparison of figures with experimental data for tension and compression and as well as the values of the rate sensitivities. It is clear that hydrostatic pressure suppress the rate sensitivity. This is shown in Fig.14 where the current levels of failure strength estimated for a hypothetical concrete in the form of points at increasing strain rates is shown versus the stress triaxiality defined as
3ffF
21
On a very high rate sensitivity of concrete failure at high loading rates and impact
Of course, for shear the triaxiality is zero, for tension -1/3 and for compression +1/3 (tension stress here is assumed as negative). The distances on each path represent failure stress OF at increasing rate sensitivities: 1.0; 10; 50 and 100 I/s. For example, the maximum distances for strain rate -lo2 l/s when connected by an iso-line produce a highly anisotropic effect of rate sensitivity for concrete. The rate sensitivity for shear is slightly lower than for tension. This may be caused by the fact that the material separation occurs partly by tension in cement paste because presence of aggregates, but also in some areas a hydrostatic component mainly due to the local inertia may be present. In compression a substantial decrease of the rate sensitivity is found. Within the framework of the multi-scale approach the hydrostatic pressure will not only suppress the micro-cracking but also will move the critical point into higher strain rates. Of course further experimental studies specially in tension and shear and with relatively large number of experiments must be performed in order to find meaningful differences between failure stresses for different paths.
STRAIN RATE EFFECTS ON CONCRETE 1.2
-
SHEAR
TENSION
1 -
0.8 -
0.6 I’ 0.4
points represent increasing strain rate
-0.4
-0.3
-0.2
o.2 -0.1
11
COMPRESSION
0
** 0.1
HYDROSTATIC COMPONENT
Fig. 14 Effect of pressure component on rate sensitivity of hypothetical concrete, increasing distances from 0 represent approximate failure stress at strain rates 1.0, 10, 50 and 100 l/s. Values of the rate sensitivities as well as transition points from single to multiple fragmentation for all three paths can be found from experimental data shown in the schematic form in Fig.15 where the failure stress is drawn versus logarithm of strain rate. The only known experimental results obtained for the same mortar, and presented in the form of Fig. 15, are those reported in [17]. The slopes of approximations by straight lines shown in Fig.15 determine the rate sensitivity PO for tension, shear and compression. Both rate sensitivities, that is values of PO and T ~ D, are presenter for mortar versus the level of triaxiality in Fig.16. This figure is clearly indicating, as already mentioned, a significant effect of stress triaxiality on rate sensitivity. Suppression of both rate sensitivities at increasing pressure is obvious. Because of scatter in original data the rate sensitivity for shear is slightly higher than for tension. A correct trend is observed for the pseudo-viscosity T ~ D. Both rate sensitivities PD and V D , but only for tension and compression, are shown versus triaxiality in Fig.17.
22
Janusz R.KLEPACZKO
TRANSITION OF FAILURE MODES
-6
-4
0
-2
2
4
Log (STRAIN RATE) [ V s ]
Fig.15 Schematic behavior of concrete in tension, shear and compression vs. logarithm of strain rate.
EFFECT OF STRESS TRlXlALlTY ON RATE SENSITIVITY OF MORTAR
'I
0.5 rl "
-0.4
-0.2
I
0
0.2
0.4
STRESS TRlAXlALllY
Fig. 16 Rate sensitivities PD and Y D for mortar vs. stress triaxiality. Figures 16 and 17 confirm existence of the "anisotropy" of rate sensitivity due to the effect of stress triaxiality. A simple explanation lies in the fact that hydrostatic stress component closes micro-cracks and the available density of the micro-cracks to be activated is reduced.
On a very high rate sensitivity of concretefailure at high loading rates and impact
23
EFFECT OF STRESS TRlAXlALlTY ON RATE SENSITIVITY OF MB 50
Y
10 -
I -0.4
n l "
-0.2
I
0
0.2
0.4
STRESS TRlAXlALlTY
Fig.17 Rate sensitivities OD and V D for concrete MB 50 vs. stress triaxiality.
DISCUSSION AND CONCLUSIONS Although it has been shown that rate sensitivity of mortars and concrete substantially increases at strain rates higher than -10 Us it is not clear what is the best approximation. Two rate sensitivities were analyzed, that is the rate sensitivity p and the pseudo-viscosity q. Another definition, related to the rate sensitivity 0, is the logarithmic rate sensitivity m, [30]
Every definition of the rate sensitivity is given in partial differentials so after integration a specific constitutive relation is obtained. Presently it is not possible to suggest the most exact approach because limited sets of experimental data that could be analyzed by statistical means. For example, the multi-scale model based on the Weibull statistics leads to the rate sensitivity p as the best and physically meaningful constant. The other approach based on the cumulative criterion derived in [34] based on the time accumulation of rate-dependent defects leads to the logarithmic rate sensitivity m as the meaningful constant. This criterion is based on some physical considerations, it is assumed that the thermal energy of atoms accompany the failure process, thus the criterion is formulated in the following integral form
24
Janusz R. KLEPACZKO
where ob , t,, and a(t) are the material constants at constant temperature. The constant t,, is the longest time of loading when the failure stress failure stressab , that
OF = (TFO
for & > t,,
OF( t,,
) approaches the quasi-static
. Thus the transition point from low to the high
rate sensitivity is defined. The exponential a depends on the absolute temperature T and is directly related to the activation energy of the material separation AGO with k being the Boltzman constant. When a proportional loading is assumed, that is 0, = E l t ,
the criterion can be written in a simplified and explicit form
where E is the Young’s modulus of the material and i is the local strain rate. The material constants obtained after experiments of spalling for MB 50 concrete are ko = 50 ps, a = 0.912 at ambient temperature T = 300 K and ob =4.2 MPa, [35,37]. For constant strain rate the cumulative criterion (16) predicts the logarithmic rate sensitivity as
m=- 1 l+a With a = 0.912 value of m is close to 1/2 so the spa11 strength increases in proportion to the square root of strain rate, Q, = l”*. The cumulative damagelfailure criterion proposed in [34] has been adopted for concrete in the FE and Discrete Element (DE) simulations with very good results [35]. The logarithmic rate sensitivity can be related to both the rate sensitivity p and the pseudo-viscosity q , the relations are given by
p = -*mF
and
v=-
1 &-(l/(Itlk7)) l+a
Since a + 1 = 2 the pseudo-viscosity can be approximated by
Thus the pseudo-viscosity should decrease with strain rate if the logarithmic rate sensitivity is a true material constant. An exponential proportion of the failure stress to the strain rate, but with the exponent 1/3, was found in the criterion of fragmentation discussed in [36]. This last criterion based on the linear fracture mechanics (with exponent 1/3) underestimates an abrupt increase of tensile failure for MB 50 concrete with strain rate. On the contrary, the cumulative criterion, Eq.( 16), based on the cumulative delay of damage reproduces better the mean value of the slope p = ’OF from Figs. 3a and 4 a . aiogi Main conclusions aRer this study are:
On a very high rate sensitivity of concrete failure at high loading rates and impact i. ii. iii. iv. v.
25
The rate sensitivity of mortars and concretes are very high in tension, shear and compression above strain rate -10 Us; Those rate sensitivities failure stress are not equal and they diminish as a function of increasing triaxiality of stress; The rate sensitivity of wet mortar or concrete is usually higher at high strain rates than for the dry materials; The modeling of quasi-static and dynamic failure based on the Weibull statistics is a promising direction in future application to concrete. Further statistical analyses of experimental data are of great importance in order to establish more exactly the rate sensitivities in tension, shear and compression for one material and to determine effects of the stress triaxiality on the failure stress.
ACKNOWLEDGEMENTS Part of this paper was presented as a seminar at the University of Florida Graduate Engineering & Research Center in Shalimar, FL (May 2002). This work was sponsored (in part) by the Air Force Office of Scientific Research, USAF, under grantkontract number F49620-00-1-0288. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsement, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government. REFERENCES 1. Abbott, B. W., and Cornish, R. H., A stress-wave technique for determining the tensile strength of brittle materials, Experimental Mechanics, 1965, pp. 148-153. 2. Landon, J. W. and Quinney, H., Experiment with the pressure Hopkinson bar, Proceedings Royal Society of London, series A : Math. Phys. Sci., A103, 1923, pp. 622-643. 3. Goldsmith, W., Polivka, M. and Yang, T., Dynamic behaviour of concrete, Experimental Mechanics, 6, 1966, pp. 65-79. 4. Mellinger, F. M., Birkimer, D. L., Measurement of Stress and Strain on Cylindrical Test Specimens of Rocks and Concrete Under Impact Loading, Technical report 4-46, U.S. Army Corps of Engineers, Ohio River Division Laboratories, Cincinati, Ohio, 1966. 5. Birkimer, D. L., Critical Normal Fracture Strain of Cement Portland Concrete, Ph.D. Thesis, University of Cincinati, Ohio, 1968. 6. Kolsky, H., An investigation of the mechanical properties of materials at very high rates of loading, Proceedings Physical Society of London, Section B, 62, 1949, pp. 676-704. 7. Rheinhardt, H. W, Kormeling, H. A., Zielinski, A. J., The SHP bar, a versatile tool for impact testing of concrete, Materials and Structures, 19, 1986, pp. 55-63. 8. Ross, C. A., Thomson, P.Y. and Tedesco, J. W., Split Hopkinson pressure bar tests on concrete and mortar in tension and compression, ACI Material Journal, 86, 1989, pp. 475-48 1. 9. Ross, C. A., Tedesco, J. W., and Kuenen, S. T., Effects of strain rate on concrete strength, ACI Materials Journal, 92, 1995, pp. 37-47. 10. Brara, A., Klepaczko, J.R., and Kruszka, L., Tensile testing and modeling of concrete under high loading rates, Proceedings, Brittle Matrix Composites 5 (BMC 5) A.M. Brandt V.C.Li and I.H.Marshall, Eds, Warsaw, Poland, 1997, pp. 281-290.
26
Janusz R. kXEPACZK0
11. Malvar, L. J., and Ross C. A., Review of strain rate effects for concrete in tension, ACI Material Journal, 95, 1998, pp. 735-739. 12. Toutlemonde, F., and Rossi, P., Major Parameters governing concrete dynamic behaviour and dynamic failure of concrete structures, DYMAT Journal, 2, 1995, pp. 69-77. 13. Ross, C. A., Jerome, D. M., Tedesco, J. W., and Hughes, M. L., Moisture and strain rate effects on concrete strength, ACI Materials Journal, 93, 1996, pp.293-300 14. Klepaczko, J. R., Behavior of rock-like materials at high strain rates in compression, International Journal of Plasticity, 6, 1990, pp.415-432. 15. Denoual, C., and Hild, F., Dynamic fragmentation of brittle solids: a multi-scale model, European Journal of Mechanics, Nsolids, 21,2002, pp. 105-120. 16. Rheinhardt, W., Strain rate effects on the tensile strength of concrete as predicted by thermodynamic and fracture mechanics models, Proceedings, Cement-based Composites: Strain Rate Effects on Fracture, S.Mindess and S.P.Shah eds, Pittsburgh, Pennsylvania, 64, 1985, pp. 1-12. 17. Schmidt, M. J., Shear strength of concrete under dynamic loads, ASME Pressure Vessel and Piping Conf., Boston MA, 1999, pp.250-258. 18. Klepaczko, J. R., and Brara, A., An experimental method for dynamic tensile testing of concrete by spalling, International Journal of Impact Engineering, 25,2001, pp. 387-409. 19. Faure, L., and Klepaczko, J. R., A Fast Video Setup with CCD Cameras, Technical Report, ISGMP-LPMM, Project GDR 972 “Impact on Materials”, Metz University, France, 1996. 20. Zielinski, A. J., Fracture of Concrete and Mortar Under Uniaxial Impact Tensile Loading, Ph.D. Thesis, Delft University of Technology, Delft University Press, 1982. 21. Franz, C., and Follansbee, P. S., Wave propagation in the split Hopkinson pressure bar, Journal of Engineering Material Technology, 105, 1983, pp. 61-66. 22. Pochhammer, L., On the propagation velocities of small oscillations in an unlimited isotropic circular cylinder, Journal fdr die Reine und Angewandte Mathematik, 81,1876, pp. 324-326 (in German). 23. Chree, C., The equation of an isotopic solid in polar and cylindrical coordinates, their solutions and applications, Cambridge Philosophical Society Transactions, 14, 1889, pp. 250369. 24. Gong, J. C., Malvern, L. E., and Jenkins, D. A., Dispersion investigations in the SHPB, Journal of Engineering Material Technology, 112, 1990, pp. 309-314. 25. Lifhitz, J. M., and Leber, H., Data processing in the SHPB tests, International Journal of Impact Engineering, 15, 1994, pp. 723-733. 26. Zhao, H., and Gary, G., On the use of the SHPB techniques to determine the dynamic behaviour of materials in the range of small strains, International Journal of Solids and Structures, 28, 1996, pp. 1-7. 27. Bacon, C., Separation of waves propagating in elastic or visco-elastic Hopkinson pressure bar with three-dimensional effects, International Journal of Impact Engineering, 22, 1999, pp. 55-69. 28. Weerheijm, J., Concrete Under Impact Tensile Loading and Lateral Compression, Ph. D. Thesis, Delf? University of Technology, Delft University Press, 1996. 29. Ross, C.A., Private communication, June 2002. 30. Klepaczko, J. R., Study of concrete a t high strain rates in tension and compression, fracture criteria and modelling, Proc. Int. Symp. Brittle Matrix Composites 6, Warsaw, 2000, pp 189- 205. 31. Grote, D.L., Park, S.W. and Zhou, M., Experimental characterization of the dynamic failure behavuior of mortar under impact loading, Journal of Applied Physics, 89, 2001, pp.2115-2123.
On a very high rate sensitivity of concrete failure at high loading rates and impact
27
32. Weibull, W., A statistical theory of the strength of materials, Roy. Swedish Inst. Eng. Res., 1939, p. 151. 33. Denoual, C. and Hild, F., A damage model for dynamic fragmentation of brittle solids, Comp. Methods Appl. Mech. Eng. 183,2000, pp. 247-258. 34. Klepaczko, J.R., 1990, Dynamic crack initiation, some experimental methods and modeling, in: Crack Dynamics in Metallic Materials, J.R. Klepaczko. Ed., Springer-Verlag, Vienna-New-York, pp. 428-450. 35. Brara, A., Camborde, F., Klepaczko, J.R. and Mariotti, C., Experimental and numerical study of concrete at high rates in tension, Mech. of Materials, 33, 2001, pp. 33-45. 36. Kipp, M. E., Grady, D. E. and Chen, E. P., Strain rate dependent fracture initiation, International Journal of Fracture, 16, 1980, pp. 471-478. 37. Brara, A., Experimental Study of Dynamic Tension of Concrete via Spalling, Ph.D. Thesis, Laboratory of Physics and Mechanics of Materials, Metz University, France, 1999, (in French).
Proc. Int. Symp. .,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
DESIGN OF ENGINEERED CEMENTITIOUS COMPOSITES (ECC) FOR PROCESSING AND WORKABILITY REQUIREMENTS Gregor FISCHER* Shuxin WANG** Victor C. LI**
* Department of Civil and Environmental Engineering, University of Hawaii 2540 Dole St, Holmes Hall 383, Honolulu, HI 96822, USA email:
[email protected] ** Department of Civil and Environmental Engineering, University of Michigan 2340 Hayward Ave., Ann Arbor, MI 48109, USA email:
[email protected], vcli@,umich.edu
ABSTRACT The design of fiber reinforced cementitious composites (FRCC) is typically governed by their mechanical properties in the hardened state, such as the tensile and compressive strength and strain capacity. The intricacies of processing and workability of FRCC, with fiber volume fractions ranging from 1.5 to 20% depending on the particular composition, are often of secondary importance in small-scale laboratory production. However, the fresh composite properties significantly influence the performance of the composite in the hardened state, often leading to substandard mechanical properties due to non-uniform fiber dispersion or inconsistent compaction. More importantly, the large-scale application of FRCC in practice is often not feasible since special mixing equipment or processing techniques are required to overcome the difficulties associated with processing and workability. In particular, the uniform dispersion of short, randomly oriented fibers in the cementitious matrix at fiber volume fractions of more than 1.5% typically requires forcebased mixing equipment, such as high speed pan mixers, planetary mixers, or so-called omni mixers, which are commercially available at the laboratory scale (5dm3 to 200dm3). These specialized mixers are relatively expensive for large capacities and are rarely on hand in most concrete mixing plants and at construction sites. This paper focuses on the fresh mix design of Engineered Cementitious Composites (ECC), which represent one type of high performance FRCC with strain hardening and multiple cracking behavior. The particular version of ECC described in this study utilizes PVA fibers (dt=39pm, lt=12mm) at a volume fraction of 2%. The presented approach is guided by consideration of the practical requirements of producing cementitious composites at large scale under field conditions. The goal of this study is to design the composite such that mixing can be conducted in a conventional, gravity-based drum mixer while retaining
30
Gregor FISCHER, Shuxin WANG and Victor C. LI
the required workability and mechanical properties observed when mixing in a specialized, small-scale laboratory mixer. A case study is presented for the development of a flowable ECC with selfconsolidating consistency. This paper will present possible approaches to meeting these requirements, including control of the particle size distribution and chemical composition of the cementitious matrix, adjusting the mixing sequence and intervals, and proper utilization of cement types and common chemical admixtures.
Keywords ECC, processing, liquefaction, workability, self-consolidating INTRODUCTION The fresh properties of concrete in general and fiber reinforced concrete in particular are of vital importance for workability in the fresh (plastic) state as well as for the material properties in the hardened state with respect to the stress-strain behavior and durability. Fresh concrete should satisfy requirements pertaining to mixing and transporting, uniformity within and between batches, flow properties, compactability, avoiding segregation during placing and consolidation, and surface finish [I]. In case of fiber reinforced concrete (FRC), the requirements on mixing equipment and mix processing as well as uniformity of the material in particular with respect to fiber dispersion are essential to the application of FRC and its reliable performance in the hardened state. Successful production of FRC hinges on proper fiber dispersion as well as workability and can be carried out by three general methods: 1) The addition of fibers to the cementitious matrix during the mixing process in a conventional, gravity-based drum mixer, which is typically limited to small fiber volume fractions below 1% and is viable for common construction purposes due to the wide availability of the required mixing equipment. However, for most FRC composites, a fiber volume fraction below 1% does not significantly alter the mechanical properties with respect to tensile strength and strain capacity. In method 2), the addition of fibers during the mixing process at moderate fiber volume fraction up to 3% in customized, force-based mixers, such as pan mixers, planetary mixers, or so-called omni-mixers is not practical for large-scale construction purposes and limited to laboratory applications due to the limited availability of large-scale mixing equipment. Similarly, method 3) placing of fibers at large volume fraction up to 20% in the formwork prior to infiltration with cementitious slurry (SIFCON) is not practical since it requires a specialized construction process. Beyond the mixing process, the flowability, compactability, segregation resistance, and surface finish of the FRC,are interrelated parameters as in conventional concrete but are additionally affected by the presence and volume fraction of fibers. While the workability is similar to that of conventional concrete, of FRC with low fiber volume fractions (4%) High Performance FRC composites (HPFRCC) with enhanced mechanical properties in terms of tensile strength and strain capacity typically entail moderate or high fiber volume fractions (>1%), which consequently requires design of the composite fresh properties for adequate workability and reliable performance in the hardened state. In particular for applications of flowable HPFRCC with self-consolidating capabilities, the adjustment of the composite fresh properties is necessary. Previous research on the fresh properties of self-consolidating Engineered Cementitious Composites (ECC), with poly vinyl alcohol (PVA, Vf=2%) [2] and polyethylene (PE, V r l % ) fibers [3] focused on the rheological design by adopting a complementary
Design of Engineered Cementitious Composites (ECC)for processing and ...
31
electrosteric dispersion and stabilization technique to obtain cement pastes with desirable flow properties at constant particle concentrations. This technique involved the optimal combination of superplasticizer (melamine formaldehyde sulfonate, MFS), which acts as an electrostatic dispersant,. with a water-soluble polymer (hydroxypropylmethylcellulose, HPMC), which acts buth as a steric stabilizer and viscosity-enhancing agent [2]. This approach lead to a fresh composite mix (Table 1) with desirable deformability, cohesiveness, and high consistency and is used as a benchmark reference (M-ref) for the work described in this paper. In essence, the combination of polymeric admixtures (MFS and HPMC) is used to limit the flocculation between cement particles with appropriate dispersion (MFS) while achieving stabilization of the cement particles (HPMC), which consequently reduces the shear viscosity of the fresh cement paste and leads to a high deformability (flowability) of the fresh cementitious matrix without gravitational sedimentation (segregation) [2]. Mixing of the cementitious composite was conducted in a high-speed mixer with planetary rotating blade. The deformability of the resulting ECC was determined utilizing a conventional slump test cone and deriving a flowability index r. While the use of HPMC was found beneficial in achieving a flowable ECC mix, it also introduces a relatively large air content in the mix (-20%). This air content consists of small pores ( I .
'\
Fig.3. The image processing stages: a) original colour image, b) binary image after thresholding, c) binary image after thinning
106
Michut A . GLINICIU and Agnieszka LITOROWICZ
Thus, for each concrete specimen it is possible to determine:
Length of cracks - L [mm] - total length of all the dendrites of each cracks on the image, Average width of cracks - W [mm] - total cracks area per total dendritic length, Area of cracks - A [mm’] - total area of each cracks on the image, Density of cracks - LA [mm/mm2] - total dendritic length of cracks per image area, Areal fraction - AA [mm2/mm2]- ratio between the area of the counted cracks to the entire area of the active image, 6. Orientation of crack system - can be shown by means of “rose of cracks direction”.
1. 2. 3. 4. 5.
TEST RESULTS Compressive strength Table 3 presents the compressive strength data. The strength is given as an average value f, of 3 measurements in each series. Values of the compressive strength obtained for concrete types W, S, S Z were similar. For series of concrete exposed to freezing action after 1 hour after mixing (Wm, Sm, SZm), the compressive strength was significantly reduced - down to 50-55 % of reference (undamaged) concrete specimens. The freezing period (2 or 4 days) had a very small influence on the compressive strength and this influence could be neglected.
Water penetration test Depth of water penetration under pressure was determined on concrete specimens after lowtemperature deterioration and on reference specimens (Table 4). It can be observed that the water penetration depth for undamaged concrete series (W, S, SZ) was similar within the range from 22 mm to 23 mm. Low-temperature damage significantly decreased the resistance to water penetration under pressure: the penetration depth was from 62 to 82 mm that is an increase of 3-4 times in comparison with undamaged concrete. The concrete specimens SZm with glass fibres, which were subjected to freezing, showed the smallest resistance to water penetration. Analysis of crack pattern Cracks were observed in the low-temperature deteriorated concrete only. Table 5 gives the crack characteristic of samples cut from 100-mm cubes. Reference concrete (Wm2, Wm4) prepared without superplasticizer and fibres showed the highest crack density at every magnification, while the lowest crack density was seen in concrete with superplasticizer
107
Application of UV image analysis for evaluation of tkerrnal cracking in concrete
(Sm2, Sm4). The results indicate that the crack density is very sensitive to the magnification factor. Table
days
Concrete
Area bm21
22.00 20.89
Wm2 Wm4 Sm2 Sm4 SZm2 SZm4
0.87 0.81 0.59 0.61 0.59 0.48
Total length Average Density [mml width [mm] [mml mm2]
I I
266.13 273.79
21.50 21.14 14.51 15.60 17.20 16.56
I I
0.082 0.076
0.040 0.036 0.041 0.039 0.034 0.029
I I
0.171 0.176
0.535 0.526 0.361 0.388 0.428 0.412
Areal fraction
I I
0.0 14 0.0 13
0.022 0.020 0.0 15 0.0 I5 0.015 0.012
Average width of cracks decreases with increased magnification and is contained in ranges: 0,71-0,82 mm, 0,54-0,65 mm and 0,29-0,41 mm at the magnification of 10, 30 and 63x, respectively. A higher magnification allows to detect also smaller defects.
108 Michal A. GLINICKl and Agnieszka LITOROWICZ Identification and analysis of cracks was carried out on samples prepared from 150mm cubes subjected previously to water penetration test. There were no cracks in the specimens not subjected to freezing. Results of crack analysis were summarized in Table 6. In this series of specimens the highest crack density was observed in concrete with fibres (SZm4) and the lowest - in reference concrete (Wm4). As it is seen from Table 4 and Table 6 a clear relationship between the water penetration depth and the cracks density is found: the water penetration in concrete increased with an increase of crack density.
I
Table 6. Results of crack analysis (150x150x150mm cubes after water penetration test)
CC ncrete Wm4 Sm4 SZm4
SZm4 Wm4
Area 18.71 37.98 50.63
0.90
Areal
Total length Average width(mm1 [mml 250.9 456.8 593.2 49.4 62.4 124.3 25.9 28.6 46.8
I
0.077 0.082 0.086
0.361
0.051 0.050 0.050
: 9 :
0.034 0.034 0.037
0.673
I
1
0.031
0.035 0.02 1 0.024
CONCLUSIONS A digital image analysis technique for the detection and quantification of cracks in concrete was elaborated using impregnated reground polished sections. Observation in ultraviolet light using an optical microscope at the magnification in the range of 10 to 63 times allowed to detect fine cracks, paste-aggregate transition zones, porous areas and air bubbles. The technique generates images with a good contrast, which are convenient for quantitative analysis. The contrast of the crack images in relation with the adjacent material was strongly dependent on the porosity of the cement paste. Low-temperature action on fresh concrete mix reduced the compressive strength of concrete by 50 - 55 ‘YOand increased the depth of water penetration by a factor of 3 to 4. Such a damage induced a system of cracks in concrete that could be identified and analysed. The crack density and the average width of crack were found to be related to the magnification factor. An increase of the crack density was related to an increase of water penetration depth. The elaborated technique can be used for quantification of cracks in concrete specimens made in the laboratory and also in elements sawn out from existing concrete structure damaged by various mechanisms (mechanical, physical or chemical) e.g. structure exposed to freezing during construction.
Application of UV image analysisfor evaluation of thermal cracking in concrete
109
ACKNOWLEDGEMENT The research was performed within the framework of NATO Science for Peace Project No. 97 1888 ,, Diagnosis of Concrete and High Performance Concrete by Structural Examination”.
REFERENCES 1. Samaha, H. R., Hover, K. C., Influence of microcracking on the mass transport properties
of concrete, ACI Materials Journal 89,4, 1992, pp 416-424 2. Jacobsen, S., Marchand, J., Boisvert, L., Effect of cracking and healing on chloride transport in OPC concrete. Cement and Concrete Research, 26,6, 1996, pp 869-881 3. Aldea, C. M., Shah, S. P., Karr, A., Permeability of cracked concrete, Materials and Structures, 32, 1999, pp 370-376 4. Gkrard, B., Marchand, J., Influence of cracking on the diffusion properties of cementbased materials. Part I: Influence of continuous cracks on the steady-state regime. Cement and Concrete Research, 30, 2000, pp 37-43 5. Glinicki M.A., Litorowicz A., Digital analysis of cracks in concrete induced by thermal action, (in Polish), XVIII Scientific-Technical Conference “Concrete and Precasting”, Popowo, April 2002, pp 6. Korhonen, Ch., Ryan R., New low-temperature admixtures, Concrete International, May 2000, pp 33-38 7. Ohtsu, M., Okamoto, T., Yuyama, S., Moment tensor analysis of acoustic emission for cracking mechanisms in concrete. ACI Structural Journal, 95,2, 1998, pp 87-95 8. Popovics, J.S., Song, W-J., Ghandehari, M., Subramaniam, K.V., Achenbach, J.D., Shah, S.P., Application of surface wave transmission measurements for crack depth determination in concrete. ACI Materials Journal, 97, 2,2000, pp 127-135 9. Ammouche, A., Breysse, D., Hornain, H., Didry, O., Marchand, J., A new image analysis technique for the quantitative assessment of microcracks in cement-based materials. Cement and Concrete Research, 30,2000, pp 25-35 10. Nemati, K.M., Monteiro, P.J.M., Scrivener, K.L., Analysis of compressive stress-induced cracks in concrete. ACI Materials Journal, 95, 5 , 1998, pp 617-630 1 1. Sicard, V., Francois R., Ringot E., Pons G., Influence of creep and shrinkage on cracking in high strength concrete, Cement and Concrete Research, 22, 1, 1992, pp 159-168 12. Darwin, D., Abou-Zeid M. N., Ketcham K. W., Automated crack identification for cement paste, Cement and Concrete Research, 25, 3, 1995, pp 605-616 13. Slate, F. O., Olsefski S., X-rays for study of internal structure and microcracking of concrete, Journal of the American Concrete Institute, 60, 5 , 1963, pp 575-587
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall. eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
ASSESSING DAMAGE LOCALIZATION IN CONCRETE CYLINDERS TESTED IN COMPRESSION Sunil P U N and Jason WEISS School of Civil Engineering Purdue University, West Lafayette, USA. email:
[email protected] ABSTRACT The compressive stress-strain behavior of concrete is a critical material descriptor that is used in the design and analysis of concrete structures. While significant research has been performed to illustrate the importance of the peak strength and initial elastic modulus, further work is needed to explain how damage develops, dissipates energy, and results in stiffness degradation. While the stress-strain response has long been considered a material property, recent research has shown that this relationship is dependent upon specimen geometry and size. This research investigated the development of damage, its localization into a band, the size of this band, and the implications of this damage band on the overall stress-strain response. In addition to load and deformation measurements, acoustic emission was used to quantify damage. Specifically, a detailed analysis using acoustic emission activity is presented to describe damage in terms of event amplitude, duration, and energy. To support the correlation between the acoustic activity and physical damage in concrete that was loaded to different levels, the damaged cylindrical specimens were sectioned, ground, polished, and imaged to inspect the extent of cracking and the resulting damage at different locations in the cylinders. Image analysis was compared to the acoustic measurements to present clear picture of how damage develops and localizes in concrete under compressive loading. Keywords Aeal compression, Acoustic emission, Concrete, Damage, Image analysis.
INTRODUCTION The stress-strain behavior of concrete is frequently used in the design of concrete structures. Over the last four decades research has focused on relating the stress-strain behavior of concrete
1 12
Sunil PURIund W. Jason WEISS
to the damage that develops in the specimen (5, 15, 18). The majority of these investigations have modeled concrete as a material that degrades uniformly throughout the specimen. Recent investigations have questioned the use of a uniform damage approach and have advocated the existence of a localized damage region (4, 12, 18, 20). Though the presence of region of local damage has gained acceptance (17), the size of compression damage zone and its role in the stress-strain response has not been fully understood (4). This paper is intended to improve on the fundamental understanding of damage development, localization and the resulting stiffness degradation of concrete when it is tested in compression. A variety of experimental techniques have been used in the past to investigate the development of damage (lo). A real-time, non-destructive technique is beneficial for assessing and locating damage as it develops. Acoustic Emission (AE) is one such technique that provides non-invasive measurement of the material that is being tested. AE has been used to investigate how concrete fractures and degrades (7, 9, 11,22). Previous researchers have offered a variety of characteristics of the acoustic wave form (number of hits, amplitude, and corresponding acoustic energy) in an attempt to separate and quantify the fracture mechanisms (7, 22). Recent work has illustrated that acoustic emission energy can be correlated to the mechanical fracture energy that develops in the specimen (8). While AE provides indirect information about damage development, an optical technique is used in this paper as a secondary method to quantify some of the physical aspects of the damage that develops. RESEARCH SIGNIFICANCE
The design of concrete structures typically utilizes the peak strength and initial elastic stiffness to approximate the stress-strain response of concrete (i.e., Whitney’s stress block) (1). While the stress-strain response is commonly thought of as a material property, it has been shown that the stress-strain response is dependent on the specimen size and geometry (5, 18). This research is aimed at investigating the initiation of microcracks, their coalescence, the development of a localized band of damage, and its effect on the overall stiffness of concrete. This paper describes the use of acoustic emission measurements to quantify the size of the compression damage zone (CDZ). By quantifying the size of the CDZ, a composite modeling approach can be used to quantify the role of the bulk and damage zones for predicting the stress-strain response of concrete. In addition, the relationship behveen optically observed damage and acoustic measurements can be established to indicate how acoustic sensors may be used in structural health monitoring. EXPERIMENTAL PROGRAM Spc cimens were prepared following the RILEM 148-SSC (1997) recommendations for determining the strain-softening response of concrete tested under uniaxial compression. Cylindrical specimens were chosen with a length-to-diameter (L/D) ratio of four in order to provide sufficient space for the compression damage zone (CDZ) to develop. The following sections describe the specimen preparation, experimental procedures, and the experimental results obtained from this study.
Assessing damage localization in concrete cylinders tested in compression
113
Specimen preparation The mixture proportions used in this investigation are based on those described in RILEM 148SSC (1997). Type I portland cement was used with a water-to-cement ratio (wk) of 0.50. A locally available sand and coarse aggregate were sieved to obtain gradations similar to those described in RILEM 148-SSC (13, 17). In addition, 50 mm polypropylene fibers (structural fibers manufactured by Grace) were incorporated (0.75% of fibers by volume) into the mixture. Standard practices for making and curing concrete test specimens were followed (2). The specimens were cast in cylindrical molds with a diameter of 76 mm (3 in.) and a height of 406 mm (16 in.). The top and bottom ends of the specimens (approximately 5 1 mm) were removed to attain a specimen with the desired length (304 mm), thereby removing any end-effects that may be present due to the casting process. Specimens were placed in a moist environment (98% relative humidity and 23°C) until the time of testing. After 28 days, the ends of the specimens were ground using a lapping wheel to ensure that ends of the specimen were flat. After grinding, the specimens were placed back in the moist-curing room where they were kept until the time of testing (approximately 90 days). Experimental configuration Results from six specimens are described is this paper. Specimens were loaded in compression using a MTS machine which was equipped with a hydraulic actuator and a 490 kN (1 10 kip) load cell. The bottom platen was fixed against rotation and the top platen was permitted to rotate. Two sheets of teflon (each with thickness of 0.254 mm) were used on each end of the specimen to reduce friction between the ends of the specimens and platens thereby reducing the confining strvses (3, 16, 17). Two linearly variable differential transformer (LVDT) displacement transducers were used to measure platen-to-platen displacement. The LVDTs and load cell were interfaced with a computer for signal conditioning and data acquisition. In addition to the mechanical measurements, four piezoelectric (375 kHz) wide band sensors were used to record the acoustic activity generated in the specimen. The location of sensors and the technique used to attach sensors on the surface of the specimen can be found in Puri and Weiss (13). Initially, a load of 2.2 kN (500 kips) was applied to the specimen to bring the platens (i.e., teflon sheets) in contact with the ends of the specimens. The LVDTs were adjusted to zero and acoustic sensors were activated to record the AE events above 50 dB. Counters on the both the acoustic emission and mechanical testing computers were synchronized at the beginning of the testing. Experimental testing The specimens were tested in compression using displacement control at a rate of 200 pdmin. After reaching predetermined load levels (58% prepeak, 78% prepeak, 98% postpeak, 80% postpeak, 60% postpeak, 38% postpeak), the specimens were unloaded. Mechanical testing data was recorded at intervals of one second. Optical damage assessment After testing the specimens were removed from the testing machine. Thorough visual inspection was performed on each specimen and the extent and location of visible damage was recorded. The specimens were air-dried and kept at room temperature conditions for atleast two weeks. After drying, the damaged specimens were prepared for image analysis using a five step
I 14 Sunil P U U and CY. Jason WEISS
approach: I ) damage stabilization, 2) sample preparation, 3) image acquisition, 4) image processing, and 5) damage quantification (14). Ultra-low-viscosity epoxy resin (Sikadur-55) was used to stabilize the damaged specimens. The specimens were placed in the molds and the ends of the molds were capped and sealed at the top and bottom. Two outlets were left at the top of the mold, one of which was attached to a vacuum pump and the other to the source of epoxy resin. A vacuum was drawn to allow the epoxy (with dissolved carbon black) to enter the damaged specimen at an atmospheric pressure of 25 mm of mercury for 30 minutes. The vacuum was released to 10 mm of mercury as fumes started forming during hardening of the epoxy resin. After the development of fumes stopped, the vacuum level was again increased to 25 mm. This procedure was repeated until bubble formation stopped which hinted that the cracks were filled with epoxy resin. The molds were detached from the vacuum pump and maintained at the room temperature until epoxy hardened. After the epoxy hardened, coordinate axes were marked as vertical grooves on the edges of the stabilized specimens. A diamond tipped saw was used to cut the stabilized specimens into 25 mm (1 inch) thick samples. The rings were labeled and their cut surfaces were coated with black spray paint. Rings were polished on a lapping-wheel using different silicon carbide grits to obtain smooth surface. Light reflection technique was used to verify proper polishing of each surface (6). The surfaces were polished until the spray paint was removed from the surface and a good reflection of light was observed. Colorless varnish was then applied to the final surface. To assess damage on the cut surfaces, the polished surfaces were scanned using a flat-bed scanner. Images (76 mm x 76 mm (3 in. x 3 in.)) were captured at a resolution of 300 pixels/inch. A coordinate axis that matches the groove locations along the specimen was also recorded on scanner surface to ensure that the ring surfaces could be reassembled for threedimensional analysis. The following section describes the results of the experimental program.
EXPERIMENTAL RESULTS
As discussed in the previous section, the specimens were unloaded at different strain values. Figure 1 shows the typical compressive stress-strain response of the cylindrical specimens. The stress measurements were normalized to the peak stress and the strain measurements were normalized by the strain corresponding with the peak stress (i.e., For specimens unloaded in the prepeak region, stress values were normalized by an average peak stress of 39 MPa and strain values were normalized by an average strain of 2500 microstrain. It can be seen in Figure 1 that the specimens have a similar response envelope. The focal point approach has been used for the analysis of unloading stress-strain slopes (13, 21). This approach was used to calculate the fracture energy that was dissipated at each point of unloading. Acoustic sensors recorded the acoustic activity. The acoustic events (hits) were categorized on the basis of their wave characteristics. This included features like amplitude (i.e., the maximum voltage recorded for the particular event) and duration (i.e., the time period for which the voltage of an event remains higher than the threshold value of the voltage). Figure 2 shows the acoustic events categorized on the basis of amplitude, superimposed on the stress-strain response of the specimen. It can be noticed that high amplitude events do not begin until higher strain levels are reached.
115
Assessing damage localization in concrete cylinders tesied in compression
Very high amplitude events (80 dB and above) begin around the time the peak load is reached. This is consistent with the idea that smaller cracks (low amplitude events) occur at low load levels whereas larger cracks (high amplitude events) occur at high stress levels (70% of peak stress and higher). A similar response has been obtained for acoustic events on the basis of their duration (13). To capture aspects of both amplitude and duration, the energy carried in the acoustic wave during the “cracking” process was assessed. Acoustic energy is defined in this paper as the absolute value of area under the acoustic waveform. Figure 3 shows the relationship between the measured acoustic energy and mechanical fracture energy density calculated from the stress-strain curve of the individual specimens (1 3). A relatively linear relationship is observed between acoustic energy and mechanical fracture energy. The triangulation process was used to determine the exact location of acoustic emission with an average velocity of sound (4200 d s e c ) . Figure 4 shows a three dimensional plot of the cumulative acoustic energy and its source location for one specimen as a hnction of increasing strain. It should be noted that not every event could be accounted for since each event must be captured by more than one sensor. It can be noticed in Figure 4 that relatively uniform energy is released along the length of the specimen till the peak stress is reached (&peak). It appears that at the peak load the energy dissipation increases in one region of the specimen (i.e., the upper region in this specimen), however the damage region was found to vary in location from specimen to specimen.
-
.
1
58% Pc Prepeak
78% Pc Prepeak
-
* 98% fc Postpeak 80% Pc Postpeak
0
I
0.5
2
1.5
Normalized Strain
Figure 1 : Normalized stress-strain curves for specimens unloaded at different levels 10000
B
B 1000
-
Y
.-u Y)
8 ;
z 5 z
100
10
I f
I.o
0.5
0.0
2.0
1.5
Normalized Strain
Figure 2: Categorization of acoustic events on the basis of amplitude _.
-
--__-
-
500
FRACTURE ENERGY DENSITY 1 - __
I
450
5
I
400
350 300 250
>b: W
$
200 150 100
50 0
0.34
0.55
1.08
1.22
1.39
1.85
NORMALIZED STRAIN
Figure 3: Relation between acoustic energy and fracture energy density
9
0 0
a
1 16 Sunil PUN and W.Jason WEISS
Figure 5 illustrates the formation and development of the CDZ that was obtained from the acoustic energy emission. In the prepeak region the damage is assumed to occur uniformly through out the specimen. After the peak load is achieved, the damage occurs primarily in the CDZ causing a reduction in the stiffness while stiffness in the bulk region remains constant. At peak load the zone of energy emission can be approximated as the top 90 mm of $ the specimen. As the strain increases, this energy emission zone (CDZ) starts expanding and it N’ grows until the strain reaches 1.6 E ‘% &peak at which time it becomes 9 approximately 160 mm long. This demonstrates that the length of CDZ grows till it reaches a length of two times the diameter of cylinder. This is consistent with the assumptions used by Palmquist and Jansen (12) for modeling the Figure 4:Location and size of CDZ postpeak behavior of stress-strain
$ $
’
ciirve.
Using this approach a series model, was used to predict the stiffness degradation of the CDZ after it begins to develop at the peak load (Equation 1). In this equation L refers to length and E to elastic modulus while the subscripts refer to either the CDZ, bulk or total regions respectively. A focal point approach (13) was used to calculate the bulk stiffness. The results of this analysis are shown in Figure 5. It can be noticed that until the peak load is reached the stiffness (damage) is assumed to be uniform throughout the specimen. Immediately after peak, the CDZ forms and the length of the CDZ begins to rapidly increase. The length of CDZ reaches a constant length at approximately 1.6 times the strain at peak.
320
E
240 C
d 160
-2: E
80
v) .Y
l o 0.0
0.2 0.4 0.6
0.8 1.0 1.2 1.4 1.6 1.8 2.0
Normalized Strain
Figure 5: Development of CDZ and its stiffness degradation
Image analysis was used to quantify damage in the specimen. Figure 6 shows a typical image from a slice of the tested specimen taken perpendicular to the axis of testing. While the visible macrocracks appear to be dark, further analysis is needed to describe the remainder of
Assessing damage localization in concrete cylinders tested in compression
117
surface. It can be noticed that the epoxy resin seeped through macrocracks, darkens the specimen and makes them distinguishable from the rest of the surface. Macrocracked
While the undamaged region appears lighter, to analyze these different areas, the images of sample surfaces were further studied under optical microscope; examples of which can be seen in Figure 7. While no cracking has been found in lighter area (i.e., Figure 7c), dark gray areas around macrocracks have been found to contain microcracking (i.e., Figure 7b). This signifies that the penetration of epoxy in microcracked region is likely responsible for providing the gray shade around the macrocracks. Each pixel of the captured image was categorized according to intensity on a numerical scale where 0 represents black and 255 stands for white.
(a) Macrocracked Rcgion
Figure 6: Typical ring surface
(b) Microcracked Region
(c) Undamaged Region
Figure 7: Different levels of damage on nng surfaces (each image is 6 mm x 4 mm) The surfaces of the sectioned specimen were categorized as damaged, partially damaged and undamaged based upon the gray scale level. Table 1 provides the gray scale range selected for different areas of ring surfaces. Ring surfaces were processed using Image Pro Plus software to obtain a final image in three colors. Table 1: Color classification for processing image
13 1-200 201-255
.',,
.
Partially damaged (microcracked) Undamaged
Figure 8 shows a typical original image and the corresponding processed image. After processing the image based upon the damage level, the number of pixels corresponding to each
1 18
Sunil P U N and
W.Jason WEISS
color was counted (i.e., damaged, partially damaged, and undamaged). The percentage of pixels corresponding to each color was assessed. To avoid erroneous counting of some of the dark colored aggregates or pores as damaged part, the aspect ratio of each feature was determined. Features with an aspect ratio (i.e., lengthlwidth) of 1.75 or smaller were screened out of damaged category. This process was applied to all the ring surfaces from the tested specimens.
(a) Original image (b) Processed image Figure 8: Processing of images Figure 9 shows the percentage of the area of the surface that was found to correspond to micro (partially damaged) and macro (damaged) level cracking at each section of the specimen which was unloaded at 38% of peak stress in the postpeak region. The bottom half of the specimen has uniform micro and macro cracking while the upper portion of the specimen shows comparatively higher damage level. A uniform level of damage in bottom section is consistent with the existence of bulk or primarily undamaged zone. Percentage Total Damaged Area 20
0
300
-I
-
250
E
f
200
40
I
250
-
200
2 150
150
-
m I
a 100
M
50
::
0
1
0
M
3
0 4 0 5 0 0amag.d tvea (%)
6
0
7
0
6
Figure 9: Percentage areas for different damage levels
0
I
,
q I
I
I I I I I b-Acouttic Energy
1
.1
.
- 1 W Percentage Total Damaged Airea
0 0
1
I
E
'p 100
'
100
80
60
1
I
7
0
3
6
9
12
Figure 10: Acoustic energy percentage total damaged area
15
18
Assessing damage localization in concrete cylinders tested in compression
119
Damage was assessed at different locations along the length of the specimen. Optical damage assessment obtained from these images was compared with the location of acoustic emission events (Figure 10). The bottom half of the specimen (0-15 cm) shows low acoustic energy. This is consistent with the macrodamage seen in the specimen. The top portion of the specimen experiences severe damage. Figure 10 depicts this both in the form of acoustic energy emission and the percentage damaged area. While the percentage of the damaged region has been found to increase near the end of the specimen, acoustic emission energy depicts an approximate constant trend.
CONCLUSIONS
This paper described the use of acoustic emission to monitor the behavior of concrete tested in compression. Acoustic events were categorized on the basis of their amplitude and duration. It was observed that low amplitude, shorter duration events occur at low stress levels while higher amplitude, longer duration events occur as the load level increases. To capture the characteristics of the waveform, acoustic energy was calculated as the absolute value of the area under the waveform. The acoustic energy was observed to have a linear relationship with the dissipated fracture energy. This implies that the acoustic energy parameter may possess the ability to noninvasively quantify mechanical damage in the concrete specimens. The results presented in this paper indicate that the compression damage zone (CDZ) develops near the peak stress. At peak load, the size of the CDZ is approximately 1.2 times the size of the diameter of the cylinder and it grows until strain reaches approximately twice the diameter of cylinder at 1.6 times the strain at peak. After the strain reaches 1.6 times the peak strain, the length of the CDZ is found to occupy a constant length. Acoustic emission analysis matches with the damage measured by using image analysis. Further work is needed to determine how the observed size of the CDZ changes for different mixture proportions, aggregate size, and length-to-diameter ratios (L/D). ACKNOWLEDGEMENTS
The authors gratefully acknowledge support received from the Center for Advanced CementBased Materials (project C- 1) and the National Science Foundation (NSF). This paper is based in part on work supported by the National Science Foundation Grant No. 0134272: a CAREER AWARD granted to the second author. This work was conducted in the Charles Pankow Concrete Materials Laboratory; as such, the authors gratefully acknowledge the support which has made this laboratory and its operation possible. REFERENCES 1. American Concrete Institute (2002), “Building Code Requirements for Structural Concrete.” ACI 3 18-02. 2. ASTM Standard Designation C192, (2000), “Standard practice for making and curing concrete test specimens in the laboratory.” The American Society for Testing and Materials.
120 Sunil PURI and W. Jason WEISS
3. Choi, S., Thienel, K.C. and Shah, S.P. (1996). “Strain softening of concrete in compression under different end constraints.” Magazine of Concrete Research, Vol. 48, No. 175, pp. 103-115. 4. Jansen, D.C. (1996). “Postpeak properties of high strength concrete cylinders in compression and reinforced beams in shear”; PhD Diss., Northwestern Uni., Evanston, IL. 5. Jansen, D.C., and Shah, S.P. (1997). “Effect of length on compressive strain softening of concrete” Journal of Engineering Mechanics, Vol. 123, No. 1, Jan., 25-35. 6. John, D.A.St., Poole, A.W. and Sims, I (1998), Concrete Petrography, A handbook of investigative techniques. 7. Kim, B., and Weiss, W. J., “Using acoustic emission to quantify damage in restrained fiber reinforced cement mortars.’’ Cement and Concrete Research, Feb, 2003. 8. Landis, E.N., and Whittaker, D.B. (2000). Acoustic emission as a measure of fracture energy. Proceedings: 14th ASCE Engineering Mechanics Conference, Austin, TX. 9. Landis, E.N., Ouyang, C. and Shah, S.P. (1991). “Acoustic emission source locations in concrete. Proceedings.” ASCE Engineering Mechanics Specialty Conference, Columbus, OH., May, 20-22. 10. Malhotra, V.M. and Carino, N.J. (1991). “Handbook on Non-destructive Testing of Concrete”. 11. Ohtsu, M., and Watanabe, H. (2001). “Quantitative damage estimation of concrete of acoustic emission.” Construction and Building Materials, 15, 2 17-224. 12. Palmquist, S.M. and Jansen, D.C., (200 1). “Postpeak strain-stress relationship for concrete in compression” ACI Materials Journal Vol. 98, No. 3, May-June, 2 13-219. 13. Puri. S. and Weiss J., Assessment of localized damage in concrete using acoustic emission, Submitted to A X E Committee for Journal of Materials in Civil Engineering, 2003. 14. Qi, C., Weiss, J. Olek, J. (2002), “Characterization of plastic shrinkage cracking in fiberreinforced concrete using image analysis and a modified weibull function.” Accepted at Materials and Structures. 15. Shah, S.P., and Chandra S. (1968). “Critical stress, volume changes, and microcracking of concrete.” Journal of American Concrete Institute, Vol. 65, 770-78 1. 16. Shah, S.P., and Sankar, R. (1987). “Internal cracking and strain-softening response of concrete under uniaxial compression.” ACI Structural Journal, Vol. 84, No. 3, 200-2 12. 17. Van Mier, J.G.M, Shah, S.P., Arnaud, M., Balayssac, J.P., Bascoul, A., Choi, S., Dasenbrock, D., Ferrara, G., French, C., Gobbi, M.E., Karihaloo, B.L., Konig, G., Kotsovos, M.D., Labuz, J., Lange-Kombak, D., Markeset, G., Pavlovic, M.N., Simch, G., Thienel, K-C., Turatsinze, A., Ulmer, M., Van Geel, H.J.G.M., Van Vliet, M.R.A., Zissopoulos, D. (1997). “Strain-softening of concrete in uni-axial compression.” Materials and Structures, RILEM 148SSC, Vol. 30, May, 195-209. 18. Van Mier, J.G.M. (1984) “Strain-softening of concrete under multiaxial loading conditions.” PhD Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands. 19. Van Mier, J.G.M. (1997), “Fracture process of concrete” CRC Press Inc. 20. Weiss, W.J., Giiler, K. and Shah, S.P. (2001) “Localization and size-dependent response of reinforced concrete beams.” ACI Structural Journal, Vol. 98, No. 5, Sep-Oct, 686-695. 21. Yankelevsky D.Z., and Reinhardt H.W. (1987), “Response of plain concrete to cyclic tension.” ACI Material Journal, Vol. 84, No. 5, Sep.-Oct., 365-373. 22. Yoon, D.-J., Weiss, W. J., and Shah, S. P., (2000) “Assessing Corrosion Damage in Reinforced Concrete Beams Using Acoustic Emission.” J. of Engineering Mechanics Division, ASCE, 126(3), 273-283.
Proc. Int. Sytnp. ((BrittleMatrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
QUANTITATIVE DAMAGE ANALYSIS OF CONCRETE Piet STROEVEN Faculty of Civil Engineering and Geosciences Delft University of Technology Stevinweg 1,2628 CN Delft, The Netherlands, e-mail:
[email protected] ABSTRACT The load-induced damage structure in concrete can be conceived as a spatial structure of dispersed surfaces of which the connectivity increases during load increase. Quantitative image analysis by line scanning in 'vertical sections' allows determination of crack surface area per unit of volume and degree of crack orientation. This paper presents the methodology, and demonstrates its applicability for assessing damage evolution characteristics in low-cycle compression fatigue domain and in direct tension. The associated tests have been conducted earlier.
Keywords Compression, cracking, damage, modelling, stereology, tension.
INTRODUCTION The damage evolution process can be considered uniquely reflecting certain loading regimes operative under specified circumstances. Vile [l] was probably the first to propose a model for meso-cracking underlying global damage evolution in direct compression. The topic also received attention by Stroeven [2], Newman & Newman [3], and Perry and Gillott [4], providing experimental evidence in support of the model. Analytical support comes from elastic solutions of single inclusions in an infinite matrix the oldest of which dates back some seventy years [5-81. The first systematic experimental investigation into damage evolution of concrete, using different techniques, was performed by the 'Cornell group' [8,9]. Images of sections were analysed two-dimensionally, however. It was concluded, among other things, that 50% of the damage at ultimate loading was already present in the virgin state [8], so not typical of the loading regime. To complicate matters further, the fractal concept has revealed such ratios to be sensitivity-dependent [lo]. Quantitative microscopy is the more common way to quantify local features of damage in concrete [ I 1,121; specimens are easy to handle and grinding and polishing operations can be automated. Applications of quantitative image analysis (stereology) for assessment of three-dimensional global damage parameters are extremely scarce [2,13-161. Yet, results can offer insight into cracking mechanisms underlying mechanical phenomena, or allow structural interpretation of macro-mechanical models.
122
Piet STROEVEN
QUANTITATIVE IMAGE ANALYSIS Apartially linear system, as a close approximation for the damage structure induced by uniform compression in a cylindrical specimen, can be emphasized as a mixture of 3-D and I-D systems. The cracks are in both systems randomly distributed as to location. In the first case, the cracks are also randomly distributed as to orientation, whereas in the second one all cracks are parallel to a line, the axis of the specimen. In a vertical secfion, the 3-D system yields a random pattern of traces, while the I-D system leads to traces parallel to the axis of the specimen. The number of intersections with a parallel line probe is indicated by P , and its density by P / L = PL. Perpendicular to the orientation axis of the traces the intersection density will have a maximum value, while a minimum is found in an orthogonal direction. It is well known that the intersection density in a certain direction, & ( O ) , is an unbiased estimator of the total projected length of the traces, per unit of area, on a line perpendicular to the grid direction, L;(O + x / 2 ) . Hence, P'(0) =.Li(O + n / 2 ) [2,16]. For the axial and transverse direction it is readily found that
in which LA, and LA, are the areal trace densities in the 1-D and 3-D system, respectively. Obviously, LA = LAI+ LA,, so that
The degree of orientation in the trace pattern can be defined by
The 3-D interpretation of a similar set of observations is equally simple! The same probabilistic principle holds. Hence 1 I F 1 2 PL(0)=-Sv3 and PL(-)=-Sv3 +-S VI 2 2 2 IF
In analogy with the 2-D case:
(4)
Quantitative damage analysis of concrete
123
In case of unifbrm tension, the actual damage structure can be conceived composed of a mixture of 3-D and 2-D systems. Again, cracks in both systems are supposed to be randomly distributed as to location, and in the 3-D set also as to orientation. In the 2-D system, all cracks are developed, however, perpendicular to the loading direction, so parallel to the socalled orientation plane. This is referred to as partially planar crack orientation. The vertical section reveals a mixture of these systems, the pattern of which is equivalent to the one obtained for the partially planar case but rotated in the plane over 90'. In analogy with eqs. (4) and (9,we have 1 R 1 2 PL(0)=-Sv3 and P L ( - ) = - S v 3 + - S v z R 2 2 2
(6)
A comparison between the two- and three-dimensional expressions for w and crack density will reveal the bias of the seemingly (but not really) simpler two-dimensional approach. The partially planar model has been used for evaluation of direct tensile tests on two-sided notched prisms, and the partially linear model for doing so for low-cycle compression fatigue tests on prismatic specimens. EXPERIMENTAL: COMPRESSION CASE Testing was performed in low-cycle compression fatigue to evaluate the effects of average stress level, stress amplitude and frequency on the number of cycles to fracture, N. The frequencies covered were 17.5 Hz and 0.175 Hz. The upper stress level,o,', was taken for all tests at 87.5% of the 28-days short-term compressive strength,o;,, , of prismatic specimens with similar composition. Hence, this is well above the so-called endurance limit. A relative stress amplitude, S, is defined by S = (0,' - o b ' ) / o ) z 8 in,which ob' is the lower stress level. S varied in the investigations between zero and 0.475. Out of the eight stress amplitude cases encompassed in the experiments, three were included in the quantitative image analysis. The selected cases, S O , S0.075 and S=0.35, represent the mechanical states of permanent loading, and of low-cycle fatigue loading with small, respectively, with large load amplitude. A total number of 72 prismatic specimens (100x100~345mm3) were cast from concrete with a maximum grain size of 8 mm and a water to cement ratio of 0.46. Average 28-days compressive strength of reference prisms amounted to 56.2 MPa. The prisms were stored 10 days under water, followed by 7 days under controlled conditions (22' C, 50%RH), whereupon the specimens were placed until the day of testing at about 1 month in the test room. Sieve curves were between the As and Bs curves of DIN 1045. A single specimen whose deformational behaviour was as close as possible to that of the group average was selected for quantitative damage analysis. Deformations were recorded by clip gauges in longitudinal and in transverse direction. Specimens were subjected to sinusoidal load variations in a servohydraulic testing machine. The loading process was automatically stopped when the transverse deformation attained a certain threshold value [ 171. This rendered possible to study the
124
Piet STROE VEN
internal damage structure of the specimens without introducing a significant bias in the number of cycles to fracture. Each selected specimen was axially sliced to yield three equally spaced sections at a distance of 27 mm [18]. Specimens were cast, compacted and stored in vertical position. Since the loading was applied also in the same direction, the longitudinal axis of the specimen can be considered an axis of symmetry of the damage structure (excluding boundary zones). Fields of 51x102 mm2 were selected at the centre of each section image. Hence, a sample encompassed three independent so-called 'vertical' fields, which were subjected to intersection counting in the two main directions. The distance between the grid lines was optimised to yield a number of intersections roughly equal to the number of cracks in a field. In doing so, a total test line length of 1734 mm was obtained. Contrast was improved by employing the filtered particle method [2,16]. Mechanical properties were generally found in agreement with published data. They were supported by the stereological outcomes [ 17-19]. Additional information is offered on underlying damage evolution mechanisms, however. Table 1 presents some illustrative data. Note that N A is the number of cracks in the section per unit of area. We will focus on a peculiar phenomenon [ 181, i.e. a prevailing direction of damage evolution perpendicular to the compression direction! This occurred under maximum amplitude (S=0.35) and maximum frequency conditions (17.5 Hz). Average loading was in that case 17.5% lower than under permanent loading (S=O). Nevertheless, these conditions proved very destructive (T is time to fracture). The proposed model by Vile [l] for damage evolution on meso-level, elaborated earlier for general use by this author [2], was applied to the present case [17,18]. The wellknown column-like structure of concrete that is subjected to a uniform state of relatively high compression is effectively broken down by debonding (thus: cracking) at aggregate-matrix interfaces perpendicular to the compression direction. This is the result of secondary tensile stresses initiated under stress release to below the so-called discontinuity point.
Table 1:Low cycle fatigue data at 17.5 Hz S
S"
0 0.075 0.350
[mm-'] 0.561 0.601 0.678
NA
0 3
~ m m - ~ ] [%I 0.127 8 0.113 11 0.151 -3
N 42.800 1361300 4,600
T [set 1 2.446 81246 263
EXPERIMENTAL: TENSION CASE Two-sided notched fine-grained concrete prisms (60x50~250mm3) were subjected to a shortterm direct tensile loading in a servo-controlled system with a maximum capacity of 100 kN. The notches reduced the cross sectional dimensions to 50x50 mm2. Concrete was composed of 375 kg/m3 Portland cement and 905, 363 and 540 kg/m3 aggregate of the size ranges 0-2 mm, 2-4 mm and 4-8 mm, respectively. The specimens were cut from larger 50 mm thick panels that were cast vertically to avoid boundary effects. Average compressive and tensile strength values at 28-days were 47.1 and 3.20 N/mm2, respectively. Specimens were glued between steel platens to promote the fracture process zone to undergo uniform deformations. Deformation measurements were executed by a series of extensometers with a gauge length of 35 mm positioned on both surfaces over the notches.
125
Quantitative damage analysis of concrete
From this study six specimens were selected which had been subjected to different postpeak deformational states. The damage state was 'frozen' by gluing aluminium strips to the longitudinal sides of the prisms. Thereupon, four equidistant and parallel 'vertical' sections were prepared of the central portion of the specimens. Spacing between the vertical sections was larger than maximum grain size (8 mm) to obtain statistically independent structural information. The surfaces of the sections were treated with a fluorescent spray [2]. Crack patterns were recorded on slide under illumination by UV light. An area of 48x35 mm2 and a smaller portion of 48x13 mm', located symmetrically with respect to the notch section, were analysed for crack extension. For that purpose Saltikov's method of directed secants was applied to about 7 to 10 times magnified pictures of the designated areas. This was accomplished by projecting a slide on a semi-transparent glass plate. All cracks visible with the unaided eye were taken into consideration, so that the sensitivity will be about a quarter of a millimetre. Rotating the grid allows assessment of the crack orientation distribution. The mechanical experiments revealed the development of a non-uniform distribution of axial deformations over the notch section at yielding (see, e.g. Fig. 4 in [20]). Hence, due to inhomogeneity-induced eccentricity the specimen was subjected to bending. This phenomenon was already known, of course, from experiments using photo-elastic coatings. In [21] this phenomenon was later studied in more detail. Yielding reduced the bending stiffness in the fracture process zone, so that locally a rotation could be accommodated. At larger global deformations, this degree of rotation was maintained. Measurements at front and backside over the notches of the specimens revealed completely different post-peak deformational behaviour even involving compaction [22]. The experimental observations were confirmed by a finite element (FE) simulation based on the smeared out crack approach using the DIANA package. For more details on the mechanical aspects one is referred to [21], and for the FE simulation to [23]. Slides of four vertical sections of the six specimens have been elaborated. Since only single specimens could be selected from the mechanical experiments, scatter between samples (as an average of four images) proved to be too large to draw quantitative conclusions on changes in damage evolution rates during yielding. The scatter was dramatic among the serial sections. For section images, see [16,22]. Table 2 gives some of the damage evolution parameters pertaining to the post-peak range; C-7 and C-5, respectively, C-4 are specimens with a residual load-bearing capacity of 75% and 50% of ultimate. Added are data on a section (C5-4) of a specimen subjected to the same loading history as in case of specimen C-7, but both specimens were unloaded in a different way [ 161. It should be noted that this table reports on data pertaining to the 13 mm wide central zone as well as to the two 11 mm wide boundary zones encompassed in the wider area of 35x48 mm2around the notched section. Table 2: Stereological damage estimates Area location notched zone boundary zone notched zone boundary zone
Damage parameter
S, in mm-l w3 in%
C-7-2 0.333 0.181 18.7 7.6
Specimen number C-7-3 C-5-4 0.543 0.218 0.366 0.146 21.3 9.3 17.5 15.9
C-4-4 0.257 0.193 13.3 3.0
Finally, images were analysed on deviations from symmetry in the damage structure of the so-called Fracture Process Zone (FPZ). Since major cracking will be perpendicular to the
1 26
Piet STROE VEN
e,(O)
global tensile loading direction, the data (in the axial direction) for the more significant cracks (after eliminating the small and widely scattered cracks) are determined separately for the two sides of the specimen [16]. Representative data on C-7-2 and C-5-4 are presented in Table 3. For a selected set of sections also N A was determined. Data obtained in this way for average 2-D crack size (=LA/ N A )fall between 0.5 and 0.7 mm. As an example, [22] gives N A4 . 4 17 mm-' for C-7-2. WithS~4.333mm-' (Table 2), the average crack size in the 13 mm central portion will be 0.65 mm. In [16] the average crack length at DP (assuming completed bond 5 avcracking) was estimated by n d o / 4 , in which do is the sensitivity level. For do~ 0 . mm, erage crack size at DP will be 0.4 mm. Hence, damage evolution between DP and the investigated post-ultimate loading situation is only moderate. The ensemble of 4x6 images reveals a very large amount of structural scatter, as illustrated by presented data (and by earlier published images). Shuffling these images like playing cards would make it impossible to restore their original position in a particular specimen! Systematic features dealing with macro-crack formation only appear in the post-peak range. But a definite delineation of the macro-crack is only found after a considerable amount of yielding has taken place, as can be concluded from a comparison of C-7 and C-4 images. The macro-crack is obviously the final result of a hazardous process of crack coalescence, initially driven by high residual stresses and later primarily by structural stress raisers. The probability of having crack coalescence in the neighbourhood of the notched section is somewhat increased by a 20% higher average stress. The latter leads to a gradually increasing crack density toward the notched section (Table 2), hence to crack concentration, a phenomenon becoming more pronounced during yielding of the specimen. Because the distances between cracks are as a consequence reduced, their interaction will promote further coalescence. The hazardous process of growth and coalescence of the widely scattered cracks on structural level that are only weakly affected by the presence of a notch is alien to the engineering concept of a single crack initiated at a notch and propagating along the notch section. Also, the concept of a fracture process zone symmetric around the notched section is an engineering concept not reflected by the damage structure that, indeed, was found a 'zone spaced without sharp boundaries' [24]. Table 3: Eccentricity in damage evolution Area location
Damage parameter
Specimen number C-7-2 c-5-4 left side right side left side right side
Notched zone
P,(O) in mm-'
0.15
0.06
0.17
0.17
Boundary zone
P,(O) in mm-'
0.12
0.06
0.10
0.14
CONCLUSIONS The interpretation of engineering mechanical behaviour in terms of cracking mechanisms and features of damage evolution by the methodology outlined in this paper allows a structural interpretation of relevant research, and renders possible at least qualitatively estimating mechanical characteristics on the basis of structural modifications. Damage is a fractal-like phenomenon. Hence, observations on damage evolution are resolution-dependent. This also holds
Quantilalive damage analysis of’concrele
127
for the present experiments. Extent of damage and characteristics of the crack orientation distribution are functions of the sensitivity level set by the researcher (here, 0.2 mm). The data presented herein, though of illustrative nature, nevertheless reveal significant structural differences implied by different loading regimes, which allows gaining a clear insight into the operative damage evolution mechanisms.
REFERENCES 1. Vile, G.W.D., Behaviour of concrete under simple and combined stresses, PhD Thesis, Univ. London, UK 1965 2. Stroeven, P., Some aspects of the micromechanics of concrete, PhD Thesis, Delft Univ. Technology, Delft, The Netherlands 1973 3. Newman, K., Newman, J.B., Failure theories and design criteria for plain concrete. In: “Structure, Solid Mechanics and Engineering Design”, M. Te’eni ed. Wiley, New York 1969, pp 963-995 4. Perry, C., Gillott, J.E., The influence of mortar-aggregate bond strength on the behaviour of concrete in uniaxial compression. Cem. Concr. Res., 5, 1977, pp 553-564 5. Goodier, J.N., Concentration of stress around spherical and cylindrical inclusions and flaws, J. Appl. Mech. ASME, 55, 7, 1933, pp 39-44 6. Sezawa, K., Nishimura, G., Stresses under tension in a plate with a heterogeneous insertion. Rep. Aeron. Res. Inst., Tokyo Imp. Univ., 6, 25, 1931, pp 25-43 7. Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen 1953 8. Hsu, T.C., Slate, F.O., Sturman, G., Winter, G., Microcracking of plain concrete and the shape of the stress-strain curve. J. ACI, 60, 2, 1963, pp 209-224 9. Slate, F.O., Olsefski, S., X-ray for the study of internal structure and microcracking of concrete. J. ACI, 60, 5, 1963, pp 575-588 10. Stroeven, P., Fractals and fractography in concrete technology. In: “Brittle Matrix Composites 3”, A.M. Brandt, Marshall I H. eds. Elsevier, London 1991, pp 1-10 1 1 . Ringot, E., Automatic quantification of microcracks network by stereological methods of total projections in mortars and concretes. Cem. Concr. Res., 18, 1988, pp 35-53 12. Saito, M., Characteristics of microcracking in concrete under static and repeated tensile loading. Cem. Concr. Res., 17, 1987, pp 2 11-2 18 13. Stang, H., Shah, S.P., Damage evolution in FRC materials modelling and experimental observations. In: “Fibre Reinforced Cements and Concretes”. Recent Developments, R.N Swamy, B. Barreds. Elsevier, London 1989, pp 378-387 14. Stroeven, P., Application of various stereological methods to the study of the grain and the crack structure of concrete. Journ. Microsc., 107, pt 3, Aug. 1976, pp 3 13-321 15. Stroeven, P., Geometric probability approach to the examination of microcracking in plain concrete. Journ. Mat. Sc., 14, 1979, pp 1141-1 151 16. Stroeven, P., Some observations on microcracking in concrete subjected to various loading regimes. Engr. Fract. Mech., 35,415, 1990, pp 775-782 17. Reinhardt, H.W., Stroeven, P., den Uijl, J.A., Kooistra, T.R., Vrencken, J.H.A.M., Einfluuss von Schwingbreite, Belastungshohe und Frequenz auf die Schwingfestigkeit von Beton bei niedrigen Brucklastweckselzahlen. Betonw. und Fertigteiltechnik, 44, 9, 1978, pp 498503. 18. Stroeven, P., A case of compression failure in concrete due to stress release. In: “Fracture Mechanics of Concrete Structures I”, F.H. Wittmann ed. AEDIFICATIO Publ., Freiburg 1995, pp 461-470
128
Piet STROEVEN
19. Stroeven, P., Mechanics of microcracking in concrete subjected to fatigue loading. In: “Mechanical Behaviour of Materials 3”, K.J. Miller, R.F. Smith eds. Pergamon Press, Toronto 1979, pp 141-150 20. Cornelissen, H.A.W., Hordijk, D.A., Reinhardt, H.W., Experimental determination of crack softening characteristics of normal weight and lightweight concrete, Heron, 3 1,2, 1986, pp 45-56 21. Hordijk, D.A., Local approach to fatigue of concrete. PhD Thesis, Delft University of Technology, Delft 1991 22. Stroeven, P., Quantitative image analysis of damage in concrete subjected to direct tension. In: “Quantitative Description of Materials Microstructure”, L.J. Wojnar, K. Rozniatowski, K. Kurzydlowski eds. Jagielian Univ. Press, Krak6w 1997, pp 515-522 23. Rots, J.G., Hordijk, D.A., De Borst, R., Numerical simulation of concrete fracture in ‘direct’ tension. In: “Numerical Methods in Fracture Mechanics”, A.R. Luxmore et al eds. Pineridge Press, Swansea 1987, pp 457- 471 24. Buresch, F.E., A structure sensitive Klc-value and its dependence on grain size distribution, density and microcrack formation. In: “Fracture Mechanics of Ceramics 4”, R.C. Bradt, D.P.H. Hasselman, F.F. Lange eds. Plenum Press, New York 1978, pp 835-847
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
IMPLICATIONS OF THE LAW OF AGGREGATION OF MATTER IN CONCRETE TECHNOLOGY
Piet STROEVEN Faculty of Civil Engineering and Geosciences Delft University of Technology, Stevinweg 1,2628 CN Delft, The Netherlands, e-mail:
[email protected] ABSTRACT
This paper introduces some fimdamental issues that govern the reliability of experimental and modelling approaches in concrete technology. These findamentals are frequently violated, so that obtained results will be biased to an unknown degree. Nevertheless, nothing is really new in what is presented. For that reason, basically the philosophy is outlined and the main set up of formulas is given. For further details, reference is made to the relevant literature. Keywords Aggregation, concrete technology, digitisation, fiactality, geometric probability, representativeness, sampling, structural sensitivity.
INTRODUCTION “Concrete in the good old days seemed to be simple, however, concrete was never simple, we were” (Gilkey, 1950)
Concrete is a particulate composite material on different levels of the microstructure. Gravel grains (and eventually macro-fibres) are aggregated on meso-level in a cementitious matrix. Sand grains become discernable upon further increase of resolution in the aggregated mass of particles dispersed in the cement paste. An even more sensitive approach would allow detecting the very particles of this paste in the fresh state, or the hydrate structure of the hardened material. The molecular structure is situated at the lowest micro-structural level. A particulate composite material reveals size segregation of particles near surfaces at a higher level of the microstructure, ranging from boundary effects in structural elements to interfacial transition zones around aggregate grains. The underlying concept of a continuous range of microstructural dimensions and the three discrete levels of aggregation, denoted by macro-, meso-, and micro-level in concrete technology, have been recognized for a long period of time in the physics and mechanics of deformable bodies. Material behaviour under forces is the reflection of material characteristics and of material structure. This behaviour is defined in terms of properties, such as mechanical ones. Properties are denoted as structure-insensitive when solely governed by material composition, e.g. mass and Young’s modulus. Contrary, structure-sensitive properties such as the crack initia-
130 Piet STROEVEN tion strength are affected by the so-called group pattern or configuration of particles. Hence, particle size and spacing are involved. Engineering properties are supposed to reflect certain aspects of the behaviour of material elements of at least representative dimensions. In such representative volume elements (RVE’s) the material parameter at issue can be contracted away. Each geometrical parameter has its independent scale of homogeneity. The same holds for properties with different degrees of structural-sensitivity. RVE’s of structure-sensitive properties will exceed those of structure-insensitive ones to a considerable degree. Heterogeneity inside the RVE will increase with a decline of the micro-structural level taken into .consideration by the selected resolution of observations or measurement equipment (e.g. strain gauges). So, heterogeneity is not a material characteristic, but a jknction of the material parameter and of the ratio of resolution (micro-structural level) and the linear dimension of the RVE involved. Insight into the size of the RVE is important for the sampling strategy, and thus for the economy of the experiment. Particular materials are three-dimensional (3-D) aggregates. Observations should therefore provide 3-D information on material structure. Oblique materials like the cementitious ones do not allow easy access to 3-D material structure, however. Geometrical statistical (i.e. stereological) tools should therefore be applied for this purpose, since they provide means for unbiased estimation of 3-D geometrical parameters of the state of aggregation on the basis of 1-D or 2-D observations. Sampling is in the present context of crucial importance. In discussing fundamentals underlying experimental and modelling approaches to cementitious materials, sampling will receive proper attention in the light of the continuous range of microscopical dimensions. This paper will use fibre concrete (FC) and shrinkage cracking (SC) as reference examples, both in the perspective of material behaviour. Major difference is that fibres are men-made and cracking is a natural phenomenon. The fibre reinforcement structure can be visualized and studied on a discrete level of the microstructure, whereas damage reveals itself differently on a continuous range of microstructures. The implications are far ranging and form the subject of this paper. SAMPLING SCIENCE IN CONCRETE TECHNOLOGY A theoretical concept underlying the dispersion of one phase in a second (in the present case,
fibres or cracks in the matrix) that is generally accepted in modelling and experimental approaches is isotropic uniform randomness (IUR). This implies that sufficiently large samples can provide representative information when drawn at arbitrary location and orientation in bulk of the material. Mostly, this concept is (seriously) violated in practice, however. The production method of the cementitious material can cause fibre anisometry (leading to isotropic behaviour) in the FC example [ 13. Unevenly distributed internal stresses in the SC case will inevitably cause anisometry in the damage structure [2]. Fig. 1 depicts both cases. Care should therefore be bestowed on how to sample (as to location and orientation), since the quality of the estimate can never be better than the quality of the sample. Confronted with structures deviating from the IUR state, quantitative evaluation of structural features in sections is in general only possible by random sampling. This would complicate experimental approaches dramatically, and is therefore in concrete technology avoided. However, serious biases have to be accepted in the three-dimensional estimation procedure when proper precautions are not taken. This author, avoiding random sampling, introduced the correct procedure some 30 years ago [3], but so far most researchers unfortunately neglect this practical proposal. We will come back to this issue later. Of course, a major parameter in the design of experiments is the size of the sample. Together with the afore-mentioned issue, this should
131
Implications of the law of aggregation of matter in concrete technology
guarantee the representativeness of the information derived from the sample. In many cases, use is made of standardized specimens in concrete technology, so that sample size in not designed, and will be found insufficient in many cases (revealed by too large scatter). This inevitably reduces the efficiency of the experimental design.
Freesurface
Slice
I
X-ray direction
I
1 X-raysample
I
Dryingspecimen
I
I Cracking in section I
Fig. 1 (left) FC case: X-ray pattern of vertical slice of fibre concrete (compacted in vertical direction) will reveal partial fibre orientation. Fig. 1 (right) SC case: vertical section of concrete specimen with one free surface reflects anisometry in shrinkage crack pattern.
Orientation sampling strategy Underwood's classical book [4] is one of the very limited stereological literature sources to which researchers in concrete technology refer. Unfortunately, for expenmental methodology, this book is at least partly outdated. New and far more powerful approaches have been developed the last 20 years [ 5 ] . But for the basic set up of stereological theory, relevant for this paper, the book is very useful. Underwood presents the various stereological parameters and the associated correlations in a single table [3,4,6]. For our purpose relevant are the following relationships:
4-
-*
S,=-LA=~PL a
Note that in standardized stereological notation PL = P/L . The bar on top of the expressions implies an averaging operation realized by a proper sampling strategy. The first sequence of formulas represents a complete historical development in volume fraction ( VV)analysis (of
132
Piet STROEVEN
pores, aggregate grains, etc). The oldest approach from 1848 is based on experimental determination of areal fractions (A,) and is due to Delesse [7]. Half a century later, Rosiwall introduced the lineal analysis [8].The method involves coverage of the section image by a randomly oriented or directed line grid, whereupon the line fraction (LL)is determined that covers the sections of the pores or grains. The last development dates back three-quarters of a century (Thomson [9] and Glagolev [lo]), and is referred to as the point counting method; instead of lines, a random (or systematic) point grid is superimposed and the point fraction (Pp) covering the pore or grain sections is determined. The second set of equations is relevant for quantitative damage (crack extension) analysis. Introduced by Saltikov in 1945, this is referred to as the method of random (or directed) secants on a plane [ 111. It allows by simple intersection point counting (PL)to assess the 2-D crack trace extension (LA),or the 3-D crack surface area density (SV).The last equation allows analysing fibre length per unit of volume (Lv) in the FC case by assessment of intersection density in the section plane (PA)[3]. All relationships require random sampling strategies unless one is confronted with the extremely rare situation of an IUR structure. In both reference examples this never occurs. Hence, an appeal is made to the ingenuity of the researcher. Fortunately, solutions, in terms of the economy of the experiment, are available in the literature. Following a suggestion by Saltikov for dispersed surfaces in space, Stroeven has elaborated some 30 years ago a practical approach that can be followed when dealing with fibres or cracks in cementitious materials [1,3,12-141. The basic assumption is that the actual dispersion of structural elements (i.e. fibres or cracks in the reference examples) can be replaced by a linear combination of 1-D, 2D and 3-D ‘random’ structures. In the 2-D and 1-D sets, the structural elements are UR dispersed as to location, but they are parallel to the so-called orientation plane (2-D set), or to the orientation line (1-D set), respectively. The 3-D set is IUR dispersed. Since generally researchers use standardized specimens in materials research (or at least specimens with simple shape), the researcher will mostly be confronted in the actual material system with an orthogonal system of preferred orientations. In the FC case, the compaction direction and the specimen dimensions govern such a Cartesian co-ordinate system of fibre orientations. In the SC case, it is the principal direction of water transport perpendicular to the free surface, and the equality of global tensile stresses parallel to this surface that govern the Cartesian coordinate system of crack orientation. This approach simplifies random sampling to so called ortrip sampling. Hence, in the most complicated case, sectioning will be required in three orthogonal directions. For fibres, the following equations can readily be derived for sections of fibre material with arbitrarily dispersed fibres (Fig. 2). Note that PA is the number of fibres per unit of area, and LV the fibre length per unit of volume.
1 PA,= - L v 3 2 in which it is assumed that the { x,y }-plane can be associated with the orientation plane (generally, perpendicular to the gravitation direction) and the lineal fibre fraction ( L n ) is oriented in the direction of the z -axis (mostly, resulting from restricted specimen dimensions). However, in a large number of cases the researcher can identify an axis of rotational symmetry, which will reduce efforts dramatically, since image analysis can be restricted to so-called vertical sections/slices. This sectiodslice is selected randomly as to location but oriented parallel
133
Implications of the law of aggregation of mutter in concrete technology
to the axis of symmetry. This author applied ortrip sampling in a Dutch-Polish co-operation project on FC [13]. But in an earlier research project this could even be avoided by combining counting operations in a section and in the X-ray projection plane of the same slice [ 11. The latter formulas are not presented here, but are quite similar to the ones presented, and can be found in the relevant literature [14]. In the shrinkage cracking case, the co-ordinate axis perpendicular to the free surface could be associated with the axis of symmetry.
.. .
PAy
. -
a
.
Fig. 2. FC case: number of fibres per unit of area, PA,can be determined for fibre concrete in an ortrip sampling scheme (g indicates the gravity force during compaction). When the latter fraction can be neglected, the vertical section is parallel to the z -axis, and P, = PAY.To assess the unknown two fibre fractions, two independent observations are required either counting fibres in two orthogonal sections, or analysing the projection image of a single vertical slice [l]. The fibre system defined by the above set of equations is called a partially linear-planar one. It suits to approach an arbitrary fibre system. When not confronted with very slender elements, we deal with a partially planar system, where Lv, = 0.It constitutes generally the optimum solution for practical applications in terms of the economy of the experiment. Similar sets of equations can readily be derived for cracks [15]. In a Cartesian co-ordinate randomly dispersed traces due to the 3-D sub-set, traces parallel to the z -axis solely stemming system we assume for the most general situation a set of 3-D cracks, hrther a 2-D set parallel to the { x,z }-plane and a 1-D set parallel to the z -axis. All sub-sets of cracks will reveal traces in the { x, y }-plane, i.e. randomly distributed crack traces in the plane due to the 3-D and the 1-D sub-sets, and traces in the y -direction due to the 2-D sub-set. In the { x, z } plane the 2-D and 1-D sub-set yield traces in the z -direction, whereas the 3-D sub-set produces randomly dispersed traces in the plane. Finally, in the { y , z }-plane we find, apart from the randomly dispersed traces due to the 3-D sub-set, traces parallel to the z-axis solely stemming from thel-D sub-set. The set up is given in Fig. 3, also presenting sketches of the aforementioned x -, y - and z -planes. Intersection counts with a superimposed line grid in the { x, y }-plane are indicated by 4. When divided by the grid line length this yields P,, . A line
134
Piet STROEVEN
grid is superimposed in the two respective Cartesian co-ordinate directions and intersection densities are determined. This yields six observations condensed to: 1 P,(x)=-Ss,,+S,, 2 1 P,(y) =-Sva + 2
2
+-S,,
r
,,?!I-+
2 r
1
= P&)=TS,,+s,,
1
= PLY(X) =,S,,
+
2 +-S,,
r 2 +-S,, 7r
1 = pL(z)=-s,, 2
Orientation axis 1-D
+IZI I
Section planes Fig. 3. SC case: intersection counts per unit of grid line length, 4,are determined in two orthogonal directions for concrete with shrinkage cracks subjected to ortrip sampling. Hence, only three independent observations are obtained. Two sections will suffice for determination of the three unknown crack portions. For the constant (projection) factors involved, see the relevant literature [1,3,16]. When symmetry is assumed around the z -axis, as in the case of shrinkage cracking, where the free surface is perpendicular to this axis, we see that S,, 4.We are confronted with apartially linear crack system, allowing determination of the two unknown crack portions from two intersection counts in a single vertical section! Resulting expressions are
Implications of the law of aggregation of matter in concrete technology
135
in which 0 3 defines the degree of orientation in the crack structure (=SV&,). We see that quantitative analysis of cracking at the surface, or alternatively in a parallel plane under the surface, can never yield the full solution in the SC case. Since a crack gradient is formed in z -direction, the solution outlined would just present a global average. Of course, when statistically independent vertical sections are produced, also the independent gradients in both S,, and S,, can be determined. This requires subdividing the vertical section in narrow ‘horizontal’ strips, compromising between sensitivity and representativeness (sample size!). Herewith, we have reduced the requirement of random sampling for deriving threedimensional structural information from the material body to sampling a single (Xrayed) vertical slice in case of FC, and to sampling a single vertical section in the SC case. When detailed information in the latter case on the structural gradient is pursued, it is proposed to analyse narrow strips of a series of vertical sections in combination with sections parallel to the free surface. The replacement of the actual structure by a linear combination of I-D, 2-D and 3-D portions of these structural elements, as developed by Stroeven, in combination with the assumption of an axis of symmetry, renders possible dramatically reducing the complexity of the experimental approach. Since the experimental approach is generally simplified in concrete technology by making unjustified assumptions (IUR state!), the proposed procedure will also dramatically improve the quality of the structural estimates and therefore the reliability of the microphysical or micro-mechanical modelling approach.
Size sampling strategy In addition to correctly sampling with respect to orientation, as discussed in the above section, the size of the sample also governs representativeness. Unfortunately, samples for structural analysis in concrete technology are mostly not designed for size, because standardized specimens are used or specimens designed for material performance. Serial sectioning can help to increase sample size, but the sections should be statistically independent, so spacing is limited to the average size of the largest structural elements at issue. In concrete technology, the rule of thumb is to have minimum sample dimensions exceeding the maximum structural dimension (mostly, maximum grain size) by a factor of 4 to 5 [3,17]. However, this is a proper approach when interested in structure-insensitive properties (such as Young’s modulus). When micro-mechanical or microphysical modelling pursues estimation of structure-sensitive global properties (e.g. crack initiation or ultimate tensile strength), and structural information is as a consequence required on configuration instead of on composition (e.g. volume fraction, specific surface area), sample size should be significantly larger [3,18-211. Scatter in the estimated global geometric parameters of material structure can be theoretically estimated. As a rule, standard deviation s can be considered proportional to the reciprocal square root value of the number of observations [3]. Hence, sample area has to be increased by a factor four when it is pursued to reduce the standard deviation by a factor two. However, this is only relevant when dealing with composition density. Different spacing parameters are available when configuration is at issue. The most common ones are the nearest neighbour distance, A3, and the free interparticle spacing, h . Their global values are directly correlated with global density values of geometrical parameters, i.e.
-
A3
0.553
=-
i/Ny
136
Piel STROEVEN
Configuration homogeneity can be based on representative information as to the distribution of either one (or both) of these spacing parameters. This will require samples significantly larger than the ones used for composition homogeneity. Factors between 5 and 10 should be accounted for [3,18]. Anisotropy in SFRC is disproportionably influenced by the degree of orientation in the three-dimensional fibre structure [ 121. The degree of orientation in the three-dimensional shrinkage crack structure can also be considered a relevant parameter in global modelling of transport of harmhl substances to the reinforcement. Although o, is not a very structure-sensitive parameter, the scatter in global density values in eq (8) should be significantly reduced to yield this parameter with sufficient accuracy. Hence, sample strategy (orientation, location, size) should be part of the design ofexperiments pursuing determination of representative structural parameters. In doing so, the researcher should be aware of the structure-sensitive character of the parameter of interest (and relevance for the physical modelling approach). AGGREGATION IN CONCRETE TECHNOLOGY Continuous scaling Well-known for a long time in the physics and mechanics of deformable bodies is the concept of a continuous linear range of microscopic dimensions, as well as the three levels of aggregation of structural elements of materials. See for this purpose, e.g. Freudental’s book on “The inelastic behaviour of engineering materials and structures”, published in 1950 [22]. This way of emphasizing material structure can also be found in Holliday’s book on Composite Materials published in 1966 [23]. Ample attention to the same topic was given during the Southampton conference on “Structure, Solid Mechanics and Engineering Design” in 1971 [24]. Stroeven [3] more explicitly introduced the ideas in concrete technology in 1973, referring to the various connotations attributed to the three levels in different material technologies. Wittmann was probably the first to refer to the intermediate level in concrete technology as the mesoscopic one [25]. Fundamental to the interpretation of experiments, however, is the continuity in aggregation levels. Changing maximum grain size in experiments would require modifying resolution and sample size to the same degree to be able properly comparing outcomes on the same level of aggregation, unless the sample size is exceeding the linear dimensions of the so called representative volume element for the coarsest-grained material. Hence, “homogeneity and isotropy of concrete on engineering level cannot be qualified as material properties” [3, p.191. Homogeneity of a geometric parameter can only be conceived for samples of representative size. “This volume can be called the representative cell, and is the imaginary unit which represents to a defined and arbitrary probability the heterogeneity of the actual material. In an isotropic material the representative cell can be imagined as a cube... It should be noted that if there are n independent geometrical parameters (such as concentration, particle size, orientation, etc.), there will be n values for the representative cells since each geometrical parameter has an independent scale of homogeneity ... To put this another way, heterogeneity cannot be uniquely described by a single geometrical variable” [22]. These principles are widely ignored in concrete technology, so that outcomes will be biased. Striking examples can be found in [3]. As an example, we can refer here to Keeton’s analysis by photo-elastic coatings of deformations at the surface of cement paste, mortar and finegrained concrete specimens of similar size, and subjected to direct compression [26]. Using the same thickness of coatings (2 mm), Keeton associated the observed increasingly chaotic shear strain contours at larger grain sizes with an increasing degree of inhomogeneity. The observations simply reflect, however, the same phenomenon on different levels of the microstructure! So, Keeton’s conclusions were incorrect. But the underlying fundamental
lmplications of the law of aggregation of matter in concrete technology
137
aggregation rule is violated frequently in concrete technology, like in the SC example, such as treated in [2,27]. This problem does not occur in case of the fibre reinforcement, where fibre volume fraction can be defined and experimentally assessed unambiguously at a single selected resolution level. Continuous scaling plays a major role, however, when dealing with the amount of damage or the total (or specific) crack surface area as in the SC case. The closer the observation, the more heterogeneous and the more extensive will appear the damage structure. Hence, observations on different levels of the microstructure will produce systematically different information on density (extension) and on dispersion (degree of orientation, degree of heterogeneity). When the material structure is modified by hydration or by adding larger sized aggregate (as in [27,28]), a similar level of the microstructure should be adapted for comparison purposes in experimental designs pursuing a study of the effects of such changes on porosity or cracking. Unless this is properly arranged, artificial effects will be mixed with fundamental ones, like in the Keeton case. Fractality A special structural feature linked up with the continuous scaling phenomenon is fractality [29-311. This should be considered highly relevant when researchers are e.g. interested in geometric parameters of cracking. Unfortunately, most researchers only consider the phenomenon of academic interest. Instead, it has fundamental impact on the observations. Still, engineers accept that cracks recorded by naked eye on the surface of reinforced concrete beams subjected to bending forces will be accompanied by smaller cracks in the concrete matrix. Hence, geometric parameters of cracking would change at a lower level of aggregation. The same conclusion should be drawn when sections of relatively small prismatic concrete specimens after test loading are scanned under relatively small magnifications by an optical microscope. Myriads of tiny cracks can be visualized in areas where the naked eye would be incapable of doing so. Hence, intuitively we accept geometric parameters of cracking (density, length, spacing) to depend on sensitivity. This is what is meant by the “coastline of Britain” effect: the coastline’s length will increase steadily starting from observations by satellite, thereupon by plane, and ending up by walking (and measuring!) along the beach [32]. Obviously, length in sections and surface area in space cannot be measured unambiguously. When dealing with (near) fractal properties [3 11, the scaling effect can be quantitatively estimated. As relevant examples, we can mention here that Stroeven has analytically demonstrated the roughness of fracture surfaces [33], the tortuosity of transport routes [34], and the amount of damage [35] to depend on the sensitivity of the experimental or modelling approaches, though none of the cases is generally of ideally fractal nature. A prerequisite is, of course, that the researcher’s design of the experiment will refer to the sensitivity or magnification level employed, thereby acknowledging that experimental ‘findings’ are indeed fundamentally depending on the scaling level. Information concerning the fractal effect on the extent of the fracture surface area and on the amount of damage can be found in the relevant literature [293 13. To get an idea of the significance of the effect, Table 1 presents estimates on the amount of damage (at ‘discontinuity’ in a simple compression test) as a function of sensitivity of the observation method. Note that A4 = d,,,/ d o ,and the particle size distribution function, f ( d ) , for an equal volume fraction mix is given by f ( d ) = 2 S d F Id”’ . Micro cracking is assumed to be restricted to particle-matrix debonding in the modelling concept. We see that over the considered sensitivity range (associated with the range of aggregate grain sizes), damage increases 50 times by reducing (step-by-step) the scaling level of the microstructure.
138
Piet STROE VEN
Magnification Vol. Fraction A4 VV 2 0.1 4 0.2 8 0.3 16 0.4 32 0.5 64 0.6 128 0.7
Size range mm 16-32 8-32 4-32 2-32 1-32 0.5-32 0.25-32
Min. size (do)
Max.size (d,,,)
mm 16 8 4 2 1 0.5 0.25
nun 32 32 32 32 32 32 32
Damage in mm-’ 0.004 0.01 1 0.023 0.044 0.078 0.132 0.217
SV
Automatic quantitative image analysis Automatic quantitative image analysis facilities render possible to significantly reduce the labour intensity of structural approaches. However, it has been demonstrated that this will lead in particular cases to significantly biased results [36,37]. The digitisation operation will not hamper determination of area fraction, but length or area measurements will be significantly biased. Area is involved in the SC case, in which assessment of crack extension is pursued. This contribution will reveal where biases are involved and how to avoid or minimize them. Nowadays available software packages for image processing and quantitative image analysis reduce the work of structural analyses. In standardized situations, hlly automised approaches constitute economic solutions. In non-standardized cases, semi-automatic approaches are preferable [38]. Moreover, the digitisation operation to which field images should be subjected has been proven a serious source of biases [36,37]. For the analysis of numbers, volume fraction, size or spacing, this problem can be overcome. This holds for the FC reference example. But when confronted with (crack or grain perimeter) trace lengths, or surface area in space, this is a major drawback of automation. Digitisation does not influence the total projection of a set of crack traces in the directions of digitisation (conventionally, 4connexity), provided trace length exceeds pixel size considerably. Total projection in any other direction is significantly different from that of the traces, however. Since, the intersection density ( P , ( B ) ) equals the total projection of line traces per unit of area in an orthogonal direction ( L ; ( B + f ) ), the rose of intersections (or intersection densities) of the digitised crack traces will be seriously biased, too. The actual traces can be replaced by a linear combination of L,, and LA3,as we have seen earlier. LA, will not be affected by the digitisation effect. Changing structural parameters, like grain size or volume fraction, will not influence both portions to the same degree. Hence, the changing combination of both portions due to indicated variations in structural parameters is under the impact of unknown digitisation effects. The same will hold, of course, for the specific crack surface area. An elegant way to display the digitisation effect on a partially oriented system of traces in a plane is given in Fig. 4. A mixture of a linear (1-D) and a ‘random’ (3-D) portion is used in Fig. 4 (top). The two circles reflect the roses of intersection of the respective portions [4,37]. The PL-values represent the summation of both roses. This would be the best estimate when the image with crack traces had been manually analysed. In the digitised image, the traces are replaced by orthogonal components only. Hence, we deal with a mixture of oriented portions. The roses of the individual portions are shown in Fig. 4 (bottom). Again, the summation yields the rose of the digitised crack traces. The disparity between the manual and automatic image analysis results for other directions than of the 4-connexity digitisation directions is obvious! When quantitative crack measures are pursued for microphysical modelling of transport phenomena in concrete, the automated approach should be avoided.
139
Implications of the law of aggregation of matter in concrete technologV
+ pLo
X
/
PLr
analogue
/--
a.,-
....
............#* *... u
.d Y
m
lY00
1400
1700 2000 Velocity ( d s )
2300
2
Number of days of degradation
Fig 4. Histograms of velocity for the sound mortar and after 15.30 and 45 days (a) longitudinal waves; (b) transverse waves; ( c) surface waves, (d) summary of the results
For concrete it is observed that the dispersion of the results increases and that the velocity shift caused by the degradation is relatively smaller to that of mortar. This observation might be explained by the fact that aggregates are not attacked and that their proportion in concrete is higher than in mortar. Figure 5 shows the attenuation coefficients. The region of validity of the results (indicated by an ellipse) corresponds to the area where the coherence function y reaches maximum values, close to unity. It is observed that the obtained plots of ccv) fit the straight line: o.(fJ = aof thus indicating the dramatic rise of the absorption expressed in terms of (dB/mMHz) as a function of the time of degradation. Fig. 5.d summarizes the increase of attenuation - relative to the attenuation of the sound half of the sample - versus time of degradation. Attenuation values are given at frequencies corresponding to the maximum energy of the wave propagating in the sample. As it may be seen in the plots of coherence function y, the absorption causes the shift of the spectrum towards lower frequencies. The results show a significant increase of attenuation with the time of degradation, specially for the surface wave, where it raises up to 8 times after 45 days of degradation.
158
F. BUYLE-BODIN. B. PIWAKOWSKL A. FNINE. M.GOUEYGOUandS. OULD-NAFFA
I S days of degradatiorl c
-I I -I
L"*
--
-
-
*.I
frequency MHz
'
-
-I
-
-,
.-
-
3
frequency MHz
( 730 days of degradation
frequency MHz
1'
"
&her
30 45 of days of degradatlon
F i g 5 (a), (b), (c) Attenuation a and associated coherence function y vs. frequency, obtained for transversal waves; (d) Summary of results obtained for longitudinal; transverse and surface waves vs. degradation time. OTHER PHYSICAL MEASUREMENTS The depth of the degradation and the open apparent porosity of the degraded mortar samples were measured after each degradation period. The open porosity of the degraded layer can be then calculated by relating to sound and degraded volumes respectively. As shown Fig.6, the global porosity and the depth of the degraded layer increase as a function of the time of degradation, whereas the calculated porosity of the degraded layer remains constant and equal to nearly 24%. n I
1 ..I*
. I
*.".I
.*.I*.
Fig.6. (a) Open porosity vs, time of degradation (b) Depth of the degraded layer vs. square root of the time of degradation
159
Assessment of deteriorated concrete cover
The porosity was also measured by mercury intrusion on bored specimens. The results are for sound mortar equal to 18.6 %, for 15 days degraded mortar 25.4 %, for 30 days degraded mortar 25.2 %, and for 45 days degraded mortar 23.2 %. The comparison of the different measurements of porosity are given Fig. 7. PoroalQ 0.3
0.25
02
iz
{ 0.15 g 0.1
0.05
I
". Wnd
I dsp15d.y.
I
I dep M day.
deg 45 day.
Fig. 7. Porosity measurements for mortar samples Regarding the pore size distribution, the main size of pore of the sound mortar is 1 pm. For degraded mortars this main size is reduced to 0.3-0.4 pm with a less sharp distribution.
MECHANICAL MEASUREMENTS After degradation and acoustic measurement, the samples were sawn up into 4 x 4 x 15 cm specimens presenting a multi-layer configuration. First these samples were tested in bending but the resulting tensile strengths could not be used for analysis. After that, the specimens were tested in compression with different arrangements of the layers: layers in series and subjected to the same stress, or layers in parallel and undergoing the same strain. Strain gauges were bonded on the different faces of the different layers (sound or degraded) in the both directions, parallel or perpendicular to the direction of loading. They gave the local deformations. Moreover the displacement of the compression platen of the loading machine was measured, giving the global deformation of the specimen. With the value of the depth of the degraded layer, it was possible to evaluate the proportions of volume of degraded and sound mortar, and using the parallel or series models to calculate the Young's modulus from the global deformation. Fig. 8 shows the different values of Young's modulus given by strain gauges (parallel and series layers), by using parallel or series models, and by using velocity measurements (see below).
160
F. BUYLE-BODIN, B. PIWAKOWSKI, A . FNINE, M.GOUEYGOUand S. OULD-NAFFA
The strain gauge measurements allow the evaluation of the Poisson's coefficient. Its values stay constant according to the accuracy of the method and equal to 0.3. Young's modulua 4
m
-*
i -
+ c
25ooo
paralldlaye~s
.sadeslam
parslldmodel .Series& - C l m wlwities
Y
-.).I
2
m
15ooo
1CC.X Swnd
15daya
30 days
45 days
Fig. 8. Different evaluations of Young's modulus of degraded mortar
ANALYSIS OF RESULTS The Young's modulus E, the dynamic modulus K and the Poisson's coefficient v can be calculated from velocities using the well-known formulas:
The Poisson coefficient and the density are assumed to be constant with the time of degradation. The parameters E and K computed from the velocity data and expressed as relative values are shown in Fig.9.a. The values of E are also copied out on Fig. 8. The comparison is good, and shows that the pulse velocities are well correlated with the mechanical characteristics. In parallel, the measurements of porosity allow estimating the compressive strength, using the well known formula of Fkret [ 101:
0=oo(I-P)2 : where p indicates the apparent porosity (%) and cq, is the compressive strength of the porosity-free mortar. Fig.9.b. summarizes the relative decrease of ts and increase of P as a function of the time of degradation.
161
Assessment of deteriorated concrete cover
a K/K,
=
WE.
_Number of days of degradation
Number of days of degradation
Fig.9 (a) Normalized elastic modules E and K vs. degradation time; (b) Normalized apparent porosity P and associated compressive strength o vs. time Finally, correlating the time of degradation and the measured acoustic velocities, the relative drops of the Young's modulus and of the compressive strength as a function of the time of degradation are shown in Fig. 10.
Fig.10 (a) Normalized elastic modulus E vs. acoustic velocity; (b) Normalized compressive strength vs. acoustic velocity
CONCLUSIONS The effect of the chemical degradation on the characteristics of cover concrete was studied by different methods at global and local scale. The chemical attack by ammonium nitrate solution creates a degraded layer . Its depth increases following a diffusion law as a function of the square root of the time. The apparent open porosity and the Poisson's coefficient of this degraded layer seems to be constant, while the main size of pore and the elastic modulus decrease. Concerning the high frequency acoustic pulse method, the effect of the degradation is evidenced for the three types of waves. As expected, a decrease of velocity and an increase of attenuation are observed. Similar trends are observed with heterogeneous concrete, but the variance of the results made their interpretation more difficult. In the case of mortar, velocity decrease is 24% for the surface wave, whereas attenuation increased dramatically up by a
162 F. BUYLE-BODIN, B. PIWAKOWSKI, A. FNINE, M. GOUEYGOUand S.OULD-NAFFA
factor of 8 for the transverse wave. The high-frequency ultrasonic wave is thus able to detect changes in the micro-structure of the cover even at an early stage. Furthermore, preliminary experiments using lower frequency (50 kHz) have shown that there is no measurable difference at such a frequency range between the degraded and the sound material. This confirms that the choice of relatively higher frequency is relevant to sense the little depth of degraded layer. Concerning the relations between acoustic and mechanical characteristics, a good correlation is observed, and the sensitivity of all the parameters to the apparent porosity is highlighted.
REFERENCES
1. Basheer, P.A.M., Chidiac, S.E., Long, A.E., Predictive models for deterioration of concrete structures, Construction and Building Materials, 10, 1996, pp 27-37. 2. Bungey, J.H., Millard, S.G., Testing of concrete in structures, Blackie Academic & Professional, Glasgow, 1996. 3. Rendell, F., Jauberthie, R., Grantham, M., Deteriorated Concrete, Thomas Telford, London 2002. 4. Bangert, F., Grasberger, S., Kuhl, D., Meschke, G.,Environmentally induced deterioration of concrete: physical motivation and numerical modelling, Engineering Fracture Mechanics, 70,2003, pp 891-910 5. Torrenti, J.M., Didry, O., Ollivier, J.P., Plas, F., La dkgradation des bttons, Hermes, Paris 1999. 6. Jauberthie, R., Rendell, F., Physicochemical study of the alteration surface of concrete exposed to ammonium salts, Cement and Concrete Research, 33,2003, pp 85-91 7. Krause, F., Comparison of pulse-echo methods for testing concrete, NDT&E International, 30, 1997, pp. 195-204. 8. Ould-Naffa, S., Goueygou, M., Piwakowski, B., Buyle-Bodin, F., Detection of chemical damage in concrete using ultrasound, Ultrasonics, 40,2002, pp 247-25 1. 9. Goueygou, M., Piwakowski, B., Ould Naffa, S., Buyle-Bodin, F., Assessment of broadband ultrasonic attenuation measurements in inhomogeneous media, Ultrasonics, 40, 2002, pp 7782 10. Carde, C., Caracttrisation et moddisation de l’altkration des propri6tks mkcaniques due B la lixiviation des mattriaux cimentaires, Doctoral thesis, Toulouse, 1996.
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
MEASUREMENT OF THE DURABILITY OF GLASS FIBRE REINFORCED CONCRETE AND INFLUENCE OF MATRIX ALKALINITY H. CUYPERS and J. WASTIELS Department of Mechanics of Materials and Constructions, Vrije Universiteit Brussel, Belgium J. ORLOWSKY and M. RAUPACH Instita fir Bauforschung, Rheinisch Westfalische Technische Hochschule Aachen, Germany
ABSTRACT Even today, one main topic of consideration regarding glass- fibre reinforced cementitious composites is the durability. At RWTH-Aachen (Germany) the durability of AR-glass yams in concrete is under investigation. The aim of these investigations is to build up a model, allowing prediction of the long-term behaviour of textile reinforced concrete. This model includes the influence of humidity, pH and temperature corditions, combined with stress (constant load). For glass- fibre reinforced cementitious composites, the pH of the matrix has a considerable influence on the durability, since glass fibres can be severely attacked by high alkalinity. To overcome this problem a new cementitious material has been developed at the VUB (Brussels, Belgium). This Inorganic Phosphate Cement (IPC) provides a now alkaline environment after hardening. Since the IPC matrix provides a neutral environment, other effects (humidity, temperature, stress) can be studied. A more common concrete mixture (micro-concrete with Ordinary Portland Cement (OPC), pH 13.5 after hardening) is also tested as a comparison material. The evolution of the tensile strength of IPC composites and OPC composites with AR-glass and with Bglass is measured and discussed. It is shown that the IPC matrix has in comparison to OPC a good durability. Keywords cementitious composite, durability modelling, alkalinity
INTRODUCTION Concrete reinforced with fibres offers several advantages as a building material. Fibre reinforced concrete (FRC) has been known for almost 30 years. Some typical fields of application are claddings, filigree construction elements and industrial floors. Textile reinforced concrete (TRC) represents an interesting new construction material, offering several advantages compared to steel or fibre reinforced concrete. These advantages dominate in those fields of applications where thin- walled, structural elements with a high load-carrying capacity are necessary. The used textiles consist out of continuous fibres (filaments) which are collected to form a yarn (roving). The diameter of the filaments is 12 to 30 pm. A roving with 2400 tex (1 tex = 1 g / 1000 m) has about 2400 filaments. Figure 1 shows on the right side a roving which is embedded in concrete.
164 H. CUYPERS, J. WASTIELS, J. ORLOWSKY and M. RAUPACH
Figure 1. Textile used as reinforcement in c:oncre:te and roving embedded in concrete. In the research project SFB 532 “Textile Reinforced Concrete - Basics of a New Technology” placed at the Technical University of Aachen (financed by the central public funding arganisation for academic research in Germany, DFG) several institutes investigate this new construction material. Some aspects of these investigations are the matrix- fibre bundle bond behaviour, load-bearing capacity, material optimisation, serviceability and durability [l]. The aim of these durability investigations is to build up a model, allowing the prediction of the long-term behaviour of textile reinforced concrete. This model includes the influence of humidity, pH and temperature conditions, combined with stress (constant load). Concerning durability, FRC and TRC are comparable because the same mechanisms of ageing happen. However, the influence on the macro- mechanical behaviour of the composite material may be different. The storage of glass fibre reinforced concrete in a water bath at elevated temperature leads to an accelerated ageing process as it has been shown, amongst others, by Litherland et al. [2]. Depending on the temperature of the water and type of glass and cement, the tensile strength of the composite material decreases with time. Two causes for the loss of tensile strength are described in many papers in different ways [2]-[4]. First the glass is chemically attacked by the high alkalinity of the cement and secondly it is mechanically attacked by hydration products. Pumell [5] is convinced that the local points of flaws in the glass, which are due to the manufacturing process, are the points of attack by chemical and mechanical forces. To protect the glass from chemical attack, 15-20 % zirconium is added to the conventional E-glass mixture. This modified glass is called AR-glass (alkali resistant). It improves the durability of the concrete reinforcement but it does not solve the degradation problems entirely [2]-[6]. To overcome this durability problem, caused by the alkalinity of ordinary cements, a new cementitious material has been developed at the VUB (Brussels, Belgium). This Inorganic Phosphate Cement (IPC) provides a norralkaline environment after hardening. At the VUB ordinary 6glass fibres are applied as reinforcement in IPC. Mechanical modelling of 6glass fibre reinforced IPC composites and possible application as faces in sandwich panels with cementitious faces for building applications have been studied by Cuypers [7]. The advantages of the neutral environment of IPC are now used to study the effect of humidity and temperature on composite materials with Bglass or AR-glass. A more common concrete mixture is also tested as a comparison material. Several testing and measurement techniques are applied to determine the evolution of the matrix, the fibres and their interaction. This paper describes the testing methods and the testing program. Then the results are presented and discussed. Finally conclusions, taken from the experimental program, and future developments are drawn.
Measurement of the durability of glass fibre reinforced concrete and influence of matrix ...
165
TEST METHODS Materials Two different types of glass are used for the investigations: (1) AR-Glass rovings with 2400 tex manufactured by the company Vetrotex (CemFil) and (2) chopped E-glass fibre mats (“2Drandom”) with a fibre length of 50mm and fibre density of 300g/m2 (Owens Coming MK12) with +540 fibres per bundle. The concrete mixture (table 1) with OPC cement, which has been used as a comparison material, was developed by the Institute for Building Materials Research (RWTH-Aachen) as a micro-concrete [8].’The pH value of this mixture is 13.5. Table 1. Composition of the micro-concrete. Binder system
Type of cement
Cement
Additives
content
Fly ash
Silica fume
kglm’
OPC
CEM I52,5
490
175
35
Water reducer
I
Stabilizer
Binder content
w/bratio
max. grain size
kglm’
-
mm
700
0.4
0.6
I’
Test program An overview of the test program is given in table 2. As already mentioned in the introduction, saturation of glass- fibre reinforced concrete, especially in solutions with high alkalinity, leads to degradation of the glass fibres. To accelerate this degradation, the specimens are stored at 50°C in water. Reference specimens are stored at 20 “C in water or in ambient conditions to obtain an idea on the acceleration factor of the experiments. Tests with E-glass in combination with OPC were not carried out since from previous investigations it is well known that Bglass is rapidly degraded in an alkaline environment [ 11, [31.
Reinforcement
AR-glass
Matrix material
OPC
IPC
ambient conditions (20°C and 65 % relative humidity) water 20 “C
90
14, 28, 90
14,90
90
water 50 OC
14, 28, 90
7, 14, 28, 90
storage conditions
E-glass
IPC
storage time in days 7, 14, 28, 56, 90
7, 14, 28, 56, 90
166 H.CUYPERS, J. WASTIELS, J. ORL.0 WSKY and M.RAUPACH IPC: 24 hours post-curing in a oven at 60 "C, followed by storage during 7 days at 23 "C and 50 % relative humidity After the presented storage conditions (table 2) were applied, the specimens were stabilised under ambient conditions for several days. For each test three specimens were used. TSP-Test with AR-glass rovings The TSP-Test (dog bone shaped specimens in tensile test) allows us to draw conclusions concerning the changes in the stress-elongation behaviour, the cracking image and the maximum roving tensile strength after climatic loading. Therefore, statements can be made about the long-term behaviour of textile reinforced concrete [6]. The geometry of the TSP specimens can be seen in figure 2. The specimens have a thickness of 6 mm. Eight single rovings are used, this corresponds to a reinforcement degree of 2,O v01.-%. The change of length is measured on two sides over 250 mm. The rovings, which are sticking out of the sample body, are glued with epoxy resin. This way the individual filaments are fixated at the end of the sample. When stress is applied, individual filaments are unable to slip towards the centre of the sample from the sample edge. Therefore the rovings can reach thkir maximum tensile strength.
I-
I
+*
roving
[mml
gauges
500 250
F-. -_._._._-._-.I-
dl -.-.-I-
fixing of the roving with epoxy resin
O*
-,
fixing of the roving with epoxy resin
Figure 2. TSP-specimens and test set-up. The application of tensile force takes place with rounded off steel elements, shown in figure 2. The TSP samples are charged in displacement control with a speed of 0.5 m d m i n until failure occurs. Figure 3 shows a typical test curve. After a linear elongation, an initial crack in the matrix appears. The curve gradient after this first crack is nearly the same as before, so it is often difficult to determine the first crack point. After the second or third crack appears, the force grows more slowly and a fine crack pattern is build. After introduction of the last crack in the matrix, further load carrying occurs via the 8 rovings until the reinforcement fails. A selE made program finds these described points (force/elongation) automatically (figure 3). The initial stiffness (before the first crack appears) is determined as a measure of the evolution of the matrix properties and the stiffness after the last crack appeared is a measure of the fibre properties.
Measurement of the durability of glass fibre reinforced concrete and influence of matrix ...
5,5 1
167
Force in kN
3-0 €-modulus of the reinforcement
2.5 -
0,O
1.0
2,O
3,O
4,O
5,O
6,O
7,O
8,O
9,0 10,O
11,O 12,O Elongation in mmlm
Figure 3 . Evaluation of the measured results. The number of matrix cracks is determined after failure of the specimen occurred due to mechanical loading. The average crack spacing () is, amongst others, function of the matrix-fibre frictional shear stress transfer (z). The relationship between and T is formulated in a rather straightforward way by the well-known ACK (AvestowCooper-Kelly) theory [9]. If this approach is adopted, the average crack spacing at the end of multiple cracking can be determined: (cs) =
1.337 onurV,,, 2zv,
Where: = the average crack spacing at the end of multiple cracking ornu = the matrix failure stress r = the fibre radius V, = the matrix volume fraction Vf = the equivalent fibre volume fraction (including effects of fibre ,orientation and fibre length) z = matrix-fibre interface shear stress All parameters in equation ( 1 ) can be determined easily, except for the matrix- fibre shear stress transfer, 2. This matrix-fibre interaction is function of some aspects that are not easily controlled. In practice fibre bundles are used rather than single fibres. These bundles are usually only impregnated partially, if being impregnated at all. Instead of matrix- fibre interaction, both matrix- fibre and fibre- fibre interaction occurs. Matrix- fibre interaction will be more prominent at the outer fibres of the bundle than at the inner fibres. For this reason z is an average matrix- fibre interaction parameter. If crack counting is performed (determination of ), equation ( 1 ) can be rewritten in order to find the average matrix- fibre shear stress, 2:
168
H. CUYPERS, J. WASTIELS, J. ORLOWSKY and M.RAUPACH
Tests on strip specimens with Eglass fibres The specimens with Bglass fibre reinforcement are laminated by hand layup technique. The amount of matrix used per layer is 800 g/m3. This way, laminates with a fibre volume fraction of about 12 v01.-% are made. After a laminate is fabricated, it is kept in ambient conditions for 24 hours. Afterwards, the laminate is post-cured for another 24 hours at 60 "C to accelerate the hardening process. During the curing and post-curing process, both sides of the laminate are covered with plastic sheets to prevent early evaporation of water. The laminates are cut in strips of 250 mm length and 18 mm width. Tensile tests are performed on the E-glass fibre reinforced specimens by an INSTRON 4505. The force is measured by a load cell and the strains are measured by an extensometer over a length of 50 mm. After loading of the specimens, the average crack spacing is determined and discussed, as explained in paragraph 2.3.3.
RESULTS AND DISCUSSION Measurement of the tensile failure strength Figure 4 shows some load-elongation curves, obtained from tensile testing on TSP specimens with AR-glass. Force In kN micro concretewith OPC
micro concrete wilh OPC
3 tests afler referenz storage: 28d at 23 'C. 95 % r.h. and
0
2
4
6
8
10
12
140
2
4
6
8 10 12 14 Elongationin m d m
Force in kN
I failure at lhe grip
3 tesls aRer referenzswage: 28d at 23 'C. 95 % r.h. and
0
2
4
6
8
10
12
140
2
4
6
8 10 12 14 Elongationin mm/m
Figure 4. TSP tests with different matrix after different storage conditions. Figure 4 top left, shows three tensile test curves with OPC and AR-glass rovings after reference storage. The tests show good conformity. The specimens fail at an average value of
Measurement of the durability of glass'5bre reinforced concrete and influence of matrix ...
169
4.8 kN. At this breaking point, only the reinforcement carries the load so it is possible to
calculate the strength of the rovings, which is then 672 N/mmz. At the top right part of figure 4, the influence of 28 days water storage at 50 "C is shown. After initial cracking, the
specimens also show an evenly distributed cracking image, but the specimens with OPC break already at an average load of 3.1 IcN (Roving strength 434 N/mmz). The results with IPC are presented in figure 4 bottom. After reference storage, the specimens fail at an average value of 5.5 kN (Roving strength 770 N/mm2). This breaking load is significant higher than the OPC specimens. The accelerated ageing storage at 50 "C in water shows no loss of function of the IPC specimens. The average failure load is still 5.5 kN. One of the three specimens of IPC broke at the grip as can be seen in figure 4. Specimens with this kind of failure were not considered in the evaluation. Figure 5 presents an overview of the results with the TSP specimens. In this diagram, the roving strength calculated from the failure force is shown as a function of storage time. The dots at zero days are the reference specimens. For the reference storage, the scatter is also shown. 4 Roving strength in Nlmm'
900
,
I
600 500 400
300 200
W
-
.-._.___
L.-.-.+
'-~
Referenz IPC
-- -65%
- - . - . - _ _- -. - - - - .
4-.Water; 50'C;
IPC
a Water; 20'C; IPC
humidity.; 20°C; IPC ReferenzOPC
4-
65% humidity.: 20%; OPC
--Water;
.Water; 50°C; OPC 20°C: OPC
The roving strength with IPC matrix after reference storage is 140 N/mm2 higher than the roving strength with OPC. This measured roving strength of 790 N/mm2 (IPC specimen) has the same magnitude as the roving strength of a single roving, tested in a tensile test. This means the manufacturing of the TSP-specimens and the IPC matrix itself does not damage the filaments initially. In comparison, the OPC matrix reduces the tensile strength of the reinforcement already after reference storage. One possible reason for the initial strength loss could be the transversal shearing of aggregates and hydration products on the filaments. Further investigations to explain this effect are necessary. The results in figure 5 show that the composite with IPC and AR-glass has a good durability. No significant loss of strength was measured, even when stored in water at elevated temperature. In contrast, specimens with OPC in water at 50 "C show a significant loss of strength. In water at 20 "C these specimens show a strength decrease only after a storage time of 14 days. After this initial decrease, the strength is constant. At 20 "C and 65 % relative humidity the OPC specimens show no loss of strength.
170
H. CUYPERS, J. WASTIELS, J. ORLOWSKY and M. RAUPACH
Figure 6 shows the evolution of the failure stress of the IPC specimens with Erglass fibres. 45
1
I
40
I
I
I
1
I I
I
i
I
I
I
12
14
16
I
I
I
a n 35
rIn 30 3
25
L
20
-$ 15
B
accelerated ageing
10
-ambient
wnditions.averageevolution
5
0 0
2
4
6
10
Figure 6. Evolution of the failure stress of IPC specimens with E-glass. In contrast with IPC with AR-glass, the IPC spepimens with Bglass fibres show ewlution of the failure stress with time. It has been mentioned by some authors [lo] that just the effect of warm water can lead to decreasing strength of glass fibres, even when the fibres are again stabilised under ambient conditions after being kept underwater. The initial composite strength of 35MPa is equivalent to a roving strength of 870 N/mm2, indicating that the initial strength of the Lglass fibres is not or hardly attacked by the IPC matrix. Measurement of stiffness and crack spacing Table 3 sbws the stiffness properties of the composite materials with AR-glass. Table 4 shows the Emodulus measured in the post-cracking zone and the average crack spacing of the IPC composites with Eglass. The E-modulus in the pre-cracking zone and the tensile matrix strength could not be determined clearly for these specimens, since multiple cracking was smeared out over a large stress interval.
'Noevaluation possible (figure 4)
strip specimens.
Measurement of the durability of glassfibre reinforced concrete and influence of matrix ...
171
The roving stiffness of the TSP specimens with IPC and AR-glass does not change significantly with climatic conditioning. The roving stiffness of the TSP specimens with ARglass an3 OPC matrix decreases after 14 days of application of accelerated ageing conditions. This roving stiffness cannot even be determined any more after 28 days. The roving stiffness of the specimens with Bglass and IPC matrix does not change with time. For the TSP specimens with OPC micro concrete the average crack spacing seems to decrease after application of accelerated ageing conditions. A possible explanation for the reduced crack spacing is the increasing hydration of the micro concrete, which results in a higher matrix- fibre interface shear stress (see equation (2)). This increase in matrix- fibre shear stress might lead to early failure due to mechanical attack of the glass fibres by hydration products, as was explained in paragraph 1. The opposite effect can be seen on the specimens with IPC matrix. The average crack spacing is constant or slightly increasing with time of storage. This would mean, according to equation (2), there is hardly any evolution in the matrix-fibre interface interaction (or maybe even a slight loss).
CONCLUSIONS Tensile testing on the different composite materials shows clear results concerning strength. Figure 7 contains an overview of the evolution of the degradation of the tested cementitious composites under accelerated ageing conditions. The strength of OPC micro-concrete reinforced with AR-glass rovings decreases up to 50 'YOof the initial strength after 90 days in water at 50 OC. In comparison, the strength of IPC matrix reinforced with AR-glass rovings stays at nearly 100 YOuntil 28 days. After 90 days at accelerated ageing conditions this composite material shows a small amount of degradation. Tests with Bglass fibre reinforced IPC show in figure 7 also a loss of strength, but the degradation is significantly lower than the combination of OPC and AR-glass. When considering figure 7, one should also keep in mind that the reference failure strength (100% in figure 7) of the OPC specimens with AR-glass (670N/mmz)is already significantly lower than the reference failure strength (100% in figure 7) of the IPC specimens with AR-glass (770N/mmz)and &glass (870N/mmz). The average matrix crack spacing decreases as a function of accelerated ageing time if OPC matrix is used and increases or hardly changes if IPC matrix is used. A possible explanation for the reduced crack spacing in OPC composites is the increasing hydration of the micro concrete, which results in a higher matrix-fibre interface shear stress. This effect is not observed if IPC is used. When IPC is reinforced with AR-glass, no or very limited decrease of failure strength is noted. It has thus been shown that, due to the use of a cementitious material with neutral pH, effects of alkalinity can be studied separately from other effects. This means the IPC matrix can be used as a reference matrix to model long-term behaviour of fibre reinforced concrete and textile reinforced concrete, thereby separating possible effects leading to degradation. If Bglass is used, there is a small decrease in failure strength. However, degradation of 6 glass fibres is rather due to the water and high temperature environment as a chemical reaction (solution of the glass) than to evolutions in the matrix-fibre interface, since no real change in average crack spacing is noted.
172
H. CUYPERS, J. WASTIELS, J. ORLO WSKY and M.RA UPACH
Strength of the composite material compared to the reference in % I
100 I
80
-
60 40
-+IPC-AR-glass
20 -+Storape
.
conditions:water at 50 TI
+IPC-E-glass
-
*OPC-AR-glass "
I
0
20
40
60
80
100 Time In days
Figure 7. Loss of strength of AR-glass and Erglass in OPC or IPC matrix. 5. REFERENCES
[31 [41
r71
PI
r91 r101
Hegger, J. et al, 1. Fachkolloquium der Sonderforschungsbereiche 528 und 532, 15. und 16. Februar 2001 in Aachen. Aachen. Lehrstuhl und Institut f i r Massivbag 2001 Litherland, K.L., Oakley, D.R., Proctor, B.A., The Use of Accelerated Ageing Procedures to predict the Long Tern Strength of GRC Composites. Cement and Concrete Research 11, Nr. 3, 1981, pp 455-466 Majumdar, A.J., Laws, V., Glass Fibre Reinforced Cement. London, BSP Professional Books, 1991 Yilmaz, V.T. , Glasser, F.P., Effect of Silica Fume Addition on the Durability of Alkali-Resistant Glass Fibre in Cement Matrices. Fly Ash, Silica Fume, Slag, and Natural Pozzolans in Concrete. Proceedings Fourth International Conference, Istanbul, May 1992 (Malhotra, V.M.(Ed)), Vol. 2, pp 1151-1166 Purnell, P., Short, N.R., Page, C.L., A Static Fatigue Model for the Durability of Glass Fibre Reinforced Cement. Journal of Materials Science 36,2001, pp 5385-5390 Brockmann, J., Raupach, M., Durability Investigations on Textile Reinforced Concrete. Durability of Materials and Components, 9th International Conference, Brisbane, Australia, 17-20 March 2002, Paper No. 1 11 (CDROM) Cuypers, H., Analysis and Design of Sandwich Panels with Brittle Matrix Composite Faces for Building Applications, Phd. T6esis W B , 2002 Brameshuber, W., Brockmann, J., Development and Optimization of Cementitious Matrices for Textile Reinforced Elements. Proceedings of the 12th International Congress of the International Glassfibre Reinforced Concrete Association, Dublin, 1416 May 2001, pp 237-249 Aveston, J., Cooper, G.A., Kelly, A., Single and multiple fracture, The Properties of Fibre Composites. IPC Science & Technology Press Ltd. London, 1971, pp15-24 Czymai, A., Eine Methode zur Bestimmung von Tiefenprofilen an korrodierten Glasfasern. Clausthal, Technische Universitat, Fakultat fiir Bergbau, Huttenwesen und Maschinenbau, Diss., 1995
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
BRIDGE RECONSTRUCTION WITH ONE LAYER CONCRETE OVERLAY
J. GALIC, I. BANJAD PECUR, N. STIRMER, V. UKRAINCZYK University of Zagreb, Faculty of Civil Engineering KaEiCeva 26, 10000 Zagreb, Croatia, e-mail:
[email protected] ABSTRACT
The paper presents the reconstruction of the damaged reinforced concrete bridge with high performance concrete modified with styrene-butadiene latex and fiber reinforcement. ARer 30 years in service the severe damages of concrete cover and reinforcement corrosion were observed. The detailed testing has shown poor quality of concrete, low strength and up to 25% reduction of certain number of reinforcing bars. The bridge reconstruction was executed with one layer concrete overlay 20 cm thick. The repair high performance concrete was designed for the following properties and purposes: - to strengthen the span structure by increasing the depth of cross section by 10 cm replacing partly the damaged concrete, insulating layer and asphalt overlay, - satisfactory resistance to freezing and deicing chemicals, - resistance to wear and abrasion, - to serve as the impermeable overlay replacing the insulation. Keywords bridge reconstruction, repairing impermeable concrete overlay
corroded reinforcement,
polymer
modified FRC,
INTRODUCTION In the past, many bridges were designed and constructed on the basis of safety and bearing capacity proof. The durability of reinforced concrete was not taken into account. ARer some 30 years many of these bridges are heavy damaged. Typical damages result from reinforcement corrosion caused by de-icing salts or carbonation and frost cycles, but also from poor design and construction or lack of maintenance. The methods of reconstruction or rehabilitation or repair of such bridges change from one case to the other. Concretes modified with different admixtures and materials are used in most cases. ARer brief description of the problem, in this paper are presented the reconstruction and repair works of the reinforced concrete bridge with one layer high performance concrete.
174 Jure GALIC, I. BANJAD-PECUR. N. $ T I M E R and V. UKRAINCZYK TEST RESULTS AND EVALUATION OF THE EXISTING BRIDGE Static system is continuous reinforced concrete plate over six spans, L=l1,0+11,5+11,35+11,6+11,75+11,2m =68,4 m, and bridge level line is placed in horizontal S-curve and vertical curve (FIGURE 1). The bridge was concreted in place 30 years ago during the cold weather and the edge parts were damaged by frost. Because the bridge is exposed to heavy traffic load high damage rate was observed. It was necessary to find quick and durable solution for its reconstruction.
FIGURE 1. View of the bridge before reconstruction. In FIGURES 2-4 typical damages are shown. Concrete strength was determined combining the results obtained by Schmidt hammer and drilled cores. Due to the low quality and poor homogeneity of concrete the characteristic strengths of bridge were very low (TABLE 1). TABLE 1. Characteristic concrete strengths
I
.P .A R T --.*
I
fck(MPa)
1
Slabs Columns Abutments
Reinforcement cover depth as measured by rebar locator ((PROCEQ))PROFOMETER 3 showed variations from more than 6 cm to 0 cm. In heavy damaged parts of structure concrete cracks and spalling around reinforcement were significant (FIGURE 3).
175
Bridge reconstruction with one layer concrete overlay
cornice
footway
of
F1 the slab
Concrete carbonation depth was estimated on drilled cores with phenolphthalein. In spite of the similar environmental conditions test results vary in wide range due to the heterogeneity of the concrete quality (FIGURE 5).
carbonatisatondepth (mm) 1501
45 40
35 30 25 20 15 10 5
-,---
0
I-
Ul -~ -
__
S1-J -
-.
- -
-
___
__
r -
S4-J - _. -
FIGURE 5. Carbonation depths
P I -SM
176 Jure GALIC, I. BANJAD-PECUR. N. S T I M E R and V. UKRAINCZYK Chloride ions contents were determined on powder samples taken by drilling subsequently into the depth of bridge parts as described in the TABLE 2. According to these data corrosion of the reinforcement is mainly caused by carbonation.
CODE S1-J u1 u2 PI-s PI-T P 1-SM PS.5-SM
STRUCTURAL ELEMENT
Column abutment abutment Slab Slab I Slab 1 Footway
DEPTH (cm)
I
0-2 . _ 0,002 0,002 0,Ol 0,002 0,0062 0,oo 1 0,006
I
-2-4 .
I
4-6 . -
I
0,002 0,064 0,023 0,002 0,002 0 0,002
0,002 0,os
0,018 0,002 0,0062 0 0,002
Besides the repair in the sense of durability of all parts of the bridge, the recalculation of the existing span structure has shown the necessity of reconstruction and strengthening. THE PRINCIPLES OF REPAIR AND RECONSTRUCTION WORKS The reconstruction principle is visible in the cross-section of the bridge span structure (FIGURE 6 ) . Existing 10 cm of asphalt overlay, waterproofing insulation and 10 cm of the upper part of concrete slab were removed using hydro demolition procedure. These three layers were replaced by new reinforced high performance concrete 20 cm thick. REPAIR PRINCIPLE Before repaii
High-.llulmo q m r m a u i
/ I
FIGURE 6.'Cross-section of the span structure. The high performance concrete was designed for the following purposes: - strengthening the span structure to increase the bearing capacity of the bridge; - specified strength 35 MPa;
- satisfactory resistance to freezing and deicing chemicals, - satisfactory resistance to wear and abrasion, - satisfactory skid resistance;
Bridge reconstruction with one layer concrete overlay
177
- to serve as the impermeable overlay instead of separate insulation.
After hydro demolition the old concrete surface was rough and the bond between old concrete and new concrete overlay was additionally assured with reinforcement web in the contact zone. Concrete curbs were exchanged with steel ones protected with epoxy resin and welded to footway reinforcement. The principles of the repair of corroded steel bars and concrete cover of columns, abutments and bottom part of the bridge deck are shown in FIGURE 9. Contaminated and damaged concrete was removed, steel bars cleaned of rust and new cover of high performance mortar was applied. The depth of cover is increased for 2 cm above the old concrete surface. The high performance mortar was designed for the following purposes: - high-alkaline mortar to recover passive protection; - good bonding between existing concrete and repair mortar in fresh and hardened state; - specified strength 30 MPa; - satisfactory resistance to freezing and thawing.
FIGURE 7. Hydro-demolition of the bottom part of the deck.
FIGURE 8 , Concreting of the bridge deck with polymer-modified FRC.
Along with the deck, new footway was concreted, because the old one was totally damaged by frost. Also, existing steel fence was replaced by new one.
repair
FIGURE 9. Repair principles.
178 Jure GALIC, I. BANJAD-PECUR, N. S T I M E R and V. UKRAINCZYK
DETAILS ON RECONSTRUCTION To fulfill the special concrete requirements, in preliminary tests the following constituents were chosen for mix design: River sand 0.. .4 mm Diabase crushed coarse aggregate 4.. .16 mm Styrene-butadiene latex Steel fibers L/d = 30/0,4 mm Polypropylene fibers L/d = 12/0,02 mm The complete quantity of special concrete for overlay was 120 m3, and the distance from the concrete factory was 100 km. Hence, it was necessary to use setting retarder, and the latex was premixed on the site just before emptying the mixer to avoid the excessive air entrainment of the mixture. The details of the two stages of completing the mix proportions are shown in TABLE 4. Concrete was pumped to its final position, compacted by internal vibrator, then leveled with the screed and again vibrated with the surface vibrating screed. TABLE 4. Mix proportions At mixing plant
Added at construction site
Total
179
Bridge reconstruction with one layer concrete overlay
FIGUIZE 10. Surface treatmznt
FIGURE 1 1. Surface roughncss
Surface roughness was achieved by dragging a broom along the concrete surface until one third of grain size had been visible (FIGURE 10 and FIGURE 11). Two days after final setting the concrete was left to dry, and then it was impregnated with the styrene-butadiene latex solution.
Proc. Int. Symp. ,,Brittle Matrix Composites 7 " A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
CEMENT-BASED THIN BONDED OVERLAYS: NUMERICAL STUDY OF THE INFLUENCE OF BOND DEFECTS AND FIBRE REINFORCEMENT Vincent SABATHIER (1,2,3), Jean-Louis GRANJU (I), Benoit BISSONNETTE (2), Anaclet TURATSINZE (l), B a d e TAMTSIA ( 2 ) (1) Laboratoire Matkriaux et DurabilitC des Constructions (LMDC) Gknie Civil INSA-UPS, 135 av. de Rangueil, 31077 Toulouse Cedex, France (2) Centre de Recherche Interuniversitaire sur le Bkton (CRIB) Dtpartement de Gtnie Civil, UniversitC Laval, QuCbec, G1K 7P4, Canada (3) Saint-Gobain SEVA BP 176, 71 105 Chalon-sur-SaBne Cedex, France
ABSTRACT The aging. of concrete structures raises the problem of repairs. Thin bonded concrete overlaying can be a suitable technique for the rehabilitation of large area structures. A variety of structures or elements are concerned, for instance slabs on grade (mainly industrial floors), pavements, bridge decks, walls and tunnels. Toppings and linings are also relevant to the same issue. The aim of the overlay may be to retrofit a damaged surface, to improve the mechanical capacity of a structure by increasing its thickness, or to do both. The durability of an overlay relies on the durability of the bond with the substrate. In fact, the real issue is this bond. Its strength and durability often remain more or less unpredictable, much more in situ than in laboratory conditions, because of the inherent variable conditions on the work site. Especially, poor preparation of the substrate to be overlaid or its contamination are the cause of local bond defects. Relying on FEM numerical modeling, a quantitative evaluation of the incidence of such bond defects on the further debonding of the overlay is proposed. The modeling tool had been previously validated with experimental results in the absence of bond defects. In the part of the work reported in this paper, bond defects of different sizes were addressed. In addition to the defect size, the influence of the strain softening behavior of the debonding interface, due to bridging and interlocking, and the influence of fiber reinforcement in the overlay by fibers were investigated. The results of this study stresses the importance of taking into account the bridging and interlocking along the debonding interface. They also confirm the beneficial role of fiber reinforcement in the overlay. At last, they demonstrate that, owing to bridging and interlocking mechanisms along the interface, the effect of an initial bond defect vanishes soon while debonding propagates. Keywords Bond, cement, concrete, debonding, defect, fibers, interlocking, modeling, mortar, overlay, reinforcement, repairs.
182
Vincent SABATHIER, Jean-Louis GRANJU, Benoit BISSONNElTE, Anaclet TURATSINZE ...
INTRODUCTION Many concrete structures throughout the world need to be repaired, often only superficially. At the moment, repair is one of the most active fields of research in several construction materials laboratories. The use of a cement-based thin bonded overlay to repair superficially a damaged concrete structure or element is a rather economic technique. It mainly concerns slabs on grade (mainly industrial floors), pavements, bridge decks, walls and tunnels. Toppings and linings are also relevant to the same issue. Since 1990, extensive studies have been performed on the subject by a number of investigators [l-61 who have pointed out that the durability of such overlay relies on the durability of its bond with the substrate structure. This bond is in fact the central issue. The work reported here deals with the overlay mechanical behavior and debonding conditions, the long-term aim being to develop the knowledge and tools that will hopefully prevent debonding from happening. It appears that whatever the cause of debonding (external loading, hygrometric loading, thermal loading, or a combination of these), the involved mechanisms are quite similar. In such a process: - debonding is initiated in the vicinity of discontinuities within the overlay (i.e. cracks); - although the interface between the substrate and the overlay is subjected to both normal and tangential stresses, only the tensile forces perpendicular to the interface will initiate the debonding process; - fiber reinforcement in the overlay delays andor slows down debonding and its propagation by limiting the cracks opening. In order to achieve a successful repair, the thin bonded overlay technique requires from the workers some special care, especially during the surface preparation of the substrate and during the pouring of the new concrete or mortar. Nevertheless, in spite of these efforts, bond defects are practically unavoidable. Since the presence of a defect results locally in a bond sometimes much weaker than elsewhere in the repair, it might play a significant role on the repair (bond) durability. The objective of this study is to evaluate through modeling the effect of a bond defect and the contribution of fiber reinforcement in the general overlay behavior. This paper presents the basics of the model that was used and the results of simulations carried out to quantify the influence of interfacial defects. The effect of fiber reinforcement upon initiation and propagation of debonding caused by this defect was also addressed. BASICS OF THE MODEL
The modeling was based on the FEM code CASTEM 2000. Its methodology is presented in details in [7]. It assumes a crack or a debonding propagation to be controlled by the calculated stresses at first node beyond the crack or debonding tip in the still continuous structure. It is a usual technique to avoid controlling the propagation by the stress state calculated at a node, the tip of the crack or of debonding, where the theoretical stress can reach an infinite value. The crack or debonding therefore propagates to the next node when the stress state at the control node does not anymore satisfy the specified stability criterion. The algorithm used was derived from that developed by Rondeau [8],Chausson [2] and Toumi [9] using the FEM code CESAR (developed by LCPC. France). After evaluating the incidence of the spatial discretization, a distance between nodes along the crack and debonding paths of 1 mm was retained.
183
Cement-based thin bonded overlays: numerical study of the irdluence of b o d s defects ...
Crack propagation in mode I The roughness of the two opposite faces of a crack results in interlocking which is at the origin of a residual strength a, which decreases with the opening of the crack w.The approach used in the present study is that developed by Bazant [lo] and referred to as smeured crack model. The empirical relationship between q and w was obtained from a literature survey. On the basis of the law suggested by Hordijk [ l l ] , the following simplified formulation developed by Toumi [ 121 was used:
where the tern R q is the tensile strength of the material and w /is the opening limits beyond which load transfer through interlocking becomes negligible. For w = wl,the absolute value of q(w) obtained from this formulation is not zero, but it is small enough to be considered negligible. The reduction in the interlocking load capacity with the crack opening corresponds to a damage of the so-called interlocking and it is thus not reversible. As a first approximation, in the phases of closing or re-opening of a crack, provided that its opening remains lower than the maximum value w,,,, previously reached, the following q-w relationship is assumed.
From the proposals of Hordijk [ l l ] , it was estimated that, for an ordinary concrete containing aggregates with maximum size of 10 mm, w~ should be close to 0.1 mm. This value was selected, as it was validated by tests carried out previously [7]. The corresponding q-w plot relationship is presented in Figure 1 (a) and was used to model the interlocking mechanism in the plain concrete. (a) 4
RUL= 3.6 MPa
0.05
Crack opening w (mm)
0.1
I
0
0.1
0.2
0.3
0.4
0.5
0.6
Crack opening w (mm)
reinforced concrete (30 kg of fibers per m' of concrete). In the case of fiber reinforced material, the post-cracking strength is defined as ctfand represents the combined contribution of interlocking and fiber reinforcement. Ribbon-like amorphous metal fibers were used and from the works performed by Chausson [2], a;/-w plot relationship presented in Figure l(b) was chosen (30 kg of fibers by m3 of material). The contribution of these fibers is characterized by an approximately constant stress orf=2.2 MPa up to a critical opening value wCf=0.15 mm, followed by a continuous reduction, assumed as linear, until the limit crack opening of W I / =0.6 mm is reached.
184
Vincent SABATHIER, Jean-Louis GRANJU. Benoit BISSONNETTE, Anaclet TUHATSINZE ...
The following relationships can thus be derived:
) ~ t ( w ) et ) (WQVcr) (Wd <W<WIO orf (w)
otr (w) = ot(w) otr (w) = orf (3) otr (w) = orr .(w-wir)/(wcrwir)
Debonding propagation along an interface Debonding at the interface between the substrate and the repair material is a very complex phenomenon. The interface can be submitted to both tensile and shear stresses, and the debonding propagation process is a result of combined fracture modes (mode I and mode 11). According to the results reported by Uchida [ 131, it was assumed that the evolution of the shear interlocking forces as function of the relative sliding, denoted s, is governed by a law similar to that describing tensile interlocking. The relationships derived from the model previously described (see equations 4 and 5) are presented in Figure 2. The potential closing and re-opening at the interface is dealt with as in the previous model. The term Run corresponds to the tensile strength along a direction perpendicular to the interface, w is the opening of the debonding interface, w,, is the maximum opening previously reached, and w i d the critical opening beyond which there is no more interlocking force. Similar variables can be obtained to describe the corresponding shear behavior and are denoted as R r d , s,,,s and s / d . The values used are from Chausson et al. results [2]. Ran and R r d were available, actually measured by direct tensile and direct shear tests on interface samples. However, the lack of data for WId and Sid have led to the use of values obtained through a reverse analysis of the available flexural data.
In addition, the evolution of tensile and shear interlocking are not independent. For example, an opening w of the debonding interface does not only cause a reduction of the tensile interlocking (according to the empirical relationships described previously), but it also reduces the shear interlocking capacity. Indeed, irrespective of the origin of damage, it breaks local cohesive andor bridging links that affect both the tensile and the shear interlocking. It is proposed to manage this interaction according to the example of tensile interlocking illustrated by the diagram shown in Figure 3. The value of tensile interlocking without considering any interaction is multiplied by a reduction coefficient. This one depends on the maximum shear damage previously reached, itself being a hnction of the maximum sliding previously reached.
The symmetrical approach is applied to the case of shear interlocking.
185
Ceinent-based thin bonded overlays: numerical study of the iifluerrce of bonds defects ...
I I
1.5 I
0
0.01
0.02
0.03
0.04
0
0.C
Opening at the interface w (mm)
0.01
0.02
0.03
0.04
0.051
Sliding at the interfaces (mm)
I
Figure 2. Mechanical characterization of the substrate-overlay interface: (a) bd-w plot relationship (mode I), (b) Td-S plot relationship (mode 11).
7dR7d
t
X
Wld
W
I
Figure 3. Effect of the tensile and shear damage interaction - Example of calculation for tensile interlocking. Modeling of the interfacial residual stresses is performed using so-calledjoint elements in the FEM-based code CASTEM 2000. These elements have normal and transverse (shear) stiffnesses. Initially in accordance with the material characteristics, these stiffnesses are adapted to describe the damage as a hnction of the relative displacements w and s. This evolution is obtained according to the equations presented previously. SIMULATION OF THE ROLE OF FIBERS UPON A BONDING DEFECT
Simulation of the presence of a defect Tests previously carried out by Chausson [2] were simulated. The composite test specimens were made of a cement-based mortar overlay with or without fibers and cast over a stiff steel substrate. The latter was a 100-mm wide hollow steel shape with an effective stiffness comparable to that of a concrete substrate, and its surface was treated to promote the mortar adhesion. The specimens were submitted to three-point flexural tests with the overlay on the tension side. The numerical results reported here are limited to the case of a 20-mm thick overlay on a 50-mm deep substrate. It is a 2-D simulation and it is assumed that a state of plane stress applies. Through a first series of calculations, a good agreement between modeling and experiment was found. Then, a bond defect was introduced and located at the specimen midlength (on the specimen axis of symmetry in the z direction), i.e. at the point of maximum bending moment stresses. It was modeled using interfacial elements having zero tensile and
186
Vincent SABATHIER, Jean-Louis GRANJU, Benoit BISSONNETTE, Anaclel TURATSCNZE ...
shear interlocking stiffness. The different defect lengths considered were respectively 20, 40, 60, and 80 mm. The simulated test is shown with its FEM mesh in Figure 4. The characteristics of the overlay and the interface were already presented and are summarized in Table 1.
Repair mortar General Without fibers E = 25 000 MPa Rot = 3,6 MPa v = 0,2 (not cracked) w1 = 0,l m v = 0 (cracked) p = 2200 kdm3 Bond defect
With fibers cr,.f = 2,2 MPa w,f= 0,15 m m wlf = 0,6 mm
Interface RCJd Rtd
= 0,5 MPa = 1,3 MPa
Wid = 0,05 mm Sld
= 0,05 mm
Imposed displacement
I
!
(with or without fibers) 20 to 80 mm
Figure 4.Illustration of the model developed to study the influence of a bond defect RESULTS AND DISCUSSION
Fiber reinforced overlay, defects with increasing size The results are presented in Figure 5 and show the evolution of the debonding from midlength as a function of the midspan deflection for various lengths of initial bond defect. The following observations can be made: As the size of the defect increases, the subsequent debonding starts less sharply. It may be explained by the increased distance of the debonded edge relative to the point of maximum curvature. That is accompanied by a slight delay of debonding initiation which may also be explained in a similar manner. When an initial bond defect is present, the midspan versus debonding progression curve systematically rejoin that calculated without any defect. The effect of the initial defect vanishes and thereafter causes no significant effect on the overall debonding process. It seems that the debonding length beyond which an initial defect will have no more influence is independent of the defect size. In the present study (50-mm substrate and 20mm fiber reinforced overlay with R,, = 3.6 MPa and S ,= 2.2 MPa, interface characteristics such as defined in Table 1) this length is about 40 mm.
Cement-based thin bonded overlays: numerical study of the influence of bonds defects ...
187
2c
a 0
50
I00
150
200
250
300
350
Mid-span deflection (pm)
Figure 5 . Debonding length from each side of the center crack as function of the midspan deflection (fiber reinforced overlay and various defect lengths)
The role of fibers The results are presented in Figures. 6 and 7. 100 '"Without fibers; No defect '."Without fibers: 40mm defect
-With
50
100
fibers; 40mm defect
150 200 250 Mid-span deflection (rm)
300
I 31
Figure 6. Debonding length from each side of the center crack as a function of the midspan deflection (overlay with and without fibers, 40-mm and 80-mm defects)
188
Vincent SABATHZER, Jenn-Louis GRANJU Betwit BZSSONVETTE, Atlaclet TUM TSZNZE ...
0
50
100
150
200
250
300
351
Mid-span deflection (vm)
Figure 7. Crack opening versus the mid-span deflection (overlay with and without fibers, 40mm and 80-mm defects) The first observation is that reinforcing the overlay with fibers significantly slows down the debonding process. For an identical midspan deflection or an identical curvature, the length of debonding can be reduced by half. The corresponding crack openings are also reduced. Alternatively, at similar overall damage (debonding length and crack opening), fiber reinforcement allows the repaired structure to withstand a much more important curvature. In addition, it appears that the larger the initial defect is, the earlier the effect of fibers arises. When there is no observable initial defect, the separation between the plain mortar and fiber reinforced mortar plots appears only after 18-mm debonding propagation. However, when there is a defect, this separation appears as soon as the debonding starts and is more pronounced as the defect size increases. Nevertheless, the results plotted in Figure 6 clearly show that fiber reinforcement of the overlay (at least for the conditions and assumptions considered in this study) does not affect the debonding length beyond which the influence of the initial defect vanishes.
CONCLUSION This work has confirmed the beneficial role of fiber reinforcement in a thin bonded overlay, Within the conditions of the present study and for a given state of deformation in the overlaid system, it was shown numerically that fibers can reduce by half the extent of debonding. The efficiency of fibers in reducing the effect of a bond defect was also studied. Fibers do not seem to influence the debonding length beyond which the defect has no more effect. Nevertheless, they act against the debonding propagation process as it starts, the effect being more important as the defect size increases. The piece of work reported in this paper is just an early step of a research project that will include laboratory testing of large overlaid concrete structural elements (test series under way). In these experiments, various overlay thickness and defect size values will be investigated. The results will then be used to refine the model.
Cement-based thLi bonded over.la.v.7:nutiierical study ofthe inflirerice of bonds defects ...
189
ACKNOWLEDGMENTS
The authors wish to express their appreciation to Saint-Gobain SEVA and the National Association for Technical Research (ANRT) for their financial support. REFERENCES
Granhaie, F., Granju, J.L., Ringot, E., Durability of pavement repairs, point of view about the role of fibers. In: Proc. "5th International Conference on Concrete Pavement Design and Rehabilitation", Purdue University, West Lafayette, USA,.20-22 April 1993, pp 195202. 2. Chausson, H., Granju, J.L., Rechargements minces adherents en beton renforce de fibres metalliques. Revue Franqaise de Genie Civil, n02, 1997, pp. 309-326. 3. Granju, J-L., Turatsinze, A., Farhat, H., Les paradoxes de la durabilite de l'adherence des rechargements minces adherents. In Proc. 3emeColloque International Francophone sur les Betons Renforces de Fibres Metalliques, Quebec, 11-12 juin 1998, pp. 63-76. 4. Granju, J-L., Thin bonded overlays : about the role of fiber reinforcement on the limitation of their debonding. Advanced Cement Based Materials, vol. 4, no 1, 1997, pp.21-27. 5. Granju, J-L., Debonding of thin cement-based overlays. ASCE Journal of Materials in Civil Enginering, vol. 32, n02, 2001, pp. 114-1 120. 6 . Bissonnette, B., Le fluage en traction: un aspect important de la problematique des reparations minces en bCton. PhD Thesis, Dkpartement de Genie Civil, Faculte des Sciences et de Genie, Universite Laval, Quebec, 1996. 7. Granju, J-L., Sabathier, V., Turatsinze, A., Toumi, A., Structures composites en beton : elements repares par rechargement mince adherent, modelisation de leur delamination.. In Proc. Forum des Associations AFGC/AUGC/IREX, Innovation et Developpement en Genie Civil et Urbain, Toulouse 30-31 mai 2002, on CD, section Materiaux Composites (edited by SCOM - Universite Paul Sabatier - Toulouse). 8. Rondeau, M-C., Modelisation des phknomknes de frottement en mode I d'ouverture de fissure par le logiciel CESAR. DEA, Genie Civil INSA-UPS, Toulouse, France, 1994. 9. Toumi, A., Etude du processus de propagation de fissures par fatigue dans le beton. Thkse de doctorat, Universite Paul Sabatier, Toulouse, France, 1998. 10. Bazant, Z.P., Crack and theory for fracture of concrete. Materials and Structures, vol. 16, 1983, pp. 155-177. 11. Hordjik, D.A., Local approach to fatigue of concrete. Thesis, Delft, Hollande, 1998. 12. Toumi, A., Bascoul, A., Turatsinze, A., Prediction de la duree de vie du beton sous fatigue - paramktres caractkristiques, Revue Franqaise de Genie Civil, vol. 4, 2000, pp. 297-307. 13. Uchida, Y.,Kurihara, N., Pokugo, K., Koyanagi, W., Determination of tension softening diagrams of various kinds of concrete by means of numerical analysis. In Proc. FRAMCOS-2, 1995 (Edit. Aedificatio, 1995), pp. 17-30. 1.
Proc. Int. Symp. brittle Matrix Composites 7 '' A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
DEBONDING OF FRC COMPOSITE BRIDGE DECK OVERLAY Rasmus WALTER, Henrik STANG, John F. OLESEN, Niels J. GIMSING Department of Civil Engineering Technical University of Denmark DK-2800 Kgs. Lyngby, Denmark, e-mail:
[email protected] ABSTRACT A new type of composite bridge deck is currently under research. The concept is to achieve composite action by the adhesion between a thin layer of fiber reinforced concrete cast on a steel plate. Of special concern is the strength of the bond between the concrete and steel plate in the case of vertical cracking of the overlay. Based on a nonlinear 2D finite element model a theoretical parameter study has been conducted in relation to debonding of a concrete overlay. Discrete crack theory was used to model vertical cracking of the overlay and interfacial cracking (debonding) between the steel plate and concrete. Two parameter studies were made. One concerns the fracture energy of the overlay and steel-concrete interface. These results show that the composite performance is dependent primarily on fracture energy of the concrete overlay, and less on the fracture energy of the steel-concrete interface. In the other, the mixed mode behaviour of the steel-concrete interface is studied in relation to the interfacial failure criterion. Keywords Debonding, FRC, fracture mechanics, steel-concrete interface. INTRODUCTION A large number of steel bridge decks suffer significantly from increased traffic intensity and higher wheel loads. This results in fatigue cracks in both welded structures and surfacing. Development of an entirely new concept of deck systems is of interest. A typical deck according to this system consists of a 40-60mm layer of Self-Compacting Steel Fiber Reinforced Concrete, (SCSFRC), bonded to an 8mm steel plate [I]. Whereas conventional composite constructions achieve composite action by mechanical fasteners, the idea here is to achieve composite action only through adhesion. The adhesion between concrete and steel is enhanced by sand blasting of the steel plate. Since a controlling factor of the composite strength is related to the vertical cracking of the overlay, the composite plate subjected to a negative bending moment is of interest. During flexural cracking of the overlay, the distribution of shear and normal stresses along the steelconcrete interface changes dramatically from that of the elastic phase. In the fracture process zone of a discrete crack. high stress concentrations develop in a plane perpendicular to the
192
Rasmus WALTER, Henrik STANG, John Forbes OLESEN and Niels Jorgen GIMSING
crack direction due to the presence of the steel plate that opposes the opening of the flexural crack. The debonding problem is known from the repairing of existing structures by thin cementbased overlays, see e.g. Granju et al. [2-31. They show that cracking of the overlay induces high interfacial tensile stresses leading to debonding between the two materials. Once initiated, the interfacial crack will propagate in a mixed mode characterized by tensile and shear stresses along the interface. The aim of this paper is to study the behaviour of the interface between concrete and steel with a fracture mechanical approach. In this study the so-called fictitious crack model (FCM) developed by Hillerborg [4]will be applied. The advantage of the model is the simplicity and the good correlation between theory and experimental tests. The basic idea of the FCM is a relationship between the stress and the crack opening. This relationship describes the stresses transferred across the crack. This method has also been applied to fiber reinforced concrete, see e.g. [S]. The two types of cracking - vertically through the overlay and interface debonding between steel and concrete - will be described by the FCM. For small crack openings, an interfacial fracture between steel and concrete shows the ability to transfer stress across the crack. This phenomenon is called ‘interlocking’ and its significance in a debonding process is described in [3]. The ‘interlocking’ effect is synonymous with the FCM. The main focus of the present paper is the presentation of a two-dimensional nonlinear finite element model to simulate the debonding process discussed above. Furthermore, the model is used to carry out two theoretical parameter studies in order to illustrate the influence of debonding on the overall behaviour.
NUMERICAL MODELLING The problem of a vertical crack penetrating a concrete layer bonded to a steel plate and the subsequent debonding is studied in a three point bending set-up according to Figure 1. The modelling is carried out as a two dimensional composite beam model, consisting of a concrete layer bonded to a thin steel plate. The vertical cracking zone in the composite beam under the applied load P corresponds to the zone near a midspan support in a bridge structure. Note that the composite beam is turned upside down for convenience.
Interface crack path, Discrete c d n g
I,_
I Loncrete Linear Elastic
L-Flexural crack path, Discrete craking
~
b
Figure 1: Experimental set-up: Simulating a negative bending moment in a bridge deck The vertical concrete cracking is modelled using standard interface elements as implemented in the applied software Package DIANA [ 6 ] . The interfacial mixed mode fracture is modelled using a composite interface model originally developed by Lourenqo and
j
193
Debonding of FRC composite bridge deck overlay
Rots [7], also implemented in DIANA. The mixed mode behaviour and the significance of constitutive material parameters are investigated through two parameter studies. Firstly, the influence of a tough concrete overlay and different fracture energies of the steel-concrete interface are investigated. Then, a parameter study is carried out concerning the failure criterion for the steel-concrete interface. Material characterisation Considering the concrete-steel interface, the state of stress is described through normal and shear stresses. In many cases the failure surface of the stress state in a steel-concrete interface is well described through a Mohr-Coulomb criterion. The failure criterion in the applied constitutive model, consist of two surfaces, denoted fi and fi, representing shear and tension failure respectively, cf. Figure 2.
Failure surfaces: f i . i=12
Id f
Figure 2: Failure surfaces f,andfi, defined by the cohesion c, slope tan(p), and the tensile strengthf;. Nonlinear softening of the interface is characterized by degradation of the tensile stress J and the cohesion c. The nonlinear softening of the tensile stress and cohesion is assumed to behave according to the following law
where co andl;o are initial values of the cohesion and tensile strength, GJ and Gy represent the fracture energy of MODE I and I1 respectively, s and w represent the slip and opening after crack initiation. The nonlinear exponential behaviour given in Equations 1(a-b), originates from experiments on mortadbrick interfaces by Van der Pluijm [8]. At the intersection between the failure surfacesf1 andfi, cf. Figure 2, a permanent coupling between tension and shear failure is present. The softening of the two surfacesfi and j ; are coupled assuming isotropic softening, meaning that the percentage of softening on the cohesion is assumed to be the same on the tensile strength. This is explained in further details in 161. Furthermore, for simplicity, all calculations are carried out assuming associated plasticity: tan(p)=tan(y), where y is the dilatation angle. Cracking of the overlay is assumed to propagate at midspan O X , using discrete crack theory. Nonlinear effects of the bulk material are not considered in this case. The stress-crack opening relationship of concrete can in many cases be modelled using a bilinear curve [S]. In the present study a bilinear curve is applied according to equation (2).
194 Rasmus WALTER, Henrik STANG, John Forbes OLESEN and Niels Jgrgen GIMSING
d w ) -b, - u , w = --
J;
6, -u,w , h2 - U 2 w ,
0I w <w W,
I wI
W?
where 61=1; and the limit w /are given by the intersection of the two line segments and w~ correspond to the intersection by the second line and the abscissa. The steel and concrete outside the crack paths is modelled as a linear elastic materials with the engineering constants E, = 210GPa, vs=0.3, E, = 30GPa and vs=0.15. The elements representing the bulk material are 8-node isoparametric plane stress elements or triangular for mesh refining, cf. Figure 3 for the applied mesh. The two crack paths - the vertical and interface crack - are modelled using so-called interface elements, available in the applied FEM-package [ 6 ] . A two dimensional configuration is considered, where the interface element relates the forces acting on the interface to the relative displacement of the two sides of the interface. In the present case, the interface element is described by a traction vector and a vector which represents the relative displacements. In the elastic regime the relationship between traction and relative displacement is given by:
I:[
=
;[ ;]
I:[
with k,,. and k.? assigned large penalty values to model initial continuous geometry. The interface elements have a thickness of zero and are placed between the steel and concrete and at midspan to represent a possible vertical crack, cf. Figure 3.
Interface elements
/\
P 2
I
Figure 3: Half beam mesh used in FEM calculations, the two thick lines represent interface elements. Study of debond mechanism Consider a load P acting on a composite beam as shown in Figure 1. The load causes a ’negative bending moment’, characterised by tensile stresses in the concrete layer. This will eventually, at some stage, lead to cracking of the concrete. The vertical crack propagates through the concrete overlay, but at some stage it is opposed by the steel plate. The opposition of the steel plate will lead to an increase of normal stress in a plane perpendicular to the vertical crack tip, i.e. in the plane of the steel concrete interface. The horizontal stress intensity is likely to introduce cracking, along the ‘weakest link’ - which in this case is assumed to be the interface between steel and concrete. The initiation of an interfacial crack is illustrated through a case study. A composite beam is studied given the geometry: L=800mm, hC=50mm,hs=8mm, b=lOOmm and a vertical crack
195
Debonding of FRC composite bridge deck overlay
described through Equation (2) given the values: J;=3MPa, a,=lOmm-', a2 =O. lmm", b2=0.5. The distribution of interface stresses is illustrated for different openings of the vertical crack. The opening of the vertical crack, called the crack mouth opening displacement (CMOD), is calculated at midspan, cf. Figure 4-a. For an opening of 0 and 0.03 mm the stress distribution is shown as a function of the x-coordinate normalised with the concrete height h,, cf. Figure 4-b. The x-coordinate is measured from midspan.
I
-2 L 0
--
L
05
1
1.5
I 2
X-coordinale/hc [mmlmm]
(a) (b) Figure 4: Stress distribution along the interface for a CMOD value of zero and 0.03mm (a) Interfacial forces and configuration (b) Stress distribution along the interface versus the xcoordinate normalised with the concrete height h,. Dashed lines represent shear stress r a n d solid line represent the normal stress 0. It is observed that for an uncracked concrete overlay (CMOD=Omm), the normal interface stresses are governed by compression. As the crack is initiated and further opened, the normal stresses changes from compression to tension, in many cases critical to the bond between steel and concrete. Further the shear stresses are significantly increased. PARAMETRIC STUDY I - Fracture energy The purpose of this parametric study is to simulate the global behaviour of the set-up given in Figure 1 for different fracture energies of the overlay and steel-concrete interface. The different simulations performed are grouped into 3 different groups denoted A-C. Simulation A1 is the reference case, and each of the other groups involves simulations where parameters have been changed in relation to this case. The different groups of simulations are: A. Variation of the bilinear (T-wrelation of the vertical crack as defined in Equation ( 2 )
B. Variation of Mode I energy for the steel-concrete interface. The nonlinear softening of the interface in Mode I is defined in Equation (1 -a) C. Variation of Mode I1 energy for the steel-concrete interface. The nonlinear softening of the interface in Mode I1 is defined in Equation (I-b)
196
Rasmus WALTER, Henrik STANG, John Forbes OLESEN and Niels Jurgen GIMSING
The different groups of simulations and their parameter values are summarized in Table 1. The first case (A) concerns the significance of the toughness of the vertical crack. The vertical crack is characterised by a bilinear crack-opening relationship according to equation (2). The bz-value may be taken as a measure of the amount of fiber used in the material, where a high bz-value corresponds to high fiber content. Finally, the significance of different mode I + I1 energies of the steel-concrete interface is studied through cases B-C. In the reference case, A l , the following numerical values of the geometry parameters were used, cf. Figure 1: L=SOOmm, h,=Smm, hC=50mm, b=l OOmm. The numerical values used for the material parameters in the bilinear 0-w relation of the vertical crack were: J;=3MPa a,=lOmm-', a2=0.1mm-', br=0.5. The numerical values of the steel-concrete interface were, J=2MPa, c=3MPa, tan( p)=O.5, G/'= G/" = 0.1N/mrn. Name
A2 A3
Changing parameter and values Reference 0.2. b, 1.8.b2
B1
0.5. Gi
B2
2.0. Gi
c1
0.5 .Gy
c2
2.0. Gy
A1
Table 1: The Parameter variation of b-Fvalue of the vertical crack and mode I+II fracture energies of steel-concrete interface. Changing the toughness of the vertical crack leads to a change in global behaviour. This is presented in Figure 5 (a), showing the maximum moment versus the opening of the vertical crack. It is observed that changing the bz-value of the vertical crack affects the global ductility significantly.
500
. --:-----. 2
600
A2
,
,'
E
E $ 1.5 E c" - 1 I
s0 P)
100nl " 0
0.5
A3
0.5 1 1.5 CMOD - Vertical crack [mm]
6 I
n
2
"0
0.5 1 1.5 CMOD - Vertical crack [mm]
2
(a) (b) Figure 5 : Graphical representation of three hypothetical cases: -Al, ----A2, -.-.A3. (a) The bending moment M=PL/4 versus the crack opening of the vertical crack - CMOD, (b) The interface crack length normalised with respect to the concrete height versus CMOD.
197
Deboizding of FRC conzposite bridge deck overlay
The relation between the interface crack length and CMOD is shown in Figure 5 (b). Here it is shown that the toughness of the vertical crack has little influence on the relation between the interface crack length and the opening of the vertical crack. Changing mode I+II energy for the interface has a larger effect on the cracklength-CMOD relation than the ductility of the vertical crack. This is illustrated in Figure 6 (b). Furthermore, a higher interfacial mode I energy, has an influence on the Moment-CMOD relationship, cf. Figure 6(a). Comparing cases B and C shows that - for these material properties - the energy consumed at the interface primarily consist of Mode I energy.
-
2
E E
1.5 E c" 1 1 I
5
F
2 0.5 b 0
0.5 1 1.5 CMOD - Vertical crack [mm]
2
0 0
0.5 1 1.5 CMOD - Vertical crack [mm]
2
(4 (b) Figure 6: Graphical representation of five hypothetical cases cf. Table 1 . (a) The bending moment M=PL/4 versus the crack opening of the vertical crack - CMOD, (b) The interface crack length normalised with respect to the concrete height h, versus CMOD. PARAMETRIC STUDY I1 - Failure surface In order to study the degree of mixed mode propagation a second parameter study is carried out. Same reference case as in previous section A l is considered. One group of simulations, denoted D, is performed. This group involves a variation of the slope of failure surfacefl, cf. Figure 2. The parameter values are summarized in Table 2. Name A1
D1 D2
Changing parameter and value Reference 2 . tan( p) 3 . tan(p)
Table 2: Parameter variation of slope of failure surface.fi, tan(a) as defined in Figure 2. For constant cohesion c a change in the slope tan(y) of,fi, will change the position of the corner of the failure criterion. Mixed shear and tension failure takes place in the corner when .fi and ,fr intersects, and is of special interest, since the steel-concrete interface crack propagates in a mixed mode.
198
Rasmus WALTER, Henrik STANG, John Forbes OLESEN and Niels Jargen GIMSING
The stress distribution during crack propagation is shown in Figure 7. Results for the cases A1 and D1 for a vertical crack opening of CMOD=O.Smm are shown. The interface crack has 1. The peak of tensile normal stresses propagated a length of around (x-coordinatelh,) represents the interfacial crack tip. The corner values for cases A1 and DI differ due to a different slope of surfaceJ. As the crack propagates along the interface, it will try to transfer maximum normal- and shear stress across the interfacial crack. Dominated by mode I fracture, the stress state in the fracture process zone will tend to stay in the corner of failure surfaces fl and fi, cf. Figure 2. Considering the cases A1 and D1, the comer of normal and shear failure before crack initiation is given by: A1 (acorner, zc0,)=(2MPa,2MPa), D 1(a,,,,,, rC,,,,,,)=(2MPa, 1MPa). As the corner values are different, a different stress distribution along the steel-concrete interface is observed. For an opening of the vertical crack (CMOD=O.Smm), the distribution of shearnormal stresses at the crack tip and along the fracture process zone is different. The crack tip is characterised by a peak of normal stress.
Case D1
Case A1 4,
I
I
21
0
0.5 1 1.5 x-coordinate/hc [mm/mm]
2
0.5 1 1.5 x-coordinate/hc [mm/mm]
2
Figure 7: Stress distribution along the interface for cases D1 and A1 for a crack opening of CMOD=O.Smm. The two line types represent the normal and shear stresses acting at the interface between steel and concrete: -0. ----t It turns out that the mixed mode state at the crack tip varies during crack propagation. In order to illustrate varying mixed mode state during crack propagation, the mixed mode state is defined by: ,B = arctan(
t)
(4)
where s and w relates to the crack opening of the interface. The relative deformation s is the cracking deformation related to mode 11 fracture and w is the mode I opening. A failure in pure opening mode (mode I) corresponds to s = 0 a p = 0' and pure shear crack propagation correspond to w = 0 3 p= 90'. The angle /lis plotted versus the crack tip position in order to illustrate the changing mixed mode state during crack propagation of the interface, cf. Figure 8. The curves of Figure 8 are given in terms of the mixed mode angle p, as defined by equation (4) versus the crack tip position. The value of p is calculated at the normal stress peak. The Figure illustrates the three cases A l , DI and D2, each possessing different slopes of failure surface f,.All cases considered start out close to mode I fracture. As the crack tip
199
Debonding of FRC composite bridge deck overlay
propagates along the steel-concrete interface, cases D1 and D2 increase in Mode I1 fracture. Case D2 corresponds to a situation where failure surfacef, intersect the g-axis and propagates almost in pure mode 11.
looi
'
I
...............
,
'
DI
D1
.
' A1
I
I
-800
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
crack tip propagationlhi [mmimml
(a)
(b)
Figure 8 (a) Mixed mode angle p as defined in Equation (4)versus interface crack tip position normalised with the concrete height h, for three hypothetical cases: -A1, ----D I , -.-.D2. The mixed mode angle is calculated at the peak of normal stress, (b) Schematic representation of the three failure surfaces considered. CONCLUSION A model to investigate the debonding process of a concrete overlay cast on a steel plate has been developed. Based on discrete crack theory, the model describes the situation where a vertical crack propagates through the concrete overlay and causes debonding between the steel-concrete interface. The interfacial mixed mode fracture has been modelled using a composite interface model taking into account nonlinear softening of the interface. The debonding process in the case of a negative bending moment has been investigated through two parameter studies. Firstly, the effect of a ductile concrete overlay has been investigated and the results show how it influences the global performance. However, a ductile concrete overlay has little effect on the relation between the interfacial crack length and the opening of the vertical crack CMOD. Secondly, mode I energy of the steel-concrete interface has in the case considered, larger effect on global ductility than mode I1 energy. Furthermore, interfacial mode I energy has a significant influence on the Moment-CMOD relationship. A second parameter study has been carried out in order to study the stress distribution along the interface. The stress distribution during crack propagation has been investigated for different shapes of the failure criterion. It can be concluded that the crack initiates in a mixed mode, where the stress distribution along the steel-concrete is dependent on the intersection between the shear and normal stress failure surfaces. Dependent on the failure criterion, the
200
Rasmus WALTER, Henrik STANG, John Forbes OLESEN and Niels Jargen GIMSING
stress state along the interfacial process zone tends to stay in the comer between shear and tension failure. The mixed mode state changes through crack propagation of the interface. From a practical point of view the model carried out attempts to illustrate the role of the different parameters, which might be considered in a design situation. In addition to the significance of high fracture energy of the overlay in the debonding situation considered, this study shows the difference in behaviour for different mode I and I1 energies of the steelconcrete interface.
REFERENCES 1. Walter, R., Stang, H., Gimsing, N.J., Olesen, J.F., High Performance Composite Bridge Decks using SCSFRC. The Fourth International Workshop on High Performance Fiber Reinforced Cement Composites, Ann Arbor, Michigan, USA, June 2003. 2. Granju, J.L., Debonding of Thin Cement-Based Overlays. Journal of Materials in Civil Engineering, 13(2):114-120,2001. 3. Sabathier, V., Granju, J.L., Bissonnette, B., Turatsinxe, A., Repair by Cement-Based Thin Overlays - Interlocking at the Interface and Modelling of Debonding. Industrial Floors’03, Technische Akadamee Esslingen, January 2 1-23,2003, p.62 1-626. 4. Hillerborg, A., ModCer, M., Petersson, P. E., Analysis of Crack Formation and Crack
Growth in Concrete by means of Fracture Mechanics and Finite Elements. Cem. Concr. Res., 6(6):773-782, 1976. 5 . Olesen, J.F., Fictitious Crack Propegation in Fiber-Reinforced Concrete Beams. Journal of Engineering Mechanics, 127(3):272-280, March 2001.
6. DIANA finite element analysis, user’s manual, release 8.1, TNO Building and Construction Research, P.O. Box 49,2600 AA Delft, The Netherlands, January 2003. 7. Lourenqo, P.B., Rots, J.G., Multisurface Interface Model for Analysis of Masonry Structures, Journal Of Engineering Mechanics, 127(7):660-668, 1997. 8. Van der Pluijm, R., Material Properties and its components under Tension and Shear. Proc., 6Ih Can. Masonry Symp., Saskatoon Canada, 1992.
Proc. Int. Symp. ),BrittleMatrix Composites 7” A.M. Brandt, V.C. Li and I. H.Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
PLENARY INVITED PAPER
MULTI-EXPONENTIAL MODELS AS DESCRIPTIVE TOOLS FOR PLAIN CONCRETE AND FRC
Ming Kien LEE and Ben BARR School of Engineering Cardiff University PO Box 925, Cardiff, UK, e-mail: LeeMK@,cf.ac.uk, BarrBIl O.cf.ac.uk ABSTRACT
The paper reports on descriptive tools developed for modelling the response of plain concrete and fibre reinforced concrete (FRC) under various types of loadings. Double and fourexponential models have been developed for use with plain concrete and FRC respectively. The first part of the paper deals with the double-exponential (double-e) model. Three shape parameters are required to fully define the strain-softening response typical of that for plain concrete. Each parameter has a different effect on the ultimate curve shape. An objective method of evaluating the shape parameters, which adds to the attractiveness of the model, is shown. The second part gives details of the four-exponential (four-e) model, which requires six shape parameters. This model was developed specifically to describe the more complex load-deformation response displayed by FRC. Similarly, an objective procedure has been developed for deriving the necessary shape parameters. Comparisons between experimental results and the descriptive models demonstrate the wide applicability of the multi-exponential models. Keywords Modelling, plain concrete, FRC, objective method INTRODUCTION
Loadstress-deformation curves’ obtained from closed-loop tests, be it compression, tensile or flexural (deformation in these cases may mean strain, crack width or deflection) tests, on plain concrete normally exhibit a strain-softening behaviour. On the other hand, the response obtained from fibre reinforced concrete (FRC) specimens is much more complex and diverse. The importance of measuring the response of concrete specimens under loading has grown since the advent of fracture mechanics in the world of concrete. Many attempts have been made to characterise the loadstress-deformation curves using various mathematical functions. Models for describing the complete stress-strain curves for
’ For compression, tensile and flexural tests this may take the form of stress-strain (0-w) and load-deflection
(P-8)curves respectively.
(0-E), stress-crack
width
202
Ming Kien LEE and B. BARR
plain concrete and steel fibre reinforced concrete (SFRC) subjected to compressive loading have been proposed [l-31. Furthermore, as a result of the celebrated work of Hillerborg and co-workers [4], the stress-crack width opening curve of concrete specimens subjected to uniaxial tensile loading have attracted widespread interest. Subsequently, efforts have been expended in characterising the strain-softening curve for specimens under uni-axial tension, in the post-cracking regime. The pre-cracking regime is normally characterised with a simple linear function 14-91. Often, many of these proposed functions are discontinuous i.e. more than one function is required. Furthermore, subjective methodologies have to be applied for the derivation of the model parameters. The objective of the research work reported here was to investigate the possibility of characterising the complete loadstress-deformation curve of plain concrete and FRC using one continuous function. Furthermore, systematic and objective methods of deriving model parameters have been examined to enhance the potential of such a model.
DOUBLE-E MODEL The double-e (short for double-exponential) model has been used to characterise the behaviour of impulse voltages [lo], and has the following general form:
f ( x ) = c, (e-'*' - e-"") where CI,CZ and c3 are independent constants controlling the shape of the f(x) curve. The f(x) curve is a general representation of the possible loadstress-deformation curves which may be measured. In the case of compression, tensile and flexural tests, the f(x) curve may represent G(E), o(u) and P(8) respectively. In this instance, o, E, u, P and 8 mean stress, strain, deformation, load and deflection respectively. The double-e model consists of two exponential functions and a typical shape is as shown in Fig. 1. It is immediately apparent that the double-e model has the ability to model as one continuous function the strain-softening shape typical of that of plain concrete. Furthermore, it has the added significant advantage of being amenable to mathematical procedures such as differentiation and integration. A parametric study has been carried out to study the effects of each model parameter on the ultimate shape of the f(x) curve [ 11,121. The procedure and method of the aforesaid study will not be repeated here in its entirety due to space constraints. Nevertheless, the main findings arising from the study are be reported here. It was found that the parameter cl can be used to take account of the ultimate load capacity of the material, such as tensile strength or compressive strength, for it primarily intluences the peak value of f(x). The parameter c2, on the other hand, significantly influences the tail-end of the f(x) curve whereas c3 influences the initial shape of the f(x) curve. Therefore, a wide range of f(x) curves may be simulated by varying the three model parameters. Additionally, it has been found that by fixing C I and the ratio C~/CZ, it is possible to stretch the f(x) curve in the positive direction of x by varying c2. This finding was significant as it meant that a variety of strain-softening response may be taken into account by simply changing the ratio a (where a = c~/cz).The effect of varying the value of a but maintaining the pre-peak response is shown in Fig. 2. It may be observed that the ratio a can be varied to model approximately brittle to elastic-plastic behaviour. When a approaches unity, the double-e model exhibits a very steep post-peak softening curve. On the
203
Multi-exponentialmodels as descriptive toolsfor plain concrete and FRC
other hand, an elastic-plastic type curve can be obtained by &signing a value of a>>O. Therefore, the ratio a can be said to be a proxy for the level of brittleness.
2
-0.4
J
:
;\
i 4.8 .:
4.8 -
1.2
-~ ~ e - 4 '
1
1
0.8
* a = 10
2 0.0 '4 0.4
0.2
0 0
O.!
0.3
0.2
04
0.5
x
Fig. 2: Plots of various f(x) by varying the model parameters. Proposed objective methodology Following the parametric study, research efforts were directed towards determining a suitable procedure for deriving the model parameters in an objective and simple manner. Such a procedure would be of considerable benefit since it provides a framework for a consistent and systematic means of comparing the performance of different grades of concrete.
Since there are three independent constants, three boundary conditions are required. In the case of testing plain concrete, the most important experimental parameter is the peak loadstress, hence making this parameter an essential boundary condition. Additionally, the value of the deflectiodstrain at which this is achieved is an important parameter as it relates to the initial stiffness of the material. Therefore, the second boundary condition is to define
204
Ming Kien LEE and B. BARR
the gradient to be zero at the deflectionistrain at which the peak loadstress occurs. The first two boundary conditions reflect the response of the material in the pre-cracking regime. The third boundary condition should be indicative of the response of the material in the postcracking regime and thus related to the brittleness of the material. It is well known that a brittle material gives rise to a very steep gradient in the post-cracking region whereas in the other extreme, an elastic-plastic type material would yield a shallow to flat gradient. For a quasi-brittle material such as concrete, the strain-softening behaviour should be captured as accurately as possible for the effective use of fracture mechanics especially in non-linear fracture mechanical analysis. It has been found that it is sufficient to employ a certain point in the post-cracking regime at a pre-determined percentage of the peak loadhtress. The parametric study carried out by the authors found that a value at 20% of the peak loadstress would be adequate for plain concrete specimens. To summarise, the three points required from any experiment to calculate the three parameters for the double-e model are illustrated in Fig. 3.
Xmax
x0.2jmax
X
Fig. 3 : Experimental values necessary to calculate model parameters The model parameters CI,CZ and c3 may be calculated using the following equations: for
[lo4 -I 17
for
for for ii.OOO1
Multi-exponential models as descriptive tools for plain concrete and FRC
where for Equation (2a), the values for xi are tabulated in Table 1. Table 1: Values of Y; for use with Eauation (2al i
0
1
2
3
4
5
xi
285
-10686
183868
-1695374
8564972
-22277264
6 23282310
Example of model application To assess the performance of the double-e model along with the proposed methodology for deriving the parameters, experimental results obtained from three-point bending tests [ 131 have been used as a basis for demonstration. The concrete in this example has a nominal cube compressive strength of 40MPa and was tested in a three-point bending configuration. The actual mix details and test details are not significant, as the aim is to assess only the performance of the double-e model with regards to actual experimental data. Additionally, the effectiveness of the objective methodology in calculating the model parameters may be appraised. Table 2 lists the necessary experimental values for deriving the model parameters and the calculated values of a,CI and c2 using Equations (2a) and (2b).
Table 2: List of experimental data and the associated model parameters.
e Expnmmlal
--Double+
0
model
0.2 0.4 0.0 0.8 1 Avcrsge mid-span dellredon, S(mm)
1.2
Fig. 4: Comparison between the experimental and double-e model P-6 curves, Fig. 4 shows the comparison between the experimental and theoretical curves. It may be observed that there is close agreement between the experimental and the theoretical curves
206
Mirig K i m LEE and B. BARR
hence confirming the applicability of the proposed model as a descriptive tool for strainsoftening responses.
FOUR-E MODEL The limitation of three model parameters has the drawback of not being able to model more complex curves such as those displayed by FRC. For a complex material such as FRC, additional parameters are required to reflect the contribution of the fibres. Therefore, to include additronal parameters to mirror the complexity of fibrous concrete, the authors developed the four-e (short for four-exponential) model [l 1, 141. The four-e model is the result of the superposition of two double-e models and may be expressed as follows:
where C I ,c2, q,c4, c5 and c6 are the model shape parameters. Also, F , ( x ) = cI(e-""-e-c'r) and F2(x) = ~4(e-'~'--e-cwr). Assumption for the four-e model Similar to the double-e model, work was carried out to develop an objective methodology for calculating the six parameters necessary for the four-e model. The task of determining six shape parameters in an objective manner may be tackled by first considering two curves which may be' generally observed for FRC materials: Response A: The initial response is approximately linear up to a peak, fmm.Subsequently, in the post-cracking regime, the f(x) curve achieves a plateau. This is shown in Fig. 5a Response B: The initial response is similar as that described above i.e. an approximately linear response up to a peak, fmax.Thereafter, a second peak is achieved in the postcracking regime. This second peak may or may not be greater than the first peak. This is shown in Fig. 5b.
r
X
X
(a) Response A
(b) Response B
Fig. 5: Schematic diagrams showing the anticipated trends for FRC curves
207
Multi-exponential models as descriptive tools for plain concrete and FRC
The first three parameters (CI,CZ and c3) will be used to reflect the response in the pre-cracking regime. On the other hand, the latter three parameters (c4,c~and cg) will be used to take into account the post-cracking regime. Response A To calculate the model parameters for curves displaying Response-type A, first consider the post-cracking regime i.e. Fz(x). In this case, the gradient is assumed to be approximately zero. This condition may be achieved by taking the ratio ap>O (where a2 = Cg/c5). By fixing the ratio of a2,only two parameters would be required to completely define Fz(x). This may be achieved by specifying two points, say at (Xa, fa) and (xb, fb). Thus:
Subsequently, the pre-cracking regime should be characterised via Fl(x). The value of a1 can be calculated by using the ratio (xmax/xo.gfmax)prepca~ i.e. the ratio of xmaxto the value of x at 90% off,, in the pre-peak region. From simulations, it has been found that the ratio a1 may be calculated using the following equation:
I
1.ooo1
Where the values of 6, and & are given in Table 3. Table 3: Values of 5, and (;k for use with Equation (4b). j/k 0 1 2 5/ -819 1481 -920 l . CEB-FIP Model Code 1990 MC 90 In the CEB-FIP Model Code 1990 MC 90 1993 [IS] the design punching shear strength of slabs is determined by
where fck = the characteristic concrete cylinder strength in MPa, U I = 4 r + 4 n: d for square columns, Fig. 1, U I = n: (D + 4d) for circular columns, Fig.1, 1+(200/d)~.~ = a size-effect coefficient. Eq. (3) is subject to restrictions 1 + (200/d)0.5 I 2 and p% I 2 . With regard to the coefficient 0.12 in Eq. (3), which includes a partial safety factor equal to 1.5, Walraven [I61 carried out an evaluation over 1 12 test results and concluded that this value of coefficient is correct. Eurocode EC2 In the European prestandard for the design of concrete structures EC2-1991 [17] the punching shear strength of slabs is given as V,,
= 0.0525
fc2'3 (1,6-d) (1.2 + 0.40 p%) ~2 d
where u2 = 4r + 3xd for square columns, Fig. 1 , u2 = n: (D + 3d) for circular columns, Fig. 1, (1.6-d) = a size-effect coefficient with d in m. Eq. (4) is subject to restrictions 1.6 - d [m] > 1 .O, p 5 0.015 and fck 5 50 MPa .
(4)
Design equations to predict the ultimate punching shear strength of slab-colunzn connections
2 15
Authors' Model The authors have developed theoretical and design expressions to determine the punching shear strength of reinforced concrete slabs with and without fibre reinforcement [ 10-121. Using a control perimeter at 1.5 d away of the load area, as in BS 8 1 10, taking the depth of the compression zone to be the harmonic mean of the compression depths for shear and flexural sections and considering the limiting shear stress equal to 0.27 fc;I3, the following design equation can be derived for plain concrete slabs V,, = 0.234 (100/d)'/6 f,,
213
ah l + a h bP
where pf, 0.145 f,, ' h = 1.60- 0.75~~ for 0.20 < a I 0.50, for 0.50 < a I 1.OO , h = 1.35 - 0.25a h = 1.20 - 0.10a for 1.00 < a I 2 . 5 0 , for 2.50 < a I 0.50, h = 1.30 - 0.14a f,. = the yield stress of steel reinforcement, (100/d)'/6 = a size effect coefficient. a=
The coefficient h in Eq. (5) indicates the effectiveness of the steel stress, i.e., the stress at which the tension steel works at the ultimate stage of punching. Details of calculation of h can be found in [12]. It is also worth reminding that Eq. ( 5 ) indicates that the punching strength of a plain concrete slab is not only proportional to fc:3 but it is also affected by the overall flexural behaviour of the slab, through the coefficient a [lo]. Furthermore, the design expression for punching strength of fibre reinforced concrete slabs is given by ah+P V,, = 0.234(100/d)'/6 fcU2I31+ah+1.25P bPd
d where
'=
(J
cu
0.145fC, ' oCu= the ultimate tensile strength of fibre concrete. It should be noted that both design equations (5) and (6) are by no means based on factors derived empirically from test data. They are, therefore, not subject to any limitation as far as the material properties and steel ratio are concerned.
COMPARISON OF DESIGN METHODS WITH FIBRE CONCRETE SLAB TESTS All four code expressions and authors' design equation have been applied to 62 tests to predict the punching strength of fibre reinforced normal weight and lightweight concrete slabs
2 16
D. THEDOROKOPOULOS and R.N. SWAMY
reported in the technical literature and failing in punching shear [l-91. In addition, the design predictions are compared with 20 test results of the corresponding control slab-column connections (plain concrete slabs) [ 1-91. The comparisons between design rules and tests are based, for the sake of comparison, on the following principles: the code equations are solved with mean values of the concrete strength and not with characteristics values, fc’or fck = 0.80 fCu( if only the cube strength is given for the test slabs), for lightweight concrete slabs a reduction factor 0.85 is used, the upper limits of the flexural reinforcement ratio and the concrete strength are not taken into account in Code expressions. It is desirable to start with the plain concrete slabs. The results are shown in Fig. 2. It can be seen that the mean value for the ratio of predicted to test ultimate load is 0.876, 1.007, 1.112, 0.894 and 0.957 for ACI 318-99, BS 8110, CEB-FIP, EC2 Codes and Eq. (5) respectively, with the greater scattering of test results being for the ACI Code. This is due to the fact that the ACI expression does not consider the size effect or the influence of p. It is also observed that BS 81 10 and Eq. (5) give comparable punching strength predictions, with those of Eq. (5) being on the safe side, and having a smaller standard deviation. For the 62 fibre reinforced concrete slabs, the results provided by the Codes and the proposed model (Eq.(6)) are shown in Fig. 3. As expected, the prediction of the ultimate loads according to the Codes greatly underestimates the true failure loads since the contribution of the fibre reinforcement is not taken into account. A comparison between the average of Vca1JVtest ratios in Fig. 2 and Fig. 3 reveals that for each Code a coefficient can be established relating its predictions for plain and fibre concrete slabs as shown in Table 1. It can be concluded that the ultimate punching strength of a fibre concrete slab can be calculated by using the provisions of each Code for plain concrete slabs multiplied by a factor of about 1.20. Furthermore, from Figs. 2 and 3, it is observed that the mean ratio and standard deviation for the sixty two fibre concrete slabs analysed by authors’ design Eq.(6), are 0.943 and 0.089 respectively and these values are of a comparable magnitude to those of the twenty plain concrete control slabs. This is due to the fact that Eq. (6) accounts for the effect of fibre reinforcement on punching shear. Table.1 Relation between Code predictions for Plain and FRC slabs ACI
BS 81 10
CEB-FIP
EC2
0.876/0.697 = 1.26
1.007/0.833 = 1.21
1.1 12/0.928 = 1.20
0.894/0730 = 1.22
The effectiveness of the design Eq.(6) in predicting the ultimate punching strength can also be seen in Figs. 4 and 5 in which the ratios VcalJVtestare presented as a function of concrete strength fCuand reinforcement ratio p respectively. Fig.4 confirms that concrete strength has an important role in controlling the ultimate strength. In Fig.5, it is observed that the authors’ predictions follow the trend of the test results data with respect to any ratio of the reinforcement p. In addition, one can see that the ACI expression underestimates the test results especially for higher values of p, as expected, whereas the higher underestimation of test results for the BS 81 10 and CEB-FIP expressions is for low values of p. The latter is due to the fact that punching strength is not a simple function of a power of f,, and p but a combined effect of the resistances offered by shear and flexural sections [ 10, 121.
2 17
Design equations to predict the ultimate punching shear strength of slab-coluinn connections
1000
//
z Y
Ave=0.876 S.D=0.265 A.C.1
1000
z Y
100
-m
100
-m
u
0
Y
3 10
100
10
10
1000
Vtest,
10
KN
1000 KN
1000
1000
Ave=l, CEB - FIP 11
2
EC2
1
z
Ave=O,894 S.D=O.178
Y
z
S.D=0.142
Y
-a
100 Vtest,
-m
100
100
0
0
Y
Y
10 100
10
10 10
100
Vtest,
1000
Vtest,
1000 KN
KN
/
Design Eq. ( 5 ) Ave=0,957 S.D=0.096
z Y
10
1000
100 Vtest,
KN
20 plain concrete slabs [I- 91
Fig.2. Comparison between predicted and experimental results: plain concrete slabs.
2 18
D. THEDOROKOPOULOS and R.N. SWAMY
1000
1000
B.S.
A.C.1
z
Ave=0.697 S.D=O.159
Y
-3
z Y
-u3
.,.".
>
aiio
"
100
~
>
loo./ 10
10
1000
1000
,
CEB - FIP Ave=Q.928
Ave=O. 730
z Y
-6m
m
100 -
Y
10
10
100
Vtest,
10
1000
KN
100
Vtest,
1000
KN
1000 -
Design Eq. ( 6 ) 2
Y
-m
100
~
9
10
10
100
Vtest,
1000
KN
-
62 Fibre concrete slabs [I 91
Fig. 3. Comparison between predicted and experimental results: fibre concrete slabs.
Design equations to predict the ultimate punching shear strength of slab-column connections
1.40
2 19
1.40
1
A.C.1
1,20 1.oo
B.S. 8110
1,20
.. . ..' ....;.-:. . . :.'f :: :
1.oo
5
0,80-
0.60 -
.
*
:,?
* .
0.40
-8 0.60 >
-
-
0.40 .
0,20 -
0.20
0,oo
0,oo i
1
1,40
.. .
1,20 . 1.oo
5- 030 3 0.60
1,40 .
W B - FIP
.:...._. _. ;;3:- . .
*
: .*.:?
EC2
1.20
5-
~
. .-f. *'@+ :
0.80
8 >
0.40
' ,'a..
1,oo
.
0.60 -
*
. :
2
0,40 .
020 -
0.20
Design Eq. (6)
1,20
1;: 0.00
1 0
,
20
,
40
fcu,
,
,
60
80
100
Mpa
Fig. 4. Variation of Vcalc I Vtest ratio versus concrete strength for fibre concrete slabs.
220
D. THEDOROKOPOULOSand R.N. SWAMY
-
1,40 1,20
5> 2
1,oo
-
0,80
1.40
.'
A.C.1
0.40
-5z 0,150
*I;. : iji
0.80
$2 i *.
0.20
0.00
7
I
1,40 1,20 1,oo
'
0.80 -
0,60
-
.) f.*
. .:
I
1.40 1,20
FEB-FIP
**
5-
*
5 >
+
1
EC2
1.00 .
--
0.60 -
.*
'i !; . i f . +
0.80
8
0,40
0,40 -
0.20
0,20
0.00
0,oo
j
0,40
0.00
> z
:
>
0,20
5-
* .
1.00
**
0.60
B.S. 8110
1.20
t
7
1.40 1.20
,
1
Design Eq. ( 6 )
A
I .oo
*1 ?i
I:
1. +
?
-
I
,
,
,
2
3
4
0,oo 0
1
5
REINFORCEMENT %
Fig. 5 . Variation of Vcalc / Vtest ratio versus steel reinforcement percentage for fibre concrete slabs
Design equations to predict the ultimate punching shear strength of slab-column connections
22 1
The data presented in Figs. 4 and 5 emphasize that punching shear strength is dependent on both the flexural and shear behaviour of the slab. As pointed out earlier, the ACI expression does not consider size effect and ignores the effect of p. The BS and CEB-FIP Codes, on the other hand, predict that the punching shear strength of a plain concrete slab is proportional to (p%)0.333.This implies that for a flat slab with a reinforcement ratio equal to 2 p%, the percentage increase in punching strength is 26%[(2~/p)O.~~~11, independently of the value of concrete strength and the initial value of p taken. The authors’ design theory Eq. (9,on the other hand, shows that the percentage increase in punching shear strength when the value of p is doubled, depends on the initial value of p. Thus, the increase will be greater for smaller values of p as would be expected. For example, according to Eq. ( 5 ) , slab with a = 1.OO (a is proportional to p) has a punching strength higher by 37.6% than that of a slab with a = 0.50, whereas the strength increase of a slab with a = 2.00, in comparison to one with a = 1.00 is 27.5%. These outcomes result from the structure of the authors’ model that punching shear strength is a h c t i o n of both flexural and shear conditions of the slab. Similar comparisons can be made for slabs with different values of concrete strength and constant value of p. These considerations explain why Code provisions impose restrictions on both f,, and p whereas the authors’ theory has been successhlly used to predict the punching strength of slabs made with high concrete strength (100 MPa) [lo].
CONCLUDING REMARKS Flat slabs offer a popular and economic form of construction with many practical advantages. However, they can sometimes be subject to a major structural weakness of sudden, brittle type of failure. Steel fibre concrete is an exciting construction material that possesses unique properties of high energy absorption and ductility. A combination of the two can therefore lead to a new structural system having a high ultimate strength and characterized by a ductile mode of failure. Many tests on slab-column connections made with steel fibre concrete show that this new structural system can offer distinct advantages of structural integrity and structural stability, particularly when dynamic forces are involved. The use of steel fibre concrete in practice is, however, very much hampered by the absence of a rational theoretical model and design method to predict the ultimate strength of flat slabs made with steel fibre concrete. Current Code provisions such as those of the ACI, BS, CEB-FIP and EC2 do not apply to fibre concrete slabs. The aim of this paper is to present design equations to predict the ultimate punching shear strength of slab-column connections. The design approach is based on the physical behaviour of slab-column connections under load and is, therefore, applicable to both normal weight and lightweight concrete as well as to slabs without or with steel fibres. The proposed design equations are applied to 20 plain and 62 fibre reinforced slab tests reported in the literature. The slabs analysed cover many variables that influence the punching shear behaviour such as type of concrete, the concrete strength, the tension steel ratio, the size of slab and loaded area as well as the type, aspect ratio and volume of fibre reinforcement. It is shown that the authors’ design equation for the ultimate load of plain concrete slabs can predict the test results in a better way than the Codes with a smaller standard deviation. When applied to fibre concrete slabs, the authors’ design equation again predicts the test results extremely well. What is impressive is that the authors’ design equations for the plain and fibre concrete slabs can predict both sets of test results equally well-with a mean theory / test ratio and standard deviation-0.957 and 0.096 for the former and 0.943 and 0.089 for the latter. There is thus convincing proof that the theory and design equations are reliable, based on sound engineering principles and reflect the true structural behaviour of the slab-column connections.
222
D.THEDOROKOPOULOSand R.N. SWAMY
REFERENCES 1. Ito, K., Hirasawa, I. and Aichi, I., Punching shear strength of steel fibre reinforced concrete slab. Transactions of the Japan Concrete Institute, 3, 1981, pp 267-272 (in English). 2. Swamy, R.N. and Ah, S.A.R., Punching shear behavior on reinforced slab-column connections made with steel fibre concrete. ACI Journal, 79-5, 1982, pp.392-406. 3. Walraven, J.C., Pat, M.G.M. and Markov, I., The punching shear resistance of fibre reinforced concrete slabs. Developments in Fibre Reinforced Cement and Concrete, RILEM Symposium, F.R.C. 86, 3rdInt. Symposium 13-17 July 1986, Sheffield.
4. Narayanan, R. and Darwish, I.Y.S., Punching shear tests on steel-fibre-reinforced microconcrete slabs. Magazine of Concrete Research, 39- 138, 1987. 5. Theodorakopoulos, D.D. and Swamy, R.N., Contribution of steel fibres to the strength characteristics of lightweight concrete slab-column connections failing in punching shear. ACI Journal, 90-4, 1993, pp. 342-355. 6. Harajli, M.H., Maalouf, D. and Khatib, H., Effect of fibres on the punching shear strength of slab-column connections. Cement and Concrete Composites, 17, 1995, pp. 161-170. 7. McHarg, P.J., Cook, W.D., Mitchell, D. and Yoon, Y-S., Benefits of concentrated slab reinforcement and steel fibres on performance of slab-column connections. ACI Structural Journal, 97-2,2000, pp. 225-234.
8. Alexander, S.D.B. and Simmonds, S.H., Punching shear tests of concrete slab-column joints containing fibre reinforcement. ACI Structural Journal, 89-4, 1992, pp. 425-432. 9. Shaaban, A.M. and Gesund, H., Punching shear strength of steel fibre reinforced concrete flat plates. ACI Structural Journal, 91-3, 1994, pp. 406-414. 10. Theodorakopoulos, D.D. and Swamy, R.N., Ultimate punching shear strength analysis of slab-column connections. Cement and Concrete Composites, Special Theme Issue, 24-6, 2002, pp.509-521. 1 1. Theodorakopoulos, D.D. and Swamy, R.N., Ultimate punching shear strength analysis of slab-column connections with steel fibres. ACI SP 182-1 1, 1999. 12. Theodorakopoulos, D.D. and Swamy, R.N., A design method for punching shear strength of steel fibre reinforced concrete slabs. ACI SP: Fiber Reinforced Concrete: Innovations for Values, in press. 13. ACI 3 18-99, Building code requirements for reinforced concrete. American Concrete Institute, Detroit, 1999, 355 p. 14. BS 81 10-85. The Structural Use of Concrete. British Standard Institution (1985). 15. CEB-FIB MC 90: CEB-FIP Model Code 1990, London : Thomas Telford 1993. 16. Walraven, L., "Design of Structures for Punching: Present Status of revision of EC-2. International Workshop on Punching Shear Capacity of RC Slabs-Proceedings, Stockholm 2000, pp. 2 1 1-224. 17. EC2-1991. Eurocode 2 : Design of Concrete Structures - Part 1: General Rules and Rules for Buildings. European Prestandards ENV 1992-1-1 : 1991, Comlte Europeen de Normalisation, Brussels, 253 p.
Proc. Int. Syrnp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C.Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTURL?K RSI and Woodhead Publ., Warsaw 2003
Mechanical Properties of Concrete Reinforced with AR-Glass Fibers Tejal DESAI*, Rimpal SHAH*, A h a PELED', and Barzin MOBASHER*
* Dept. of Civil and Env. Eng., Arizona State University, Tempe, AZ, USA +
Structural Engineering Department, Ben Gurion University, Beer Sheva, Israel
ABSTRACT Mechanical properties of concrete mixtures with AR glass fibers are studied. Two types of concrete mixtures representing a lean mixture and an HPC (High Performance Concrete) mixture are used. Two types of AR Glass fibers High dispersion (HD) and High Performance (HP) with different sizing formulations to help with distribution, bonding and durability were considered. High dispersion (HD) AR Glass fibers of several different lengths were used to evaluate the effect of fibers which disperse thoroughly throughout the mixture. These were compared with High Performance (HP) type AR Glass fibers which maintain the bundle characteristics throughout the mixing and casting and are designed to help with long temi strength and ductility. A formulation based on the R-Curves is presented to measure the contribution of the fibers to the overall toughening mechanism.
Keywords Fiber reinforced concrete, cement composites, glass fibers, alkali resistant fibers, toughness, strength, toughening, and mechanical testing. INTRODUCTION Reinforcing ordinary concrete materials with glass fibers has been attempted for more than 20 years [ 1][2][3]. Use of Alkali Resistant (AR) glass fibers in concrete presents an area of opportunity to utilize the strength and stiffness of fibers in reinforcing the brittle matrix. Concrete materials produced with short randomly distributed AR Glass fibers would be superior to other FRC (Fiber Reinforced Concrete) materials for several reasons. In comparison to steel fibers, the small diameter of the individual glass fibers ensures a better and more uniform dispersion. In addition, the high surface area and relatively small size of glass fiber bundles offers significant distribution capability and crack bridging potential as compared to steel fibers. The glass fibers are randomly distributed offering efficiency in load transfer. Furthermore, the bond strength of the glass fiber is far superior to the polypropylene fibers, thus increasing the efficiency of fiber length so that there is limited debonding and l i i x r pullout. Finally, due to the highly compliant nature of the glass fiber bundles which bridge thc matrix cracks at a random orientation, they are able to orient so as to carry thc Ioatl across the crack faces. In the present work, two types of AR Glass fibers are considered as concrete reinforcement, High dispersion (HD) and High Performance (HP) to provide Iioth
224
Tejal DESAI, Rinpal SHAH, Alva PELED and Barzin MOBASHER
strengthening and toughening mechanisms. Various fiber lengths and contents are studied for both fiber types. Two types of concrete mixtures were prepared with the fibers representing a lean mixture and an HPC (High Performance Concrete) mixture. Control specimens without fibers were prepared in both mixtures for comparison. Theoretical modeling of the experimental results is conducted by means of proper determination of response in the context of both strengthening and toughening. The R-curve approach is used for this purpose. The bond parameters of the glass fibers with the matrix affect these models in the context of the closing pressure formulations. Procedures are proposed to back-calculate the materials properties from experimental data.
EXPERIMENTAL PROCEDURE
Specimen Preparation Two different concrete mixtures were selected to cover the wide range of matrix materials and their weight proportions presented in Table 1. The first mixture had characteristics of a high performance concrete mixture with a w/c ratio of 0.4, while the second mixture with a w/c ratio of 0.55, had a characteristic strength of 40 MPa and a slump of 50-55mm. Class F fly ash equivalent to 10% cement replacement was also used. Two types of AR glass fibers were obtained from VETROTEX, Cem-FIL SAINTGOBAIN, HD and HP. High dispersion (HD) AR Glass fibers were used in chopped strand form to evaluate the effect of fibers which disperse thoroughly throughout the mixture. These fibers are formulated for mixing with concrete, mortar, and other cement-based mixes where a uniform dispersion is of primary importance. The effect of sizing is to provide full dispersion characteristics in order to control and prevent early-age cracking in concrete. The dosage of HD glass fiber was limited to 0.6 and 5 Kg/m3 and aimed at early age strength and plastic shrinkage crack control. HP AR glass fibers maintain the bundle characteristics throughout the mixing and casting and were designed for abrasion resistance and integrity during mixing with both concrete and mortar. The dosage of HP glass fiber in this category was in the range of 5-20 Kg/m’ and aimed at long-term strength and ductility. Several different lengths of fibers, 6, 12, 24 and 40 mm were used. After 24 hours, specimens were demolded and placed in a water tank saturated with calcium hydroxide at a temperature of 23°C (700 F) for 3 , 7 and 28 days. Compression and Flexural Tests Compression tests were conducted using a 450 KN closed-loop controlled testing machine. A special ring type fixture was developed to attach two LVDTs (Linear Variable Differential Transducer) to measure the axial strain in the specimen. Three replicate compression cylinders 76.2 mm in diameter by 152 mni long were used for each mixture. A gage length of 64 mm was used for the axial strain using a fixture that permitted the deformations to be measured as the specimen underwent the post peak response. A chain type fixture was placed around the specimen, and an extensometer was used to measure the transverse strain. The axial mode of control operates the test during the prepeakThe post-peak response was obtained by using circumferential microcracking phase. displacement as the controlled variable. The circumferential deformation always increases throughout the test; however, its increase may not be sensitive to the loading during the pre-
225
Mechanical properties of concrete reinforced with AR-glass fibers
peak regime. Obtaining the post peak response clearly demonstrates the behavior of the specimen in terms of its ductility and energy absorption capacity especially when low volume fraction of fibers is used. Dry weight per m3 Cementitious materials (Cement + flyash)
Type #1, Kg
Type #2, Kg
876
341
20-10 mm Aggregates
460
600
10-5 mm Aggregates
300
388
Fine Aggregates 578 75 1 WaterKement Ratio 0.4 0.55 Table 1. Mix design for the two concrete blends used. Flexural beam specimens 368 x 101 x 101 mm in size with an initial notch were tested in a 3-point bending configuration. A test span of 304 mm, and a notch depth of 12.7 mm was used. A three-point bend loading fixture was used to eliminate extraneous support settlements. The crack mouth opening displacement (CMOD) was measured across the face of notch using extensometer. The deflection of the beam was also measured using a springloaded linear variable differential transducer (LVDT) with a 2.54 mm (0.1 in) range. In consideration to the reduced depth of the beam due to the notch, the maximum load was normalized with respect to the modified section modulus of the specimen and referred to as the nominal flexural stress. The area under the load deflection curve was calculated by numerical integration of the load-deflection response. Fracture energy Gf was defined as the area under entire load-deflection curve normalized with respect to crack ligament area. EXPERIMENTAL RESULTS Compression Test Results
A summary of the experimental test data is shown in Table 1. Note that the MIX. ID in the table presents the type of fiber (HP or HD), fiber length (12, 40 or 24 mm) and fiber content (5, 10 or 0.6 kg/m3). For example, the sample HP12-5 is a specimen produced by HP fibers with a length of 12 mm and fiber content of 5 kg/m3. Figure 1 presents the Stress vs. Circumferential Strain for specimens containing 20 Kg/m3 and 10 Kg/m3 HP12mm AR glass fiber reinforced sample for various ages of 3, 7 and 28 days. It is observed that the use of circumferential strain is a successful means of obtaining the post peak response. Several distinct regions are observed in the response. The first region is the initial linear ascending stress strain response. The second region is due to initiation of microcracks that results in a reduction in the stiffness and thus the non-linear behavior of the specimen. This zone terminates at the ultimate strength. In the strain softening region, it is observed that there is significant ductility in the circumferential strain pointing out to the effect of dilatation. The effect of duration of curing is clearly shown in this figure by a significant increase in the strength and toughness of the composite with aging, in both fiber content systems. This is due to the ability of the fibers to bridge the microcrakcs in the pre-peak region of the response. When comparing between the two fiber contents (Figs. l a and Ib) it is observed that the contribution of the fibers in the post peak region of the high volume fraction (Fig Ib) is
226
Tejal DESAI, Rimpal SHAH, Alva PELED and Barzin MOBASHER
not as much as the case with the lower volume fraction shown in Figure l.a., i.e., a better toughening of the lower fiber content system (Fig. la) is observed, this is mainly after 28 day of aging. This is due to the higher strength, a higher magnitude of energy is released, resulting is strengthening but added brittleness since the fibers are unable to absorb the energy released as the specimen enters the post peak response. Figure 2.a shows the effect of length of fiber on the compressive stress strain response at 7 day curing. A comparison is made between HP12, and HP40. It is seen that the concrete with HP12 exhibits significant higher compressive strength and toughness than the concrete with HP40. Comparatively, note that HP12 fibers result in a significantly higher strength and ductility as compared to the control samples with an increase in the compressive strength in the range of 35% as shown in Table 2. The ductility of HP12 is as much as 140% higher than the HP40 and the control samples. This may be due to a better dispersion of the shorter fiber composite, HP12 as compared to poorer dispersion of the longer fiber, HP 40. The closer fiber to fiber spacing for the size of specimen considered with the shorter fibers. Also, differences in fiber failure can occur due to the different in lengths. The shorter fiber may mainly pulled out during testing as the longer fiber may fractured.
“1
Vf
=
1
IOKgim’
L
30 -
=
--
+
HPI210-7 HP1210-3
w/c=o4
to
01
0
’
I
0.002
‘
I
0.004
’
I
0.006
’
( ‘ 1
0.008
Circumferential Strain, mm/mm
0.01
0
0.002
0.004
0.006
0.008
0.01
Circumferential Strain. inrnimm
Figure 1 effect of age on the compressive stress strain response of glass fiber reinforced concrete containing a) 10 Kdm3 b) 20 Kg/m3. Figure 2.b shows the effect of fiber volume fraction on the strength and ductility. Note that as the volume fraction is increased, the strength is increased, however, the ability of the fibers to maintain the cracked specimen together beyond the peak load dirninishcs as the strength of the composite is increased.
227
Mechanical properties of concrete reitforced with AR-Glassfibers
Table 2 Compression Test results 40
30
^^
p\
w/c = 0.55
,
Vr=5Kg/m3
d 20 2
-
5
10
W/C = 0.4
IiP1210-28 HP1220-28
6,:dOO
0.002
0.004
0.006
0,008
Circumferential Strain. m m h m
0.010
~
0
0.002
0.004
0.006
0.008
Circumferential Strain, m n h m
0.01
Figure 2 a) Effect of fiber length on the compressive stress strain response. b) Effect of fiber volume fraction on the strength and ductility. Flexural Test Results A summary of the results of the flexural tests are shown in Table 3. Figure 3 shows the flexural response of the concrete with various lengths of fibers at the same volume fraction. It is shown that the flexural response is significantly increased with the addition of the fibers, however, the magnitude of strength is only slightly improved with increasing the length of fibers. All the samples containing 6 , 12, and 24 mm fiber length behave in a
228
Tejal DESAI, Rimpal SHAH, Alva PELED and Barzin MOBASHER
relatively similar manner. Figure 4 compares the flexural load carrying capacity of concrete with different volume fraction HP glass fibers. As expected, it is shown that concrete with 20 Kg/m3 AR Glass fibers exhibit a higher flexural strength and also ductility after 28 days as compared to the other mixes. The flexural response as a function of age for two sets of fiber composites at different lengths and volume fractions are compared in Figure 5 , by using the entire flexural load canying capacity in terms of load vs. crack mouth opening displacement for 3 , 7 , and 28 days of curing. A comparison of responses as a function of age for 0.6 Kg/m’ of High dispersion fibers (HD24) and 5 Kg/m3 of High Performance (HP40) is presented. It is evident from the graph that both concretes with HD24 and HP40 AR Glass fibers exhibits better flexural strength after 28 days as compared to the other ages. There is only a small marginal difference between the HD12 and HP40 mixtures despite the large difference in the volume fractions. This indicates a benefit in flexural behavior for the shorter fiber, similar to the trend observed in Fig. 2 in compression behavior, while having improved dispersion. The better dispersion of HD type fibers would make it easier for a uniform distribution of the short fibers. The two mixtures are almost equivalent as far as 3 to 28 days strength are concerned. This points out that there might be an optimum level of fiber reinforcement which is a function of volume fraction and also the length of the fibers. Such behavior should further be studied.
A direct comparison of dispersion shown by HD type and maintaining the bundle characteristics are shown in figure 6 where the HP and HD fibers are directly compared at the 5 Kg/m’ level with a control specimen. Note that the HP fibers result in a significantly higher ductility. This is attributed to the bundle effect and fiber pullout, resulting in energy absorption mechanisms. In comparison the HD fibers serve to provide strengthening function due to the good dispersion and bond characteristics.
Age = 28 Days
10
-
. L LHP24
HP12 HP6
+-
8
2--J Control
E
3-
s
AR Glass fibers
6 4
2 n v
-
0
0.2
0.4
0.6
CMOD, mm
Figure 3 . Effect of fiber length at the same volume fraction on the flexural response.
0
0.2
0.4
CMOD, mm
Figure 4. Effect of volume fraction on the flexural response.
0.6
229
Mechanical properties of concrete reitlforced with AR-glass fibers
8000
6000
1 AY6Kg t LW 1 8000
28 days 7 days 3 days
w/c
6000
= 0.55
vf = 5 Kdm3
WIC = u.33
__ 28 days
-
7 days
2 dnvc
z
$4000 e)
$4000
3
nnn
2000I
I
0.0
0.2
0.4
0.6
CMOD,mm Figure 5.a Effect of age on the flexural load-CMOD response.(fiber length 24 mm)
0.0
I
0.4 CMOD,mm
0.2
I 0.6
Figure 5.b Effect of age on the flexural loadCMOD response.(fiber length 40 mm)
Table 3 Summary of the Flexural Test Results.
230
Tejal DESAI, Rirnpal SHAH, Aha PELED and Barzin MOBASHER
.- -
a
Control
HD12 Vf=ZOKg/m3
W/C=04 Age = 28 Days
4
-,
2I " 0 - ' 0 0.1 02
'
'
'
03
I " '
0.4
0.5
0.6
CMOD, mm
Figure 6 Comparison of flexural response of HP and HD fibers.
Figure 7. schematics of crack growth in a fiber reinforced composite
ANALYTICAL SIMULATION OF TOUGHENING A simple model is proposed to address the toughening due to the crack bridging of fibers. The bridging force, expressed as a stress intensity factor, works to reduce the overall applied stress intensity factor. These stress intensity factors are directly obtained from the stresses that are required to pull the fiber out of the matrix, and expressed as:
where P(u) represents the force carried by a bridging fiber as a function of crack opening. The fiber is located at distance "x" from the tip of a crack length "a". Parameter g( l,x/a) represents the green's function representing the stress intensity due to a unit load. The process of toughening can be modeled by means of R-curves and is shown in Figure 7. R represents the increased resistance of the material from the base level R , due to the growth of the crack and increases with incremental crack growth "Aa" due to the presence of bridging. It is observed that as we load the material containing a small flaw, it will begin to grow (under an increasing applied stress intensity factor) until the process zone is fully developed. The crack in the process zone has a different shape because of the forces of the bridging fibers. In figure 7, a simplified approach shows the amount of toughening due to each intersected fiber may be accounted as nlAR. Once the zone has developed fully, then the whole crack may move forward with the process zone size remaining a constant size, at an energy level of R,,,+ nzAR. By controlling the microstructure and properties of the material to result in such an R-curve behavior, we can over certain limits of flaw size ensure that cracks are stable. This mechanism is thus able to explain why for many cement based composites, reduction of inter-fiber spacing results in formation and growth of significant cracking
23 1
Mechanical properties of concrete reinforced with AR-Glass fibers
without causing catastrophic fracture. The criteria for the cracking can be defined in terms of energy balance: d R dG R(a) =G(a) = (K,+K,F)' -=E' * da da A procedure for the modeling of the R-curve has been developed earlier where a closed form solution for the R curve for quasi-brittle materials proposed by Ouyang, Mobasher and Shah [4]. Using this approach the fracture resistance of a material is defined by two parameters Aa, and fJ representing the R-curve. Their magnitudes can be obtained by fitting the loadCMOD or deflection plots and expressed as:
Since R varies with the crack length, it can not be viewed as a single valued function, and the extension of the stable cracking is determined entirely by the geometry and loading. The procedure used in the present approach is based on calculating R parameters corresponding to the load-deformation history of the specimen as suggested by Mobasher, Ouyang and Shah [ 5 ] . The procedure is based on calculation of the fit parameters which describe the effect of fibers in the context of the resistance curve, R and also the amount of critical crack length Aa,.
-Model Prediction 3 Days
0.20
-Model Prediction 28 Days Model Fit, 28 days
0.15
E 2-0.10 c4 0.05
0.00
0
20
40
60
Crack Extension. mm
80
100
0.0
0.I
0.2
0.3
0.4
CMOD, mni
Figure 8 Modeling the effect of age on the flexural and R curves of fiber reinforced concrete. According to Figure 8 it is possible to model the effect of age of the composites by developing a nonlinear curve fit model to the experimental data for the flexural load-CMOD response based on R-curves. Using these R-curves, one can calculate the contribution of fibers to toughening using Equation 3. Figure 9 represents the model fit parameters for the study of the effect of fiber volume fraction on the flexural response. load-CMOD plot and b) the R-curve response. the By conducting a nonlinear fit to the experimental load-CMOD responses, the two parameters, critical crack length Aac, and also the parameter
232
Tejal DESAI, Rimpal SHAH, A h a PELED and Barzin MOBASHER
representing the R-curve are obtained. In this case the ranges of R values obtained are from 5.64 to 6.28 N/m and the range of critical crack extensions are in the range of 20-35 mm. 0.02 *-*-+Control
z
Simulation Sirnulatio
Q - 8 - 0 10 Kg/m3
10
8
M
4
2 0 0
I
0.2
0.6 CMOD, nun 0.4
0.8
1
ole' 10
'
20
'
'
30
'
'
40
'
I
50
Crack Extension, mm
Figure 9 Modeling the fiber volume fraction using R-curves, a) load-CMOD plot and b) the R-curve response.
CONCLUSION Effect of short AR glass fibers on the strength and ductility of concrete was studied and indicate a potential for reinforcing the concrete material both from an early age property modification and also from the strengthening and toughening perspective. Closed loop testing was conducted to characterize the response of specimens in compression, and flexure. It was observed that concrete with 12 mm HP fibers exhibits higher compressive strength than other fiber lengths. During the early ages, due to the fact that the concrete strength is sufficiently low, fibers contribute to toughening, whereas during the later stages of age, the contribution is mainly in increasing the strength. The ability of AR Glass fibers to provide both strengthening and toughening mechanism for concrete was investigated using an RCurve approach. 1. 2. 3. 4.
5.
REFERENCES Frondistouyannas, S., "Flexural Strength Of Concrete With Randomly Oriented Glass Fibers", Magazine of Concrete Research, 29 (100): 142-146 1977. Mobasher, B. and Li, C. Y . , "Mechanical Properties of Hybrid Cement Based Composites," ACIMuterials Journal, Vol. 93, No.3, pp.284-293, 1996. Mobasher, B., and Shah, S. P.,"Test Parameters in Toughness Evaluation of Glass Fiber Reinforced Concrete Panels", ACI Materials Journal, Sept-Oct. 1989, pp. 448458. Ouyang, C. S., Mobasher, B., and Shah, S. P., Eng. Fracture Mech., 37, 4, 901-913, 90. Mobasher, B., Ouyang, C., and Shah, S. P., Int. J. ofFract.. SO: 199-219, 1991.
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSIand Woodhead Publ., Warsaw 2003
BEHAVIOUR OF GLASS-FILAMENT-YARNS IN CONCRETE AS A FUNCTION OF TIME AND ENVIRONMENTAL CONDITIONS
J. ORLOWSKY, U. ANTONS and M. RAUPACH Institute of Building Materials Research, Technical University Aachen (ibac), Germany ABSTRACT At the Institute for Building Materials Research of the University Aachen (Germany) the durability of AR-glass yarns in concrete is investigated, within the scope of a large project on textile reinforced concrete. Textile reinforced concrete represents an interesting new construction material which offers several advantages compared to steel or fibre reinforced concrete. These advantages dominate in the field of applications, where thin-walled, structural elements with a high load-canying capacity are necessary. Especially AR-Glass yarns can be used to manufacture the textile reinforcement. These multifilament yarns (rovings) consist of more than 500 filaments with diameters about 12-30 pm. The aim of the durability investigations is to build up a model which allows predictions about the long-term behaviour of textile reinforced concrete. The long-term behaviour of textile reinforced concrete is affected by the chemical attack of hydration products on the glass yarns. Aim of the presented investigations is to determine the influence of static load on the durability of this composite material. The results show the importance to investigate the combination of static load and water. The water changes the bound behaviour of the reinforcement which can lead in the worst case to a failure of the specimens. Keywords concrete, glass fibre, durability, alkalinity
1. INTRODUCTION In textile reinforced concrete steel which is usually used as reinforcement is substituted by technical textiles, which have a defined position and direction in the concrete. One of the advantages is that no minimal concrete cover is necessary because of the lack of possible corrosion. Therefore it is possible to produce thin elements with a high load bearing capacity. In the research project SFB 532 “Textile Reinforced Concrete - Basics of a New Technology” placed at the Technical University of Aachen, financed by the central public funding organization for academic research in Germany, DFG, several institutes investigate this new construction material. At this point in project most of the used textiles are made of glass rovings. Rovings are made out of more than 500 single filaments, which have an average diameter of 12 - 30 pm. Life time and durability predictions are extremely important for the use of this new composite material.
234
Jeanette ORLOWSKY, U.ANTONS and Michael RAUPACH
The durability of glass in concrete is mainly dominated by the chemical attack of the hydration products in the concrete, which results in a loss of tensile strength. Storing the composite materials under water at increased temperature (i.e. 50 “C) can accelerate this loss of tensile strength. Because of local cracks and flaws the realistic tensile strength of glass is much lesser than the theoretical tensile strength /Or103/. Pumell /PurO 1/ developed a thesis on the durability of textile reinforced concrete, which bases on the conclusion that the local flaws grow extremely fast under the influence of alkalinity and external applied forces. This leads to an early failure of the composite specimens. This thesis on the fatigue strength of textile reinforced concrete is investigated at the Institute for Building Materials Research (ibac) currently. First results are shown in this paper. 2. MATERIALS
AR-Glass rovings with 2400 tex (1 tex = Ig/km) manufactured by the company SAINT GOBAIN VETROTEX are used for these investigations. To protect the glass from chemical attack, zirconium is added to the conventional E-glass mixture. This modified glass is called AR-glass (alkali resistant). The used 2400 tex rovings are made of more than 1000 single filaments, each of the filaments has a diameter of approx. 27 pm (Internal description of the roving: VET-RO-ARG-2400-1-00). As shown in figure 1 the single filaments are not totally parallel orientated in the roving instead their orientation is “wavy”. Therefore the length of the single filaments varies from the used test length of 500 mm. The tensile strength of this roving at a length of 500 mm is 625 N/mm2. A single filament of the same roving has a tensile strength of approx. 2000 N/mm2. The two reasons that are in charge of this extreme loss of tensile strength, are the wavy orientation and the fracture of single filaments emerged during the production process of the rovings. Less than 50 % of the filaments in the roving are responsible for the breaking load because they are parallel orientated and not damaged. The rest of the filaments fails partly before and after the breaking point /Bra02/.
Figure 1: Filament alignment in a roving with 2400 tex /Bra021 The concrete mixture (table 1) was developed by the Institute for Building Materials Research as a micro-concrete. In order to achieve a total compound a high floating ability and low diameters of aggregate is required. The addition of silica fume and fly ash to the mixture reduces the amount of alkali ions and calcium hydroxide in comparison to Portland cements. The pH value of this mixture is 13.5.
Behaviour of glass7filanient-yarns in concrete as a function of time and environmental conditions 235
Binder
Type of
system
cement
Additives
Cement
content
Fly ash
Silica
fume
Water reducer
35
1'
Stabilizer
kg/m' OPC
CEM152,5
490
175
Binder content
w/bratio
Max.
grain size
kg/m'
-
mm
700
0.4
0.6
The used test specimens (dog bone shaped specimens - called TSP) pass through a two week preparation phase before testing. After the production process the specimens stay in the mould for approx. 24 h at 23°C and 95 YOrelative humidity. After demoulding the specimens are stored for 6 days at 23 "C and 95 % humidity. The final shape of the specimens - at this point they are 500 mm long, 100 mm wide and 6 mm thick - is milled. As shown in figure 2 the central part of the specimen is 250 mm long and 60 mm wide. The transition between the two widths of 60 mm and 100 mm is 75 mm long and formed as a clothoid. The last production step is the fixation of the out sticking VET-RO-ARG-2400-1-00 rovings with epoxy resin. This prevents individual filaments to slip within the sample. During this preparation process, which takes up to 7 days, the samples are stored at 23 "C and 50 % humidity.
500
/
roving
[mml
fixing of the ioving with epoxy resin
Figure 2. Geometry of the TSP-specimens The test setup for static load tests was developed at the ibac and is shown in figure 3. This setup applies the tensile force in the clothoid shaped area of the test specimens. The first load step is applied with a force-controlled hydraulic cylinder. After reaching the desired load this load is constantly adjust with a weight at a crank of a lever. The force- and elongation-curves are measured by one load cell and two different kinds of elongation gauges (strain sensors DDl and inductive gauges). Until the first crack the strain sensors mounted on the center part of the sample determine the elongation curves. The curves are determined as a change of length of the 250 mm long center part based on a homogenous distribution of elongation. After the first crack the inductive gauges mounted on the mounting brackets continue the measurements (figure 4). The two advantages of this setup are, a continuously ongoing
236
Jeanette OIUOWSKK LI. ANTONS and Michael RAUPACH
measurement for underwater storage and the collection of data of cracks in the mounting zone are both possible. The calculated elongations of the first crack can be used for calibrating the inductive gauges. This is required because the mounting brackets might settle during raising the force to its defined level and so the elongations would be increased by mistake.
TSP-specimen
point of load application permanent load tank with water
Figure 3. Setup of the test facility to measure the behaviour of textile reinforced concrete under static load The ibac provides 9 such static load test facilitys, which are in a defined climate of 23 "C and 50 % humidity. The required cylinder for the water storage can be mounted on the lower mounting bracket. In order to avoid a change of the load because of the additional load of the cylinder and the water a hydraulic cylinder is used again. The water temperature can be raised up to 50 "C.
Figure 4. Arrangement of the inductive gauges in the test facility
Behaviour of glass-filainent-yarns in concrete as a function of time and environmental conditions 237
In order to control the functions of the static load setup, especially the force application, some samples were cracked until the total failure. The force-elongation curves were recorded as shown above and compared to curves recorded with a displacement controlled Instron testing machine. Cypers et al /CypO3/ describe the tensile test of TSP samples using the Instron testing machine. The velocity of the displacement controlled test was 0,5 mndmin. The load controlled test was performed at 16 N/sec. Picture 5 shows the accordance of the two curves. Force in kN
0
2
4
6
8
10
12
Elongation in r n d m
Figure 5. Comparison of the failure load a) displacement controlled in the Instron testing machine and b) load controlled in the static load test facility 3. AMOUNT OF TESTS
The following parameters were examined during the test phase:
- Humidity: 50 % relative humidity and water storage - Temperature: 23 "C and 50 "C - Static load: 60 - 85 % of the failure load Each of these parameters was examined with two specimens. This paper only includes a part of the results, because the tests are not finished yet. 4. RESULTS AND DISCUSSION 4.1 Tests at 23 OC and 50 YOrelative humidity The results of the specimens, which were charged with 80 % of the failure load, are shown in figure 6. The diagram shows the percental increase of the elongation over time (creep). The percental increase of the elongation refers to the beginning of the static load phase after the use of the hydraulic cylinder. It can be seen that during the first hours the elongations increase noticeable. After this time the increase of elongation reduces, until after 50 - 100 hours only a small, linear increase remains. Because of difficulties during the test phase the elongation curve of the specimen TSP8O-1 could not be determined completely. But it is still obvious that the two curves are strongly similar - both show a curved area, which leads into a linear area. The percental increase of elongation of specimen TSP8O-1 in the curved area is nearly
23 8
Jeanette ORLOWSKY, U.ANTONS and Michael RA UPACH
twice as high as the increase of specimen TSP80-2, whereby the absolute final elongations of both samples are nearly the same. This shows the reciprocal ratio between percental increase of elongation and absotute values at the beginning of the static load-testing phase. The elongation measurements were stopped after approx. 200 h, but the specimens still remained under load for two more month. A failure of the samples was not predictable. increase of elongation in %
30
20
-
0
.
0
,
50
'
!
100
'
1
150
'
I
'
200
1
.
250 300 time in h
Figure 6. Behaviour of the TSP under static load at 80 % of the failure load and 23 "C, 50 Yo relative humidity The specimens show an average crack distance of 0,8 mm and the cracks are very evenly distributed. The crack wide scatters between 0,05 mm to 0,15 mm wide. 4.2 Tests at 23 "C in water
The results of four TSP-specimens, which were stored under water at 70 YOof their failure load, are shown in the left diagram in figure 7.
time in h
time
in h
Figure 7. Behaviour of the TSP under static load at 70 % of the failure load in water at 23 "C
Behaviour ofglass7filatnen~-yarrlsin concrete as a jirnction oftirne and eirvironmental conditions 239
The storage under water started 24 h after the static load was applied. As seen in the right diagram in figure 7 the curves during the first 24 h are similar to the curves shown in figure 6. Two of the four specimens (TSP70 water sample 1 and 3) stayed under static load and under water for two month and a failure could not be predicted - figure 7 left. The samples TSP70 water 2 and 4 failed within a few minutes respectively a few hours after the storage under water. An obvious increase of elongation (1 5-33 % regarding the elongation at the beginning) while applying the water can be seen in the right diagram of figure 7 for all test specimens. The results of the specimens stored under water at 70 % of their failure load show directly opposite results. One part of the specimens endures a long time under load, the other part of the specimens fails after a short period of time. But all specimens show an obvious increase of elongation after having contact to water (see also figure 8). This increase of elongation can be explained with the geometry of the roving: as seen in figure 1 the roving is made of various single filaments, which lay wavy to each other and are not connected to the concrete over their total length and wide /Rau02: Wa103/. The spaces between the filaments enable the water to flow into them and decrease the friction between the filaments, which leads to an increase of elongation. At this point the tests show that specimens with a crack width of more than 0,l mm fail directly after storing them under load and water, whereby specimens with a crack width below 0,l mm are not affected. So far these tests were only performed with loads 2 70 % of the failure load. At the moment the tests are continued with various crack width and static loads.
4.3 Tests at 50 O C in water The results of a TSP-specimen, which was stored under water at 50 "C and at 70 % of its failure load, are shown in figure 8.
Figure 8. Behaviour of the TSP under static load at 70 % of the failure load in water at 50 "C The specimen were stored under water after 24 h of already being under load. This test also show an obvious increase of the elongation after applying water. The specimen still remains under load for additional 14 days and at this moment there is no loss of fatigue strength detectable. This test points out that Purnell's thesis (the increase of flaws in glass under
240
Jeanette ORLOWSKY,U. ANTONS and Michael RA UPACH
increasing tension which leaves to an early failure) /PurOl/ might not be right. Rather the loss of strength of glass under a static load and accelerated aging (water at 50 "C) seems not as big as the loss of strength of samples, which were aged accelerated without a mechanical influence. During the preliminary tests with small static loads this behaviour was already noticed. Regarding this point more tests are performed.
5. CONCLUSIONS AND FUTURE WORK In order to investigate the durability of textile reinforced concrete under static load a test setup was developed at the Institute for Building Materials Research (ibac). This setup enables to perform tests with concrete specimens reinforced with textiles or rovings under different static loads and in different climates. A reduction of the fatigue strength of the specimens at 23 "C and 50 % relative humidity under a static load of 70-80 % of the failure load could not be detected. The storage of the specimens under water at 23 "C shows different results. One part of the specimens was not affected by water, whereby the other part of the specimens failed nearly directly when they came in water contact. It seems, that the fatigue strength of the specimens, which were tested under water at a temperature of 23 "C, is mainly effected by the crack width after applying a certain amount of the failure load. All specimens show an increased elongation after water contact, which maybe is the result of the decreased friction between the inner filaments. Purnell's thesis /PurOl/ could not be confirmed by the specimen tested at 50 "C under water and a static load. According to this result the static load has no negative effect on the tensile strength of the composite material during the amplified chemical attack caused by the tempered water. In order to verify these early results the tests are continued at this time.
6. REFERENCES Brameshuber, W. ; Brockmann, T.: Development and Optimization of Cementitious Matrices for Textile Reinforced Elements. London : Concrete Society, 2001. - In: Proceedings of the 12th International Congress of the International Glassfibre Reinforced Concrete Association, Dublin, 14-16 May 2001, S. 237-249 Brameshuber, W. ; Banholzer, B. ; Gries, T. ; Al-Masri, A,: Methode zur Untersuchung des Versagensmechanismus unter Zugbelastung von MultijilamentGarnenfir die Betonbewehrzing. In: Technische Textilien 45 (2002), Nr. 2, S. 98-99 Cuypers, H.; Wastiels, J.; Orlowsky, J.; Raupach, M.: Investigations on the Durability of glass fibre reinfoced concrete and influence of matrix alkalinity. In: Brittle Matrix Composites 7, Proceedings of the Seventh International Symposium, Warsaw, Poland, 13 - 15 October 2003 Orlowsky, J. ; Raupach, M.: Einfuss der Umgebungsbedingungen auf die Dauerstandfestigkeit von Textilbeton. Berlin : Deutscher Verband fur Materialforschung und -prufung, 2003. - In: 35. Tagung des DVM-Arbeitskreises Bruchvorg&ge am 18. und. 19. Februar 2003 in Freiburg, S. 325-334 Purnell, P. ; Short, N.R. ; Page, C.L.: A Static Fatigue Model for the Durability of Glass Fibre Reinforced Cement. In: Journal of Materials Science 36 (2001), S. 53855390
Behaviour of glasslfilarnent-yarns in concrete as a function of tirile and environmental conditions 24 1
[6]
[7]
Raupach, M. ; Brockmann, J.: Untersuchungen zur Dauerhafiigkeit von textilbewehrtem Beton : Chemische und mechanische Beanspruchung von Textilien aus Glas. In: Beton 52 (2002), Nr. 2, S. 72-74,76,78-79 Walk-Lauffer, B. ; Orlowsky, J.; Raupach, M.: Verstarkung des inneren RovingVerbundes im textilbewehrten Beton durch Polymerdispersionen. Weimar : BauhausUniversitat, 2003. - In: 15. Internationale Baustofftagung, - ibausil -, 24. - 26. September 2003 in Weimar
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15,2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
DESIGN OF HYBRID-FIBER REINFORCEMENT FOR SHRINKAGE CRACKING BY CRACK WIDTH PREDICTION Michele F. CYR’, Chengsheng OUYANG’ and Surendra P. SHAH’ ‘Center for Advanced Cement-Based Materials Northwestern University2 145 Sheridan Rd., Evanston, IL, 60208, USA, e-mail:
[email protected];
[email protected] 2 Office of Materials Iowa Department of Transportation 800 Lincoln Way, Ames, IA, 500 10, USA, e-mail:
[email protected] ABSTRACT The use of fiber reinforcement to reduce shrinkage cracking is becoming increasingly common. The effectiveness of fiber reinforcement can be enhanced using multiple types of fibers. A means of predicting the shrinkage performance of hybrid-fiber reinforcement would facilitate its design. A model to predict shrinkage crack widths in restrained ring shrinkage tests is being developed. The ability of the fibers to transfer stress across a crack and free shrinkage behavior are used to determine crack width. To facilitate calibration of the model, a procedure for establishing tensile performance from flexural test data using fracture mechanics has been developed. The crack width model and the procedure for predicting tensile performance are presented. The initial phase of calibrating the model, verification of the tensile performance prediction, is discussed. Keywords Hybrid-fiber-reinforced concrete and mortar, shrinkage, fracture mechanics
INTRODUCTION As concrete dries, it shrinks due to the loss of water. Shrinkage of concrete is generally classified as autogenous, plastic, or drying. Autogenous shrinkage occurs at low water-tocement ratios due to the consumption of water in hydration. Plastic shrinkage occurs when the concrete is still fresh. Drying shrinkage refers to shrinkage in hardened concrete. If concrete is restrained, it is unable to shrink freely. As a result, tensile stresses will develop, and the concrete might crack. While shrinkage cracks are usually not large enough to compromise structural integrity, they do allow the ingress of water and other corrosive agents, reducing the durability of the concrete. Shrinkage cracking is of particular concern in elements with a high ratio of surface area to volume. Recently, the use of short, discontinuous fibers as reinforcement for concrete has been studied [I]. Because fibers can severely limit the workability of fresh concrete, they can only be added in limited volumes. While these small amounts of fibers cannot provide sufficient
244 Michele F.CYR, Chengsheng OUYANG and Surendra P. SHAH reinforcement to replace conventional steel reinforcing bars, they can significantly reduce shrinkage cracking. In restrained shrinkage tests, fiber reinforcement delays the onset of shrinkage cracking and reduces shrinkage crack widths [2]. In the field, fibers are used as shrinkage reinforcement in slabs, bridge decks, and pavements. Researchers have demonstrated that the performance of fiber-reinforced concrete can be tailored for specific applications with the use of hybrid-fiber reinforcement [3. 41. Two or more different fiber types, sizes, or shapes are combined to achieve the benefits of each. Larger and longer macrofibers, which prevent the opening of macrocracks, can be combined with smaller and shorter microfibers, which limit the growth of microcracks. Stronger but relatively brittle fibers can be combined with weaker, more ductile fibers to enhance both composite strength and ductility. Portions of costly, “high-performance” fibers can be replaced with less expensive fibers. To determine the effect of hybrid-fiber reinforcement on shrinkage crack resistance, restrained shrinkage tests were performed on mortar reinforced with various combinations of glass and polypropylene (PP) fibers and only glass and only polypropylene fibers in the current study. Often, restrained ring shrinkage tests are used to assess experimentally the shrinkage behavior of concrete. Due to the geometry of the test, the rings usually do not crack until at least a week after casting. For design purposes, it would be helpful if shrinkage cracking potential could be assessed more quickly. The effects of different fiber reinforcements could be estimated before large-scale testing was performed. RILEM TC 162-TDF [5] has proposed a model developed by Olesen and Stang [6] to predict shrinkage crack widths in fiber-reinforced concrete slabs. In this paper, the model is adapted for use with a ring geometry. In addition, a method is presented to derive tensile specimen response from flexural test data. This method eliminates the need for uniaxial tension tests, which can be extremely difficult to perform and yield specimen-size dependent results. Ultimately, it is desired to use the model as a design tool to predict the shrinkage performance of various hybrid-fiber combinations.
RESTRAINED SHRINKAGE TESTS Experimental program Restrained ring tests were performed to evaluate the shrinkage resistance of hybrid-fiber combinations of glass and polypropylene fibers. A mortar matrix was used to reduce the age of cracking and amplify the effect of the fibers. A 50 mm-thick mortar ring was cast around a 25 mm-thick steel annulus. The inner diameter of the mortar ring was 300 mm. For each type of fiber reinforcement, two rings were cast and cured in the molds for 24 hours. The molds were removed, and the rings were placed in an environmental chamber at 50% relative humidity (RH) and 22OC. The rings were inspected daily, and the age of cracking was noted. Cracks were measured periodically using a handheld microscope. A schematic of the restrained ring test setup is shown in Figure I .
Figure I . Restrained ring shrinkage test setup.
Design of hybridSfiberreinforcementfor shrinkage cracking by crack width prediction
245
Fiber-reinforced mortar was prepared at I :2:0.5 cement:fine aggregate:water, by weight. To improve the workability of the mortar, 15%, by volume, of the cement was replaced with Class F fly ash. Bundled glass fibers and fibrillated polypropylene fibers were added at 0.38% volume fraction. If the ratio of fibers to cement paste is kept constant, this is equivalent to 0.25% fibers in a I :2:2:0.5 cement:fine aggregate:coarse aggregate:water concrete. Hybrid combinations of I :2, I :1, and 2: 1 glass:PP ratios at a total fiber volume fraction of 0.38%were also tested. Fiber properties are shown in Table I . Filaments Tensile Elastic Fiber Diameter Length Per Strand Strength Modulus TYPe 108 1700MPa 72 GPa Glass 14pm 12 mm N/A 700MPa 5GPa N/A 19mm PP
Results The addition of fiber reinforcement significantly reduces crack widths and induces multiple cracking. Figure 2 shows the total crack widths of mortar with no fibers, only glass fibers, only polypropylene fibers, and several combinations of glass and polypropylene fibers at a total fiber volume fraction of 0.38%. Each curve is an average of the first crack width for two specimens. All of the fiber reinforced specimens showed some degree of multiple cracking. However, for the specimens with polypropylene fibers, the secondary cracks often did not extend the entire length of the ring, and as a result were not measured. The total crack widths for all the fiber-reinforced mortars are significantly smaller than the single cracks that developed in each plain mortar ring. The occurrence of multiple cracking in the rings of fiber-reinforced mortar reduces the permeability of the mortar. Water flow, or permeability, is proportional to crack width cubed [7], which means mortar with multiple smaller cracks is less permeable than that with one larger crack.
1.5 A
-g E E
1.0
i5
-1:ZG:PP *l:1 G.PP -21 GPP
Y
g
.-r
0.5
u. 0.0 0
10
20
-
30
40
Age = t o Age of Cracking (days)
Figure 2. Shrinkage crack widths in restrained ring shrinkage tests of fiber reinforced mortar.
246
Michele F. CYR. Chengsheng OUYANG and Surendra P. SHAH
Figure 2 shows the additive effects of the hybrid-fiber reinforcement. The crack widths of the hybrid specimens fall between those for mortar reinforced with only glass fibers and only polypropylene fibers. Although none of the hybrid combinations tested outperformed the mortar reinforced with only glass fibers, they did have exhibit smaller cracks than the purely polypropylene mixture. If polypropylene were chosen as the primary reinforcing fiber, crack widths could be reduced by replacing a portion of these fibers with glass fibers.
SHRINKAGE CRACK WIDTH MODEL In fiber-reinforced concrete, fibers increase the tensile strength of the matrix by preventing or delaying the coalescence of microcracks and enhance ductility by transferring stress across cracks. Hillerborg's fictitious crack model can be used to describe this stress transfer in the post-peak response of fiber-reinforced concrete in uniaxial tension [8]. Olesen and Stang used the fictitious crack model to develop a method to predict crack widths in fiber-reinforced concrete slabs-on-grade subjected to thermal or shrinkage strains [ 6 ] . Olesen and Stang [6} studied an infinitely long, longitudinally restrained slab. Stress develops when the slab is subjected to thermal or shrinkage strains. This stress is described as a function of the shear between the slab and its substrate. When the stress in the slab reaches the tensile strength of the concrete, the slab cracks, and the stress redistributes. The deformation in the slab, or the crack width, is derived from the stress distribution in the cracked slab, giving crack width as a function of stress. A uniaxial tension test is performed to determine the amount of stress the fibers,can actually carry across a given crack width. Then, from the stress in the slab due to shrinkage strains, the corresponding crack width can be calculated. Two basic changes are made to adapt this model for use with restrained ring shrinkage tests. First, the stress in the concrete ring is expressed as a function of the geometry of the ring and the shrinkage strains that develop, instead of as a function of the interface between the concrete and the restraint. Second, the tensile stress-crack width relationship is approximated as a bilinear relationship, as presented by Olesen [9] and shown in Figure 3, instead of as a constant for all crack widths, which Olesen and Stang used to simplify their model for use in design.
t
=t
t'l
w1=-
a.
bl- bz
,w2=-
al-a2
bz a2
al
Crack Width (w)
Figure 3. Bilinear approximation of post-peak tensile stress vs. crack width, The post-peak tensile stress-crack width relationship is approximated as two lines obtained from a linear regression of experimental data. As in the fictitious crack model, stresses are assumed to be elastic prior to cracking. After cracking, the stress is given by the tensile stress-crack width approximation. Thus, the stress in the ring is written as
Design of hybrid-fiber reinforcementfor shrinkage cracking by crack width prediction
247
o=&E before cracking o = o ( w ) = ( b i -a,w)f, after cracking,
where cs= tensile stress, E = strain, E = elastic modulus, w = crack width, f, = tensile strength, and ai and bi are the parameters for the bilinear approximation of the tensile stress crack width relationship shown in Figure 3. Prior to cracking, the strain, E, is simply the shrinkage strain, which is determined from a free shrinkage profile of the concrete. After the ring has cracked, the strain in the ring-resulting from the restraint that prevents drying shrinkage-is still equal in magnitude to the shrinkage strain, but it is separated into two components: the strain due to the change in the circumference of the ring as a result of the crack and the strain due to the residual stress that the fibers carry across the crack,
where ow(w), the post-peak tensile stress, is a function of crack width as shown in Figure 3, and r is the radius to the center of the concrete ring. If the shrinkage strain as a function of tensile stress and crack width is known, the crack width can be expressed as a function of shrinkage strain. The shrinkage strain at the age of cracking is determined from the free shrinkage profile of the concrete.
MODEL CALIBRATION Required testing To use the model, the shrinkage strain, E,, elastic modulus, E, tensile strength, f,, and the postpeak tensile stress as a function of crack width are required. The shrinkage strain is determined from free shrinkage measurements. For fiber-reinforced concrete, free shrinkage is measured in accordance with ASTM C341-96 [lo]. It is assumed that fiber reinforcement has no effect on free shrinkage. Thus, the measurements for the unreinforced matrix can be applied throughout the study. The elastic modulus, tensile strength, and stress-crack width relationship can all be determined from a uniaxial tension test. However, uniaxial tension tests are extremely unstable and difficult to perform, and the test results can be specimen-size dependent. It would be much easier if the tensile behavior could be derived from material fracture parameters measured based on a more reliable test, such as a flexural test. Some current techniques involve time-consuming, iterative processes with ambiguous results [ I I]. An analytical method developed using R-curves to derive tensile performance from flexural stress vs. crack mouth opening displacement (CMOD) measurements is described below. Tensile behavior from flexural performance An R-curve, fracture resistance as a function of crack extension, can be generated from threepoint bend flexural test data. From this R-curve, the critical stress intensity factor, K,,, and critical crack tip opening displacement, CTOD,, can be calculated. K,,and CTOD, are material parameters, independent of specimen geometry or testing configuration. Once these parameters have been determined, the appropriate equations and geometry factors can be applied to generate the R-curve for uniaxial tension specimens. From the new R-curve, tensile stress and crack width can be calculated. To begin, three-point bending tests are performed on notched beams to generate loadCMOD curves. The span is four times the depth of the beam, and the notch is one-third of the
248
Michele F. CYR. Chengsheng OUYANG and Surendra P. SHAH
depth. An extensometer is mounted across the notch to measure the CMOD and provide feedback to control loading. Two LVDTs are mounted in a yoke on either side of the specimen to measure deflection. A schematic of the test setup and a typical load-CMOD curve for fiber-reinforced concrete are shown in Figure 4.
Y S=4b
CMOD Figure 4. Typical load-CMOD curve and three-point bend test setup.
From the load vs. CMOD data, the flexural stress, ofinex, IS calculated, and crack extension, a, is determined [12, 131. cflex
3PS =2b2t
Then, the stress intensity factor, KI, is determined and used to calculate fracture energy, G.
At fracture, fracture energy is equal to fracture resistance, G = R, so the R-curve for a threepoint bend specimen is plotted. The expression for the R-curve is also written as [ 121
R = pv/(awhere
rn1)L
1 a-1 1 a-1 q 2=-g--+ -i--
a
[4
a
21%
Design of hybrid-fiber reinjorcementfor shrinkage cracking by crack width prediction
249
and a,, = initial notch length. a and p are parameters determined by curve fitting from the Rcurve measured using the three-point bending beam. After a and p are determined, the fracture parameters. Ki, and CTOD,, are back calculated from expressions for a and p.
a=
P=
Kk (d,a - a + 1) Ea(d, -d,)(aa,
where f , and f 2 are geometry factors. For three-point bend beams, fl = I . 123 and f 2 = I .42. For uniaxial tension specimens, fl = I . 123, and f l = 1.454. Once KI, and CTODc have been determined, a and p are calculated for uniaxial tension. Then, the R-curve for uniaxial tension is generated. The R-curve obtained in this manner is based on values of KI, and CTOD,, which are determined by the fracture behavior at peak load. In a fiber-reinforced concrete beam, most of the debonding and slipping of the fibers occurs in the post-peak stage, resulting in inelastic energy. The previously obtained R-curve shall be modified to account for this inelastic energy during the post-peak stage, as shown in Figure 5 . The total energy is considered to be the sum of elastic and inelastic energy contributions. The elastic energy is expressed in the calculated R-curve. The inelastic energy is expressed as the difference between the R-curve generated from experimental data and the calculated R-curve in the post-peak region, the shaded area in Figure 5. The ratio of the inelastic R-curve to the elastic R-curve i s expressed as a power law function of the post-peak crack extension. The inelastic to elastic ratio is determined for the R-curve for the beam and applied to the R-curve for tension. To generate the tensile R-curve, R is taken as the elastic energy before the peak load and t h e sum of the elastic and inelastic energy after the peak.
0.7 0.6
.
0.5
0.4
k 0.3 a
0.2 0.1 ~
0.0 0
20
40
Crack Length
60
(rnrn)
Figure 5. Elastic and inelastic portions of R-curve.
80
250
Michele F. CYR, ChengshengOUYANG and Surendra P. SHAH
From the R curve, the tensile stress, 0,for a given crack length, a, is calculated from the energy balance of G = R.
Then, CMOD is calculated using LEFM [ 131.
Finally, the load point displacement, or overall specimen elongation, is determined from compliance [ 121. The energy release rate, G, can also be written in terms of compliance, C.
This expression is integrated to obtain compliance.
c = c, + p d a 02b2t
And, elongation, 6,is simply load multiplied by compliance.
Verification with existing data The accuracy of the tensile performance prediction was verified using data previously obtained by another researcher [14], who performed both flexural and uniaxial tensile tests on concrete reinforced with 0.5% steel macrofibers and 0.29% PVA microfibers. Details of the materials and the experiments performed are discussed elsewhere [ 141. The procedure was applied to derive the tensile stress vs. crack width relationship from flexural stress vs. CMOD test data. Figure 6 shows the derived tensile stress vs. crack width together with experimental data from a uniaxial tension test. Crack width is determined by subtracting the elastic deformation, calculated as stress divided by elastic modulus multiplied by length, from the total displacement. Figure 6 shows excellent agreement between the predicted and actual uniaxial tensile performance. Similarly good results were obtained for a plain concrete specimen and a steel-fiber-reinforced specimen. These results show that this prediction is acceptable. For future work with this model, the tensile stress-crack width relationship will be derived from flexural test data using this technique. It will not be necessary to perform uniaxial tensile tests.
Design of hybrid;fiber reinforcementfor shrinkage cracking by crack width prediction
0.0 I 0.00
0.05
0.10
0.15
0.20
0.25
25 1
0.30
Crack Width (mm)
Figure 6. Experimental [ 141 and predicted tensile performance. From the predicted tensile behavior, a bilinear approximation of the post-peak performance can be made using linear regression. From Figure 6, it is clear where the two lines can be drawn. The bilinear expression of post-peak tensile behavior will be used, together with the free shrinkage strain profile, to calculate total shrinkage crack widths in the next phase of this study.
CONCLUSIONS The additive effect of glass and polypropylene hybrid-fiber-reinforcement is evident in the restrained shrinkage behavior of mortar. The crack widths of the hybrid-fiber-reinforced mortars are larger than those of the glass-fiber-mortar and smaller than those of the polypropylene-fiber-reinforced mortar. The adaptation of Olesen’s and Stang’s shrinkage crack width model to the restrained ring geometry is discussed. The model requires the tensile behavior as input. To facilitate calibration of the model, a fracture-mechanics based technique to derive tensile behavior from flexural test data, using R-curves, is developed. This technique provides excellent agreement between the predicted and experimentally determined uniaxial tensile performance. This indicates that specimens can be tested in a flexural configuration, eliminating the need for unstable, size-dependent uniaxial tensile tests.
ACKNOWLEDGEMENTS This work was supported by the Center for Advanced Cement-Based Materials at Northwestern University. Dr. John S. Lawler provided data to calibrate the tensile curve prediction. Lennart Ostergaard offered a number of helpful suggestions for beginning this work. Their assistant is gratefully acknowledged.
252
Michele F. CYR, ChengshengOUYANG and Surendra P. SHAH
REFERENCES 1. Balaguru, P., Shah S.P., Fiber-Reinforced Cement Composites. McGraw-Hill Book Co., Singapore 1992 2. Shah, S.P., Weiss, W.J., Yang, W., Shrinkage cracking-can it be prevented? Concrete International, 1998, pp 51-55 3. Lawler, J.S., Wilhelm, T., Zampini, D.. Shah, S.P., Fracture processes of hybrid fiberreinforced mortar. Materials and Structures, 36, 2003, pp 197-208 4. Mobasher, B., Li, C.Y., Mechanical properties of hybrid cement-based composites. ACI Materials Journal, 93, 1996, pp 284-292
5. RILEM TC 162-TDF, Design of steel fibre reinforced concrete using the 0-w method: principles and applications. Materials and Structures, 35,2002, pp 262-278 6. Olesen, J.F., Stang, H., Designing FRC slabs on grade for temperature and shrinkage induced cracks. In: Fibre-Reinforced Concretes (FRC) BEFlB'2000 - Proceedings of the 5Ih International RlLEM Symposium, P.Rossi and G. Chanvillard eds. Lyons 2000. pp 337-346 7. Fox, R.W., McDonald, A.T., Introduction to Fluid Mechanics, 4'h ed. John Wiley & Sons, Inc., New York-Chichester-Brisbane-Toronto-SingaporeI992 p 350
8. Hillerborg, A,, Analysis of fracture by means of the fictitious crack model, particularly for fibre reinforced concrete, The International Journal of Cement Composites, 2, 1980, pp 177184 9. Olesen, J.F., Fictitious crack propagation in fiber-reinforced concrete beams. J. of Engineering Mechanics, 127,2001, pp 272-280 10. ASTM C 341-96 Standard test method for length change of drilled or sawed specimens of hydraulic-cement mortar and concrete. In Annual Book of ASTM Standards, ASTM, Philadelphia, PA 2000 v. 04.02 1 I . Stang, H., Olesen, J.F., On the interpretation of bending tests on FRC materials. In: Fracture Mechanics of Concrete Structures, Proceedings FRAMCOS-3, vol. I . H. Mihashi and K. Rokugo eds. Aedificatio Publishers, Freiburg, Germany 1998 pp 5 I 1-520
12. Shah, S.P., Swartz, S.E., Ouyang, C., Fracture Mechanics of Concrete. John Wiley & Sons, Inc., New York-Chichester-Brisbane-Toronto-Singapore I995
13. Tada, H., Paris, P.C., Irwin, G.R., The Stress Analysis of Cracks Handbook, 2'ld ed. Paris Productions, St. Louis, MO 1985 14. Lawler, J.S., Hybrid Fiber-Reinforcement in Mortar and Concrete. Ph.D. Dissertation, Northwestern University, Evanston, IL 2001
Proc. Int. Symp. ,,BrittleMatrix Coniposites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
THE CRACKING BEHAVIOUR OF SFRC BEAMS CONTAINING LONGITUDINAL REINFORCEMENT David DUPONT, Lucie VANDEWALLE Department of Civil Engineering Catholic University of Leuven Kasteelpark Arenberg 40,300 1 Heverlee, Belgium, e-mail: David. Uupont(a)bwk.kuleu ven,ac .be ABSTRACT Durability of concrete is in a great extent determined by the crack widths that are formed in the structure and that allow water to infiltrate in the concrete so that corrosion of the reinforcement bars can occur. The analysis of the cracking behaviour in concrete has always been a topic of interest for investigation by many scientists. In general it is assumed that the durability of the structure is assured when the crack widths are limited to 0.3 mm. One of the often-used approaches to limit the crack widths is the use of steel fibre reinforced concrete (SFRC). Steel fibre concrete is generally known to reduce crack widths because of its postcracking tensile strength. At the Department of Civil Engineering of the Catholic University of Leuven, Belgium, a test program has been executed on 19 full-scale SFRC beams containing longitudinal reinforcement. All beams have been tested in four-point bending. The tests were performed in different load steps until failure of the beam. The load steps were chosen so that the beams failed after 10 to 15 steps. At each load step the crack widths and spacing were measured. The results of the test program illustrate the strong beneficial effect of steel fibres on the crack widths as well as on the crack spacing. The addition of fibres to the concrete can lead to a reduction of the crack width of up to 40%. The crack widths of the beams of the test program have been calculated by means of the new Rilem guideline as well as with a newly developed physical cracking model for reinforced SFRC beams. The physical model takes into account the bond between the reinforcement bars and the SFRC matrix as well as the influence of the steel fibres on the stress in the reinforcement bars. A comparison of the calculated results and the experimental results shows that there is a relatively good correlation between the two. The input parameters for the calculation model are the concrete compressive strength, the dimensions of the beam, the position and diameter of the reinforcement bars, the tensile strength and the post-cracking tensile strength of the SFRC material and the bond stress-slip relation. The new calculation model provides a very good understanding of the crack formation process. It also creates the possibility to determine for example the necessary post-cracking strength of the SFRC, given that the crack width of the beam must be lower than a certain value. Furthermore, also the influence of the bond stress-slip relation can be taken into account. This creates the possibility to use the crack model for other types of reinforcement than steel rebars (e.g. GFRF' rebars).
254
David DUPONTand Lucie VANDEWALLE
INTRODUCTION It is generally known that steel fibres are a possible way to limit crack widths and enhance the durability of a structure. Crack widths have to be controlled, since if they become too large, it becomes easy for water and other aggressive agents to penetrate into the concrete. This in turn can lead to corrosion of the reinforcement and a fast degradation of the structure. To control the crack width in an economical way, a good calculation method is needed. The formation of cracks is influenced by a large number of parameters. The most important are the dimensions of the cross section, the bond stress-slip relation, the tensile strength and the post-cracking tensile strength. Several calculation methods can be found in literature. These can be divided into semi-empirical relations and physical models. The semi-empirical relations [I, 2, 3, 4, 51 are mostly validated with a large number of experimental results. On the other hand, they can only be applied with great caution for applications in which one of the influencing parameters falls outside the reach of the original collection of experimental results used to derive the empirical relation. To counter this problem, several physical models have been developed [6, 7, 81. These physical models should have the advantage that the influencing parameters are taken better into account, so that the physical model can be extrapolated more safely to other applications. However, after a literature review, the authors have found that most existing physical models are a strong simplification of the reality. Important influencing parameters are often not at all recognised or not taken into account in a proper way. For this reason, the authors have developed a new physical cracking model.
SEMI-EMPIRICAL CALCULATION METHOD The semi-empirical method used in this paper has been first proposed by [S] and later taken over as design recommendation by Rilem TC162-TDF. The method is based on the method of Eurocode 2 [4], with a few small changes to incorporate the influence of the steel fibres. The crack width is calculated as:
= average steel strain;
where ,s,
= average
final crack spacing.
They can be calculated as:
where:
p I is a coefficient to take into account the bond properties of the reinforcing steel; p l is a coefficient to take into account the duration of the load; osis the stress in the reinforcement calculated on the basis of a cracked section (Fig. 1);
The cracking behaviour of SFRC beams containing longitudinal reinforcement
255
osris the stress in the reinforcement calculated on the basis of a cracked section at the moment of cracking (Fig. 1); kl is a coefficient that takes into account the bond properties of the reinforcing bars; k2 is a coefficient that takes into account the f o i p of the strain distribution; 4 is the bar diameter; Lr / dr is the aspect-ratio of the fibre; pr is the effective reinforcement ratio = A, I ACe6 is the concrete section surrounding the tensile reinforcement up to a height of 2.5 times the distance of the centre of the reinforcement to the most stretched fibre.
through the steel stresses osand cssr For the crack The fibres have an influence on spacing the fibres are taken into account by the factor 50 / (Lr I dr). The boundary condition however is that the aspect-ratio is larger than or equal to 50.
---I---\
Figure 1. Stress distribution in a cracked section for plain concrete (a) and SFRC (b).
PHYSICAL CRACKING MODEL The new physical model is made in two steps. In the first step the anchorage length and the crack spacing are calculated. The second step then uses the crack spacing to calculate the crack width for a series of bending moments. Calculation of the average final crack spacing For the calculation of the anchorage length, a part of a beam between a cracked section (section 2) and a section that is just about to crack (section 1) is considered. In section 1 a tensile strength is assumed equal to I .2 times the experimentally determined flexural tensile strength fct,n,while in section 2 a tensile strength is assumed equal to 0.8 times fct,n. This is to take into account the scatter on ths,flexural tensile strength. The position of the neutral axis can be calculated exactly in section 1 and 2. For sections in between it is assumed that the neutral axis is constant over a small distance and evolves stepwise from section 1 to section 2, proportional with the slip 6 between reinforcement and concrete. An important parameter is the post-cracking tensile strength of.It is proposed by the authors to take this equal to 0.39 x fRI [9]. fRI is the residual flexural tensile strength determined on a Rilem 3-point bending test [ 101. The steel strains and concrete strains can be calculated in section 1 and section 2 using a static equilibrium of axial forces and bending moments.
256
David DUPONTand Lucie VANDEWALLE
Skss DistfituUon
Seerion I
secrwn 2
(Cracked)
(Uncmckd)
L
I-
I
Fs
i
4-
. .
cc
F, + dF,
ccc
Figure 2. Beam part between a cracked sechon and a section that is just about to crack. One of the most important parameters in the model is the bond stress-slip (r-6) relation. This is taken as [l I]:
where: T =bond stress; 6 = slip; p and h are shape factors. T~~~ = maximal bond stress. For small concrete covers (c < 34), a splitting failure is likely to occur; in this case rmax can be determined as: 1+(1-K).0.3535 ri
1
with c=(rU-q)and4=2ri
K,f. fc
where: ru = distance between the centre of the reinforcement bar and the side of the beam. fct= axial tensile strength. Recent research [ 121 has shown that p is dependent on the fibre dosage and concrete cover, while h is only dependent on the concrete cover. It was shown that for the concrete cover used in this test program, h can be taken equal to 8.25/mm, while p is equal to 0.782
The cracking behaviour of SFRC b e a m containing longitudinal reinforcement
257
for plain concrete and equal to 0.883 for a fibre dosage of 60 kg/m3. For smaller fibre dosages an interpolation is done. The strain in the reinforcement bar is composed of two contributions. The first contribution is the strain in the surrounding concrete, while the second contribution is due to the slipping of the reinforcement bar relative to the surrounding concrete: €, =.5,-+-
d-z
d6(x)
Y
dx
If the horizontal equilibrium of a small part of the reinforcement bar is considered (Fig. 2), the following relation can be found:
where A, = reinforcement section; $ = bar diameter; E, = Young's modulus of steel. By using a static equilibrium of normal forces and bending moments for a section, the strain E~ can be written in fimction of E ~ .If this is then substituted in equation (6), and after that equation (6) is derived for x, then the following differential equation can be found using equations (4) and (7):
The solution of this differential equation is found numerically by using the following boundary conditions:
where: E , ~and are the strains in section 1 in the steel reinforcement, the bottom fibre of the beam, respectively. For the calculation of the anchorage length, the beam is loaded with the cracking moment. In this case the second boundary condition is equal to 0 (the steel strain is equal to the strain in the surrounding concrete).
258
David DUPOhTand Lucie VANDEWALLE
The solution of equation (8) gives the slip 6 as a function of x. From this also the bond stress T can be found as a function of x (equation 4). The length L of the model (Fig. 2) can now be determined by considering the global static equilibrium of horizontal forces of the reinforcement bar:
Once the length L is known, it is assumed that this is the minimal crack spacing and that the maximum crack spacing is equal to 2L. The average crack spacing would then be equal to 1.51,.
Calculation of the average crack width at different bending moments. To calculate the average crack width, the length of the model is taken equal to 0.75L (Fig. 3). The position of the neutral axis in section I is assumed at the same level as in the cracked section 2. The calculations have shown that if a slightly different position of the neutral axis is assumed, this only has a negligible effect on the value of the calculated average crack width.
4--. .
I
F, I
ES&A Figure 3. Beam part between a cracked section and a section that liesjust in the middle of two cracks.
The cracking behaviour of SFRC beams containing longitudinal reinforcement
259
In doing this it can no longer be assumed that the strain Etl is equal to the strain at cracking. , Etl are now determined using a static equilibrium of axial Therefore the strains ~ ~ ~~l1 and forces and bending moments in section 1 and using equation (lo), where the integration is now only done up to 0.75L. The crack width is now found as two times the slip 6 in section 2. EXPERIMENTAL PROGRAM To validate the physical model, a test program was executed at the Department of Civil Engineering of the Catholic University of Leuven (Belgium). The test program involved 19 4-point bending tests (Fig. 4) on full-scale SFRC beams containing longitudinal reinforcement. All beams had a cross section of 200 mm x 300 mm. The span of all beams was equal to 2300 mm. The investigated parameters were the fibre dosage (0 kg/m3, 20 kg/m3, 40 kg/m3 or 60 kg/m3), the fibre type (RC 65/60 BN, RC 80/35 BN or RL 45/50 BN), the reinforcement ratio and bar diameter (3 Cp 20 or 3 Cp 16). The tests were load-controlled. The load was applied in 10 to 15 steps until failure (mostly shear failure). After each load step, the load was registered together with the deflection, the strain on top and at the bottom of the beam as well as the crack widths in the zone between the load points. The measurement of the crack width was done at 1 cm above the bottom of the beam with a small, calibrated microscope. The accuracy of the microscope was k 0.02 mm. Furthermore, due to the freaky shapes of the crack, it was sometimes difficult to decide on the crack width. Also the smallest crack that could be detected had already a width of at least 0.02 to 0.03 mm. All smaller cracks could therefore not be detected and not used for the calculation of the average experimental crack width. For all these reasons the authors state that, although the measurements were taken with great care, caution is needed when the experimental results are analysed.
Figure 4. Test set-up for the full-scale beams. Together with each full-scale beam, 8 small Rilem beams were cast to perform a 3point bending test for the characterisation of the post-cracking tensile strength. Also 10 cubes were cast to measure the compressive strength. The experimental results of the crack widths were compared with values predicted by means of the proposed physical model as well as with calculations made with the semi-
260
David DUPONT and Lucie VANDEWALLE
empirical method proposed by Rilem TC162-TDF [5]. The results of the calculations can be seen in Figures 5-7.
No Fibers, 3 4 20
No Fibers, 3 I$ 16
-
0.2
x
I 20 40 60 80 100 Bending Moment (kNm)
0
0
I 20 40 60 80 100 Bending Moment (kNm)
0
Experimental crack width
0
Experimental crack width
-
-Rilem TC162-TDF - - .Physical model
Rilem TC162-TDF
- - .Physical model
Figure 5. Comparison between experimental results and calculations for plain concrete.
-'/I
20 kglm' RC 65/60 BN, 3 4 16
20 kglm' RC 65/60 BN, 3 I$ 20
0.2 T
-
I
g5 Y
Oa2
T
0.15
0.1
! 0.05
0
v
P
P
.Q
0
0
20
40
60
80
100
20 40 60 80 100 Bending Moment (kNm)
0
Bending Moment (kNm) Experimental crack width -Rllem
TC162-TDF
- - .Physical model
0
Experimental crack width
-RilemTCl62-TDF - - *Physicalmodel
Figure 6. Comparison between experimental results and calculations for SFRC with 20 kg/m3 fibres.
The cracking behaviour of SFRC be am containing longitudinal reinforcement 60 k g l d RC 65/60 BN, 3 4 20 0.2
26 1
60 kglm' RC 65/60 BN, 3 4 16
T
-
-5 2
0.2
T
0.15 0.1
*u
2 0.05
0
20
0
40
60
80
100
0
20
0
Experimental crack width
-Rilem
40
60
80
100
Bending Moment (kNm)
Bending Moment (kNm) 0
Experimental crack width
-Rilem TCl62-TDF - - 'Physical model
TCl62-TDF
- - .Physical model
Figure 7. Comparison between experimental results and calculations for SFRC with 60 kg/m3 fibres.
CONCLUSIONS A completely new physical model has been developed to simulate the cracking behaviour of steel fibre reinforced concrete beams containing longitudinal reinforcement. The most important input parameters of the model are the bond stress-slip relation, the tensile strength of the concrete and the post-cracking tensile strength. To validate the model a test program was carried out involving 19 4-point bending tests on full-scale beams. The investigated parameters were the reinforcement ratio, the fibre dosage and the fibre type. The experimentally determined crack widths are compared to calculations done with the proposed physical model as well as with predictions done with the calculation method proposed by Rilem TC162-TDF. The comparison shows that both calculation methods provide relatively good predictions of the average crack width. Since the semi-empirical Rilem method is by far the easiest calculation method of the two, the authors think that this method is the most suited method for standard calculations. For special applications however (glass fibre reinforcement or CFRP sheets), the proposed physical model can be of great interest. The influence of a different bond stress-slip relation can be taken correctly into account.
ACKNOWLEDGEMENTS A part of this study is done in the framework of the Brite Euram project "Test and Design Methods for Steel Fibre Reinforced Concrete", contract no BRPR-CT98-08 13. The partners in the project are: N.V. Bekaert S.A. (Belgium, coordinator), Centre Scientifique et Technique de la Construction (Belgium), Katholieke Universiteit Leuven (Belgium), Technical University of Denmark (Denmark), Balfour Beatty Rail Ltd. (Great Britain), University of Wales Cardiff (Great Britain), Fertig-Decken-Union GmbH (Germany),
262
David DUPONTand Lucie VANDEWALLE
Ruhr-University-Bochum (Germany), Technical University of Braunschweig (Germany), FCC Construccion S.A. (Spain), Universitat Polytkcnica de Catalunya (Spain).
REFERENCES 1 . ACI Committee 3 18: Building code requirements for structural concrete (ACI 3 18-95) and commentary (ACI 3 18-95R), American Concrete Institute, Farmington Hills, Michigan 1995 2. Frosch, R.J., Another look at cracking and crack control in reinforced concrete, ACI Structural Journal, Vol. 96 (3), 1999, pp 437-442 3. Frosch, R.J., Modeling and control of side face beam cracking, ACI Structural Journal, Vol. 99 (3), 2002, pp 376-385 4. ENV 1992-1- 1: 199 1 Eurocode 2, Design of concrete structures-part 1 : General rules and rules for buildings, 1991 5. Vandewalle, L., Cracking behaviour of concrete beams reinforced with a combination of ordinary reinforcement and steel fibers, Materials and Structures, Vol. 33,2000, pp 164-170. 6. Al-Taan, S.A., Al-Feel, J.R., Predictions of crack width in fibrous reinforced concrete members. Fibre Reinforced Cements and Concretes: Recent Developments, Elsevier Science Publishers Ltd.: Essex (UK), 1989, pp 209-218 7. Tan, K-H., Paramasivam, P.& Tan, K-C., Cracking characteristics of reinforced steel fibre concrete beams under short- and long-term loadings, Advanced Cement Based Materials, Elsevier Science inc., Vol. 2, 1995, pp 127-137 8. Padmarajaiah, S.K.& Ramaswamy, A., Crack-width prediction for high strength concrete fully and partially prestressed beam specimens containing steel fibres, ACI Structural Journal, Vol. 98 (6), 2001, pp 852-861 9. Dupont, D. & Vandewalle, L., A practical proposal to derive a stress-strain relation with residual tensile strengths, Annex 5.1.3 of Subtask 3.1 of the Brite Euram project BRPRCT98-0813 “Test and design methods for SFRC”, June 2002, ISBN. 90-5682-358-2. 10. Rilem TC162-TDF 2002, Test and design methods for steel fibre reinforced concrete: Bending test, Materials and structures, Vol. 35,2002, pp 579-582 11. Vandewalle, L., Bond between reinforcement and concrete in normal and cryogenic circumstances (in Dutch), Doctoral thesis, Catholic University of Leuven (Belgium), 1988 12. Dupont, D., The use of steel fibres as reinforcement in structural concrete, Doctoral thesis, Catholic University of Leuven (Belgium), 2003.
Proc. Int. Symp. ,.Brittle Matrix Composites 7” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-1S, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
TENSILE BEHAVIOR OF A RECYCLED CONCRETE Hiroshi AKITA, Hideo KOIDE and Mitsuo OJIMA Tohoku Institute of Technology 35-1 Yagiyama Kasumicho, Taihaku-ku, Sendai 982-8577, Japan e-mail:
[email protected] ABSTRACT Tensile behavior of such a recycled concrete in which all the components were reused fine and coarse aggregates after simple crushing was studied. For compressive strength and durability the recycled concrete was already confirmed to be almost equivalent to the original concrete when the water to cement ratio was by 5% lower than original one. The uniaxial tension test showed that tensile strength and fracture energy were reduced considerably in the case of the recycled concrete even though it had the same level as the original concrete in compression and durability Keywords Recycled concrete, tensile strength, fracture energy, uniaxial tension, tension softening
INTRODUCTION
In order to use concrete materials effectively and save space for waste materials, used concrete should be reused as recycled concrete. When used concrete is recycled, it is not a good solution to use much labor or energy for removing mortar from coarse aggregates or throw away fine particles in order to get high quality aggregates. The authors have made a recycled concrete in which all the used concrete was reused as fine and coarse aggregates after simple crushing. For the recycled concrete, it has been confirmed to be almost equivalent to the original concrete in compressive strength and durability when the water to cement ratio was by 5% lower than original in one, [I]. The main purpose of the present study is to examine tensile
264
Hiroshi AKITA, Hide0 KOIDE and Mitsuo OJIMA
behavior of the recycled concrete in comparison with the original one. The original concrete was cast and examined by uniaxial tension and other tests to compare its properties before and after recycling. Then the concrete was exposed outdoors for two years in order to make a kind of used concrete. Then the concrete was simply crushed and used as both fine and coarse aggregates. Due to the high amount of mortar attached to the original coarse aggregates, the ratio of recycled coarse aggregates was relatively high. Natural sand was added to balance the sand percentage neglecting the attached mortar. The recycled concrete was examined in the same way as the original concrete. The uniaxial tension test showed that tensile strength and fracture energy were reduced considerably in the case of the recycled concrete. The main reason was estimated to be the relatively small ratio of original coarse aggregates. This was confirmed by the observation of the broken cross-sections where a small number of original coarse aggregate grains were found. Thus, the recycled concrete using additional sand and simply crushed concrete as aggregates was inferior to the original concrete in tensile behavior even though it had the same level in compression and durability.
EXPENMENTAL PROCEDURE The original concrete was cast with mix proportions shown in Table 1. The original concrete was examined by uniaxial tension and other tests and then exposed outdoors for two years before being recycled. The concrete was simply crushed using 30mm and 20mm size crushers without much labor and energy to remove mortar or fine particles. Crushed concrete by the 30mm crusher was sieved and only the particles larger than 20mm were crushed secondarily by the 20mm crusher. The particles larger than 5 mm were used as coarse aggregates and all the remaining were used as fine aggregates. The ratio of recycled coarse aggregates was relatively large, because of the high amount of mortar attached to the original coarse aggregates. Fresh sand was added to balance the sand percentage neglecting the attached mortar. The resulting mix proportions of the recycled concrete are shown in Table 2, adopting by 5% lower amount of water to cement ratio than in original one. Table 1 Mix proportions of original concrete Unit content (kglm’)
Water cement Ratio
Cement
Aggregates
Chemical admixture
0.019
265
Tensile behavior of a recycled concrete
Table 2 Mix proportions of recycled concrete Unit content (kg/m’)
Water cement
Chemical
Ratio
0.0 I 9
The uniaxial tension test was performed by eliminating secondary flexure, using the gear system originally designed by the authors, [ 2 ] . It is essential to eliminate the secondary flexure in order to obtain exact behavior of concrete in the uniaxial tension test. Manual operation of the gear systems was used for the original concrete, whereas automatic controlled gear systems were used for the recycled concrete. Fig. 1 shows the experimental set-up using the automatic controlled gear systems. The specimens were cast in the form of prisms of 100x100x400mm with notches in the center on four laterals as shown in Fig. 2 .
Guide notch
Extensometer
400
Unit: mm
Fig. 1 Experimental set-up
Fig. 2 Prismatic specimen
RESULTS AND DISCUSSIONS Fig. 3 shows the load-deformation curve (P-6 curve) of the original concrete. A smooth curve was obtained despite the elimination of secondary flexure by manual operation. The specimen has reached the peak load equal to 22.5 kN but the first crack appeared near the load of 2 kN.
266
Hiroshi AIUTA, Hide0 KOIDE and Mitsuo OJIMA
Fig. 4 shows the load-deformation curve of the recycled concrete. A complete curve was obtained until the applied load became almost zero. The applied load slightly decreases and increases around peak. This vibration was sometimes observed in the recycled concrete, but hardly observed in the original concrete.
__
I
20?
215: v
a
.
10: 5-
Fig. 4 Load-deformation curve (recycled concrete)
Fig. 3 Load-deformation curve (original concrete)
Fig. 5 shows four tension softening curves (G-w curves) for the original concrete. All specimens were broken around the applied load of 2kN. This was usual when the manually operated gear systems were used for eliminating secondary flexure. Some curves are not smooth and vibrating at times. This shows that secondary flexure was not eliminated smoothly by manual operation. 3.5
3.5 3
3
2.5
2.5
!& v
R
2L 1.5
b. 1
..j
2
1
. . . . . . . . . . .
b
I
\.
\.
. . . .. . . . . . . . .
0.5 0
-
0.5
; . .
-......._. ..__ __ .--.----.
0
0.05 0.1
0.15 0.2 0.25
w (mm) Fig. 5 Tension softening curves (original concrete)
1.5 1 0
.3 0.
0
0.05
0.1
0.15
0.2
0.25
w (mm) Fig. 6 Tension softening curves (recycled concrete)
0.3
267
Tensile behavior of a recycled concrete
Fig. 6 shows four tension softening curves for the recycled concrete. The descending slopes of these curves at the beginning are steeper than those of original concrete shown in Fig. 5. Fracture energy expressed by the area under each softening curve is estimated smaller than that of original concrete. All curves are smooth because of the use of the automatically controlled gear systems. Fig. 7 shows the tensile strengths of the original and recycled concrete with respect to the same four specimens shown in Fig. 5 and 6 . They are presented in descending order. Tensile strength is clearly reduced by recycling.
I
#
1
#
2
#
3
#
4
Specimen
Fig. 7 Tensile strength
#
1
#
2
#
3
#
4
Specimen
Fig. 8 Fracture energies
Significant reductions were found in fracture energies of recycled concrete in comparison with the original concrete as shown in Fig. 8. These reductions can be easily expected after comparison of Fig. 6 and 5. The four points from respective specimens are presented in the same order as Fig. 7. However, they are not always in descending order. It means that large tensile strength does not correlate to large fracture energy.
Fig. 9 Broken cross-section (Original concrete)
Fig. 10 Broken cross-section (Recycled concrete)
268
Hiroshi AKITA. Hide0 KOIDE and Mitsuo OJIMA
Both faces of the broken cross-sections are shown in symmetry in Fig. 9 and 10, correlating to the original and recycled concrete specimen, respectively. In Fig. 9, relatively large numbers of original coarse aggregate grains are found and most of them exhibit symmetrical figures, which express that they were broken without coming out. On the other hand, a relatively small numbers of original coarse aggregates can be found in Fig. 10. The small numbers of the original coarse aggregate grains are considered to be one reason of the low fracture energy of the present recycled concrete.
CONCLUSIONS The recycled concrete made with simply crushed concrete as both fine and coarse aggregates with additional sand was inferior to the original concrete in tensile behavior, even though it had the same level in compression and durability. The main reason for the low fracture energy of the recycled concrete is considered to be the relatively small ratio of original coarse aggregates.
REFERENCES 1. Kitazume, Y., Akita, H. and Tomon, M., “A recycle of used concrete intending zero emission”, Proc. Japan Concrete Institute, V01.2 1, No. 1, 1999, pp. 145- 150. (in Japanese) 2. Akita, H., Koide, H., Sohn, D. and Tomon, M., “A testing procedure for assessing the uniaxial tension of concrete”, ACI International, SP-201, 200 1, pp. 75-91. 3. ACI Committee, “Removal and reuse of hardened concrete”, ACI Mater. J., Vo1.99, No.3, 2002, pp.300-325.
Proc. Int. Symp. I, Brittle Matrix Composites 7” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
TOUGHENING MECHANISMS IN CONCRETE: INFLUENCE OF AGGREGATE TYPE Wastimil B ~ L E K Testing Laboratory of Building Materials ZPSV Uhersky Ostroh, a s . Kudelova 8,602 00 Brno, Czech Republic, e-mail:
[email protected] ZbynCk KERSNER, Pave1 SCHMID Faculty of Civil Engineering, Institute of Structural MechanicdTesting Laboratory Brno University of Technology VeveiY 95,662 37 Brno, Czech Republic, e-mail:
[email protected], schmid,p@fce,vutbr.cz
ABSTRACT The paper is concentrated to identification of the toughening mechanisms of concrete with different type of aggregates and to development/change of these mechanisms during the first months of curing. Concretes with addition of three types of aggregates - river gravel, lightweight aggregate (LiaporB) and glass “aggregates” - were submitted to fracture tests at the ages of 7, 28 and 90 days. The mortadmatrix was also prepared and tested. The self-curing effect of pre-wetted Liapor aggregates was also studied. Keywords Concrete, fracture toughness, fracture energy, glass, light-weight aggregate, toughening mechanisms.
INTRODUCTION It is well known, cement paste shows nearly brittle fracture, while concrete shows significant non-linear behaviour. That is, some toughening mechanisms are active and they control tension softening of these cement-based materials. Four of them are very important distributed interfacial cracking, crack deflection, crack bridging and trapping. The importance of the mechanisms is very strongly influenced by properties of aggregates. On the other hand - shrinkage (especially self-desiccation) affects mechanical properties and especially fracture properties of High Performance Concrete (HPC). To avoid this influence self-curing can be applied. The self-curing can be performed using pre-wetted lightweight aggregates. But these aggregates have poor mechanical properties and they can decrease the mechanical properties of HPC.
270
Vlastirnil BiLEK, Zbyngk KERSNER and Pave1 SCHMID
TOUGHENING MECHANISMS IDENTIFICATION The impact of various toughening mechanisms on fracture parameters of cement-based composites was monitored. The mathematical models by Lange-Kornbak [ l ] based on Li [2] were used. These models can work with the concrete/matrix fracture toughness ratio (rlheor). The effective crack model of Karihaloo and Nallathambi (see e.g. [3]) was used for the determination of effective fracture toughness KlCeof the studied composites and matrix. Thus it is possible to distinguish four toughening mechanisms (M) controlling tension softening: The distributed interfacial cracking (microcracking; with notation A , i.e. MA),crack deflection (MB), crack bridging (Mc) and trappin (MD). In a symbolic way we can write K/cenconcrele/ I/.? K/ce,motrrr = (MA. MB . (Mc+ MD)) . Input variables of these models are summarised in Table 1.
Table 1 Input variables of toughening mechanism models
Variable Unit aggregate content Density of aggregate Poisson’s ratio of matrix Poisson’s ratio of composite Average aggregate size Maximum size of coarse aggregate Fracture toughness of matrix Uniaxial tensile strength of aggregate
Model of mechanism A, B, C, CD A, B, C, CD A, C, CD A, C, CD Mm C, CD Mm C, CD MPa.m’” C, CD C, CD MPa Unit Kg kg/m3
Aggregates: Glass, Liapor, Gravel 1061,350, 1080 2560,850,2600 0.22 0.22, 0.15, 0.22 8,6,6 8, 8, 8 See Table 3 50, 1.1, 10
The theoretically obtained values of the ratio r,heor were compared with the measured value rleslobtained from tests of concrete and matrix (mortar) specimens. This procedure was
repeated for each age of composite. It enabled the distinction of different toughening mechanisms controlling the fracture at different ages. The authors have applied this approach to various types of cement [4].
MATERIALS, MIX PROPORTIONS AND CURING ENVIRONMENTS Three concrete mixtures were prepared by using different types of aggregates - see Table 2 for details of mix proportions. The sand was river sand 0-4 mm in all the mixtures. Glass spheres 8 mm in diameter were used as aggregate. The volume occupied by the glass aggregates is 414 1. The same volume was occupied by lightweight aggregates in the next mixture. The aggregates were produced by expanding clays and they have trade name LiaporB. The fraction of Liapor 4-8 mm was used. Finally, river gravel 4-8 mm was used. Portland cement CEM 142.5 R (EN 197) was used in combination with drinking water and a superplasticizer based on polycarboxylates. The lightweight aggregates are very moisture absorbent and for this reason they were immersed in water 7 days before making of the concrete mix. The water was added to achieve a constant workability (slump 80 20 mm) during mixing.
*
27 1
Toughening mechanisms in concrete: injluence of aggregate type
1
Table 2 Mix proportions (in kg/m3)
CEM 142.5 R Water Superplasticizer Sand 0-4 mm Glass balls 8 mm Liapor 4-8 mm (dry) Gravel 4-8 mm
I
I (Matrix)
Mortar
Glass
I
785 2f
460 ;1
1280
750 1061
-
Liapor
Gravel
460 140;80
460
750
750
1;10 -
350
1080
Concrete and mortar beams 65x65~360mm (depthxwidthxlength) were made for fracture tests. The specimens were stored in foil to avoid moisture exchange with the environment. The effective fracture toughness K/o (and also modulus of elasticity) [3] was determined for ages of specimens 7, 28 and 90 days. Because the load-deflection diagram was continuously recorded, the fracture energy GFcan be computed from the area below this curve [5].
RESULTS AND DISCUSSION Results of fracture tests for three different series are presented: values of modulus of elasticity (Fig. l), values of effective fracture toughness (Fig. 2; Table 3) and values of fracture energy (Fig. 3). Mean values and coefficients of variation are depicted in all these figures. The fracture toughness ratios from tests are given in Table 4 - mean values f standard deviations. The theoretical fracture toughness ratios are presented in Tables 5-7 (possible toughening mechanisms are highlighted). There are different tendencies in fracture toughness and fracture energy development. We can see some decrease of the values for glass and gravel. It is a consequence of shrinkage of the hardening cement paste. Between 28 and 90 days there is significant self-desiccation, because the hydrating cement grains consumed a lot of water. The self-desiccation affects shrinkage and microcracking of the paste. If larger aggregate were used in a previous study, the decrease of fracture toughness and fracture energy were more conspicuous [6] and for this reason we believe that differences in constant volume of aggregates and shrinking paste can control the decrease. But in the present experiments there is small size of maximum aggregate and only shrinkage of the paste can control the decrease. Fracture parameters show lower values for Liapor, but the values don’t decrease between 28 and 90 days. This is a consequence of self-curing of the concrete from the side of lightweight saturated aggregates. The low values of fracture parameters of glass aggregate concrete are very conspicuous. There are not any other toughening mechanisms except microcracking at the interface. Maybe the interface is very weak, because the surface of aggregates is smooth and the glass is not alkali resistant. The Liapor has lower mechanical properties than natural gravel or glass. For this reason no toughening is recorded. The mortar from natural sand has higher values of fracture parameters and Liapor aggregates cause their decrease. A wider study is conducted to investigate the optimum proportion of Liapor coarse aggregate to Liapor fine aggregate.
272
Vlastimil BiLEK, Zbyngk KERSNER and Pavel SCHMID
-
0 Glass COV Glass
0 Liapor 0 COV Liapor
Gravel
El COV Gravel
1
n
1
90
7
Fig. 1 Modulus of elasticity vs. age for different aggregate type OGlass
- OCOV Glass
0 Liapor
aGravel 50
OCOV Liapor
40
F Y
C
.-0 Y
30 .E! 2 LI-
0
20
.-al
g
10
0 7
28
90
Age [days]
Fig. 2 Fracture toughness vs. age for different aggregate type
4
273
Toughening mechanisms in concrete: influence of aggregate type
-
UGlass 0 COV Glass
Liapor 0 COV Liapor
1
80
z
-
3
Y
60
v
30
x
P 5
40
2 =l
Y
U
d
’
20
0
90
Fig. 3 Fracture energy vs. age for different aggregate type
Age [days] 7 28 90
Effective fracture toughness [MPa.m”’] Matrix Glass Liapor Gravel 0.620k0.14 0.686k0.04 0.55 1k0.05 0.870k0.16 0.695k0.02 0.702*0.0 1 0.469k0.04 1.027k0.16 0.460*0.05 0.990k0.15 0.805rt0.07 0.632k0.17
Table 4 Fracture toughness ratio from tests Glass 1.163k0.27
[-I Liapor 0.934k0.23
Gravel 1.475-10.43
1.01 1k0.03
0.675k0.06
1.479k0.23
0.79 1k0.22 0.571 + 1.011)
0.576rt0.08 (0.496 - 0.656)
1.239k0.22 (1.0191 1.459)
rlesl
Age [days] 7
.zx
274
Vlastimil BILEK, Zbyn6k KERSNER and Pave1 SCHMID
7 days
3.513 3.696 3.750 4.039 4.098 4.31 1 4.71 1
28 days
CD AC BC ACD BCD ABC ABCD
3.23 1 3.338 3.387 3.714 3.769 3.893 4.332
90 days
CD AC BC ACD BCD ABC ABCD
2.923 2.939 2.983 3.361 3.410 3.429 3.92
CD AC BC ACD BCD ABC ABCD
Table 6 Theoretical fracture toughness ratio (dimensionless) - Liapor aggregate
7 days
2.487
ABCD
I
2.466
-
90 days
28 days
ABCD
I
2.445
ABCD
Toughening mechanisms in concrete: influence ofaggregate type
275
From the viewpoint of toughening mechanisms, only MA and MBare active for glass balls (see also [7]), especially at the age of 7 days. At 90 days the fracture toughness and fracture energy are lower than for mortar. The weak interface and smooth surface of glass balls affect this behaviour. A similar situation occurs for concrete with Liapor aggregates at age of 7 days. The lowest fracture toughness ratio was recorded for Mc mechanism. All of the Liapor grains on the fracture surface were broken and it is in good accordance with Mc.As the fracture toughness of mortar increases and fracture toughness ratio decreases, there are no indications of toughening at 28 and 90 days. The combination of MA,MBand MCcontrols the toughening of concrete with natural gravel at ages of 7 and 28 days. At the age of 90 days the hardened cement paste around of aggregates is microcracked. For this reason only two mechanisms (iM,, and Mc or MB and Mc) affect the toughening.
CONCLUSIONS The same mechanisms were identified for aggregate with high strength but very smooth surface and for lightweight, low-strength aggregates. However, as natural gravel does not have high strength or a relatively smooth surface, significant toughening is induced by the aggregates (irregular grains). There are some indications of self-curing in the long-tern1 development of fracture characteristics.
ACKNOWLEDGEMENTS The authors thank for funding under grant No. 103/03/1350 from the Grant Agency of the Czech Republic and under the research project reg. No. CEZ: 53-2/98: 261 100007. Financial support of railway sleepers producer, APSV Uhersky Ostroh, a s . , Czech Republic, is also grateful 1y appreciated.
REFERENCES I . Lange-Kornbak, D., Karihaloo, B. L., Design of concrete mixes for minimum brittleness. Advanced Cement Based Materials, No. 3, 1996, pp 124-1 32 2. Li, V. C., Huang, J., Relation of concrete fracture toughness to its internal structure. Engineering Fracture Mechanics, Vol. 35, No. 1/2/3, 1990, pp 39-46 3. Karihaloo, B. L., Fracture mechanics of concrete. Longman Scientific & Technical, New York 1995 4. KerSner, Z., Bilek, V., Influence of microstructure on toughening mechanisms of concretes. Engineering Mechanics, Vol. 5 , No. 3., 1998, pp 199-201 5 . Elices, M., Guinea, G. V., Planas, J. On the measurement of concrete fracture energy using three-point bend tests. Materials and Structures, Vol. 30, 1997, pp 375-376 6. Bilek, V., KerSner, Z., Schmid, P., Mosler, T., The toughness of concrete is not interesting for us, unless it loses it. In: Proc. Int. Symp. Non-Traditional Cements and Concrete, Brno 2002, pp 424-435 7. Merchant, I. J., Macphee, D. E., Chandler, H. W., Henderson R. J., Toughening cementbased materials through the control of interfacial bonding. Cement and Concrete Research. 31,2001, pp 1873-1880
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
FAILURE OF NORMAL AND HIGH STRENGTH CONCRETE UNDER MONOTONIC AND CYCLIC TENSILE LOADING Christoph KESSLER-KRAMER*, Viktor MECHTCHERINE and Harald S. MUELLER Institute of Concrete Structures and Building Materials, University of Karlsruhe, Germany * now: Deutsche Bahn AG (German Railway Construction Inc.), 76139 Karlsruhe, Germany e-mail:
[email protected] ABSTRACT In this investigation the fracture of normal and high strength concrete under monotonic and cyclic tensile loading was studied in order to describe its softening behaviour on the basis of fracture mechanical conceptions. A series of deformation controlled uniaxial tensile tests on notched and unnotched concrete prisms was carried out. The main parameters in the experiments were the number of cycles to failure, the deformation rate, the concrete grade and the curing conditions. Additionally, the fracture surfaces were studied using projected fi-inges technique in order to gain a more detailed glance on the formation and propagation of cracks under tensile loading conditions. The experimental results show in particular that with an increasing number of load cycles the uniaxial tensile strength decreases. Further, for an increasing number of load cycles the corresponding envelope curves differ significantly from the monotonic curve. This clearly shows that the conventional fissumption of a unique envelope curve for the fatigue behaviour of concrete is admissible only for a low-cycle fatigue loading, but cannot be maintained for the high-cycle fatigue. Keywords High strength concrete, fracture mechanics, cyclic loading, fractology, material law.
INTRODUCTION In practice the majority of concrete structures are exposed to more or less severe cyclic loadings, such us traffic loads, temperature changes, wind gusts and in some cases waves or vibrations due to operation of machinery. Therefore, a profound knowledge of the fatigue behaviour of concrete and concrete structures is indispensable for safety and economical reasons. Furthermore, appropriate constitutive laws are required in order to be able to analyse the formation and propagation of cracks in concrete as well as the deformation behaviour or possibly a failure of concrete structures subjected to cyclic loading. The existing constitutive relations are based on experimental investigations with a low number of load cycles which are generally of minor interest for the practical design. Fatigue experiments with a higher number of load cycles have been always performed using stress controlled Wohler tests. Such tests do not allow studying the softening behaviour of concrete
278
Christoph KESSLER-KRAMER, Viktor MECHTCHERINE and Harald S. MULLER
after reaching the peak load. Therefore, in this investigation the fracture of concrete subjected to low-cycle and high-cycle fatigue loading was studied in order to describe the fatigue behaviour of concrete using fracture mechanical approach.
FRACTURE MECHANICAL EXPERIMENTS Geometry and preparation of the specimens In the experimental part of this study deformation controlled uniaxial tension tests on dog-bone shaped as well as on notched concrete prisms were carried out. Figure 1 shows a schematic view of the geometry of the two types of specimens applied in the experimental programme.
Figure 1. Geometrical dimensions of the concrete specimens (thickness of both specimens d = 100; data in [mm]) The dog-bone shaped prisms were used in monotonic tensile tests to study the pre-peak behaviour of the stress-strain relations in order to obtain reliable values of the uniaxial tensile strength f,, the Young's Modulus (tangent modulus of elasticity) and the strain at peak stress c,,, to be used as basic data for the formulation of the material law. On the notched prisms monotonic as well as low-cycle and high-cycle fatigue tension tests were carried out to obtain the softening behaviour of concrete under such loading conditions. Table 1. Composition of the investigated concretes Water
Cement CEM 132.5 R wm31 wm31
Concrete
w/c
HSC
0.30
125
470
NSC
0.55
175
318
Silica fume wm31
Superplasticizer wm31
Aggregate wm31 012 218 8/16
45
21
516
654
551
1.20
555
703
592
The compositions of two investigated concretes, namely a high strength concrete (HSC) and a normal strength concrete (NSC), are given in Table 1. For both mixtures an ordinary Portland cement CEM I 32.5 R was used. As aggregates quartzite Rhine sand and gravel with a maximum aggregate size of 16 mm were applied. For the high strength concrete additionally silica fume was used in the form of a suspension. Further, a sodium naphthalene sulfonate type superplasticizer was added in order to achieve the same consistency for both mixtures.
Failure of normal and high strength concrete under tnonotonic and cyclic tensile loading
279
All specimens were cast horizontally in metal forms. After demoulding at an age of one day, an aluminium foil was glued by means of an epoxy resin to the specimens termed as sealed in order to protect them against desiccation. However, the zones where the crack formation was expected were wrapped with a polyethylene foil before sealing with the aluminium foil. By this measure a contribution of the epoxy resin and the aluminium foil to the bearing capacity of the specimens could be excluded. A continuous control of the specimen weight proofed the quality of the chosen sealing. With this kind of curing the moisture condition in mass concrete was simulated. The specimens termed as unsealed were stored in a climatic chamber at a relative humidity of 65% and a temperature of 20°C immediately after demoulding. These specimens represent the moisture condition in slender concrete members without proper curing. The properties of the investigated concretes in fresh and hardened state are given in Table 2. The compressive strength and the Young’s Modulus were determined at a concrete age of 28 days. The values for the standard deviation are given in parentheses. Table 2. Properties of the fresh and hardened concretes Slump Concrete
[cm]
Air void contents [Vol.-%]
wlc
Gross density Compressive Young’s strength fc,150 Modulus E [kg/m3] , [MPa] [MPaI
HSC
0.30
39 (6.1)
1.6 (0.30)
2467 (15)
109.9 (3.21) 36490 (1280)
NSC
0.55
39 (3.7)
1.2 (0.19)
2407 (9)
50.5 (2.16) 27750 (1270)
Loading regime and test parameters Since a very stiff test set-up is required for the deformation controlled cyclic tests all tests have been performed with non-rotatabre boundary conditions. Therefore, the concrete specimens have been glued to stiff metal adapters applying an extra strong two component adhesive. Finally, the metal adapters were firmly connected to the bearing platens of the testing machine. The mean value of two LVDTs with a gauge length of 250 mm for the dog-bone shaped prisms and 50 mm for the notched prisms (compare Figure 1) was used as a control signal for the testing machine to run the tests with the desired deformation rate. The basic approach for the test control in the fatigue experiments is shown in Figure 2. The increase of the total deformation within the measuring length corresponding approximately to the crack opening is given by the deformation increment A6, which bas kept constant from cycle to cycle (i.e. A6 = d61dn = const, where n = number of load cycles). When the preset value for the deformation A6 in the following cycle is reached, the specimen will .be unloaded until the lower reversal point 6min is attained. The lower reversal point ti,,,, was defined as a function of the lower load level F,i, = const = 0 N. The deformation rate d6ldt was kept constant throughout the complete loading cycle. The deformation increment A6 was determined by dividing the critical crack opening (i.e. the crack opening at which no tensile stresses can be transmitted any more across the crack) as known from the monotonic tests by the desired number of load cycles to failure. As the maximum crack opening in the monotonic case a constant value of wcr= 160 pm was chosen from the literature, see [l]. The main parameters in the experiments were the number of cycles to failure ranging from 1 (monotonic loading) up to 100,000 load cycles, the curing conditions and the grade of concrete.
280
Christoph KESSLER-KRAMER, ViktorMECHTCHERINE and Harald S. MULLER
cr,
s
0
4
deformation 6
time t
Figure 2. Typical load-deformation relation (left) and deformation control procedure (right) in the fatigue experiments The tests were performed applying two different strain rates 8 . For the tests on the dogbone shaped prisms 8 I = lo4 I/s and 8 2 = 10” l/s were chosen. The experiments on the notched prisms were performed with the deformation rates of 6 1 = 5 p d s and 8 2 = 0.5 p d s , which correspond to the chosen strain rates considering the actual gauge length of 50 mm. The age of concretes at testing was 280 days. For each investigated combination of the parameters at least five specimens were tested.
FRACTOLOGICAL STUDIES In order to gain more information on the process of the crack formation and propagation in concrete under cyclic loading phenomenological investigations were additionally performed by means of an acoustic emission (AE) analysis during fracture mechanical tests. Further, the fracture surfaces of the tested concrete specimens were studied using projected fringes technique. In the following the main findings of the fractological investigations will be presented. Concerning the AE analysis, a detailed description of the measurement technique, the used test set-up as well as the applied analytical evaluation may be found in [2].
object
(fracture surface)
;\
i
’\.\
’.
reflector 1
fringe projector
reflector 2
c]
camera
Figure 3. Projected fringes technique: schematic view (left) and photograph (right) of the test set-up
Failure of normal and high strength concrete under monotonic and cyclic tensile loading
28 1
A schematic view of the test set-up using projected fringe technique is shown in Figure 3. Height differences of the surface induce a lateral displacement of the projected strip pattern [3]. Together with the geometrical data of the test set-up the phase shift of the projected fringes allows for the contour information at intervals of 0.16 mm (giving a mesh of 375 x 625 data points for each failure surface). To avoid larger areas of receiving no information due to a shade on the fractured concrete surface a projection from two sides (using the reflectors 1 and 2) was necessary. From the optical measurement data the roughness Rs and the fractal dimension DGSwere determined (Table 3). The roughness RS was defined as the surface area measured with the finest resolution (0.16 mm) divided by the projected area. The determination of the fractal dimension DGSwas performed by means of the grid scaling method [5].
Table 3. Roughness'and fractal dimension of concrete fracture surfaces of the concretes under investigation (standard deviations are given in parentheses) Concrete grade; curing conditions; deformation rate; number of load cycles NSC; sealed; 8 = 5 p d s ; N = 1
[-I
[-I
1.281 (0.003)
2.043 (0.005)
NSC; sealed; S
=5
p d s ; N = 10
1.297 (0.017)
2.043 (0.004)
NSC; sealed; b
=5
p d s ; N = 1000
1.325 (0.032)
2.050 (0.002)
1.335 (0.033)
2.05 1 (0.003)
pds;N=1
1.291 (0.017)
2.047 (0.001)
8 = 0,5 p d s ; N = 1 HSC: sealed; 8 = 5 u d s : N = 1
1.290 (0.030)
2.046 (0.004)
1.245 (0.027)
2.041 (0.003)
8
NSC; sealed;
NSC; unsealed; NSC; sealed;
=5pds;N=
8
=5
100,000
Roughness Rs
Fractal Dimension DGS
As can be seen by the results given in Table 3 an increase of the number of load cycles leads to an increase of both investigated parameters Rs and D G ~Further, . the use of an unsealed specimen as well as a lower deformation rate leads to higher values of the roughness Rs and the fractal dimension DGS,whereas for the high strength concrete lower values of Rs and DGSwere found in comparison to the normal strength concrete.
Figure 4. Typical fracture surfaces of the investigated concretes: high strength concrete (left) and normal strength concrete (right)
282
Ciiristoph KESSLER-KRAMER. Viktoi.MECHTCHERINE and Harald S.MULLER
The differences in the condition of the fracture surfaces of the normal strength concrete and the high strength concrete are illustrated in Figure 4.The effect of the concrete grade is already visible by a close inspection without any fkrther technical aid: high strength concrete shows a smoother surface with a pronounced fracture of aggregates, while the crack propagation in normal strength concrete occurs along the contact zone between coarse aggregates and mortar.
MAIN EXPERIMENTAL RESULTS AND DISCUSSION The uniaxial tension tests on the dog-bone shaped prisms provided stress-strain relations for the HSC always running above the corresponding curves for the NSC. Further, in the case of the high strength concrete the shape of the ascending branch of the o-Erelation remains nearly linear up to a considerably higher stress level in comparison to the corresponding relations for the normal strength concrete. An increase of the strain rate by a factor of 10 resulted in higher values of the uniaxial tensile strength 6, the Young's Modulus E~Jand the strain at peak stress EN. These results agree well with the data given by [4,5].The observed strain rate dependency may be explained by considering the crack development in concrete as a function of time. The cracks always strike the path with the lowest resistance, which runs along the aggregates in the case of normal strength concrete. With increasing rate of loading the cracks can grow faster because of a higher energy supply per time unit. Therefore, some of the cracks go straight through the aggregates following the shortest distance to cover.
6.0 I
I
I
I
I
8 = 0.5 p d s 4 NSC, unsealed, 8 = 5 p d s -0NSC, sealed, 8 = 5 p d s 0 I oo 10' 1o4
l.o
s
I
-0- NSC, sealed,
-0- NSC, sealed,
number of load cycles N
[-I
1o6
8 = 0.5 p d s
1o2 10' number of load cycles N
1
o6
[-I
Figure 5. Effect of the number of load cycles to failure on the net tensile strength (left) and the fracture energy (right) in the uniaxial tension tests on the normal strength concrete and the high strength concrete for different deformation rates and curing conditions The sealed specimens provided in all tests higher values of the uniaxial tensile strength fi, the Young's Modulus & and the strain at peak stress E~ than the unsealed specimens. This can traced back to the fact that the desiccation in the case of the unsealed specimens leads not only to a lower degree of the cement hydration but also to pronounced moisture gradients over the cross section of the specimen, which finally results in stress gradients reducing the bearing capacity of the specimen. Further, due to shrinkage of the cement paste considerable eigenstresses develop
Failure of normal and high strength concrete under monotonic and cyclic tensile loading
283
in concrete leading to the formation of micro cracks in the contact zone between coarse aggregates and mortar. The corresponding crack pattern could be clearly observed in the fractological investigations (see also Table 3). The results obtained from the tests on the notched concrete prisms show that with an increasing number of load cycles the net tensile strength fi, decreases (Figure 5, left). However, in the low-cycle region up to 100 load cycles the fm-valuesremain approximately constant. This observation is in accordance with the experimental findings on three-point bend tests on notched beams [6]. The tensile strength obtained for the unsealed specimens is lower than the corresponding values for the sealed specimens. This agrees well with the results obtained from the tests on the dog-bone shaped prisms. The effect of the strain rate in the experiments on notched concrete prisms is similar to that observed in the tests on dog-bone shaped prisms. In comparison to the values obtained for the normal strength concrete the net tensile strength of the HSC is always higher due to its denser microstructure fixther resulting in a higher capacity to store energy. The denser microstructure of the HSC also lead to smoother fracture surfaces and consequently to lower Rs- and DGs-values (Table 3). Figure 5, right shows a considerable decrease of the fracture energy GF in the high-cycle fatigue tests with an increasing number of load cycles. The GF-values were calculated as the area under the measured stress-deformation curves. In the case of the cyclic tests the envelope curves of the corresponding stress-deformation relations have been chosen for the derivation of the f i x ture energy. Therefore, a possible contribution of the area within hysteresis loops was not considered. Since the decrease of the investigated material parameters with an increasing number of load cycles is approximately the same for the normal strength concrete and the high strength concrete, it can be concluded that the effect of the fatigue loading is similar for the both types of concrete (HSC and NSC).
4.0
1
cyclic tests Lr,
3
envelope curves for monotonic tests, N= 1 low-cycle fatigue tests, N = 10 high-cycle fatigue tests, N = 1000 high-cycle fatigue tests, N = 100,000
0
200
400
deformation 6
600
deformation 6 [pm]
Figure 6. Envelope curves of the stress-deformation relations obtained from the monotonic and the fatigue tests performed on the sealed specimens made of NSC
284
Cliristoph KESSLER-KRAMER. Vibor MECHTCHERINE and Harald S.MULLER
The main finding in the experiments is that for an increasing number of load cycles the envelope curves of the 0-6 relations differ significantly from the corresponding monotonic curve, see Figure 6. The ascending branches show approximately the same shape and the same stifhess for all curves. Because of the lower f,-values for the high-cycle fatigue tests (Figure 5, left) these curves are below the curves for the monotonic and the low-cycle fatigue tests in the first, steeper part of the stress-deformation relation. This also leads to the lower Gpvalues (Figure 5, right) with an increasing number of load cycles which is mainly due to lower energy consumption in this part of the softening curve. Additionally, the curves from the highcycle fatigue tests are steeper than the curves for the monotonic and the low-cycle fatigue tests, see Figure 6. In the second, shallow part of the softening curve the average curves for the cyclic tests are nearly congruent when a deformation of about 150 pm is reached. The curve for the monotonic loading is slightly higher at this deformation region and coincides with the curves for the cyclic loading at a deformation of about 350 pm. Nevertheless, the contribution of the second part of the softening curve to the value of the fracture energy is limited, since it covers a minor amount of energy compared to the first part of the softening curve. The mentioned observations clearly show that the conventional assumption of a unique envelope curve for the fatigue behaviour of concrete cannot be maintained, especially for highcycle fatigue loading. Further results for additionally investigated mechanical and fracture mechanical parameters such as miscellaneous deformations, characteristic length etc. under cyclic tensile loading may be found in [2]. MODELLING THE FATIGUE BEHAVIOUR OF CONCRETE The experimental results obtained in this study restrict the validity of the existing constitutive relations to the range of low-cycle fatigue since they are completely based on the assumption that the monotonic stress-crack opening curve fits the envelopes for fatigue loading regardless of the number of load cycles to failure, see e.g. [ 1, 71. Based on the findings attained in this investigation a new constitutive law on the basis of a rheological-statistical model was currently developed, which considers in particular the number of load cycles, time effects and the heterogeneity of concrete (Figure 7). The model consists of simple rheological elements like springs, friction blocks and dashpots representing the elastic, frictional and viscous deformation components of concrete. The chosen basic model consists of two Kelvin-Voigt elements and three dashpots (in Figure 7 framed with dotted lines). The concrete behaviour resulting in the hysteresis loops is modelled by a serial arrangement of two friction blocks and two Kelvin-Voigt elements. Duda [7], who also used a rheological approach, applied in his model only springs and friction blocks to describe the cyclic tensile behaviour of concrete. In the new material model presented here the dashpots qi,l and qi,2 arranged parallel to the spring elements Ei.1 and Ei.2 enable to consider the rate dependency of concrete behaviour and the effects resulting from the load history. The parallel arrangement o f a further friction block Y ~ Jallows the modelling of the phenomenon that loosened or pulled out aggregates or hardened cement paste particles may dislocate while the crack is open, which leads to local tensile as well as compressive stresses in the case of unloading, i.e. closing of the crack. Since this phenomenon just appears within the hysteresis loops, the associated friction coefficient ~ i . 3is given as a function of the number of load cycles N (Figure 7).
Failure of normal and high strength concrete under monotonic and cyclic tensile loading
285
Figure 7. Rheological-statistical model for the description of the fatigue behaviour of concrete under tensile loading The complete model consists of n basic models arranged parallel. The governing parameters Y, E and q are statistically distributed following an exponential function after Weibull. By this approach the heterogeneity of concrete has been considered. The bulk behaviour of the undamaged concrete is taken into account by an additional spring element Ebulk. A new constitutive law for the description of the stress-crack opening relation of concrete under tensile fatigue loading was developed on the basis of the presented rheologicalstatistical model. Further details concerning the mathematical formulation, the adjustment of the decisive coefficients and the practical application may be found in [2].
SUMMARY AND CONCLUSIONS In this study the effects of the number of load cycles to failure, the strain rate and the curing conditions on mechanical and fracture mechanical parameters of high strength and normal strength concrete under monotonic and cyclic tensile loading were investigated. Therefore, deformation controlled uniaxial tensile tests on dog-bone shaped prisms as well as on notched prisms were carried out. The tests on dog-bone shaped prisms showed a significant increase of the uniaxial tensile strength f,, the Young’s Modulus Eo and the stain at peak stress Etu with an increase of the strain rate by a factor 10. For the sealed specimens the values of these three parameters were found to be higher than for the unsealed specimens. For the high strength concrete the ft-, Eoand q,-values were significantly higher in comparison to those for the normal strength concrete. Concerning the tests on notched concrete prisms the net tensile strength ftnand the critical crack opening w,, decrease with an increasing number of load cycles. The fracture energy GF
286
Clvistoph KESSLER-KRAMER. Viktor MECHTCHERINE and Harald S. MULLER
and the characteristic length lch decrease with an increasing number of load cycles as well. The tests on sealed specimens provided higher GF- and I,h-values as the tests on unsealed specimens. The effect of the number of load cycles on the behaviour of HSC in tension is similar to that of NSC. As a main result it could be shown that for an increasing number of load cycles the envelope curves of the stress-deformation relation differ significantly from the corresponding monotonic curve. This observation restricts the validity of all existing material laws to the low-cycle region. Therefore, a new constitutive law based on a rheological statistical model was developed. Further, the fracture surfaces were studied using projected fringes technique in order to gain a more detailed glance on the formation and propagation of cracks under tensile loading conditions. As a result, strong correlations have been found between the calculated values of the roughness and the fractal dimension, respectively, and the fracture mechanical properties of concrete as measured for different combinations of the investigated parameters. REFERENCES 1. Hordijk, D. A., Local Approach to Fatigue of Concrete. Dissertation, Delft University of Technology, Delft 1991 2. Kessler-Kramer, C., Tensile Structural Behaviour of Concrete under Fatigue Loading (in German). Institute of Concrete Structures and Building Materials, University of Karlsruhe, VOl. 49,2002 3. Gutmann, B., Determination of the Phase Field in the case of Projected Fringe Optical Measurements with an improved Branch-Cut Method (in German). Dissertation, Faculty of Chemical Engineering and Process Technology, University of Karlsruhe, Shaker Publisher, Aachen 2000 4. ACI Committee 446: State-of-the-Art Report on Dynamic Fracture. Report ACI 03.95 R8860,1995 5. Mechtcherine, V., Fracture Mechanical and Fractological Investigations on the Formation and Propagation of Cracks in Concrete (in German). Institute of Concrete Structures and Building Materials, University of Karlsruhe, Vol. 40,2000 6. Kessler, C., Mueller, H. S., Experimental Investigations on Fracture and Damage of Concrete due to Fatigue. In: “Fracture Mechanics of Concrete Structures” (Proc. FRAMCOS-3), H. Mihashi and K. Rokugo eds., Gifu 12-16 Oct. 1998, Aedificatio Publishers, Freiburg 1998, pp 377-386 7. Duda, H., Fracture Mechanical Behaviour of Concrete under Monotonic and Cyclic Tensile Loading (in German). German Association of Concrete Structures (DAfStb), Vol. 419, Beuth Publisher, Berlin, 1991
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
THE USE OF VISCOSITY ENHANCING ADMIXTURES TO IMPROVE THE HOMOGENEITY OF FIBRE DISTRIBUTION IN STEEL FIBRE REINFORCED CONCRETES Liberato FERR4RA Politecnico di Milano - Department of Structural Engineering Piazza Leonard0 da Vinci 32 20133 Milano, Italy e-maiI : li berato.ferrara@,uolimi.it
ABSTRACT This work presents the early results of a research program aimed at evaluating the influence of viscosity enhancing admixtures (VEA) on the fibre distribution in Steel Fibre Reinforced Concrete (SFRC) elements. First of all their influence has been investigated with reference to fibre distribution along casting direction in cylinder specimens. As a further step of the investigation small-scale prototypes have been cast with the same mixes previously tested and the distribution of fibres, as influenced by the mix-design of concrete, has been evaluated along the thickness, the cross-section and the longitudinal axis of the prototypes. Results are really promising in sight of structural applications. In this framework some full-scale prototypes have been cast with the “optimum” mix, as came out from previous experiments, and the repeatibility of results previously obtained has been checked with reference to them.
Keywords: steel fibre reinforced concretes, viscosity agents, fibre distribution, roof elements
INTRODUCTION Starting from the pioneeristic idea of Batson et al. (1972), relevant studies have been carried out over the past almost thirty years about the partial or even total replacement of conventional shear reinforcement with metallic fibres in reinforced concrete structural elements. Among the several benefits which may come from such an operation, the possibility of achieving a continuous and, hopefully, homegenous distribution of reinforcing “wirelike” elements, spaced closerly than the minimum distance obtainable with the smallest traditional bars (Romualdi and Batson, 1963) was earliest recognised and regarded as a sound motivation for promoting research in this field. Recent experiences, focused on the use of steel fibres as completely substitutive of traditional shear reinforcement in precast prestressed thin web roof elements, have clearly assessed the reliability of this technology (di Prisco and Ferrara, 2001 ; Meda et al., 2002a; di Prisco et al., 2003). The same experiences, together with other studies on steel fibre reinforced concrete prestressed X-beams (Elliot et al., 2002, a-b), have once again confirmed that the homogeneity of fibre distribution inside a structural element, as well as the repeatibility of these homogenity features, stand as a crucial point that must be tackled aiming at efficaciously and efficiently implementing the Steel Fibre Reinforced Concrete
288
Liberato FERRARA
(SFRC) technology in structure building processes, mainly as far as a series production of precast elements is dealt with (di Prisco et al., 2000,a-b; Failla et al., 2000; 2002). It is infact well established that the addition of steel fibres to a traditional concrete may have sever unfavourable effects on the workability and rheology properties of the fresh mix, this negative influence mainly depending on the fibre content and aspect ratio (Bayasi and Soroushian, 1992). The glueing of fibres into bundles, creating a lower aspect ratio during mixing, is surely helpful in avoiding balling and formation of fibre nodules (see for example Ramakrishnan et al., 1980); furthermore the use of superplasticizers (in percentages ranging from 1 to 2% by mass of cement) together with extrafine particles, such as silica fume leads to an improvement of the workability. Nevertheless, whenever it can be guaranteed a homogeneous distribution and random orientation of fibres within the fresh concrete mass when poured out of the mixer, the casting of concrete into formworks and the subsequent compaction by vibration may not only lead fibres to be oriented along preferential directions lying in predictable planes (Edgington and Hannant, 1972) but also to show a not negligible tendency to segregation. These deviations from the homogeneous and random distribution of fibres have been shown to strongly influence the measured material properties, at the laboratory specimen scale, to an extent even such to shadow the effects of other likewise relevant factors (e.g. the specimen size or, in direct tension tests on notched cylinders, the specimen slenderness and notch depth - see Barragin, 2002). Furthermore, when dealing with practical applications to full scale structural elements, the lack of homogeneity in fibre distribution may be called to explain, e.g., non-conventional failure mechanisms accompanied and featured by unattained theoretical strength and ductility levels (di Prisco et al., 2003). In this framework, a sinergy between the technologies of self-consolidating and steelfibre reinforced concrete may by fruitfully employed, leading to an engineered cementitious composite, all the enhanced properties of which may be fully exploited by precast industry (Groth and Nemegeer, 1999; Khayat and Roussel, 1999). On one hand in fact it is dealing with a fresh concrete which, by its own weight, and needing no compaction by vibration, is able to fill any corner of a formwork, whatever its geometry be, perfectly wrapping up the reinforcing bars even when highly congested, and without showing any significant segregation of its constituents. This eliminates, or at least strrongly reduces, the causes which are likely to alterate the homogeneous distribution of fibres, despite introducing some dependence of the orientation of the same fibres on the direction of flow of the fresh concrete in the formworks. On the other hand, the use of fibres may lead to a significant reduction of the production times and workmaship costs due to the placement of traditional reinforcement, furthermore contributing to enchance the performances of concrete, during its settlement, hardening and hardened states. As an obvious outcome of all the "passim" above recalled benefits, the durability of structural elements made with a self compacting steel fibre reinforced concrete is also likewise significantly improved. RESEARCH SIGNIFICANCE AND EXPERIMENTAL PROGRAMME
In order to reliably set up a series production of precast prestressed roof elements in which all transverse reinforcement is replaced by fibres, a crucial role is surely played by the optimisation of the mix design of concrete. The final aim of the whole research project, in the framework of which this work has been conceived, is to achieve an enhanced engineered concrete composite, reinforced with hooked-end steel fibres, furthermore featured, in its fresh state, by high workability and rheological stability. This work focuses on the role which Viscosity Enhancing Admixtures (VEA) may play in enhancing and guaranteeing the above said rheological stability, as far as it is dealt with the positive effects which the enhanced
The use of viscosily enhancing admixtures to improve the homogeneity offibre distribution ...
289
fresh state properties may have on the homogeneous and random distribution of fibres. It can be in fact reasonably hypothesised that the above said correlation between fresh state properties and fibre distribution, when efficaciously established, may also have positive effects on the hardened state properties of the composite, as far as not only their values are concerned but also their repeatability in a continuing production, as typical of precast factories, and their “spatial” dispersion in real scale structural elements. To the above exposed purpose, it has been hence first of all evaluated the effect that vibration times may have on fibre distribution along casting direction in cylindrical specimens. Starting from an ordinary steel fibre-reinforced concrete, the influence of viscosity enhancing admixtures (type and dosage) has been first of all checked. Furthermore, SelfCompacting Steel Fibre Reinforced Concretes (SCSFRC) have been investigated (in these last cases the cylinder specimens have not been vibrated). The influence of mix design on the strength and most of all on toughness properties of the engineered concrete composites has been also evaluated through four point bending tests on notched prisms. For a further check some small-scale prototypes of thin-walled roof elements (4 m span) have been cast, with the different investigated mixes. By coring the prototypes in several suitable positions, information on the distribution of fibres along both longitudinal and transversal directions as well as along the thickness of the thin-walled slabs has been got. It has been also tried to set up some correlation between this information and results from fourpoint bending tests on small thickness slabs, both companion specimens of the prototypes and cored from them. The results obtained in this stage of the work lead to definitively chose one mix, the characteristics of which has been further checked with reference to large scale prototypes (25 m long), further considering the influence of fibre type and aspect ratio.
RESULTS FROM CYLINDER SPECIMENS The first step of the work consisted in evaluating the distribution of fibres along the casting direction in cylinder specimens, as influenced by both viscosity-enhancing admixtures and times of vibration. A reference steel fibre reinforcing concrete, the mix design of which is reported in Table I, was first of all considered. Seven cylinders, 300 tnm high and with a diameter equal to 150 mm, were cast, pouring the mix directly into a plastic tube through a suitable extension and without any manual tamping, so to reproduce as close as possible the real casting conditions of a precast element. The specimens were further submitted to different times of vibration (0, 1, 2, 4, 8 and 16 minutes - 2 cylinders vibrated 8 min). After even only one day of aging, the cylinders were cut into six equally thick. Each slice was then crushed under a press and, by means of a magnet, fibres were separated from the matrix and weighted, their weight being hence referred to the previously measured volume of the slice. The results, in terms of fibre density in the six slices (named downward from A to F) are shown in Figure 1. For longer vibration times, of the same order of magnitude of those generally underwent by precast elements, the random distribution of fibres is significantly altered and a clear tendency of fibres to downward segregate appears. Cement type CEM I 52.5 R Fly ashes Water Steel Fibres type 45/30 (hooked ends- zinc coated)
380 kg/m’ Sieved sand 0/3 mm 60 kg/m’ Natural sand mix 0/12 mm 150 lt/m’ Gravel 8/15 mm
50 kg/m3 Acrylic superplasticiser
Table 1. Mix-design of the reference SFRC
120 kg/m’ 920 kg/m3 865 kg/m’
3,5 1 t h 3
290
Liberato FERRARA 30
z(mm)
casting direction
25
+n
0 0 *.
A
a
+X
20
vibrotion times
0
15
+
t-omin t:lmin
+
0
t=8min
X
t :2mm
10
A 0 0 P+ t=4min
= 16min
t
z (min)
5
m a r
fibre content (kg/m3)
0 0
10
30
20
40
50
60
Figure 1 : influence of vibration on fibre distribution along casting direction - reJ SFRC 30
30
z (mm), casting m +
z(mm)
~
25
\J
direction
25
0
2o
A 15
0
+
0
+m
t=omin t=Zmin
/
I
15 10
t=8min
t I
I
t=16min
5 0
era a63
t=Zmin
= 4 min
+aA
vibration t I mes
20
t=Omin
t
10
‘0 ‘+O
A
vibration times
casting direction
= 4 min
+
t:Bmin
0
t=16min
I30
0
5 1 fibre content (kg/m 3 )
a; ;a
20 30 40 VEA type A
50
0
10
fibre content (kg/m 3 ) e o
0 60
0
10
20 30 40 VEA type B
50
60
Figure 2: influence of vibration and type of VEA on fibre distribution along casting direction
In order to study the influence of viscosity enhancing admixtures, different concrete mixes have been considered, simply adding the chosen dosage of VEA to the reference fibre reinforced concrete. Two types of admixtures have been herein considered, in a dosage such to guarantee their rheological stabilising action without detriment to workability (Table 11). The basic constituent of the first one (named VEA type A in this work) is amorphous silica dispersed in a water solution; the second one (here labelled as VEA type B) mainly consists of water-soluble polymers. Eight cylinders for each VEA-added mix were cast and vibrated 0, 2, 4,8 and 16 minutes respectively (one cylinder for lower times and two cylinders for each of the longer times). The addition of viscosity enhancing admixtures has some quite significant stabilising effects on fibre distribution. The performances of VEA type B, as a matter of fact, appear to be more effective in limiting the downward segregation of fibres even for longer vibration times (Figure 2 - for longer vibration times the mean values of the two cylinders are shown i n the graphs).
The use of viscosi& enhancing admixtures to improve the homogeneity offibre distribution ...
Mix Reference SFRC (mix 1) Reference SFRC + 0.5 It/m’ VEA type A (mix 2) Reference SFRC + 0.5 It/m” VEA tvue B (mix 4)
29 1
Slump (mm) 180 150 140
Table 11. Influence of VEA on workabilihj offi-esli mixes
I Cement tvne < . CEM I
I
1 400 kdin’ 1 Sieved sand 0/3 mm
52.5 R Calcareous fi 11er Water Steel Fibres type 45/30 I (hooked ends- zinc coated)
50 k&-’ Natural sand mix 0/12 mm 160 Wm’ Gravel 8/ 1 5 mm 5o k,,,m3 Acrylic superplasticiser -- - - D... 1 VEA (tvDe A or B)
I
-, r - - -, aiuinp flow diameter (VEA tvoe B)
I
825 kg/m’ 1 190 kg/m’ 135 !@in’ 6 It/m-’ 2 It/m’ I
1
63 cm
Table 111: mix-desigiz and wor-kabili@tesl r-essults,/orself compacting SFRCs 30
z (mm)
casting direction
25
+
a
A
AOM
20
A
r e f sfrc
0
r e f sfrc
+
scc
10
5
u i %
reference sfrc
15
+
veo type A veo type
B
A
O
scc + veo type A +
A
vea type B
10
20
30
O
+
O
4B
fibre content (kg/m3) 0 0
D
40
50
60
Figure 3: distribzitiorz offibre along cylirider lieightjor diflerent mixes (no vibration)
As a further step two self compacting steel fibre reinforced concretes have been designed, each one of them containing one of the two types of the investigated VEA. The mix-design and the results of slump-flow tests for the measurement of workability (Khayat, 1999; Ferraris et al. 1999) are reported in Table 111. Cylinders made with these concretes (one for each mix) have not been vibrated; the distribution of fibre content along the height of the specimens is shown in Figure 3 and compared with the ones detected in not-vibrated specimens made with other concretes. No significant difference can be detected in the random distribution of fibres (except for scc mix with VEA type A which showed some abnormally high content of fibres). The advantage of self compacting mixes stands in the possibility of achieving, as far practical applications are concerned, the same quality of the structural element without any vibration, as it will be further specified, thus removing one of the main causes of fibre segregation. Some tests aimed at assessing mechanical properties of the different investigated mixes have been also performed. Besides compression tests on cubes. four-point bending tests on notched prisms have been performed (see the specimen geometry in Figure 4). Test results are
292
Liberato FERRARA
summarized in Table IV (mean values and corresponding standard deviations, computed on the referred number of tests, are reported). As far these data: - the first-cracking strength fir is defined as the nominal stress stress at a Crack Tip Opening Displacemen (CTOD) equal to 25 microns; - equivalent strengths fq 0-0.6 and fq 0.63 are defined as equivalent stresses computed for CTOD values respectively ranging from 0 to 0.6 mm and fiom 0.6 to 3 mm.
-
ductility indices DOand DI are respectively computed as
feq0-0.6 and
feq0.6-3 ~
flf
fir
Despite some differences have been measured in the compressive strengths, which turned out to be lower in self compacting concretes, no significant differences have been detected as far as the first cracking strength is concerned. Furthermore, and this is even far more signifcant, some improvements for equivalent strengths have been obtained when shifting from ordinary SFRCs, tough added with VEA, to self-compacting ones. The similar tendencies detected for ductility indices, which furthennore result in a percentually larger increase for the second one, may lead to hypothesize that the above measured improvements are due, on one hand, to a better homeogeneity inlhe distribution of fibres within the concrete matrix, and, on the other, to a better bond between the matrix and the fibrous reinforcement (similar to what is well assessed for traditional reinforcement bond with scc matrices; Sonebi and Bartos, 1999; Sonebi et al., 2001). It has to be equally emphasised the lower scattering in test results which has been obtained with self compacting mixes, reliably attributable to an improved stability of the fresh mixes, exerting its positive effects also on the toughness properties of the composite. , 15Omm
I
150mm-
I
150mm - ---
1 --
. ..
I ..
.. ..
-t
mm . _. 450 . . .-._--. -... ..-.- . . ..- .. -_ - . - .... . .600..mm
Figure 4: specimen geometry for 4-point bending tests
no of tests -
I
Mix
I
l 33
RefetenceSFRC
Ref. SFRC + VEA type A
I SCSFRC -
fir
VEA type A
1
5
80.5
4
88. I
I2
68.2
4
75.8
I
fcq0.63
3.3% 5.9
15.1% 6.2
1 18.9% ;;;;2
, 4.95
I;
K3.1%
I
SCSFRC - VEA type B
fqO-O.6
~
5.2 5.1 %
Table IV: results of 4 point bending tests
I .09
The use of viscosity enhancing admixtures to improve the homogeneity offibre distribution ...
293
DISTRIBUTION OF FIBRES IN SMALL SCALE PROTOTYPES The further step of the investigation took into account small scale prototypes of roof elements, having a 4 m span and the cross section skected in Figure 5 , where also the casting direction is indicated by means of arrows. Besides the reference prototype (25 m long) two small prototypes made with SFRC+VEA (one for type A and one for type B) and two small prototypes made with Self Compacting SFRC (one with VEA type A and one with VEA type B) were cast, for a total number of four small scale prototypes, to be compared with the reference real scale one. Prototypes made with ordinary SFRCs have been vibrated 15 minutes, while for SCFRC prototypes vibration was reduced only to one minute. It is by the way significant to remark that even for prototypes made with scc, probably due to the thinwalled thickness and to the quite steeper side slabs, topping-up from the opposite side of the cross section from which fresh concrete were cast together with a short-time vibration were needed. This may callfor a further optimisation of the mix in sight of the structural application at issue or even for some more stringent requirements on the self-compactability of fresh mixes. It may be also called for some dedicated self-compactability tests, besides the ones already accepted in the practice (Khayat, 1999; Ferraris et al., 1999), suitably calibrated on the relevant geometrical features of the structural elements to be cast. 14 cm diameter cores have been extracted from both the wing and the central slabs of the prototypes, according to the scheme in Figure 6 and the content of fibers in each one of them has been evaluated as specified in the previous chapter.
\Il
t
TOPPING-UP
CASTING
i/ '
Figure 5: cross section of t h e p r o t o ~ p e s
_~
............. -. . . . . . . . . .
...
.-
I
,33 34
Figure 6: sclreme ofcores extracted from the prototypes (plari view)
294
I
Liberato FERRARA
The diameter of the cores was chosen as a reasonable compromise between two counteracting needs: on one hand the core size has to be suitably large in order to reliably include the representative volume element of the material and of the structure. On the oher, also in the sight of setting up a "not rmich destnrctive" and cheap test method to be implemented in a statistical quality control procedure for a series production of SFRC precast elements, the core size has to be kept small enough so to induce a moderate damage in the structure which could be furthermore easily repaired. (Meda et al. 2002b). It has to be remarked that cores identified with an even number in the scheme in Figure 6 have been furthermore split into two slices along their thickness, so to have information about the tendency of fibers to segregate along the direction of casting. A first synoptic view of test data is given in table V: the mean values of fiber content, as evaluated from the eighteen cores extracted from each prototype, with the related mean standard deviations, confirm the efficacy of viscosity engancing admixtures, coupled with the self compacting concrete technology, in achieving a more homogeneous distribution of fibers even at the scale of a small roof element prototype. The slightly worst results obtained with self compacting mixes, with respect to ordinary ones simply added with viscosity enhancing admixtures, are adequately compensated by the advantage got with the strong reduction of vibration times.
Prototype
1) reference SFRC
2) ref. SFRC + VEA type A 3) ref. SFRC + VEA type A 4) SCSFRC - VEA type A 5) SCSFRC - VEA type B
(kg/m3)
Fiber content standard deviation (kg/m3)
48.27 46.22 48.73 5 1.95 47.38
8.2 4.1 2.58 4.12 4.84
mean value
variation coeff. 6 17 Yo
9 Yo 5 Yo 8%
~
10 Yo
All the above said statements also holds if the distribution of fiber content in cores extracted from the prototypes are analysed collecting data by rows or columns (Tables VI -VI ). The influence of casting modalities can be clearly got from the lowering values of fiber content when passing from the upper to the lower row of cores in the wing and to the row extracted from the central flat slab. The efficacy of VEA and most of all of the self compactability properties of the mix labelled as 4 and 5 can be clearly appreciated also with reference to this specific problem. The most important effect played by VEA and self compacting concrete techniques stands by the way in the strong reduction of the tendency of fibers to downward segregate. The results of differences in fiber contents obtained from the two slices in which each even-numbered core had been previously cut, gave a strong confirmation to the above said statement, which was, in a sense, the moving idea of all this work (Figure 7). It has been hence attemped to set up some correlation between the results obtained with respect to fiber dispersion within small scale prototypes of structural elements and the ones from four point bending tests on small thickness slabs, which have been either cored from the prototypes and cast at the same type with mixes from the same batches (companion specimens). It has to be remarked that.slabs cored from the prototypes were tested on both sides with respect to the casting direction, in the sense the tests were performed in such a way that the original intradox of the prototype was either the intradox (slabs downward tested) or the extradox (slabs upward tested) of the slabs under test.
The use of viscosity enhancing admixtures to improve the homogeneity offibre distribution ...
295
Table VI: distribution offibre content - ana(iais along longitudinal axis ofprotoppes
I
I
Cores
I
11-21-31 12-22.
Prototype
Mean std. dev.
13-23-33
std. dev.
I
15-25-35 16.26.36 std. dev. 1.57
5?o'
2.82 46.91 2.07
2.37
49.48 3.34 46.86
49.53
3.12 45.42 3.68
Table VI I: disti-ibzitioii offibre content along cr-oss-sectiorialseggmerits ofpi-ototypes 0-
50
E
40
7 0
t
*-
+ +
prototype 1
A
prototype 2
A
prototype 3
+
+
30
Q ) \
u r n
5L k -0
proto4
0
proto 5
& l o * *
2
Q)
y.
+
0
$ a
:0
A
A
a
4
-10
11 13 15
21 23 25
core number 31 33 35
Figure 7: absoltite diflerences i1i.fibr.e content along thickems ofeven-nzmber-ed cores
296
Liberato FERRARA
Slabs were 150 mm wide and 500 mm long, with a thickness equal to 60 mm for companion specimens and to about 75 mm for core ones, and were tested according to the scheme shown in Figure 8, where relevant details of the experimental set-up are also shown. Test results are plotted, in tenns of nominal stress vs. crack opening curves, still in Figure 8. It can be observed that the addition of viscosity enhancing admixtures and the use of self compacting mixes leads to a better uniformity of test results, as far as the behaviour of cores and companion specimens in concerned, and, most of all, to a significantly more homogeneous behaviour between upward and downward tested core slabs. This results is of the utmost importance in sight of the predictable structural applications of the designed enhanced concrete composites. The number of performed test remains by the way quite low and further quantitative confirmation should be needed from a possibly quite large number of test and from statistical interpretation of results.
150mm
CJ
150mm 150mm
1.1.
10
*: '6
A
(MPa)
1~
+
+
ref. SFRC
+
.
+
++
+
I
cores - upward
+
cores - downword
:ACoq(mm7
04 10.1 0.3 0.5
+
companion
A
cores upward
10
CJ
1
companion
A
A
200 mm
COD measurement
10
(MPa)
++
1.2
1.8
+
(MPa)
companion cores - upward
A
~
I
cores -dawnward
5
cores - downward
t +* ++
I
+ +
* - +-
I
+ prototype -I----,
0
ref SFRC + VEA type A
0.1 0.3 0.5
10
CJ
(MPa)
cob (mm)
1.2
+
cores upword
+
cores -downward
A.+
%.
+*
3
---\
A
+*.
-4.
COD (mm)
O*
1.2
0.1 0.3 0.5
10
CJ
(MPa)
-
A
-
11ref SFRC + VEA type B
1.8 companion
+
/
++
++
1.8
+
companion
A
cores - upward
+ +cores - downward
+
+
+
A
COD (mm) 0 0.1 0.3 0.5
1.2
1.8
0.1 0.3 0.5
1.2
Figure 8: geonietr?~-scheine of test specimen and stress-COD ciirves 4pb tessls on small thickness slabs (companion and core specimens)
1.8
The use of viscosity enhancing admi.xtures to improve the homogeneity offibre distribution ...
297
FINAL CHECK ON FULL SCALE PROTOTYPES
In the previous stages of this work it has been - step by step - shown as through a careful calibration of the mix design of concrete, starting from the mere addition of viscosity enhancing admixtures till to the setting up of a full sinergy between self consolidating and fiber reinforced concrete techniques (SCSFRC Self Compacting Steel Fibre Reinforced Concrete), it has been possible to obtain, within small scale prototypes of roof elements, a more homogeneous distribution of fibers than with ordinary SFRC mixes. It has been also shown that the progressive modifications to the composition of the concrete composite, despite some lower values of the cube compressive strength were obtained, lead to a slight but not negligible improveinent of toughness properties of the material, as usually measurable, with a lower dispersion in the results of the material characterization tests. These last statements, despite based on a few number of tests and hence needing of a confirmation based on a larger test number with an eventual statistical interpretation of their results, confirmed the reliable efficacy of the sinergy between self compacting and steel fiber reinforced concrete technologies, mainly in guaranteeing a better cooperation between the concrete matrix and the reinforcement. As a first confirmation of all the above exposed results a check has been made on full scale prototypes of roof elements (25 m span), made with a self compacting steel fiber reinforced concrete containing viscosity enhancing admixture type B (the performances of the two different investigated VEAs were negligibly different; since the research was supported by a company the choice of VEA B was essentially due to marketing reasons). This prototype was hence compared with the analogous reference one, as already done for small scale ones in thc previous chapter. It has been also decided to check the influence of the fiber reinforcement type: beside low carbon hooked-end zinc-coated fibers, 30 mm long and with an aspect ratio equal to 45, as till now used, high-carbon non-coated fibers, 30 mm long and with an aspect ratio equal to 80 were also considered. Fiber dosage was always kept equal to 50 kg/m3. Hence, besides the two above said full scale prototypes, two further ones (one with the reference SFRC mix and the other one with the SCSFRC mix) were cast. All prototypes had the cross section already shown in Figure 5. The number of cores taken from each one of the SCC prototypes in order to evaluate the distribution of fiber content was enlarged according to the scheme shown in Figure 9. Four point bending tests on notched prisms have been also performed for a further check of the properties of self compacting steel fiber reinforced concrete mixes, also taking for the addition of different types of fibers. As far as the homogeneity of fiber reinforcement within the prototype are concerned, the results confirm what has been above said with reference to small scale prototypes. The efficacy of the enhanced mix design in achieving a more homogeneous distribution of fibers can be clearly appreciated from the results summarized in Tables VlII and IX and from results shown in Figure 10 and referring to the fiber distribution along the thickness of the slabs of the prototypes. The above said efficacy appears, by the way,to clearly depend on the adopted type of fibers: the enhancement in the homogeneity of fiber content appear to be proportionally more significant for fibers with a low aspect ratio, this last parameters having, as well known, some negative effects on the workability of the fresh mix. This also appear to be confirmed by results of characterisation tests, summarised in Table X. In the framework of a general improvement of material toughness properties, id est of equivalent post-peak stresses (despite with a lower compressive strength), it can be observed that the improvements are percentually larger for the mix reinforced with fibers type 45/30 than in the other case and that also the positive effects on the experimental scattering are more significant in the first case. This may call for further research work as far as the optimisation of enhanced concrete mixes is concerned with reference to different types of fibrous reinforcement.
298
Liberato FERRARA I 1 12
.
...
.
.
12.1 11.2
. ,= . .... .
,21 .P.
?I
I3 I 4
I 5 I6
3
.= P
24
Prototype
Fibre content
..
+fibre 45/30 . ._. - ... .. .... . . ... . 41 ,a
__
. .
.
.
.
-
10 %
+fibre 45/30
..
6.8 15 % +fibre 80130 d)SCSFRC 54 11 % 5.9 +fibre 80130 1 Figure 9: scheme of cores extracted,fionzfuN Table VIII:,fiberdistribution in cores scale SCCprototypes extracted,fr-ornSCC prototypes SI J?
53 Y
I
I
I I
I I
I
I
1 I
'% 54.49 11% 50.78 15% I56.88! 8% Table VIII: distribution offibre content along longitudinal axis of full-scale proto&ws
53.85
Cores 11-21-31 I 13-23-33 I 15-25-35
I 12.1-12.2-22.1-
Table IX: distribution offibre content along cross-sectional segments offitll-scale prototypes
Table X: results of 4pb tests - mixes offiill scale prototypes
The rise of viscosity enhancing udmixtures to improve the homogeneity offibre distribution ... 50 A
ref SFRC45/30
A
SFSFRC45/30
A
+
ref SFRC 80/30
'8
0
A
A
'
?
299
A
40
A
A
0.
SCSFRC80/30 A '
O A
6
A
n'
0
.zo a
0 L
A
111315
A
212325
corenumber 313335
41
5153
Figure 1 0 difletwices i1i.fibr.e content along thickness ofeven-number-ed cores extracted porn ,fill1 scale prototypes
CONCLUDING REMARKS The present work allowed to check the reliability of a sinergy between self compacting and steel fiber reinforced concrete techniques, in the sight of a possible application to the series prodution of precast prestressed roof elements. The aim was to obtain a concrete composite in which the enhanced toughness properties, which are typical of fiber reinforced concretes and which are responsible of better statical and durability perfonnances of structural elements, are coupled with a better workability of the fresh mix which, on one hand, allow for a reduction of vibration times, and on the other, reduces the sensitivity of the concrete quality to the "human variable". As a matter of factor the enhanced rheological properties of the composite hrthermore allow to achieve a more homogeneous distribution of fibers within a structural element. It is worth remarking that with the enhanced mix design of the concrete it has been possible to sensibly reduce the differences in fiber content along the small thickness of the examined prototypes, thus obtaining an homogenus behaviour of the element, both along its intadox and extradox faces. The obtained better homogeneity of fiber reinforcement, besides guaranteeing a better behaviour of the structural element, also reduces the possibility of defects due to anomalies occurring during casting and vibration operations and thus implies a lower scattering in the experimentally detected behaviour of the prototypes, which is fundamental for a series production. Such a lower scattering has been significantly checked with reference to suitably designed material and structure characterisation tests.
ACKNOWLEDGEMENTS The author wishes to thank Magnetti Larco Building, namely MSc Eng.s Claudio Failla, Sergio Signorini and Francesco Sonzogni, for having supported and promoted this research.
REFERENCES B. BARRAGAN (2002): Failure and toughness of steel fiber reinforced concrete under tension and shear, Doctoral Thesis, UPC, Barcelona, pp. 15I+appendices
3 00 2 3 4
5 6 7 8 9
10 11
12
13 14 15 16 17 I8
19 20 21
Liberato FERRARA
G. BATSON, E. JENKINS, R. SPATNEY ( 1 972): Steel fibers as shear reinforcement in beams, ACI Journal, 69,640-644 .M. Z. BAYASI, P. SOROUSHIAN (1992): Effect of steel fiber reinforcement on fresh mix properties of concrete, ACI Materials Journal, 89, 369-374. M. di PRISCO, C. FAILLA, R. FELICETTI, F. IORIO (2000,a): Precast high strength fibre reinforced roof elements , Studi & Ricerche, 21, 55-94 (in Italian) M. di PRISCO, R. FELICETTI, F. IORlO (2000,b): FRHPS roof elementsa. From constitutive to structural behaviour i n bending, Proc. BEFIB 2000, Lyon, 13-15 September 2000, P. Rossi and G. Chanvillard eds., 253-262 M. di PRISCO, L. FERRARA (2001): HPFRC pre-stressed thin-web elements: some results on shear resistance, Proc. FraMCoS4, Cachan 28 May- I June 2001, R. de Borst et al. eds., Balkema, Rotterdam, 895-902. M. di PRISCO, F. IORIO, G.A. PLIZZARI (2003): HPSFRC prestressed roof elements, in Test and Design Methods for Steel Fibre Reinforced Concrete Background and Experiences -,B. Schniitgen and L. Vandewalle (eds.), Rilem Publications, 161-188 J. EDGINGTON, D.J. HANNANT (1972): Steel fibre reinforced concrete. The effect on fibre orientation of compaction by vibration, Materiaux et Constructions, 5, 41 -44. K.S. ELLIOT, C.H. PEASTON, K. A. PAINE (2002,a-b): Experimental and theorectical investigation of the shear resistance of steel fibre reinforced prestressed concrete X-beams - Part I: experimental work - Part I[: theoretical analysis and comparison with experiments, Materials and Structures, 35, 5 19-535 C. FAILLA, G. TONIOLO, L. FERRARA (2000): Design criteria for structural use of fibre-reinforced concrete in prestressed precast roof elements, BEFIB 2000,253-262. C. FAILLA, G. TONIOLO, L. FERRARA (2002): Structural design of prestressed precast roof elements made with steel fibre reinforced concrete, Proc. BIBM 2002. C. F. FERRARIS, L: BROWER, C. OZYILDIRIM, J. DACZKO (1999): Workability of self-compacting concrete, Symp. Proc. of PCI/FH WA/FIB Int. Symp. on “High Performance Concrete: The Economical Solution for Durable Bridges and Transportation Structures” ,Orlando (FL) September 2527,2000 P: GROTH, D. NEMEGEER (1999): The use of steel fibres in self-compacting concrete, Proc. 1 Int. Rilem Symp. on Self-Compacting Concrete, 497-507. K.H. KHAYAT (1 999): Workability, testing and performance of self-consolidating concrete, ACI Materials Journal, 96, 346-353. K. H. KHAYAT, Y. ROUSSEL (1999): Testing and performance of fiber-reinforced self-consolidating concrete, Proc. 1’‘ Int. Rilem Symp. on Self-Compacting Concrete, 509-52 1. A. MEDA, F. MINELLI, G. PLIZZARI, P. RIVA, C. FAILLA (2002a): Shear Behaviour of precast fibre-reinforced beams, Proc. CTE Conference 2002,453-464 A. MEDA, G. A. PLIZZARI, F. SONZOGNI, T. LAMPERTI (2002b): Fibre distribution in fibre-reinforced structural elements, Proc. CTE Conference 2002, 247256 (in Italian) V. RAMAKRISHNAN, T. BRANDSHAUG, W.V. COYLE, E.K. SCHRADER (1980): A comparative evaluation of concrete reinforced with straight fibers and fibers with deformed ends glued together into bundles, ACI Journal, 77, 3, 135-143 J.P. ROMUALDI, G.B. BATSON (1963): Mechanics of crack arrest in concrete, AASCE Journal of Engineering Mechanics, 89, EM3, 147-168. M. SONEBI, P. J. M. BARTOS (1999): Hardened SCC and its bond with reinforcement, Proc. 1 ’‘ Int. Rilem Symp. on Self-Compacting Concrete, 275-289. M. SONEBI, W. ZHU, J. GIBBS (2001): Bond of reinforcement in self- compacting concrete, Concrete, 7, 26-28
’‘
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H.Marshall, eds. Warsaw, October 13-15 2003 ZTUREK RSIand Woodhead Pirbl., Warsaw 2003
OPTIMISATION OF THE RHEOLOGICAL AND FRACTURE MECHANICAL PROPERTIES OF LIGHTWEIGHT AGGREGATE CONCRETE Viktor MECHTCHERINE, Michael HAIST, Lothar STAERK and Harald S. MUELLER Institute for Concrete Structures and Building Materials, University of Karlsruhe 76 128 Karlsruhe, Germany, e-mail:
[email protected] ABSTRACT In this paper the basic procedure for the development of self-compacting lightweight concrete (SCLC) is presented. By using a rheological optimization approach SCLC with different unit weights could be developed. Further, the experiments carried out on hardened SCLC showed that its mechanical and fracture mechanical properties are comparable to those of LWAC with equal compressive strength. With regard to the brittle failure of LWAC and SCLC the effect of the addition of different amounts of steel, polypropylene and glass fibres on the rheological properties of fresh SCLC as well as on the properties of hardened concrete was investigated. Furthermore, a series of deformation controlled direct tension tests on notched prisms was performed in order to investigate the fracture mechanical behaviour of the developed concretes with and without fibre reinforcement. Keywords: self-compacting concrete, lightweight aggregates, rheology of fresh concrete, fibre reinforcement, fracture mechanics
INTRODUCTION Structural lightweight aggregate concrete (LWAC) possesses a number of favourable mechanical and physical properties such as high compressive strength in combination with a low unit weight and good thermal insulation capabilities. For this reason such a material is especially interesting in the field of renovation and retrofitting of existing structures. However, these advantages are opposed by the fact that the production, placement and compaction of LWAC are afflicted with various problems. Furthermore, at the hardened state, LWAC exhibits a high brittleness and, consequently, a pronounced tendency to the formation of cracks, e.g. due to high moisture or temperature gradients over the cross-section of the concrete structure. The problems concerning the properties of fresh concrete can be attributed to the fact that structural lightweight concrete is normally produced using porous aggregates. Unless stored under dry conditions these aggregates tend to absorb up to 40 mass% of water. This circumstance has to be accounted for in the mix design, for example by pre-wetting the dry aggregates. Used for the production of LWAC, such saturated aggregates reduce the risk of a premature stiffening of the mixture, which may lead to poor compaction (see Figure 1, left).
302
Victor MECHTECHERINE, Michael HAIST. Lothar STAERK and Harald S.MULLER
However, when exposed to accelerations due to the compaction process, the saturated aggregates tend to release parts of the absorbed water resulting in a sudden increase in the water content of the matrix. Strong variations of the effective water-cement ratio, a pronounced softening of the consistency or even segregation (“bleeding”) of the concrete are the consequences (see Figure 1, right).
Figure 1. Typical damages observed on structures made of lightweight aggregate concrete due to insufficient fresh concrete properties and improper concrete placement: poor compaction and leaking formwork (left) and “bleeding” of concrete due to overcompaction (right) Against this background it seems to be possible to strongly improve the quality of LWAC by using self-compacting lightweight concrete and therefore omitting the compaction process. This paper reports on the development and optimization of mixes for SCLC as well as on its rheological and mechanical properties. OPTIMISATION OF THE RHEOLOGICAL PROPERTIES I
Basic approach The principal demands concerning the rheological properties of SCC, like a high flowability, safe de-airing and sufficient cohesion of the batch as well as a high resistance against segregation (see [ 11) also apply to self-compacting lightweight concrete. However, with regard to the development of suitable mixes for SCLC, two major specific phenomena have to be considered: (1) lightweight aggregates absorb parts of the mixing water, which can lead to a premature stiffening of SCLC as well as to the total loss of self-compactability, (2) lightweight aggregates show a pronounced tendency to segregate (attributed to buoyancy). The first phenomenon can be countered by simply pre-wetting the porous aggregates with a defined amount of water. However, in order to inhibit the segregation of the concrete it is necessary to precisely adjust the rheological properties of the fines paste and the mortar, as these are the key to the successhl production of SCLC. For this purpose it is helpful to consider the forces acting on an aggregate grain dispersed in a surrounding liquid, i.e. mortar (see Figure 2). According to this simplified view, segregation, i.e. the reciprocal movement of the aggregate grain and the surrounding liquid, is only possible if the gravitational force G and the outer friction JrdO are exceeded by the buoy-
ancy force B. Therefore, in order to prevent segregation the optimisation of the rheological
Optimisation of the rheological and fracture mechanical properties of lightweight aggregate ...
303
properties of the mortar matrix should be aimed at maximising the outer friction acting upon the grain. However, the de-airing process, which is essential for the self-compaction, underlies the same basic mechanisms, though it deteriorates with increasing friction. It is therefore necessary to find an optimum between these two opposed requirements: a high resistance against segregation and a sufficient de-airing of concrete.
B = G + jr(y).dO 0
Figure 2. Requirements on the rheological properties of SCLC after placing in a formwork Against this background a series of experiments on lightweight pastes, mortars and concretes was carried out. The rheological properties of these materials, the viscosity p and the shear resistance to according to the Bingham model, were determined using a rotational rheometer [2]. By optimising the viscosity and the shear resistance of fines paste and mortar the resistance of SCLC against segregation could be increased significantly while ensuring an excellent workability and sufficient self-compacting properties of the lightweight concrete [2,3]. Composition and properties of fresh concrete Based on the results of the tests on paste and mortar, numerous different concrete mixes were developed by combining the optimized mortars with different kinds and amounts of coarse lightweight coarse aggregates [3,4]. The compositions of two representative mixes for SCLC are given in Table 1. Further, a representative LWAC mixture was investigated for reasons of comparison.
Table 1. Composition of the investigated lightweight aggregate concretes
cement fly-ash mixing water superplasticizer viscosity agent expanded clay sand 014 natural sand 012 expanded clay 418 unit weight of fresh concrete
[kg/m3] [kg/m3] [kg/m3] [kg/m3] [kg/m3] [kg/m31 [kg/m’] [kg/m3] [kg/m3]
SCLC 1 SCLC 2 LWAC 316 318 320 208 208 105 163 171 215 3.1 5.3 3.2 0.47 0.95 329 340 618 425 354 424 1770 1450 1460
304
Victor MECHTECHENNE, Michael HAIST, Lothar STAERK and Harald S.MULLER
In all mixes along with Portland-composite cement also fly-ash was used as binding agent. The use of a great amount of fly-ash leads to an increase in the flowability of SCLC while reducing the mortar density, due to its low unit weight (pra = 2.2 g/cm3). As fine aggregate natural quartzite sand (unit weight of solid particles 2.60 g/cm3, fines content 0.6 vol.%) was chosen for the production of SCLC 1, while for SCLC 2 and LWAC expended clay sand (unit weight of solid particles 1.3 g/cm3, fines content 20 vol.%) was used. Expanded clay with particle sizes ranging between 4 and 8 mm and a unit weight of solid particles of 1.1 g/cm3 was applied as coarse aggregate. All initial weights of the components given in Table 1 refer to oven-dry masses. The coarse aggregates were slightly pre-wetted with 10 mass% of the initial weight in the case of SCLC 1 and SCLC 2, while for the LWAC the pre-wetting amounted to 3 mass%. For the fine aggregates again 10 mass% of water for the pre-wetting were needed for expanded clay sand, whereas the natural sand was not pre-wetted. In order to achieve a good self-compactability 3.1 or 5.3 kg/m3 of a polycarboxilat-ether type superplasticizer and 0.47 or 0.95 kg/m3 viscosity agent were added to SCLC 1 and SCLC 2, respectively. In the case of the LWAC a sodium naphthalene sulfonate type superplasticizer was used. The unit weight of fresh concrete was 1770 kg/m3, 1450 kg/m3 and 1460 kg/m3 for SCLC, SCLC 2 and LWAC, respectively. Table 2 shows the most important results of the experiments on fresh concrete. The developed mixes provided slump flow values between 67 and 72 cm and thus correspond to the usual values for SCC with normal-weight aggregates. In contrast to earlier investigations [2], it was possible to significantly reduce the spreading time t5o and the v-funnel flow time below 10 s. Besides an excellent flowability the self-compacting concretes SCLC 1 and SCLC 2 showed a high resistance against segregation also during the placing by pumping. The results of corresponding laboratory and large scale experiments are presented in [ 5 ] . Table 2. Properties of the fresh self-compacting lightweight aggregate concretes slump flow spreading time t501’ v-funnel flow time [cml Is1 [SI 5 7 SCLC 1 67 SCLC 2 72 8 10 1) time for slump flow to reach a diameter of 50 cm concrete
The properties of the hardened concretes are given in Table 4. They will be presented and didcussed in the next chapter. OPTIMISATION OF FRACTURE MECHANICAL PROPERTIES
The development of self-compacting lightweight aggregate concrete (SCLC) leads to a highperformance building material, which however shows a rather brittle fracture behaviour, typical for all lightweight aggregate concretes. In order to increase the ductility of such concretes a fibre reinforcement may be applied. Within this research project, the effect of the addition of different amounts of steel, polypropylene and glass fibres on the rheological properties of fresh SCLC as well as on the properties of hardened SCLC was investigated.
Optirnisation of the rheological and fracture mechanical properties of lightweight aggregate ...
305
Properties of fresh SCLC with fibre reinforcement For this investigation, SCLC 2 (see Table 1) was chosen as a reference mix, on which the influence of the addition of different types and amounts of fibres was studied. Therefore, the properties of fresh concrete, i.e. the flowing behaviour of mixes containing fibres, were measured using the slump-flow test. Table 4 gives the properties of the fibres used in these experiments. Table 3. Properties of the fibres used in the experiments Properties material of fibres
unit weight wcm31 7.80 0.91 2.70
steel, drawn wire polypropylene glass, alkali-resistant
modulus of elasticity [MPaI 210 000 13 000 72 000
length [mml 35 12 12
Figure 4 shows the effect of the fibre content for various types of fibres on the slumpflow behaviour of the reference mix (concrete SCLC 2, see Table. 1). According to these results, even relatively small additions of polypropylene or glass fibres of up to 0.2 vol.% of the concrete volume cause a reduction of the slump flow of up to 34 %, whereas the effect of the addition of steel-fibres is much less pronounced. This observation was traced back to the fact, that due to their fineness, both polypropylene and glass fibres possess - in comparison to steel fibres - a much larger specific surface, which has to be bedewed by the mixing water. Further, a too high dosage of fibres results in an accumulation of fibres and coarse aggregates in the centre of the slump flow (comparable to hedgehog-like structures) and a very uneven slump flow. This is especially true for mixtures containing steel fibres, which were significantly longer and stiffer than the other fibres used.
80
-s 70 Y
g
60
G=
g 50 40
; 1
+SCLC 2 with steel fibres
I
1 -0-SCLC2withPPfibres
I
I
I
--&-SCLC 2 with glass fibres
30 I 0.00
0.20
0.40
I
I
0.60
0.80
1.oo
fibre content [vol.%]
Figure 4. Effect of the type and content of fibres on the slump flow of SCLC 2 On the basis of the results of the experiments on fresh concrete it can be concluded, that the maximum content of fibres, which can be added to SCLC without affecting its flowability and self-compactability, strongly depends on the type of fibres. This “limit content” is approx.
306
Victor MECHTECHERINE, Michael HAIST, Lothar STAERK and Harald S.MULLER
0.5 vol.% for steel fibres and approx. 0.1 vol.% for polypropylene or glass fibres, respectively. Properties of hardened concretes with and without fibre reinforcement For the experiments on hardened concrete SCLC 2 without reinforcement was again chosen as a reference. Based on its composition three further concretes containing the limit contents (compare previous section) of steel, polypropylene and glass fibres, respectively, were produced and tested. In order to clarify the effect of the self-compactability on the mechanical and fracture mechanical properties of lightweight aggregate concrete also the concrete LWAC was tested, both without fibres and with 0.5 vol?? of steel fibres. Furthermore, investigations on the self-compacting concrete with quartzite sand SCLC 1 without fibres were carried out. The compressive strength was determined on cubes with a length of 150 mm, which were demolded one day after concreting, stored in a constant climate at 20°C and 98% r.h. up to the age of 7 days and at 20°C and 65% r.h. up to the age of testing (28 days). Table 4 gives the average values of the compressive strength fc,& and the modulus of elasticity Eo for the investigated concretes. The self-compacting concretes provided higher values of the compressive strength. This holds true especially for the concrete SCLC 1, which was produced using natural quartzite sand. The addition of steel fibres showed practically no effect on this material property in the case of the LWAC. For the self-compacting concrete SCLC 2 however a slight increase of the fc,cuh-valuescould be observed as a result of the fibre reinforcement, both with polypropylene or steel fibres. One reason for this might be the decrease of the effective waterhinder ration due to the “binding” of some part of the mixing water on the surfaces of fibres. On the other hand the fibres seem to hinder the propagation of the cracks at this stage already, which leads to a higher load-carrying capacity of the concrete. In the case of the LWAC, the modulus of elasticity Eo did not change significantly due to the addition of fibres (see Table 4). For the concrete SCLC 2 nearly the same Eo-values were measured as for the LWAC. In the case of SCLC 2 the addition of fibres leaded to a slight but clear increase of the modulus of elasticity, unrespectable of the type of fibres. The highest Eovalues equal to 24.3 GPa were obtained for SCLC 1. The measured Eo-values correspond well to the modulus of elasticity as estimated according to the German building code DIN 1045-1 [6], on the basis of the measured compressive strength of SCLC. Table 4. Results of the mechanical and fracture mechanical experiments Compresive Modulus of strength fc,cuh elasticity Eo WaI [GW LWAC without fibres 33.2 15.7
Type of concrete
Net tensile strength fm WaI 1.55
Fracture energy GF m/m1 31
LWAC with 0.5 vol.% of steel fibres SCLC 1 without fibres
32.8
14.8
1.50
1700
5 1.9
24.3
2.80
51
SCLC 2 without fibres
40.9
15.5
1.70
37
SCLC 2 with 0.1 vol.% of polypropylene fibres
43.7
17.4
1.85
42
SCLC 2 with 0.5 vol.% of steel fibres
47.2
17.1
1.85
2000
Optimisation of the rheological and fracture mechanical properties of lightweight aggregate ...
307
In order to investigate the fracture mechanical behaviour of the concretes deformation controlled direct tension tests were performed on notched prisms. Figure 5 shows the used test set-up. The specimens had a length of 250 mm and an effective cross-section of 60x 100 mmz. All specimens were cast horizontally in metal forms. After demoulding, the specimens were wrapped in a thin plastic sheet in order to protect the concrete against desiccation. All specimens were tested at a concrete age of 28 days. The tension tests were performed with non-rotatable boundaries. For this purpose stiff metal adapters were glued to the specimens. Finally, the metal adapters were firmly connected with the bearing platens of the testing machine. In the tests, the deformation rate was controlled by means of the average signal of two LVDTs with a gauge length of 25 mm, which were placed on the notch tips (LVDTs 1 and 6 in Figure 5). Further LVDTs with a gauge length of 25 mm and 50 mm, respectively were placed on the notch tips, notch mouth and in the middle of the crosssection on both sides of the specimen in order to measure local deformations. Because of the localized cracking due to the notches and the reduction of the gauge length for the control of deformation rate to 25 mm the descending branch of the 0-6 relation could be determined up to nearly complete separation of the specimens into two parts.
-
-
-
100 0
Figure 5. Set-up of the direct tension tests on concrete prisms (left) and schematic view of the positioning of the LVDTs (right, geometrical data in [mm])
308
Victor ivfECHTECHERINE. Michael HAIST, Lothar STAERK and Harald S.MULLER
The tensile tests were performed with a deformation rate of 6 = 5.10' m d s . For each investigated parameter at least three specimens were tested. Further details concerning the test set-up and the carrying out of the experiments may be found in [7]. The mean curves for the stressdeformation relations obtained from the direct tension tests for several of the investigated concretes are given in Figure 6. Special focus was hereby directed at the differences of the curve shape after exceeding the peak stress. The curves for the concretes without fibres - SCLC 1, SCLC 2 and LWAC - do not differ significantly (therefore, for the reason of clearness only the mean curve for SCLC 2 is shown in Figure 6), besides some differences mainly due to the variation of the net tensile strength (see the f,-values in Table 5).
0.00
0.05
0.10
0.15
0.20
0.25
deformation 6 [mm] Figure 6. Mean stress-deformation relations obtained from the direct tension tests on the concrete prisms with and without fibre reinforcement The addition of the polypropylene fibres (0.1 vol.%) to SCLC 2 has only minor influence on the softening behaviour of this concrete: The mean curve for SCLC 2 with fibre reinforcement runs only slightly above the corresponding curve for this concrete without fibres at deformations (or crack openings) of approx. 0.03 mm and greater (see Figure 6). Nearly the same results were obtained also for SCLC 2 with glass fibres (not shown here). However, in the case of concretes with steel fibre reinforcement, a very pronounced increase of the ductility for both the LWAC and SCLC 2 could be observed. The stress-deformation relation for SCLC 2 runs clearly above that curve for the LWAC up to a deformation of approx. 0.8 mm (not shown in Figure 6). Beginning at this deformation the curves for both concretes are nearly identical (at least up to an entire deformation of 1.O mm, at which the experiments were finished, because of the limited capacity of the LVDTs).
Optirnisatiori of the rlieological and fracture mechanical properties of lightweight aggregate ...
309
The observed higher ductility of self-compacting concrete SCLC 2 containing the same amount of fibres as LWAC can be explained by the fact that due to a very high flowability of SCLC 2 a more pronounced orientation of the fibres during the casting process of the forms placed horizontally is achieved. Further, supposedly a better bond between the binder matrix and fibres develops because of a denser structure of the binder lime and a better coating of fibres with the lime in the case of the self-compacting concrete. Table 4 gives the values of the net tensile strength ftn and the fracture energy GF evaluated on the basis of the stress-deformation relations. For both SCLC 2 and LWAC, practically no effect of fibres on the fm-values could be observed. The effect of the composition of nonreinforced concrete is however evident. Self-compacting concrete SCLC 2 provided a higher net tensile strength than the ordinary LWAC. This can be traced back to a lower water/binder ratio of SCLC 2. The highest average ftn-value equal to 2.8 MPa was obtained for SCLC 1, which possesses the mortar matrix with natural quartzite sand. The fracture energy GF is defined as the energy per unit area needed for the separation of a specimen into two parts. This value corresponds to the area under the complete stressdeformation diagram (for this reason an extrapolation of the measured curves was carried out for deformations greater than 1.0 mm in the case of concretes with steel fibres). The fracture energy of the self-compacting concrete SCLC 2 is slightly higher than the corresponding value of the LWAC, but slightly lower than the fracture energy of SCLC 1 (SCLC with quartzite sand). The addition of the polypropylene fibres (0.1 vol.%) to the concrete SCLC 2 leads only to a minor increase of the GF-value from 37 N/m (without fibres) to 42 N/m (with fibres). The addition of steel fibres has a much more pronounced effect on the values of the fracture energy. For the LWAC with 0.5 vol.% of steel fibres an average GF-value equal to 1700 N/m was measured. The self-compacting concrete SCLC 2 with the same fibre content provided the fracture energy of 2000 N/m. CONCLUSIONS
In this study, self-compacting lightweight aggregate concretes were developed and optimized by investigating the rheological behaviour of paste, mortar and subsequently concrete. This approach enables to obtain concretes with the desired properties efficiently and rapidly. Further, the effect of the addition of fibres on the properties of the fresh and hardened SCLC was studied. The workability of SCLC remains sufficient only up to some defined percentage of fibres. This limiting content depends strongly on the type of fibres. Considering the mechanical properties of SCLC, the addition of steel fibres causes a great increase of the fracture energy, whereas with regard to the compressive strength and the net tensile strength of these concretes only a minor improvement could be achieved. The fracture mechanical properties of self-compacting lightweight aggregate concrete are superior to those of ordinary LWAC for the testing conditions used in these investigations. REFERENCES 1. Okamura, H., Ozawa, K., Ouchi, M., Self-compacting concrete. Structural Concrete, Vol. 1, NO. 1,2000, pp 3-17 2. Mueller, H. S., Mechtcherine, V., Haist, M., Development of self-compacting lightweight aggregate concrete. Proceedings of the Second International Symposium on Self-Compacting Concrete, K. Ozawa and M. Ouchi eds., COMS Engineering Corporation, Kochi, Japan, 2001, pp 737-742
3 10
Victor MECHTECHERINE, Michael HAIST, Lothar STAERK and Harald S.MULLER
3. Haist, M., Mechtcherine, V., Mueller, H. S., High performance self-compacting lightweight aggregate concrete with and without fibre-reinforcement. 6* Int. Symposium on Utilisation of High StrengthlHigh Performance Concrete, Conference proceedings, Leipzig, Germany, 2002 4. Mechtcherine, V., Haist, M., Hewener, A., Mueller, H. S., Self-compacting lightweigbt concrete - a new high-performance building material. The First fib Congress, Conference proceedings, Osaka, Japan, 2002 5. Haist, v., Mechtcherine, V., Beitzel, H., Mueller, H. S., Retrofitting of building structures using puntpable self-compacting lightweight concrete. Proceeding of the 3'd International Symposium on Self-compacting Concrete, Iceland, 2003 (accepted for publication) 6. DIN 1045-1, Structures of Concrete, Reinforced Concrete and Pre-stressed Concrete, Part 1: Design Rules (in German). Berlin, Beuth Verlag, Germany, 2001 7. Mechtcherine, V., Fracture Mechanical and Fractological Investigations on the Formation and Propagation of Cracks in Concrete (in German). Institute of Concrete Structures and Building Materials, University of Karlsruhe, Vol. 40,2000
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Wursaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
DESIGN AND TESTING OF SELF-CO IPACTING SIFCO i PRODUCED WITH LOW STRENGTH SLURRY Lucie Svermova, Mohammed Sonebi, Peter J.M. Bartos Advanced Concrete and Masonry Centre University of Paisley Paisley, PA1 2BE, UK, e-mail:
[email protected] ABSTRACT Slurry Infiltrated Fibre Concrete (SIFCON) is produced by a process in which fibres are put into an empty mould, after which the fibre mass is infiltrated by a cement slurry. Generally, the infiltration of the slurry into the layer of fibres is carried out under intensive vibration. Recent research has investigated the development of slurries which do not require to be vibrated when SIFCON is produced. Samples of self-compacting SIFCON were produced and tested for flexural and compressive strength. Three different orientations of fibres in testing samples were obtained. A three-point bending test with displacement control system was used for testing the beams. Basically, the results showed higher flexural strength and energy absorption compared with plain cement slurry. The anisotropy of SIFCON was shown from results of samples which had different orientation of fibres. Keywords Compressive strength, flexural strength. self-compacting SIFCON
INTRODUCTION New developments in steel fibre-reinforced cement composites have appeared during the last forty years. Slurry Infiltrated Fibre Concrete (SIFCON) can be regarded as a special type of steel fibre-reinforced cement composite. Normally, fibre reinforced concrete contains I-3% fibres by volume, while SIFCON contains between 4-25% fibres [I]. The volume of fibres is influenced by fibre type and manner of fibre placing [2]. The first introduction of cement composites with a high content of fibres infiltrated with Portland cement-based materials was made by Haynes in 1Y6X 131. It was first to use the principle of adding fibres into a mould first and then infiltrating the fibre mass by a cement slurry. This approach introduced the possibility 0 1 producing concrete with high volumes c,f' steel fibres and later this kind of material becam: known as SIFCON. Naanian et el proposed the use of SIFCON for 101 . t b in seismic resistant reinfoi,ced concrete frames [4]. SIFCON would be used only in stnall parts of the frames. These parts would be designed to bc affected during seismic 1oadi:ig and form 'plastic hinges', which would ,ibsorb the frachire energy and protect the constructions against coilape. '%r: challenge
3 12
Lucie SVERMOVA. Mohammed SONEBI and Peter J.M. BARTOS
is to ensure that the frame would crack in the areas where moderate/low strength SIFCON has been placed. When hardened, SIFCON exhibits high fractional energy absorption and is capable of transferring load even after considerable deformation. It can also be repaired. Previously, the infiltration of fibres could only be achieved with the assistance of intensive vibration. Bartos and Marrs [ 5 ] came up with the idea of producing SIFCON without vibration. More research on self-compacting SIFCON was carried out, particularly concerning the behaviour of fresh cement slurries containing limestone powder [6,7]. This research brought about the possibility of designing ‘low strength slurry’ for the production of self-compacting SIFCON, which should guarantee the formation of ‘plastic hinges’ in reinforced concrete frames during seismic loading. The aim of this research was the investigation of flexural and compressive strength of self-compacting SIFCON produced with ‘low strength slurry’ and different orientations of fibres, which were obtained by the shape of the moulds. The flexural strength was tested on cut and directly produced beams by a three-point bending test with displacement control. The compressive strength was tested on cut and uncut samples. Cube and beam samples from plain cement slurry were produced and the results of SIFCON samples and plain sluny samples were compared. MATERIALS Slurries were produced from Ordinary Portland cement (class 42.5 N), limestone powder, superplasticiser, viscosity agent, fine sand and tap water. The grading of limestone powder produced from carboniferous limestone of a very high purity was 98% < 45 pn and 25% < 5 pm, and limestone powder was finer than cement. The relative density of the limestone powder was 2.65. Fine sand with a maximal grain size of 0.6 mm was used. A modified polycarboxylate superplasticiser, containing 30% solids by mass and 1.1 1 specific gravity, was used. Powdered microbial polysaccharide welan gum was used as a viscosity agent. Dramix RL-45/35-BN steel hooked fibres with length 35 mm and aspect ratio (1engWdiameter) 48 were used to assess the penetrability of cement slurry measured by the Jfibre penetration test which was introduced in references [6,7] and was used for verification of produced mixes. All samples of SIFCON which were tested for flexural and compressive strength in this study were produced from low carbon steel hooked fibres with a tensile strength 950 MPa Dramix RL-45/50-BN, are 50 mm in length and have an aspect ratio of 48. SHAPE OF SAMPLES Previous researches underlined the anisotropy of SIFCON which is caused by the orientation of fibres in samples [%lo]. The orientation of fibres was influenced by the shape of the mould and turning of the samples after production. The test samples had been produced either in the beam position mould (100 mm high) or the column position mould (350 mm high), which caused different orientations of fibres to the plane of rupture during testing of samples. The beams had dimensions of 100 mm x 100 mm x 350 mm. The other approach for the production of samples was to cut beams and cubes from the block of SIFCON. The reason for this approach was the elimination of the wall effect of fibres in the sides of mould. Three 510 mm x 410 mm x 190 mm prism blocks of SIFCON were produced. One prism was 410 mm high and the other two had a height of 190 mm to obtain the required orientation of fibre. Three beams with dimensions of 100 mm x 100 mm x 350 mm and three cubes 100 mm long were sawed from each block (Figure 1).
Design and testing of self-compacting SIFCONproduced with low strength slurry
313
Straight cast cubes of SIFCON 100 mm long were produced for verification of the difference between straight cast and sawed samples.
MIX PROPORTIONS
The proportional design of slurry was selected following the previous results obtained from a fractional factorial statistical design model for five independent variables (waterhinder ratio (WE%),proportion of limestone powder (LSP) and sand, and dosage of superplasticiser (SP) and viscosity agent (VA)) [6,7]. The statistical model was valid for mixes with 10-50% limestone powder as replacement of cement, 0.02-0.06% viscosity agent by mass of cement, 0.6-1.2% superplasticiser and 50-150% sand (% mass of binder) and 0.42-0.45 W/B. The selected mix in this study was made with 0.44 W/B (where binder is the content of cement and limestone powder), and 45% of LSP. The dosages of SP and VA were 0.70% and 0.05%, respectively. Finally, the proportion of sand was 50%. The volumes of fibres in the test samples were calculated from the weight of fibres placed into the moulds. The percentage volume of fibres varied from 9.2% to 10.8%0, depending on the shape of mould. The least volume of fibres (9.2%) was obtained when fibres were randomly poured by hand into the column position mould. The samples produced in the beam position moulds had fibre volume of 9.4%. The cubes had fibre volume of 9.7%. Finally, both types of SIFCON blocks had 10.8% volume of fibres. The different percentages of fibres in the different shapes of mould underline the wall effect of fibres at the sides of the moulds, which decreased the volume of fibres in the samples. This claim is apparent from the volume of fibres in the column shape mould, where the volume of fibres was 1.17 times smaller than the samples which were produced from much larger blocks of SIFCON. PRODUCTION OF TEST SPECIMENS
Three blocks of SIFCON, three column samples, six beam samples and six cubes were produced for testing the flexure strength and compressive strength of SIFCON. Three beam and three cube control samples without fibres were produced and their results were compared with the results of SIFCON samples.
3 14
;ucici SVERMOVA. Mohammed SONEBI and Peter J.M. BARTOS
Firstly. the fibres were placed into the mould by hand to make sure that the fibres occupied the entire moulds. The required volume of slurries was calculated and produced. Two 60-litre mixes and one 75-litre mix were prepared for the production of all samples. The following approach was used for production of the slurry mixes: firstly, the dry mix of cement, limestone powder and viscosity agent powder were mixed together. Then, a mix of water and superplasticiser was preparcd in the mixer. The dry mix of cement, limestone powder and viscosity agent was sieved into the mix of water and superplasticiser during mixing. All components were mixed together for 15 minutes. Mixing time was measured from the start of the addition of the dry mix into the mixer. This approach was found useful for producing a homogenous mix of cement slurry which was able to infiltrate the mass of fibres prepared in the moulds. Slurry was cast into the moulds through a sieve to control the speed of pouring and thus prevent the slurry filling the top of the moulds and trapping air among the fibres at bottom. The second reason for sieving the slurry into the moulds was to ensure thorough mixing of all components. The samples were demoulded after two days and left in the same conditions in the laboratory, because the blocks of SIFCON were too big and heavy to be put into a water bath. The blocks were sawed during the four weeks after casting to produce 3 beam and 3 cube test samples. TESTING OF SAMPLES All samples were tested at 28 days. A three-point bending test with displacement control was chosen to obtain ‘post-peak’ behaviour. The speed of loading was 1 mm per minute. The span of roll supports was 300 mm. A 20 mm deep notch was sawed in the middle of each beam sample. Three variables of fibre orientation had been obtained and for each variable three samples were produced. Two different fibre orientations to the plane of rupture were obtained from the moulds in beam position. The first types of beam samples were tested in the classical position for steel fibre reinforced concrete, i.e. the samples were turned in such a way that the casting surface was perpendicular to the notch and loading force (Figure 2a). The second type of samples had parallel orientation of casting surface, notch on beams and loading force (Figure 2b). The beams which were produced in the column shape mould were the third type of test samples (Figure 2c). The beams cut from the blocks of SIFCON were divided into the same three sample types from the point of view of orientation of casting surface and load cell. The only difference was the cutting away of the parts with wall effect at the sides of moulds. The compressive strength was tested with a constant increase of load. The straight cast cubes were tested with two different orientations of fibres. Firstly, the casting surface was turned perpendicular to the loading cells (Figure 3a) and secondly, the load was applied on the casting surface (Figure 3b) The cubes cut from the SIFCON blocks had the same position of casting surface to the loading cells as the straight cast cubes.
315
Design and testing of self-compacting SIFCON produced with low strength d u r n ,
Load cell
25
150
Casting surface
150
Load cell
I00
25
25
w
150
150
25
100
I r
Load cell
25
150
Casting surface
Casting surface
150
25
I00
I
Figure 2: Placing and dimensions (in mm) of beam samples during test (a)
(b) Load cell
Load cell
w Figure 3: Placing and dimensions (in mm) of cube samples during test
TESTS RESULTS AND DISCUSSION Flexural strength The flexural strength f, corresponding to the maximal obtained load was calculated using the following expression:
where F,, = is equal to the highest value of the load (N/mni'), L = span ot the specimen (mm),
3 16
Lucie SVERMOVA, Mohammed SONEBI and Peter J.M. BARTOS
b = width of the specimen (mm), h = distance between tip of the notch and top of cross section (mm). The results of the flexural behaviour are presented in Table 1. Figures 4 and 5 represent the typical displacement vs. load behaviour of the individual types of test beam samples. Each time, three samples were tested and from these samples one was chosen and illustrated in these figures. The values of maximal load, average maximal load with coefficient of variation, flexural strength fl and average flexural strength with coefficient of variation for individual types of samples are shown in Table 1. Volume of fibres
Sample
(“/.I
load (kN)
1
Plain slurry 2
0
3 1
a
2 3
9.4
1
Cast
b
2 3
9.4
1
c
2 3
9.2
1
a Cut
b
2 3
10.8 10.8
2.2 2.3
38.2 40.7 38.8 25.9 26.6 32.0 12’0 10.2 11.6
33.5 32.2 40.1 31.6 31.0
Average Flexural Average Energy Average maximal strength flexural energy absorption load strength absorption ( k ~ ) ( ~ / m m, * m/mm2) ). (N.m) W.m) 0.5 2.1 la4 1.6 o.6 0.7 (9.8 %)
39.2 (3.3 %)
28*o 28.0 25.2
(9.8 %)
0.9
(31.2 %)
27.1
405*8 440.2 434.2
426.7
(6.0%)
(13.9%)
11.3
17” 17.3 21.7 8.3 7.8
(8.4%)
8.0
35.3
24‘4 26.4 28.6 20.5 21.1 4.8 7.0
28‘2 (11.9%)
(12%)
31.3 (1.4%)
1 7.7 2 10.8 9.2 3 7.2 (16.6%) (Bracket values): coefficient of variation c
1.6 1.7
5.0
18.7
8.0
270’6 287.4 333.7
(4.3 %)
297.2 (11.0%)
125.7
(3.1 %)
130.3 131.3
(7.0%)
26.5
367’7 339.8
389.0
(7.9%)
(16.1 %)
(2.0%)
459.5 355.2 345.9
77.6
(21.7%)
72’6 110.6 49.7
20.8
350.6 (1.9%)
(39.6%)
Table 1: Flexural strength of SIFCON Most types of samples had a coefficient of variation less than lo%, which is related to good correlation between the test results of individual test samples. Only the samples which were straight cast and with the casting surface parallel to the load cell had a coefficient of variation for flexural strength equal to 13.9%. The cut samples from the 410 m m high block had the highest coeficient of variation for flexural strength, which was 21.7%. The highest load was transferred by samples which were cast straight to the mould and had the casting surface perpendicular to the load cell. The 39.2kN average maximal load was measured and the calculated flexural strength was equal to 27.1 N/mm2. Similar average
317
Design and testing of self-compacting SIFCONproduced with low strengih slurv
flexural strength of 26.5 N / m 2 was calculated from the samples with the same orientation of casting surface to the load cell, but these samples were cut from a SIFCON block and their average maximal load was 35.3 kN. These samples had the most suitable orientation of fibres to the plane of rupture to transfer increasing load. 3 1.5 kN average maximal load was measured on samples with parallel orientation of the casting surface and the load cell which were cut from a SIFCON block and the average flexural strength was equal to 20.8 Nlmm’. The cast samples in the same position had 28.2 kN average maxima1 load and 18.7 N/mm2 average flexural strength. The volume of fibres turned to the plane of rupture in a suitable direction decreased, which caused decreased flexural strength compared with the previous example. The lowest maximal flexural strength was obtained by the samples which were cast in the column position mould and in the prism block with a height of 410 mm. The cut beam samples produced from these shaped moulds were able to transfer maximal load of 7.7 kN, compared with the 11.3 kN by straight cast samples. Maximal flexural strength was equal to 5.6 N/mm’ for cut beams and 8.0 N/mm’ for beams cast straight into the moulds. The average maximal load and the related flexural strength of the plain cement slurry beams were 2.1 kN and 1.6 N/mm’, respectively. The test results were influenced by volume of fibres in the samples and method of production, i.e. whether they were straight cast or cut from the blocks. The samples which were cut from the blocks did not have the wall effect of fibres at the sides of the mould and the volume of fibres in these samples was higher than in the samples cast straight into the moulds. On the other hand, the fibres on the sides of the cut samples were shorter after cutting and were able to transfer a lower load, mainly during the bending test, because the shorter fibres are easily pulled out from the cement slurry and are not able to transfer high load.
30
1
beam(1a)
ccut
10
0 0
5
10
15
20
25
30
35
Displacement (m)
Figure 4:Typical load-displacement curves for beams cut from blocks of SIFCON
3 18
Lucie SVERMOVA. Mohamtired SONEBI and Peter J.M. BARTOS
...
30
.
-
10
-.
- .
..
-
-
plan slurry (2) cast beam(3c) -V
- ’.._. *,
0 0
5
10
1s
20
25
30
35
Displacement (m)
Figure 5 : Typical load-displacement curves for straight cast beams
Energy absorption The ‘post-peak’ part of the load-displacement curves of SIFCON decrease gradually compared with the example of plain cement slurry. This behaviour was recorded by all SIFCON samples and indicated high ductility and high capacity for energy absorption. This typical behaviour of SIFCON makes it a suitable material to use in seismic resistant frames, because it is able to transfer relatively high load even when broken. The value of energy absorption was calculated as the area under the load-displacement curve for displacement from 0 to 15 mm (Table 1). The highest values of energy absorption corresponded with the highest maximal load and maximal flexural strength. The cast and cut beams with perpendicular orientation of cast surface to the load cell and the notch had average energy absorption of 426.7 Nm and 389.0 Nm, respectively. The beam saniples cut and cast with parallel orientation of cast surface, load cell and notch on beam had energy absorption of 350.6 Nm and 297.2 Nm. The lowest values of energy absorption (125.7 Nm and 77.6 N m ) were calculated on the cast and cut beams produced in the column position mould, respectively. The average value of energy absorption (0.7 Nm) on plain slurry beams wits calculated for the comparison of much lower energy absorption for this type of concrete. Compressive strength The compressive strength of SIFCON (f,) was measured on thc straight cast cubes and cubes which were cut from the blocks. The influence of the fibre orientation in the samples was verified. Table 2 shows the individual and average values of measured maximal load and calculated compressive strength obtained from the three measurements on each type of samples and the average results of the three plain cement slurry samples. The coefficients of variation are also given in Table 2.
319
Design and testing of self-compacting SIFCONprodticed with low strength slurry
Average Volume Maximal Average Compressive compressive offibres load strength f, strength load (%) (m) (kN) (N/m2) (N/mm2)
Sample
1 Plain slurry 2 3
0
1
a
2 3
b
2 3
Cast
9.4
1
9.4
1
a cut
2 3
10.8
321 318 300 273 282 284 343 3 67 543 335 311 316
313.0 (3.6%)
279.7
-
417.7 (26.1 %)
320.7 (3.9 %)
1
793 891.7 904 3 978 (10.4%) (Bracket values): coefficient of variation b
2
10.8
32.1 31.8 30.0 27.3 28.2 34.3 36.7 54.3 32.7 30.3 30.7 80.9 87.3 96.4
31.3 (3.6 %)
28.0 . _-
41.11 (26.1 %)
31.2 (4.1 Yo)
88.2 (8.8 %)
Table 2: Compressive strength of SIFCON The coefficients of variation for results of compressive strength are mostly lower than the coefficient of variation for flexural strength. Only the straight cast cubes with casting surface parallel to the load cell had a high value of coefficient of variation equal to 26.1%. The main influences on the results were the orientation of fibres and the method of sample production. The highest compressive strength (88.2 N/mmz) represented the samples which were cut from the SIFCON blocks and had the casting surface parallel to the load cell. The compressive strength 41.8 N/mm2 represented the cubes which were cast straight in the moulds and also had parallel orientation of the casting surface to the load cell. The samples with perpendicular orientation of the casting surface to the load cell had similar or even smaller compressive strength than the plain cement slurry. The compressive strength of plain slurry and the cube samples cut from a block represented strength of 3 1.2 N/mm2 and 3 1.3 N/mm2, respectively, while the compressive strength of the straight cast sample was 28 N/mm2. CONCLUSIONS Several tests of flexural and compressive strength on SIFCON with different orientations of fibres were carried out and the following conclusions can be made: The test results underline the expected unisotropy of SIFCON. Even though the test samples were produced from the same components and same type of fibres, the results of the maximal flexural strength and compressive strength are different and depend on the orientation of fibres to the plane of rupture. The flexural strength of SIFCON is between 3.7 times and 18 times higher than that of plain cement slurry. This depends on the orientation of fibres to the plane of rupture.
320
Lucie SVERMOVA, Mohammed SONEBI and Peter J.M.BARTOS
Whether the samples were straight cast or cut from a block of SIFCON had no serious influence on flexural strength. The ‘post-peak’ behaviour of all SIFCON samples showed this material to have low brittleness and high ductility and energy absorption, which suggested the suitability of this material for use in seismic areas. The compressive strength of SIFCON was affected by the placing of fibres and by the method of production (straight cast samples or samples cut from a block of SIFCON). The cut cubes with the orientation of fibres mostly parallel to the load cell had 2.8 times higher compressive strength than the plain slurry. On the other hand, the straight cast samples with the casting surface oriented perpendicular to the plane of rupture had compressive strength 1.1 times smaller than the plain cement slurry.
References 1. Naaman, A.E. and Baccouche, M.R., Shear response of dowel reinforced SIFCON, ACI Structural Journal, 92, 1995, pp. 587-596. 2. Reinhardt, H.W. and Fritz, C., Optimization of SIFCON mix, fibre reinforced concrete recent developments, Ed. by Swamy, R.N., and Ban-, B., Elsevier Applied Science, 1989, pp. 11-20. 3. Haynes, H., Investigation of fibre reinforcement methods for thin shell concrete, Naval Civil Engineering Laboratory, Port Hueneme, CA, N-979, 1968, pp. 1-26. 4. Naaman, A.E., Wight, J.K. and Abdou, H., SIFCON connections for seismic resistant frames, Concrete International, 1987, pp. 34-49. 5. Bartos, P.J.M. and Marrs D.L., Development and testing of self-compacting grout for the production of SIFCON, In: Proc.Int.Work. “High performance fibre reinforced cement composites”, Ed. by Reinhardt, H.W. and Naaman, A.E., RILEM, Mainz 16-19 May 1999, pp. 171-179. 6. Svermova, L. and Bartos, P.J.M., Development of in-situ SIFCON for connections in precast concrete and seismic resistant structures. In: Proc.Int.Conf. “27Ih Conference on Our World in Concrete & Structures”, Singapore 29-30 Aug 2002, pp. 553-559. 7. Sonebi M., Svermova L. and Bartos, P.J.M., Development of Cement Slurries Containing Limestone Powder for Self-compacting SIFCON by using Factorial Design Plans. Submitted to ACI Material Journal, 2003. 8. Wang, M.L. and Maji A.K., Shear properties of Slurry Infiltrated Fibre Concrete (SIFCON), “High Performance Fibre Reinforced Cement Composites”, Ed. by Reinhardt, H.W., and Naaman, A.E., RILEM, 1991, pp. 203-212. 9. Van Mier, J.G.M. and Timmers, G., SIFCON subject to shear: effect of material anisotropy on strength and stiffness, “Fibre Reinforced Cement and Concrete”, Ed. by Swamy R.N., Proceedings of the 4Ih International Symposium, Sheffield 1992, pp. 245-256. 10. Svermova, L., Anisotropy of concrete with high content of fibres, the Eleventh Annual BCNConcrete Society Conference on Higher Education and the Concrete Industry, Manchester, Concrete Communication Conference 2001, pp. 367-377.
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt. V.C. Li and I. H. Marshall, eds. Warsaw. October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
THE INFLUENCE OF SELECTED COMPOSITION FACTORS ON THE RHEOLOGICAL PROPERTIES OF FIBRE REINFORCED FRESH MORTAR
Tomasz PONIKIEWSKI, Janusz SZWABOWSKI The Silesian University of Technology, Department of Building Processes Akademicka 5,44- 100 Gliwice, Poland, e-mail:
[email protected];
[email protected] ABSTRACT
In the paper the methodology and test results of the investigation are presented and discussed on the influence of fibres on rheological properties of modified standard mortars. The rheological parameters of fibre reinforced fresh mortars (FRFM) - yield value and plastic viscosity were determined. FRFM behaves as a Bingham body, their rheological parameters were determined by using rheometer to pastes and mortars. In the research, an experimental verification of a significance of an influence: WIC ratio, volume fraction of fibres, lengths and kind of materials of fibres on rheological properties of FRFM was investigated. In the paper the results obtained for mixes with polypropylene, steel, carbon and glass fibres are presented. The first step of the procedure was a rheological identification of fiber-mortars, which was completed based on the delimitation of the tension due to an assignment of characteristic dependence - speed of non-dilatational strain, in the form of a curve flow and acceptance of adequate model and rheological equalizations. This equalization is a base to the experimental analyses which influences composition factors of mixtures on the character of their flowing and rheological parameters. The analysis of the results of these measurements permitted on the following qualifications: reliable statistics of rheological parameters from variables, indications of workability forms of mortars with fibres and approximate reliability among rheological parameters of FRFM. Keywords Fresh fibre reinforced mortar, rheology, ANOVA
INTRODUCTION
Fibre-reinforced concrete (FRC) is one of several special concretes that differs significantly from normal concrete with respect to the measurement of workability and mixture proportioning. Fibre parameters such as type, length, aspect ratio and concentration in the concrete matrix have a profound effect on workability measured by any method, [I]. The influence of these factors is still not recognized in sufficient measure. Concrete mixtures are proportioned to provide the workability needed during construction and the required properties in the hardened concrete. The workability of freshly mixed FRC is the property which determines the ease and homogeneity with which it can be mixed, placed, consolidated, and finished, [3][6]. Workability is a function of the rheological properties of concrete. Influence of fibre on FRFM rheological parameters is very significant but presented in only a few publications, [ 2 ] [ 5 ] .
322
Tomasz PONIKIE WSKI and Janusz SZWABO WSKI
Fibers are incorporated in the brittle cement matrix to control cracking, to provide high ductility, improved impact resistance, to increase the tensile and flexural strengths, and to provide a strain-hardening type of response, [4]. However the addition of fibres will cause problems with workability to occur. Many examples of research into the use of fibres in concrete mixes has shown that the stardard test results are unreliable and ambiguous, 171. METHODS AND MATERIALS The rheometrical workability test The main goal for the research presented was the determination of the rheological behaviour of FRFM investigated with a rotary rheometer - Viskomat NT (Fig.l), [3]. It is necessary to qualify the rheological properties of FRFM, using the rheometrical workability test (RWT), described in [3]. The test relies on: - experimental determination of the relation between torque M for the shear resistance of the mortar and the rotational speed N of the impeller rotating in the mortar flow curve, - as fresh mortar and concrete behaves as a Bingham body, their rheological parameters yield value and plastic viscosity can be evaluated from a rearranged Bingham’s (equation 1) by regression analysis experimental data of the relation M-N:
h = K,qpl and K1, KZ- constants of rheometer g and h are rheological parameters which values are respectively proportional to yield value and plastic viscosity q,,, .
0
7
0
-----
-
20
40
80
80
- --r- 100 120 140 160 180 200 220 240 Time Is]
Fig. 1. Measuring procedure and the rotary rheometer - Viskomat NT Materials and methods The investigation was carried out on standard mortar according to PN EN 196-1: 1996, because of the similar nature of mortar and concrete. The lower cost and labour involved was also an advantage. The mortar was modified because of variable W/C ratio (0.45-0.47-0.50-0.53), length and volume fraction (0.1%, 0.3%, 0.5%) of different types of fibres (table 1).
The influence of select composition factors on rheological properties o f j b r e reinforced fresh ...
323
Table 1. Characteristics of the fibers
~~
~~~~~
~~~
The temperature of the mortar was 2W2OC. The content of superplasticizer FM 34 was constant and equal to 1% of the cement weight. Portland sulfate resistant cement, called ,,road" CEM I MSR 42,5 was used. The mixing methods of the components of the samples was according to PN EN 480-1, with exception of fibres, which were added to the dry components (steel and glass fibres) or mixed with water and superplasticizer (another type of fibres) before adding sand and cement to the batch. This paper shows results of research into rheological parameters FRFM: yield value g and plastic viscosity h. All yield value and plastic viscosity results presented are the mean of 3 specimens. The research design is presented in Table 2. The following factors were taken into consideration in researches: - W/C ratio and superplasticizer dosage; - length of fibres; - volume fraction of fibres; - different types of fibres. rable 2. Research desien I. 2. 1.
II
"I
Influence of polypropylene fibres 2. (SP = 1%) 3. 4. Influence ofglass fibres 1. (SP = IYO) 2. I. Influence of steel fibres 2. (SP = IYO) 3. I. Influence of carbon fibres 2. (SP = IYO) 3.
Variables W/C ratio - 0.43-0.454.47-0.50 SP content - 0; 1; 2% W/C ratio - 0.45-0.47-0.50-4.53 Type of polypropylene fibres - fibrillated; monofilament Fibre length - 3; 6; 12; 19 mm Fibre v o l k e fraction - 0.1; 0.3; 0.5% W/C ratio - 0.45-0.47-0.50-0.53 Fibre volume fraction - 0.1; 0.3; 0.5% W/C ratio - 0.45-0.47-0.50-0.53 Fibre length - 6; 13 mm Fibre volume fraction - 0.1; 0.3; 0.5% W/C ratio - 0.45-0.47-0.50-0.53 Fibre length - 3; 6; 10 mm Fibre volume fraction - 0.1; 0.3; 0.5%
The isolated effect of each factor was assessed by eliminating interaction of other factors (all other factors were kept constant in research stage). Having regard to the limited volume of this paper, the results for FRFM with low W/C ratio (0.45 - 0.47) are not presented. In this paper the rheological results only for decreasing velocity of measuring procedure were presented.
324
Tomasz PONIKIEWSKI and Janusz SZWABOWSKI
RESULTS AND DISCUSION Effect of WIC ratio and superplasticizer dosage Analysis of variance (ANOVA) of obtained rheological parameters for mortars without fibres are presented in Table 3. ANOVA shows that W/C ratio have the significant influence on yield value and plastic viscosity of tested mortars without fibres. This is the major reason why the next ANOVA's for mortars with different types of fibres have variable factor W/C ratio.
Sum of Mean Squares d.f* square
Source of variation
I
I
AN OVA^^^:
Sig. Sum of F-ratio Level Squares d.f.
I
Yield value g
Mean square
Sig. F-ratio Level
I
Plastic viscositv h
I
MAIN EFFECTS AWIC B: SP content C:Measurement repetition INTERACTIONS AC
104.334 8.170 1.106
26.084 35.395 0.000 8.170 11.087 0.016 0.553 0.75 0.512
4 1 2
9.800 8 0.369 2 4.422 6 123.428 23
1.225 0.184 0.737
0.267 0.001 0.006
1.662 0.276 0.25 0.787
4 1 2
0.021 8 0.000 2 0.0025 6 0.3153 23
0.067 159.039 0.000 0.001 2.784 0.146 0.003 6.798 0.029 0.003 0.000 0
6.282 0.019 0.03 0.971
Effect of polypropylene fibres addition ANOVA of obtained rheological parameters for polypropylene FRFM are presented in Table 4. ANOVA shows that type of fibres and fibre volume fraction have the significant influence on yield value and W/C ratio have the significant influence on plastic viscosity of tested polypropylene FRFM.
Source of variation ~~
A T O V r
Sum of Squares d.f.
7
Mean square ~~
F-ratio
Sig. Sum of d.f. Level Squares
~
I
Yield value g
Mean square
Sig. F-ratio Level
I
Plastic viscosity h
MAIN EFFECTS A: W I C B: Type of fibres C: Fibre length D: Fibre volume fraction INTERACTIONS BD Residual Total (corrected)
294.400 2855.114 628.107 1388.200
5 58.880 1.036 2 1427.557 25.120 4 157.027 2.763 2 694.100 12.214
1541.723 4 3864.47 68 11236.56 85
378.681 56.831
0.404 0.000 0.034 0.000
6.663 0.000
0.597 0.020 0.142 0.020
5 2 4 2
0.119 0.010 0.036 0.010
11.8 0.991 3.514 0.987
0.043 4 0.6879 68
0.011 0.010
1.072 0.377
0.000 0.377 0.012 0.378
1.6347 85
The results of the rheological investigation of polypropylene FRFM in Fig. 2 and Fig. 3 give additional information. For mortars without fibres, it was observed that their was a small increase of g and h value with a decrease in W/C ratio in the mortar. The rheological
The influence ofselect composition factors on rheologicalproperties offibre reinforced fresh ...
325
properties of polypropylene fibrillated FRFM are better than for FRFM with other types of fibres (Fig. 2). For W/C = 0.53 changes of yield value and plastic viscosity are consequence of fibre volume fraction changes but remain on the same low level for all of the fibre length. For W/C = 0.50 changes of rheological parameters are generally of the same nature and level but for FRFM with H19 fibres increase of yield value was observed. High increase of yield value for polypropylene monofilament FRFM was observed (Fig. 3). Changes of yield value and plastic viscosity are consequence of fibre volume fraction changes but influence of fibre length was observed as well. Increasing dosage of fibres cause increase of yield value. Clearly highest yield values were obtained for FRFM with 0.5% of F12 fibres.
a) b) Fig. 2. Influence the length and volume fraction of polypropylene fibrillated fibres on rheological parameters of FRFM; a) W/C = 0.53; b) W/C = 0.50
%----
-
~
50. 0.5%
-
1 +F3
1
+F6
> 20.
-A-F12,
20
0.3%
15 10.
0.3% 1
92
0,3 0.4 0,5 0.6 0,7 Plasticviscosity h [Nmnin]
0.3
0,4
0.5
0.7 0,8 Plasticvkcdtyh[Nmnin] 0,6
4 b) Fig. 3. Influence the length and volume fraction of polypropylene monofilament fibres on rheological parameters of FRFM; a) W/C = 0.53; b) W/C = 0.50
326
Tomasz PONIKIEWSKIand Janusz SZWABOWSKI
Effect of glass fibres addition ANOVA of obtained rheological parameters for glass FRFM are presented in Table 5 but only for one length of fibres. ANOVA shows that fibre volume fraction have higher influence than W/C ratio on yield value and W/C ratio have higher influence than fibre volume fraction on plastic viscosity of tested glass FRFM. High increase of yield value and plastic viscosity for glass FRFM was observed (Fig. 4). Increasing dosage of fibres cause increase of yield value and plastic viscosity, but for plastic viscosity remain on the same level for all fibre volume fraction.
Sum of Mean Squares d*f. square
Source of variation ANOVA for:
Sig. Sumof Mean F-ratio Level Squares d*f* square
Yield value g
F-ratio
Sig. Level
Plastic viscosity h
MAlN EFFECTS A: W I C B: Fibre volume fraction Residual Total (corrected)
221.340 321.798
3 2
73.780 160.899
62.806
1
62.806
452.468
6
1.175 0.567 2.562 0.398
0.007
0.001 0.001 0.016
3 2
0.002 0.000
1
0.001
1.925 0.470 0.262 0.810
6
Effect of steel fibres addition ANOVA of obtained rheological parameters for steel FRFM are presented in Table 6 and shows that W/C ratio have the significant influence on yield value. While W/C ratio, fibre length and fibre volume fraction have the significant influence on plastic viscosity of tested steel FRFM. The rheological properties of steel FRFM are comparable with properties of polypropylene fibrillated FRFM (Fig. 4). Changes of yield value and plastic viscosity are consequence of fibre length changes but remain on the same low level for all of the fibre volume fraction. Increasing dosage of fibres cause increase of plastic viscosity for FRFM but with 0.3% of S 13 fibres only.
Sum of Mean Squares d*f* square
Source of variation
I
ANOVA for:
I
F-ratio Sig. Sum of Mean Level Squares d*f. square
I
Yield value e
F-ratio
Sig. Level
Plastic viscositv h
1
MAIN EFFECTS 196.727 3 A: W I C 47.649 1 B: Fibre length C: Fibre volume fraction 46.888 2 9.590 2 DMeasurement repetition INTERACTIONS 23.106 3 AB 47.114 6 AD 57.561 2 BC 7.104 2 BD 26.074 4 CD 314.5096 39 Residual 741.29 64 Total (corrected)
65.576 47.649 23.444 4.795 7.702 7.852 28.781 3.552 6.518 8.064
8.132 5.909 2.907 0.595
0.000 0.020 0.067 0.557
0.516 0.107 0.088 0.000
0.955 0.974 3.569 0.44
0.424 0.456 0.038 0.647
0.003 0.006
0.808 0.528
3
I 2 2
3
0.172 110.301 0.000 0.107 68.578 0.000 0.044 28.154 0.000 0.000 0.231 0.795
0.001 0.001
0.708 0.553 0.688 0.661
2 2
0.011
0.000
6.81 I 0.003 0.212 0.81C
0.000 4 0.0608 39
0.000
0.061 0.993
0.021
0.000
6
0.8127 64
0.001
The influence of select compositionfactors on rheological properties ofjbre reinforcedfresh ...
I u s 3 I
321
0
a) b) Fig. 4. Influence the length and volume fraction of glass and steel fibres on rheological parameters of FRFM; a) W/C = 0.53; b) W/C = 0.50 Effect of carbon fibres addition ANOVA of obtained rheological parameters for carbon FRFM (Tabl. 7) shows that carbon fibre volume fraction have the significant influence on yield value. While W/C ratio and fibre volume fraction have the significant influence on plastic viscosity of tested carbon FRFM. The rheological properties of carbon FRFM are the worst than for FRFM with other types of fibres (Fig. 5). For carbon FRFM the yield value g resulted in the highest value. Changes of yield value are consequence of fibre volume fraction changes. Generally increasing dosage of carbon fibres cause high increase of yield value and decrease of plastic viscosity for FRFM was observed. Table 7. Analysis of variance for yield value and plastic viscosity of carbon FRFM. Sum of Squares d.f.
Source of variation
1
AN OVA^^^:
'
MAIN EFFECTS
1
Mean square
Sig. Sum of Mean F-ratio Level Squares d*f* square
Yield value g
I
588.376 3 196.125 2.425 0.078 A: W I C 892.934 3 297.645 3.680 0.019 B: Fibre length 12460.93 2 6230.467 77.041 0.000 IC: Fibre volume fraction 120.005 2 60.003 0.742 0.482 D:Measurement repetition INTERACTIONS 213.676 9 23.742 0.294 0.973 AB AD 330.615 6 55.102 0.681 0.66.5 112.882 6 18.813 0.233 0.964 BD Residual 3639.225 45 80.8716 20991.04 76 Total (corrected)
F-ratio
Plastic viscosity h
0.161 0.101 0.238 0.017
3 3 2 2
0.039 9 0.035 6 0.008 6 0.2823 45 1.2259 76
Sig. Level
I
0.054 8.551 0.000 0.034 5.349 0.003 0.1 19 18.998 0.000 0.008 1.343 0.271 0.004 0.006 0.001 0.00627
0.696 0.709 0.931 0.483 0.208 0.973
328
Tomasz PONIKIEWSKIand Janusz SZWABOWSKI
I
I
+c3
-&-CO I,
I
I
m
-a! 3
F 10.
00,O
.
0,l 0,2 0,3 0.4 0,5 Plastic viscosity h ["nin]
0.6
a) b) Fig. 5. Influence the length and volume fraction of carbon fibres on rheological parameters of FRFM; a) WIC = 0.53; b) WIC = 0.50 Figure 5b also indicates that there is a critical fibre content beyond which yield value g increase very rapidly or resulted in an unmeasurable value. Problems with the rheological measurements from WIC = 0.50 and lower WIC ratio for fibre content of 0.5% by volume especially for carbon (Fig. 5b) and glass fibres (Fig. 4b) were observed. The influence of fibre content and type of fibres on the plastic viscosity h was considerably less than on the yield value g. The increase in plastic viscosity h is connected with the increased content of fibres but only for the steel FRFM. The plastic viscosity h generally is constant for polypropylene monofilament and glass FRFM (Fig. 3, Fig. 4), decrease for carbon FRFM (Fig. 5) and is connected with the increase content of fibres.
CONCLUSIONS It has been shown that in investigated range of composition factors of FRFM the addition of fibres to the fresh mortar changes the composite rheology. Analysis of variances (ANOVA) of obtained rheological parameters for FRFM showed that: - type of fibres and fibre volume fraction have the significant influence on yield value but WIC ratio have the significant influence on plastic viscosity of tested polypropylene FRFM, - fibre volume fraction have higher influence than WIC ratio on yield value but WIC ratio have higher influence than fibre volume fraction on plastic viscosity of tested glass FRFM, - WIC ratio have the significant influence on yield value and WIC ratio, fibre length and fibre volume fraction have the significant influence on plastic viscosity of tested steel FRFM. - fibre volume fraction have the significant influence on yield value but WIC ratio and fibre volume fraction have the significant influence on plastic viscosity of tested carbon FRFM. Yield value g and plastic viscosity h of tested FRFM does not depend significantly on the rheological parameters of the matrix.
The influence of select composition factors on rheological properties offibre reinforced fresh ...
329
The influence of the type of fibre and fibre volume fraction on rheological properties of FRFM are important factors. The length of fibres do not have the significant influence on yield value and plastic viscosity of FRFM. The significant influence of the length of fibres on plastic viscosity of tested steel FRFM was observed only. The rheological properties of polypropylene fibrillated and steel FRFM from workability point of view are better than for FRFM with other types of fibres. In case of glass and carbon fibres the workability of FRFM worsens with the increase of their volume fraction. ACKNOWLEDGEMENT The authors gratefully acknowledge the financial support by the research grant from the State Committee for Scientific Research (KBN-Poland), project: No 8 T07E 033 21. REFERENCES 1. Johnston C.D.: Comparative measures of workability of fibre-reinforced concrete using slump, Ve-Be and inverted cone tests, Special Conretes: Workability and Mixing, edited by J.M.Bartos, E & FN Spon., 1993, pp 107-118. 2. Kucharska L., Logon D.: The influence of fly ash on rheological and mechanical properties of cement mortars reinforced with pitch-based carbon fibres, in: Proc. Int. Symp. ,,Brittle Matrix Composites 5", A.M.Brandt, I.H.Marshal1, V.C.Li eds. Warsaw 1997, pp 113-122. 3. Szwabowski J.: Rheology of cement based mixes, The Silesian University of Technology, Gliwice 1999 (in Polish). 4. Peled A., Shah S.P.: Parameters related to extruded cement composites, in: Proc. Int. Symp. ,,Brittle Matrix Composites 6", A.M.Brandt, V.C.Li, I.H.Marshal1, Warsaw 2000, pp 93-100. 5. Kucharska L., Logon D.: Mixture composition of matrices and the reinforcing effect of thin composite elements by carbon microfibres, in: Proc. Int. Symp. ,,Brittle Matrix Composites 6",A.M.Brandt, V.C.Li, I.H.Marshall, Warsaw 2000, pp 147-157. 6. ACI Manual of Concrete Practice, Part 2: Construction Practices and Inspection Pavements, American Concrete Institute, 200 1. 7. Szwabowski J., Ponikiewski T.: Rheological properties of fresh concrete with polypropylene fibres, 3rd International Conference: Concrete&Concrete Structures, Zilina, Slovakia, 24-25.04.2002 r., pp 33 1-338.
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodliead Publ.. Warsaw 2003
MIX DESIGN OF THE SELF-COMPACTING CONCRETE
Maria KASZYIhKA Technical University of Szczecin Piastow 50, 70-3 1 1 Szczecin, Poland e-mail: mkasz@os.@ ABSTRACT
Self-compacting concrete can by made in various ways. The optimum mixtures are sensitive with regard to characteristics of components, such as type of the cement, type and amount of superplasticizer, type of sand and fillers. The fabrication of self-compacting concrete requires a more rigorous quality control of materials and selection of the mixture at all stages of mixing and casting. The objective of this paper is to present the effect of additions and admixtures on performance of the self-compacting concrete. The tests confirmed the importance of the quantity of superplasticizers and of compatibility between cement and superplasticizer. Keywords: Self-compacting concrete, cement, superplasticizer, silica hme, flowability, passing ability, stability, compressive strength. INTRODUCTION
Self-compacting or Self-Consolidating Concrete (SCC) has been described as “the most revolutionary development in concrete construction for several decades”. SCC can be used in precast applications or for concrete placed on site. In designing the mix, the size and the shape of structural elements, dimensions and density of reinforcement and the cover depth should be taken into consideration. The development and use of self-compacting concrete in many countries have shown that it can be successfidly produced from a wide range of component materials but it is difficult and often impossible to predict the final properties of that concrete,
r 1,2,31.
There are no design codes for SCC. This concrete is very sensitive with regard to the proportions of the mix and quality of workmanship. Inaccuracies in proportions of ingredients, varying characteristics of the applied components and varying curing conditions, can result in a failure to obtain the required properties of the SCC, i.e. its filling ability (flowability), its passing ability (free from being blocked by reinforcement) and its resistance to segregation (stability). Many different test methods have been developed in an attempt to specifjr the properties of SCC, but so far there is no single test available to measure all three properties. This paper presents some of the results from a broader study dealing with the relationships between the properties of SCC pastes, mortars and concretes. A similar range of tests have
332
Maria KASZYIVSKA
been carried out on both the mortar and concrete i.e. spread and slump flow tests and Vfbnnel tests.
MATERIALS AND MIX PROPORTIONS The tests were performed for paste, mortar and concrete mixtures made using five types of Portland cement. Notation used for the Portland cements is shown in Table 1. Table 1. Notation used for the Portland cements 1
2 3 4 5
Portland Cement CEM 152,s R Goraidze CEM I 52,s R Chelm CEM I 42,s R Goraidze CEM 142,s R Cemcon CEM 132,s R Gorazdze
Notation G 52,s CH 52,s G 42,s C 42,s G 32,s
For the considered mixtures, a superplasticizer and pozzolanic additives: fly ash and/or silica fbme were used. Four different modified polycarboxylic ether superplasticizers were considered: Sika ViscoCrete 3, Isola Polymer BV-10, Woerment FM-787 and Woerment FM 375. The characteristics of the superplasticizers are shown in Table 2.
Superplasticizer Sika ViscoCrete 3 Isola Polymer BV 10 Woerment FM 787 Woerment FM 375
Chemical description Polycarboxylic ether Polycarboxylic ether Polycarboxylic ether Polycarboxylic ether
Notation Si BV WFI wF2
Specific gravity 1.09 1.06 1.07 1.08
The tests were performed for six selected powder compositions for each cement type. Table 3 shows the applied powder compositions. Table 3. Powder compositions
Mortar proportions were identical but with the addition of sand, (mortars are denoted by M1, M2, M3, M4, MS and M6). The volume fraction of sand (> 0.125 mm) in mortars was fixed at 40%. In the first part, the volume of water was calculated on the basis of test executed on
333
Mix design of the self-compacting concrete
cement pastes. In the second part of investigation a constant volume of the water in mortars was applied equal to 160 Vm3.
EXPERIMENTAL PROCEDURE In the study, the following parameters were considered: - type of Portland cement: G52,S; G42,S; G35,2; C42,S: CH52,S; - type of superplasticizer: Si; BV; WFl; WF2; - amount of superplasticizer: from 0.5% to 3.0 YOof the cement mass; - addition of silica fume: 10% of cement mass;
Design of paste composition The water to powder volume ratio has to be determined on the basis of paste and mortar flow cone test. Initially the water to powder ratio for zero flow (pp) was determined in the paste, with the selected proportions of cement and additions. The flow cone tests were performed for the watedpowder ratios by volume of 1.1, 1.2, 1.3 and 1.4 for the selected powder compositions. The test results for cement G 32,s are shown in Fig. 1. The point of intersection with the y-axis is designated as pp value, called “water retaining ratio”. 1.5
I
1
7
0,8
1
0,7 0
1 2 3
4 5 6
7 8 9 1 0 1 1 1213
r
1.2
;1,l
0
1
2
3
4
5
6
7
8
P
Fig.2. Test results of determination of the water/powder ratio Pp
334
Maria KASZYI~SKA
Figure 2 shows the comparison of the test results for the water retaining ratio pp for all tested mixtures and cements. The mixes with higher amount of fly ash (p1 and P2) had lower values of pp than the mix P6 with silica fume. This means that the pastes with fly ash powder had higher flowability with lower volume of water __ rn P1
P2
0 P3 0 P4 P5 HP6
CEM l52,5R Chehn
CEM I52.5R G6ratdLe
CEM l42.5R G6raZdLe
CEM l42.5R
Cemcon
CEM I32.5R GdraZdte
Portland Cements I
Fig.2. Test values of water retaining ratio Sp for different cements Determination of mortar composition To estimate the optimum volumetric watedpowder ratio and the superplasticizer dosage the tests with flow cone and V-Funnel for mortars were performed for waterlpowder ratios in the range of (0.8 - 0.9)ppand for varying dosages of superplasticizer. Test results for selected Table 4. Slump-flow (r) and V-funnel(t) test results for mortars
335
Mix design of the self-compacting concrete
mixtures from different amounts and types of superplasticizer and volume of the water calculated from tests for pastes are presented in Table 4 for cement C 42,5 and G 32,s. All the measurements of slump-flow and v-finnel time were performed within 10, 30 and 60 minutes after mixing the concrete. The comparison of the test results for mixtures with constant amount of superplasticizer are shown in Figs. 3 and 4. I
Cement C 42.6, 1XSuperplasticirerSi
Cement G 32.6, 1.2 % SuperplasticizerBV
-
-.e
60
C
'C
w30
zc
10
0
50100150200250300350
10
0
SLUMP-FLOW [mnf
1
60
50
100 150 200 250 SLUM-FLOW [lnlll]
3M)
350
Fig. 3. Slump-flow test results
I
Cement G 32.6. 12% Superplasticizer BV
30 60 TIME AFTER MIXING [min]
I
Cement C 42.6. 1% Superplasticizr Si
10 30 60 TIME AFTER MIXING [min]
Fig.4. V-funnel time test results The study showed that even for the same type and amount of the superplasticizer and binder the varying proportions of powder had a considerable effect on the slump flow and duration time for the SCC properties. After 60 minutes, some of the mixtures lost their free flow properties required for SCC. This was caused by non-compatibility problems between cements and superplasticizers. The test results for selected mixtures with a constant volume of water but with different amount and type of superplasticizers are presented in Table 5. The best properties of filling ability for each mortar are marked. Target values for the slump-flow are of 24 to 26 cm (r,,, = 5 ) , and V-finnel time of 7 to 1 1 seconds (R,,, = 1).
where: r = 0.5 (rl + rz) rl, rz - measured diameter of the mortar in two perpendicular directions, r,, - base diameter of mortar cone, r, = 100 mm,
336
Maria KASZYNSKA
R,=lO/t
where: t - flow time (sec) Table 5. Slump-flow and V-fbnnel test results for mortars with cement G 32,s
Test of concretes The test results are presented here for selected concrete mixtures: M2, M3 and M5. The study focused on the filling ability and the compressive strength of concrete. The fresh concrete mix was tested to establish the required deformability, flowability and segregation resistance properties. The slump flow test was performed using the Abram’s cone. It is the most commonly used test, it gives a good assessment of the filling ability and it may also serve as an indication for the resistance to segregation.
337
Mix design of the self-compacting concrete
Time was measured for the concrete to reach a 500 mm spread circle (denoted by T50m) and the final diameter of the concrete in two perpendicular directions was measured (the average value is the slump-flow in mm). Typical range of values for slump-flow for SCC is from 650 mm to 800 mm and for T50cnlfrom 2 to 5 sec, [4,5,6]. All the measurements of spread circle were performed within 10, 30 and 60 minutes after mixing the concrete. To determine the filling ability (flowability) and passing ability of the concrete the Vfunnel test and L-box test are used. The V-funnel is filled with about 12 liters of concrete and the time taken for it to flow through the apparatus is measured. After that, the funnel could be refilled with concrete and left for 5 minutes to settle. If the concrete showed segregation then the flow time increased significantly. For SCC a flow time of 10 seconds and minimum value of H2/Hl = 0.8 were considered as appropriate. The concrete compressive strength was determined after 3, 7 and 28 days of curing. Test results for selected mixtures with G 32,s cement are presented in Table 6.
M2 M3
Workability tests Slump-flow V-funnel T5o [sec] r[mm] [sec] 7.5 760 11.8 6.1 770 13.8
M T
760
Mixture
122
L-box H~/HI 0.89 0.88 094
Compressive strength 2days 7days 28 days [MPal [ma1 [ma] 35 52 69 43 51 66 62
80
81
The concrete reached very high compressive strength. It has been found that the highest strength could be obtained for mixtures that satisfied the self-compacting criterion. Increase or decrease of the slump flow beyond the accepted limits can cause a decrease of the compressive strength. This is due to poor compacting in the case of reduced slump flows and segregation of components for excessive slump flows.
CONCLUSIONS The study showed that even for the same proportions of ingredients, the type of cement has a considerable effect on the slump flow and duration time for the SCC properties. For the selection of the mixture proportions for self-compacting concretes, it was very important to select the most suitable superplasticizer' for the given cement. In addition, the considered mixtures were checked with regard to sedimentation and segregation. The optimum quantity of superplasticizer was determined to maximize the slump flow without segregation. The fabrication of self-compacting concrete requires a more rigorous quality control of materials and an appropriate selection of the mixture proportions for different structural elements. The tests confirmed the importance of the superplasticizer quantity and of the compatibility between cements and superplasticizers. The tests and analyses have shown also that the determination of the optimum properties of self-compacting concrete is most efficient when the paste and the mortar are subjected to preliminary tests.
338
Maria KASZYNSK~
REFERENCES 1. Jin, J., Domone, P.L., Relationships between the fresh properties of SCC and its mortar component. Conference Proceedings of First North American Conference on the Design and Use of Self-Consolidating Concrete, 2003,pp 33-38 2. Walraven J., Self-Compacting Concrete in the Nethertands, Conference Proceedings of First North American Conference on the Design and Use of Self-Consolidating Concrete, 2003,pp 399-405. 3. Bui, V.K.,Shah, S.P., Akkaya,Y., A new Approach in Mix Design of Self-Consolidating Concrete, Proceedings of First North American Conference on the Design and Use of SelfConsolidating Concrete, 2003,pp 71-76 4. Okamura, H.,Ozawa, K., Self-Compacting High Performance Concrete, Structural Engineering International 4/96 5. Specification and Guidelines for Self-Compacting Concrete, EF'NARC, 2002. 6. Takada, K., Pelova, G.I., Walraven, J.C.,Development of Self-Compacting Concrete in the Netherlands - 1998 (report from internet).
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
INFLUENCE OF CEMENT AND SUPERPLASTICIZER ON RHEOLOGICAL PROPERTIES OF MORTARS Jacek GOLASZEWSKI Silesian University of Technology Akademicka 544-100 Gliwice, Poland, e-mail:
[email protected] Janusz SZWABOWSKI Silesian University of Technology Akademicka $44-1 00 Gliwice, Poland, e-mail:
[email protected] ABSTRACT Effectiveness of superplasticizer is an effect of complex system of factors connected mainly with concrete components properties, concrete composition and concreting conditions. From among these factors the key role for the superplasticizer effectiveness plays interaction of cement and superplasticizer. Selection of cement - superplasticizer system determines also workability of fresh concrete and thus also possibility of performing of HPC. In the paper methodology and results of the investigation into the influence of different superplasticizers on the rheological properties of modified, for the sake of superplasticizer addition and W/C ratio, standard mortars (according PN EN 196-1:1996) with different cements are presented. The rheological parameters of these mortars, yield value and plastic viscosity were determined using a rheometrical methods. In the research program the influence of following factors: chemical origin of superplasticizers (SNF, SMF, PC and PE superplasticizers), cement composition (cements of different C3A, Na20eq and SO3 content) and cement specific surface, superplasticizer dosage and WIC ratio were investigated. On the basis of test results the relationships between cement and superplasticizer properties and rheological properties of cement mortars were defined and discussed. These relationships in form of mathematical models can be used in workability shaping process to select optimal cement - superplasticizer system. Keywords: Workability, High -range water reducers, Rheology, Mortar
INTRODUCTION The definition of workability in concrete technology should be considered in terms of the state of the system concrete mix - method of processing. This state is determined by the interaction between two factors: the rheological properties of given mix and the forces acting on it during processing [ 13. The rheological properties are determined by composition of the mix only. They characterise its strain and flow - stress behaviour. Therefore, concrete mix workability is determined by the reaction of the mix to the forces acting on it during transport and mechanical processing as the resistance of its structure to these forces. Required
340
Jacek GOtASZEWSKIand Janusz SZWABO WSKI
workability can be achieved in two ways: rheological properties of concrete mix are adjusted to the given method and conditions of concrete processing or method and conditions of concrete processing are adjusted to the given rheological properties of concrete mix. In practice the first way is usually used. High performance concrete (HPC) is widely used in civil engineering as structural material assuring high strength, durability and reliability of concrete structures [2, 31. To assure required workability of low water cement ratio various superplasticizers are used. Only by using superplasticizers rheological properties of HPC mix can be adequately adjusted to the method and conditions of concrete processing. Effectiveness of superplasticizer is an effect of complex system of factors connected mainly with concrete components properties, concrete composition and concreting conditions [2, 41. From among these factors the key role for rheological properties and workability of fresh HPC plays interaction of superplasticizer - cement system [2,3]. Unfortunately the quantity of experimental data on this topic is limited [5, 6, 71. In the paper influence of cement specific surface, cement composition and superplasticizer on rheological properties of fresh HPC was investigated. The influence of these factors was studied on modified standard mortars (PN EN 196-1:1996), which can be considered as a model of HPC concrete [8, 91. It was proven that influence of superplasticizer and cement characteristics on rheological properties of mortars and concretes is qualitatively the same [9, 10, 111. The rheological properties of superplasticized mortars are described by Bingham's model parameters - yield stress g and plastic viscosity h. The rheological parameters were determined using a rheometrical test. EXPERIMENTAL Testing programme In the research the influence of cement and superplasticizer on rheological properties of cement mixes was investigated. The following factors were taken into consideration: superplasticizer type (see Table 2); specific surface of cement (320; 370; 420 m2kg according Blaine method); chemical and phase composition of cement (C3A content - 2; 7; 12%; alkalis content (NazO,,= NazO + 0.658 K20) - 0.3; 0.7; 1.1% and SO3content 2.5; 3; 3.5% see Table 1); W/C ratio (0.55 and 0.45) and superplasticizer dosage (1,2 ,3% of cement by weight). The range of cement composition changes accepted in tests corresponds to variability of typical commercial cements. All tested cement were specially prepared. The cement clinkers used for cements preparation have similar S03/Na20,, mole proportion - due this soluble alkalis content in total alkalis content was kept on the same level in all tested cements. In order to avoid problems with cement hydration process, the SO3 content in cement was accepted in relatively narrow range of changes. The investigation programme was planned in a manner making possible to define changes of rheological properties of mortars without superplasticizer and with SNF, PE, PC superplasticizers as a function of C3A, NazO,, and SO3 content.. Particular series of tests for different superplasticizers and cements of different specific surfaces were performed on the basis of central composite 2"3 + star experiment design accepting polynomial of a second degree with second order interactions as a response function. Rheological model of fresh mortars It is well documented that fi-esh mortar, like a fresh concrete, behaves as bingham body, whose properties can be expressed by the two fundamental rheological parameters, i.e. yield stress and plastic viscosity according the formula: T = T 0 +Tllpl.Y (1)
34 1
Influence of cement and superplasticizer on rheologicalproperties of mortars
where T (Pa) is the shear stress at shear rate i (Us) and T, (Pa) and qpl (Pas) are the yield value and plastic viscosity respectively [1, 12, 131. The physical interpretation of yield value is that of the stress needed to be applied to a material in order to start flowing. When the shear stress is higher then the yield value the mix flows and its flow resistance depends on plastic viscosity. Detailed rheological properties of fresh mortars and concretes are presented and discussed in [l. 9, 12, 131.
Fig. I . Viskomat PC and its measuring element
Measurements of rheological parameters of fresh mortars Rheological parameters of fresh mortar can be measured by applying a given shear rate and the measuring the resulting shear stress. Because of non-linear character of rheological behaviour of mortar, the measurements should be taken at no less than two considerably different shear rates. In this work rheological parameters were measured using Viskomat PC. (Fig. 1) With this instrument, a rotation rate N is applied to a paddle and the torque T of sample shear resistance is measured. The rheological parameters are determined by regression analysis according to the relation [ 1, 91: T=g+Nh (2) where g (Nmm) and h (Nmmmin) are parameters corresponding to yield value T~ and plastic viscosity qpl, respectively. By suitable calibration of rheometer it is possible to express g and h in fundamental units. In the present investigation, where the object was to determine the character of rheological parameters changes in relation to superplasticizer and cement type, calibration was unnecessary. The two-point test and its principles are presented in [ 1,9]. Cement Cements # I Cements#2 Cements #3 Cements#4 Admixture PC PE I PE2 PE3
SNF SMF
Table I . Chemical and phase composition of cements Chemical composition [%] C,S C2S C3A C4AF Na20eq so3 59.6 19.3 2.01 16.6 0.3 0.7 1 . 1 2.5 3.0 3.5 51.5 27.8 6.9 10.5 0.3 0.7 1.1 2.5 3.0 3.5 58.9 16.4 12.2 8.5 1.1 2.5 3.0 3.5 57.9 14.5 12.1 9.5 0.3 0.7 2.5 3.0 3.5
Specific surface [m2kl 320 370 420 320 370 420 320 370 420 320 370 420
Table 2. Properties of tested superplasticizers Density [g/cm3] Concentration [%I Chemical base polycarboxylate acid I .06 40 polyeter (LMW) 1.09/1.05 17/18 polyeter (MMW) 1.05 polyeter (HMW) I .05 36 naphthalene sulphonate acid 1.11 36 melamine sulphonate acid I .09 36
342
Jacek GOEASZEWSKI and Janusz SZWABOWSIU
Materials and mixes Laboratory prepared CEM I type cements and commercial superplasticizers were used for the investigations. Their main properties are presented in Tables 1 and 2. The sand used was PN EN 196:1996 CEN model sand (2 mm max.). The mix proportions of all tested mortars were based on standard mortar proportioning according to PN EN 196:1996 (3: 1 sanacement by weight). Watedcement ratio and superplasticizer type and dosage varied as a part of the programme, this variations is given in the results below. Mortar mixing and testing procedures The PN EN 196:1996 mortar mixer was used. The mixing procedure was according to PN EN 196:1996. Superplasticizer was added with water or delayed 30 s depending on its type and test programme. After end of mixing the sample of mortar was transferred to Viskomat PC and was tested according to procedure presented on Fig. 2. The procedure roughly simulates process of transport in truck concrete mixer. Because measurement at the constant velocity of the impeller rotation for the VISKOMAT PC makes possible the investigation of shear resistance only, which at a given speed consists of yield value and plastic viscosity, at 10 and 60 minutes the speed was changed from 120 to 20 Umin to define the rheological parameters from flow curves. The correlation coefficients calculated from the flow curves used to determine rheological parameters of the mixes were in range of 0.95 0.99 with less then 5% failing below 0.90. In the research range effects of segregation were not observed.
-
I
C .-
E
r
I
2
Time [min]
Fig. 2. Measuring procedure used in investigation.
RESULTS AND DISCUSSION On the base of statistical analysis of obtained results concerning influence of cement specific surface and C3A, NazO,, SO3 content on rheological properties of W/C = 0.55 mortars without superplasticizer, it was found that rheological parameters g and h depends successively on: C3A content in cement, specific surface of cement, interaction of these two factors and NazO,, content in cement. It was found also that in the investigated range of changes influence of SO3 content in cement on rheological parameters of mortars is insignificant. The lack of influence of SO3 on rheology of tested mortars does not mean of course that influence of SO3 content is insignificant at all cases. It means only that when SO3 content in cement is properly adjusted, its other characteristics are decisive for rheological properties of cement mix. The influence of cement specific surface and C3A and NazO,, content on rheological parameters g and h of mortars of W/C=O.55 without superplasticizer is presented on Fig. 3 and 4. Increasing C3A content increases g value of cement mortars. The range of this increase depends on cement specific surface and alkalis content in cement but obtained relationships show ambiguous trends. Increase of specific surface of cement from 320 to 370 m’kg cause
343
Influence of cement and superplasticizer on rheologicalproperties of mortars --c Na20q - 0.3%; 320 m’ikg -m- Na20, - 0.3%; 370 rn’lkg
0.5
120
-&-
+
100
-
*
0.4
+ -a-
80
-A-
.-
E
-
Na20q 0.3%; 420 rn’ikg - 0.7% 320 rn2/kg Na20, - 0.7%: 370 rn’lkg Na20, 0.7%; 420 m’ikg Na20, 1 .l%; 320 rn’ikg Na20q 1.1%; 370 rn‘ikg Na20q 1.1%: 420 rn’ikg
+ NarO,
-
0.3
E E E
60
3
CD
=
0.2
40
0.1
20 U
C
0 0
4
8
C A content
I
4
12
r/*]
0 C,A content [“%I
12
- .
cement of smific surface 320 rn‘/ka glo =-49.O7+O.87A+31.916+39.92~-1.O8A6-O.27AC-13.046C+O.51A2-l.09B2-4.44C?; = 0.990 P = 0.938 hio = 1.~-0.021A-0.518B-0.373C-O,010AB-O, 004AC+O,0316C+O.OOlA’+O. 27082+0.053C?; cement of specific surface 370 m’/kg gro = 273.1-3.16A-113.00B-138.00C+3.28AB-0.25AC-4.44BC+O.51AZ+49.0082+22. 85c‘; 8 = 0.975 hw = -O.049+8.979A-O.392B+O.246C+O.OO8AB+O.OOOAC+O.128BC+0.000A‘+0.004B2-0.055C?; = 0.880 cement of specific surface 420 m‘/kg gro = 117.5+24.05A-90.80B-67.89C+2.04AB-1.47AC-12.176C-1.00A2+72.766’+13.33C?; ? = 0.996 hm = 0.781-0.076A-0.518B-0.179C+0.024AB+0.009AC+0. 1836C+0.002A2-0.1096‘+0.004C?; P = 0.877 where A CJn content in cementfi]; 6 Na20, content in cement [%I; C - SO, content in cement [%]
r
-
-
Fig. 3. Influence of cement specific surface and C3A and NazOcqcontent in cement on rheological properties of W/C = 0.55 mortars 10 min after end of mixing (cements of S03=3%)
’1 1-51
-A-
-03
I . . . . . . .4
Na20,-
1.1%
-5
0
4 8 C A content [“h]
12
0
I
4
8
CSA content [%I
12
Fig. 4. lnfluence of C3A and NazOcqcontent in cement on rate of rheological properties changes in time of cement mortars with and without PEI superplasticizer (cements of specific surface = 320 m’kg, S03=3%)
344
racek GOLASZE WSKI and Janusz SZWABO WSKI
120
- 0.3Oh;320 m2kg - 0.3%; 370 rn‘kg - 0.3%; 420 m2kg + Na20, - 0.7%; 320 m2kg 4 a - Na20, - 0.7%;370 m’kg + NalO, - 0.7%; 420 m’ikg -0Naa, - 1.1Oh; 320 m2kg + Na20, - 1.1%; 370 rn‘ikg + Na20, - 1.1%; 420 rn’kg --t Nap, -WNa20, -t- Na20,
0,s
100 0.4
80
-
P
E
3
60
W
--
0.3
E E
!?
=
0.2
40
0,1
20
0
0 4
8
C A content ph]
12
I
0
8
4
12
C A content p/.]
cement of smiric surface 320 m2ka gro = 32.34+6.27A- 16.226+22.09~2.8OAB+O.17AGl.56BC-0.1 2A2+18.376‘-3. 47c‘; ? = 0.992 hro = -0 408-0.019A+O.~86+O.388C+O.0l2AB+O,000AC-O,0166C+O.001A2-0.00282-0.083~; ? = 0.891 cement of specMc surface 370 d k g gro = 168.W.45A-122.106-77.37C+4.64AB+1.13AC+22.35EC+O.17A2+27.236’+9.48c‘; ? = 0.900 hro = 0.729+0.011A-0.2656+0.62BCO.00SAB-O.010AC+0.0906C+0.OO1A2+0.01BB1-O. 1lOc‘; ? = 0.897 cement of spec& surface 420 d k g gio = 123.5+12.79A-83.876-78.87Gl.OMB+O. lOAC+9.306C-O.823A2+37.5382+12.38c‘; ? = 0.924 hra = 0.239+0.001A+0.253B-O.193C+O~005AE+O.OOlAGO.055BC-O.OOlA2-0.08&+0.039c‘; ? = 0.907 when, A C A content in cemen@6]; 6 - Na20, content in cement C SOscontent in cement
-
m]; -
Fig. 5. Influence of C,A and Na20, content in cement and cement specific surface on rheological properties of mortars with PEI superplasticizer 10 min after end of mixing (W/C = 0.55; SP = I%, cements of S03=3%
slight decrease of g value of mortars. Further increase of specific surface to 420 m’kg cause distinct increase of g value. It is worth to notice that effect of specific surface on g value of mortars is negligible when cements of low C3A content are used. Effect of alkalis content on g value of mortars is ambiguous and disclose generally for cements of high C3A content. Generally value of g trends to decrease with increasing alkalis content when cements of 2 and 7% C3A are used, and shows minimum for 0.7% alkalis content when cements of 12% C3A are used. Plots on Fig. 3 show that h value of cement mortars depends mainly on specific surface of cement, C3A and NazO,, content are for h value factors of minor importance. Increasing specific surface of cement cause tendency to decrease of h value of mortars. Influence of C3A and NazO, content in cement on h value shows ambiguous trends and generally from workability shaping point of view is out of importance. Influence of cement composition on rheological parameters rate of changes with time was determined only for mortars with cements of specific surface 320 m’kg. Increase in cement specific surface accelerates rate of changes of g and h values with time and causes rapid increase of shear stress of cement mortars. By reason of this measurements of rheological parameters of mortars with cements of specific surface 370 and 420 m’kg after 60 min were not possible to manage. As can be seen on Fig. 4 cement composition influencing mainly changes of g value with time, its influence on changes of h value with time are negligible. Decisive for the rate of g changes with time is C3A content. Value of g always increases with time and rate of this increase increases in direct proportion to C3A content. Influence of NazOeq content is significant only for mortars with cements of 2% C3A content - for such mortars rate of g value increase decreases with increasing NazOe, content.
345
Influence of cement and superplasticizer on rheological properties of mortars
Influence of addition of SMF, SNF and PEl superplasticizers on rheological properties of W/C=0.55 mortars is presented on Fig. 5 and 6. Generally addition of superplasticizer cause drop of g and h values of W/C=0,55 mortars. Only in case of mortars with cements of high C3A content and with SMF superplasticizer g value after 10 min from end of mixing increases in comparison to mortars without superplasticizer. This increase is caused by accelerating action of SMF superplasticizer on cement setting [4]. Effectiveness of PE1 superplasticizer is always higher then of SNF and SMF superplasticizers. It is also worth to underline that low h value of superplasticized mortars creates segregation effects. On the ground of statistical analysis and plots on Fig. 5 and 6 it was found that rheological parameters g and h of superplasticized W/C = 0.55 mortars depend on superplasticizer type and successively on C3A content, NazO,, content, specific surface of cement and interaction of these factors. Content of SO3 in cement in tested range, likewise for mortars without superplasticizer, doesn't influence rheological properties of superplasticized mortars. Value of g of superplasticized W/C=0.55 mortars increases with increasing content of C3A. This increase depends on superplasticizer type and is clearly lowest in case of PE1 superplasticizer addition. Plots on Fig. 5 and 6 well illustrate importance of cement selection for effective usage of superplasticizer and workability shaping. Mortars with cements of 7 and 12% C3A content have, despite superplasticizer addition, higher g value then mortars with cement of 2% C3A content and without superplasticizer. The influence of NazO,, content on g value of W/C=0.55 mortars with SMF and SNF superplasticizers has extreme character and increases with increasing C3A content. For these mortars minimum g value occurs when NazO,, content is 0.7%. 120
-
P
100.
-
-
0.3.
'5
E
--C Na20,
- 0.3%
--tNa20,+Na20, NazO, -ANa20, +Na20, +Na20, +Na20,-
1.1% 0.3% 0.7% - 1.1% - 0.3% - 0.7% 1.1%
i
+Na20, - 0.7% ~
-
E
60
40
0.4
-
80.
4m
0,s
E
z =
-
0.2.
p~
SM F
0.1
20.
0 4
0
0
8
4
CIA
12
content [ O h ]
0
-
I
4
8
C,A
12
content ph]
mortars with SNF superplasticizer gro = 219.0~.01A-97.928-119.2OC+1.87AB+O. 68AC-0.23BC+0.42A2+63.66Bz+19.186; P = 0.925 hro = -0.630+0.025A+0.3628+0.4 13C-O,008AB+O.002AC+0,023BC-O.O02A2-0.290B2-0.0716; ? = 0.966 mortars with SMF superplasticizer gro = 341.90+6.27A-l35.90B-211.30C+6.81AB-0.68AC+lO. 70BC-0.04Az+55.57B2+34.6 2 e ; ? = 0.933 hm = -0.442+0.014A+0.4688+0.282C-0.01lAB-0.006AC-0.064BC-0.002AZ-0.142BZ-0.0456: P = 0.900 .. ~ mortars with PE1 superplasticizer 910 = 163.50-1.07A-180.20B-68.863C+5.83AB+0.04AC+21.04BC+0.18A2+67.88B2+9.266; P = 0.904 hro = 1. 172-O.O38A+O.25O8-O.6OlC-O,OlOAB+O.OO3AC-O.OO38C+O.W2Az-O. 137B2+0.096~; ? = 0.960 where A CIA content in cementfi]; B NazO, content in cement fi];C - SO3content in cement PA] ~~
-
.
-
Fig. 6 . Influence of cement specific surface and CpA and Na20,, content in cement on rheological properties o f mortars with SNF, SMF and PEI superplasticizers 10 min after end o f mixing. (W/C = 0.55; SNF, SMF = 2%; PEI = I%, cements of specific surface = 370 m'kg, S03=3%)
346
Jacek GOLASZE WSIU and Janusz SZWABO WSIU
-
120
0.5
-
100. 0,4.
80
10.3-
1
e=
60I
D
OV2
--t Na20,
0.1 20.
0
1
-
:
-
:
-
1
- 0.3%; 320 m2kg
+ Na& - 0.3% 370 m2kg + Na,O, - 0.3%; 420 m'kg + Na20, - 0.7% 320 m'kg
40
.*
d- Na&-0.7%;
Nap, -0- Na20, -a- Na20, --b Na20,
O+
37Om'kg
- 0.7%; 420 m'kg
- 1.l%; 320 m2kg - 1.I%; 370 m'kg - 1.I%; 420 m'kg 1
Influence of cement and superplasticizer on rheological properties of mortars
347
possible to obtain mortars with negligible low changes of g value with time. When the cements of 7% C3A content are used rate of g value increase with time for mortars with SNF and SMF superplasticizers average appropriately 0.79 and 0.90 N m d m i n and is clearly higher then rate of g increase of mortars without superplasticizer (0.60 Nmdmin) and mortars with PE1 superplasticizer (0.3 Nmdmin). When the cements of 12% C3A content are used rate of g value increase with time for mortars without superplasticizer average 0.80 N d m i n , for mortars with SNF superplasticizer and cement of 0.7% NazO,, content 1.3 N d m i n and for mortars with PE1 superplasticizer - 0.65 N d m i n . Content of NazO,, is important factor for mortars with SNF and SMF superplasticizer rate of g changes with time. For mortars with cements of 2 and 7% C3A rate of g changes with time decreases with increasing NazO,, content. In case of mortars with PE1 superplasticizer the same trend can be observed but influence of NazO,, on rate of g increase with time is weaker. Changes of h value with time of superplasticized W/C = 0.55 mortars shows ambiguous trends depending on superplasticizer type, NazO,, and C3A content. (Fig 4) Value h of mortars with PE1 superplasticizer increases or doesn't changes with time, while h value of SNF and SMF mortars decreases with time. Generally range of h value changes with time is generally low and doesn't influence workability. Character of influence of superplasticizer on rheological properties of cement mix changes depending on W/C ratio [12, 151. Comparing to high W/C ratio mixes, mixes of low W/C ratio are distinguished by considerably higher h value and higher range of changes of g and h values with time [12, 151. Influence of specific surface and cement composition on rheologicat properties of W/C = 0.45 mortars with PE1 superplasticizer is presented on Fig. 7. It is worth to notice that at 3% addition of PE1 superplasticizer mortars of W/C = 0.45 after 10 min from end of mixing characterise by lower g values and considerably higher h values then corresponding mortars of W/C = 0.55 and 1% of PE1 superplasticizer. On the base of statistical analysis was established that g value of W/C=0.45 mortars with PE1 superplasticizer depends successively on: C,A content in cement, NazO,, content in cement, interaction of these two factors and, but in a lesser degree, on cement specific surface and interaction of cement specific surface and C3A content. Simultaneously h value of such mortars depends successively on: specific surface of cement, Na20eqand C3A content. Character of influence of cement composition on rheological properties of W/C=0.45 mortars with PEl superplasticizer changes depending on cement specific surface. In case of mortars with cements of specific surface 320 m2kg g value after 10 min practically doesn't depend on cement composition while h value depends on NazO,, content and increases with its increasing content. Also C3A content influences h value. Character of this influence depends on Na20, content - for cements of low NazO,, content increase of C3A content cause increase of h value, while for cements of high Na20eq content increase of C3A content cause decrease of h value. In case of mortars with cements of specific surface 370 and 420 m2kg its rheological parameters are more strongly influenced by cement composition. Value g of these mortars increases with increasing C3A and NazO,, content. Simultaneously h value increases with increasing C3A content and decreases with increasing NazO,, content. Specific surface of cement alone only slightly influences g value of W/C=0.45 mortars with PEl superplasticizer - increase of specific surface of cement increases g value. In the same time increase of specific surface of cement causes significant drop of h value. Range of h value chan5es due cement specific surface variations is higher then range of h value changes due variations of cement composition.
348
Jacek GOLASZEWSKIand Janusz SZWABO WSH
+Na20,
- 0.3%
100
+Na20,-Na20,
- 0.3%
80
-&-NaZO-, +Na20,
120
1.1%
-
+Na20,-
z $
0.5
0.4
1.1% 0.3%
-B
1.1%
B =
60
0.3
L.
I
3
m
0.2
40
0,1
20
Y
0
0
I
8
4
I
12
4 8 CIA content ph]
C,A content ph]
mortars with PE2 superplasticizer gro = 74.65+0.98A+24.89B-50.5lC-O,03AB+0.20AC-5.41BC-0.01AZ-3.75P+9.04cZ; ? = 0.953 hro = -0.118-0.033A+0.2228+0. l89C4,Ol5AB+O,OllAC-O,O42BC+O.00lAz4.O33BZ-O.035cZ~? = 0.887 mortars with PE3 superplasticizer gro = 156.3(r2.4OA-45.748-85.79C+4.38AB-O.17AC+O.66BC+O. 16A2+26.9682+13.62C1; f = 0.934 hro = ~.278+0.002A+O.089B+O.431C-O.O1OAB-O.001AC+O.062BC+O.000AZ-0. 166Bz-0.078cf; f = 0.895 mortars with PC superplasticizer gro = 141.4-2.13A-76.348-72.O3C+3.3BAB+O.26AC+8.29BC+O.O8Az+31.62~+1O. 75cZ; ? = 0.921 hro = 0.O95-0.~2A+0.4328+0.006C+0.wOAB-0.004AC-0.074BC+0.001Az-0.156B2+0.012 e ; f = 0.917 where A C A content in cementi%]; B NazO, content in cement [%I; C SO, content in cement [%I 8. Influence of CjA and NazO, content in cement on rheological properties of cement mortars with PC,
-
Fig.
12
-
-
PE2, PE3 superplasticizers 10 min after end of mixing (W/C=0.45; SP-2%; cements of specific surface = 370 m2/kg, S03=3%) 120
100
E E
3
NaSO,
- 0.3%
--tNa20,-9-Na20, +i+ Na20, +Na20,+Na20, +Na20, -Na20,-
- 0.3% - 0.7% 1.1% - 0.3% - 0.7%
-4-
80
0.5
1.1%
0.4
-
1.1%
0.3
B
1
60
3
m
=
0.2
40
0.1
20
I
0 0
4
8 C,A content ph]
12
0
4 C,A
12
content [%I
Fig. 9. Influence of C,A and Na20, content in cement on rheological properties of cement mortars with PC, PE2, PE3 superplasticizers60 min after end of mixing (W/C=0.45; SP-2%; cements of specific surface = 370 m’kg, SO&%)
Influence of cement and superplasticizer on rheological properties of mortars
349
Value g of WIC = 0.45 mortars with 3% PE1 superplasticizer addition increases with time, while h value of these mortars, in opposite to WIC = 0.55 mortars with PEl superplasticizer, strongly decreases. Character of changes of g value with time of WlGO.45 mortars with 3% PE1 superplasticizer is generally similar to changes of g value of WlC=O.55 mortars without and with 1% PE1 superplasticizer. (Fig. 4) Rate of g value increase with time of W/C=O.45 mortars with 3% PE1 superplasticizer depends on specific surface of cement - increases from 0.20 Nmm/min for mortars with cements of 320 m’kg to 0.42 Nmdmin for mortars with cements of 420 m2ikg, on C3A and NazO,, content - increases with increasing C3A and Na20, content, and on interaction of these factors. Rate of h value decreases with time depending on complex interaction of specific surface of cement and C3A and NazO,, content and reach minimum for mortars with cements of specific surface 320 m2/kg, 2% C3A and 1.1% Na20e, content. Generally h value rate of decrease increases with increasing specific surface of cement and C3A content and decreasing Na20, content. Statistical analysis of obtained results and plots on Fig. 8 and 9 indicate that for particular specific surface (in discussed case 370 m2/kg) character of influence of cement composition on rheological parameters of W/C=O.45 mortars with PC, PE2, and PE3 superplasticizers is qualitatively similar. Rheological properties of these mortars depend successively on: g value - C3A and Na20eq content and interaction of these factors, h value - NazO,, content, interaction between C3A and Na20eqcontent and C3A content. There are the same factors and in the same order like in case mortars with PEl superplasticizer. Also for mortars with PC, PE2, and PE3 superplasticizers it was found that, in investigated range of changes, SO3 doesn’t influence rheological parameters. Values g of WIC = 0.45 mortars with PE3 and PC superplasticizers 10 min after end of mixing are similar. In that case g value increases with increasing C3A and NazO,, content and influence of increasing NazO,, content is especially meaningful when cements with high C3A content are used. Values g of WIC = 0.45 mortars with PE2 at a lesser extend depends on C3A content, showing in the same time strong dependence on Na20eq content and tendency to increase with increasing NazO,, content. Values h of WIC = 0.45 mortars with PE2, PE3 and PC superplasticizers 10 min after end of mixing depends mainly on type of superplasticizer. In case of superplasticizers PE3 and PC addition, which characterise by higher then and PE2 molecular weight, h value of mortar is clearly higher. Character of cement composition influence on h value of mortars with PE2, PE3 and PC superplasticizers depends on type of superplasticizer added. Increasing C3A content in cement causes decrease of h value of mortars with PC and PE2 superplasticizers, while h value of mortars with PE3 superplasticizer increases or decreases depending on NazO,, content. Increase of Na2Oeq content doesn’t influence or decreases h value of mortars with PC and PE superplasticizers. Rate of g value increase with time of W/C = 0.45 mortars with PC and PE3 superplasticizers is lower then mortars with superplasticizer PE2. Rate of increase of g value in time of these mortars increases with increasing C3A content and reach maximum for cements with 0.7 YO NazO,, content (PC 1, PE3 superplasticizers) or 1,1% NazO,, content (PE2 superplasticizer). The least changes of g value with time proceeds for mortars with cements of 2% C3A content and 0.3% Na20eq content. Value h of all tested WIC = 0.45 mortars, independently on cement composition and superplasticizer type, decreases with time. The rate of h value decrease depends first of all on superplasticizer type and is clearly higher for mortars with PC superplasticizer then for mortars with PE2 and PE3 superplasticizers. Rate of h value decrease depends also on C3A and Na20,, content - in case of mortars with PE2 superplasticizers decreases with increasing C3A content, in case of mortars with PE3 and PC superplasticizers minimum rate of h value decrease appears for cements of 7% C3A. Higher Na20eqcontent in cement foster higher rate of h value decrease.
3 50
Jacek GOtASZEWSKI and Janusz SZWABOWSKI
On the base of obtained relationships a simple mathematical models can be developed. Such models, developed for mortars without and with SNF, SMF, PC and PE superplasticizers (see Fig. 3 8), include wide range of C3A, Na20, and SO3 contents in cements and can be successfblly used for initial selection of cements and superplasticizers from point of view of its compatibility and character of its influence on rheological parameters of cement mixes. Simultaneously, for the sake of possibility of significant differences between effectiveness of different superplasticizers and omission of influence of form of gypsum and interaction of cement specific surface and cement accuracy of such selection of cement and superplasticizer should be experimentally confirmed.
-
SUMMARY Workability shaping of fresh HPC should be conducted on the ground of rheology - required workability can be achieved by adjusting rheological properties of concrete mix to the given method and conditions of concrete processing. Basis of fresh concrete rheological properties shaping are data and relationships from rheological studies performed using rheometrical methods. In the presented investigation basic relationships of influence of cement specific surface and cement chemical and mineral composition on rheological parameters of superplasticized model mortars were defined using rheometrical test. These relationships provide unequivocal physical information on character of cement and superplasticizer influence on properties of HPC concrete and can be used for choice of compatible cement superplasticizer system and for workability of HPC shaping.
LITERATURE [ l ] Szwabowski J.: Rheology of cement based mixes (in Polish). Wyd. Politechniki Slqskiej, Gliwice, 1999. [2] Aitcin P-C.: High Performance Concrete, EF&N SPON 1998. [3] Aitcin P-C.: Durable high performance concrete art and knowledge (in Polish). Conference ”Beton na progu nowego milenium”, Krakow, 2000, pp. 383 - 413. [4] Ramachandran V.S.: Concrete Admixtures Handbook. Properties, Science and Technology, Ed. V.S. Ramahandran, Noyes Publications, Park Ridge, New Jersey, USA, 1995. [5] Proceedings of the International RILEM Conference ,,The Role of Admixtures in High Performance Concrete” Ed. J.G. Cabrera and R. Rivera - Villarreal. Monterrey, Mexico, 1999. [6] Proceedings of International Congress “Creating with Concrete” Ed. Ravinda K Dhir & others, Dundee, Scotland, UK, 1999. [7] Proceeding of Sixth CANMET/ACI International Conference on Superplasticizers and Other Chemical Admixtures in Concrete. Ed. V.M. Malhorta, Nice, France, 2000. [8] Teubert J.: Measuring the consistency of concrete mortar and its importance to the workability of fresh concret, Betonwerk + Fertigeil Technik, (4), 1981, p. 6. [9] Banfill P.F.G.: The rheology of fresh mortar. Mag. of Concrete Research, Vol. 43, No 154, 1991, pp.13-21. [lo] Meader U., Kustrerle W., Grass G.: The rheological behaviour of cementitious materials with chemically different superplasticizers, in Proceedings of the International RILEM Conference ,,The Role of Admixtures in High Performance Concrete”, ed J.G. Cabrera and R. Rivera - Villarreal, Monterrey, Mexico, 1999, pp. 357 - 316. [ l 11 Giergiczny Z., Matolepszy J., Szwabowski J., Sliwihski J.: Cements with mineral additives in concretes of new generation (in Polish). Wydawnictwo Instytut Sl4ski sp. z 0.0. w Opolu, Opole 2002, p 189. [12] Faroug F., Szwabowski J., Wild S.: Influence of Superplasticizers on Workability of Concrete, Journal of Materials in Civil Engineering, Vol. 11, No. 2, 1999, pp. 151-157. [ 131 Tattarsall G.H., Banfill P.F.G: The Rheology of Fresh Concrete, Pitman Books Limited, Boston 1983. 1141 Jiang S.; Kim B-G.; Aitcin P-C.: Importance of adequate soluble alkali content to ensure cernenthperplasticizer compatibility. Cement and Concrete Research. Vol. 29, 1999, pp. 71-78. [15] Golaszewski J, Szwabowski J.: Rheological behaviour of fresh cement mortars containing superplasticizers of new generation. Kurdowski Sympozjum. Science of cement and concrete. Krakow, 2001, pp. 1 11- 135.
-
Proc. Int. Symp. ,,Brittle Matrix Composites 7 ” A.M. Brandt, KC. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
ANALYSIS OF CONCRETE PROPERTY FIELDS AND SEARCH FOR THE BEST COMPOSITIONS USING MONTE CARL0 METHOD Tatiana LYASHENKO, Vitaly VOZNESENSKY Odessa State Building and Architecture Academy PO Box 76 Main Post Office, Odessa 65001, Ukraine, e-mail:
[email protected] Shimon BOIKO Concretec Ltd. Har-Hozvim, PO Box 45010, Jerusalem 91450, Israel David SHTAKELBERG Standard Institution of Israel 7 Yad Harutzim St., PO Box 10258, Jerusalem 93420, Israel ABSTRACT Rational compositions that would guarantee the required levels of six properties of ready-mix in-situ concrete for framed buildings have been determined. To do this computational experiments on property fields in composition coordinates have been carried out using experimental-statistical models and Monte Carlo method. For compositions providing a fixed level of specific property isoparametric analysis has been fulfilled to evaluate the variations in other properties. Keywords In-situ concrete, guaranteed quality, computational experiment, optimization, isoparametric analysis.
INTRODUCTION The concept of fields Y(x) of composite properties Y in coordinates of mix proportions and technological parameters (vector x) is aimed at deriving, as much as possible, information about multi-component materials behavior from experimental data [ 13. For this purpose computational experiments on property fields, described by structured multifactor experimental-statistical (ES) models [2], are carried out. They allow materials science regularities to be evaluated and solutions that would guarantee required quality of the material to be found with specified risk taken into account. To account for the risk the modeldeterminate level of property field at any point in the region of composition and process parameters is transformed into random value by inclusion of the model error related to experiment [3]. So, analysed in computational experiments, using Monte Carlo method, are full and local fields, which can be random or “of guaranteed level”[ I]. Generalising numerical indices of the fields [4] make it possible to compare the fields, to estimate their transformations as composition and technological factors change, to evaluate changing
352
T. LYASHENKO,
v. VOZNESENSKY, s. BOIKO, D. SHTAKELBERG
correlation between the properties [3, 51. Thus the concept and special means of its operation allow rational compositions and technological parameters to be assigned that would provide required levels of properties. The analysis of property fields described on the data of designed experiments has made it possible to evaluate the influence of composition on properties of mixes, characteristics of structure and hnctional properties for a number of composites [ 11. Such analysis helps to find optimal compositions, with levels of quality criteria guaranteed, for some jobs that impose specific requirements on the materials, in particular, on in-situ concrete for framed buildings. CONDITIONS OF EXPERIMENT AND MODELLING The experiment was carried out at the Standard Institution of Israel (by international and Israel standards). Mix components and base mix proportions were received from ready-mix producer. Variables in the experiment (according to optimal design) were the quantity of cement (C), XI= 280 -I 30 kg/m3, crushed aggregate-sand ratio (CNS, by mass), X2 = 2.23 ? 0.25, and two modification factors - dosages of admixture (A, of D-G type), X3 = 0.56 0.14, and of fine-grained dolomite filler (F, 190 m2/kg), X4 at levels of 10, 50, 60 kg/m3. Constant content of water, 200 dm3/m3,was conditioned by NMR-procedures used to analyse structure formation process [6]. Based on values of properties of concrete mix and hardened concrete of 18 compositions, corresponding to optimal design of experiment, four-factor non-linear ES-models (with normalized I x, 151) were built to describe the property fields in composition coordinates. Such model (presented in [3] in structured form) for strength R (MPa) of 28-day concrete has 8 significant terms (at experimental error SR =1.34 MPa and one-sided risk 0.1):
R = 24.74 + 4.27~1- 0.71~2+ 1.90~:
+ 1.58xlX4 + 1.15X2X3 + 0 . 7 6 ~ 2 ~+40 . 6 6 ~ 3 ~ 4
The main generalizing indices of the field “composition - compression strength”, R(x), estimated by the model above, are: R,, = 34.4 at X I = x2 = x3 = x4 = +1 (C=310, CA/S=2.48, A=0.70, F=60), R,,, = 18.1 at X I = x3 = -1, xz = 0.29, x4 = +1, absolute increase AR= 16.3 MPa, relative increase 6R= 190%. To determine the rational compositions of the concrete the fields of six properties have been analysed in computational experiments on the fields, using Monte Carlo method with ES-models analogous to equation R(x) shown above. The levels of three from six criteria were specified. Firstly, the concrete had to be of grade B-20 (Israeli Standard 118), i.e., to provide average strength R 1 2 4 . It was decided, however, to set harder requirement, since R levels estimated by ES-model for any composition xu, when searching for the best one, would be within confidence interval R, = R(x,) k AR(x~),where AR(x,) = s R tu . [d(~”)]’.~,ta - quantile of standard normal distribution corresponding to certain risk a (acceptable when making technological decision), d - depending on xu prediction variance hnction (defined by experiment design and model structure). So average value (over region of x, with a = O.l), AR = 1.72, has been added to specified level of R, giving the lowest value of R = 25.72 that would guarantee required 24 MPa. Secondly, the slump (S) of concrete mix had to be not less than 12 cm (Israeli Standard 26). To guarantee this level more severe requirement has been fixed, S 2 12.6 cm. Thirdly, special requirement was imposed on mixes for in-situ construction of framed buildings. Column specimens 2.4 m high were made from each of the 18 mixes, by vertical placement of concrete in pipe forms of 10 cm diameter, to be cut into cylinder slices after 28
353
Analysis of concrete property fields and searchfor the best compositions using Monte Carlo ...
days of hardening. As agreed with the customer the ratio of strength in lower cylinder (RL)to that of upper cylinder (Ru), KLU = 100(Rr/RU), had to be within 95-105%. This would eliminate the occurrence of substantial gradients in the fields of strength along the vertical concrete elements of building frames. The inclusion of confidence intervals AKLUhas led to harder requirement, 98 I KLUI 102%. No rigid requirements have been posed for three other criteria but it has been proposed to improve their levels, with respect to median level, Y M=~O.S(Y,,+Y,i,), of the fields of these criteria in coordinates of mix proportions. Thus, it would be useful to maximize elastic modulus of the concrete, beyond E = 16.1 GPa, minimize the shrinkage, to E less than 0.53 m d m , and minimize special index of non-uniformity in pole element, defined as the ratio of strength in strongest and weakest fragments, 6 = 100(RmaX/R"'"),below 6 ~ , = 114%. OPTIMISATION
Prior to multi-criterion search for rational compositions of the concrete, the compositions optimal by each individual quality criterion (Table 1) have been analysed. Table 1
Characteristics of optimal compositions by individual criteria of concrete quality
Levels of )articular criteria
Quality criteria of in-situ concrete for framed buildings sei :rely specified S, crn
:optimised
P
23.3 -
10.3 14.1
0.39
18.2
0.36 -
20.9
0.42
12.6
0.53
104
1
114
As it could be expected none of the five compositions in Table 1 would satisfy the stringent standard requirements for all three criteria. In particular, the composition of Em, (XI= +1, x2 = x3= x4 = -1; C=310, CA/S=1.98, A=0.42, F=lO), which complies with requirements for R and S, would be unacceptable by KLU. Multi-criterion search for admissible compositions in four-factor region ( X I , x2, x3, xd} of property fields has been fulfilled with algorithm using Monte Carlo method iteratively (for multi-dimensional random scanning). At first iteration N = lo4 uniformly distributed random points (compositions) have been generated in the intervals -1 I X I , x2, x3, I + I and for them 10000 values of each quality criterion (S, R, KLU,E, E, 6) have been calculated. The generated compositions (with added 16 at vertices of 4-dimension cube) which would not comply with all the requirements defined above were deleted. All guaranteeing requirements (on S, R, KLU) would be fulfilled only by 169 compositions (out of 10016), the greatest elimination being by strength gradient oriented
354
T. LYASHENKO, V. VOZNESENSKY,S.BOIKO, D. SHTAKELBERG
down along the pole (violating KLU 102). The algorithm determined automatically the volume of permissible compositions region R 1.7% (of all the region of compositions). If the requirements have not been stringent the size of permissible region would be near 8%. Accounting for three additional quality criteria (requirements for E, E, and 6 being not worse than their median levels) reduce the number of acceptable compositions to 22. These present the region of compromise; its volume R, 0.2%. Table 2 shows some results of the first iteration. After reducing the region of search almost 500 times a number of compositions have been found which not only meet the stringent requirements for S , R, and KLU,but have three optimality criteria at levels not less than median as well. The composition providing Rm,, = 30.7 MPa and all other properties approaching their best levels has been of special interest, but corresponded to increased level of cement, 3 10 kg/m3. Table 2
Characteristics of compromise compositions obtained at 1-st iteration
Levels of Darticular criteria
Limits
-
Quality criteria of in-situ concrete for framed buildings severely specified to be optimised
Factors
XI
1
x2 x3 x4 1 0.9
0.2 -1
0
1
-1 -0.E
1 0 - 1
12.8
25.9
98.2
16.1
0.41
105
16.4
26.3
100.8
16.5
0.52
114
18.2
0.42
109
18.1
0.41
107
16.6
0.46
105
1 1 - 1 1
Best value
1
-1
0
-1
1
-1
0
-1
12.8
30.2
98.2
1 1 - 1 1
15.1
30.7
99.0
1
15.8
28.5
99.0
1
I
-1
1
-1
1
The analysis of the location of compromise region along the axis of each factor allows the results to be refined at the second iteration. Helpful in the analysis are frequency polygons (Fig. 1) for values of factors corresponding to compositions obtained at the first iteration (22 points enclosed in region of compromise). These polygons define the shortened intervals in which next lo4 random points could be generated. Thus amount of cement can be varied as 0 I X I S +I (the lower limit being offset by average step of scanning at previous iteration, Ax = 0.2). Since values of three other factors (CNS, A, F) for promising compositions have grouped near the boundaries of factor intervals, three possible combinations fotm compositions clusters A, B, C: A + x2 from 0.8 to+1, x3 from -1 to-0.7, x4 from 0.8 to+1; B + x2 from0.8 to+1, x3 fromO.l to +1, ~4 fkom-1 to-0.5; C -+ x2 from -1 to -0.3, x3 from 0.1 to + I ; x4 from -1 to -0.5. Between these three clusters 10000 random points have been distributed at the second iteration of the search for adequate compositions, the proportion being 1:2: 19 (accounting for number of compositions in respective zones after 1'' iteration). Guaranteeing requirements have appeared to be fulfilled by 915 of 10016 concrete
Analysis of concrete property fields and search for the best cornpositions using Monte Carlo ...
355
Figure 1. Distributions of factor values in compromise compositions found at the 1'' iteration compositions analysed at the 2"d iteration. To choose the best from them by optimality criteria (E, E, and 6 ) step-by-step reduction of compromise region has been carried out, starting with median levels of the criteria as boundary levels. In particular, minimal level set for E could be increased by O.l.(E,,,m-E~e) = (26.0-16.1) = 0.1 GPa at each step. Only 10 compositions have been left within the final zone of compromise, where 18.11 E 5 18.7,0.411 E 1 0.44, and 1.07 5 6 5 1.09. Nine of them have approximately the same C N S = 2.48, quantities of admixture, A = 0.42 kg/m3, and filler, F = 60 kg/m3 (XI= x4 = +I, x3 = -1; with accuracy equal to step of scanning at 2"d iteration Ax = 0.08), minimal amount of cement being about 290 kg/m3 (XI= 0.7). This composition meets all the requirements imposed on the concrete. It has S = 15 cm, R = 29 MPa, KLU= 99%, and rather high levels of the properties which have been optimised: E -1 8.5 GPa, E = 0.44 m d m , and 6 = 106.
ISOPARAMETFUC ANALYSIS
To make the final choice of the composition it has been reasonable to analyse the local fields of six properties Y(x1, x2) at x3 = -1 and x4 = +1, in coordinates of cement content and crushed aggregate-sand ratio at low concentration of the admixture and high quantity of the filler. The fields are represented in Figure 2 (heavy net corresponds to forbidden compositions and the star to the optimal one). The difference in shape of the fields substantiates the complexity of the problem - to provide the necessary levels for many criteria of concrete quality through controlling concrete composition. The requirement KLU = 100 f. 2 imposed on concrete in the column elements has proved to be extremely tough. This can be seen in Figure 2. So, it has been reasonable to estimate the changes of other properties in this narrow range of KLU. The problem is solved with isoparametric analysis [7]. The movement along the line KLU = 100 (along projection of the arrow shown in Fig. 2) on the field of respective property could be realized in computational experiment, by increasing cement content from X I = -1 to + I . To keep KLU at indicated level the crash aggregate-sand ratio should be varied by non-linear dependence XI = 0.71 + 0.15X1+ 0 . 1 6 ~ 0~. ~ 12~1 ~0.16~1~. Monte Carlo method provides rather simple way to obtain the information on variations in properties of compositions that would give the same level of some property (KLU= loo), with isoline being transformed into the strip (KLU= 1OOf.2, formed by required boundaries).
356
T.LYASHENKO, V. VOZNESENSKY, S. BOIKO, D. SHTAKELBERG
1
1
1
1
1
1
1
1
Figure 2. The fields of concrete properties in coordinates of C and C N S at fKed dosages of modifiers Shown in Figure 3 are the results of isoparametric analysis of five quality criteria of ready-mix concrete at conditions providing practically the same values of concrete strength in lower and upper fragments of the column. Placed inside a given corridor, along the line KLU(X~, x2) = 100, are 200 of 2500 generated points. The values of five properties for these 200 compositions also form the corridors in which properties change as quantities of components are varied. Concrete strength grows, naturally, as the content of cement increases (at constant water
Analysis of concrete property fields and searchfor the best compositions using Monfe Curlo ...
S
357
6
"1
I
E
KLU
30 28 26 24 22 20
I8 16
1
0.5
0
-0.5
-1
Figure 3. Isoparametric analysis (along the line KLU= 100) of ready mix concrete properties (at A = 0.4 and F = 60 kg/m3) content) and achieves the level R = 25.6 (marked with star in Fig.' 3), that would guarantee standard requirement of 24 MPa, at C > 280 kg/m3 ( X I > 0). The levels of all other properties therewith also comply with the requirements discussed above. It should be noted that R grows throughout cement content range, whereas the increase of E and decrease of slump stop just from C = 280. The results of isoparametric analysis allow the composition of ready-mix concrete for insitu construction of framed building, found after two iteration of multi-criterion search with the use of Monte Carlo method, to be accepted as guaranteeing multi-criterion requirements.
CONCLUSION Computational experiments on the fields of composites properties in coordinates of compositions, specifically, using Monte Carlo method, serve as effective means of computational materials science. The tools presented make possible the controllable multicriterion search for optimal compositions and evaluation of relations between composite properties when one of them is invariable. Determined have been the rational compositions of ready-mix concrete with account for criteria of uniformity of the material in pole elements.
358
T. LYASHENKO, V. VOZNESENSKY, S. BOIKO, D. SHTAKELBERG
REFERENCES 1. Lyashenko, T.V. Building Materials Property Fields (Concept, Analysis, Optimisation). Abstract of Thesis for Doctor of Science Degree (in Ukrainian). Odessa State Building and Architecture Academy, Odessa, 2003, pp 34 2. Lyashenko, T.V. Brittle matrix composites optimization on the base of structured experimental-statistical models. In: Proc.Int.Symp. “Brittle matrix composites 3”, A.M. Brandt and I.H. Marshall eds., Elsevier Applied Science, London 1991, pp 448-457 3. Lyashenko, T.V., Voznesensky, V.A. Modelling and analysis of varying correlation between properties of brittle matrix composites. In: Proc.Int.Symp. “Brittle Matrix Composites 5”, A.M.Brandt, V.C.Li, and LH.Marshal1 eds., Woodhead Publ. Ltd. - Bigraf, Cambridge-Warsaw 1997, pp 417-426 4. Voznesensky, V.A., Lyashenko, T.V., Modelling, analysis and optimization of brittle matrix composites properties fields. In: Proc.Int.Symp. “Brittle Matrix Composites 4”, A.M.Brandt, V.C.Li, and I.H.Marshal1 eds., Woodhead Publ. Ltd. - BigraE CambridgeWarsaw 1994, pp 255-263 5. Lyashenko, T.V, Voznesensky, V.A, Krovyakov, S.A. Analysis of water effect on fracture toughness in cement-based composites using computational materials science methods. In: Proc.Int.Symp. “Brittle Matrix Composites 6“,A.M.Brandt, V.C.Li, and I.H.Marshal1 eds., Woodhead Publ. Ltd. - ZTUREK, Warsaw 2000, pp 210-219 6. Lyashenko, T., Voznesensky, V., Boiko, S., Shtakelberg, D. Experimental-statistical modeling and analysis of the chain “composition - NMR-signal - properties” of cement composite. In: Proc.lOth Int. Congress on Chemistry of Cement, V.3., Gothenburg 1997, pp 4~003,s 7. Voznesensky, V.A., Lyashenko, T.V., Ivanov, Y.P., Nikolov, I.I., Computers and Optirnisation of Composite Materials (in Russian). Budivelnik, Kiev 1989, pp 240
Proc. Int. Symp. ,,BrittleMatrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
CEMENT-BASED MATERIALS INCORPORATING RUBBER AGGREGATES: SHRINKAGE LENGTH CHANGES Anaclet TURATSINZE'", Sandra BONNET (I9*) and Jean-Louis GRANJU ( I ) ( I ) Laboratoire Matkriaux et Durabilitk des Constructions (LMDC) 135, av de Rangueil, 31077 Toulouse cedex 04, France (*)Agence De I'Environnement et de la Maitrise de I'Energie (ADEME) 2, Square Lafayette, 49004 Angers, France ABSTRACT Cement-based materials are brittle. As a consequence to their poor straining capacity and their sensitivity to shrinkage, they generally present cracking detrimental to the durability of structures. Nowadays, a solution to prevent or to delay the shrinkage cracking remains a research issue. Fibre reinforcement, restraining the crack opening, is one of the most documented way to partly reach this objective. This paper focuses on a second option to decrease the brittleness of cementious materials: the incorporation of low modulus aggregates. The study aims to design a composite exhibiting a high straining ability before macrocracking localisation. It has been assumed that incorporating aggregates with low deformation modulus should succeed with the challenge. Rubber aggregates were chosen. They confer to the work a second facet: the opportunity to recycle rubber tyres, fulfilling a demand of clean environment conservation. The results presented compare the properties of a plain mortar with the ones of two mixes obtained by partially replacing the sand aggregates by rubber aggregates. Two ratios of sand replacement, 20 and 30 % by volume, were investigated. In both cases (natural sand and rubber aggregates), a maximum grain size of 4 mm was used. Previous results had shown that rubber aggregates are strongly detrimental to the composite strength. In return, the modulus of elasticity of the mortar incorporating rubber aggregates is substantially decreased and its straining capacity before failure is significantly increased. On another hand rubberised mortars suffer higher length changes due to shrinkage than plain mortar. In order to weigh up benefits and deficits, ring tests have been carried out and their results clearly demonstrate the benefit: the straining capacity enhanced by rubber aggregate substitution widely offsets the additional shrinkage length changes. The future prospects are the combination of the beneficial effects of both the fibre reinforcement and the rubber aggregate substitution to design a cimentitious composite exhibiting enhanced ductile failure. Keywords Brittleness, straining capacity, modulus of elasticity, compressive and tensile strengths, length changes, rubber aggregates, shrinkage cracking, ring test, ecology.
360
Anaclet TURATSINZE, Sandra BONNET and Jean-Louis GRANJU
INTRODUCTION Cement-based materials, the prominent fraction of construction materials, are perfectible. Due to their poor straining capacity and their low tensile strength, they are sensitive to cracking particularly to shrinkage cracking. For instance, large area elements (slabs on grade, pavements.. .) are often cracked, this cracking being strongly marked in the case of restrained shrinkage. The cracking of cement based repairs also is relevant of a similar problematic. It has been evidenced that such a cracking is the main cause of their debonding initiation and, consequently, of the limitation of their service life [ 1-21. Fibre reinforcement is generally used to limit the detrimental effect of cracking, but the ideal solution to avoid the handicaps would be to improve the straining capacity of the material before cracking localisation. In this regard, it has been assumed that incorporation of aggregates with low deformation modulus would be a solution. In our research programme rubber aggregates obtained from shredded non reusable tyres have been used, conferring to the study an ecological interest. Previous results confirmed that rubber aggregate substitution is detrimental to both compressive and tensile strengths. In turn, as expected, a cement composite containing such particles presents low deformation modulus. Four-point flexure tests show that it exhibits a high straining capacity before the peak load in accordance with the research objective. However, the presence of such deformable particles as aggregates implicitly infers that the internal restraint by the aggregate is reduced, inducing an increase of free drying shrinkage length change. Consequently, rubber aggregate substitution leads to a couple of phenomenons with opposite effects in relation with restrained shrinkage cracking. Ring tests demonstrate that the balance between the improved straining capacity and the increased shrinkage length change is beneficial.
BACKGROUNG Materials Preliminary tests have been performed in order to access the influence of rubber aggregate substitution on the basic mechanical properties of cement-based materials. The experimental setup is reported in [3]. The control material is a mortar with a CEM I 52.5 R Portland cement and natural sand. Its mix proportions are given in table 1. Modified mixes are made of the same mortar with a volume percentage of rubber aggregates replacing the same volume of natural sand. In order to reduce the bleeding and segregation prominently noticed when rubber aggregates are added (densities of sand and rubber aggregates are 2.7 and 1.2 respectively), an admixture was used as a stabiliser. Known as Underwater Concrete System (UCS), this admixture was designed to increase cohesion and to prevent cement washout. The stabiliser may affect the properties of the material. For this reason, in order to point out the actual influence of rubber aggregate substitution, the stabiliser was also used in the mix without rubber aggregates. The grading curves of sand and rubber particles are given in figure 1 and two rubber aggregates contents have been investigated: 20 and 30 % of the aggregate total volume. The different mixes studied will be designated using their rubber aggregate substitution ratio, the letters M and R referring to Mortar and Rubber respectively. For instance M30R means the mix incorporating 30 % of rubber aggregates.
Cement-based materials incorporating rubber aggregates: shrinkage length changes
36 1
100
#
E
40 20
0 0.01
0.1 1 Sieve size (mm)
10
Figure 1 - Grading curves of sand and rubber aggregates Basic mechanichal properties Whatever the particle size and shape, it is well established that rubber aggregate substitution is detrimental to tensile and compressive strengths of the cement-based composites [4-61. Our results are presented in figures 2, 3 and 4. They confirm this general trend. Figures 2 and 3 show that the maximum of rubber aggregate substitution should be limited if a minimum strength is required. For instance 30% of rubber aggregates substitution induces about 80% compressive strength loss and about 70% tensile strength loss. The variation of the deformation modulus with rubber aggregates substitution is presented in figure 4. As expected, the results show a significant decrease of the compressive deformation modulus when rubber aggregate content is increased. Eldin et al. [5] explained this trend through the low elasticity modulus of rubber aggregates, which they considered as acting as large pores. Such a view is not strictly accurate. Although rubber can undergo very high deformations, it exhibits a bulk modulus of the order of 1 GPa with the associated capacity to transfer stresses. Evaluation of the tensile deformation modulus (not presented here) shows a similar trend but with an amplitude about 1.5 times higher.
0
10
20
30
Rubber aggregate contents (Oh)
Figure 2 - Compressive strength versus rubber aggregate substitution
362
Anaclet TURATSINZE?Sandra BONNET and Jean-Louis GRANJU 41
2
E. 5m
-.--e E
3'
2.
a,
e
f
-
1.
0%
Figure 3 - Tensile strength'versusrubber aggregate substitution
25000
1
-. 0
10
20
30
Rubber aggregate contents (%)
Figure 4 - Compressive modulus of deformation versus rubber aggregate substitution STRAINING CAPACITY OF RUBBERISED MORTAR
Experimental setup The straining capacity has been evaluated through four-point flexure tests. The test setup is presented in figure 5. LVDT
c
a=
14Oinin
. - .
& :
c= S5
min
b Figure 5 - Ex:erimental
setup forevaluation of straining capacity
Cement-based materials incorporating rubber aggregates: shrinkage length changes
363
The tests were carried out at 28 days on a series of four prismatic specimens (85x50~420 mm’) that had been continuously cured at 20°C and 100% R.H. The deflection 6 of the specimen was measured with a yoke by reference to the specimen itself. The tests were controlled by this deflection 6 at the rate of 50pdmin. The load F and the deflection 6 were automatically and continuously recorded by a data acquisition system. Results and discussion Curves in figure 6 are representative of the test results. It is well known that in flexure crack is initiated largely prior to the peak load. However, as far as the post peak zone is not reached, there are grounds to believe that microcracks coalescence is not achieved. For this reason we have considered the straining capacity of the material before cracking localisation as the deflection 6 corresponding to the peak load. With regard to such a definition, results illustrated by the curves in figure 6 show that rubber aggregates significantly increase the straining capacity of cement-based mortars. For instance, it turns about three times higher when the volume fraction of rubber is increased from 0 to 30%. It is an interesting result with regard to the objective. Such a behaviour can be explained by the rubber particles capacity to absorb energy when the microcrack tips run into their interface with cement paste, denying a mechanism for further propagation and delaying the macrocrack formation. In this sense, they act as crack arresters.
‘OR
51
0
M2OR
4
I
0.1
0.2 0,3 Deflection (mm)
0.4
0,5
Figure 6 - Four-point flexure tests: load versus deflection curves, influence of rubber aggregate substitution . SHRINKAGE LENGTH CHANGES
As it has been shown, rubber aggregates substitution enhances the straining capacity of cement based composites. However such a finding is not enough to conclude that the composite is less sensitive to drying shrinkage cracking. Actually, shrinkage cracking is the result of the coupled effects of three factors: the free shrinkage, its degree of restraint [7-81 and the straining capacity of the material. Free shrinkage tests Free shrinkage tests have been carried out in accordance with NF P 15-433 recommendation. The used 40x40~160mm’ prismatic specimens were continuously exposed to drying, the
364
Anaclet TURATSINZE,Sandra BONNET and Jean-Louis GRANJU
curing conditions being 20°C and 50% relative humidity. Plots of free shrinkage versus time are presented in figure 7 where each point results from the average of three tests.
f
3000
-
1500
-
I000
-
500
0
1 & : I : : : : : : ;
0
50
i : i : : : : : : ; : : : : ;
100
150
200
i : : : ; : : : : ; : :
250
300
350
::I
400Time(days)
Figure 7 - Free shrinkage versus time, influence of rubber aggregates substitution. Higher free shrinkage is obtained with the presence of rubber particles. It is consistent with the lower restraint brought by less stiff aggregates. In order to balance the benefit due to the improved straining capacity against the higher free shrinkage, restrained shrinkage cracking tests by means of ring-tests have been performed. Results should give a good idea of the potential of rubberised cement-based composites to reduce the risk of shrinkage cracking which particularly affects large cementbased area, first of all slabs, pavements.. ... If this potential is proved, such a composite should be suitable to design more durable structures, such as cement-based repairs [9-lo], toppings and linings. Restrained shrinkage cracking tests The shrinkage restraint was obtained by the use of steel ring according to NF P15-434 recommendation. A 35-mm thick and 140-mm deep mortar ring cast around a 25-mm thick stainless steel ring was used. The external diameter of the steel ring was of 250 mm. As outer mould, we used two steel semi-cylindrical shells that can be easily dismantled and reused. The steel ring and the mould were concentrically fastened onto a stainless steel base and the free space was filled with the mortar mixture. The outer mould was removed 24 hours after casting and the specimens were immediately exposed to drying at 21°C and 50% RH. A silicone sealing was used to prevent drying from the upper face of the mortar ring. Generally, it is assumed that the shrinkage along the height of the specimens is uniform when its height is higher than four times its thickness [ 111. As detailed in figure 8, such a criterion was fulfilled.
Cenierrt-based materials incurparating rubber aggregates: skrinlnge length changes
365
Figure 8 - Ring-test setup A video microscope was used to detect cracks as soon as their initiation, to monitor their propagation and eventually, to quantify their opening. Obtained results are presented in figures 9a to 9c and summarised in table 2. For the studied mixes and using two front views (A and B) of each ring mortar, the crack network after 55 days is accurately drawn: localisation, length (L) and maximum crack opening (MCO) are indicated on the figures and details are given through micrographs. The age at each crack initiation (CI) is also given.
CI = 6 days MCO= 1.1 mm L = 140 mm
Figure 9a - Restrained shrinkage cracking: control mortar (MOR)after 55 days
3 66
Anuclet TURATSINZE.Snndru BONNET und Jean-Louis GRANJU
CI = 9 days MCO = 0.8 mm L = 140 mm
Figure 9b - Rcstrained shrinkage cracking: mortar incorporating 20 % of rubber aggregates (M20R) after 55 days
CI = 21 days MCO = 0.07 mm L=9Omm
CI = 17 days MCO = 0.1 1 mrn L=60mm
CI = 17 days MCO = 0.10 mm L=90mm
Cl = 21 days MCO = 0.08 mm L=SOrnm
Figure 9c - Restrained shrinkage cracking: mortar incorporating 30 % of rubber aggregates (M30R) after 55 days
Ratio of rubber aggregate substitution Age at the first crack initiation (days) Number of cracks after 55 days Main crack length (mm) Maximum crack opening (mm)
0% (MOR)
16 1 140 11.1
20% (M20R) 19 1, discontinuous 140, discontinuous 10.80
3% (M30R) 117
I
4
90 10.11
I
Cement-based rnaterials incorporating rubber aggregates: shrinkage length changes
367
With regard to restrained shrinkage cracking, these results clearly demonstrate the benefit of rubber aggregate substitution. On the one hand restrained shrinkage cracking is delayed, on the other hand the crack openings are significantly decreased. An other interesting benefit is the discontinuous crack path of the mortar incorporating 20% rubber aggregates (M20R) and the multiple cracking of the mortar incorporation 30% rubber aggregates (M30R). This behaviour contrasts with the one of plain mortar (MOR) exhibiting a single and wide crack cutting the specimen along its full height. However, rubber particles being detrimental to the composite tensile and compressive strengths, deriving maximum benefit from such interesting behaviour remains incompatible with high strength priority. In other respects, it is well known that fibre reinforcement is a solution to reduce the detrimental effects of restrained shrinkage cracking and combining this traditional technique with rubber aggregate incorporation is expected to lead to enhanced performance: first results now available are promising.
CONCLUSIONS Results presented here show that incorporation of rubber aggregates obtained from shredded non reusable tyres in cement-based mortars is a suitable solution to limit their brittleness. Despite some drawbacks such as high decrease of tensile and compressive strengths and an increased free shrinkage length change, tests demonstrated that rubberised mortars exhibit an interesting increase of their straining capacity. Ring-tests have been carried out to balance these opposite properties with drying shrinkage cracking. Results show a clear benefit of rubberised mortar. Ongoing investigations explore effectiveness of the combination of rubber aggregate substitution with fibre reinforcement to reduce the detrimental effect of shrinkage cracking. The first results available are highly promising. Moreover, this programme presents a second facet, the use of rubber aggregates in cimentitious materials provids an opportunity to recycle rubber tyres and by the way, to achieve an environmental goal. ACKNOWLEDGEMENT
The authors acknowledge the financial support of the (( Agence de I'Environnement et de la Maitrise de I'Energie )) (ADEME) and of the (( Manufacture Franqaise des Pneumatiques MICHELIN v . REFERENCES 1. Chanvillard, G., Aitcin, P-C., and Lupien, C., Field evaluation of steel fibre reinforced concrete overlay with various bonding mechanisms. Transportation Research Record, n"l226, 1989, pp 48-56 2. Granju, J-L., Thin bonded overlays : About the role of fibre reinforcement on the limitation of their debonding. Advanced Cement Based Materials, vol. 4, n"1, 1996, pp 21 -27 3. Bonnet, S., Turatsinze, A. Granju, J-L., Capacite de deformation des mortiers incorporant des granulats caoutchouc. Forum des Associations AFGC / AUGC / IREX., Innovation et Developpement en GBnie Civil et Urbain. Toulouse, 30 et 31 mai 2002, CD, edited by SCOM, Universite Paul SABATIER, Toulouse
368
Anaclet TURATSINZE, Sandra BONNET and Jean-Louis GRANJU
4. Toutanji, H. A., The use of rubber tire particles in concrete to replace mineral aggregates. Cement and Concrete Composites, 18, 1996, pp 135 - 139 5 . Eldin N.N., Senouci A.B, Observations on rubberized concrete behaviour. Cement, Concrete and Aggregates, vol. 15, nol, 1993, pp 74 - 84 6. Li, Z., F. Li, F and Li, J.S., Properties of concrete incorporating rubber tyre particles. Magazine of Concrete Research, vol. 50, n04, 1998, pp 297 - 304 7. Shiotani, T., Bisschop, J., Van Mier J.G.M., Temporal and spatial development of drying shrinkage cracking in cement-based materials. Engineering Fracture Mechanics, 70, 2003, pp 1509-1525 8. Hobbs, D.W., The dependence of the bulk modulus, Young's modulus, creep, shrinkage and thermal expansion of concrete upon aggregate volume concentration. Materiaux et construction, Vol. 4, n"20, 1971, pp 107-1 14 9. A. Turatsinze, A., Farhat, H. , Granju, J.-L. ,The impact of precracking on the durability of thin bonded overlays. In: Proc. Int. Conf. Infrastructure regeneration and rehabilitation Improving the quality of life through better construction. A vision for the next millennium, Sheffield, 28 june - 2 july, 1999, Ed. R. Narayan Swamy, Sheffield Academic Press, pp 861868 10. A. Turatsinze, A., Farhat, H. , Granju, J.-L. , Durability of metal-fibre reinforced concrete repairs: drying shrinkage effects. In: Proc. Symp. "Brittle matrix composites 6", A.M. Brandt, V.C. Li and I.H. Marshall eds. Warsaw 9-11 oct., 2000, Woodhead Publishing Limited, Cambridge and Warsaw, 2000, pp 296-305 11. Grzybowski, M., Shah, S. P., Shrinkage cracking of fiber reinforced concrete, ACI Materials Journal, vol. 87, no, 1990, pp 138-148
Proc. Int. Symp. ,,Brittle Matrix Composites 7” A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and WoodheadPubl.. Warsaw 2003
ADVANCED CONSTRUCTION MATERIALS FROM FLY ASH
Hwai-Chung WU and Peijiang SUN Advanced Infrastructure Materials Laboratory Department of Civil and Environmental Engineering Wayne State University, Detroit, MI 48202, U.S.A. e-mail:
[email protected] ABSTRACT
In this paper, we will report the development of “ductile” high performance fly ash composites. These fly ash composites are made from 100% fly ash or with various amounts of chemical promoter (NaOH). An innovative process involving mixing, mechanical pressing and hydrothermal reaction is being developed. These three major steps follow a sequential order. After mixing, a fly ash mix is filled in the mold, then compressed by a press machine to specified pressures up to 20 m a . After reaching specified pressure, the mold is heated to moderate temperatures up to 3OO0C and for a period of specified times, during which hydrothermal reaction develops and solidifies the samples. In addition, a small amount of short fibers is added to the mix to hrther increase the ductility and crack resistance of the high strength fly ash composites. Both Class C and Class F fly ash have been used in this study. The differences in the types of fly ash and optimal processing conditions (pressure, temperature and time) will be discussed, together with their mechanical performance. Keywords Fly ash, masonry, high performance, hydrothermal, fiber reinforcement. INTRODUCTION Coal Combustion Byproducts Burning coal generates electrical power. This process also produces a residue material called coal combustion byproduct. Ash typically contains about 80 percent fly ash. It is collected in an air pollution control device called an electrostatic precipitator as flue gasses pass through large chambers. The remaining 20 percent, bottom ash falls into a collection hopper beneath the boiler. Fly ash produced at different power plants or at one plant with different coal sources may have different colors, particle size and shape characteristics, and chemical compositions depending on the source and uniformity of the coal, the degree of pulverization prior to burning, and the type of collection system used. Depending on how hot a coal plant is burning, the fly ash’s carbon content changes. Rapid cooling of the ash from the molten state as it leaves the flame causes fly ash to be predominantly noncrystalline (glassy) with minor
370
Hwui-Chung WU and Peijiung SUN
amounts of crystalline constituents, carbon, and varying quantities of lime. Fly ash is divided into two classes based on the chemical composition of the ash [I]. Ashes from subbituminous and lignite coals are Class C ashes and may contain more than 20 percent CaO. Ashes from bituminous and anthracite coal are Class F ashes and generally contain less than 10 percent CaO. Typically, Class C ashes contain 1 to 3 percent free lime and are reactive with water. Class F ashes generally contain no free lime. In the Civil Engineering construction industry, Fiber Reinforced Cementitious (FRC) composites have been used for almost five decades. However the idea of using natural fibers such as straw in construction materials could go back to 2500 B.C. Most recently, many studies show that the uses of FRC in applications such as new construction, insulation, and repair give very promising results. Additionally lightweight materials are increasingly used to make lightweight concrete. The most important advantage of using lightweight concrete is significant weight reduction. Besides reduction of dead load, faster construction, lower transport and handling costs, and reduction of labor become dominant factors for using lightweight concrete. Low themial conductivity is another characteristic of lightweight concrete. As reducing energy or fuel consumption during operation of buildings becomes necessary, demands for lightweight concrete increase. In this project, we attempt to incorporate short fibers into lightweight cementitious matrix to achieve both lightweight and high strengthhigh ductility. Current Applications Using Fly Ash At present, roughly 60 million tons of ash is produced in the U S . each year, but just 25% finds its way into other products [ I , 21. Of that total, more than eight million tons, or fourteen percent, is used in cement and concrete applications [3]. The remaining 11% is used in all other industrial and agricultural applications [4]. Among the current uses in construction in US, fly ash is primarily used as a partial replacement for cement in the following applications: High Volume Fly Ash Concrete 1. There are several benefits resulting from the use of fly ash in concrete. Typical gains include: a. increased strength gain after the age of 28 days due to its continuing pozzolanic reaction b. improved workability due to the spherical nature of fly ash c. increased durability due to reduced permeability since additional (C-S-H) forms that block bleed channels and fill pore space reduced heat of hydration leading to lower temperature rise and reduction in thermal cracking d. reduced cost However, these advantages disappear when the amounts of fly ash exceed certain optimum values for any given concrete mix design. By careful selection of mix proportions and the use of chemical admixtures, the optimal fly ash content can reach 70% [5,6,7].Even within this limit, the Clean Air Act has resulted in fly ash containing higher carbon concentrations, and has made them unusable. Once carbon levels get above lo%, fly ash begins to interfere with the air-entrainment process, leading to unreliable pours 181. It is perhaps more important to point out that the abovementioned benefits are somewhat marginal, hence they are not regarded as high performance products. Cost saving is almost entirely obtained from the cost differences between cement and fly ash. It is true that reduction in cement
Advanced construction materialsfrom fly ash
37 1
consumption can save energy and reduce COz emission from cement production [I], however, these additional cost savings are difficult to be quantified and realized by fly ash concrete users. Because of cement hydration concern, allowable variations of fly ash compositions have to be narrowly defined and permit very little room for adjustment on each individual job site. 1. Autoclaved Cellular Concrete (ACC) ACC originated in Sweden in 1926. Its manufacture involves mixing Portland cement, lime, aluminum powder, water, and a silica-rich material. The aluminum powder reacts with the calcinated materials, forming hydrogen gas, which causes the concrete to rise due to bubble formation. The air filled concrete thus gives its lightweight, approximately one-quarter to one-fifth the normal weight of concrete. The silica in ACC is typically derived from sand. A number of other countries (e.g. Britain and China) have successhlly used fly ash [9,10]. ACC is particularly popular in Europe, where 95% of construction materials are made of masonry. The main use for non-reinforced ACC products is as blocks in loadbearing internal and external walls, for partition wall, filler walls, linings and coverings, as well as fillers in flooring construction; reinforced ACC products are used as roof and floor slabs, wall panels that are loadbearing or non-loadbearing, as well as lintels [9]. In the US, a revived effort towards development of ACC technology for the US marketplace is pursued by North American Cellular Concrete (NACC) under hnding provided by Electric Power Research Institute (EPEU). A demonstration project involving a mobile plant and tour through several utilities' service areas and producing ACC blocks from each of the utilities' fly ash was successhlly completed in late 1994. All blocks were autoclaved at 190 "C (375°F) and 1.5 atmosphere for 10 to 12 hours. Among the many exploratory uses of the ACC blocks in the EPRI project, it is perhaps most noticeable for the construction of a 1400-square-foot house in Pittsburgh. ACC blocks made with fly ash were used throughout the structure, except for the roof trusses. A traditional wood-frame house with the same dimensions was also constructed for direct comparison. The ACC-block home cost 9 percent less than its woodframe counterpart [ 101. It is also projected a 17% energy savings for the ACC house because of the superior insulation of the ACC blocks.
2. Flowable Fill Large quantities of fly ash, Fixed with a small amount of portland cement and water, can be used as backfills or road bases including foundation and embankment [ 10,11,12]. These types of applications involve large volume but typically low unit price. Hydrothermal Process (Autoclave) Hydrothermal processing also is commonly known as autoclaving. A process involves moderately high temperature and water. Silicate materials including cement, sand, and clay are typically mixed with water to produce moldable mixture that can be used to make various products with simple geometry. During molding process, low mechanical pressure may be applied to produce a more compact green material with adequate green strengths for subsequent handling. The molded but non-hardened units are then cured at a controlled environment of 38 to 150 "C (100 to 300 OF) and saturated moisture at one-to-several atmosphere pressure for a period of time ranging from 6 to 12 hours. Comparing with regular air cured products, autoclaving has advantages of high strength and more stable dimensions. This technology is a well-known industrial process, especially in the masonry industry. '
372
Hwai-Chung W a n d Peijiang SUN
Hydrothermal Hot Pressing In a recent study on recycling pulverized concrete waste, Sat0 et a1 [13] attempted to use hydrothermal hot-pressing technique to solidify the waste. Hydrothermal hot-pressing is a solidification method for inorganic powder. This method involves mechanical compression and hydrothermal reaction simultaneously. This solidification process is similar to ordinary sintering reaction for ceramics, possessing dissolution, precipitation and the formation of new crystalline components in the presence of an appropriate amount of water [14]. It should be noted that the compositions of the concrete wastes in Sato’s study (1996) are similar to that of fly ash, especially Class F. Atter mixing with water, the pulverized concrete waste was discharged to a pressure fixture. The applied pressure was 20 MPa, the temperature was from 120 to 300 “C,and the residence time was between 10 to 40 minutes [13]. Tensile strength of the solidified concrete waste was determined to be (4 to 5) MPa that already exceeds the strength of ordinary concrete. Sat0 et a1 also discovered that by partial replacement of the concrete waste the maximum tensile strength could reach 13 MPa under the following conditions : 30-50 wt. % Mast hrnace slag, 20 wt.% water, and 15 minutes at 230 “C. In another case, the tensile strength also reached 12.6 MPa with the following conditions: 50 wt.% Portland cement, 30 wt.% water, and 20 minutes at 230 “C. These tensile strengths represent three to four times higher than ordinary concrete. To improve the toughness and ductility of the strong but brittle material, Sat0 et al added various short fibers to the mix. With only 1 volume-percent fiber, they found an 870 times increase in fracture toughness [ 131. EXPERIMENTAL PROGRAM In this project, we intend to develop high performance construction materials from fly ash [ 151. This process under development is based on hydrothermal (autoclaving) and mechanical pressing as discussed above. The term “high performance” is defined to have compressive strength higher than 30 MPa, flexural strength higher than 10 MPa, and ductility (with fiber reinforcement) more than 1.5 % strain while possessing equal or less unit weight compared to concrete. Some preliminary results and findings are reported in this paper. The starting material used in this experiment is a mixture of fly ash (both class C and F), water, short fiber and a small amount of sodium hydroxide serving as activator. The ratio of water to fly ash is 1:3. The amounts of sodium hydroxide vary from 0 to 10Y0of fly ash by weight. Atter mixing for 5 minutes, the mixture is filled in the cylinder chamber of the mold. The mold will be mounted on a universal testing machine and will be compressed to designated pressures. The MTS machine slowly pushed the piston, permitting a pressure built-up to 20 MPa in about 20 minutes. During this period, the entire mold is heated to specified temperatures in a split tube fbmace (AVS Series 3210) that also is mounted on the MTS machine. The mold is heated to various temperatures for a range of time periods from 0.5 to 5.5 hours, during which time hydrothermal reaction develops and solidifies the samples. More details about the mold design can be found elsewhere [ 151. Preliminary Results After completely cooled, the sample is demolded. Figure 1 shows a typical sample, 1 inch diameter and 5 inch long. All the samples have very smooth surfaces. Subsequently tensile strengths of the samples are determined from splitting tensile tests. Figure 2 shows the splitting tensile test setup on the MTS test machine. The ages of all samples were two days‘ old at the time of testing.
klvunced coristruction materialsfroin,fly us11
373
Figure 1: Typical fly ash sample.
Figure 2: Splitting tensile test setup on MI'S test machine
It has been identified that key factors in the process under development are: hydrothermal temperature and content of sodium hydroxide [ 151. In the following discussions, attention will be given to the effect of fibers. Process and other effects can be found elsewhere [ 15,161. Fiber Effect To improve brittleness of such fly ash products, a small amount of short fibers is added to the mix. Fiber reinforcement has been well recognized to be very effective in improving ductility and toughness of brittle cement and concrete [ 17,181. Two types of fiber are employed in this project to improve the properties of the fly ash products: PVA fiber (from Kuraray Co., Japan) and Kevlar-29 fiber (from Dupont), which properties are listed in Table 1.
374
Hwai-Chung WU and Peijiang SUN
Table 1 : Fiber Properties Fiber
~i~~~~~~
Length
(pm)
(mm)
specific
Modulus of
Tensile Strength
Elongation at
Elasticity (GPa)
(GPa)
Brfakage (“h)
PVA
37
15.0
1.30
40
Kevlar-29
14.8
35.0
1.44
70.5
.
..-* -
.. 2.92
3.6
#
When short fiber is used to reinforce fly ash matrix, several properties, especially the ductility of the composites are enhanced significantly. The effects of fiber reinforcement on Class C fly ash samples are shown in Fig.3. The concentration of the NaOH solution is 10M and the liquid to solid ratio (US) ratio is 0.62 for all samples. The pressure on each sample is 20MPa. For one set of samples, set-A, 130°C of processing temperature and 5.5 hours of heating time are employed. For the other set, set-B, the parameters are 15OoC and 2.5 hours. The age of the samples is 2 days. The fiber used here is PVA fiber, and its volume ratio is 1.0%. Fig.3 shows the changes in strength and ductility when the fiber is added. For set-A, when no fiber is used, the sample is brittle, and the first crack strength, also the ultimate strength, is 5.44MPa. With the addition of 1.0% PVA fiber, the sample shows excellent ductility, and the ultimate strength (the highest load registered) is 7.68MPa, almost a 50% increase from 5.44MPa. Its first crack strength is 5.03MPa, a little less than that without fiber, and the reason for this phenomenon might be due to poorer workability of the mortar with fiber. For set-B, the first crack strengths are 5.16MPa with 1.0% PVA fiber and 5.03MPA without fiber, but both the ultimate strength and the ductility are significantly increased when fiber is employed. Fig.4a and 4b are direct comparison of the failure modes between two samples after the splitting tensile tests, one of which has no fiber and the other has 1.O% PVA fiber. It can be seen clearly the brittle failure of the sample without fiber and the ductile failure of the sample with fiber.
0
Displacement (mm) Figure 3: Fiber Effect on the Ductility of Class C2 Fly Ash Samples (Pressure: 20MPa, NaOH: IOM, US=0.62, Age: 2Day).
Advatreed ccmstruction litaterialsfrom j l y ash
375
Typical values of density and modulus for Class C samples produced with NaOH activation and fiber reinforcement are 2.0-2.2g/cm3 and 18-20GPa, respectively, almost the same as those without fiber.
Figure 4a: Different failure modes of Class C samples during testing [without fiber (lef?) and with 1.O% PVA fiber (right)]
Figure 4b: Class C samples after lest showing brittle failure (without fiber, left) and ductile failure (with 1.O% PVA fiber, right)
Fiber Content Effect When fiber is used, the properties of the Class C fly ash samples are largely improved. In order to further understand the effect of fiber, the parameter of fiber content is investigated, and the results are illustrated in Fig.5 and Fig.6. Four Class C fly ash samples are prepared with different fiber volume ratios of O.O%, OS%, 1.0% and 1.5%. The fiber used is PVA fiber. The process conditions are 20MPa pressure on the samples, 15OoC of heating temperature, and 2.5 hours of heating duration. The concentration of the NaOH solution is 10M and the L/S ratio is 0.62 for all samples. The age of the samples is 2 days. The sample without fiber is brittle as expected, and its first crack strength, also its ultimate strength, is 5.03MPa (Fig. 5). For other samples with fiber content from 0.5% to 1.5%, they demonstrate extensive ductility and their failure modes are ductile (Fig.6). The first crack strengths vary between 5.2MPa and 5.4MPa, a little higher than 5.03MPa. It is evident that the ultimate strengths of the samples with fiber are much higher than 5.03MPa. When the fiber content is 1.O%, the ultimate strength reaches the highest value of 6.9MPa, and the ductility is the best among the samples under investigation. As fiber content increases
376
Hwai-Chung W a n d Peijiang SUN
to 1.5%, there is no further property improvement because of poor workability resulting in mixing difficulty. In other words, 1.O% is the optimum fiber volume ratio for Class C fly ash. 7.0
-2
6.0
I, 5
Be! m --
5.0
c
c"
.z 3
u)
.........
.._ .....
4.0
+First
Crack Strength
+Ultimate
Strength
3.0 0.0
OS
1.5
PVA Fiber Content (%)
Figure 5: Effect of fiber content on strength of Class C fly ash samples (Pressure: 20MPa. Temperature: 15OoC, Heating Time: 2.5Hrs, NaOH: 10M, US=0.62, Age: 2Day)
I
0
0.5
0 0% PVA Fiber
0 5% PVA Fiber
1 0% PVA Fiber
1 5% PVA Fiber
1 1.5 Displacement (mm)
2
2.5
Figure 6: Splitting tensile strength vs displacement curves (Pressure: 20MPa, Temperature: 150°C, Heating Time: 2.5Hrs, NaOH: 10M, L/S=0.62, Age: 2Day) CONCLUSIONS The preliminary data confirm that the process under development in this project can solidify fly ash. The resulting fly ash samples are very strong in tension (ranging from 1.0 to 10.0 MPa) depending on specific processing conditions. However, they are very brittle. With
Advanced construction materialsfrom fly ash
377
addition of (0.5%-1.5%) fibers by volume, the fly ash samples can show significant increase in ductility and toughness.
REFERENCES 1. American Coal Ash Association, Technical Brief, TB-1 I , January 1998. 2. Tamcone, P., “Fly Ash for Hire”, Civil Engineering, October 1991, p.46-49. 3. American Coal Ash Association, Coal Combustion Product (CCP) Production and Use USA, Alexandria, Virginia, 1997. 4. American Coal Ash Association, Buy Recycled Coal Fly Ash, Alexandria, Virginia. 5. Malhotra, V.M., “Superplasticized Fly Ash Concrete for Structural Concrete Application”, Concrete International, V. 8, No. 12, 1986, p.28-3 I . 6. Berry, E., Hemmings, R., Zhang, M., Cornelius, B., and Golden, D., “Hydration in HighVolume Fly Ash Concrete Binders”, ACI materials Journal, V. 91, No.4, 1994, P. 382389. 7. Jiang, L., Lin, B., and Cai, Y., “Studies on Hydration in High-Volume Fly Ash Concrete Binders”, ACI materials Journal, V. 96, No.6, 1999, P. 703-706. 8. American Society of Civil Engineering, Civil Engineering, September 1998. 9. Golden, D.M., “Ash-Derived Autoclaved Cellular Concrete Building Materials Amve in North America”, in Proc. 1Ith Inter. Symp. On Use and Management of Coal Combustion By-products, Orlando FL, American Coal Ash Association, 1995, p.35-1-9. 10. Valenti, M., “Using Fly Ash for Construction”, Mechanical Engineering, May 1995, p. 82-86. 1 I . Jalali, S., “The Effect of Compactive Efforts on the Final Strength of Lime-Fly Ash mixtures”, in Proc. 1l‘h Inter. Syrnp. On Use and Management of Coal Combustion ByProducts, Orlando FL, American Coal Ash Association, 1995, p.68-1-13. 12. Hemmings, R.T., Berry E.E., and Golden, D.M., “Investigation of No-Cement Concretes Produced from AFBC By-products and PFA”, in Proc. I l l h Inter. Symp. On Use and Management of Coal Combustion By-products, Orlando FL, American Coal Ash Association, 1995, p.79-1-10. 13. Sato, K., Hashida, T., Takahashi, H. and Yamasaki, N., “Development of a Solidification Method for Pulverized Concrete Waste by Hydrothermal Hot-Pressing and Fiber Reinforcement”, in Proc. ASCE 4Ih Materials Engineering Conference, Ed. K. Chong, 1996, p.684-693. 14. Nakane, Y . , Sato, K., Takahashi, H., Yamasaki, N. and Hashida, T., “Development of Solidification Technique for Recycle of Concrete Waste By Hydrothermal Hot-Pressing and Its mechanical Property”, J. Cer. SOC.Of Japan, Vol. 102, No.4, 1994, p.405-407. 15. Wu, H.C., and Sun, P., “High Performance Ductile Fly Ash Composites,” in CD Proc. 151hInter. American Coal Ash Association Symp. On Management & Use of Coal Combustion Products, St. Petersburg, FL, 2003. 16. Wu, H.C., and Sun, P., “High Performance Masonry Products from 100% Fly Ash”, Project Report, Department of Civil and Environmental Engineering, Wayne State University, Detroit, 2003. 17. Wu, H.C., and Li, V.C., “Trade-off Between Strength and Ductility of Random Discontinuous Fiber Reinforced Cementitious Composites”, Cement & Concrete Composites, 16, 1994, p23-29. 18. Li, V.C., Mishra, D.K., and Wu, H.C., “Matrix Design for Pseudo Strain-Hardening Fiber Reinforced Cementitious Composites”, RILEM J. of Materials arid Structures, 28, 1995, ~586-595.
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C.Li and I. H. Marshall, eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Woodhead Publ.. Warsaw 2003
IMPLICATIONS OF MATURITY AND ULTRASONIC WAVE SPEED MEASUREMENTS IN QC/QA FOR CONCRETE Cole GRAVEEN', Jason WEISS', Jan OLEK' and Tommy NANTUNG" 'Purdue University, School of Civil Engineering .* Indiana Department of Transportation, Research Division West Lafayette, IN, United States, email:
[email protected] ABSTRACT Recently, maturity testing has become more widely used to describe the rate of concrete strength development. Maturity predictions can be used to indicate when loading can be applied to a concrete pavement or structure. While the implementation of the maturity method has numerous potential benefits, it is important that potential limitations are recognized as well. Test methods are needed to signal when the predictions made using the maturity approach are not conservative. This paper will focus on three main aspects of quality controVquality assurance (QC/QA) testing using the maturity method. First, it will illustrate that mixture proportion variations can influence the maturity predictions. Second, this paper will illustrate that the use of an ultrasonic wave velocity screening technique can indicate when the maturity-strength relationship may over-predict the strength in a structure. Finally, this paper will demonstrate that supplementing maturity predictions with the use of early-age mechanical property measurements can improve the estimate of long-term performance while providing rapid information on the acceptability of the concrete. Keywords Early-age, maturity, non-destructive testing, quality control, ultrasonics, variability
INTRODUCTION During the construction of concrete pavements and structures it is common to find that a minimum level of strength is required before specific construction operations can be performed. For example, this frequently includes the removal of formwork and shoring [ 11 or the opening of a concrete pavement to construction traffic [2]. Typically, agencies determine the acceptability of concrete by testing companion specimens cast from concrete that is sampled during construction of the concrete structure or pavement. Testing can be costly however, and the strength of these companion specimens may not necessarily represent the actual strength of the in place concrete. In addition to differences in placement and compaction procedures, the curing conditions used for the companion specimens may differ from the curing conditions of the actual structure. Although the strength-maturity relationship should be independent of curing temperature, significant differences have been
380
Cole GRA VEEN, W.Jason WEISS, Jan OLEK and Tornmy NANTUNG
reported in specimens exposed to a high temperature at early ages [3]. Companion specimens may not represent changes that occur in the microstructure due to high temperature curing at early ages which may result in an over-prediction of the mechanical properties (including strength) of the in place concrete The maturity method has been proposed as one approach to estimate the in situ strength of a concrete structure [4]. In general, the maturity method is based on the concept that strength development in concrete is uniquely related to the product of the time and temperature (i.e., a maturity index). This maturity index can be measured in a concrete structure or pavement and used with a previously established strength-maturity relationship (determined from laboratory experiments) to estimate in situ strength of the concrete. It should be noted however that the use of the maturity method involves several assumptions. For example, the maturity method assumes that the concrete in the specimens and the concrete in the structure have been properly placed, compacted, and cured. If proper placement and compaction procedures are not followed, defects such as honeycombing, segregation, or excessive bleeding can occur. These defects cannot be detected by the maturity method and will result in an erroneous estimate of in-place strength. In addition, the maturity method cannot detect if the supply of moisture for hydration is not provided (i.e., improper curing). When this happens, the concrete will not continue to gain strength, however the maturity method will continue to indicate an increase in strength with time. Third, the ultimate strength of the concrete has been reported to be sensitive to the temperature of the concrete during curing. If sufficiently high or low temperatures are experienced (especially at early ages) the maturity approach may need to be adjusted [5]. Finally, the maturity method inherently assumes that the concrete for which the in-situ strength is being estimated was made using a concrete with identical constituent materials and mixture proportions as the concrete that was used in the creation of the strength-maturity relationship. If the material properties of the constituent materials change, or the concrete mixture proportions vary, an error can be introduced into the estimate of strength. It should be noted that in practice variations in the mixture proportions typically occur in large-scale concrete construction projects. For example, the variation in water-to-cement ratio (w/c, as calculated based on batch 16 weights after accounting for aggregate moisture and trim water) is presented in Figure 1 for sixty-four sublots (each sublot covers an area of approximately 2000m’) of a 350 mm thick concrete pavement. This concrete had a target w/c of 0.42 and was produced using a mobile batch plant. As the water-to-cement ratio (w/c) is potentially the most influential mixture design parameter with respect to the strength-maturity relationship, it is critical that the implications of the 0.38 0.4 0.42 0.44 0.46 variation in the w/c on the maturityWater-To-Cement Ratio strength relationship are known. In the case presented in Figure 1 the w/c was observed to vary from slightly above 0.45 Figure 1: Variation in the Water-Toto slightly below 0.40. While the extent Cement Ratio (wlc) for an Actual of variation that can be expected on any Concrete Pavement
bnplications of maturity and ultrasonic wave speed measurements in QC/QAfor concrete
38 1
given project will differ depending on the contractor and quality control procedures implemented, some variation will allows be present. The information presented in Figure 1 was used to develop the bounds of experimental program that is discussed in this paper.
RESEARCH SIGNIFICANCE This paper presents results from a recent study in which the flexural strength of concrete was estimated using the maturity method. It will be shown that slight variations in the mixture proportions, consistent with those that may be observed during a construction project, may cause variations in the maturity predictions that may be either conservative or unconservative. An approach is presented in which the use of ultrasonic testing may signal when the predicted strength from maturity may be non-conservative. In addition, an approach is presented which uses early mechanical testing in conjunction with the maturity method to improve the maturity-strength predictions.
MIXTURE PROPORTIONS, CASTING, AND TEST PROCEDURES Testing was conducted to assess how variations in the water-to-cement ratio (w/c) influence the strength prediction made using the maturity-strength approach. This was performed to illustrate how slight variations in the mixture proportions, consistent with those that commonly occur in concrete construction, may translate into changes in the flexural strengthmaturity response. The mixture proportions used in this study are provided in Table 1. This baseline mixture is similar to the typical mixture proportions used in a concrete pavement, however it should be noted that the cement content was increased by approximately 11.8 kg/m' to facilitate laboratory mixing and placement procedures. Slight changes in water-tofrom the baseline mixture (Table 1, w/c = 0.42) to simulate construction variability. While the w/c
was the Of aggregate was maintained the same as the baseline
Material Cement Water
Type Type 1 I
Fine Aggregate Coarse Aggregate Air Water Reducer
#23 Sand
#8 Stone*' Daravair 1400 WRDA 82
Mixture Proportions* 320 134 868 972 145 2.44
kglrn3 kg/m3 kglm3 kglrn3 rnl/rn3 rnllkg
The test specimens that were prepared for this research consisted of 152 x 152 x 535 mm beam specimens. The beams were cast in steel molds in accordance with ASTM C 192. The concrete was mixed in the laboratory using a pan mixer and internal vibration was used to consolidate all of the beams. Two thermocouples were placed in one beam from each batch of concrete to record the temperature history. The temperature at each thermocouple was measured every minute and the average temperature over a ten-minute interval was recorded using a Campbell Scientific, Inc. CRlOX Measurement and Control System. After finishing, the beams were covered with wet burlap and a layer of plastic. The specimens were removed from the molds approximately twenty-four hours after casting and placed in a temperature
382
Cole GRA VEEN, W.Jason WEISS, Jan OLEK and Tommy NANTUNG
controlled moist curing room (23OC +/- l0C, 95% €34) where they were kept until the time of testing. It should be noted that one series of beams with a w/c of 0.42 was exposed to high temperature during the curing process as described later in the paper. A series of tests were conducted on the beam specimens that included: the measurement of temperature history using the aforementioned thermocouples, measurement of the P-wave velocity using a pulse velocity te'st apparatus in the direct transmission mode along the length of the beam, and measurement of flexural strength testing using third-point loading in general accordance with ASTM C 78. The flexural strength and P-wave velocity were determined for the design mixture (w/c = 0.42) at ages of 1, 1.5, 3, 7, 14, and 28 days, while the flexural strength and P-wave velocity for the mixtures with the other w/c were determined at 7 and 28 days only.
EXPERIMENTAL RESULTS The Maturity-Strength Relationship for the Baseline (w/c = 0.42) Mixture The temperature-time factor (used as the maturity index (M) in this paper) was calculated using equation 1.
In equation 1 At is the time interval (ten minutes), T, is the measured average temperature in the concrete during the time interval, and To is the datum temperature which was assumed to be -10 "C based on standard Indiana Department of Transportation assumptions [2]. Once the maturity index (M) was known, a strength-maturity relationship could be created for the baseline mixture as shown in Figure 2. The points represent the average of two strength measurements and the line represents the offset hyperbolic strength-maturity relationship as described by Equation 2:
where f loo is the ultimate flexural strength (i.e., the strength as the time tends toward co), k T is the rate constant, and M, is the offset maturity (i.e., maturity at set). The three parameters (f rm, kT, and M,) were determined for the strength-maturity relationship using the procedure suggested by Knudsen [6] which has also been described by Carino [4]. The value of the ultimate flexural strength was determined using the tests at 7, 14, and 28 days while the offset maturity and rate constant were determined using early-age tests (i.e., 1, 1 %, and 3 days). The parameters computed for the baseline mixture (w/c = 0.42) were f,, = 5.76 MPa, k T = 0.004169 I/"C-hr, and M, = 498 'C-hr. It can be noticed that the hyperbolic strength function represents the data well, provided sufficient data is collected at the early ages to enable k T and Mo to be determined accurately [8].
Implications of maturity and ultrasonic wave speed measurements in QC/QA for concrete
383
Once the strength-maturity relationship was ' ' ' ' ' ' developed for a given concrete (Equation 2 and 6 ' ' ""I ;ii Figure 2), this relationship can be used to estimate the strength in a structure or pavement f,s, = 5.76 MPa made using this concrete. To do this, the user would simply record the temperature that g develops in the structure or pavement, compute 2 a maturity index using this measured 2temperature, and use the relationship shown in Figure 2 to estimate the strength in the structure 3 ,M~ = 498 "C-hr for the given maturity index. As previously $ ' mentioned, this assumes that the concrete that was placed in the structure has the same 1000 10000 constituent materials and mixture proportions as Maturity, M (i.e., the TimeTemperature Factor OC-hr) those used in the development of Figure 2. To illustrate the importance of variations in the Figure 2: Maturity-Flexural mixture proportions on the predictions made Strength Relationship using the approach described above, a series of tests were performed where the w/c was varied over a range that is consistent with variation that may be expected in the field (i.e., Figure 1). The results of this investigation are described in the following section. 1 ' 1 1 1
Influence of Variation in WIC and Temperature During Curing on Predicted Strength Flexural strength was measured for the mixtures in which the w/c was varied (i.e., 0.40, 0.41, 0.43, 0.44, 0.47) at 7 and 28 days. In addition, the maturity index (time-temperature function) was computed based on the average of two thermocouples from one beam in each batch. Variations in the w/c resulted in variations in the measured flexural strength as expected, with the measured flexural strength decreasing with increasing w/c (Table 2). A lone exception occurred for the measured strength at 28 days for the specimen with a wlc equal to 0.44. It should be noted that multiple batches were required to cast the specimens For each mixture due to the size of the mixer, therefore slight variations between each mixture may have occurred and this is expected to be responsible for this lone discrepancy. It should be noted that even small changes in the w/c (0.0 1 to 0.02) can introduce error in the estimate of flexural strength. Figure 3 shows the ratio of the strength that would be predicted for each of the mixtures made using the hyperbolic strength relationship and the actual strength measured in the beams with the slight differences in the w/c. It should be noted that the strength-maturity relationship generally underestimates strength for mixtures with a w/c lower than the design ratio, which is conservative, and overestimates strength for mixtures with a w/c greater than the design, which is non-conservative. To prevent overestimating the strength of concrete (this may result in acceptance of an inferior or low strength structure or pavement) an additional screening method may be desirable.
3 84
Cole GRA VEEN, W.Jason WEISS, Jan OLEK and Tommy NANTUNG
Table 2: Results from the P-Wave Measurements in the Beam Exposed to High Temperatures at Early Ages and the Beams Made with Various WIC's Predicted Water-toFlexural Strength Actual Measured Measured PCement Flexural Strength Wave Velocity Age (Days) Using Maturity Ratlo~(wIc) (mrs) (MPa) (MP4
Strength Predicted I Prediction Actual Flexural Considered Valid Strength After Ultrasonic Wave Testing
'High Tenperature Specimen
It should be noted that even small changes in the w/c (0.01 to 0.02) can introduce error in the estimate of strength. Figure 3 shows the ratio of the strength that would be predicted for each of' the mixtures made using the hyperbolic strength maturity relationship and the actual strength measured in the beams with the slight differences in the w/c. It should be noted that the strength-maturity relationship generally underestimates strength for mixtures with a w/c lower than the design ratio, which is conservative, and overestimates strength for mixtures with a w/c greater than the design, which is non-conservative. To prevent overestimating the strength of concrete (this may result in acceptance of an inferior or low strength pavement) an additional screening method may be desirable. Although the standard beam stored at temperature (23OC) exhibited a temperature rise that was less than 4OC above ambient temperature during hydration, thermocouples in the core of a concrete pavements show that these pavements can easily reach 43-45OC even under mild ambient temperatures (23-25'C). I.2 Testing was also conducted to assess how high temperature conditions during curing can influence the .Conservative strength estimated using the maturity Predictions method. To illustrate this effect, three additional beams were cast with the mixture proportions used in Conservative the baseline mixture (w/c = 0.42), Predictions 0.9 with one beam stored at regular temperature (w/c = 0.42, 23°C) and , , D;ig,nW,ater;-l two of' the beams were cured at Cement Ratio = 0.42 0.8 elevated temperature (w/c = 0.42, 0.40 0.42 0.44 0.46 0.40 temperature history described Water-To-Cement Ratio below). The high temperature beams were placed in an insulated box with Figure 3: Ratio of Strength Predicted heaters that were used create the Using the Hyperbolic Strength elevated temperatures which Function (wlc = 0.42) and the simulated temperatures similar to Measured Strength (Various wlc) what may be expected to occur in
--t a
1
,
385
.Implications of maturity and ultrasonic wave speed measurements in QUQAfor concrete
thick concrete pavements on a hot summer day. The temperature of the beams was maintained at 23°C for approximately 2 hours before the temperature of the box was increased causing the temperature in the beam to rise (nearly linearly to a temperature of 55°C at an age of 10 hours). The beam was held at this temperature until an age of 17 hours when the temperature was reduced to ambient temperature. The strength predicted for the regular temperature beam at a maturity index of 1050 "C-hrwas 31% higher than the strength measured in the beams stored at higher temperature. This indicates that high temperature curing can introduce a significant error in the estimate of strength. Combining the Use of Ultrasonic Wave Speed Measurements and Maturity An alternative to using only maturity by itself to predict the strength of the in-place concrete is to combine maturity by with other methods of non-destructive testing. The following section describes how maturity and P-wave velocity techniques can be used jointly to indicate when maturity measurements may not be conservative. The advantage of using the maturity and P-wave velocity methods in parallel lies in the differences between the test methods [8]. The strength estimated from the maturity method is a function of time and temperature. As such the maturity index can be thought of as being related to the chemical reactions during hydration. Alternatively, the strength estimated from the P-wave velocity is a function of the structure of the material, including the density, air voids, and the aggregate contribution. Therefore, combination of these approaches may provide complimentary information. Figure 4 illustrates the strength-P-wave velocity relationship for the design mixture. It can be seen that a bi-linear relationship exists where the behavior at early-ages (1, 1.5, and 3 days) shows a greater slope than the data at later ages (7, 14, 28 days). At early ages the P-wave velocity is more sensitive to strength changes which can be attributed to the fact that at earlyages the flexural strength is dependent almost solely on the properties of the matrix since cracking occurs around the aggregate. The relationship between the P-wave velocity and the flexural strength changes as fracture paths in the beams is observed to change from a crack that primarily occurs through the mortar to a crack that propagates through the aggregate. This has recently been confirmed in subsequent testing by Barde et al. [7]. As previously described, the use of maturity-strength relationship as determined from time-temperature predictions with information from ultrasonic pulse velocity-strength relationship may provide complimentary information. For example, if the strength estimate from the strength-P-wave velocity relationship is equal to or in excess of the estimate of strength from the strength-maturity relationship, the estimate of strength from the maturity test method could be considered as conservative. However, if the estimate of strength using ultrasonic wave speed was lower than the estimate from the maturity test method, additional action may be required, such as conventional strength
x
Q U
Design Water-toCement Ratio = 0.42 4200
4400
4600
4800
P-Wave Speed (mls) Figure 4: Variation in P-Wave Speed as a Function of Strength
386
Cole GRA VEEN, W.Jason WEISS, Jan OLEK and Tommy NANTUNG
testing. Table 2 provides results from the ultrasonic measurements in the mixtures with the variable w/c and the specimen that was cured at a higher temperature. It is interesting to note that when using the maturity method alone, the predicted strength was greater than the actual strength in 5 of the 9 cases. However, when both methods (P-wave velocity and maturity) are used in combination each of the five non-conservative cases would have been identified. Of the four cases where the predicted strength using the maturity method alone was less than the actual strength, only one of the cases (w/c = 0.44 at 28 days) was indicated to not be valid using the combined methods (It should be noted that in this case the predicted and actual strength were very similar to one another). While this approach is not ready to move into practice immediately and some bands may be necessary to allow for typical variability in each test, it should also be noted that the cost associated with developing the P-wave velocity vs. strength relationship may be trivial as ultrasonic wave speed can be determined at the same time the maturity strength relationship is obtained. The approach described in this paper may also be amenable to in-situ stress wave measurements using sensors placed inside the concrete during construction. Although the ultrasonic wave speed was discussed in this paper as measured using the P-wave speed from direct transmission it is easily foreseeable that the information on wave speed could be obtained using one-sided velocity, impact echo, pulse echo, or one-sided wave reflection approaches. This could enable these measurements to be made in-situ, potentially leading to a reduction in the reliance of separate testing of companion samples thereby facilitating a move to more in-situ based testing.
Using an Early-Age Test Result In Combination Maturity Prediction Another possible way to consider the influence of material variations with the maturity method is to use an early-age third-point flexural test in combination with maturity to estimate a long-term strength. Using an early-age test could provide the contractor with rapid feedback thereby facilitating changes in the construction operation during the construction process to allow the specified strengths (or other properties) to be achieved. One option would be to use the early-age test result (for example a measurement of flexural strength at 1 or 3 days) to verify that the pavement flexural strength is acceptable at an earlyage and then to use this early-age strength value in conjunction with a maturity prediction to estimate the later-age strength (28 days for example) for use in life-cycle predictions or pay determination. An equation of the following type could than be used to estimate the 28 day strength using some predetermined maturity index (M28);
where, Meartyage is the maturity measured at an early age (1 or 3 days for example), and Mzg is the maturity at 28 days. For illustrative purposes the results of this method are presented in Table 3 using the earlyage measured strength at 7 days, the measured maturity at 7 days, and the measured maturity
387
Implications of maturity and ultrasonic wave speed measurements in QC/QAfor concrete
at 28 days to predict the 28-day strength in mixtures with two different w/c’s. It can be seen that when equation 3 is used, the predicted strength is closer to the actual measured strength than the prediction made using maturity alone (i.e., equation 2). Table 3: Using Early Flexural Strength with Maturity to Predict Long-Term Strength When Variations in Mixture Proportions Exist
wlc
0.41 0.43
Predicted Actual Actual Strength At 28 Strength Strength Days Using At 7 Days At 28 Days Maturity Alone (Eqn 2) MPa 5.81 5.21
MPa 6.16 5.34
Percent Percent S t ~ ~ ~ Difference ~ ~ ~ Z Difference 8 Days Using Eqn Between Equation Between Equation 2 and the Actual 3 and the Actual 3 28 Day Strength 28 Day Strength
MPa 5.70 5.70
% 81 6.2
MPa 6.02 5.41
% 2.3 1.2
It should be noted that for curing of QCIQA beams at a constant temperature, equation 3 can be rewritten as equation 4 f’, (28duys)= f ’ , (early uge).C
where C is a strength gain coefficient (as illustrated in Figure 5) which depends on the rate of strength gain coefficient (KT), the offset maturity (Mo) (although to a lesser extent), and the age at which the specimen is tested. Equation 3 was simplified to obtain equation 4 through two assumptions: 1) it is assumed that the Mo value is similar for a series of mixtures and 2) the maturity at any given testing time and the maturity at 28 days can be approximated as the product of the time and temperature. It should be noted that if very early ages of testing are desired, specific attention should be paid to the value of Mo that is used in the development of the strength gain coefficient [8].
-
0,
(4) 2.50
U
.-0
2.25
I -3
Days
2.00 0
4-
.-m
1.75
(3
1.50
KT = 0.004169
5 1.25
2
cii
1.00
.? 0 0 0
0
0 .?
0 0
0
0
0
r
0 0
0 0 0
0
0 0
.?
0
0
.?
Rate Constant, K, (l/(C-hr)) Figure 5: Strength Gain Coefficient as Determined From Maturity Concepts
SUMMARY AND CONCLUSIONS This paper has reiterated the fact that although the use of maturity shows great potential application for assessing strength gain in concrete structures and pavements, ‘it is not prudent to rely solely on measurements of in-place maturity to verify the attainment of a required level of strength” [ 11. This paper also indicates that although the same materials and mixture proportions may be specified, day to day variations in batching may result in fluctuations in the water-to-cement ratio for a given concrete mixture. Although these variations are expected, they can result in errors in the maturity based estimation of strength of +/- 10% for
388
Cole GRA VEEN, K Jason WEISS, Jan OLEK and Tommy NANTUNG
variation of +/- 0.02 in the w/c for the mixtures investigated in this work. High temperature curing was also observed to result in non-conservative strength predictions. This paper suggests that the combination of maturity and ultrasonic wave speed may provide additional information to indicate cases where the maturity predictions may not be conservative. For example, combination of maturity and ultrasonic pulse velocity was able to identify all the mixtures where strength was over-predicted by the maturity method in cases with both high water-to-cement ratio and high temperatures during early age curing. In addition, the combination of early-age strength testing with maturity may make it possible to reasonably predict strength at any age while providing the contractor with feed-back very early in the construction process which ultimately could result in concrete with improved performance. ACKNOWLEDGEMENTS The authors gratefully acknowledge support received from the Indiana Department of Transportation through the Joint Transportation Research Program Project Number 6561284-0 1 15, “Performance Related Specifications for Concrete Pavements In Indiana” which is administered under the direction Dr. Tommy Nantung. The views expressed in this paper are those of the authors, and as such are not intended to represent the official views and policies of the sponsors nor do they reflect a standard, specification, or regulation. The second author also wishes to thank the National Science Foundation for support received through NSF Grant No. 0034272, a Career Grant. The authors also wish to thank J. Johnson for assistance with beams used in the high temperature testing. REFERENCES
1. 2. 3.
4. 5.
6. 7. 8.
Naik, T.R., “Concrete Strength Prediction by the Maturity Method”, ASCE Journal of Engineering Mechanics, Vol. 106, No. EM3, 1980. Indiana Department of Transportation, Standard Specijkations, 1999. Chanvillard, G. and D’Aloia, L., “Concrete Strength Estimation at Early Ages: Modification of the Method of Equivalent Age”, ACI Materials Journal, Vol. 94, No. 6, pp. 520-530, 1997. Carino, N. J., “The Maturity Method”, CRC Handbook on Nondestructive Testing of Concrete, Malhotra, V.M. and Carino, N. J., Ed., CRC Press, Florida, 1991, 101-1 46. Carasquillo, R., and Myers, J. J., “HPC Bridge Newsletter,” Knudsen, T., and Geiker, M., ‘Chemical shrinkage as an indicator of the stage of hardening,” International Conference on Concrete at Early-Ages, Vol. 2, RILEM, Paris, 1982, pp. 163-166 Barde, A., Mazzotta, G., and Weiss, W. J., “The Influence of Aggregate Behavior on Flexural Strength Development, Cracking and Maturity Predictions”, Under Development Weiss, W. J., “Experimental Determination of the ‘Time-Zero’, to,”, Early-age Cracking in Cementitious Systems, RILEM Report 25, ed. A., Bentur, 0 2003 pp. 195-206.
Pvoc. Int. Sytnp, ,,Brittle hIafri.x Composites 7” A.M. Brana‘t, V.C. Li and I. H. Marshall. eds. Warsaw, October 13-15, 2003 ZTUREK RSI and Wooa’head Publ.. Warsaw 2003
PLENARY INVITED PAPER
ON THE DETERMINATION OF ELASTIC MODULI WITH BRITTLE MATRIX COMPOSITES Dieter LOIDL, Stephan PUCHEGGER, Herwig PETERLIK, Karl KROMP Institute of Materials Physics; University of Vienna Boltzmanngasse 5; A - 1090 Vienna, Austria e-mail: karl.
[email protected] ABSTRACT Composite materials behave in general elastically anisotropic. For the purpose of designing constructive parts under load by finite element calculations, the elastic moduli in dependence on orientation and on temperature have to be known. A short survey on practicable procedures for the determination of the elastic moduli, their applicability to composites and their extension to measurements at high temperatures are given. A new procedure, based on the Resonant Beam Technique, and its application to anisotropic composites at high temperatures is presented together with results gained from a 2,5D carbon fibre-reinforced carbon composite up to 1800 “C. Finally an outlook on a new procedure, a combination of Resonant Ultrasound Spectroscspy and Resonant Beam Technique is given. Keywords Elastic moduli, carbon fibre-reinforced carbon composite, anisotropy, high temperature
INTRODUCTION In the course of the rapid progress in e.g. aerospace and communication technologies during the last decade specific high performance materials for special applications were developed. The materials, intermetallics, high performance ceramics and ceramic composites are predominantly anisotropic. For the purpose of designing constructive parts under load by finite element calculations, the dependence of the elastic constants (the coefficients of the elastic stiffness or compliance tensor) on orientation and on temperature have to be known (the engineering “elastic moduli” can be calculated directly from these elastic constants). The knowledge of the elastic constants is also important for the investigation of thermophysical properties, in particular for phase transitions of high performance materials. Thus, there is a strong interest in practicable experimental procedures for the determination of the elastic constants in dependence on orientation and on temperature.
390
Dieter LOIDL, Stephan PUCHEGGER, Henvig PETERLIK and Karl KROMP
ELASTIC PROPERTIES OF COMPOSITES In general composite materials are elastically anisotropic. Following theory of elasticity the elastic properties of composites are characterised by the stiffness tensor C or the compliance tensor S, with its coefficients (the elastic constants) Ci, and Si, , respectively. The composites generally applied for constructional purposes have independent elastic constants as listed below, from low symmetries up to highest symmetry: orthothropic (orthorhombic): 9 elastic constants, a;tb#c, a=P=y=9O0, e.g. 2,5D composite quadratic (tetragonal): 6 elastic constants, a=b#c, a=P=y=9O0, e.g. 2D composite hexagonal (transversely isotropic): 5 elastic constants, a=b*c (a=b, isotropic), e.g. UD composite (4 components for single ply quadratic) isotropic: 2 elastic constants, e.g. chopped fibre composite When anisotropy, a specific feature of composite materials, has to be taken into account, the elastic behaviour can only be h l l y characterised by the elasticity tensor with a certain number of independent coeficients (the elastic constants). This number depends on the crystallographic symmetry of the composite as shown above. Certain methods allow the determination of the elastic constants, while other the determination of the elastic engineering moduli (Young's moduli, shear moduli and Poisson's ratios, Eii , Gij , vij). From the coefficients of the elastic compliance tensor, Sij, the elastic moduli can be calculated and vice verse.
OVERVIEW OF MEASUREMENT PROCEDURES In general two main groups of procedures for the determination of elastic properties may be distinguished: quasi-static (isothermal) procedures e.g. tension (compression and torsion) tests and bending tests (3- or 4-point) dynamic (adiabatic) procedures e.g. direct measurement of sound velocities and measurement of resonant frequencies The results from isothermal and adiabatic procedures in general differ by far less than I%, depending on temperature, extension coefficient and specific heat at the given temperature and thus this difference generally is neglected. Contrary to quasi-static procedures (mechanical test methods), the determination of elastic properties by dynamic procedures (sound velocities and resonant frequencies) is not based on the evaluation of the stress-strain response over a given deformation range obtained under quasi-static loading conditions, but is based on non-destructive dynamic measurements at very small amplitudes. The values of Young's moduli, shear moduli and Poisson's ratios determined by the two kinds of procedures may not be comparable because of these reasons, particularly for ceramic matrix composites which exhibit ?on linear stress-strain behaviour. Therfore only results from dynamic procedures and values of the initial tangent moduli in the limit of zero strain from quasi-static procedures can be compared.
On the delamination of elastic constunls wifli ht-ittle matri,v composites
39 1
SPECIFIC MEASUREMENT PROCEDURES
In the following the advantages and disadavantages of specific methods of the two main groups of procedures, will be characterised shortly. Existing standards for the measurement of composites will be mentioned. The quasi-static (isothermal) procedures: The methods applied are based on the determination of stress-strain response with tension (compression and torsion) tests and bending tests (3- or 4-point). Observations for composites show that the strains, at which the measurements were performed, have considerable influence on the results. As mentioned above, a comparison to results from dynamic procedures is only in the limit of zero strain straightforward. For ceramic matrix composites the quasi-static loading methods are standardised in EN 658-1, ENV 658-2, ENV 1892, ENV 1893, ENV 12290 and ENV 12291 with EN: Euronorme, ENV: Euronorme Volontaire. The dynamic (arlinbntic)procedures: The most representative method for procedures using the determination ofsound velocities is the “Ultrasound Wave Spectroscopy” [ 1,2], standardised for ceramic matrix composites in ENV 14186. This method is based on the measurement of the time delay between ultrasonic wave pulses through materials with low attenuation (ceramics, hard metals, intermetallics, ceramic composites). The determination of the elastic constants is carried out by calculating the coefficients of the propagation equation of an elastic plane wave from a set of properly chosen velocity measurements along known directions: A thin specimen of known crystallographic orientation with planparallel faces is immersed in an acoustically coupling fluid (e.g. water or oil). The specimen is placed between an emitter and a receiver which are rigidly connected to each other and have two rotational degrees of freedom, Using appropriate signal processing, the propagation velocities of each wave in the specimen are calculated. Depending on the angle of incidence, the pulse sent by the emitter is refracted within the material in one, two or three bulk waves (one longitudinal wave, one transverse wave or two transverse waves), which propagate in the solid at different velocities and in different directions. The receiver collects one, two or three temporally delayed pulses, corresponding to each of these waves. The difference in propagation time of each of the waves and the propagation time of the emitted pulse in the coupling fluid without the specimen is measured. The great advantage of this method is that the complete elastic tensor for composites down to orthothropic symmetry can be determined. The disadvantage is that the method is restricted to room temperature or modest temperatures corresponding to the coupling h i d (oil). A frequently applied method is the “Ultrasound Pulse Propagation” (Pulse-Echo Method), standardised for monolithic ceramics in ENV 843-2 at room temperature, which can be adopted to composites too. The principle is similar to the ultrasound wave spectroscopy mentioned above. Two transducers (emitter and receiver) are acoustically coupled to the planparallel surfaces of the specimen. For longitudinal waves the ultrasound pulse is applied perpendicularly to the surface, for transverse waves parallel to the surface. The elastic constants or the elastic moduli can then be calculated from the differences of the propagation times (sound velocities) if the specimen is oriented. For the time being the method is restricted to room temperature or to moderate temperatures, because the transducers have to be coupled directly to the specimen. Another method based on the measurement of sound velocities is the “Ultrasound Phase Spectroscopy” [3]. T w o transducers of the same kind are attached to opposite sides of a specimen with planparallel faces. One trailsducer is used to transmit a continuous, harmonic longitudinal elastic wave into the specimen, the other one is used to receive the transmitted
392
Dieter LOIDL, Stephan PUCHEGGER. Henvig PETERLIK and Karl KROMP
signal. The number of phase periods as well as the magnitude ratio between the input and the output signal are measured. The group velocity can be deduced from the slope of a plot of the number of phase periods against the frequency. From this group velocity the elastic constant Cii can be calculated. The method has the disadvantage that only one constant in direction of transmission can be measured. For the time being it is restricted to room temperature, because the attenuators have to be coupled directly to the specimen. The great advantage of this method is that it can be performed with highly attenuating materials, such as fibrous materials, plasma-sprayed materials with high porosity and in the thickness direction of laminates. Bodies of elastic materials have characteristic sets of natural resonant frequencies (“eigenmodes”), which are determined by the elastic constants, the crystallographic orientation, the density, the dissipation and the shape of the bodies. It is evident, to use these frequencies as a tool to determine the elastic constants (the elastic moduli). “Resonant Ultrasound Spectroscopy” (RUS) is the most general case of the methodology, where all elastic constants can be acquired from (small) rectangular parallelepiped-shaped specimens or other specific shaped specimens (discs, cylinders) [4-81. The method also was extended to higher temperatures [9]. An overview of the method and its development is given in [4]. With RUS, small rectangular parallelepiped-shaped specimens down to 2 x 2 ~ 2mm3, with the main symmetry axes oriented parallel or pkrpendicular to the sides of the specimens, can be investigated. In principle the full set of elastic constants can be determined from the measurement of one single specimen. The set of elastic constants is determined by minimising the difference between observed and calculated resonant frequencies, using a least squares method. In order to fit the calculated to the measured eigenfrequencies with the elastic constants (elastic moduli), some prior knowledge of the constants has to exist. The theory of RUS is based on a series solution of the three dimensional free body problem. The sample shape and the accuracy needed are reflected in the order of the series solution, which in turn is reflected in the size of the matrix equation, that needs to be solved. Exploitation of crystallographic symmetry can reduce the matrix sizes dramatically, but until relatively recently such computations required large computers [4]. Other methods using resonant frequencies are more or less special cases of this spectroscopic measurement, restricted to e.g. specific geometry of specimens. One of these methods in use for decades is the “Resonant Beam Technique” (RBT), [lo]. In principle this method can only be applied to isotropic materials, which includes quasi-isotropic brittle composites such as chopped fibre materials. Standards exist for monohthio ceramics e.g. ENV 843-2, I S 0 17561, ASTM C1198-01 and C1259-01, JIS R1602, extended to high temperatures in prENV 820-5, for glass and glass-ceramics ASTM C623-85 and ceramic whitewares ASTM C848-94. With this method a prismatic bar of a length to width ratio of more than ten is excited to bending vibrations. From the dimensions of the bar, its density and the resonant frequency of the fundamental mode the Young’s modulus can be calculated, in principle by solving the Euler-Bernoulli equation. Exciting torsional vibrations by specific excitation the shear modulus can be calculated. For the calculations only the frequency of the fundamental mode is used, because the higher modes exhibit a shear perturbation which is not included in the Euler-Bernoulli equation. Another frequently used method is the “Impulse Excitation Method”, [ 1 I]. In principle this method can only be applied to isotropic or quasi-isotropic materials (see last method), standards only exist for monolithic ceramics, e.g. ENV 843-2. The excitation to resonant vibrations is performed by light mechanical impact. The Young’s modulus is calculated for isotropic and regular shaped test pieces from the resonant frequency of the hndamental mode, solving the Euler- Bernoulli equation, the shear modulus from the wave equation for torsional vibration, which has to be excited separately. Additionally, the internal
On the detertnination of elastic constants with brittle matrix coniposite.s
393
friction can be determined from the exponential decay of the vibration. This method was successfully extended to high temperatures (1 750 “C), [4] and is standardised in the European pre-standard prENV 820-5.
THE RESONANT BEAM TECHNIQUE WITH ANISOTROPIC COMPOSITES IN DEPENDENCE ON TEMPERATURE The classical Resonant Beam Technique (RBT) is frequently used to determine the dynamic elastic moduli in Standardisation (examples see above). All these applications have in common that they neglect the influence of shear, which increases with the order of the mode of vibration. For the calculation of results the Euler-Bernoulli equation, valid for the basic mode only, is applied and it is combined with correction factors for higher modes (in general only the first mode i.e. the first overtone is considered additionally to the fundamental mode). The shear moduli itself are determined separately from torsional vibrations. The development of the method described below was started in our working group in 1988, following the method of Forster [lo], with the introduction of corrections for higher modes and a graphical solution of the problem for anisotropic ceramic matrix composites (Carbon fibre-reinforced Carbon, C/C), [ 121. The method developed and applied at the Institute of Materials Physics now turns around the problem: The higher modes, which show the influence of the shear deformation, are measured up to the sixth order. Timoshenko’s equation, that includes a perturbation for shear, can now be used to calculate the Young’s modulus and additionally the shear moduli. The Young‘s modulus being the longitudinal modulus in the length direction of the prismatic test piece, the shear moduli being the moduli along the height and along the width of the test piece, respectively (Poisson‘s ratios can be calculated from these moduli). Thus it is important to cut out the specimen with respect to the crystallographic orientation. For example from a 2,5D or a 3D composite (orthothropic symmetry) test pieces can be cut out perpendicular to each other in reinforcing directions x, y and z, so that the Young’s moduli E,, E,, E, and the shear moduli GxyrGyz, G,, can be obtained. As already mentioned above, contrary to mechanical test methods, the determination of elastic properties by the Resonant Beam Technique described here is not based on the evaluation of the stress-strain response over a given deformation range obtained under quasi static loading conditions, but is based on a non-destructive dynamic measurement from vibrations at very small amplitudes. Therefore the values of Young’s moduli, shear moduli and Poisson’s ratios determined by quasi static and dynamic methods may not give the same results, particularly for ceramic matrix composites which can exhibit non linear stress-strain behaviour.
Measurement of moduli by the “Resonant Beam Technique (RBT)”, measurement procedure The test piece, a long thin prismatic bar (ratio of length to width or length to height larger than ten), cut out from the composite along a specific orientation of interest is excited to bending vibrations. The mechanical excitation at continuously variable frequencies is provided by means of a transducer that transforms cyclic electrical signals to cyclic mechanical forces on the test piece. A second transducer senses the resulting mechanical vibrations of the test piece and transforms them into electrical signals. The resulting spectrum (amplitude in dependence on frequency) is measured via a network analyser. From the resonant frequencies i.e. the peaks of the spectrum (fundamental vibration and harmonics up to the sixth mode), the dimensions
394
Dieter LOIDL, Stephan PUCHEGGER, Henvig PETERLIK and Karl KROMP
and the density of the test piece, the engineering elastic moduli can be calculated by numerically solving Timoshenko's equation. Starting with estimated values for Young's and shear moduli, those moduli are computed by an iterative process, which minimises the difference between the measured and the calculated eigenfrequencies. The result for every specimen is one Young's modulus and two shear moduli in directions perpendicular to each other. The specific equations and the calculation procedure are summarised in [ 131, the theoretical background was taken from [ 14-171. At the Institute of Materials Physics, University of Vienna this technique was extended for the application to temperatures up to 2000 "C [ 131. Most of other methods proposed for the measurement of elastic constants with anisotropic materials are, at least at the moment, restricted to room temperature, see e.g. [ 1,2]. Testing equipment for high temperatures Specific transducer systems (emitter-receiver) have been developed. The specimens are suspended from the transducers by loops of carbon fibre bundles (several hundred fibres each) and excited to bending vibrations via the loops. The specimen hangs between graphite heating elements in a vacuum chamber, Fig. 1, [13].
r-J
controland
evaluation unit
networkanalyser
I
1; transmitter
I temperature con Ll I
I
receiver
heating element
I
FIG. 1 : Scheme of the resonant frequency apparatus "ELASTOTRON 2000" (left). The prismatic specimen is excited to bending vibrations by carbdn fibre-bundle loops attached to transducers in water-cooled housings (right). Most important and decisive is the software: data acquisition and evaluation are performed online by a single software package in connection with a network analyser (HP 875 IA). The software encloses an effective user interface and operates on a standard personal computer. Meanwhile the third prototype of equipment has been built up, see Figs. 2 and 3.
011
the detmtnitiution of elastic cotzstnttts with brittle ttrutrix composites
395
FIG. 2: Resonant frequency apparatus "ELASTOTRON 2000", overview, vacuum vessel closed.
FIG. 3 : Resonant frequency apparatus "ELASTOTRON 2000": transducers in watercooled housings (top), attached carbon fibre-bundle loops with C/C specimen in graphite heating element (open). Example of measurements with a 2,5D-reinforced ceramic matrix composite In the frame of a co-operation project with Snecma Propulsion Solide, Le Haillan, Bordeaux we received specimens from needled woven 2,SD carbon-fibre reinforced carbon composites (C/C-composites) out of the hot zone of the nozzle of the booster of the Ariane 5 . The specimens were cut out in three directions perpendicular to each other. The orientation of the specimens is given in Fig. 4.
396
Dieter LOIDL, Stepl~anPUCHEGGER. Henvig PETERLIK and Karl KROMP
Fig. 4: Orientation of specimens out of the nozzle of Ariane 5 From Fig. 4 it can be assumed that the specimens in direction x cannot follow the curvature, thus the reinforcement will not be homogeneous along the length of the specimen, though the inner radius of the nozzle is rather big (0,9 m). The material “Novoltex” is produced by winding a 2D carbon fibre fabric around a mandrel, finally the cylindric body is needled with chopped fibres perpendicular to the fabrics. The reinforcement in direction z thus is rather weak. The pyrocarbon matrix is deposited by chemical vapour infiltration (CVI), then the composite is heat treated. Kesults at room temperature An example of a frequency scan of a specimen cut out in direction x is given in Fig. 5. The resonant modes identified up to the sixth order are marked (the non marked ones are torsional modes). The prismatic specimens with the dimension 65x10~5mm3 exhibit resonant sites at different directions of bending vibration (flatwise, fw means vibration along thickness 5 mm and edgewise, ew along width 10 mm), denoted as f and e in Fig. 5, respectively.
-60
-
-
-00
m
-0
c
.-c0 m r’
-100 -120
Q)
E
-140
fl
el
f2
f3e2
f4 e3 f5 e4 f6 e5
e6
-160 2
3
4
5
6 7 8 9 1 0
20
30
40
50 60
frequency [ kHz ] Fig. 5: Frequency scan and resonant modes of bending vibration of composite Novoltex at room temperature, orientation x.
397
On the determination of elastic constants with brittle matrix cotnposites
By the procedure described above and using all the modes identified, the Young’s and shear moduli for the three specific orientations of specimens (x,y,z), perpendicular to each other, were computed. As mentioned above. the result for every specimen with the RBT is one Young’s modulus and two shear moduli in directions perpendicular to each other. The results at room temperature are given in Fig. 6.
1‘
E y = 17.1 GPn
3.2
= 31.3 GPa
Fig. 6 : Young’s and shear moduli for specific orientations (x, y, z) and different directions of vibration (flatwise, fw and edgewise, ew) with C/C-composite Novoltex at room temperature. Two general features should be anticipated before discussing the results: during the measurements in direction x it turned out that the values of the resonant frequencies did not follow precisely the theoretically predicted ones, this is argued to be a consequence of the fact that the straight specimens in direction x do not follow the curvature of the structure of the nozzle (see Fig. 4). On the other hand the measurements with specimens cut in direction z in general showed resonant sites less distinct and thus exhibited larger errors, because the reinforcement in this direction is rather weak. The Young’s moduli in directions (x, y, z) differ significantly from each other. As the Young‘s moduli should directly reflect the structure of reinforcement (the fibre structure) this result could be expected. The largest value, Ex is measured in direction of warp, the median value, E, in direction of weft and the smallest value, E, in direction of reinforcement by needling with chopped fibres, see Fig. 6. The shear moduli are influenced by both, matrix and reinforcement. The stronger reinforcement is in the plane (x y), i.e. warp and weft. The weaker reinforcement is in the planes (x z) and (y z) by chopped fibres. Thus the G,, are larger than the G,, and the Gyr, respectively. The G,, and the G,, should show nearly the same values, as it is the case (see Fig. 6). It is to expect that edgewise vibration in orientation x (Gxy)gives the same result as edgewise vibration in orientation y (Gxy).because the reinforcement in this plane is the same for both the directions of vibration.
398
Dieter LOIDL. Stephan PUCHEGGER. Henvig PETERLIK and Karl KROMP
On the other hand the results for the G,, in the different directions of vibration (ew and fw) should be identical, the same should hold for the G,, considering the errors [13] this is the case. For reasons of weak reinforcement in z mentioned above, the results for G,, and G,, measured with the z-specimen showed the largest error, thus these values were not introduced into the high temperature graph in Fig. 7b. Results at high temperatures The measurements in dependence on temperature were performed in vacua of 3.IO4 mbar. The measurements were followed up to a maximum of 1800 "C (to go up to 2000 "C would need Argon atmosphere, to prevent damage on the graphite heating system).
__ 1000
temperature ["C]
a)
1500
.
2000
500
1000
1500
2000
temperature ['C]
b)
Fig. 7: Dependence on temperature of a) Young's moduli for specific orientations (x, y, z); b) shear moduli for specific plains (xy, xz, yz) with C/C-composite Novoltex Fig. 7a exhibits a continuous increase of Young's moduli with temperature, the same for the shear moduli in Fig. 7b. G,: means shear in the plain (xy), measured with the specimen cut out in direction y, analogous for the other notations (compare Fig. 6 ) . in the graphs the error bars are shown together with the symbols. The G,- and G,, -values measured with specimens cut out in direction z are not shown in the graphs, because of reasons mentioned above. Summarising it can be stated that all the moduli of this C/C-composite raise continuously with temperature. Polished cuts through the material and microscopic investigation exhibited a high content of pores and interlaminar, intralaminar and intrabundle microcracks. Most of the microcracks open during cooling down of the composite from heat treatment temperature to room temperature. It is argued that most of these microcracks close with raising the temperature and contribute to the stiffening of the composite. On the other hand the rather weak bonding between fibre and matrix (for C/C not much more than van der Waals) is improved by continuously raising clamping between fibre and matrix when
On the determination of elastic constants with brittle tnntrii cotnposites
3 99
temperature approaches the heat treatment temperature. Both these effects contribute and thus result in raising the moduli.
RESONANT ULTRASOUND SPECTROSCOPY (RUS) AND RESONANT BEAM TECHNIQUE (RBT)
RUS and RBT are two very successful procedures to determine the elastic properties of composites. RUS is an option for the determination of the complete set ofelastic constants of specimens with various shapes (eg. small cubes or parallelepipeds) and with the option to extend the procedure to application to high temperatures. RBT is an easy to handle technique up to high temperatures with the restriction to specific shapes of specimens (long thin bars) and the corresponding engineering moduli. The problem with RUS is that exciting an e.g. cubic specimen results in a very dense spectrum of resonant frequencies (more than 30 resonant sites). A solution of this problem only is possible, if some precise knowledge on the elastic constants already is available. The idea now is to combine these two procedures. At the Institute of Materials Physics in our working group a new software has been developed to be easily extensible and flexible. This software has been adapted to the different requirements, which are specific to the problem, e.g. the fitting of the calculated frequencies to the measured frequencies can now be optionally performed by “simulated annealing” and will thus not easily end up in a local instead of the global minimum, which would give wrong results. The number of polynomials used to approximate the true displacement function along the different axes can be better adapted to Timoshenko-beam like geometries, which results in a drastic decrease of the computational time needed at a steady level ofaccuracy. By means of this new software the complete set of eigenfrequencies of RBT-shaped specimen can be calculated. Now the procedure proposed is to gain preliminary results with RBT and then to continue with RUS by introducing these preliminary results. Results on simulation calculations for this case were already achieved [ 181. ACKNOWLEDGEMENT The financial support by the Austrian Science Foundation FWF under Project P14294 and Project P15670 is acknowledged. Many thanks to our Partner M. Bourgeon from Snecma Propulsion Solide in Le Haillan, Bordeaux and his support in the frame of the co-operative Project PPO8275LOOO.
REFERENCES 1. Baste, S., El Bouazzaoui, R., An experimental investigation of stiffness reduction and cracks geometry in an unidirectional brittle matrix composite; J. Compos. Mater., 30/3, 1996, pp 282-308 2. Castagnkde, B., Jenkins J. T., Sachse, W., Baste, S., Optimal determination of the elastic constants of composite materials from ultrasonic wavespeed measurements; J. Appl. Phys. 67, 1990, pp 2753-2761 3. Wanner, A., Elastic modulus measurements of extremely porous ceramic materials by ultrasonic phase spectroscopy; Mater. Sci. Eng. A248, 1998, pp 35-43
400
Dieler LOIDL, Stepharz PUCHEGGER, Herwig PETERLIK and Karl KROMP
4. Migliori, A. M., Sarrao, J. L., Resonant ultrasound spectroscopy; John Wiley and Sons, New York, Chicester, Weinheim, Brisbane, Singapore, Toronto; 1997; ISBN 0-471- 12360-9 5. Leisure, R. G., Willis, F. A., Resonant ultrasound spectroscopy; Phys. Today, J. Phys. Condens. Matter 9, 1997, pp 600 1-6029 6. Maynard, J., Resonant ultrasound spectroscopy; Phys. Today, 4911, 1996, pp 26-3 I 7. Migliori, A., Sarrao, J. L., Visscher, W. M., Bell: T. M., Lei Ming, Fisk, Z., Leisure, R. G., Resonant ultrasound spectroscopic techniques for measurement of the elastic moduli of solids; Physica B 183, 1993, pp 1-24 8. Maynard, J. D., The use of piezoelectric film and ultrasound resonance to determine the complete elastic tensor in one measurement: J. Acoust. SOC.Am. 91/3, 1992, pp 1754-1762 9. Goto, T., Anderson, 0. L., Apparatus for measuring elastic constants of single crystals by a resonance technique up to 1825 K. Rev. Sci. Instrum. 59/8. 1988, pp 1405-1408 10. Forster, F., Ein neues Verfahren zur Bestimmung des Elastizitatsmoduls und der Dampfung; Z. Metallkd. 29, 1937. pp 109- I 15 11. Roebben, G., Bollen B., Brebels, A., Hurnbeeck J. Van, Biest, 0. Van der, Impulse excitation apparatus to measure resonant frequencies, elastic moduli and internal friction at room temperature and high temperature; Rev. Sci. Instrum. 68/12, 1997, pp 451 1-45 I5 12. Wanner, A., Kromp, K., Young's and shear moduli of laminated carbodcarbon composites by a resonant beam method; in: "Brittle Matrix Composites 2", ed. by A.M. Brandt and I.H. Marshall, Elsevier Appl. Sci. Publ., London-New York 1988, pp 280-289 13. Lins, W., Kaindl, G., Peterlik, H., Kromp, K., A novel resonant beam technique to determine the elastic moduli in dependence on orientation and temperature up to 2000 "C; Rev. Sci. Instrum 7017, 1999, pp 3052-3058 14. Timoshenko, S. P., On the correction for shear of the differential equation for transverse vibrations of prismatic bars; Phil. Mag. 41, 1921, pp 744-746 15. Timoshenko, S. P., On the transverse vibrations of bars of uniform cross section; Phil. Mag. 43, 1922, pp 125-131. 16. Huang, T. C., The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions; J. Appl. Mech. 28, 1961 pp 579-584 17. Kaneko, T., On Timoshenko's correction for shear vibrating beams; J. Phys. D: Appl. Phys. 8, 1975 pp 1927-1936 18. Puchegger, S., Loidl, D., Kromp, K., Peterlik, H., Elastische Moduln anisotroper Verbundwerkstoffe bei Hochtemperatur; 14. Symposium ,,Verbundwerkstoffe und Werkstoffverbunde", July 2nd-4th, 2003, Wien; Proc. by Wiley-VCH, D-69469 Weinheim, Germany, in print
Proc. Int. Symp. ,,Brittle Matrix Composites 7" A.M. Brandt, V.C. Li and I. H. Marshall, eds. Warsaw. October 13-15, 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003
PLENARY INVITED PAPER
A MECHANICAL STUDY OF REINFORCED-CONCRETE BEAMS REPAIRED WITH COMPOSITE SHEETS Stephane AVRIL', Alain VAUTRI", Patrice HAMELM', Yves SURREL3 'SMS/MeM, ENSMSE, 158 cours Fauriel, 42023 Saint- Etienne Cedex 2, France. email:
[email protected],
[email protected] 'L2MS, Universite Claude Bernard Lyon I, 43 bd du 1 1 Nov. 1918, 69622 Villeurbanne Cedex, France, email:
[email protected] 1 .fr 'BNM-PJM, CNAM, 292 rue Saint Martin, 7 5 I41 Paris, France, email:
[email protected] ABSTRACT This paper deals with rehabilitation of Reinforced-Concrete infrastructures with externally bonded carbon-epoxy sheets. The flexural behaviour of repaired structures under service loads is addressed, focussing mainly on the problem of crack width prediction. Firstly, the state-of-the-art methods for crack width prediction in concrete beams are recalled. Then, they are confronted to experimental data obtained with a full-field optical method onto small scale beams. Those experiments conducted on physical models show that classical formulae are not suited for the prediction of crack widths in the repaired beams, because they do not take into account the crack bridging effect due to bonding between the composite sheet and concrete. In order to elaborate a numerical modelling, a multi-scale approach is suggested. It is based upon the definition of a relevant Representative Volume Element of beam. The assets are that input parameters have a physical meaning and that the simulated mechanical behaviour is consistent with the one characterized experimentally. Finally, the main results obtained in this study are verified in beams whose scale is representative of real infrastructures. The paper focuses mainly on the validation of the numerical model for computing crack widths in the repaired beams. The interest for the identification of bonding properties between the composite sheet and concrete is also poir.:ed out. Keywords Repair with composites, crack bridging, Reinforced-Concrete, full-field measurements. grid method, bonding.
402
Stephane AVRIL. Alain VAUTRIN, Palrice HAMELIN- and Yves SURREL
INTRODUCTION The context of this work is within the rehabilitation of civil engineering infrastructures. The issue of upgrading the civil engineering infrastructures has become of great importance for over n decade [ 11. The main reasons are increasing traffic volume. lack of maintenance, environmentally induced degradation, earthquakes.. . Many experimental studies have shown that CFRP (Carbon Fibre Reinforced Plastic) sheets are mechanically effective for upgrading damaged RC structures. Especially concerning Hexure, bonding CFRP sheets can significantly increase the moment of failure of damaged beams [2, 31. For the design, both the Ultimate Limit State (ULS) and the Serviceability Limit State (SLS) of the structure must be verified. Despite of the moment of failure increase, the experimental studies cited previously have also shown that externally bonded composites do not really enhance the serviceability. This has been confirmed by on-site investigations. Hag-Elsafi et al. [4]have applied CFRP composite laminates to strengthen an aging reinforced-concrete T-beam bridge in the USA. They have shown that rebar stresses were only moderately reduced after installation of the laminates. Actually, the structural effect of the CFRP sheet is only clear after yielding of internal steel rebars, ie. beyond the Serviceability Limit State of the structure. [ndeed, on one hand, CFRP materials have high strength and no large amount of CFRP are needed for ULS. On the other hand, the modulus of elasticity of CFRP manufactured directly onto the damaged structure can be relatively low (60 GPa). Higher amounts of CFRP may be needed to introduce sufficient stiffness for meeting the serviceability design criteria.
As both ULS and SLS must be taken into account for the design, serviceability appears more restrictive than failure for the repaired beams. Among serviceability aspects, the most critical one is often cracking. Crack widths should be limited for insuring infrastructures durability. In the absence of specific requirement and for exposure classes 2-4, Eurocode2 [S]recommends that a limit of 0.3 mm under quasi-permanent (long-term) loads should be satisfied. Wide cracks are also harmful for the durability of RC beams repaired with CFRP sheets because wide cracks may be at the origin of CFRP debonding [6, 71. Therefore, the value of 0.3 mm utilized in Eurocode2 should be kept as the SLS of repaired beams. However, the use of this limit value as a design criterion implies that sound methods are available for the assessment of crack widths in repaired beams. This problem is addressed in this paper. Firstly, the state-of-the-art methods for crack width prediction in concrete beams are recalled. Then, they are confronted to experimental data obtained with a full-field optical method onto small scale beams. It is shown that classical formulaes are not suited for the prediction of crack widths in repaired beams, because they do not take into account the crack bridging effect due to bonding between the composite sheet and concrete. For modelling numerically this effect, a multi-scale approach is suggested, using the Finite-Element-Method (EM).Finally, the paper focuses on the validation of the model for computing displacement fields, crack widths and curvatures in real scale repaired beams.
THEORETICAL BACKGROUND Concrete reinforced with steel rebars The post-cracking behaviocr of f C s t h t u r e s depends on a great number of influencing factors: the tensile strength of concrete, anchorage length of embedded rebars, concrete cover, steel
A mechanical study of reinforced-concreie beams repaired with composiie sheets
403
spacing, which are strongly related to the bond characteristics between concrete and steel. The approach which has been the most widely used for assessing crack widths in concrete reinforced with steel rebars is based on the theory of multiple cracking (Figure I ) and on bond-slip models [8,91 whose basic formulae is: AJt 1,, = rmC0 where: 0
r, is the average bond stress over a given transfer length ltr (the subscript 712 is linked to the word “average”), is the tensile strength of concrete (the subscript t is linked to the word “tensile”),
0
ft
0
Co is the bar perimeter.
Figure 1: Multiple cracking of RC elements in tension From the strain distribution, the crack width W I ; can be defined as the total difference of elongations between the reinforcement and the concrete matrix measured between two adjacent cracks, which is equivalent to the crack spacing. Structural concrete codes generally use this type of approach for computing allowable crack width. For example, the relation supplied by Eurocode 2 [ 5 ] for the design of reinforced concrete beams writes: wk = PScrmErn
(2)
where: 0
w k is the assessed crack width (the subscript k is linked to the word “crack”),
0
E,
is the average tensile strain difference between the steel and the concrete, taking into
. account bond stress, tension stiffening, shrinkage effects ... 0
s,., is the average crack spacing for the final load,
0
/3 is a design coefficient.
The use of this theory for crack widths prediction in flexure is based on a large number of simplifying assumptions. Crack width can not be assumed to be constant over the depth of the element, naturally equalling zero in zones of compressive stress for example. Moreover, tests have shown that the concrete cover can have a significant effect on surface crack widths. Attempts to apply eq. (2) have led to the development of simple empirical equations to compute E., For example, the approach adopted by CEB-FIP [ 101 is based on the average strain in the member. It has been kept by Eurocode2:
where:
404
0
0
0
0
Sfkphane AVRIL, Alain VAUTRIN Patrice HAMELIN, and Yves SURREL
is the stress in the tension steel under the service conditions being considered, calculated on the basis of a cracked section (the subscript s is linked to the word “steel”);
fs
fsr is the stress in the steel rebars under the relevant conditions that just causes the tensile strength of concrete to be reached, calculated on the basis of a cracked section;
Dl is a coefficient that accounts for the bond properties of reinforcements, which are responsible for the tension stiffening effect, Pz is a coefficient that accounts for repeating stressing of the bars.
Equation (3) obviously has an empirical basis but it leads to quite good results For RC beams [lo]. Concrete reinforced with steel rebars and external FRP sheets The post-cracking behaviour of RC beams strengthened with composites is quite similar to unstrengthened ones [ 11, 121. It is still relevant to assess crack widths by using bond-slip models. However, bonding properties between concrete and the composite must be taken into account for crack width prediction in RC beams repaired with C F W sheets. Its role has already been evidenced for reinforced concrete beams st‘rengthened with steel plates [ 13, 14, 151. It has not been proved yet if the adherence of the laminate onto concrete can significantly contribute to bridge the cracks in the damaged concrete structure. Models involving tension stiffening are scarce. Some authors [16] attempted to introduce crack bridging effects in beam equations but refined experimental studies are still necessary to understand those local phenomena and their influence onto the global behaviour of the structure. Consequently, design guidelines provided presently by the task groups [7] and utilized in practice are based upon Eurocode 2 [5]. However, experiments conducted by Fenier et al. [ 171, and which are recalled in this paper (Figure 2 ) have shown that they do not lead to a good assessment of crack widths after repair. It penalizes greatly the use of composites for tackling serviceabilitydeficiencies in concrete structures. In view of that, the main objective of the study which is described below is to contribute to a more accurate prediction of crack widths after repair.
“P 4
S 300
5P 200 0
5
E
0
100
0
L 0 -crack
Load I(kN)
I
20
40
width measured after repair
60 -crack
80
100
width predlcted b y EC2
Figure 2: Comparison of the crack widths assessed with Eurocode 2 formulae and the experimentally measured crack widths in a RC beam repaired with a composite sheet
A niecliairical study ojreinforced-concrete hecims repaired with composite sheets
405
EXPERIMENTAL CHARACTERIZATIONOF SMALL-SCALE BEAMS Details of the specimens For characterizingthe mechanical behaviour of cracked beams externally reinforced with CFRP sheets, tests have been carried out firstly onto a physical model of beam (Figure 3). The physical model is actually a small-scale beam. It has a cross section of 84 x 50 mm2, a total length of 770 mm, and an effective span of 667 mm. The longitudinal and shear steel reinforcements are the same for all these specimens: 2 44.5 rebars and 2 20-mm-spaced stirrup. The cover concrete is 8 mm thick. Similar mixed concrete is used for all the beams. The cement : sand : gravel proportions in the concrete mix are 1 : 2.2 : 3 by wcight. The waterkement ratio is 0.52 and 462 kg/m3 type I Portland cement (CPA 55) is used. The maximum size of the aggregate is 5 mm. The average compressivestrength of concrete is 39 MPa. The elastic modulus is 41 GPa.
\
'\i,paii~*.'uUlh,11
r
E4rr3a.l.
Figure 3: Details of the small-scale beams.
Figure 4: Photography of the experimental set-up utilized for small-scale beams. Small-scale beams were designed by applying the similitude thcory which leads to the different scale factors to be used with respect to the real-scale reference model [18]. Not only steel bars and stirrups diameter but also aggregate size and granulometry of the concrete havc
406
Stkphane AYRIL, Alain YAUTRIN. Patrice HAMELIN. and Yves SURREL
been multiplied by a scale factor in order to match with the reduced dimensions of the beams. These factors are obtained on the basis of a dimensional study [ 191. The basic scale factor for lengths is 1/3. The suitability of the physical model to represent the mechanical behaviour of real-scale specimens is discussed in the last section of the paper. Five small-scale RC beams have been tested in four-point-bending before bonding the composite sheet. The main objectives of this first test are to create tensile cracks and to characterize the mechanical behaviour of cracked beams before repair. Since the maximum tensile strain is reached in concrete, several vertical cracks occur in the tensile part of the beam. The global equilibrium is kept because the internal steel rebars bear the tensile stresses. Each test is stopped once 60% of the load corresponding to the rebars yielding is reached. Afterwards, the beams are unloaded. A second bending test is carried out directly up to failure on one of the beams. This beam is used as the reference unstrengthened beam. Four, out of the five pre-cracked beams, are repaired with a composite laminate bonded onto the bottom surface. The bonded CFRP laminate is made of a unidirectional high modulus carbon fibers taffetas (330 g/m2 reference Hexcel 46320) and epoxy resin (Ciba LY 5052). It is directly polymerized on the specimen, the first epoxy resin layer working as the bonding joint. The thickness of the bonding joint is 0.4 mm and the thickness of the composite is 0.8 mm. A tensile test carried out on such a laminate provides a Young modulus of 55 GPa. After polymerization, the repaired beams are loaded in flexure up to the steel rebar yielding load. The bending test and instrumentation are the same as the one used in the case of unstrengthened beams. Each beam is instrumented with a bi-directional grid laterally over a 140 x 84 mm rectangular surface in the constant moment span. The grid is utilized as a spatial carrier to measure the displacement fields over the lateral surface of the specimen [20]. The grid is made of the superposition of horizontal and vertical black lines printed over a white surface. Such a pattern is easy to realize. It is obtained in our experiments by printing the grid over a transparent sheet and transferring it over the surface of the specimen firstly painted in white (Figure 4). The lines of the grid must be separated by the same distance p , which is called the grid period. The grid period is p = 571 p m here. A numeric BASLER A1 13 1200 x 1000 pixels CCD sensor connected to a PC is used for grabbing images. The displacement computation is performed with an in-house software called Frangyne2000, applying the principle described in the following section. The resolution of the measurement, i.e. the smallest displacement which can be detected, is about 2 or 3 pm, depending on the quality of the grid transfer. The spatial resolution is 1.2 mm [21,22].
The grid method The principle of me_asurements is quite simple: a given point hfo+of. the space is determined by its position vector R ( X ,Y )in the reference Cartesian frame (0, i, j ) . In the initial undeformed configuration, the material point M coincides with Mo.In the final deformed configuration, another material point M‘ coincides with the spatiaf point Mo. The position of M’ in the initial undeformed configuration was characterized by R’(X’, Y’)in the Cartesian reference frame (Figure 5). In the initial undeformed state, the reflected light at point A40 is the light reflected by the material point hf.Its intensity writes: I ( @ = I0 { 1 where:
+ r f r g n [27rP.ii]}
(4)
407
A mechanical study of reillforced-concrete b e a m repaired with cotnposite sheets
is the local intensity bias,
0
I0
0
y is the contrast,
0
f r g n is a 2x-periodic function,
0
Lu'denotes the dot product of both vectors G(uZ,uv)and u'(u,,
0
L.,,):
is the spatial frequency vector. It is orthogonal to the grid lines and its amplitude is the spatial frequency of the grid. If the gridlines are vertical, they are parallel to meaning that the spatial frequency vector writes F ( l / p ,0). If the grid lines are horizontal, they are parallel to meaning that the spatial frequency vector writes F ( 0 , l/p).
y,
z,
When a loading is applied, there is a deformation of the structure and the grid is also deformed. The reflected light at spatial point ibl~has become the light reflected by the material point M'. As the position of M' in the undeformed configuration is determined by @(X,Y ) , the new intensity at point A40 is actually:
T(8)= 1, { 1 + r j r g n [2nF.@]}
(6)
The deformation from the undeformed config_ura_tionto the deformed configuration is described mathematically by the displacement field U(R)= l? - d,, but also by the inverse displacement field 6-'(2)= n' - ?I (Figure 5 ) . Therefore eq. (6) writes:
[(a)= I , (1 + y j r g n [ 2 x F . (a- ~ - ' ( 8 , ) ] }
(7)
The phase of the function f r g n at the point M varies of 2xF.6-'(8) from the undeformed to the deformed state. [f the assumption of small deformations is valid, 6-'(f?) and 6(@are similar. Therefore, it can be written in the deformed state:
Z(R) = t o ( 1 + y f r g n [27rF.(a- 6(")]}
(8)
The first component U,(x, y) of the displacement is calculated from the phase of the function f r g n when the grid lines are vertical, the second component U , ( z , y ) when the grid lines are horizontal. A suitable algorithm of signal processing [22] is utilized to compute the phase of the function f r g n .
Figure 5: Displacement vector and inverse displacement vector at the pixel location
408
Stepphane AVRIL, Alain VAUTRIN Patrice HAMELIN, and Yves SURREL
Figure 6: U,(rc, y) and Uy(z, y) displacement fields.
tributary
new vertical
crack
crack
Figure 7: Detection of cracks in a repaired beam from full-field measurements. Experimental characterization of cracking Examples of displacement fields measured onto the lateral surface of a repaired beam have been plotted in Figure 6. Whether the beam has been repaired or not, the V,(z,y) field is discontinuous. Discontinuities are always linked to the presence of a crack, as it was shown in a previous study [23]. Maps of these discontinuities are plotted in Figure 7, where continuous black lines represent the cracks. The smallest crack width which can be detected is 5 pm [20]. In Figure 7, the cracks are mapped out: 0
at the beginning of the test, the pre-existing cracks of the RC beam are still open because of the non-linear friction behaviour of the concrete-steel interface,
A mechanical study of reinforced-concrete b e a m repaired with composite sheets
a
409
at the end of the test, i.e. at 100%of the steel yielding load, new crack have occurred and grown.
During the four bending tests, the new cracks which appear (Figure 7) are classified in two types: a
0
most of them are oblique shear cracks : they do not propagate up to the neutral axis but they are deflected towards the neighbouring pre-existing crack at the level of the internal re-bars. They are called tributary cracks. a few are vertical and appear halfway between two pre-existing contiguous cracks. They are not deviated in their propagation towards the neutral axis. They may result of tensile stresses in the concrete induced by the action of crack bridging of the composite laminate.
The creation of new cracks, especially tributary ones, is a phenomenon specific to repaired beams. None are detected when the reference unrepaired beam is loaded up to failure. For one of the detected cracks, the motion of the left hand side lip and the motion of the right hand side lip have been plotted versus the ordinate g on the same graph (Figure 8). This motion is measured with a precision of 1 pm. It is better that the resolution of displacement measurements because data are averaged on both sides of the crack. The graph in Figure S shows that the motion of the crack lips is affected near the soffit after repair. On the other hand, beyond the height of steel re-bars, the motion depends linearly of y and it is parallel to the motion of the lips before repair. The width reduction is only induced by the stiffening effect provided by the composite sheet after repair. Finally, the essential effect observed here is the local bridging of the tensile cracks by the composite laminate. This effect is located mainly in the cover concrete where the crack opening is hindered by the bond stresses. This phenomenon is responsible for the occurrence and the growth of new cracks after repair [ 121.
Figure 8: Detection of cracks in a small-scale beam from full-field measurements before and after repair. Characterization of plane cross sections Experiments have shown that the cracking behaviour after repair is quite different of the one before repair because new cracks occur between the preexisting ones. [n order to verify if the
4 10
Sriphane A VRIL, Alain VAUTRIN, Patrice HAMELIN, and Yves SURREL
theory of multiple cracking exposed in the Section “Theoretical background” is still relevant, it has been checked if the crack widths can still be defined as the total difference of elongations between the reinforcement and the concrete over a given length. For that, the measured displacement fields have been compared with the one predicted by the beam theory of Bernoulli. Locations where the modelled and the experimental field U,(z, y) are equal are detected (Figure 9). The following criterion is used : at one pixel, if the absolute difference between the experimental and the modelled displacement is less than 2 pm, then the pixel is black, else it is white. A cut off value of f 2 m has been chosen because it is the resolution of the grid method. In the tensile region, few locations are detected. They are mostly concentrated in narrow strips aligned perpendicularly to the length of the b e q . The cross sections located at the middle of each strip can be considered as the only ones to remain plane. It must be noticed that only the displacement of the lateral surface of the beam is measured. The internal behaviour is not addressed. Yet, the particular cross-sections identified here actually delimit lengths of beam over which Bernoulli’s theory is verified in average [12]. Finally, two consecutive plane cross sections define a length of beam containing only one vertical crack which has already grown before repair. It can also contain some new cracks occumng after repair. The existence of plane sections is directly linked to the parameter,,s, of eq. (2), i.e. the crack spacing in the RC beam before repair. The average distance separating two consecutive cross sections remaining plane is,,,s and the average distance between a crack and a cross section remaining plane is scrm/2[ 111. It means that eq. (2) is still relevant for assessing the width a vertical crack after repair, provided that the contribution of new cracks is subtracted from the expression of E., This major result is used for modelling crack opening in the repaired beam.
Figure 9: Locations where the experimental displacement field and the Bernoulli-modelled one are similar, for an unrepaired beam in picture 1 and for a repaired beam in picture 2.
t
I IP
4 12
Stephane A V N L , Alnin VAUTRIN, Patrice HAMELIN, and Yves SURREL
[24].The bonding law between steel and concrete can be approached by an elasto-plastic model: a.
If
IT/
shown in Fig.1. In the first step, the thermomechanical load is imposed on thc coliipositc laminate, without causing any cracking. In the following steps, the multiple p l y - c r x k s timi one after another without simultaneous occurrence of two or more cracks under the unchanged external load that has been imposed on the specimen. Given an applied laminare stress the number of cracks is a discrete random variable, N , which takes on a non-negati\.e number, n, (n=O, I, 2 , , ..,a). The probability hnction of the random variable, N , denoted by f ( n , o , 2 L ) , represents the failure probability that the exact n-cracks appear sequentially within the gauge length, 2L, under the constant load, u .
L
-I
Cracks appear one aRer another under unchanged load
Z
< 1
T
I-
2L
-
Figure. 1 A quasi-static and sequential process model for multiple fractures in composite laminates.
462
K. P. HERRMANN and Junqian ZHANG
The first crack will appear at a location where the composite material toughness is smaller than the potential energy release rate for the first cracking, i.e. 5 GI (o,L,cI). Since the variation of the lamina fracture toughness with the location is totally random the crack could be with an equal chance at any location among those locations where the fracture criterion holds true. Because it has been assumed that the fracture takes place one after another under the constant applied load, 0 ,the satisfaction of l- I GI (cr,L,cI) ensures the appearance of the first crack, but does not exclude any other events of more fractures after the first cracking under an unchanging stress. Therefore, the probability that ply cracks, regardless of the number of cracks, appear in a composite laminate under a constant load can be expressed by
The probability of an uncracking ( n = 0 ) can be derived from equation (5) as follows
Let us consider the second ply cracking within the gauge length under the constant load after the first crack has been fomied. By using the fracture criterion given by equation (1) the second ply cracking could occur at a location where r I G?(G,L,c?,c, ) holds true. By noting the fact that the variation of r with the location is totally random, the probability that the second ply cracking takes place (N22) can be expressed by
The probability of a single crack in the laminate is then given by f ( n = I , o , L ) = P ( N 1 I,o, L ) - P ( N 2 2 , 0 , L )
The probability analyses of the third cracking, the fourth cracking and so on can be conducted by a similar procedure which has been just discussed for the second ply-cracking. By repeating the procedure (n-])-cracks can be formed sequentially under constant load. A new cracking, the n-th ply cracking, is controlled by the fracture criterion r I G,,(G,L, D,,) . Again, among locations where the fracture criterion holds true there is not a preferential location where the new cracking occurs. Therefore, the probability of the n-th cracking within the laminate takes on the form of
463
Prediction of non-uniform multiple cracking in polymer composites using an energy-based .. .
It is implied that the multidimensional integral in this equation has the physical meaning of the failure probability that the number of cracks is less than 11. i.c.
Consequently the probability that exact @])-cracks appear sequentially is expressible as , f ( n - I,o, L ) = P( N 2 n - I,o,L ) - P( N 2 n,o, L ) ,
(1 1)
for n 2 l . Now the probability function, f ( n ,CT, L ) , has been expressed as a function of the potential energy release rates as well as the Weibull parameters of the fracture toughness. Knowing the potential energy release rate the multidimensional integral, P ( N < n,o, L ) given by equation (lo), can be evaluated numerically. The probability function , f ( n , a ,L ) can then be easily calculated from equation (1 I). A simplified expression for P ( N < n.o. L ) has been obtained in [6], which involves only three-dimensional integrals regardless of the number of cracks. i.r.
for n>2 and where
$,I’
=
Q:? (1 + x) 2 tanh(hL(l - c)) + tanh(2ALc) - tanh(2hLl) h
g,’,’) = Q?”? (I + h
(1 3a)
2
(tanh(hLc) + tanh(hL(/ - c)) - tanh(hLf))
.
By introducing the crack density. d,, = n / 2 L , the average crack density, determined via the mean number of cracks. E , as follows
2,
can be
464
K. P. HERRMANN and Junqian ZHANG
where the probability function of the crack density, d,,, is
It is implied that the crack density is a complex function of the applied stress and the fracture toughness distribution.
RESULTS In order to illustrate the predictability of the model we consider the [+8/904], glass fiber composite laminates. The laminates were tested by Joffe et a1 (2001) subject to uniaxial tension. The experimental data of the average crack density versus the laminate stress were reported there. The material properties used in the analyses are El=44.73 GPa, Ez=E3=12.76 GPa, GI2=GI3=5.8GPa, G23=4.49 GPa, 1' C , ~12=~13=0.297, V 2 ~ ~ 0 . 4 2ct:, = 8 . 6 ~ I" C , cty = ct: = 22.1 x ply thickness = 0.144 mm, temperature difference, T, = -105°C. In figure 2 the curves of the averaged crack density versus the laminate stress, which are generated from the experimental data and from the prediction of the deterministic model, are plotted together in order to show a comparison. For the same reason the experimental data and the present probabilistic model are putted together in figure 3. From both figures it can be seen that both the deterministic and the probabilistic models are able to predict the thickness effect on the multiple cracking in the laminates, namely, the thicker the laminate is, the smaller the stress that produces the same number of cracks. Figure 2 suggests that the deterministic model predicts a very rapid accumulation of ply cracks succeeding the first ply-
Fig. 2 Comparison of the deterministic model predictions (lines) with experiincntal data (discrete symbols ) in terms of the crack density in the 903 ply in the glass fiberlepoxy composite [fW90,,,lT(lJ laminates as a function ofthe applied stress.
Fig. 3 Comparison of the probabilistic model predictions (r,= 750 J/m', p = 10. lines) with experimental data (discrete symbols ) iii terms o f the crack density i n the 905 -ply in the glass fiherlepxy composite [M902mMl]laminates as a function of the applied stress
Prediction of non-uniformmultiple cracking in polymer composites iising an energy-based ...
465
cracking. In contrast Figure 3 shows that the probabilistic model presents a smooth increase of the crack density with applied stress. The latter one is closer to the observed values in the experiments.
CONCLUSIONS We have presented an energy based probabilistic theory to predict the evolution of transverse ply cracking in a composite laminate as a function of the underlying statistical fracture toughness and the applied load. The variation of the ply-level fracture toughness was characterized by a probability density function, p ( r ) . The probability function ,fi, (d,,,o,L) of the crack density, a discrete random variable, was determined from the fracture toughness distribution and the solution for the potential energy release rate. The mean crack density was formulated as a function of the applied load. In contrast to the deterministic models which predict a very rapid accumulation of the number of cracks the probabilistic model shows a smooth increase of the crack density against the applied load.
ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support by the Alexander von HumboldtFoundation of Germany and the National Science Foundation of China under grant number 19972076.
REFERENCES Zhang, J., Fan, J. and Soutis, C. (1992), Analysis of multiple matrix cracking in [+€I m/9On]s composite laminates: part 11, development of transverse ply cracks. Composites 23,299-304. 2. Joffe, R., Krasnikovs, A., Varna, J., (200 I ) , COD-based simulation of transverse cracking and stiffness reduction in [S/90,], laminates, Composites Science & Technology, 61, 637656. 3. Kashtalyan, M and Soutis, C (2000), Modelling stiffness degradation due to matrix cracking in angle ply composite laminates, Plastics Rubber and Composites, 29 (9), 482488. 4. Liu, S and Nairn, J. A. (1992), The formation and propagation of matrix microcracks in cross-ply laminates during static loading, J. Reinjorced Plustics and Composites, 11, 158178. 5. McCartney, L.N., (2000), Model to predict effects of triaxial loading on ply cracking in general symmetric laminates, Composites Science & Technology, 60, 2255-2279. 6. Herrmann, K. P., Zhang, J. and Fan. J. (2002). An energy-based statistical model for multiple fractures in composite laminates, subniifted to J. of Multiscale Compututiorial Eng. 1.
Proc. Int. Synip. Brittle Matrix Coinposites 7” A M Brandt, V.C. Li and I. H. Marshall, eds. Warsaw, October 13-15. 2003 ZTUREK RSI and Woodhead Publ., Warsaw 2003 I,
FRACTURE MECHANICS AND PLASTICITY MODELLING OF THE SPLIT CYLINDERTEST John Forbes OLESEN, Lennart BSTERGAARD and Henrik STANG Department of Civil Engineering, Technical University of Denmark Brovej, Building 1 18, DK-2800 Kgs. Lyngby, Denmark, e-mail: j foO,bvg.dtu.dk
ABSTRACT The split cylinder test is subjected to an analysis combining nonlinear fracture mechanics and plasticity. The fictitious crack model is applied for the analysis of splitting tensile fiacture, and the Mohr-Coulomb yield criterion is adopted for modelling the compressive crushing/sliding failure. Two models are presented, a simple semi-analytical model based on analytical solutions for the crack propagation in a rectangular prismatic body, and a finite element model including plasticity in bulk material as well as crack propagation in interface elements. A numerical study applying these models demonstrates the influence of varying geometry or constitutive properties. For a split cylinder test in load control it is shown how the ultimate load is either plasticity dominated or fracture mechanics dominated. The transition between the two modes is related to changes in geometry or constitutive properties. This implies that the linear elastic interpretation of the ultimate splitting force in term of the uniaxial tensile strength of the material is only valid for special situations, e.g. for very large cylinders. Furthermore, the numerical analysis suggests that the split cylinder test is not well suited for determining the tensile strength of early age or fibre reinforced concrete.
Keywords Fictitious crack model, hinge model, concrete, fibre reinforced concrete, size effect. INTRODUCTION The split cylinder test, also known as the Brazilian split test, has been accepted in many countries as a standard test method for assessing the uniaxial tensile strength of concrete and similar materials. This test is performed by loading a cylindrical specimen along diametrically opposed generators of the cylinder until failure. The diametrically loading of the cylinder induces an almost uniform tensile stress normal to the plane of loading, and the failure load is interpreted as the load at which these tensile stresses reach the uniaxial tensile strength of the material. The tensile strength based on this interpretation is known as the splitting tensile strength. For a perfectly brittle material the splitting tensile strength would coincide with the uniaxial tensile strength. However, concrete is not a perfectly brittle material but a so-called quasi-brittle
30s
.John Forbes OLESEN, Lennari OSTERGAARD and Henrik STANG
material, and it is well-known that for noiinal strength concrete the splitting tensile strength overestimates the true uniaxial tensile strength. Thus, the splitting tensile strength is normally reduced by an empirical factor in the range of 0.6-0.9 when estimating the uniaxial strength. D The overestimation of the concrete tensile strength when based on the result of a split cylinder test is due to the quasi-brittle nature of concrete fracture. Here we adopt the fictitious crack model, a model first proposed by Hillerborg et al. [ I ] for modelling crack propagation in concrete and similar quasi-brittle Figure 1: Yield lines of the assumed plastic failure mode. materials. In this model a linear elastic pre-crack behaviour is assumed and crack initiation and localization is assumed to take place when the tensile stress reaches the uniaxial tensile strength of the material,&. This is followed by a crack opening phase where aggregate bridging is responsible for crack bridging stresses. The bridging stress. as,, is related to the width of the crack, w, through the tension softening curve or stresscrack opening relationship, which is a curve descending from the peak stressf;. The stress-crack opening relationship must be established experimentally e.g. by performing a uniaxial tension test in closed loop control or by some indirect method such as the wedge splitting test in combination with an inverse analysis method, see [ 2 ] . Originally, Hillerborg et al. [ I ] assumed a linear tension softening behaviour for concrete, however, a bilinear representation of the stress-crack opening relationship gives a more precise description of the behaviour of concrete and fibre reinforced concrete. Thus, a bilinear relationship is applied here, and it is given by the following expression:
""={ f;
I-a,w,
05w<w,
b2-a,w,
w,Iw<w,
The stresscrack opening relationship may be seen as a constitutive relationship for a crack and as such it may be implemented in a finite element model, e.g. through interface elements as done by Bstergaard et al. [3] and described below. The simple bilinear representation of the stress-crack opening relationship allows for an analytical solution to the problem of crack propagation in simplified situations such as flexural cracking of a straight beam o f rectangular cross-section. This is demonstrated by Olesen [4] who developed a so-called nonlinear hinge element incorporating the effects of crack propagation due to moment and normal force loads. Later it will be shown how this hinge element may be applied to the split cylinder test configuration to produce a semi-analytical model. The failure of the split cylinder specimen is characterized by a splitting crack beginning at the centerline and propagating towards the loading points. If the material is sufficiently brittle the splitting will proceed until the specimen is divided into two halves. In this case the ultimate load is governed by the tensile strength as well as the tension softening behavior of the material. However, if the material is not sufficiently brittle the splitting process will not be completed before a compressive crushingkliding failure develops, which then governs the ultimate load. In compressive failure concrete may be modelled as a rigid-plastic material with a Mohr-Coulomb
friction yield criterion, cf. [ 5 ] . Upper-bound solutions exist for the rigid-plastic failure of the split cylinder test and will be given later. These solutions are characterized by the formation ofwedgelike regions under the loading strips, simultaneously splitting the rest of the specimen. The compressive failure of concrete in the form of the Coulomb friction hypothesis may also be implemented in a finite element model as will be demonstrated. In the present paper it will be shown how the split cylinder test may be modelled to cope with materials ranging from perfectly brittle to ideal plastic, thus nonlinear fracture mechanics as well as plasticity is modelled. A finite element modcl will be presented, together with a simple semi-analytical model based on the hinge element in combination with a simple plastic solution.
LINEAR ELASTIC SOLUTION
A circular disk with a diameter D acted upon by two equal and diametrically opposite forces P is a classical problem in elasticity. The state of stress in the plane of loading is uniform tension perpendicular to this plane [6], and the magnitude of these tensile stresses is c =2P/(nD). In the split cylinder test the loads are applied over a certain width (2a) as shown in Figure 1. This will affect the state of stress, and if it is assumed that the loads are distributed evenly over the loading strips, the tensile stress at the centre of the disk should be modified according to the following expression [ 7 ] :
In the case of the split cylinder test we have that P = PJL, where P, is the total load on the cylinder and L is the length of the cylinder. For a perfectly brittle material - disregarding the risk of a compressive failure - the ultimate load of the split cylinder is given by ( 2 ) with c =A, the uniaxial tensile strength. This load, PE , is referred to as the linear elastic splitting load.
IDEAL PLASTIC SOLUTION
An ideal rigid-plastic solution to the problem of the split cylinder test is presented by Nielsen [ 5 ] . Here concrete is modelled as a so-called modified Coulomb material with a sliding failure condition given by the angle of Friction 4 and the cohesion c. The sliding failure condition is overruled by a separation failure condition stating failure when the tensile stress reaches the uniaxial tensile strength. The solution is based on a failure mechanism with yield lines as shown in Figure I , Based on this mechanism and introducing the uniaxial compressive strengthh, the following optimal upper-bound solution to the load-carrying capacity of the cylinder is found:
470
John Forbes OLESEN, Lennart 0STERGAARD and Henrik STANG
Figure 2: (a): Finite element mesh, 0=100 mm, a=5 mm. (b): Deformation plot. FEM IMPLEMENTATION One quarter of a cylinder is modelled by finite elements in a commercial programme environment, DIANA [S]. The elements are three-node triangular isoparametric plain strain elements (type T6EPS), and the mesh is shown in Figure 2a. It is assumed that a crack may develop in the vertical plane of symmetry; thus, interface elements (type LSF) are attached at the vertical face of the quarter cylinder. Symmetry boundary conditions are specified along the vertical and horizontal sections defining the quarter cylinder, i.e. deformations normal to these sections are suppressed. All vertical displacements of the nodes on the loaded horizontal surface of the loading strip are tied together to ensure synchrony. For concrete in solid elements the constitutive behaviour is described by a linear elastic model in combination with a Mohr-Coulomb yield criterion. The angle of friction for concrete is set to 37", and the cohesion is given by c =,fJ4, wheref, is the compressive strength. After crack initiation the normal relative deformation is governed by a bilinear stress-crack opening relationship as described by ( I ) . The FEM formulation of the split cylinder test constitutes a highly nonlinear problem with snap-back effects. The iterative scheme applied is based on the tangent stiffness matrix and the arc length method. The problem is solved under an adaptive load step control, and the convergence criterion is based on an energy norm. Figure 3a shows the results of a number of FE-calculations of the split cylinder test. The figure depicts load versus deformation. The load is noniialized with respect to the linear elastic load at crack initiation PE, and the deformation is the total compression of the specimen. Different materials are represented differing only by the value of the tension softening parameter a l . The remaining material parameters were kept constant at values representing a normal strength concrete:f; = 2 MPa, E = 30 GPa, a? = 0.2 mm-', b2 = 0.1. The softening parameter al describes the initial toughness ofthe material, and a value o f a l = 20 mm-' would apply to normal strength concrete. For large values of a i , i.e. al > 5 mm'l we observe snap back of the load deformation curve, for smaller values of a , , however, there is no snap back behaviour. All curves
47 1
Fracture mechariics and plasticity modelling of the split cylinder test
2.0
--1
P P , Iu
1 !, l
05
I
'
i
1
i !' I '
on i 11 0
no
~
02
U I
u [mm]
I1 1
-i no
-02
0.6
0-1 1:
08
10
[mm]
Figure 3: FE-results for normalized load versus specimen compression 11. shown in Figure 3a exhibit a behaviour where the first part is linear until a crack is initiated in the centre of the cylinder. This crack propagates towards the loading points as the load is increased, however, the crack also opens and as a consequence the crack bridging stresses decrease according to the stress-crack opening relationship, especially the a1 parameter. At some point the load reaches a maximum and subsequently drops while the crack opening continues. During crack opening redistribution of stresses in the whole specimen takes place, and at large crack openings the load is primarily canied through compression and bending of the almost separated semi-cylinders. The load carrying capacity at this stage is governed by the Mohr-Coulomb yield criterion, which is responsible for the second part of the load defomiation curve. After the load has dropped to this curve it increases again as the deformation increases. In the end the load approaches a constant yield level. The finite element load deformation curves are obtained by controlling the crack opening. However, split cylinder tests are normally performed in load control, thus only the ascending part of the curve may be obtained, i.e. only the first peak load is found from the test. On the other hand, if the test were deformation controlled with the compression 11 as the controlling parameter, the full load deformation curve could be obtained only for materials with a sufficiently low value ofthe softening parameter a t , ruling out the risk of snap-back. In Figure 2b the deformed finite element mesh is plotted at an extreme load step with extreme deformations for a1 = 20 nim-'. The figure illustrates the almost plane opening of the splitting crack, which, however, is prevented from penetrating all the way through the cylinder due to compressive stresses below the loading strip. Furthermore, it illustrates the plastic deformations in a region near the loading point. In Figure 3b finite element results for load deformation curves are shown for different values of the tensile softening parameter 62. The remaining material parameters have been kept constant atf;= 2 MPa, E = 30 GPa, a1 = 20 mm-' and a2 = 0.2 mm-I. The softening parameter b2 defines the level of the second part of the stress-crack opening curve, and is the one parameter, which is most directly influenced by the addition of fibres to concrete. The curve representing b2 = 0.1 is identical to the curve shown in Figure 3a representing CII = 20 mm-'. We note that bZ= 0.35 marks the point of transition kom a situation with a distinct peak preceding the plastic
472
John Forbes OLESEN, Lennart 0STERGAARD and Henrik STANG
Figure 4: Geometry and loading of WST-specimen. Strut and tie model and hinge element. behaviour. Thus, for values of b2 < 0.35 the caRacity of the split cylinder test in load control is determined by the peak governed by the magnitude of a , , whereas the capacity for larger values of b2 is determined by the plastic yield capacity. SEMI-ANALYTICAL MODEL
A simple model has been developed for the analysis of the splitting of a cylinder. The model is based on the so-called nonlinear hinge model [4], which is an analytical solution to the crack propagation in a rectangular prismatic body due to moment and normal force loads. The model is based on the fictitious crack model with a bilinear tension softening curve. Another hndamental assumption of the hinge model is that it is modelled as independent incremental layers, thus neglecting the shear stiffiess of the hinge. The hinge solution is expressed in terms of the normalized angle of rotation B = $~hE/(:fi),where $O is the angle of rotation of the rigid boundary lines of the hinge, see Figure 4c, and where h is the height of the hinge, E is the elastic modulus and s is the length of the hinge. The hinge solution may be found in [4] and it furnishes the relative crack depth a =d/h and the normalized moment p = 6M&h2t) as functions of the relative normal force p = Nh/V;ht), where Mh and Nh are the hinge moment and normal forces, respectively, and d is the depth of the crack and I is the width of the hinge. The solution comprises four distinct phases, the elastic pre-crack phase and three cracked phases differing in how much ofthe softening curve that has been activated. The simple split cylinder model assumes that the state of stress in the cylinder caused by the diametrically opposite loads may be replaced by the strut and tie model shown in Figure 4a, where w denotes the strut inclination angle and z denotes the distance of the horizontal tie from the centre of the cylinder. Now the hinge element is incorporated in place of the horizontal tie, and the tie force is referred to the mid-height of the hinge producing a moment loading of the hinge. The loads are thus given by N = % f t a n q and M = N(%h-z). So far the simple split cylinder model has only considered one half of the cylinder. In order to model the cooperation of the two halves, an elastic interaction is ensured by a rotational spring counteracting the rotational deformation p o f the hinge. Equilibrium of the hinge and spring system requires that = M,,($o,N ) + K