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Minimum specimen size for fracture parameters of site-casting dam concrete
Construction and Building Materials xxx (2015) xxx–xxx
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Minimum specimen size for fracture parameters of site-casting dam concrete Junfeng Guan a,b,c, Qingbin Li b,⇑, Zhimin Wu c, Shunbo Zhao a, Wei Dong c, Shaowu Zhou d a
School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou 450011, PR China State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, PR China c State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, PR China d China Three Gorges Corporation, Beijing 100038, PR China b
h i g h l i g h t s All specimens were cast at one-time by mixing tower system of an arch dam. The complete P-CMOD and P-CTOD curves of dam concrete were obtained. Independent fracture parameters of dam concrete were obtained. The minimum specimen size for dam concrete was determined.
a r t i c l e
i n f o
Article history: Received 25 December 2014 Received in revised form 27 March 2015 Accepted 1 May 2015 Available online xxxx Keywords: Dam concrete Site-casting One-time pouring Fracture parameters Minimum specimen size
a b s t r a c t This paper presents the minimum specimen size for experimental determination of the fracture parameters of site-casting dam concrete. Five series of wedge-splitting specimens for dam concrete with maximum aggregate size of 150 mm were tested, casting in the site of an actual super-high arch dam with its mixing tower system. The complete load-crack mouth opening displacement and load-crack tip opening displacement curves of the specimens were acquired. The fracture parameters, including fracture energy, effective fracture toughness, and critical crack tip opening displacement, were also obtained. Furthermore, the effect of specimen size on fracture parameters was discussed, and it was found that the minimum specimen size for determining the independent fracture parameters of the site-casting dam concrete should satisfy that ligament length is six times larger than the maximum aggregate size. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Many 300 m-level super-high concrete arch dams have been built in Southwest China, others are under construction or to be built. These dams include Xiluodu arch dam (285.5 m high), Baihetan arch dam (289 m high), Wudongde arch dam(240 m high), Jinping arch dam(305 m high), and Xiaowan arch dam (295.5 m high) [1–4]. The construction scale, difficulty, and complexity of building super-high arch dams are very high. Dam concrete is required building a 300 m-level super-high arch dam, as a specific type of concrete used for dam construction with maximum aggregate size (dmax) larger than that of normal concrete. Studies on the fracture behavior of dam concrete must be carried out to reasonably evaluate the cracking risk and analyze the
⇑ Corresponding author. Tel.: +86 10 6277 1015; fax: +86 10 6277 3576. E-mail address: [email protected] (Q. Li).
stability of cracks in a dam. Therefore, determining the real fracture parameters of dam concrete is a key problem for dam construction. A large number of experimental studies on the fracture behavior of concrete have shown that the fracture parameters from small size specimens are size dependent [5–9]. Mindess [5] conducted an investigation using three-point bending specimens, with depths of 100 mm, 200 mm, and 400 mm, maximum aggregate size of dmax = 13 mm, and the ratio of initial crack length to depth, i.e. a0/H of approximately 0.5, and concluded that the fracture energies and fracture toughness for the two smaller size beams appeared to be independent of specimen size, but those for the largest size beams increased considerably. Nallthambi [6] tested three-point bending specimens with depths of 140 mm, 200 mm, 240 mm, and 300 mm and dmax = 20 mm, and got the conclusion that for a given a0/H (0.2, 0.3, 0.4, 0.5, and 0.6, respectively), fracture toughness increased as the depth of the specimen increased, whereas the fracture toughness for specimens with a0/H of 0.3 and 0.4 increased
http://dx.doi.org/10.1016/j.conbuildmat.2015.05.060 0950-0618/Ó 2015 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Guan J et al. Minimum specimen size for fracture parameters of site-casting dam concrete. Constr Build Mater (2015), http://dx.doi.org/10.1016/j.conbuildmat.2015.05.060
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(a)
(b)
(c)
(d)
Fig. 1. Actual specimen cast in a construction site of a super-high arch dam: (a) super-high arch dam; (b) mixing tower; (c) casting; (d) curing.
Table 1 Mixture proportion. Cement, (kg/m3)
Fly ash, (kg/ m3)
Water, (kg/ m3)
w/c
129
69
81
0.41
Aggregate (kg/m3)
5–20 (mm)
20–40 (mm)
40–80 (mm)
80–150 (mm)
377
427
599
498
with increasing depth up to 200 mm, and then remained constant. Hillerborg [7] summarized the test data of 700 concrete beams, and found that fracture energy increased with size increasing. Alexander and Blight [8] reported the results of the fracture parameter tests for 69 concrete beams with depths varying from 100 mm to 800 mm, a0/H 0.2, 0.3, 0.4, 0.5, and 0.6, respectively, and dmax = 20 mm that the fracture toughness showed a tendency to increase with increasing specimen size, and postulated that the specimen depth has to be more than 100 mm to achieve a valid fracture test. Brameshuber and Hilsdorf [9] observed that fracture energy increased by 20% when the concrete beam depth increased from 100 mm to 800 mm (with dmax 16 and 32 mm, a0/H 0.5), but that for the mortar beam (with dmax = 2 mm) showed a decreasing tendency when the depth increased up to 200 mm. As far as the real fracture parameter of dam concrete is concerned, only the size of the test specimen could be large enough to a certain value that the fracture parameter stabilizes, and the actual fracture performance of dam concrete can be reasonably evaluated based on the test results by this size of specimen. To confirm the real fracture parameters of dam concrete, the
Sand (kg/m3)
High-range water reducing admixture (kg/m3)
Airentraining agent (kg/m3)
571
1.188
0.0257
Fig. 2. Geometry of notched wedge-splitting specimens.
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Table 2 Dimensions of the wedge-splitting specimens. Specimen
FG800-6 FG1000-6 FG1200-6 FG1500-6 FG2250-6
Number of companion specimens
3 3 3 3 3
Dimensions of wedge splitting specimen
H (mm)
H1 (mm)
W (mm)
a0 (mm)
D (mm)
H2/ dmax
830 1030 1230 1530 2280
800 1000 1200 1500 2250
800 1000 1200 1500 2250
320 400 480 600 900
450 450 450 450 450
3.2 4.0 4.8 6.0 9.0
corresponding size of the specimen is assumed to be the minimum size when these parameters stabilize and stop increasing with the dam size. Several scholars have conducted extensive investigations on the fracture behavior of normal concrete specimens cast in laboratories to obtain fracture parameters independent of size [10–15]. Those results showed that the fracture parameters of normal concrete are dependent on specimen size within a definite range, but independent of specimen size over a certain value. Xu [10] studied the fracture parameters by wedge-splitting specimens with dmax = 10 mm, effective depths H1 = 100 mm, 200 mm, 400 mm, 600 mm, 800 mm, 1000 mm and 1200 mm, respectively, a0/H1 = 0.50, and the ligament length H2 = 75 mm, 100 mm, 200 mm, 300 mm, 400 mm, 500 mm and 600 mm, respectively, and found that the effective fracture toughness K eIc showed no size effect when H1 is over 400 mm corresponding to H2/dmax = 20, and that the calculated critical crack tip opening displacement (CTODc) using the experimental critical crack mouth opening displacement (CMODc) showed no size effect, when H1 is over 1000 mm corresponding to H2/dmax = 50. Xu et al. [11–13] also conducted an investigation by using wedge-splitting test on compact tension specimens with H1 = 200 mm, 300 mm, 400 mm, 600 mm, 800 mm, and 1000 mm, respectively, a0/H1 = 0.40, dmax = 25 and H2 = 120 mm, 180 mm, 240 mm, 360 mm, 480 mm, and 600 mm, respectively, and found that the fracture energy GF was
Fig. 4. Test setup for 2250 mm wedge-splitting specimen.
independent of specimen size when H2/dmax P 14.4 [11], K eIc remained stable when H2/dmax P 9.6 [12], and CTODc did not increase when H2/dmax P 14.4 [13]. Wu et al. [14] tested wedge-splitting specimens with H1 = 200 mm, 400 mm, 500 mm, and 700 mm, respectively, a0/H1 = 0.50, and dmax = 20 mm and found that K eIc was size independent when H2/dmax beyond 12.5, CTODc was size independent when H2/dmax beyond 10. Wittmann [15] conducted an investigation with compact tension specimens with depths H = 375 mm, 750 mm, and 1500 mm, respectively,
Fig. 3. Configuration of the test set-up.
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Fig. 5. Measured curves of P-CMOD: (a) FG800; (b) FG1000; (c) FG1200; (d) FG1500; (e) FG2250.
dmax = 16 mm, H2 = 150 mm, 300 mm, and 600 mm, respectively, and found that GF increased with increasing H2/dmax up to 18.8, and then became constant. Though limit investigation has been conducted on the fracture behavior of dam concrete specimens cast in laboratories to obtain fracture parameters, the same conclusion as normal concrete has been achieved that the fracture parameters of dam concrete are dependent on specimen size within definite range, but independent of the specimen size over a certain value. Saouma [16] conducted an investigation using wedge-splitting specimens with H2 = 200 mm, 610 mm, and 1070 mm, respectively and dmax = 38 mm, and found that GF and K eIc were independent of specimen size when H2/dmax over 5.3, but the calculated values of CTODc were dependent on specimen size in the range of the test specimens [17]. In the study of Zhao [18], the test values of GF for wedge-splitting specimens with H2 = 225 mm, 400 mm, and 500 mm, respectively, and dmax = 80 mm does not increase when H2/dmax over 5.0.
It should be noted that the experimental specimens in the afore-mentioned researches for dam concrete to study the fracture behavior of dam concrete were cast all in laboratories. As known, a laboratory concrete mixer operates with a much lower capacity than a mixer at a construction site and thus produces representative concrete mixtures inferior to those produced by a construction site mixer. The only option when molding specimens with larger volumes and greater quantities in the laboratory is to mix and pour concrete batch by batch using the same mix proportion. Thus, the overall uniformity of the cast specimens in the laboratory by different batches differs from those made on site by a single batch. Meanwhile, the random distribution of aggregates in the dam concrete produced in the laboratory is inferior to that in the construction site. Moreover, the curing conditions differ between the concrete from the laboratory and the construction site. On the contrary, the dam concrete produced by a construction site mixer can be directly used to pour and shape fracture specimens on site, the uniformity, composition, and random
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J. Guan et al. / Construction and Building Materials xxx (2015) xxx–xxx Table 3 Fracture properties of site-casting dam concrete specimens. Specimen
Ph,max (kN)
GF (N/m)
K eIc (MPa m1/2)
Gf (N/m)
GF/Gf
CMODc (mm)
CTODc (mm)
FG800-6-1 FG800-6-2 FG800-6-3 Mean Dispersion coefficient
57.716 60.179 73.615 63.837 0.109
436.32 543.52 534.88 504.907 0.096
1.495 1.694 1.904 1.698 0.098
85.63 109.95 138.90 111.493 0.195
5.10 4.94 3.85 4.630 0.120
0.230 0.275 0.294 0.266 0.101
0.090 0.103 0.121 0.105 0.121
FG1000-6-1 FG1000-6-2 FG1000-6-3 Mean Dispersion coefficient
105.375 88.730 84.680 92.928 0.096
608.94 576.26 516.43 567.210 0.068
1.896 1.951 1.773 1.873 0.040
137.73 145.84 120.44 134.671 0.079
4.42 3.95 4.29 4.220 0.047
0.271 0.325 0.285 0.294 0.078
0.081 0.128 0.108 0.106 0.182
FG1200-6-1 FG1200-6-2 FG1200-6-3 Mean Dispersion coefficient
117.858 112.503 125.397 118.586 0.045
653.17 551.23 727.03 643.810 0.112
1.693 2.017 1.944 1.885 0.074
109.82 155.87 144.79 136.829 0.143
5.95 3.54 5.02 4.835 0.205
0.235 0.339 0.290 0.288 0.148
0.064 0.124 0.082 0.090 0.279
FG1500-6-1 FG1500-6-2 FG1500-6-3 Mean Dispersion coefficient
167.019 129.953 183.972 160.315 0.141
876.24 632.93 – 754.585 0.161
2.853 2.159 3.027 2.680 0.140
311.86 178.59 351.06 280.506 0.263
2.81 3.54 – 3.177 0.116
0.565 0.416 0.583 0.521 0.144
0.180 0.126 0.232 0.179 0.241
FG2250-6-1 FG2250-6-2 FG2250-6-3 Mean Dispersion coefficient
202.733 197.390 192.469 197.531 0.021
795.03 832.37 651.74 759.713 0.102
2.759 2.459 2.312 2.510 0.074
291.65 231.67 204.80 242.709 0.150
2.73 3.59 3.18 3.167 0.112
0.652 0.537 0.495 0.561 0.118
0.221 0.192 0.156 0.190 0.140
800 mm 450 mm, 1000 mm 1000 mm 450 mm, 1200 mm 1200 mm 450 mm, 1500 mm 1500 mm 450 mm, and 2250 mm 2250 mm 450 mm, respectively. The experimental research was conducted to investigate the size effect of dam concrete. The minimum size of specimen for size-independent of fracture parameters of site-casting dam concrete was obtained. 2. Experiment 2.1. Materials
Fig. 6. GF with effective specimen depth.
distribution of aggregates of the specimens can be the same as those of concrete poured in the dam site. Moreover, site-casting specimens can be produced and cast in the same period and kept in the same environmental conditions as the dam itself. Thus, the fracture parameters of dam concrete obtained through an experiment can be directly used to monitor the dam in real time and to simulate the real-time dam behavior numerically. A practical method for casing specimens on site ensuring the one-time pouring and shaping of all dam concrete specimens was presented in Ref. [19]. Till now, very limited research has been conducted on the fracture behavior and the size effect of site-casting dam concrete. The minimum specimen size for determining the fracture parameters of site-casting dam concrete has not been reported in available publications. Accordingly, the objective of this paper is to study the fracture behavior of dam concrete by wedge-splitting specimens cast from a single batch by mixing tower systems of an actual super-high dam in southwest China. The dimensions of the specimen were used with dmax = 150 mm were 800 mm
All test specimens were cast on a construction site of an actual super-high arch dam in southwest China on January 16, 2012, as shown in Fig. 1(a). The concrete mixtures were from the system of the mixing tower at the bank slopes of the arch dam at an altitude of 600 m, as shown in Fig. 1(b). This production of the mixing tower can ensure one-time pouring and shaping of all specimens on site. The concrete mixtures were produced at the same time, transported and kept under the same conditions as the dam concrete. Wood molds were placed at the bank slopes of the arch dam as support. The concrete mixtures were transported from the mixing tower to the casting site through side discharging cars. The casting dam concrete specimens are shown in Fig. 1(c), and the curing of dam concrete specimens is shown in Fig. 1(d). The mixture proportion for dam concrete is given in Table 1. Type I Portland cement was used in all mixtures. The mixtures contained fly ash to save cement and reduce the heat of hydration for practical applications. Crushed basalt with sizes ranging from 5 mm to 150 mm was used as coarse aggregate. River sand was used as the fine aggregate. A high-range water-reducing admixture was used to achieve good workability. The air contents were approximately 5.0–6.0%. The compressive strength, splitting tensile strength, and elastic modulus of the dam concrete were determined based on an average result of three identical 450 mm 450 mm 450 mm cubes at the age of 180 days. All cubes for the compressive strength and elastic modulus tests were treated with antifriction. The measured compressive strength of dam concrete was 29.37 MPa, correspondingly. The measured splitting tensile strength of dam concrete was 3.04 MPa, and the measured elastic modulus was 26.12 GPa. 2.2. Specimens Five groups of specimens with different sizes, denoted by FG800, FG1000, FG1200, FG1500, and FG2250, were cast in this program. The geometry of the wedge- splitting specimens is shown in Fig. 2, in which, H denotes the depth of a wedge- splitting specimen, H1 denotes the effective depth, H2 denotes the ligament length, and W denotes the width of the specimen with W = H1. And the ratios H2/dmax for each group are 3.2, 4.0, 4.8, 6.0, and 9.0, respectively. The detail dimensions of the specimens are listed in Table 2.
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Table 4 Values of H2/dmax for stable GF.
*
Reference
dmax (mm)
fc (MPa)
ft (MPa)
E (GPa)
H2/dmax
GF (N/m)
H2/dmax for GF being constant
Test method
Wittmann [15]
16
42.9
–
–
CTT
25
53.3
5.21
14.4
WST
Saouma [16]
38
24.8
2.67
35.54 34.01 33.04 32.97 32.06 28.54 16.9
5.3
WST
Zhao [18]*
80
51.7
–
39.6
5.0
WST
This paper
150
29.37
3.04
26.12
124 162 158 173 199 194 225 203 230 238 223 259 470 660 600 504.907 567.210 643.810 754.585 759.713
18.8
Xu [11]
9.4 18.8 37.5 4.8 7.2 9.6 14.4 19.2 24.0 5.3 16.1 28.2 2.8 5.0 6.3 3.2 4.0 4.8 6.0 9.0
6.0
WST
GF was obtained from the figures in Ref. 18.
Fig. 7. GF/fc with dmax. Fig. 8. K eIc with effective specimen depth. 2.3. Test set-up The tests were conducted in a computer-controlled servo-hydraulic closed-loop testing machine with 10,000 kN load capacity. Load cells with capacity of 100 kN and 300 kN were used to measure the applied load (P). The clip gauge was used to measure the crack mouth opening displacement (CMOD), whereas the clip gauge installed at the tip of the notch was used to measure the crack tip opening displacement (CTOD). Two hinge roller supports were located at 65 mm from the center of the specimen, as shown in Fig. 3. Two massive steel loading devices, both equipped with roller bearings on each side, were placed on top of the specimen; the roller bearing is also located at 65 mm from the center of the specimen. A stiff steel profile with two identical wedges was fixed at the upper plate of the testing machine. The wedges were centered between the roller bearings on each side, thereby applying a horizontal splitting force (Ph). Ph is the horizontal component of the force acting on the roller bearings, and calculated by considering the wedge angle (h):
Ph ¼
P 2 tan h
ð1Þ
where P is the applied force and h is the wedge angle, which is 15° in the test set-up. Frictional forces were reduced and can be neglected by using the roller bearings with a low coefficient of friction and carefully polishing the wedge surface [16]. The actual wedge-splitting specimen and test set-up is shown in Fig. 4.
3. Results and discussions In this paper, each test was performed at the age of 180 days, and finished within 10 days. Since the mechanical properties of
dam concrete exhibited a slight change as specimen age was increased, the effect of specimen age was neglected in this discussion. 3.1. Fracture energy In this experimental study, the testing was stopped until prefabricated crack fully extended, resulting in a characteristic plateau on the load-crack mouth opening displacement (P-CMOD) diagram. The complete P-CMOD curves of site-casting dam concrete are shown in Fig. 5; wherein for the FG1500-3 specimen, only the ascending branch of P-CMOD curves was obtained. The fracture energies GF for the wedge-splitting specimen was calculated based on the total work of the area under the Ph-CMOD curve and unit crack surface. The GF for site-casting dam concrete are listed in Table 3. The variation of fracture energies GF with H1 is shown in Fig. 6. This result indicates that GF does not increase with increasing H1 when H1 approaches 1500 mm, as shown in Fig. 6, that is to say, GF shows a characteristic plateau and is independent of specimen size when H1 is over 1500 mm corresponding to H2/dmax P 6.0. The mean value of GF of site-casting dam concrete specimens is 757.662 N/m.
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J. Guan et al. / Construction and Building Materials xxx (2015) xxx–xxx Table 5 Values of H2/dmax for K eIc being constant. Reference
dmax (mm)
fc (MPa)
ft (MPa)
E (GPa)
H2/dmax
K eIc (MPa m1/2)
H2/dmax for K eIc being constant
Test method
Xu [10]
10
29.56
–
29.64
WST
20
33.2
3.3
31.2
12.5
WST
Xu [12]
25
53.3
5.21
9.6
WST
Saouma [16]
38
24.8
2.67
35.54 34.01 33.04 32.97 32.06 28.54 16.9
5.3
WST
This paper
150
29.37
3.04
26.12
0.861 0.987 1.339 1.446 1.455 1.387 1.256 1.433 1.884 2.009 1.982 1.696 1.690 1.728 1.774 1.730 1.743 0.86 0.99 1.23 1.698 1.873 1.885 2.680 2.510
20.0
Wu [14]
7.5 10.0 20.0 30.0 40.0 50.0 60.0 5.0 10.0 12.5 17.5 4.8 7.2 9.6 14.4 19.2 24.0 5.3 16.1 28.2 3.2 4.0 4.8 6.0 9.0
6.0
WST
The test results of GF got in this paper and those reported by other authors (Xu et al. [11]; Wittmann et al. [15]; Saouma [16] and Zhao et al. [18]), through a wedge-splitting test (WST) or compact tension test (CTT), are all listed in Table 4. It can be seen that the values of H2/dmax for stable GF decrease with increasing of dmax. These values got in this paper are similar to those from Saouma [16] and Zhao [18], with a difference in the exact value of H2/dmax since the dmax in Refs. [11,16] are relatively smaller, 25 mm and 16 mm, respectively. An empirical formula for stable fracture energy changing with the maximum aggregate size (dmax) and the compressive strength (fc) is obtained:
GF ¼ ð0:1616dmax þ 1:0263Þf c
ð2Þ
With a mean ratio of the test value to the calculated value from the formula is 1.034, and the dispersion coefficient is 0.175. A formula recommended by Comité Euro-International du Béton was proposed in its CEB-FIP Model Code [20]:
f 0:7 2 c GF ¼ 0:0469dmax 0:5dmax þ 26 10
ð3Þ
As shown in Fig. 7, the calculated value from the formula in this study is consistent with the test value. The recommended formula by CEB-FIP Model Code obtains large deviations for the estimation of stable fracture energy with dmax P 80 mm. 3.2. Effective fracture toughness K eIc In the present study, the effective fracture toughness K eIc is determined by the maximum horizontally applied force Ph,max and the effective crack length ac. There are many methods for determining the values of ac. Jenq and Shah [21] proposed an unloading and reloading procedure performed with a closed-loop system to evaluate the ac in the two parameter fracture model (TPFM). Karihaloo and Nallathambi [22] proposed a regression expression to calculate ac in the effective crack model (ECM). Xu and Reinhardt [23] introduced a linear asymptotic superposition assumption and proposed another method for determining the effective crack length ac for nonstandard wedge-splitting specimen
according to experimental P-CMOD curves, the formula can be expressed as follows to evaluate the ac for nonstandard wedge-splitting specimen [24]:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi# CMODc E D 1 13:18 þ 9:16 Ph;max
" ac ¼ H1
ð4Þ
where ac is the crack length corresponding to Ph,max, CMODc is the crack opening displacement corresponding to Ph,max, and E is the elastic modulus of the concrete. Based on the ac value, the value of K eIc of every specimen can be numerically computed using the finite element method. The crack tip was modeled using a rosette with singular elements [25]. Because high stress gradients exist in the region around crack tip, special attention should be paid in that region. Therefore, a circle was set at the tip of crack, in which the crack tip is the center of the circle and the radius of the circle is 6 mm. The first row of elements around the crack tip had a radius of 3/2 mm, and their mid-side nodes were placed at the quarter points, i.e. had a radius of 3/8 mm [26–28]. The stress condition was assumed as plane stress [29]. The Poisson’s ratio and density are 0.18 and 2663 kg/m3, respectively, which were employed from the material parameter test for the super-high arch dam. The other parameters were determined through the experiment in this paper. The results of effective fracture toughness K eIc are shown in Table 3 and in Fig. 8. It can be seen that K eIc shows a plateau trend and does not increase when H1 approaches to 1500 mm, that is to say, K eIc tends to be stabilized and is independent of specimen size when H2/dmax P 6.0. The mean stable K eIc value of site-casting dam concrete specimens is 2.595 MPa m1/2. Table 5 lists the experimental results from this paper and from other authors (Xu et al. [10]; Xu et al. [12]; Wu et al. [14] and Saouma [16]). The value of K eIc from Ref. [16] was obtained using the compliance method. K eIc appears to increase slightly with increasing specimen size. However, taking into consideration the scatter of as much as 20% in the evaluated fracture toughness values using the compliance method, K eIc can be considered to be size independent. These results also indicate that the value of H2/dmax corresponding to stable K eIc decreases with the increase of dmax.
Please cite this article in press as: Guan J et al. Minimum specimen size for fracture parameters of site-casting dam concrete. Constr Build Mater (2015), http://dx.doi.org/10.1016/j.conbuildmat.2015.05.060
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Fig. 9. Measured curves of P-CTOD: (a) FG800; (b) FG1000; (c) FG1200; (d) FG1500; (e) FG2250.
Specific fracture energy (Gf) corresponds to the area under the initial tangent of the softening stress-separation curve [30]. It plays a more important role in the finite element analysis of concrete structures. If the K eIc of dam concrete is solved, the following formula can be used to calculate Gf: 2
Gf ¼
ðK eIc Þ E
ð5Þ
The calculated Gf of the results got in this paper is shown in Table 3. Bazˇant [30] estimated that GF/Gf ranged from 2.0 to 2.5. The GF/Gf ratio of site-casting dam concrete poured in the site is from 3.167 to 4.835, which is different from those found in previous studies. 3.3. Critical crack tip opening displacement (CTODc)
Fig. 10. CTODc with effective specimen depth.
The experimental P-CTOD curves of site-casting dam concrete are shown in Fig. 9; wherein, only the ascending branch of
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J. Guan et al. / Construction and Building Materials xxx (2015) xxx–xxx Table 6 Values of H2/dmax for CTODc being constant. Reference
dmax (mm)
fc (MPa)
ft (MPa)
E (GPa)
H2/dmax
CTODc (mm)
H2/dmax for CTODc being constant
Test method
10
29.56
–
29.64
WST
20
33.2
3.3
31.2
10.0
WST
Xu [13]
25
53.3
5.21
14.4
WST
This paper
150
29.37
3.04
35.54 34.01 32.97 32.06 28.54 26.12
0.0196 0.0269 0.0455 0.0565 0.0648 0.0705 0.0613 0.0125 0.0282 0.0296 0.0294 0.0328 0.0415 0.0551 0.0605 0.0594 0.105 0.106 0.090 0.179 0.190
40.0
Wu [14]*
7.5 10.0 20.0 30.0 40.0 50.0 60.0 5.0 10.0 12.5 17.5 4.8 7.2 14.4 19.2 24.0 3.2 4.0 4.8 6.0 9.0
6.0
WST
Xu [10]
*
*
CTODc was obtained based on the experimental CMODc.
P-CTOD curves was obtained for specimens of FG1500-3 and FG2250-2. In which, the CTODc corresponds to the peak load. Fig. 10 shows the variation of CTODc with H1 of specimens. CTODc tends toward stable when H1 approaches 1500 mm, as shown in Fig. 10; that is, CTODc is independent of specimen size when H2/dmax P 6.0. The mean stable CTODc value of site-casting dam concrete specimens is 0.185 mm. The experimental results got in this paper and those reported by different authors (Xu et al. [10]; Xu et al. [13]; and Wu et al. [14]) are all listed in Table 6. The results show that the value of H2/dmax corresponding to stable CTODc decreases with the increase of dmax. 4. Conclusions To determine the minimum specimen size for the fracture parameters of the site-casting dam concrete, five groups of wedge-splitting specimens with different sizes were cast at the same time using mixing tower systems of an actual super-high arch dam in China. The dimensions of the specimen with dmax = 150 mm were 800 mm 800 mm 450 mm, 1000 mm 1000 mm 450 mm, 1200 mm 1200 mm 450 mm, 1500 mm 1500 mm 450 mm, and 2250 mm 2250 mm 450 mm, respectively. This paper has shown that it is possible to cast the test specimens at the construction site to obtain the real fracture parameters of a super-high arch dam, and the fracture parameters of the site-casting dam concrete obtained in this paper are significantly different from those of other studies. The following conclusions can be drawn: 1. The variations of fracture parameters with effective size of specimens were analyzed. The results show that the fracture parameters for site-casting dam concrete, including fracture energy (GF), effective fracture toughness (K eIc ) and critical crack tip opening displacement (CTODc), remains stable and appears independent of specimen size when the effective depth H1 over 1500 mm, corresponding to the ratio of ligament length versus maximum aggregate size H2/dmax P 6.0. That is to say, the minimum specimen size for site-casting dam concrete should satisfy the requirement that H2 is six times larger than dmax.
2. The mean values of the stable GF, K eIc and CTODc for site-casting dam concrete specimens investigated in this research, are 757.662 N/m, 2.595 MPa m1/2 and 0.185 mm, respectively. It should be pointed out that the above conclusions were true only for the dam concrete investigated in this study, other types of dam concrete need further testing. The stable fracture parameters of the site-casting dam concrete can represent the real fracture properties of the super-high arch dam and can be directly applied to the super-high arch dam. Acknowledgements The financial supports for this research provided by the National Natural Science Foundation of China (Nos. 51339003, 51209094, 51478084, and 51478083) and the State Key Laboratory of Coastal and Offshore Engineering Foundation of China (No. LP1211) are gratefully acknowledged. References [1] Li QB, Guan JF, Wu ZM, Dong W, Zhou SW. Fracture behavior of site-casting dam concrete. ACI Mater J 2015;112(1):11–20. [2] Li QB, Lin P. Demonstration on intelligent dam. J Hydropower Eng 2014;33(1):139–46 (in Chinese with English summary). [3] Guan JF, Zhu XX, Lin P, Li QB. Study on the individual control for cantilever height of super-high arch dams. J Hydraulic Eng 2013;44(1):97–103 (in Chinese with English summary). [4] Guan JF, Li QB, Wu ZM. Determination of fully-graded hydraulic concrete fracture parameters by peak-load method. Eng Mech 2014;31(8):8–13 (in Chinese with English summary). [5] Mindess A. The effect of specimen size on the fracture energy of concrete. Cem Concr Res 1984;14(3):431–6. [6] Nallthambi P, Karihaloo B, Heaton B. Effect of specimen and crack sizes, water/ cement ratio and coarse aggregate texture upon fracture toughness of concrete. Mag Concrete Res 1984;36(129):227–36. [7] Hillerborg A. Results of three comparative test series for determining the fracture energy GF of concrete. Mater Struct 1985;18(5):407–13. [8] Alexander MG, Blight GE. A comparative study of fracture parameters in notched concrete beams. Mag Concrete Res 1988;40(142):50–8. [9] Brameshuber W, Hilsdorf H. Influence of ligament length and stress state on fracture energy of concrete. Eng Fract Mech 1990;35(1/3):95–106. [10] Xu SL, Zhang XF, Zheng S. Experimental measurement of double-K fracture parameters of concrete with small size aggregate. J Hydraulic Eng 2006;37(5):543–53 (in Chinese with English summary).
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[11] Xu SL, Bu D, Zhang XF. Determination of fracture energy of concrete using wedge-splitting test on compact tension specimens. J Hydraulic Eng 2007;38(6):683–9 (in Chinese with English summary). [12] Xu SL, Dan Bu, Zhang XF. A study on double-K fracture parameters by using wedge-splitting test on compact tension specimens of various sizes. Chin Civ Eng J 2008;41(2):70–6 (in Chinese with English summary). [13] Xu SL, Zhang XF, Bu D. Relationship between crack tip opening displacement (CTOD) and crack mouth opening displacement (CMOD) throughout development of concrete crack. Eng Mech 2011;28(5):64–70 (in Chinese with English summary). [14] Wu ZM, Xu SL, Wang JL. Fracture parameter of concrete based on the fictitious crack model. J Hydraulic Eng 1999;30(7):12–6 (in Chinese with English summary). [15] Wittmann FH, Mihashi H, Nomura N. Size effect on fracture energy of concrete. Eng Fract Mech 1990;35(1/3):107–15. [16] Saouma VE, Broz JJ, Brühwiler E, Boggs HL. Effect of aggregate and specimen size on fracture properties of dam concrete. J Mater Civil Eng ASCE 1991;3(3):204–18. [17] Broz JJ, Brühwiler E, Saouma VE. Fracture model evaluation of dam concrete. J Mater Civil Eng ASCE 1991;3(4):235–51. [18] Zhao Z, Kwon SH, Shah SP. Effect of specimen size on fracture energy and softening curve of concrete: Part I. experiments and fracture energy. Cem Concr Res 2008;38(8/9):1049–60. [19] Guan JF, Li QB, Wu ZM, Zhou SW. The necessity and feasible way of studying the true fracture parameters of super-high arch dam concrete. J Hydropower Eng 2014;33(5):152–8 (in Chinese with English summary). [20] Comité Euro-International du Béton. CEB-FIP Model Code 1990. London: Thomas Telford; 1991.
[21] Jenq YS, Shah SP. Two parameter fracture model for concrete. J Eng Mech ASCE 1985;111(10):1227–41. [22] Karihaloo BL, Nallathambi P. Effective crack model for the determination of fracture toughness (Ke IC) of concrete. Eng Fract Mech 1990;35(4/5):637–45. [23] Xu SL, Reinhardt HW. Determination of double-K criterion for crack propagation in quasi-brittle fracture, part II: analytical evaluating and practical measuring methods for three-point bending notched beams. Int J Fract 1999;98(2):151–77. [24] Xu SL, Reinhardt HW. Determination of Double-K criterion for crack propagation in quasi-brittle fracture, Part III: compact tension specimens and wedge splitting specimens. Int J Fract 1999;98(2):179–93. ˇ outil L. Two-parameter fracture mechanical analysis of a [25] Seitl S, Vesely´ V, R near-crack-tip stress field in wedge splitting test specimens. Comput Struct 2011;89(21/22):1852–8. [26] Dong W, Wu ZM, Zhou XM. Calculating crack extension resistance of concrete based on a new crack propagation criterion. Constr Build Mater 2013;38(1):879–89. [27] Dong W, Zhou XM, Wu ZM. On fracture process zone and crack extension resistance of concrete based on initial fracture toughness. Constr Build Mater 2013;49:352–63. [28] Dong W, Zhou XM, Wu ZM. A fracture mechanics-based method for prediction of cracking of circular and elliptical concrete rings under restrained shrinkage. Eng Fract Mech 2014;131:687–701. [29] Gopalaratnam VS, Ye BS. Numerical characterization of the nonlinear fracture process in concrete. Eng Fract Mech 1991;40(6):991–1006. [30] Bazˇant ZP, Becq-Giraudon E. Statistical prediction fracture parameters of concrete and implications or choice of testing standard. Cem Concr Res 2002;32(4):529–56.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Minimum specimen size for fracture parameters of site-casting dam concrete Junfeng Guan a,b,c, Qingbin Li b,⇑, Zhimin Wu c, Shunbo Zhao a, Wei Dong c, Shaowu Zhou d a
School of Civil Engineering and Communication, North China University of Water Resources and Electric Power, Zhengzhou 450011, PR China State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, PR China c State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, PR China d China Three Gorges Corporation, Beijing 100038, PR China b
h i g h l i g h t s All specimens were cast at one-time by mixing tower system of an arch dam. The complete P-CMOD and P-CTOD curves of dam concrete were obtained. Independent fracture parameters of dam concrete were obtained. The minimum specimen size for dam concrete was determined.
a r t i c l e
i n f o
Article history: Received 25 December 2014 Received in revised form 27 March 2015 Accepted 1 May 2015 Available online xxxx Keywords: Dam concrete Site-casting One-time pouring Fracture parameters Minimum specimen size
a b s t r a c t This paper presents the minimum specimen size for experimental determination of the fracture parameters of site-casting dam concrete. Five series of wedge-splitting specimens for dam concrete with maximum aggregate size of 150 mm were tested, casting in the site of an actual super-high arch dam with its mixing tower system. The complete load-crack mouth opening displacement and load-crack tip opening displacement curves of the specimens were acquired. The fracture parameters, including fracture energy, effective fracture toughness, and critical crack tip opening displacement, were also obtained. Furthermore, the effect of specimen size on fracture parameters was discussed, and it was found that the minimum specimen size for determining the independent fracture parameters of the site-casting dam concrete should satisfy that ligament length is six times larger than the maximum aggregate size. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Many 300 m-level super-high concrete arch dams have been built in Southwest China, others are under construction or to be built. These dams include Xiluodu arch dam (285.5 m high), Baihetan arch dam (289 m high), Wudongde arch dam(240 m high), Jinping arch dam(305 m high), and Xiaowan arch dam (295.5 m high) [1–4]. The construction scale, difficulty, and complexity of building super-high arch dams are very high. Dam concrete is required building a 300 m-level super-high arch dam, as a specific type of concrete used for dam construction with maximum aggregate size (dmax) larger than that of normal concrete. Studies on the fracture behavior of dam concrete must be carried out to reasonably evaluate the cracking risk and analyze the
⇑ Corresponding author. Tel.: +86 10 6277 1015; fax: +86 10 6277 3576. E-mail address: [email protected] (Q. Li).
stability of cracks in a dam. Therefore, determining the real fracture parameters of dam concrete is a key problem for dam construction. A large number of experimental studies on the fracture behavior of concrete have shown that the fracture parameters from small size specimens are size dependent [5–9]. Mindess [5] conducted an investigation using three-point bending specimens, with depths of 100 mm, 200 mm, and 400 mm, maximum aggregate size of dmax = 13 mm, and the ratio of initial crack length to depth, i.e. a0/H of approximately 0.5, and concluded that the fracture energies and fracture toughness for the two smaller size beams appeared to be independent of specimen size, but those for the largest size beams increased considerably. Nallthambi [6] tested three-point bending specimens with depths of 140 mm, 200 mm, 240 mm, and 300 mm and dmax = 20 mm, and got the conclusion that for a given a0/H (0.2, 0.3, 0.4, 0.5, and 0.6, respectively), fracture toughness increased as the depth of the specimen increased, whereas the fracture toughness for specimens with a0/H of 0.3 and 0.4 increased
http://dx.doi.org/10.1016/j.conbuildmat.2015.05.060 0950-0618/Ó 2015 Elsevier Ltd. All rights reserved.
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(a)
(b)
(c)
(d)
Fig. 1. Actual specimen cast in a construction site of a super-high arch dam: (a) super-high arch dam; (b) mixing tower; (c) casting; (d) curing.
Table 1 Mixture proportion. Cement, (kg/m3)
Fly ash, (kg/ m3)
Water, (kg/ m3)
w/c
129
69
81
0.41
Aggregate (kg/m3)
5–20 (mm)
20–40 (mm)
40–80 (mm)
80–150 (mm)
377
427
599
498
with increasing depth up to 200 mm, and then remained constant. Hillerborg [7] summarized the test data of 700 concrete beams, and found that fracture energy increased with size increasing. Alexander and Blight [8] reported the results of the fracture parameter tests for 69 concrete beams with depths varying from 100 mm to 800 mm, a0/H 0.2, 0.3, 0.4, 0.5, and 0.6, respectively, and dmax = 20 mm that the fracture toughness showed a tendency to increase with increasing specimen size, and postulated that the specimen depth has to be more than 100 mm to achieve a valid fracture test. Brameshuber and Hilsdorf [9] observed that fracture energy increased by 20% when the concrete beam depth increased from 100 mm to 800 mm (with dmax 16 and 32 mm, a0/H 0.5), but that for the mortar beam (with dmax = 2 mm) showed a decreasing tendency when the depth increased up to 200 mm. As far as the real fracture parameter of dam concrete is concerned, only the size of the test specimen could be large enough to a certain value that the fracture parameter stabilizes, and the actual fracture performance of dam concrete can be reasonably evaluated based on the test results by this size of specimen. To confirm the real fracture parameters of dam concrete, the
Sand (kg/m3)
High-range water reducing admixture (kg/m3)
Airentraining agent (kg/m3)
571
1.188
0.0257
Fig. 2. Geometry of notched wedge-splitting specimens.
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Table 2 Dimensions of the wedge-splitting specimens. Specimen
FG800-6 FG1000-6 FG1200-6 FG1500-6 FG2250-6
Number of companion specimens
3 3 3 3 3
Dimensions of wedge splitting specimen
H (mm)
H1 (mm)
W (mm)
a0 (mm)
D (mm)
H2/ dmax
830 1030 1230 1530 2280
800 1000 1200 1500 2250
800 1000 1200 1500 2250
320 400 480 600 900
450 450 450 450 450
3.2 4.0 4.8 6.0 9.0
corresponding size of the specimen is assumed to be the minimum size when these parameters stabilize and stop increasing with the dam size. Several scholars have conducted extensive investigations on the fracture behavior of normal concrete specimens cast in laboratories to obtain fracture parameters independent of size [10–15]. Those results showed that the fracture parameters of normal concrete are dependent on specimen size within a definite range, but independent of specimen size over a certain value. Xu [10] studied the fracture parameters by wedge-splitting specimens with dmax = 10 mm, effective depths H1 = 100 mm, 200 mm, 400 mm, 600 mm, 800 mm, 1000 mm and 1200 mm, respectively, a0/H1 = 0.50, and the ligament length H2 = 75 mm, 100 mm, 200 mm, 300 mm, 400 mm, 500 mm and 600 mm, respectively, and found that the effective fracture toughness K eIc showed no size effect when H1 is over 400 mm corresponding to H2/dmax = 20, and that the calculated critical crack tip opening displacement (CTODc) using the experimental critical crack mouth opening displacement (CMODc) showed no size effect, when H1 is over 1000 mm corresponding to H2/dmax = 50. Xu et al. [11–13] also conducted an investigation by using wedge-splitting test on compact tension specimens with H1 = 200 mm, 300 mm, 400 mm, 600 mm, 800 mm, and 1000 mm, respectively, a0/H1 = 0.40, dmax = 25 and H2 = 120 mm, 180 mm, 240 mm, 360 mm, 480 mm, and 600 mm, respectively, and found that the fracture energy GF was
Fig. 4. Test setup for 2250 mm wedge-splitting specimen.
independent of specimen size when H2/dmax P 14.4 [11], K eIc remained stable when H2/dmax P 9.6 [12], and CTODc did not increase when H2/dmax P 14.4 [13]. Wu et al. [14] tested wedge-splitting specimens with H1 = 200 mm, 400 mm, 500 mm, and 700 mm, respectively, a0/H1 = 0.50, and dmax = 20 mm and found that K eIc was size independent when H2/dmax beyond 12.5, CTODc was size independent when H2/dmax beyond 10. Wittmann [15] conducted an investigation with compact tension specimens with depths H = 375 mm, 750 mm, and 1500 mm, respectively,
Fig. 3. Configuration of the test set-up.
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Fig. 5. Measured curves of P-CMOD: (a) FG800; (b) FG1000; (c) FG1200; (d) FG1500; (e) FG2250.
dmax = 16 mm, H2 = 150 mm, 300 mm, and 600 mm, respectively, and found that GF increased with increasing H2/dmax up to 18.8, and then became constant. Though limit investigation has been conducted on the fracture behavior of dam concrete specimens cast in laboratories to obtain fracture parameters, the same conclusion as normal concrete has been achieved that the fracture parameters of dam concrete are dependent on specimen size within definite range, but independent of the specimen size over a certain value. Saouma [16] conducted an investigation using wedge-splitting specimens with H2 = 200 mm, 610 mm, and 1070 mm, respectively and dmax = 38 mm, and found that GF and K eIc were independent of specimen size when H2/dmax over 5.3, but the calculated values of CTODc were dependent on specimen size in the range of the test specimens [17]. In the study of Zhao [18], the test values of GF for wedge-splitting specimens with H2 = 225 mm, 400 mm, and 500 mm, respectively, and dmax = 80 mm does not increase when H2/dmax over 5.0.
It should be noted that the experimental specimens in the afore-mentioned researches for dam concrete to study the fracture behavior of dam concrete were cast all in laboratories. As known, a laboratory concrete mixer operates with a much lower capacity than a mixer at a construction site and thus produces representative concrete mixtures inferior to those produced by a construction site mixer. The only option when molding specimens with larger volumes and greater quantities in the laboratory is to mix and pour concrete batch by batch using the same mix proportion. Thus, the overall uniformity of the cast specimens in the laboratory by different batches differs from those made on site by a single batch. Meanwhile, the random distribution of aggregates in the dam concrete produced in the laboratory is inferior to that in the construction site. Moreover, the curing conditions differ between the concrete from the laboratory and the construction site. On the contrary, the dam concrete produced by a construction site mixer can be directly used to pour and shape fracture specimens on site, the uniformity, composition, and random
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J. Guan et al. / Construction and Building Materials xxx (2015) xxx–xxx Table 3 Fracture properties of site-casting dam concrete specimens. Specimen
Ph,max (kN)
GF (N/m)
K eIc (MPa m1/2)
Gf (N/m)
GF/Gf
CMODc (mm)
CTODc (mm)
FG800-6-1 FG800-6-2 FG800-6-3 Mean Dispersion coefficient
57.716 60.179 73.615 63.837 0.109
436.32 543.52 534.88 504.907 0.096
1.495 1.694 1.904 1.698 0.098
85.63 109.95 138.90 111.493 0.195
5.10 4.94 3.85 4.630 0.120
0.230 0.275 0.294 0.266 0.101
0.090 0.103 0.121 0.105 0.121
FG1000-6-1 FG1000-6-2 FG1000-6-3 Mean Dispersion coefficient
105.375 88.730 84.680 92.928 0.096
608.94 576.26 516.43 567.210 0.068
1.896 1.951 1.773 1.873 0.040
137.73 145.84 120.44 134.671 0.079
4.42 3.95 4.29 4.220 0.047
0.271 0.325 0.285 0.294 0.078
0.081 0.128 0.108 0.106 0.182
FG1200-6-1 FG1200-6-2 FG1200-6-3 Mean Dispersion coefficient
117.858 112.503 125.397 118.586 0.045
653.17 551.23 727.03 643.810 0.112
1.693 2.017 1.944 1.885 0.074
109.82 155.87 144.79 136.829 0.143
5.95 3.54 5.02 4.835 0.205
0.235 0.339 0.290 0.288 0.148
0.064 0.124 0.082 0.090 0.279
FG1500-6-1 FG1500-6-2 FG1500-6-3 Mean Dispersion coefficient
167.019 129.953 183.972 160.315 0.141
876.24 632.93 – 754.585 0.161
2.853 2.159 3.027 2.680 0.140
311.86 178.59 351.06 280.506 0.263
2.81 3.54 – 3.177 0.116
0.565 0.416 0.583 0.521 0.144
0.180 0.126 0.232 0.179 0.241
FG2250-6-1 FG2250-6-2 FG2250-6-3 Mean Dispersion coefficient
202.733 197.390 192.469 197.531 0.021
795.03 832.37 651.74 759.713 0.102
2.759 2.459 2.312 2.510 0.074
291.65 231.67 204.80 242.709 0.150
2.73 3.59 3.18 3.167 0.112
0.652 0.537 0.495 0.561 0.118
0.221 0.192 0.156 0.190 0.140
800 mm 450 mm, 1000 mm 1000 mm 450 mm, 1200 mm 1200 mm 450 mm, 1500 mm 1500 mm 450 mm, and 2250 mm 2250 mm 450 mm, respectively. The experimental research was conducted to investigate the size effect of dam concrete. The minimum size of specimen for size-independent of fracture parameters of site-casting dam concrete was obtained. 2. Experiment 2.1. Materials
Fig. 6. GF with effective specimen depth.
distribution of aggregates of the specimens can be the same as those of concrete poured in the dam site. Moreover, site-casting specimens can be produced and cast in the same period and kept in the same environmental conditions as the dam itself. Thus, the fracture parameters of dam concrete obtained through an experiment can be directly used to monitor the dam in real time and to simulate the real-time dam behavior numerically. A practical method for casing specimens on site ensuring the one-time pouring and shaping of all dam concrete specimens was presented in Ref. [19]. Till now, very limited research has been conducted on the fracture behavior and the size effect of site-casting dam concrete. The minimum specimen size for determining the fracture parameters of site-casting dam concrete has not been reported in available publications. Accordingly, the objective of this paper is to study the fracture behavior of dam concrete by wedge-splitting specimens cast from a single batch by mixing tower systems of an actual super-high dam in southwest China. The dimensions of the specimen were used with dmax = 150 mm were 800 mm
All test specimens were cast on a construction site of an actual super-high arch dam in southwest China on January 16, 2012, as shown in Fig. 1(a). The concrete mixtures were from the system of the mixing tower at the bank slopes of the arch dam at an altitude of 600 m, as shown in Fig. 1(b). This production of the mixing tower can ensure one-time pouring and shaping of all specimens on site. The concrete mixtures were produced at the same time, transported and kept under the same conditions as the dam concrete. Wood molds were placed at the bank slopes of the arch dam as support. The concrete mixtures were transported from the mixing tower to the casting site through side discharging cars. The casting dam concrete specimens are shown in Fig. 1(c), and the curing of dam concrete specimens is shown in Fig. 1(d). The mixture proportion for dam concrete is given in Table 1. Type I Portland cement was used in all mixtures. The mixtures contained fly ash to save cement and reduce the heat of hydration for practical applications. Crushed basalt with sizes ranging from 5 mm to 150 mm was used as coarse aggregate. River sand was used as the fine aggregate. A high-range water-reducing admixture was used to achieve good workability. The air contents were approximately 5.0–6.0%. The compressive strength, splitting tensile strength, and elastic modulus of the dam concrete were determined based on an average result of three identical 450 mm 450 mm 450 mm cubes at the age of 180 days. All cubes for the compressive strength and elastic modulus tests were treated with antifriction. The measured compressive strength of dam concrete was 29.37 MPa, correspondingly. The measured splitting tensile strength of dam concrete was 3.04 MPa, and the measured elastic modulus was 26.12 GPa. 2.2. Specimens Five groups of specimens with different sizes, denoted by FG800, FG1000, FG1200, FG1500, and FG2250, were cast in this program. The geometry of the wedge- splitting specimens is shown in Fig. 2, in which, H denotes the depth of a wedge- splitting specimen, H1 denotes the effective depth, H2 denotes the ligament length, and W denotes the width of the specimen with W = H1. And the ratios H2/dmax for each group are 3.2, 4.0, 4.8, 6.0, and 9.0, respectively. The detail dimensions of the specimens are listed in Table 2.
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J. Guan et al. / Construction and Building Materials xxx (2015) xxx–xxx
Table 4 Values of H2/dmax for stable GF.
*
Reference
dmax (mm)
fc (MPa)
ft (MPa)
E (GPa)
H2/dmax
GF (N/m)
H2/dmax for GF being constant
Test method
Wittmann [15]
16
42.9
–
–
CTT
25
53.3
5.21
14.4
WST
Saouma [16]
38
24.8
2.67
35.54 34.01 33.04 32.97 32.06 28.54 16.9
5.3
WST
Zhao [18]*
80
51.7
–
39.6
5.0
WST
This paper
150
29.37
3.04
26.12
124 162 158 173 199 194 225 203 230 238 223 259 470 660 600 504.907 567.210 643.810 754.585 759.713
18.8
Xu [11]
9.4 18.8 37.5 4.8 7.2 9.6 14.4 19.2 24.0 5.3 16.1 28.2 2.8 5.0 6.3 3.2 4.0 4.8 6.0 9.0
6.0
WST
GF was obtained from the figures in Ref. 18.
Fig. 7. GF/fc with dmax. Fig. 8. K eIc with effective specimen depth. 2.3. Test set-up The tests were conducted in a computer-controlled servo-hydraulic closed-loop testing machine with 10,000 kN load capacity. Load cells with capacity of 100 kN and 300 kN were used to measure the applied load (P). The clip gauge was used to measure the crack mouth opening displacement (CMOD), whereas the clip gauge installed at the tip of the notch was used to measure the crack tip opening displacement (CTOD). Two hinge roller supports were located at 65 mm from the center of the specimen, as shown in Fig. 3. Two massive steel loading devices, both equipped with roller bearings on each side, were placed on top of the specimen; the roller bearing is also located at 65 mm from the center of the specimen. A stiff steel profile with two identical wedges was fixed at the upper plate of the testing machine. The wedges were centered between the roller bearings on each side, thereby applying a horizontal splitting force (Ph). Ph is the horizontal component of the force acting on the roller bearings, and calculated by considering the wedge angle (h):
Ph ¼
P 2 tan h
ð1Þ
where P is the applied force and h is the wedge angle, which is 15° in the test set-up. Frictional forces were reduced and can be neglected by using the roller bearings with a low coefficient of friction and carefully polishing the wedge surface [16]. The actual wedge-splitting specimen and test set-up is shown in Fig. 4.
3. Results and discussions In this paper, each test was performed at the age of 180 days, and finished within 10 days. Since the mechanical properties of
dam concrete exhibited a slight change as specimen age was increased, the effect of specimen age was neglected in this discussion. 3.1. Fracture energy In this experimental study, the testing was stopped until prefabricated crack fully extended, resulting in a characteristic plateau on the load-crack mouth opening displacement (P-CMOD) diagram. The complete P-CMOD curves of site-casting dam concrete are shown in Fig. 5; wherein for the FG1500-3 specimen, only the ascending branch of P-CMOD curves was obtained. The fracture energies GF for the wedge-splitting specimen was calculated based on the total work of the area under the Ph-CMOD curve and unit crack surface. The GF for site-casting dam concrete are listed in Table 3. The variation of fracture energies GF with H1 is shown in Fig. 6. This result indicates that GF does not increase with increasing H1 when H1 approaches 1500 mm, as shown in Fig. 6, that is to say, GF shows a characteristic plateau and is independent of specimen size when H1 is over 1500 mm corresponding to H2/dmax P 6.0. The mean value of GF of site-casting dam concrete specimens is 757.662 N/m.
Please cite this article in press as: Guan J et al. Minimum specimen size for fracture parameters of site-casting dam concrete. Constr Build Mater (2015), http://dx.doi.org/10.1016/j.conbuildmat.2015.05.060
7
J. Guan et al. / Construction and Building Materials xxx (2015) xxx–xxx Table 5 Values of H2/dmax for K eIc being constant. Reference
dmax (mm)
fc (MPa)
ft (MPa)
E (GPa)
H2/dmax
K eIc (MPa m1/2)
H2/dmax for K eIc being constant
Test method
Xu [10]
10
29.56
–
29.64
WST
20
33.2
3.3
31.2
12.5
WST
Xu [12]
25
53.3
5.21
9.6
WST
Saouma [16]
38
24.8
2.67
35.54 34.01 33.04 32.97 32.06 28.54 16.9
5.3
WST
This paper
150
29.37
3.04
26.12
0.861 0.987 1.339 1.446 1.455 1.387 1.256 1.433 1.884 2.009 1.982 1.696 1.690 1.728 1.774 1.730 1.743 0.86 0.99 1.23 1.698 1.873 1.885 2.680 2.510
20.0
Wu [14]
7.5 10.0 20.0 30.0 40.0 50.0 60.0 5.0 10.0 12.5 17.5 4.8 7.2 9.6 14.4 19.2 24.0 5.3 16.1 28.2 3.2 4.0 4.8 6.0 9.0
6.0
WST
The test results of GF got in this paper and those reported by other authors (Xu et al. [11]; Wittmann et al. [15]; Saouma [16] and Zhao et al. [18]), through a wedge-splitting test (WST) or compact tension test (CTT), are all listed in Table 4. It can be seen that the values of H2/dmax for stable GF decrease with increasing of dmax. These values got in this paper are similar to those from Saouma [16] and Zhao [18], with a difference in the exact value of H2/dmax since the dmax in Refs. [11,16] are relatively smaller, 25 mm and 16 mm, respectively. An empirical formula for stable fracture energy changing with the maximum aggregate size (dmax) and the compressive strength (fc) is obtained:
GF ¼ ð0:1616dmax þ 1:0263Þf c
ð2Þ
With a mean ratio of the test value to the calculated value from the formula is 1.034, and the dispersion coefficient is 0.175. A formula recommended by Comité Euro-International du Béton was proposed in its CEB-FIP Model Code [20]:
f 0:7 2 c GF ¼ 0:0469dmax 0:5dmax þ 26 10
ð3Þ
As shown in Fig. 7, the calculated value from the formula in this study is consistent with the test value. The recommended formula by CEB-FIP Model Code obtains large deviations for the estimation of stable fracture energy with dmax P 80 mm. 3.2. Effective fracture toughness K eIc In the present study, the effective fracture toughness K eIc is determined by the maximum horizontally applied force Ph,max and the effective crack length ac. There are many methods for determining the values of ac. Jenq and Shah [21] proposed an unloading and reloading procedure performed with a closed-loop system to evaluate the ac in the two parameter fracture model (TPFM). Karihaloo and Nallathambi [22] proposed a regression expression to calculate ac in the effective crack model (ECM). Xu and Reinhardt [23] introduced a linear asymptotic superposition assumption and proposed another method for determining the effective crack length ac for nonstandard wedge-splitting specimen
according to experimental P-CMOD curves, the formula can be expressed as follows to evaluate the ac for nonstandard wedge-splitting specimen [24]:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi# CMODc E D 1 13:18 þ 9:16 Ph;max
" ac ¼ H1
ð4Þ
where ac is the crack length corresponding to Ph,max, CMODc is the crack opening displacement corresponding to Ph,max, and E is the elastic modulus of the concrete. Based on the ac value, the value of K eIc of every specimen can be numerically computed using the finite element method. The crack tip was modeled using a rosette with singular elements [25]. Because high stress gradients exist in the region around crack tip, special attention should be paid in that region. Therefore, a circle was set at the tip of crack, in which the crack tip is the center of the circle and the radius of the circle is 6 mm. The first row of elements around the crack tip had a radius of 3/2 mm, and their mid-side nodes were placed at the quarter points, i.e. had a radius of 3/8 mm [26–28]. The stress condition was assumed as plane stress [29]. The Poisson’s ratio and density are 0.18 and 2663 kg/m3, respectively, which were employed from the material parameter test for the super-high arch dam. The other parameters were determined through the experiment in this paper. The results of effective fracture toughness K eIc are shown in Table 3 and in Fig. 8. It can be seen that K eIc shows a plateau trend and does not increase when H1 approaches to 1500 mm, that is to say, K eIc tends to be stabilized and is independent of specimen size when H2/dmax P 6.0. The mean stable K eIc value of site-casting dam concrete specimens is 2.595 MPa m1/2. Table 5 lists the experimental results from this paper and from other authors (Xu et al. [10]; Xu et al. [12]; Wu et al. [14] and Saouma [16]). The value of K eIc from Ref. [16] was obtained using the compliance method. K eIc appears to increase slightly with increasing specimen size. However, taking into consideration the scatter of as much as 20% in the evaluated fracture toughness values using the compliance method, K eIc can be considered to be size independent. These results also indicate that the value of H2/dmax corresponding to stable K eIc decreases with the increase of dmax.
Please cite this article in press as: Guan J et al. Minimum specimen size for fracture parameters of site-casting dam concrete. Constr Build Mater (2015), http://dx.doi.org/10.1016/j.conbuildmat.2015.05.060
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J. Guan et al. / Construction and Building Materials xxx (2015) xxx–xxx
Fig. 9. Measured curves of P-CTOD: (a) FG800; (b) FG1000; (c) FG1200; (d) FG1500; (e) FG2250.
Specific fracture energy (Gf) corresponds to the area under the initial tangent of the softening stress-separation curve [30]. It plays a more important role in the finite element analysis of concrete structures. If the K eIc of dam concrete is solved, the following formula can be used to calculate Gf: 2
Gf ¼
ðK eIc Þ E
ð5Þ
The calculated Gf of the results got in this paper is shown in Table 3. Bazˇant [30] estimated that GF/Gf ranged from 2.0 to 2.5. The GF/Gf ratio of site-casting dam concrete poured in the site is from 3.167 to 4.835, which is different from those found in previous studies. 3.3. Critical crack tip opening displacement (CTODc)
Fig. 10. CTODc with effective specimen depth.
The experimental P-CTOD curves of site-casting dam concrete are shown in Fig. 9; wherein, only the ascending branch of
Please cite this article in press as: Guan J et al. Minimum specimen size for fracture parameters of site-casting dam concrete. Constr Build Mater (2015), http://dx.doi.org/10.1016/j.conbuildmat.2015.05.060
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J. Guan et al. / Construction and Building Materials xxx (2015) xxx–xxx Table 6 Values of H2/dmax for CTODc being constant. Reference
dmax (mm)
fc (MPa)
ft (MPa)
E (GPa)
H2/dmax
CTODc (mm)
H2/dmax for CTODc being constant
Test method
10
29.56
–
29.64
WST
20
33.2
3.3
31.2
10.0
WST
Xu [13]
25
53.3
5.21
14.4
WST
This paper
150
29.37
3.04
35.54 34.01 32.97 32.06 28.54 26.12
0.0196 0.0269 0.0455 0.0565 0.0648 0.0705 0.0613 0.0125 0.0282 0.0296 0.0294 0.0328 0.0415 0.0551 0.0605 0.0594 0.105 0.106 0.090 0.179 0.190
40.0
Wu [14]*
7.5 10.0 20.0 30.0 40.0 50.0 60.0 5.0 10.0 12.5 17.5 4.8 7.2 14.4 19.2 24.0 3.2 4.0 4.8 6.0 9.0
6.0
WST
Xu [10]
*
*
CTODc was obtained based on the experimental CMODc.
P-CTOD curves was obtained for specimens of FG1500-3 and FG2250-2. In which, the CTODc corresponds to the peak load. Fig. 10 shows the variation of CTODc with H1 of specimens. CTODc tends toward stable when H1 approaches 1500 mm, as shown in Fig. 10; that is, CTODc is independent of specimen size when H2/dmax P 6.0. The mean stable CTODc value of site-casting dam concrete specimens is 0.185 mm. The experimental results got in this paper and those reported by different authors (Xu et al. [10]; Xu et al. [13]; and Wu et al. [14]) are all listed in Table 6. The results show that the value of H2/dmax corresponding to stable CTODc decreases with the increase of dmax. 4. Conclusions To determine the minimum specimen size for the fracture parameters of the site-casting dam concrete, five groups of wedge-splitting specimens with different sizes were cast at the same time using mixing tower systems of an actual super-high arch dam in China. The dimensions of the specimen with dmax = 150 mm were 800 mm 800 mm 450 mm, 1000 mm 1000 mm 450 mm, 1200 mm 1200 mm 450 mm, 1500 mm 1500 mm 450 mm, and 2250 mm 2250 mm 450 mm, respectively. This paper has shown that it is possible to cast the test specimens at the construction site to obtain the real fracture parameters of a super-high arch dam, and the fracture parameters of the site-casting dam concrete obtained in this paper are significantly different from those of other studies. The following conclusions can be drawn: 1. The variations of fracture parameters with effective size of specimens were analyzed. The results show that the fracture parameters for site-casting dam concrete, including fracture energy (GF), effective fracture toughness (K eIc ) and critical crack tip opening displacement (CTODc), remains stable and appears independent of specimen size when the effective depth H1 over 1500 mm, corresponding to the ratio of ligament length versus maximum aggregate size H2/dmax P 6.0. That is to say, the minimum specimen size for site-casting dam concrete should satisfy the requirement that H2 is six times larger than dmax.
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Please cite this article in press as: Guan J et al. Minimum specimen size for fracture parameters of site-casting dam concrete. Constr Build Mater (2015), http://dx.doi.org/10.1016/j.conbuildmat.2015.05.060