Minimum specimen size for fracture parameters of site-casting dam concrete

Highlights

• 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.

Abstract

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.

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], [2], [3], [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 (d_max) 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 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], [6], [7], [8], [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 d_max = 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 d_max = 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 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 d_max = 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 d_max 16 and 32 mm, a₀/H 0.5), but that for the mortar beam (with d_max = 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 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], [11], [12], [13], [14], [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 d_max = 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 $K_{\text{Ic}}^{\text{e}}$ showed no size effect when H₁ is over 400 mm corresponding to H₂/d_max = 20, and that the calculated critical crack tip opening displacement (CTOD_c) using the experimental critical crack mouth opening displacement (CMOD_c) showed no size effect, when H₁ is over 1000 mm corresponding to H₂/d_max = 50. Xu et al. [11], [12], [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, d_max = 25 and H₂ = 120 mm, 180 mm, 240 mm, 360 mm, 480 mm, and 600 mm, respectively, and found that the fracture energy G_F was independent of specimen size when H₂/d_max ⩾ 14.4 [11], $K_{\text{Ic}}^{\text{e}}$ remained stable when H₂/d_max ⩾ 9.6 [12], and CTOD_c did not increase when H₂/d_max ⩾ 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 d_max = 20 mm and found that $K_{\text{Ic}}^{\text{e}}$ was size independent when H₂/d_max beyond 12.5, CTOD_c was size independent when H₂/d_max beyond 10. Wittmann [15] conducted an investigation with compact tension specimens with depths H = 375 mm, 750 mm, and 1500 mm, respectively, d_max = 16 mm, H₂ = 150 mm, 300 mm, and 600 mm, respectively, and found that G_F increased with increasing H₂/d_max 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 d_max = 38 mm, and found that G_F and $K_{\text{Ic}}^{\text{e}}$ were independent of specimen size when H₂/d_max over 5.3, but the calculated values of CTOD_c were dependent on specimen size in the range of the test specimens [17]. In the study of Zhao [18], the test values of G_F for wedge-splitting specimens with H₂ = 225 mm, 400 mm, and 500 mm, respectively, and d_max = 80 mm does not increase when H₂/d_max 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 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 d_max = 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. 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.