For concrete dams built in areas with frequent seismic activities, the safety of the dam against earthquakes is crucial [1,2]. The dynamic loadings are generally complex and may lead to the fast cracking of the concrete, which exerts an adverse influence on the bearing capacity and durability of the structures [3,4]. The study on the fracture behavior of mass concrete, especially under dynamic loadings, is beneficial for postponing and mitigating crack initiation and propagation, and provides technical support for measures taken to alleviate the cracking, thus improving the durability and safety of the dam [5,6,7].

Fracture mechanics was introduced to investigate the nonlinearity of concrete ever since Kaplan conducted fracture tests on concrete beams based on Griffith’s theory in 1961 [8]. Opening-mode cracks have been the focus of experimental research, as they cause the low-stress fractures of structures. For the tests of opening-mode cracks, the wedge-splitting test and the three-point bending test have been widely used by scholars, and formulae for calculating the fracture toughness are available. Bruhwiler et al. [9] conducted wedge-splitting tests on concrete containing preset cracks, and there was no size effect on the fracture toughness obtained by the two-parameter model. Zhang et al. [10] evaluated the double-K fracture toughness of concrete using wedge-splitting tests and the simplified Green’s function method, simplified equivalent cohesive force method, four-terms weight function method, and Gauss–Chebyshev integral method, and found that the results obtained from the experiment were in good agreement with the four analysis methods. Xu et al. [11] proposed a numerical method to obtain the K_R curve of concrete by considering the fracture process zone in three-point bending tests. Dai et al. [12] investigated the fracture process zone (FPZ) of concrete using digital image correlation (DIC) and the acoustic emission (AE) for the three-point bending test containing preset cracks. Zhang et al. [13] captured the crack initiation based on the AE for three-point bending tests containing preset cracks. In addition, Lu et al. [14] explored a nonlinear uniaxial strength criterion for concrete under dynamic loading conditions. Chen et al. [15] investigated the ultimate load-carrying capacity of short thin-walled steel tubes reinforced with highly ductile concrete experimentally. This study provides an important experimental basis and theoretical support for the application of thin-walled steel pipe–concrete composite structures in bridges and buildings. Zhang et al. [16] focused on analyzing the multi-crack stress intensity factor of rib-to-floor beam weld details in orthotropic anisotropic steel bridge panels under vehicle loading. The results of the study are important for guiding the design and maintenance of orthotropic anisotropic steel bridge panels. Fang et al. [17] evaluated the early crack resistance performance of concrete mixed with ternary minerals using a temperature stress testing machine.

Many concrete structures are subjected to dynamic loads in addition to static loads, and the effects of these loads may have a larger impact on concrete fracture. Different concrete structures have different fracture mechanical properties due to differences in their properties, and these differences may be more pronounced under dynamic loading. Therefore, it is necessary to perform fracture tests on concrete. Nogueira et al. [18] conducted tests on mortar and plain concrete under direct shear by ultrasonic pulse velocity. Musiket et al. [19] found that the fracture toughness and fracture energy release rate of recycled aggregate concrete increased with the increase in the loading rate. Cadoni et al. [20] and Brara et al. [21] carried out SHPB tests, Mindess et al. [22] performed drop hammer impact tests, and Zhang et al. [23] conducted three-point bending tests, and each found that the fracture energy increased with an increasing loading rate. Ruiz et al. [24] found that the fracture toughness and fracture energy increased with the loading rate by conducting three-point bending tests. At high loading rates, the increase in the fracture toughness and fracture energy is significant due to the inertial effect and the initiation of multiple microcracks under impact loading. John et al. [25] and Ngo et al. [26] found that the rate of concrete crack expansion increased with an increasing loading rate by using the three-point bending test.

The experimental study mentioned above was carried out on small-sized wet-sieved concrete specimens, which is a concrete mix in which large-sized aggregates are screened out after mixing well, whereas mass concrete is used in practical dam projects. Since it is difficult to cast and test mass concrete specimens, the parameters of the sieved specimens are often revised to approximate those of mass concrete. However, there are limitations in this practice, mainly because the content of cement mortar and aggregates in mass concrete differs from that of wet-sieved concrete, and the internal composition of the specimens changes after being sieved. Li et al. [27,28] conducted direct tension tests on mass concrete and wet-sieved concrete and found that the fracture energy of the mass concrete was approximately 1.40–2.23 times that of wet-sieved concrete. Due to limited experimental data, the relationship between the fracture parameters obtained from the mass concrete and wet-sieved concrete could not reach a consensus, so it is necessary to carry out fracture tests on mass concrete. Guan et al. [29] carried out wedge-splitting tests on mass concrete and found that the initial fracture toughness and fracture energy increased with age. Li et al. [30,31] carried out fracture tests on mass concrete including preset cracks through wedge-splitting tests and found that the fracture energy of the specimens cast in summer was higher than those cast in winter. Gao et al. [32] and Guan et al. [33] conducted wedge-splitting tests on mass concrete including precast cracks and found that, if the ratio between the ligament height and maximum aggregate particle size ratio exceeded six, the initial fracture toughness and unstable fracture toughness did not change with the ratio. Saouma et al. [34] and Mohsen et al. [35] performed wedge-splitting tests on mass concrete including preset cracks and found that there was no significant size effect on the fracture toughness when the ratio of the ligament height to the maximum aggregate size was equal to eight. Xu et al. [36] found that the fracture toughness and fracture energy were insensitive to the change in the preset crack length by conducting wedge-splitting tests. Zhao et al. [3] and Ghaemmaghami et al. [37] found that the fracture energy of the mass concrete of a dam increased with the increase in the specimen height by conducting wedge-splitting and three-point bending tests. Bakour et al. [38] carried out wedge-splitting tests on mass concrete and evaluated the local FPZ properties by using DIC monitoring.

Although it is convenient to calculate the fracture toughness and fracture energy for three-point bending tests, the specimens may break during handling, and, more importantly, the self-weight of the specimens may affect the test results. The wedge-splitting test avoids the influence of self-weight, lowers the requirements concerning the stiffness, and is simpler to install. However, the vertical loading induces additional moments that affect the stress field at the crack tip, which may affect the fracture parameters of the specimens obtained. It is known that concrete is more vulnerable when subjected to tension as compared to compression [39,40]. As the most direct method of determining the tensile properties of concrete, the tensile strength measured by direct tension testing is the closest to the real strength of concrete [41]. Wittmann et al. [42] determined the fracture parameters of concrete with the compact tension test. Chen et al. [43] investigated the tensile properties of concrete at high strain rates using the split Hopkinson pressure bar. Wang et al. [44] drilled core samples of an arch dam and obtained the dynamic tensile strength by carrying out direct tension tests. Guo et al. [41] conducted direct tension tests on plain concrete cylinders using AE and DIC techniques. By detecting the AE signals, the internal fracture damage of the specimen can be monitored, and by using the DIC technique, the microcracks and macrocracks on the surface of the specimen can be tracked. By using the AE technique in the direct tension testing of prismatic concrete specimens, Li et al. [45] found that microcracks are easy to nucleate and grow in the aggregate–mortar interface transition zone, and they eventually develop into macrocracks, resulting in the overall failure of the material. Fan et al. [46] carried out direct tension tests on concrete, monitored the internal damage of the concrete in real time by the AE, and studied the dynamic performance and failure mechanism of the concrete. The direct tension test is the most straightforward method to measure the strength and fracture parameters of concrete; however, the testing process is difficult due to the stress concentration at both ends and the centering of the specimen during the test.

In 1996, Melenk et al. [47] proposed the unit decomposition method; in 1999, Belytschko et al. [48] studied crack extension in elastomer models based on minimally reconfigurable meshes; in 2000, Daux et al. [49] introduced continuous functions in the study of multi-crack problems and named it the extended finite element method (XFEM). Compared with the finite element method (FEM), XFEM is based on the unit decomposition method, in which the crack is allowed to pass through the mesh, as shown in Figure 6. At this time, due to the jumping phenomenon on both sides of the crack, its displacement field is no longer continuous, and the stress concentration phenomenon occurs at the tip of the crack. The intermittency is reflected by introducing strengthening functions, including the stress asymptotic function at the crack tip and the intermittent jump function, which are used to increase the nodal degrees of freedom. The displacement field functions as follows:

where N_i and u_i are the shape function and corresponding node displacement of the regular unit node; N_j and α_j are the shape function and corresponding node displacement of the completely penetrated unit node, whose corresponding node sets are shown as in Figure 6; N_k and $b_k^{\alpha }$ are the shape function and corresponding node displacement of the unit node at the crack tip, whose corresponding node sets are shown as in Figure 6; H(x) is the hopping function, which denotes the discontinuity of the displacement at the crack surface, also called the Heaviside function; ϕ_α(x) is the stress asymptotic function, which denotes the stress singularity at the crack tip, whose expression in the polar coordinate system is as in Equation (5).

Since no analytical solution is available regarding the fracture toughness of the current tests, a coupled approach of experimental and numerical simulation based on XFEM was used. The stress intensity factor was calculated by employing the J-integral method. The J-integral is path-independent for curved surface integrals around the crack tip, and its fracture toughness index is presented in the form of energy. The interaction integral method provides a reasonable and natural description of the total energy release. The interaction integral method was obtained by introducing an auxiliary field (denoted as state 2 in the following equations) superimposed on the real field (denoted as state 1) to obtain the J-integral component, which is expressed as follows:

where A is an arbitrarily closed loop around the crack tip, W^(1,2) is the strain energy density, and q_j is the unit normal vector of the closed loop, with the direction pointing outward.