## 1 Introduction  
A series of super-high arch dams (height over 200 m) have been constructed or are being planned in China. Most of them are distributed in the mountainous areas in southwest China (Figure 1), and therefore are subject to complex engineering challenges, such as high seismic intensity, high slope, huge water thrust, and so forth. The geological conditions are also very complex, for example, the deep-cutting valley, high ground stress, and some unfavorable geological conditions, such as atypical faults, dislocation interfaces, altered rock masses, and weak rock masses [1; 2; 3]. The complex geological conditions may lead to the crack of dam concrete or foundation, which eventually leads to dam failure [4]. Therefore, the construction of super-high arch dams still faces many challenges. Cracks may initiate in the outlets [5], heel [6], surface, and interior of dam concrete blocks [2], then propagate and coalescence along horizontal or vertical directions in concrete blocks. The main cracking factors include temperature variations, heat from concrete hydration, shrinkage and creep, dam foundation uncoordinated deformation, earthquake, and seepage effect [4]. Some research studies have been done related to the cracking mechanism on concrete blocks of dams experimentally and theoretically. Study on thermal mechanics of the concrete dam includesthe temperature variation of the external environment and heat from concrete hydration. When the temperature gradient changes dramatically inside the dam, the thermal stresses will concentrate and cause the cracks to initiate under cold wave conditions [7], in cold areas [8], under unfavorable solar radiation [9], and in dry, hot valley regions [10]. Temperature load is the main cracking factor of the Karaj arch dam [11]. The nonlinear analysis of concrete arch dams is necessary to check the stability of cracks in high tensile stress areas. [PERSON] et al. [12] investigated the mechanical properties and showed that stress relaxation is affected by the concrete temperature. They used a finite-element modeling procedure for assessing the thermal mechanical behaviors of concrete dams, and successfully reproduced the oblique cracks present on the downstream face of Daniel Johnson dam. The distribution of stresses in roller-compacted concrete dams is greatly affected by the starting date of the roller-compacted concrete placement schedule [13]. Self-weight and weak foundation [14; 15], uneven settlement of arch dam foundation, and earthquake [16; 17] can also lead to the cracking of arch dams. [PERSON] et al. [18] assessed seismic cracks in three types of concrete dams, namely gravity, buttress, and arch, using an improved 3D coaxial rotating smeared crack model. The cracking factors of arch dams often interact with each other in a nonlinear manner, and therefore cannot be considered separately. The concrete dam cracking problems have been studied by different methods in the past 30 years as follows. (1) The finite element method (FEM) is widely used in the numerical simulation of dam cracking, including the FEM based on elastoplastic mechanics, the FEM based on fracture mechanics [19; 20], and the FEM based on damage mechanics [21; 22]. Based on linear elastic crack mechanics and three-dimensional boundary element modeling, [PERSON] et al. [23] presented a procedure to analyze the cracks in arch dams. [PERSON] et al. [24] introduced the existing constitutive model of large, light, reinforced concrete structures and the deficiency of the design procedure, and they also presented a three-dimensional nonlinear cracking response simulation procedure for outlet structures. The overall stability of arch dams is analyzed by the three-dimensional numerical simulation [25]. [PERSON] et al. [26] simulated the thermal stress of a concrete dam by three-dimensional linear elastic FEM, and the autogenous shrinkage strain was added to the thermal strain.