## 1 Introduction  
In a ground-anchored suspension bridge, the anchorage performs the function of supporting the tension force acting on the main cable. As one of the construction methods of anchorage, gravity-type anchorage (GTA) (see Figure 1) is widely used due to a variety of advantages such as simple mechanical configuration, ease of construction, and its vast applications [1]. The GTA resists the cable load via the weight of the anchorage structure itself, and this depends on the frictional resistance between the anchorages (concrete) and the foundation (rock). For designing the GTA, many guidelines are recommended to assess the stability of a GTA using the gravity method [2; 3; 4; 5; 6], and it is coupled with the Mohr-Coulomb (M-C) criterion, which is defined by several parameters such as friction angle and cohesion. However, some guidelines assume the M-C parameters to be a conservative constant value (e.g., \(c=0\) and \(tan\phi~{}=~{}0.6\)) [5; 6] in the vicinity of the joint between the anchorage and the foundation. The rough geometry of the joint is also neglected in the gravity method. Such oversimplifications related to joint properties may lead to a conservative stability analysis, and it may require a huge amount of earth and rock excavation and concrete consumption, which may result in high construction costs and environmental damage in GTA. Therefore, it is crucial to extensively investigate the frictional resistance and failure behaviors around the joint structure between concrete and rock surfaces (i.e., concrete-rock joint) with rough geometry under shearing. The problem of the failure of the concrete-rock (C-R) joint under shearing has been considered as a special case of the failure of rock mass containing rough joint surfaces (i.e., rock-rock joint) under shearing. The problem of rock-rock (R-R) joints subjected to shearing has been investigated extensively, and several models for this problem have been proposed [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. These studies have examined the major factors that affect the behavior of the R-R joint, considering the rock mass properties around the rock joint, joint surface roughness, and boundary conditions applicable to joints, and some useful solutions have been proposed. Based on the research and knowledge regarding the shear behavior of the R-R joints, several investigations of the interaction of C-R joint surfaces have been performed by researchers through direct shear tests on the C-R joints under constant normal loading (CNL) and constant normal stiffness (CNS) conditions. [PERSON] et al. [11] performed a direct shear test on regular triangular C-R joint surfaces under several CNS conditions. As an extension of their study, [PERSON] et al. [12] proposed analytical solutions to predict the development of the shear resistance in rock-socketed concrete piles, which can be idealized as a C-R joint problem under CNS conditions. [PERSON] and [PERSON] [27] investigated the shear behavior of C-R joints with irregular triangle asperities, and they compared the obtained results with the case of regular triangular asperities. They revealed that the major difference between irregular and regular asperities is in the fact that an irregular joint presents more ductile behavior than a regular joint does. Similarly, [PERSON] et al. [28] carried out a direct shear test with fractal profiles under several CNL conditions, and the results were compared with a case of regular triangular asperity. The response of the joint with fractal profiles showed more ductile behavior and presented a significantly lower peak overall strength than the case with regular asperity, because each single asperity in the fractal profile was progressively fractured rather than simultaneously fractured. [PERSON] et al. [29] investigated the shear behavior of a bonded shotcrete-rock joint.