## 1 Introduction  
The CSGR dam [1; 2; 3] is a new type of dam that has developed rapidly in recent years, but its constitutive model is still in discussion. Some scholars have established corresponding constitutive model of CSGR based on test results. In recently published articles, [PERSON] et al. [4] established the double yield surface constitutive model, [PERSON] et al. [5] and [PERSON] et al. [6] put forward the binary parallel model based on the assumption of consistent strain, [PERSON] [7] considered the rigid elastic model of material softening after reaching the peak stress, and [PERSON] et al. [8] proposed a new model for the dilatancy of CSGR. Though the elastic stage of the constitutive curve is important to the engineering design of CSGR dams, the above constitutive models pay only limited attention to it. The linear elastic constitutive model by [PERSON] [9] and [PERSON] [10] from Japan supposed the cemented sand gravel (CSG) as linear elastic material and proposed to take the elastic ultimate strength as designing strength. Despite being widely used in CSGR dam structural calculation and analysis in China, as the strength of weathered material is weaker than traditional sand, gravel, and stone material, the stress-strain test curve of it presents significant nonlinear elasticity, resulting in distortion of the material's characteristics with the linear elastic constitutive model. Therefore, it is necessary to consider the nonlinear elasticity in the constitutive model. The six-parameter nonlinear elastic constitutive model put forward by [PERSON] et al. [11] exhibits better suitability for the nonlinear elastic behavior of materials; however, the complication of its parameters makes it difficult to apply in engineering practice. Few constitutive models of weathered materials in dam-building have been put forward so far. Moreover, different kinds of additives, such as [PERSON] et al. [12; 13], will also have a great impact on the mechanical properties of dam materials. This research improves the Saenz constitutive relation [14] by introducing equivalent strain, so that the model would accommodate both cemented sand, gravel, and weathered materials for the Xjiang project. Due to some special requirements for critical conditions such as floods and earthquakes, along with the characteristics of weathered material showing large dispersion, low strength, and unevenly distributed mud and water containment, the mechanical properties of CSGR with weathered material can present great diversity, which calls for the bearing capacity of dam structure to be studied to ensure the safety of the dam. At present, the methods available for measuring the bearing capacity of CSGR dam are mainly the overload method and the strength-reduction method. Regarding Shou Koubao CSGR dams, [PERSON] [15] used a plastic damage model and bulk density overload method to analyze the bearing capacity to compare the results with the RCC gravity dam of the same height and found that the comprehensive bearing capacity of the dam structure was higher than that of the RCC gravity dam. However, he did not conclude the difference of failure modes and vertical stress on the foundation between the two dam types. [PERSON] et al. [16] also applied the overload method and the strength-reduction method to calculate and analyze the bearing capacity of the Hei Shuihe reservoir but lacks comprehensiveness. [PERSON] et al. [17] claimed that the failure mode of the hard-fill dam is tensile fracture in an upstream area and dam heel. [PERSON] et al. [18] revealed that the strength of the CSG dam's building material is low, but its safety under earthquake load is consistent with that of the gravity dam. Though the differences between the CSG dam, the hard-fill dam, and the CSGR dam cannot be simply dismissed, they are fundamentally similar. Based on the proposed model and relevant literature, it is important to study the dam body's bearing capacity using the strength-reduction method and overload method.