# Determining Rock Joint Peak Shear Strength Based on GA-BP Neural Network Method
## 1 Introduction
The authors also analyzed the joint surface morphologies before and after shear and developed a method to predict joint damage during shear [10]. [PERSON] et al. established an empirical formula for evaluating the shear strength of rock joints by shear tests of regular tooth-shaped rock joints under different normal stresses [11]. [PERSON] et al. proposed a peak shear strength model considering anisotropic characteristics by considering the fluctuation angle and fluctuation amplitude of rock mass rock joints [12]. [PERSON] et al. proposed a new standard for the peak shear strength of rock joints by using two three-dimensional shape factors, namely, the maximum apparent inclination angle and the roughness factor [13]. [PERSON] et al. proposed a factor to characterize the roughness of the joint surface, and proposed an empirical formula for shear strength based on three-dimensional topography factors [14]. [PERSON] et al. carried out three-dimensional scanning tests on 39 joint specimens, proposed morphological factors to describe joint roughness, and established a peak shear strength model [15]. [PERSON] et al. established a new peak shear strength standard through three-dimensional morphological scanning and direct shear test, compared with the JRC-JCS model and Grasselli model. The new model significantly improved the fitting effect [16]. [PERSON] et al. further modified the three-dimensional shape factor system of the Grasselli rock joint, and obtained a prediction model that can reflect the shear mechanism of the rock joint, revealed the control effect of distribution factors on the shear resistance of the rock joint, and proposed a peak shear strength prediction model [17]. [PERSON] et al. proposed a new model of joint peak shear strength in the form of a negative exponent by using normal stress, tensile strength and joint roughness factors [18]. Based on the relationship between peak dilatancy angle and normal stress, joint morphology and joint deformation resistance, an empirical formula of shear strength of irregular rock joints is proposed by [PERSON] et al. [19]. These scholars have established a peak shear strength prediction formula by considering the three-dimensional morphological factors, anisotropy and other factors of the rock joint. Table 1 shows the specific formulas of these papers. In Formula (1), \(\tau\) is the peak shear strength predicted value; \(\sigma_{n}\) is the normal stress; \(JRC\) is the roughness coefficient of the rock joint; \(JCS\) is the compressive strength of the rock joint wall; \(\varphi\) is the basic friction angle. In Formula (2), \(x\) and \(y\) are the sharing coefficients of rock wall and concrete walls. In Formula (3), \(\theta^{*}\) is the apparent dip; \(\beta\) is the dip angle; \(\sigma_{t}\) is the tensile strength; \(A_{0}\) is the contact area; \(c\) is the fitting factor. In Formula (4), \(K_{\beta}\) is the correction coefficient of the comprehensive internal friction angle of the structural plane, and \(K_{c}\) is the correction coefficient of the comprehensive cohesion of the structural plane. In Formula (5), \(\alpha\) is a constant with a value of \(1/3\), and \(A\) is the average fluctuation amplitude coefficient of the structural plane. In Formula (7), \(m\) is the topothesy. In Formula (8), \(C^{\prime}\) is the factor of the distribution. In Formula (9), \(h\) is the average joint height; \(n\) is the roughness factor; \(\sigma_{c}\) is the uniaxial compressive strength. In Formula (12), \(\mu\) is the Poisson ratio, \(R_{\text{s}}\) is the contour surface. With the gradual popularization of machine learning, some scholars use neural networks and other methods to predict peak shear strength. [PERSON] et al. considered the influence of joint wall strength in combination with normal stress and joint roughness, and established a neural network model [20]. Considering the complex mapping relationship between joint shear strength and influencing factors, [PERSON] et al.