# Determining Rock Joint Peak Shear Strength Based on GA-BP Neural Network Method
## 1 Introduction
proposed a prediction model of rock joint shear strength based on a back propagation (BP) neural network, which can comprehensively consider various influencing factors, including external shear test conditions and joint factors [21]. [PERSON] et al. collected the shear experimental data of previous scholars wherein the stable topological structure was obtained by a cross-validation algorithm and optimized a BP neural network by using MBGD, Adam and RMSprop algorithms. The effects of initial undulation angle, normal stress and water content on the strength, deformation characteristics and failure mode of red sandstone joints were analyzed [22]. [PERSON] et al. used three machine learning (ML) algorithms, support vector machine (SVM), BP neural network (BPNN) and random forest (RF), to establish regression models for predicting the peak shear strength of joints [23]. [PERSON] et al. constructed an intelligent prediction model by optimizing a BP neural network through a genetic algorithm; they realized the construction of a quantitative mapping relationship between fractal dimension, roughness, normal pressure, friction coefficient and mechanical properties of jointed rock. They also brought \begin{table}
\begin{tabular}{c c} \hline \hline [PERSON] [1] & \(\tau=\sigma_{n}\tan[\varphi+JRC]_{\text{g}}(\frac{ICS}{\sigma_{s}})]\) & (1) \\  & \(\tau=\sigma_{n}\tan[\varphi+JRC]_{\text{g}}(\frac{ICS_{\text{g}}}{\sigma_{s}})]\) & \\ [PERSON] [8] & \(JCS_{ab}=xJS\)\(CS_{b}+yJS\) & (2) \\  & \(y=41.889\theta^{*}10^{-1}91\) & \(x+y=1\) \\ [PERSON] [10] & \(\tau=\sigma_{n}\tan[\varphi(\frac{\sigma_{n}}{c})^{1.188\cos\beta}][1+\exp(- \frac{\sigma_{n}}{9A_{0}c\sigma_{t}})]\) & (3) \\ [PERSON] [11] & \(\tau=\sigma_{n}\tan(\varphi+k_{\beta})+k_{c}\cdot i\) & (4) \\ [PERSON] [12] & \(\sigma_{n}\tan\Bigl{\{}\left\{10.725\ln[A^{a}(\frac{\tau}{SR_{\text{g}}})^{-1} -4]+24.202\right\}\cdot\lg(\frac{ICS}{\sigma_{n}})+\varphi\Bigr{\}}\) & (5) \\ [PERSON] [13] & \(\tau=\sigma_{n}\tan(\varphi+\frac{\sigma_{n}}{c}\cos^{-\frac{\sigma_{n}}{c}})^{ -\frac{\sigma_{n}}{c}})\) & (6) \\ [PERSON] [14] & \(\tau=\sigma_{p}\tan[\varphi+\frac{\arccos(1/R_{\text{g}})}{(\sigma_{p}+1)^{1}}]\) & (7) \\ [PERSON] [15] & \(\tau=\sigma_{n}\tan(\varphi+\frac{16\sigma_{p}\cdot\frac{\sigma_{n}}{c}}{(\frac {\sigma_{n}}{c})^{-\frac{\sigma_{n}}{c}}})\) & (8) \\ [PERSON] [16] & \(\tau=\sigma_{n}\tan[\varphi+\frac{16\sigma_{p}\cdot\frac{\sigma_{n}}{c}}{(\frac {\sigma_{n}}{c})^{-\frac{\sigma_{n}}{c}}}]\) & (9) \\ [PERSON] [17] & \(\sigma_{n}\tan\Bigl{\{}\varphi+\frac{90^{*}(1-0.0015^{1/c})}{\tau}\times[1+\exp (-\frac{90^{*}(1-0.0015^{1/c})}{18}\cdot\frac{\sigma_{n}}{\sigma_{t}})]\Bigr{\}}\) & (10) \\ [PERSON] [18] & \(\tau=\sigma_{n}\tan[\varphi+\frac{8A_{0}\theta^{*}\tan}{c+1}\exp(-\frac{c^{- 0.51\sigma_{n}}}{c})]\) & (11) \\ [PERSON] [19] & \(\tau=\sigma_{n}\tan[\varphi+\arccos(1/R_{\text{g}})\cdot\frac{\sigma_{n}}{\frac {\sigma_{n}}{c}(\frac{\sigma_{n}}{c}+1})]\) & (12) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Peak shear strength models. to light the formulation of an intelligent prediction method for mechanical properties of jointed rock by considering joint morphology characteristics [24]. [PERSON] et al. collected 1080 data sets, including SH, p-wave velocity, PLS and UCS. All data sets were divided into three categories (sedimentary rock, igneous rock and metamorphic rock) according to lithology. Based on the data sets of three rock types, a combined model combining random forest and linear regression was used to predict the uniaxial compressive strength of rock [25]. [PERSON] et al. established an artificial neural network (ANN) method to predict the uniaxial compressive strength (UCS) of sedimentary rocks by using different input factors, such as dry density, tensile strength of Brazilian splitting, and wet density [26]. These studies are listed in Table 2. There are also many machine learning methods applied to the prediction of rock strength, such as the prediction of rock strength factors by convolutional neural networks [27; 28; 29; 30].