# Determining Rock Joint Peak Shear Strength Based on GA-BP Neural Network Method
## 3 Peak Shear Strength Prediction Model  
### Correlation Analysis of Shear Factors  
Using SPSS software (PASW Statistics 18), through the correlation analysis of various factors, the correlation between various factors and peak shear strength was discovered. Using the SPSS bivariate correlation analysis method, Pearson was used to represent the correlation coefficient, and a bilateral significance test was performed. The factors of the testare \(\sigma_{n}\), \(JRC\), \(JCS\), \(\varphi\), \(size\), \(v_{n}\), and peak shear strength. The test results are shown in Table 3. The null hypothesis (\(H_{0}\)) of the Pearson correlation hypothesis test is that there is no linear relationship between the factors and the peak shear strength, and the alternative hypothesis (\(H_{1}\)) is that there is a linear relationship between the factors and the peak shear strength. The \(p\)-value can represent the significance level of each factor. The \(p\)-value is compared with 0.05 and 0.01. If \(p>0.05\), this indicates that the null hypothesis is established: there is no linear relationship between the selected factors and the peak shear strength. If \(p\leq 0.05\), it shows that the \(p\)-value is in the rejection domain, the null hypothesis is not valid, and there is a linear relationship between the selected factors and the peak shear strength. In the range \(0.01\leq p\leq 0.05\), the significance level is higher, and \"**\" is used to indicate that. If \(p\leq 0.01\), the significance level is very high, and \"**\" is used to indicate that.  
\(r_{xy}\) represents the relationship between the factors and the peak shear strength. It can be seen from Table 4 that the correlation coefficient between \(\sigma_{n}\) and peak shear strength is the highest, and the rest are \(JRC\), \(\varphi\), \(v_{n}\), \(JCS\), and \(size\), in order of absolute value. \(JCS\) and \(size\) are negatively correlated with the peak shear strength. The influence of \(JCS\) on the peak shear strength is not independent, while the correlation analysis method only considers the influence of \(JCS\) itself on the peak shear strength, without considering the normal stress, so there is a negative correlation. According to the JRC-JCS model, the correlation analysis of \(\tau_{t}/\sigma_{n}\) and \(JCS/\sigma_{n}\) was carried out, and at \(p<0.01\), the correlation coefficient was 0.357 **.  
The JRC-JCS model is widely used to predict peak shear strength. The four factors contained in the model are strongly correlated with the peak shear. The calculation formula of the JRC-JCS model is given, as shown in Formula (1). The peak shear strength of rough/undulating joints such as tension surfaces can now be predicted with acceptable accuracy from a knowledge of only one factor, namely the effective joint wall compressive strength or JCS value [1].  
Using the JRC-JCS model to predict 205 sets of data, the prediction results of the JRC-JCS model were obtained, and the \(R^{2}\), \(MAE\), \(MBE\) and \(RMSE\) predicted by the JRC-JCS model were calculated, as shown in Table 4. The results calculated by the JRC-JCS model were compared with the experimental values, and the figures are shown in Figure 5.