# Hybrid Machine Learning Model for Predicting Shear Strength of Rock Joints
## 3 Dataset Description and Processing  
### Data Processing  
The shear strength of rock joint is influenced by multiple factors, including the mineral composition of the rock, loading conditions, and joint surface morphology [52]. However, due to the inherent complexity of rock mass structures and the limitations of field data collection [53], it is challenging to comprehensively account for all the potential influencing factors [54]. Consequently, studies on joint shear strength typically focus on a selection of key parameters. Previous research has extensively reported that joint shear strength is closely related to parameters such as the joint roughness coefficient (JRC), normal stress (\(\sigma_{n}\)), basic friction angle (\(\varphi_{b}\)), Young's modulus (\(E\)), and uniaxial compressive strength (\(\sigma_{c}\)). For instance, as shown in Figure 5, [PERSON] and [PERSON] [34; 55] conducted a series of direct shear tests on replicas of natural rock joints. Their laboratory experiments systematically investigated the effects of these factors on joint shear strength. Based on these findings, this study compiles the experimental data obtained by [PERSON] and [PERSON] [34; 55] to develop a dataset for developing ML models. The dataset employs JRC, \(\sigma_{n}\), \(\varphi_{b}\), \(E\), and \(\sigma_{c}\) as input variables, with joint shear strength (\(\tau_{p}\)) as the output variable. And finally 84 sets of valid data were obtained. The establishment of this dataset not only enhances the accuracy of the shear strength predictions but also provides valuable references for subsequent numerical simulations and engineering applications. Detailed information regarding the direct shear tests can be found in references [34; 55]. Statistical analysis was conducted to examine the distribution characteristics of the dataset, and a violin plot was generated accordingly, as shown in Figure 6. The box line box in the violin plot represents data from the lower quartile to the upper quartile, the black line extending from it represents data from 1.5 times the quartile distanc  
Figure 5: Typical direct shear test [34]. represents the kernel density estimator. As can be seen from Figure 6, there are no outliers or few outliers in the dataset, indicating that the dataset is reasonably constructed. When a dataset contains a large number of rows and columns, data analysis becomes increasingly complex. Therefore, descriptive statistical methods are commonly used to analyze the dataset based on parameters such as mean, confidence interval, kurtosis, minimum value, maximum value, and standard deviation. Table 1 provides the descriptive statistics of 84 rock samples. As shown in Table 1, the dataset encompasses a broad range of rock properties, including JRC (4-20), \(\sigma_{n}\) (0.57-2.5 MPa), \(\varphi_{b}\) (28-34\({}^{\circ}\)), \(E\) (2.88-11.91 GPa), and \(\sigma_{c}\) (8-52.5 MPa), indicating its robustness and representativeness. Figure 6: Violin plots of each variable. Training a machine learning model on the entire dataset can result in overfitting. Therefore, it is common practice to divide the dataset into two parts: one for training the model and the other for evaluating its predictive performance [56, 57]. For instance, as described in references [58, 59], the dataset is randomly split into a training set and a test set at a ratio of 4:1. Similarly, the collected dataset in this study was processed in the same manner. Specifically, the training set contains 67 data points, while the test set includes 17 data points. The machine learning model is first trained on the training set and then evaluated on the test set to assess its predictive capabilities. After dividing the training set and the test set, the data in the dataset is regularized according to the Equation (7). This translates features at different scales to the same scale so that ML models can learn better.