# Strength Prediction Model for Cohesive Soil-Rock Mixture with Rock Content
## 4 Numerical Simulation on Mechanical Properties of Cohesive SRM  
### Modeling  
The discrete element numerical simulation in this study was based on the PFC\({}^{\text{3D}}\) software, which is mainly employed to simulate bulk particles or systems that can be simplified to bulk particles. In PFC\({}^{\text{3D}}\) software, spherical particles serve as the basic modeling units. These spherical particles represent the corresponding particle gradation of the tested soil material and can be bonded to simulate the solid material, such as the rock blocks in this study. The model employs walls to establish boundaries, and the contact forces arise from the overlapping interactions between particles and between particles and walls. Based on the experimental results, the most suitable intrinsic model is selected for the existing program of PFC\({}^{\text{3D}}\). Given the relative simplicity and high computational efficiency of the linear contact model, which can significantly reduce the computational time and resource consumption in the large-scale simulation or complex engineering analysis of cohesive SRMs, this study adopted the linear contact model. Since walls in PFC\({}^{\text{3D}}\) cannot be directly loaded with stress, the constant confining pressure applied to the sample needs to be achieved by adjusting the wall velocity through a numerical servo mechanism.  
For clay particles, PFC\({}^{\text{3D}}\) controls the number of particles mainly by adjusting the porosity. The relationship is as follows Equations (1) and (2). e is the matrix porosity ratio; e\({}_{\text{max}}\) is the matrix maximum porosity ratio; e\({}_{\text{min}}\) is the matrix minimum porosity ratio; Dr is the matrix relative compactness. In this test, Dr = 0.3 and n = 0.43, which are dimensionless. For the blocks, this study designs an R\({}_{\text{block}}\) rectangular block template with a length-to-width-to-height ratio of 2:1:1. The long axis of R\({}_{\text{block}}\) can be controlled to be 8 mm. In this paper, the flexible particle film servo method is selected, in order to ensure that the specimen is subjected to a stable lateral pressure, and the servo control system of the PFC software must be used to precisely regulate the speed of the wall movement in order to achieve the predetermined lateral pressure. In this study, five different loading rates were chosen, i.e., 0.25, 0.20, 0.15, 0.10, and 0.05 m/s. In order to balance the model computational accuracy and computational time, a loading rate of 0.15 m/s was chosen for simulation in this model ([PERSON] et al., 2005) [26]. The parameters related to numerical modeling are shown in Table 2.  
\[e=e_{max}-(e_{max}-e_{min}) \tag{1}\]  
\[n=\frac{e}{1+e} \tag{2}\]  
Figure 8: Relationship curve between P\({}_{\text{BV}}\) and shear strength.  
This study developed a flexible triaxial compression numerical model of the cohesive SRM with 40% P\({}_{\text{BV}}\) and an \(\alpha\) of 30\({}^{\circ}\) using PFC3D software. The model was calibrated through the laboratory large-scale triaxial compression test results, and the calibrated micro-mechanical parameters for the cohesive SRM samples are summarized in Table 3. As revealed in Figures 9 and 10, the deviatoric stress versus axial strain curves and the failure modes of the samples obtained from the numerical tests were largely consistent with the laboratory test results. These observations confirmed the validity of the numerical model presented in this study.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Relative Density of** & \multicolumn{2}{c}{**Block Length-to-Width-to-Height Ratio**} & \multicolumn{2}{c}{**The Long Axis of \(\mathbf{R_{block}}\)**} & \multicolumn{1}{c}{**Loading Rate**} \\ \hline Dr = 0.3 & 2:1:1 & 8 mm & 0.15 m/s \\ \hline \end{tabular}
\end{table}
Table 2: Table of model parameters.  
Figure 9: Calibration results.