# Study on the Effect of Anchor Cable Prestress Loss on Foundation Stability
## 3 Numerical Simulation
### Constitutive Model and Calculation Parameters  
In numerical simulation, the selection of the constitutive model and determining the parameters of rock and soil mass are crucial. The Mohr-Coulomb model is the most commonly used constitutive model to represent geological materials, as shown in Figure 3a. The Mohr-Coulomb strength criterion is usually applied to intact rock mass, which is difficult to reflect in a complex field situation. Therefore, the Mohr-Coulomb model is used in this study to simulate the soil body in the formation, while the highly weathered diabase can be treated as a general soil layer due to its poor integrity. The Hoek-Brown model is used to simulate the moderately weathered and slightly weathered diabase, as shown in Figure 3b. The Hoek-Brown (H-B) strength criterion was first developed by \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Anchor** \\ **Cable** \\ **Number** \\ \end{tabular} & \begin{tabular}{c} **Free** \\ **Section** \\ **Length** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Anchor** \\ **Section** \\ **Length** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Prestressing** \\ **Locking** \\ **Value (kN)** \\ \end{tabular} & \begin{tabular}{c} **Drilled** \\ **Hole** \\ **Diameters** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Inclidence** \\ **Angle (\({}^{\circ}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Horizontal** \\ **Spacing** \\ **(mm)** \\ \end{tabular} &
\begin{tabular}{c} **Vertical** \\ **Spacing** \\ **(mm)** \\ \end{tabular} \\ \hline MS1 & 5 dps15.2 & 15,000 & 7500 & 300 & 150 & 25 & 1500 & 3500 \\ MS2 & 6 dps15.2 & 11,000 & 7000 & 300 & 150 & 20 & 1500 & 3500 \\ MS3 & 5 dps15.2 & 8000 & 6000 & 300 & 150 & 15 & 1500 & 4000 \\ MS4 & 4 dps15.2 & 5000 & 6000 & 300 & 150 & 15 & 1500 & 4000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Anchor cable parameters. Figure 1: Schematic diagram of a typical geological section of the support structure. [PERSON] and [PERSON] in 1980 on the basis of a large number of mechanical tests and laboratory experiments of mine rock mass. It has been gradually improved after continuous revision, and the influence of rock mass structure, rock mass strength, stress state, and other factors has been comprehensively considered. It can reflect the inherent nonlinear failure characteristics of rock and rock mass and is one of the most widely used and influential rock strength criteria so far. The generalized H-B criterion is expressed as follows:  
\[\sigma_{1}=\sigma_{3}+\sigma_{ci}\bigg{(}m_{b}\frac{\sigma_{3}}{\sigma_{ci}}+s \bigg{)}^{\alpha} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Stratigraphic Type**} & **Depth of** & **Soil Weight** & **Elasticity** & **Poisson** & **Cohesive Force** & **Internal Friction** \\  & **Stratum (m)** & **(kN/m\({}^{3}\))** & **(MPa)** & **Ratio (-)** & **(kPa)** & **Angle (\({}^{\circ}\))** \\ \hline plain fill & 2.2 & 18.5 & 5 & 0.35 & 5 & 12 \\ coarse gravel sand & 2.3 & 20.5 & 36 & 0.27 & 0 & 35 \\ medium-fine sand & 3.1 & 20.0 & 60 & 0.25 & 0 & 38 \\ silty clay & 2.6 & 19.8 & 15.4 & 0.3 & 13.7 & 14.9 \\ highly weathered diabase & 8.5 & 24.5 & 350 & 0.26 & 35 & 40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Basic calculation parameters. Figure 3: Mohr–Coulomb and Hoek–Brown yield surfaces in the principal stress space. (**a**) Mohr–Coulomb model; (**b**) Hoek–Brown model. Figure 2: Schematic diagram of calculation model size. where \(\sigma_{1}\) and \(\sigma_{3}\) are the maximum and minimum effective principal stresses (MPa) of rock mass, respectively. \(\sigma_{ci}\) is the uniaxial compressive strength (MPa) of intact rock. \(m_{b}\), \(s\), and \(\alpha\) are empirical parameters related to discontinuities such as rock joints. \(s\) reflects the degree of fragmentation of the rock mass and ranges from 0.0 to 1.0. For intact rock mass, \(s=1.0\).