# A Stability Analysis of the Ancient Site of Liye Based on the Strength Reduction Method
## 5 Stability Analysis
### Model Establishment  
Four dangerous sections (as identified in Figure 6) are selected for on-site investigation, namely, section B-B, section E-E, section H-H, and section J-J; and the section sizes are shown in Figure 7.  
Figure 5: Electron microscope images of wall soil samples and trench soil samples. (**a**) Wall soil samples; (**b**) trench soil samples. To avoid errors in the determination of section sizes and angles that were probably caused by manual modeling, the design drawing of the section was completed using the AutoCAD software. A DXF file was created and imported into the ABAQUS software in the form of a sketch for modeling. The model material parameters were defined according to the results obtained from the laboratory test (Tables 1 and 2). Among them, under condition 1, the initial cohesion and internal friction angle of soil were 24.01 kPa and 14.06\({}^{\circ}\), respectively. Under condition 2, the initial cohesion and internal friction angle of soil were 16.15 kPa and 11.95\({}^{\circ}\), respectively. The soil layer properties adopted the elastic-plastic constitutive model and the Mohr-Coulomb yield criterion. The number of field variables was set to 1, and then the cohesion and internal friction angle that varied with the field variables was set according to the strength reduction formula in the plastic part. The significance of the field variables lies in the strength reduction coefficient which serves to amplify strength. As it was convenient to search the limit failure state, and since the  
Figure 6: Location of dangerous sections. Figure 7: Location of dangerous sections. (**a**) section B–B; (**b**) section E–E; (**c**) section H–H; (**d**) section J–J (distances are in mm). initial value of the strength reduction coefficient is generally less than 1, we set the initial value as 0.5 and allowed for a linear increase to produce a piecewise linear simulation, with increases equal to 0.25 and a final value of 1.5. The research object of this paper is the earth ruins that have existed for hundreds of years, and the soil structure and geological conditions are basically stable. Secondly, when establishing the numerical model, the width and depth of the model have been set very large to avoid the size effect affecting the simulation results. Third, because the soil site only has surface soil sample spalling and no large-area collapse, the numerical model only focuses on the displacement of the existing soil site and the topsoil of the trench, and there is no movement of bedrock or outcrop. After the finite element model was established, the grid element type of the model adopted a four-node bilinear plane strain quadrilateral element (C3D8R), and the approximate global size of the grid was 1:1. Fixed constraints were used at the bottom of the model to limit its displacement and rotation in the transverse and longitudinal directions. Orientation constraints were set at both ends of the model to limit its displacement in the transverse direction. To prevent the given load step from being too large and resulting in iterative divergence and difficulty in achieving convergence, the initial value of the incremental step size was set to 0.001 and the minimum value was \(1\times 10^{-20}\). The final simulation models of four dangerous sections of the Liye trench are shown in Figure 8.  
The numerical simulation was divided into the following two working conditions. For condition 1, the soil moisture content was 20%, considering the self-weight of the soil (\(\gamma\) = 20 kN/m\({}^{3}\)), which is the current actual state of the trench. For condition 2, the moisture content of soil layer was 26% with the self-weight of the soil being considered (\(\gamma\) = 20 kN/m\({}^{3}\)). This simulated the state of the site in the event of abundant rain or excessive long-term water storage in the trench.