## 3 PLAXIS Numerical Simulation
### Analysis Methods and Models  
PLAXIS 2D software is used to address soil-structure interaction problems encountered in various geotechnical engineering applications. It can analyze behaviors such as deep excavation, slope stability, reinforced retaining walls, soil rails, ground anchors, internal bracing, raft foundations, pile foundations, seepage, tunnels, and other related issues, making it a powerful tool for geotechnical engineering analysis. PLAXIS provides multiple constitutive models for users to choose from to simulate the stress-strain behavior of soils.  
Parameter Configuration and Modeling for Numerical Simulation Analysis  
Due to space constraints in this paper, detailed content regarding the basic principles of PLAXIS is available in the user manual [4]. The following key points are summarized:  
* Parameter Configuration1. Soil Parameters: In this study, the Mohr-Coulomb model, which is a built-in model within PLAXIS, was selected to simulate the soil behavior. The Mohr-Coulomb model is an elastic-perfectly plastic failure model based on elastoplastic theory. It considers factors such as the satisfaction of Hook's Law during the elastic stage, yielding criteria, and the flow rule. The soil parameters required for this model are explained as follows:
* Elastic modulus (_Es_): In general, the soil can be assigned an elastic modulus of 50% of the ultimate strength, known as the secant modulus (E50).
* Poisson's ratio (_v_): In most cases, the value of \(v\) for soils ranges between 0.3 and 0.4.
* Cohesion (_c_): According to the PLAXIS user manual, a value of c greater than 0.2 kPa can be input for computational convenience.
* Internal friction angle (_\(\Phi\)_): The internal friction angle of the soil can be determined based on the soil type and shear strength tests conducted in the field or laboratory.
* Dilation angle (_\(\psi\)_): For cohesive soils, the dilation angle can be assumed to be 0. In the case of sandy soils, the angle is very small and sometimes even close to zero or negative (_\(\psi\coloneqq 0^{\circ}\)_ or _\(\psi<0^{\circ}\)_); therefore, it can be assumed as_ \(\psi=0^{\circ}\) _during the analysis. By utilizing the Mohr-Coulomb model with the specified soil parameters, PLAXIS facilitates the simulation of soil behavior in this study. (2) Retaining Structure Parameters The retaining structure parameters are referenced from the original design calculations. It should be noted that different types of retaining walls have varying input parameters required for numerical analysis (refer to Section 3.2.4 for detailed research).
* Boundary Conditions for Numerical Analysis Modeling In addition to the configuration of the relevant important parameters mentioned above, the determination of the boundary conditions is a crucial aspect of the simulation process. Factors that may affect the boundaries include _W\({}_{T}\)_ (boundary width), _E\({}_{w}\)_ (full cross-section excavation width), _e\({}_{w}\)_ (half of the excavation width), _E\({}_{D}\)_ (final excavation depth), and _D\({}_{T}\)_ (boundary depth). In the context of boundary considerations, domestic scholars [PERSON] [37] and [PERSON] [38] have proposed different boundary conditions for reference. From an international perspective, scholars such as [PERSON] et al. have stated: \"The distance from the lateral boundary of the model and the distance between the lower bound of the model from the top should be taken as sufficient so that the effects of the boundaries in the numerical model on the results are minimized. The displacement and the stress contours in the finite element software indicate that this distance is sufficient\" [39; 40; 41]. ### Case Analysis