# Applicable Conditions of Room-and-Pillar Mining Goal Treatment Methods under a Traffic Load
## 2 Stability Analysis of a Goaf under Traffic Load Conditions
### Analysis of Traffic Load Disturbance Depth
#### 2.1.1 Numerical Simulation of Traffic Load and Discriminant Conditions of Disturbance Depth  
Numerical simulation. Midas GTS software was used to establish the calculation model of traffic load disturbance depth. The schematic diagram of the model is presented in Figure 2. The x direction of the model is the cross-section direction of the road, and the y direction is the longitudinal-section direction of the road, where the length \(\times\) width \(\times\) height of the model under the road = 100 m \(\times\) 25 m \(\times\) 70 m, and the width of the bottom of the subgrade is 27.5\(\sim\)34.5 m, according to the subgrade height of 1-7 m; that is, a slope ratio of the subgrade slope of 1:1. During the grid division, smaller grid sizes were adopted for the subgrade, surface layer, base layer, and foundation, and the model as a whole was distributed from the subgrade to the surrounding boundary from dense to sparse.  
This model was divided into four parts: the surface layer, base layer, subgrade, and foundation. The parameter settings of each layer are presented in Table 1. The surface and base layers were set as linear elastic constitutive models, and the subgrade and foundation were set using the Mohr-Coulomb constitutive model. The calculation of the model was performed in two steps. First, prior to analyzing the disturbance depth of the traffic load, the boundary constraint condition of the model was set as the elastic boundary. An eigenvalue analysis was then conducted under this boundary condition to obtain the periodically calculated damping coefficient and maximum modal frequency of the model. Second, following the eigenvalue calculation, the boundary condition was changed from an elastic to viscous absorption boundary, the vehicle load condition was set, and the periodic calculation damping coefficient and maximum modal frequency were set, which were calculated in the first step in the analysis settings to begin the analysis and calculation of the traffic load disturbance depth (the purpose of setting the viscous absorption boundary was to prevent the traffic load from bouncing back when it was transferred to the boundary, which affects the correctness of the analysis results).  
Discriminant conditions. Disturbance depth is related to the foundation type and load size. Combined with domestic and foreign research results and engineering experience, it can be determined that when the additional stress, \(\sigma_{\mathrm{z}}\), of a traffic load in the foundation is lower than 10% of the self-weight stress, \(\sigma_{\mathrm{b}}\), of soil (presented in Figure 3), it is considered that the additional stress will no longer affect the deformation of soil at this depth and below [28], and depth \(Z\) can be taken as the disturbance depth of the traffic load.  
Figure 1: Schematic diagram of influencing factors of traffic load disturbance depth.  
Figure 2: Schematic diagram of numerical calculation model of traffic load disturbance depth. (In the numerical model, the thickness of the surface layer is set to 0.2 m, and that of the base layer is set to 0.4 m). (**a**) Numerical simulation model dimensions, (**b**) schematic diagram of a three-dimensional numerical simulation model.