# Surface Subsidence Modelling Induced by Formation of Cavities in Underground Coal Gasification
## 3 Simulation Results  
### Stress Distributions  
Figure 2 shows the vertical stress profile generated by the gravitational force, indicating that the vertical stress was about 6.1 MPa at a depth of 300 m. Figures 3 and 4 show the distributions of maximum and minimum principal stresses of the two stages for Scenario I. The corresponding distributions for Scenario II are shown in Figures 5 and 6. As expected, there were significant tensile stresses developed at both the roof and the floor of the cavities, and the maximum compressive stresses appeared in the side walls. For Scenario I, the maximum tensile stresses were 1.32 and 1.42 MPa, and the maximum compressive stresses were 11.82 and 11.90 MPa, for stage 1 and stage 2, respectively. For Scenario II, these values were 1.25 and 1.42 MPa and 11.76 and 11.90 MPa for stage 1 and stage 2, respectively. Compressive and tensile stresses at stage 1 for Scenario I were slightly higher than those of Scenario II. However, the values after four cavities were completely formed for both scenarios were identical. In other words, the gasification sequence only affected the stresses at the intermediate stage but not the final stress distributions. Note the validity of this conclusion is clearly limited only to the elasticity regime without the consideration of plasticity and failure during the gasification process (cf. Section 3). Figure 1: One-half model used in this study: (**a**) model size, (**b**) cavity layout at section \(y\) = 15 m, (**c**) cavity size and arrangement. Figure 2: Gravity (z-direction stress). Note that the compressive stress is negative (unit: Pa). Figure 4: Distributions of the minimum principal stress for Scenario I. Note that the compressive stress is negative and the tensile stress is positive (unit: Pa). Figure 5: Distributions of the maximum principal stresses for Scenario II. Note that the compressive stress is negative and the tensile stress is positive (unit: Pa). Figure 3: Distributions of the maximum principal stress for Scenario I. Note that the compressive stress is negative and the tensile stress is positive (unit: Pa). Figure 9 shows the z-direction displacement profiles on horizontal cross sections at different depths from the surface. It can be seen that at the depth near the cavities, the z-direction displacement decreased quickly as it moved away from the center position. The z displacements on a cross section became more and more uniform as the section moved further away from the cavities. At the surface (z = 0 m), the z-direction displacement of the cross section was the modelled surface subsidence, which showed a profile with small variations (Figure 9), suggesting the impact of cavities on the subsidence profile was significantly reduced for areas far away from the cavities. Figure 10 show the maximum z-direction displacement at different depths from the surface. This position is at the center line through subsidence. Figure 11 shows the z-direction displacement contour plots on the horizontal cross section at z = 0 m (note the different color scales). After four cavities were formed, the same z-direction displacement profiles were observed for Scenario I and Scenario II and they followed approximately an upside-down elongated bell shape, with the maximum z-direction displacement in its center (shown in Figure 11). The maximum z-direction displacement was 9.8 mm, occurring at the center position (x = 82.5, y = 0). However, the subsidence profiles at stage 1 for the two scenarios were different. The maximum subsidence was 5.0 mm for Scenario I and 4.7 mm for Scenario II at the completion of the stage 1 gasification. The surface subsidence curves along the central horizontal line at y = 0 m are displayed in Figure 12. Clearly, the surface subsidence profiles were asymmetrical in stage 1 (largest on top of stage 1 gasification cavities) but became symmetrical in stage 2 for both scenarios (note the center point is at x = 82.5 m). The variability of the subsidence of stage 1 for Scenario I was higher compared with that for Scenario II.