# Surface Subsidence Modelling Induced by Formation of Cavities in Underground Coal Gasification
## 5 Conclusions  
In this study the subsidence corresponding to the gasification of four cavities (C1, C2, C3, and C4) of size of 30 m \(\times\) 30 m \(\times\) 15 m, separated by 15 m wide pillars at a depth of 300 m was modeled under the elasticity regime. Two gasification scenarios were investigated, including Scenario I: gasification of C1 and C2 (stage 1), followed by C3 and C4 (stage 2); and Scenario II: gasification of C1 and C3 (stage 1), followed by C2 and C2 (stage 2). For both scenarios, the final maximum surface subsidence after the completion of all four cavities was 9.8 mm and the maximum compressive stress and tensile stress around cavities were 11.9 MPa and 1.42 MPa. The surface subsidence profile was an approximate upside-down elongated bell shape with the maximum subsidence occurring at the center position of the four cavities (x = 82.5 and y = 0). The maximum z-direction displacement at the cavity roof was 156.0 mm and the z-direction displacement profile at the horizontal section directly above the cavities was an upside-down bell shape. The variations in z-direction displacements on horizontal cross sections became more and more uniform as the section moved further away from the cavity and got closer to the ground surface. The gasification scenarios (sequences) only affected the stress and subsidence distributions at the intermediate stage (stage 1), not the final results after all four cavities were formed, which was due to the elasticity regime considered. For Scenario I, at stage 1, the maximum surface subsidence was 5.0 mm, the maximum z-direction displacement at the cavity roof was 154.2 mm, the maximum compressive and tensile stresses around the cavities were 11.82 MPa and 1.32 MPa, respectively. For Scenario II at stage 1, the maximum surface subsidence was 4.7 mm, the maximum z-direction displacement at cavity roof was 147.4 mm, the maximum compressive and tensile stresses around the cavities were 11.76 MPa and 1.25 MPa, respectively. For the smallest cavity (152 m\({}^{3}\)) modelled, the maximum surface subsidence was 0.016 mm, while for the largest cavity (30 \(\times\) 30 \(\times\) 15 m\({}^{3}\)), the maximum surface subsidence reached 7.14 mm. The relationship between surface subsidence and cavity volume in this case was approximately linear, though a nonlinear relationship is expected at larger cavity volumes. A prediction model of surface subsidence deformation was built up using the elastic plate theory, and the formula of the surface deformation at a random point was given. The comparison between numerical results and the proposed model demonstrated that the proposed method can be used to predict the ground subsidence induced by UCG. Figure 17: Comparison between proposed model and field data in an actual case of multiple cavities. **Author Contributions:** Conceptualization, Y.J. and B.C. ; methodology, L.T. ; software, Y.W. ; validation, Y.J. and B.C. ; formal analysis, L.T. ; investigation, Y.J. ; resources, B.C. ; data curation, B.C. ; writing\(-\)original draft preparation, Y.W. ; writing\(-\)review and editing, Y.J. ; visualization, Y.J. ; supervision, F.X. ; project administration, L.T. ; funding acquisition, L.T. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by The project of Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, grant no. SKLGME023023, Slope safety control and disaster prevention technology innovation team of \"Youth Innovation Talent Introduction and Education Plan\" of Shandong Colleges and Universities (grant no. Lu Jiao Ke Han [2021] no. 51); National Natural Science Foundation of Shandong Province of China (NSFC) (grant no. ZR2022 ME188), Jinan City \"new university 20\" research leader studio project (grant no. 20228108). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable.