A Study on Karst Cave Collapse Based on Improved Terzaghi Theory and Upper Limit Analysis

Karst areas exhibit intricate geological attributes, and the geological and environmental issues caused by urban development cannot be ignored, especially the issue of karst surface collapses. In this study, we developed two analytical methods and analyzed the stability of the overburden stratum of 3D spherical karst caves with surface load, vacuum absorption erosion force, and groundwater table considerations. The first analytical method is based on the improved Terzaghi theory, while the second analytical method is based on the upper limit analysis. A case study was conducted in Wuhan, China. The results from both analytical methods indicated a potential susceptibility to collapse, suggesting the excellent accuracy of these two methods. The results were also compared with the numerical solutions from previous studies. Notably, the accuracy of the upper limit analysis was inversely proportional to the depth ratio, while the results obtained through the improved Terzaghi theory were consistent with those of the numerical solutions, particularly under conditions of relatively high depth ratios. This study examined various facets, including the development of karst caves, soil shear strength, groundwater table fluctuations, and boundary failure angles. Furthermore, we explored the effects of geometric and geotechnical parameters on the stability of karst caves.