# A Study on Karst Cave Collapse Based on Improved Terzaghi Theory and Upper Limit Analysis
###### Abstract  
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. improved Terzaghi theory; upper limit analysis; residual collapse resistance; critical surface load; karst surface collapse +
Footnote †: journal: Applied Sciences  
article  
[color=gray!20,] [color=gray!20,] [color=gray! In the study of engineering geological discrimination, [PERSON] and [PERSON] [5] examined karst surface collapses in the central plain of the Hamedan region of western Iran and they discovered that these collapses predominantly developed in groundwater discharge areas near the base of karstic limestone. [PERSON] et al. [6] analyzed the genetic mechanisms of a karst collapse and the settlement of surrounding buildings in Spain. Their investigation suggested that the extraction and drainage of karst groundwater during the construction of adjacent subterranean parking lots induced the loss of the upper sand layers. In summary, engineering geological discrimination facilitates the elucidation of the mechanisms behind geological hazard processes and qualitative conclusions [7]. The mechanism of karst ground collapse is analyzed from the aspects of topography, formation structure, and hydrogeological conditions, and the overburden is taken as an important analysis object. However, such a kind of method inherently lacks the capacity for quantitative assessments. Due to the concealment of the disaster-causing process of karst surface collapse, it is difficult to directly study the collapse mechanism of actual cases. Therefore, indoor physical model tests are commonly used research methods. [PERSON] et al. [8] examined soil permeability resistance through physical model tests and revealed hydrodynamic conditions for the migration of soil particles. [PERSON] et al. [9] simulated the formation of collapses in sand-rich strata using tank model experiments. They analyzed various factors influencing cavity formation, expansion, and upward migration in response to different cavity water levels. These tests have intuitively restored the process of collapse and obtained the law of collapse and suggestions for prevention and treatment. Similar to engineering geological discrimination, physical model tests offer valuable insights into the verification of the mechanisms and prevention of collapse [10; 11]. However, it is important to note that these tests are resource-intensive and time-consuming. In terms of numerical simulation of karst ground collapse, the main methods used include finite element method (FEM), finite difference method (FDM), and discrete element method (DEM) [12; 13; 14; 15]. The emergence and development of numerical simulations have profoundly advanced the study of karst surface collapses.