# A Study on Karst Cave Collapse Based on Improved Terzaghi Theory and Upper Limit Analysis
###### Abstract
Through the simulation of karst surface collapse processes under varying conditions [16; 17], the collapsing mechanisms can be revealed from the perspective of the geotechnical mechanical characteristics. They facilitate the analysis of factors influencing the stability of karst caves. However, as reported by [PERSON] et al. [18], the existing karst cave models face challenges in terms of data availability and the informational content of existing data, rendering the attainment of accurate conclusions a challenging endeavor because of the inability to closely reflect reality. Mechanical analysis methods for assessing the stability of karst caves predominantly rely on conventional engineering theories or empirical formulas. Currently, common traditional calculation techniques include [PERSON]'s pressure arch theory, Terzaghi theory, empirical formula methods, and roof collapse sealing methods [19]. Nevertheless, there is the issue of oversimplification and empiricism in the calculation of karst cave stability using traditional theoretical methods, which only consider the gravity, cohesion, and friction of soil, ignoring or simplifying the influence of groundwater and vacuum absorption erosion force. It is difficult to accurately summarize the law of karst cave stability. For instance, in [PERSON]'s pressure arch theory, calculation results rely on the empirical coefficient of Protodyakonov. [PERSON] et al. [20] employed Terzaghi theory and considered excessive pore water pressure to analyze the karst surface collapses; the results of this study are satisfactory. However, referring to the strata above karst caves as a uniform medium, this study ignored the groundwater table factor, potentially leading to inaccuracies in the calculations. Therefore, these oversimplified methods can only reflect the intricate relationships between karst cave stability and partial factors. To overcome the shortcomings of oversimplification and empiricism of traditional stability analysis methods, the limit analysis method with higher accuracy and precision has become a widely used tool in geotechnical engineering. As early as 2003, [PERSON] et al. [21] introduced the limit analysis method to assess the stability of karst cave overburden. In recent years, the limit analysis method has been increasingly applied to evaluate the stability of karst caves and tunnels. [PERSON] et al. [22] conducted a parameter study on the undrained stability of spherical cavities in clay by employing a finite element limit analysis method under axisymmetric conditions. Their study explored the influence of cavity coverage depth ratios and other dimensionless factors on the ultimate surface load. Through a combination of the lower bound theorem of the limit analysis method and the finite discretization method, [PERSON] et al. [23] proposed a 3D collapse mechanism capable of considering the simultaneous collapse of tunnel roofs and sidewalls. The limit analysis method was employed to calculate the upper limit of the 3D support pressure, and the results aligned favorably with numerical findings from prior studies. While the implementation of the limit analysis method in existing research has yielded valuable insights into the potential failure modes of karst collapses, the impact of groundwater on the collapse of karst cave overburdens is frequently ignored. Mechanical analysis needs to combine more factors to ensure the reliability of the calculated results and adopt more reasonable failure models to make them fit reality. In this study, we employed an improved Terzaghi theory and limit analysis method to conduct a mechanical analysis of the 3D stability of a karst cave overburden. New types of collapse failure models and the interplay between groundwater and karst caves were considered. Furthermore, we performed this analysis using numerical simulations to validate the actual collapse cases. Additionally, we explored the effects of karst cave development, soil shear strength, groundwater table, and boundary failure angles on the occurrence of karst collapse.