Modeling cover-collapse sinkhole based on the theory of shells

The shape and height of a natural balanced soil arch are two of the critical factors for the development of a sinkhole. The exposure of the natural balanced soil arch can be described as the initiation of the surface-collapse phase of the cover-collapse sinkhole in karst terrain. In this paper, by simplifying the natural balanced soil arch as a thin shell in a limit equilibrium state, a theoretical model is developed using the nonmoment theory of rotary shells with the shape and height of the natural balanced soil arch derived based on the Protodyakonov’s theory. First, the developed model is validated using a case study (a cover-collapse sinkhole occurred in Guizhou, China). It demonstrates that the shell theory used in this study can describe the equilibrium state of a natural balanced soil arch reasonably well. After model validation, a series of numerical simulations are then carried out to investigate the critical factors which govern the collapse of a sinkhole. The results show that buried depth serves as a compulsory condition for the formation of the natural balanced soil arch. Furthermore, it shows that a buried depth less than six times of the radius of a cave could result in the formation of a natural balanced soil arch in the cone surface.