karst failure, computer simulation, Drucker-Prager fracture criterion, meshless SPH code.

Karst manifestations are widespread in many regions and pose a significant danger to residence and economic activity. Failing funnels arise during the collapse of rocks over underground voids (caves, workings, etc.), formed during karst formation or in the process of anthropogenic doing in the rock massive. However, not every karst or technogenic cavity gives rise to a failure of the earth’s surface, and as a rule, its occurrence is unexpected. In this work, we consider the dynamics of the formation of dips of the earth’s surface in the form of a collapse pipe. To do this, the geomechanical problem is solved by the meshless code Smoothed Particle Hydrodynamics (SPH). The method allows to obtain a solution to the problem taking into account large deformations and possible discontinuities in the process of changing the stress-strain state. The Drucker-Prager fracture criterion is used, the parameters of which change over time in accordance with the accumulation of damage, which determines the temporary development of the fracture process, its beginning and speed.

Trofimov Vitaly Aleksanrovich, Dr. Tech. Sciences, Head Lab., Institute of Comprehensive Exploitation of Mineral Resources Russian Academy of Sciences, Moscow, Russia.

Shipovsky, Ivan Evgenievich Cand. Tech. Sciences, Senior Researcher, Institute of Comprehensive Exploitation of Mineral Resources Russian Academy of Sciences, Moscow, Russia.