| Summary: | 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. Various options for the formation of a vertical dip are considered depending on the geometrical parameters of the initial cavity, its depth and materials composing the rock mass, as well as the features of the destruction of various materials composing the mass during the formation of the dip. Relations are obtained that relate the depth of the cavity, the horizontal size of the hole, the strength properties of the rocks (adhesion, angle of internal friction), the coefficient of lateral pressure in the array. The features of wave processes generated by the formation of a dip are considered, for which a velocity field is obtained near the fracture zone at various time points in the fracture process.
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