Experience of mining potash and potash-magnesium salt is reflective of extremely high number of accidents and deprivations of mines even when most advanced technologies are used. Difficult maintenance of long-term accident-free performance of geotechnical systems through all mining phases at rock salt deposits is connected with the extremely complex and yet understudied nonlinear processes of rock displacements governed by alteration of impermeable strata in-between stoping and aquifers. These nonlinear displacements induce through-the-thickness permeable cracks in the impermeable strata. Generally, the zone of permeable cracks is composed of two hydraulically interconnected systems of induced fractures: exfoliation joints and through-the-thickness dip joints. When the upper boundary of the permeable fracture zone reaches the lower boundary of a body of water, these channels become available for water flow to underground openings. One of the most efficient ways to study such nonlinear processes is modeling using equivalent materials. However, this method has some constraints connected with the requirements to ensure integrated similarity of the compression, tension and bending strengths which are critical in the research of rock movement processes. This article offers a modification of modeling using equivalent materials based on the better similarity achieved in strength parameters of rocks and the method of discrete change of a movement trough at the level of productive strata, which ensures simulation of the movement trough on ground surface with regard to the linear scale of modeling. The main research finding is the forecast of nonlinear displacement processes in rock mass and the refinement of jointing and exfoliation parameters which, given certain conditions, can initiate through-the-thickness permeable channels.