Solving the task of rock pressure with a non-linear function of softening using the finite difference method
A possible solution of the task of determining the rock pressure is given for a flat close to the axisymmetric problem, taking dilatancy into account. Stress non-linear softening function is used in the description of the prohibitive deformation zone. To develop it, the approximation of the envelope curve of Mohr's limit circles by the non-linear parabolic strength conditions is used. A new dilatancy correlation using the associated flow law is developed, independent of voltage. This condition corresponds with the well-known experiments. The loading history is taken into account. The final solution is obtained by sequential solution of tasks for elastic and prohibitive zones using the option of explicit finite difference method developed by the authors. The proposed method is implemented in a computer program that predicts the rock pressure on the contour of working.