Modelling the static stress–strain state around the fan-structure in the shear rupture head

Abstract

• Mathematical model of an equilibrium fan between elastic half-planes is constructed. • Length of the fan is evaluated based on the singular solution for edge dislocation. • Potential mechanisms of fan-structure formation in a fault are considered. • Original method of superposition of dislocations is suggested. • Fields of stresses and displacements around the fan-structure are computed. The mathematical model of an equilibrium fan-structure in the interface between two elastic blocks, simulating the shear rupture head in a hard rock under high confining pressure, is constructed. The stress–strain state far from the fan-structure is analyzed with the help of a solution of the problem on edge dislocation. The fan length is estimated using this solution. The model of formation of two oppositely directed fans due to the localized action of tangential stress, which pushes two edge dislocations with antiparallel Burgers vectors, is proposed. In complete formulation, the problem on an equilibrium fan-structure in the interface between infinite elastic half-planes is analyzed by means of original method of superposition of dislocations, leading to two nonlinear integral equations in the fan zone. To solve them numerically, the method of successive approximations is applied. Based on this method, fields of stresses and displacements around the equilibrium fan modelling of a deep-seated shear rupture in the seismogenic zone of the Earth’s crust are computed. Such fields can be used, when setting the initial data in the analysis of dynamics of the fan-shaped mechanism.