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Up to now remains open the question of constructing fundamental solutions of the two-dimensional statics of an elastic body with arbitrary anisotropy. Also in the scope of BEM method, the question of calculating stresses in boundary points and points located close to the boundary of the region still remains actual. In this work, fundamental solutions of the static problem for elastic plane with arbitrary anisotropic properties are obtained as the sum of residues with complex variable function. The assessments of fundamental solution and theirs derivatives are presented in closed form. In the distribution space obtained are the regular representations for the Somigliana formulas and the stress calculation formulas. The numerical implementation of the BIE method in direct formulation has been realized in standard way. The test results performed for circular hole in anisotropic plane of rhombic system show a higher compliance with the boundary values of displacements and stresses and with nodes placed close to boundary. The results of analysis of the stress-strain state in the vicinity of rectangular mining chambers located deep from day surface are presented in tables and pictures of isolines.

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.