Monitoring of parallel galleries in the region of horizontal motion of lithospheric plates

The problem of estimating the stress-strain state of underground openings of solid minerals, which form long parallel underground galleries, is considered. Several papers studied the local causes of accidents that occur in underground galleries during mineral extraction due to variations in the stress-strain state of the medium. The influence of formation of new galleries, which violate the balance of vertical stresses in the walls between the galleries, is also studied. At the same time, the problem on the influence of horizontal displacements of lithospheric plates on the stress-strain state of parallel galleries is little studied. These displacements affect the horizontal components of the contact stress vector arising between the upper and lower layers and the walls between the galleries. In this paper, the theory of estimating the stress-strain state in underground openings with arbitrarily many parallel galleries of various dimensions is developed under the assumption that the tangential components of the stress vector exist in the contact regions between the layers and the walls. The study is based on factorization methods, block element method, and a topological approach.