On the issue of optimizing the shape of geological excavations and topology of their strengthening

Relevance. At mining and formation of excavation, the array natural stress-strain state, surrounding the extraction, changes. The result is the deformation of the rock and redistribution of stresses around the excavation, which could lead to its collapse. These stresses strongly depend on the shape of the cross section of the development and type of additional fortifications of the vault gallery. Thus, the ability to predict these processes, and especially to control them, developing optimal forms and types of arches strengthening, may reduce the probability of a tunnel destruction and increase their reliability. The aim of this work is modeling and shape optimization of excavations in the form of long tunnels that can be considered under plane strain state; design of optimal topology of the supporting structure around the excavation for optimal form of arches, perceiving the main load of its own weight and the weight of the overlying rocks. Methods. For mathematical modeling of the excavation behavior the authors have used the methods of finite and boundary elements for problems in mechanics of deformable body and the methods of elastic bodies forms optimization developed by the authors. For strengthening the arch of tunnels the method of topological optimization was used. Results. The authors developed the algorithms and programs of optimization of shape and topology optimization for a planar problem of elasticity theory. By the example of the model problem the authors demonstrate the possibility of optimizing the arch shape of the excavation and its optimal external strengthening with the steel structure for reducing the maximum shear stress (criterion Cod), thus decreasing these stresses.