The dissertation on competition of a scientific degree of the candidate of technical sciences (doctor of philosophy) on a specialty 05.23.01 - "Building constructions, buildings and constructions" (192 - Construction and civil engineering). - Odessa National Maritime University of the Ministry of Education and Science of Ukraine, Odessa,2019. Problemsin the dissertation work related to mathematical modeling of the joint work of retaining structures and soil massif in conditions of dense urban development are considered. These studies make it possible to most accurately determine its stress-strain state and to assess the deformation and the possibility of destruction of nearby and projected structures, taking into account the elastic-plastic deformations of all model elements, which often significantly exceed the elastic ones. To achieve the goal of the study, eight tasks have been set and consistently solved in the work. As a result of solving the tasks the main results are obtained: as a result of solving problem 1: the existing calculation methods, as well as models of materials and soils are analyzed, which allowed us to conclude that to more accurately determine the stress-strain state of the considered systems, it is necessary to take into account the joint work of all its elements. It is also concluded that to take into account the elastic-plastic properties of structural materials and soils, theories of plasticity with hardening should be used, which allow to take into account the process of complex loading. Modeling of the soil environment by the Coulomb method or by the theory of the ultimate stress state does not allow to determine the deformations, and, consequently, the changes in the stress state during loading. As a result of solving problem 2: an extended elastoplastic model of the retaining structure has been developed, which takes into account the process of complex loading and, as a single system, can include the following elements: 1) directly the retaining structure; 2) part of the soil massif located next to it; 3) structures previously built or designed on these grounds; 4) groundwater. Such an extended model makes it possible to most accurately determine its stress-strain state of the system. As a result of solving problem 3: based on the use of the theory of plastic flow with hardening, based on the application of the Mises maximum principle, the following equations were obtained in a form convenient for application to the calculation of supporting structures. As a result of solving problem 4: developed an algorithm for solving the resulting system of nonlinear algebraic equations of the problems under consideration. It uses an iterative process to accomplish the following tasks: - linearization of the original equations; - return of the stress vector to the area bounded by the loading surface; - solution of the considered boundary value problems with a given accuracy. As a result of solving problem 5: the PLASTICA software package, written in C #, was improved. The author of the thesis has written and debugged a number of subroutines (Pisarenko-Lebedev condition, improved user interface regarding input of initial data and output of calculation results), which are included in this complex. As a result of solving problem 6: on the basis of the calculations of the retaining structure of the pit slope, it can be noted that the action of the previously built structures and the own weight of the soil raises it inside the pit and decreases its width with depth. The left extreme point of the foundation slab, previously built to the left of the building's foundation pit, dropped after the end of construction by an additional 4 cm, and the right only by 1 cm, so the building together with the foundation slab tilts to the left. In the second layer of soil near the side walls of the foundation pit, plastic deformations occur. On the basis of the calculations performed, the anti-landslide structures of the slope can be determined that the maximum soil pressure on the sheet pile wall is 44.58 kN / m2, and the resultant pressure is 406.65 kN / m. As a result of solving problem 7: a comparison of the calculation results obtained using the PLASTICA and PLAXIS software systems, as well as the classical Coulomb method with experimental tests of three different authors, has shown their satisfactory agreement. As a result of solving problem 8: the results of the study were successfully implemented when adjusting the project “Bank protection works with a length of 280 m of the Kremenchug reservoir in the area of the village. Bolshaya Andrusovka, Svetlovodsky district of the Kirovograd region " and others.Supporting documents are given in the appendix. Key words: mathematical modeling, retaining structure, soil mass, elastic-plastic deformations, stress-strain state, complex loading process, loading function, system of basic nonlinear equations, algorithm, software package.
