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Particle transport in a porous medium occurs in environmental, chemical and industrial technologies. The transport of suspended concrete grains in a liquid grout through porous soil is used in construction industry to strengthen foundations. When particles are transported by a fluid flow in a porous medium, some particles are retained in the pores and form a deposit. The aim of the work is the construction and study of a one-dimensional mathematical model of particle transport and retention in the porous medium, taking into account the simultaneous action of several particle capture mechanisms. The model consists of mass balance equation and the kinetic equation of deposit growth. The deposit growth rate is proportional to the filtration function of the retained particles concentration, and the nonlinear concentration function, which depends on the concentration of suspended particles. The use of a new parameter, depending on the distance to the porous medium inlet allows to construct a global asymptotic solution in the entire area of the mathematical model. Asymptotics is obtained as a series in two small parameters. The global asymptotics is close to the numerical solution at all points of the porous medium at any time.

Abstract. Aim.When conducting engineering and geological surveys at the conceptual stage of the feasibility study, it is necessary to create an automated system that allows the designer to take all possible factors into account and choose the most optimal design solution for the shoring of excavations.Method. The study is based on dynamic programming methods based on the principle of Bellman optimality. Logical convolution matrices are applied according to the dichotomy method.Results. As a result of the logical convolution of the aggregated criteria of the environmental parameters K12 along with the parameters of the surrounding buildings K34, a comprehensive assessment of the design solution for a foundation shoring fence is obtained such as to ensure the technical characteristics and safety of the development zone. However, a considerable influence on the choice of the design solution for the building envelope is exerted by the cost of its construction. Therefore, the indicator of a comprehensive assessment of the shoring fence considering the economic efficiency of the KOE is obtained by combining the indicator of a comprehensive assessment of the foundation shoring fence KO with the criterion of economic efficiency of the design decision K5.Conclusion. The analysis of methods for solving optimisation problems demonstrates that the method of complex estimates based on the theory of active systems is optimal for the task of evaluating design solutions for foundation shoring fences.

Currently, a lot of new construction is underway in the large cities and megacities territories. Large residential complexes and shopping centers are erected at the sites of former industrial zones and factories. The issue of the accidents in foundation pits arising from the errors in their barriers’ projecting has recently been an acute question. And this is directly related to the fact that construction has to be carried out in very difficult straitened development conditions with the presence of existing utilities and underground facilities. The main designer’s task is the selection of an optimal project solution. Any project decision for the foundation pit barrier is characterized by both the technical characteristics, in particular the materials used, and its construction cost. Therefore, the designer faces a difficult question of the price and quality ratio for this project decision. And it is complicated by the fact that the specific engineering and geological conditions imply the possibility of various project decisions for the foundation pit fencing and the materials corresponding to the calculations results for the limiting states. This paper describes in detail the methodology for assessing the project decisions for foundation pit fencing and the choice of the materials used in barriers’ design based on the active systems theory.