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The article presents the formulation and implementation of the variable task of finding a rational outline of the back face of a retaining wall. In the framework of the Coulomb theory, an analysis is made of a system consisting of a retaining structure and soil pressing on it for the possibility of formulating a rational design problem. The simplest example shows the possibility of formulating the problem of finding the rational geometry of the back face of a retaining wall within a given horizontal projection. The substantiation of the operation of the energy method of rationalization in solving the problem under consideration is given. The essence of the proposed method for finding the rational geometry of the back face of the retaining wall is to approximate the curved generatrix of the back face of the retaining wall with a broken line. For each broken section, key dependencies are derived for its effect on the nature of the stress-strain state of the structure, in particular, in the formulation under consideration, on the magnitude of the bending moment in pinching. Key dependencies are derived and an algorithm for solving the problem is described. An illustrative example shows that, given the characteristics of a loose granular moment, the moment of pinching can actually be described through a combination of the angles of inclination of each of the sections, and in general the form of such combinations is infinite. The problem is reduced to searching for such a combination αi, in which the introduced criterion (in the formulation under consideration, the moment in pinching) takes its lower value. The implementation of the approach is demonstrated by a numerical example. The proposed approach allows a variable method to determine the surface configuration of the retaining wall, rational from the standpoint of the accepted criterion. The example given in the work clearly proves the correctness of the statement of the problem and its solution. The operation of this method is advisable in the computing information environment. In particular, the practical application of the presented approach is possible by formulating and solving the linear programming problem by the simplex method. Keywords: Retaining wall, curvilinear surface, approximation, variational approach.

This paper contains research of the seismic effects on the design of retaining walls. The present state of the technique of determining the pressure of the bulk medium on the side surface is analyzed. The basic theory of soil pressure on the retaining walls in static formulation is the Coulomb theory, according to which the pressure of the bulk medium on the lateral surface is determined by the condition of static equilibrium of a rigid wedge formed in the layer between the rear face of the structure and the sliding surface. In the works of Okabe and Mononobe, the proposed theory has evolved in the direction of dynamic influence accounting. To date, these studies are at the heart of current regulations. the issue of seismic component consideration in the calculation of retaining walls in the world design practice was analysed. The differences between the calculated dependencies of the US, Ukraine and Eurocodes codes are given. The reasons for the analyzed differences are identified and recommendations for their correction are offered.