Retaining Wall Surface Optimization

The paper presents the formulation and implementation of the problem of finding a rational external geometry of a retaining wall. The purpose of the research is to formulate and test the mathematical model of the specified problem. In this connection, the working hypothesis is the assumption of accepting the criteria for rationalizing the system in the form of requirements for minimizing the potential strain energy of system (PSE) on the set of allowable values of variable parameters and equalizing the potential strain energy density (PSED) within the designated model. These criteria are an integral structural part of the bioenergetic optimization method, however, this paper considers the problem of improving external (geometric) parameters based on the exploitation of only the 1st criterion. In the framework of the exploitation of the Coulomb theory, the procedure of formation of the geometry of the structure is defined when the pressure of the ground on it is applied. The simplest example is the algorithm for solving the problem of finding rational geometry of the rear face of a subsurface wall with its given horizontal projection. The essence of the proposed approach is the approximation of the curvilinear forming the rear face of the subsurface wall by a broken line. For each section of the divided structure key dependencies are built for the components of the stress-deformed state of the structure. It is shown that for given soil characteristics, the value of the potential energy of deformation of the system can be described through a combination of the slope angles of each of the sections. The problem is reduced to finding a combination of these angles in which the entered criterion takes the minimum (exact lower bound) value. The conclusion about the representativeness of the obtained solution is made on the basis of the compiled alternative information model. The implementation of the approach is illustrated by a numerical example. The results obtained can be applied in the search for a rational geometry of a retaining wall in the process of building design.