Finite Element Method for Retaining Walls Subjected to Swelling Pressure

Abstract

Finite Element Method (FEM) is a widely used method of solving initial boundaryvalue problems from mechanical engineering. It allows addressing irregular domains and force terms, while enabling careful analysis of the approximated solutions. In this capstone project, a standard derivation of FEM from the mechanical engineering standpoint is presented, then all the necessary mathematical machinery is introduced to facilitate the discussion. Once the proper introduction to FEM is given, the paper dives into the two main subjects of the matter. First, the derivation of the EulerBernoulli beam equation is presented. It is a standard model for the analysis of retaining walls. Then a brief derivation of the swelling force, which models the effect of soil swelling onto the retaining walls, is given. Second, the finite element solution to the problem is derived, and the results are presented.