Application of inverse FEM to earth pressure estimation

In order to process measurement data in structural mechanics, an inverse FEM is formulated with displacement and loads as unknowns. A cost related to both loads and discrepancies between measured and estimated values is minimised, under constraint that equilibrium be verified. The constrained minimisation problem is discretised using Galerkin's method, and solved using Lagrange multipliers. For quadratic costs and linear structures, this yields a linear system of equations with three times more unknowns than the corresponding forward FEM model. The technique is applied to estimate soil pressures acting on a small-scale model of a retaining wall, using bending strain measurements. Repeatable and realistic results were obtained, providing valuable information for the formulation of a design guideline for coffer dams and similar structures.