On the variational solution of a limiting equilibrium problem involving an anchored wall

This paper presents a solution of an anchored retaining wall problem using the approach of classical variational calculus, that allows the three equilibrium equations to be taken into account. The problem is formulated as an isoperimetric problem of variational calculus and a closed-form solution of Euler's equations is found. The analysis is validated by means of the classical Coulomb's wedge method that is obtained when the moment equilibrium is omitted. Unfortunately, in the general case, extremes of the functionals that are involved in the formulation of the problem can not be found in an analytical way. In this case, a crucial point was to establish bounds for the domain of the investigations of the functional maxima. Next, based on these bounds, a numerical procedure for finding maxima has been worked out. Several numerical analyses for the case of wall embedded in a non-cohesive soil have been carried out. An important finding is that the classical Coulomb's wedge method, which ignores the moment equilibrium equation, is an unconservative approach and hence provides an unsafe solution for the anchor force.