Analytical solution of seismic pseudo-static active thrust acting on fascia retaining walls

This paper presents a limit equilibrium method, based on the approach of Mononobe and Okabe, for calculating the active thrust on fascia retaining walls, where common methods cannot be used owing to the narrowness of the backfill which does not permit the development of the thrust wedge in the shape and sizes predicted by these methods. The proposed method examines three distinct failure mechanisms, called Mechanism 1, Mechanism 2 and Mechanism 3, where the thrust wedge is formed by one, two or three blocks, respectively; separated by plane slip surfaces. The seismic forces have been simulated with the pseudo-static method. For all three mechanisms, the active thrust is obtained in closed form: in particular, with a cubic equation for Mechanism 2, and with a system of two equations, one cubic and the other quartic, for Mechanism 3. Mechanisms with more than three blocks cannot have analytical solutions. The study is completed by an examination of some significant cases from which the higher attenuation of the seismic thrust, with respect to the static, emerges as the backfill width reduces.