Using a virtual back in retaining wall design

The computation of lateral earth pressures acting on gravity and semi-gravity retaining walls is often simplified by considering the pressures to act on a vertical plane passing through the heel of the wall. This plane is called either a ‘virtual back’ or a ‘virtual wall’ in the literature. The wall is designed to resist the active soil thrust acting on this virtual back, with the weight of the soil between the virtual back and the wall contributing to the stability of the wall. The virtual back approach is described in various soil mechanics texts, as well as in design guides and British Standard BS 8002:1994. There is, however, a variation in the recommendations given in the literature regarding the magnitude of friction angle (δ) to be assumed along the virtual back. The sensitivity of retaining wall design to the δ value selected along the virtual back is explored here, considering the design requirements to prevent forward sliding and overturning of the wall. A simple analytical study considers a design example similar to the examples proposed by Trenter. It is shown that, where δ is assumed to equal the angle of mobilised friction for the soil (φ′_m), the virtual back model does not represent a statically admissible failure mode for gravity retaining walls. Design examples are presented to quantitatively illustrate the implications of this finding for design practice.