Reliability of traditional retaining wall design

Retaining wall design has long been carried out with the aid of either the Rankine or Coulomb theories of earth pressure. To obtain a closed-form solution, these traditional earth pressure theories assume that the soil is uniform. The fact that soils are actually spatially variable leads, however, to two potential problems in design: do sampled soil properties adequately reflect the effective properties of the entire retained soil mass, and does spatial variability of soil properties lead to active earth pressure effects that are significantly different from those predicted using traditional models? This paper combines non-linear finite element analysis with random field simulation to investigate these two questions and assess just how safe current design practice is. The specific case investigated is a two-dimensional frictionless wall retaining a cohesionless drained backfill. The wall is designed against sliding using Rankine's earth pressure theory. The design friction angle and unit weight values are obtained by sampling the simulated random soil field at one location, and these sampled soil properties are then used as the effective soil properties in the Rankine model. Failure is defined as occurring when the Rankine predicted force acting on the retaining wall, modified by an appropriate factor of safety, is less than that computed by the random finite element method employing the actual soil property (random) fields. Using Monte Carlo simulation, the probability of failure of the traditional design approach is assessed as a function of the factor of safety used and the spatial variability of the soil.