Reliability of passive earth pressure

Abstract

Passive earth pressure calculations in geotechnical analysis are usually performed with the aid of the Rankine or Coulomb theories of earth pressure based on uniform soil properties. These traditional earth pressure theories assume that the soil is uniform. The fact that soils are spatially variable leads to two potential problems in design: do sampled soil properties adequately reflect the effective properties of the entire soil mass and does spatial variability in soil properties lead to passive earth pressures that are significantly different from those predicted using traditional theories? This paper combines non-linear finite element analysis with random field simulation to investigate these two questions. The specific case investigated is a two-dimensional frictionless passive wall with a cohesionless drained soil mass. The wall is designed against sliding using Rankine's earth pressure theory. The unit weight is assumed to be constant throughout the soil mass and the design friction angle is obtained by sampling the simulated random soil field. For a single sample, the friction angle is used as an effective soil property in the Rankine model. For two samples, an average of the sampled friction angles is used. Failure is defined as occurring when the Rankine predicted passive resistance acting on the wall, modified by a factor of safety, is greater than that computed by the random finite element method. Using Monte Carlo simulation, the probability of failure of the traditional design approach is assessed as a function of the factor of safety using and the spatial variability of the soil.