Abstract: Traditional assessments of active earth pressure are typically deterministic and assume a homogeneous soil layer. However, soil properties exhibit inherent random variations due to geomorphic processes or poor construction control. To address this limitation, we employ the random limit analysis method (RLAM) to investigate the influence of spatial variability in soil strength parameters on the active earth pressure. We enhance the conventional three-dimensional (3D) rotational failure mechanism by applying a spatial discretization technique that enables rigorous coupling with random-field simulations. We derive an explicit equation for 3D active earth pressure based on the upper-bound theorem of limit analysis. The validity of RLAM is verified by comparing it with a deterministic numerical method and with the random finite difference method (RFDM). Furthermore, through extensive uncertainty analyses, a reliability assessment framework is established for gravity retaining walls that explicitly incorporates the spatial variability of soil strength parameters. It is found that under different random field design scenarios, the decay curves of system failure probabilities for the retaining wall intersect within a specific range, providing valuable guidance for the design and construction of retaining walls.

Key words: active earth pressure, retaining wall, spatial variability, random field, soil strength parameters