In this study, an analytical model was proposed to extend the Log-Spiral-Rankine (LSR) method (for estimation of the active and passive earth pressures) to a more general scenario in which the ground surface and wall are inclined. The LSR method adopts the limit-equilibrium concept coupled with the method of slices to investigate the internal and external equilibrium conditions of the backfill at the moment when the failure (or sliding) surface forms. The geometry of the failure surface is determined using the stress states of the soil at the two boundary regions (namely, in the region close to the ground surface and at the wall-soil interface) of the mobilized soil mass. The mobilized soil mass is then discretized into a small number of vertical slices to allow for stress redistribution between the two boundary regions. Local equilibrium of each soil slice and global equilibrium of the entire mobilized soil mass are examined to formulate the governing equation set that satisfies both the stress and force equilibrium conditions, for both static and seismic cases.

The analytical model also extends the classical Rankine solution for application to c-φ backfill soils under the seismic condition and fixes a known problem of Rankine solution which yields symmetrical solutions for up-hill and down-hill slopes. The potential dangerous zone during soil excavation on a slope as well as the corresponding force and moment demands imposed on the retaining wall can thus be more accurately estimated.

The proposed model has been implemented using the MATLAB^© programming language, and the results have been compared with those predicted by existing analytical models and those obtained from experimental test programs and finite element simulations using the commercial program, ABAQUS. Overall, the proposed analytical model is more robust and can generate better predictions of the lateral earth forces as compared to the existing models.

Parametric studies were then performed to investigate the effects of various backfill soil and geometrical parameters on the predicted earth pressures. The results show that the increase in the backfill inclination angle increases the magnitude of both active and passive earth pressures while increase in wall inclination angle and horizontal seismic coefficient lower the magnitude of passive earth pressure and increase that of the active earth pressure. The soil friction and wall-soil interface friction angles; backfill soil cohesion and wall-soil interface adhesion, increase the magnitude of passive earth pressure while they decrease that of active earth pressure.

The analytical model introduced above, although more robust and accurate, involves some iterative steps searching for the converged solution of the highly coupled, nonlinear, multivariate governing equation set, making it too complicated to be implemented by the field engineers. A simplified semi-analytical closed form solution, using the Mononobe-Okabe’s (M-O) as the base model, for the extended LSR method is thus developed in the last part of this study. The M-O model is currently recommended by many retaining wall design guidelines/codes, primarily because it is simple to apply, though it considerably overestimates the passive earth pressure when the wall-soil interface friction angle and backfill inclination angle are high. The aim is to harness the advantage of the accuracy of LSR and simplicity of M-O model while eliminating their drawbacks, to derive a closed-form formula that is suitable for use in the daily design work.

Together with the proposed semi-analytical closed-form equation, this study provides a reliable means for quick static and seismic earth pressure assessment which can be easily integrated into the retaining wall design guidelines and/or manuals issued by geotechnical design regulatory agencies such as AASHTO LRFD, CALTRANS, and Hong Kong GEO.