An alternative to the Mononobe–Okabe equations for seismic earth pressures

Abstract

A closed-form stress plasticity solution is presented for gravitational and earthquake-induced earth pressures on retaining walls. The proposed solution is essentially an approximate yield-line approach, based on the theory of discontinuous stress fields, and takes into account the following parameters: (1) weight and friction angle of the soil material, (2) wall inclination, (3) backfill inclination, (4) wall roughness, (5) surcharge at soil surface, and (6) horizontal and vertical seismic acceleration. Both active and passive conditions are considered by means of different inclinations of the stress characteristics in the backfill. Results are presented in the form of dimensionless graphs and charts that elucidate the salient features of the problem. Comparisons with established numerical solutions, such as those of Chen and Sokolovskii, show satisfactory agreement (maximum error for active pressures about 10%). It is shown that the solution does not perfectly satisfy equilibrium at certain points in the medium, and hence cannot be classified in the context of limit analysis theorems. Nevertheless, extensive comparisons with rigorous numerical results indicate that the solution consistently overestimates active pressures and under-predicts the passive. Accordingly, it can be viewed as an approximate lower-bound solution, than a mere predictor of soil thrust. Compared to the Coulomb and Mononobe–Okabe equations, the proposed solution is simpler, more accurate (especially for passive pressures) and safe, as it overestimates active pressures and underestimates the passive. Contrary to the aforementioned solutions, the proposed solution is symmetric, as it can be expressed by a single equation—describing both active and passive pressures—using appropriate signs for friction angle and wall roughness.