Generalized Rankine solutions for seismic earth pressures: Validity, limitations & refinements

The conditions giving rise to a uniform Rankine stress field involving straight stress characteristics in the soil behind a gravity retaining wall under pseudo-dynamic loading, are revisited. Considering combined gravitational and seismic body forces, exact closed-form solutions are derived for: (1) the coefficients of active and passive earth pressures, (2) the critical values of the five governing problem parameters required to generate the Rankine stress field i.e., wall inclination, wall roughness, backfill inclination, soil friction angle, and body force vector inclination. It is shown that the above parameters are not independent, as the critical value (termed “Rankine value” in this paper) of any of them can be derived as a function of the rest. It is further shown that when the critical wall roughness required to generate a Rankine stress field is smaller, in absolute terms, than the actual wall roughness, the generalized Rankine solution is conservative, overestimating active earth pressures and overestimating the passive, although it does not correspond to a limit state. When this condition is violated i.e., when the critical wall roughness is larger, in absolute terms, than the actual one, the trend reverses and the Rankine solution becomes both unconservative and not physically realizable. Further, if the Rankine wall roughness changes sign (i.e., turns negative for active conditions or positive for passive), the solution becomes even more conservative, yet implicitly corresponds to a kinematically unfeasible wall movement. A parametric investigation of these solutions is provided, with emphasis on practical situations and numerical examples, shedding light into the physics of the problem.