Analytical solution of seismic passive earth pressure for negative friction angle of wall-soil interface

Most of the existing analyses of passive earth pressures behind retaining walls deal with the case of positive wall-soil interface  friction angles (the wall moves downwards relative to the backfill), while the researches on passive earth pressures for the negative wall-soil interface friction angle case (the wall moves upwards relative to the backfill) are still lacking. Based on the planar rupture surfaces hypothesis, a theoretical formula for the seismic passive earth pressure coefficient, the resultant force of earth pressure and the application point of the resultant is obtained by using the Kötter equation and the combination of pseudo-static approach with the limit equilibrium method of analysis for the negative wall-soil interface friction angle case. The seismic passive earth pressure coefficients always decrease with the increase of the vertical seismic acceleration, but the horizontal seismic acceleration results in either an increase or a decrease in the earth pressure coefficients, depending on the combinations of the wall batter angles, wall-soil interface friction angles and soil friction angles. The variation of seismic passive pressure coefficients increases with the increase of the magnitude of the earthquake acceleration. The proposed analysis lies in its ability to compute the point of application of the passive thrust, for which moment equilibrium condition of failure wedge is effectively utilized. The application point of the passive thrust decreases with the increasing values of horizontal seismic acceleration coefficients. The computed values of the seismic passive pressure coefficients and the point of application of passive thrust agree with the available results, which can be served for anchor and transmission line foundations under uplift loading.