Upper-bound analysis of seismic yield acceleration for rotational failure of gravity retaining walls using the horizontal slice method

Gravity retaining walls may undergo toe-rotational failure during strong earthquakes, making reliable seismic stability assessment essential. Existing upper-bound methods based on the oblique slice method (OSM) impose upward movement on part of the backfill, which may overestimate rotational stability. To address this limitation, a horizontal slice method (HSM) is proposed, in which the failure wedge is discretized into infinitely many horizontal rigid slices and a kinematically admissible velocity field satisfying the associated Mohr–Coulomb flow rule is constructed. Using the principle of virtual power, an energy-balance equation is established to determine the seismic yield acceleration coefficient kcr. The HSM results agree well with those from the limit equilibrium method (LEM). Compared with HSM, OSM consistently gives larger kcr values, with an average relative difference of 14.30%. The proposed HSM provides a mechanically interpretable upper-bound framework without requiring a predefined seismic earth-pressure application point.