A generalized iterative solution for seismic analysis of retaining wall subjected to coupled tensile shear failure

A refined theoretical framework is presented to estimate seismic active thrust, developed following a limit equilibrium-based pseudo-static approach guided by a logarithmic spiral failure surface. A cohesive frictional soil with pre-existing vertical cracks subjected to external surcharge load is considered for analysis. An extended Rankine's equation is proposed to determine the tension crack depth, which incorporates all the affecting wall soil backfill parameters. Conventional earth pressure coefficients are formulated, leading to the innovation of earth pressure ratios that efficiently interpret the effect of distribution of backfill soil mass above and below the crack zone, post its occurrence. Influence of the tension crack on backfill soil weight, failure surface, and the resulting active earth thrust is assessed for wall stability under seismic loading. A unique parameter K is derived, which demonstrates the seismic interdependence of all ratios comprehensively. A generalized moment-based equation is adopted to determine the application point of the active thrust through iterative equations expressed in the normalised form. Effect of cohesion accompanied by tension crack, surcharge under seismic effect for different friction angles are assessed on results of magnitude and location of the application point. Observations include, in battered walls neglecting tension cracks might lead to incorrect estimation of application point, potentially compromising wall stability and economy. The results from proposed study are found to be in good agreement with the existing literature. Plots for the earth pressure ratios and normalised application point for a spectrum of backfill inclination and wall batter angles are presented.