Generalized analytical expression for dynamic active thrust from c-φ soil backfills

In geotechnical engineering, there has been a need for the generalized analytical expression in explicit form for the dynamic (or seismic) active thrust from the c-phi (c=cohesion and phi=angle of shearing resistance) soil backfills on the rigid retaining walls since the early developments of explicit Rankine's, Coulomb's, and Mononobe-Okabe's (M-O)'s analytical expressions. An attempt is made here to present a derivation of such an explicit generalized analytical expression based on the pseudo-static approach, considering the most field parameters related to the wall geometry, soil backfill, and loadings, such as wall height, wall-backfill face inclination, backfill slope angle, tension cracks, wall friction, wall-backfill adhesion, cohesion and angle of shearing resistance of backfill, surcharge, and both the horizontal and the vertical seismic loadings. The development of an explicit analytical expression for the critical inclination of the failure plane within the soil backfill is also presented for the generalized case. It is found that the generalized analytical expressions, as special cases, result in the simpler expressions reported previously in the literature for several specific field situations under static and dynamic loading conditions.