Dynamic Active Earth Pressure Against Retaining Walls

Equations of equilibrium expressed along the stress characteristics are transformed onto the Zero Extension Line (ZEL) directions. The new dynamic equilibrium equations are then applied to simple ZEL field (composed of Rankine, Goursat, and Coulomb zones) behind retaining walls. Integration of differential equilibrium equations along the assumed field boundary, thus provide the final equations for the active static (Kast) and dynamic (Kady) earth pressure coefficients, which are functions of friction and dilation angles of the soil and friction angle of the wall surface. Numerical evaluation of Kast, and Kady indicates that these coefficients are not sensitive to the wall roughness for practical values of angle of friction of backfill material between 35° and 45°. In this range, the coefficients can be approximated by: Kast=tan2(π/4 -φ/2) and Kady =tan(π/4 - ν/2)