Earthquake effect and strain for active state

Earthquake effect on earth pressure

Ground shaking adds inertia forces to the soil wedge behind the wall. In the pseudo-static (Mononobe-Okabe) method these are taken as horizontal $k_h W$ and vertical $k_v W$ forces, where $k_h$ and $k_v$ are seismic coefficients.

• The active thrust increases to $P_{ae} = \tfrac12\gamma H^2(1-k_v)K_{ae}$, with $K_{ae} > K_a$.
• The passive resistance decreases.
• The resultant acts higher (the dynamic increment about $0.6H$ above the base), increasing overturning moment.
• Water-saturated loose sand may liquefy, causing large extra pressure. Walls in seismic zones must be designed for these forces.

Horizontal strain needed to reach the active state

• (i) Coarse-grained soil (sand): very small, about 0.001 to 0.005 times $H$ (0.1 to 0.5%) of wall movement; dense sand needs less, loose sand more.
• (ii) Fine-grained soil (clay): much larger, about 0.01 to 0.04 times $H$ (1 to 4%).