Cyclic shear strain builds excess pore-water pressure in loose saturated sand. Using the Seed–Booker degradation model, the pore-pressure ratio after N shaking cycles (Nliq = cycles to full liquefaction) is:
r_u(N) = (2/π)·asin[ (N/N_liq)^(1/2θ) ], θ ≈ 0.7, capped at N ≥ N_liq → r_u = 1
Nliq rises with cyclic resistance ratio (denser sand, higher Dr) and falls with cyclic stress ratio (stronger shaking, CSR ≈ 0.65·amax/g). As r_u → 1, effective stress and shear strength collapse. The gently sloping crust is driven downslope toward the free face by its own weight while the liquefied layer beneath resists:
τ_drive = γ'·H·sin(β) (gravity component on the slope)
τ_resid = γ'·H·tan(φ_r)·max(0.02, 1 − r_u) (residual strength of the liquefied layer)
Spreading only begins once τ_drive exceeds τ_resid — i.e. once pore pressure has risen enough to knock the residual strength below the driving stress. From that point, blocks of crust slide toward the free face at a rate proportional to the excess stress (τ_drive − τ_resid), exactly the "sliding block" logic used in real deformation analyses. Because nothing confines the ground right at the free face, displacement is largest there and decays inland — which is why real lateral spreads open a fan of parallel tension cracks (grabens) that narrow with distance from the riverbank or slope toe.
- Peak ground acceleration — stronger shaking raises CSR, shortens Nliq, and builds r_u faster.
- Relative density Dr — denser sand resists liquefaction longer and keeps more residual strength.
- Slope and layer thickness — both raise τ_drive, the gravitational stress the softened layer has to hold back.
Real-world relevance: this is the same mechanism behind bridge-abutment and riverbank failures in the 1964 Niigata and 1989 Loma Prieta earthquakes, where meters of permanent lateral ground displacement damaged foundations without any building ever sinking.