Surficial slides accelerate retreat velocity of retrogressive breaching failure

Existing formulas for submarine face-retreat velocity are formulated for, and validated against, time-averaged, grain-by-grain breaching conditions; we hypothesized that they systematically underestimate the retreat velocity during surficial sliding events, and that this underestimation grows with the position along the face. The pointwise comparison confirms this: at the grain-by-grain level all three formulas reproduce the measured velocities only weakly (R² < 0, negligible or negative correlation), indicating that their parameters were calibrated for aggregated rather than pointwise retreat.

During surficial sliding the discrepancy is larger and, critically, the enhancement ratio E = v_measured/v_e is not constant but increases with height above the toe H (r ≈ +0.78) and decreases with the local face angle α (r ≈ −0.57). We therefore introduce a height-dependent correction, v_SF = v_e + δ₀ + c(H/H₀)^d, where the constant δ₀ = −0.248 cm/s captures a systematic baseline offset and the power-law term c(H/H₀)^0.61 (c = 0.532) represents the additional transport driven by the sliding wedge, whose thickness and potential energy grow with height.