Surficial slides accelerate retreat velocity of retrogressive breaching failure
Description
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. This model explains 54% of the pointwise variance (R² = 0.542, RMSE = 0.094 cm/s) and is preferred over the constant-correction model by ΔAIC = 105. To interpret and reuse the data: (i) columns in each spreadsheet are defined in the README; (ii) the isSF flag in S2 labels each observation as grain-by-grain (0) or surficial-slide (1) according to the five events in the manuscript; (iii) a measured SF velocity can be predicted from the corresponding Eq.(3) velocity v_e and the point height H using Eq.(4); and (iv) the full pipeline can be rerun from S1 with the MATLAB scripts in /MATLAB_scripts.
Files
Steps to reproduce
The raw data were collected from laboratory flume experiments simulating a submarine incised valley with a near-vertical sand face (runs C1–C3, two repetitions each; six profiles, 529 digitized points over 0–30 s). At discrete time steps, the slope face was digitized into points recording coordinates x and y, height above the toe H, local face angle α, and the goodness of fit (R²) of each local profile fit. All processing was fully scripted in MATLAB R2025b (seven scripts in /MATLAB_scripts). For each profile and each pair of consecutive times, points were matched by nearest y-coordinate (tolerance 0.35 cm) and the retreat velocity was computed as v = (x₂ − x₁)/Δt. Negative velocities (toe deposition), points with α ≤ φ = 32° (physically invalid for the formulas), and v = 0 degenerate points were removed, yielding 257 valid observations (153 grain-by-grain, 104 surficial-slide). Three published formulas (Breusers 1977; Alhaddad et al. 2020; Mastbergen & Van den Berg 2003) were evaluated pointwise using the sediment parameters listed in the manuscript. The new surficial-slide model, v_SF = v_e + δ₀ + c(H/H₀)^d, was fitted by nonlinear least squares (a one-dimensional search for the exponent d combined with a closed-form linear solution for δ₀ and c), giving δ₀ = −0.248 cm/s, c = 0.532, d = 0.611, and R² = 0.542. To reproduce the study, run step1–step7 sequentially in /MATLAB_scripts starting from S1_Profile_coordinates.xlsx.
Institutions
- Ocean University of ChinaShandong, Qingdao