Landslide debris flow (Voellmy–Salm depth-averaged)

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Slope failure begins with a Mohr–Coulomb infinite-slope assessment over a susceptibility field (with Newmark-style seismic, effective-stress rainfall, and lahar triggers), converts susceptible steep cells into an initial debris mass, and routes it with the depth-averaged Voellmy–Salm equations using Rusanov mass fluxes and a semi-implicit momentum update. μ and ξ are free calibration parameters — the platform ships an endpoint to fit them against an observed runout.

Execution mode

Kaggle kernel (numpy, CPU instance); local in-process for calibration & Monte-Carlo server/kaggle/simRunner.ts:126-141 server/kaggle/localRunner.ts:1-15

Verification

MEASURED locally — convergence/conservation script PASS re-executed

Wire scenario type

landslide — contract at src/services/kaggleSim.ts:28-240; job API at Simulation job API

Governing equations and coefficients

Source attribution as stated in the kernel header (verbatim):

Voellmy-Salm friction law: τ_b/ρ = μ_c·g·h·cos²θ + g·u·|u|/ξ where μ_c = tan φ_res is the residual (dynamic) basal friction and ξ (m/s²) is Voellmy's turbulent coefficient. Debris: φ_res ≈ 14°, ξ ≈ 300.

∂h/∂t + ∇·(h·u) = 0; ∂(hu)/∂t + ∇·(hu⊗u) = −g·h·∇(h+z) − τ_b/ρ

τ_b/ρ = μ·g·h·cos²θ + g·u·|u|/ξ (μ capped by driving stress — yield behaviour)

FS = (c + σ′·tanφ) / (γ·h·sinθ), σ′ = γ_soil·h_soil·cosθ·0.5

seismic: fs_seismic = fs − a/(g·sinθ) (Newmark criterion a_max > g(FS−1)sinθ); rainfall: fs·(1 − 0.7·rain_factor); volcanic: exp(−r/0.25·gs)·(slope>15°)

ln PGA[g] = 3.586 + 0.707·M − 1.093·ln(r+10) − 0.0053·(r+10) [site term 0.25·ln(760/760) ≡ 0]

E = min(entrainment_rate·|u|·dt·(1 − h/(h+ent_ref)), bed)

Coefficients and named constants

Parameter contract

Landslide parameters. Shared request envelope (validated at the client boundary before dispatch).

Outputs

Spatial-origin semantics

Square domain; row 0 = north. Documented axis-naming quirk: internally dz_dx is the north–south (row-axis) gradient and dz_dy the east–west (column-axis) gradient; the code comment records that the old mapping was swapped and would have driven debris across slopes on real terrain. Runout is measured from the depth-weighted source centroid. kaggle-kernels/landslide-sim/main.py:147-148,465-475,457-463

Documented validity limits (verbatim from the code)

'The genuine conservation proof is the closed-box test (verify_closed_box) and the grid-convergence script, not this algebraic bookkeeping.' · axis-mapping note: 'The old mapping was swapped, which on *real* terrain would drive debris across the slope instead of down it' · susceptibility raw mask note: 'The raw mask (susceptibility > 0.3) covers ~99% of the grid, so the "pile" is a grid-wide slab that blows up and renders as a hollow rim.' · "Certified-grade" debris-flow modelling requires the free parameters to be fit to a real slide, not guessed … Sample runout resources: Hungr et al. (2001) runout databases

The closed-box verifier exists in main.py but is NOT invoked by main() (unlike flood/tsunami/volcano); the authoritative gates are validate_convergence.py (conservation 1e-8, runout refinement ≤ 0.25, upsampling RMSE ≤ max(10 %, 30 m)) and the /api/kaggle/calibrate grid fit. kaggle-kernels/landslide-sim/main.py:808-857 kaggle-kernels/landslide-sim/validate_convergence.py:19-21,35-98

Measured runs and timings

Reproduction

Commands

# Convergence/conservation gates (in-process, no Kaggle):
cd <repo>/kaggle-kernels/landslide-sim && python3 validate_convergence.py
# → 'PASS — all gates OK'

# Calibrate μ×ξ to an observed runout (documented-event value required):
python3 calibrate.py --observed-runout-km 2.9 --grid-size 128

# Server-side UQ:
curl -s -X POST http://localhost:3001/api/kaggle/landslide/quantify \
  -H 'Content-Type: application/json' -d '{ "request": {…landslide params…}, "samples": 16 }'