Infinite Slope Critical Depth for a Target FS
The critical failure-plane depth at which the FS drops to a target.
Example
You enter
- Slope angle beta (deg) 25
- Effective friction angle phi' (deg) 30
- Effective cohesion c' (psf, must be > 0) 200
- Soil unit weight (pcf) 120
- Target factor of safety (e.g. 1.5) 1.5
You get
- Critical failure-plane depth 16.6 ft
- Deep (cohesionless) FS limit 1.24 (tan phi' / tan beta)
Details, formula, and sources
H = c' / (gamma cos beta (FS sin beta - cos beta tan phi')). A 25 degree cut in c' 200 psf, phi' 30, gamma 120 soil reaches FS 1.5 at about 16.6 ft deep. FS is high at the surface (cohesion helps) and falls with depth toward the cohesionless limit tan phi'/tan beta - a target below that is met at any depth. Needs c' > 0. Translational, no seepage; a screening aid, the geotech governs.
H = c' / (gamma cos(beta) (FS sin(beta) - cos(beta) tan(phi'))), the inverse of FS = (c' + gamma H cos^2(beta) tan(phi')) / (gamma H sin(beta) cos(beta)); a finite depth exists only for c' > 0 and a target FS above the deep limit tan(phi')/tan(beta).
The infinite-slope stability model (Das, Principles of Geotechnical Engineering; NAVFAC DM-7), solved for the critical failure-plane depth, by name.
NAVFAC DM-7 is public-domain and free online; the infinite-slope relations are public in the standard geotechnical texts.
Estimate. AHJ and licensed professional govern.
Field names used by the API: beta_deg, phi_deg, c_psf, gamma_pcf, target_fs, critical_depth_ft, deep_fs_limit
- Critical depth H = c' / (gamma cos(beta) (FS sin(beta) - cos(beta) tan(phi')))infinite-slope model (Das / NAVFAC)
- Deep limit FS falls with depth toward tan(phi')/tan(beta); a target below it is met at any depthinfinite-slope model
- No seepage dry slope or water table below the plane; needs c' > 0; steady-seepage and seismic cases are separatescope of this tile