Infinite Slope Stability with Seepage
Why a slope that stood dry all summer slides in the spring.
Example
You enter
- Slope angle beta (deg) 18
- Effective friction angle phi' (deg) 32
- Saturated unit weight (pcf) 125
- Depth to failure plane H (ft) 8
You get
- Fs seep 0.9631
- Fs dry 1.9232
- Driving shear stress 293.9 psf
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeWith steady seepage parallel to the slope and the water table at the surface, FS = (c' + (gamma_sat - 62.4) H cos^2 beta tan phi') / (gamma_sat H sin beta cos beta). The pore pressure cuts the friction term to the buoyant weight while the driving weight stays saturated, so a cohesionless factor of safety drops to (gamma_sat - 62.4)/gamma_sat -- about half. A phi = 32 sand at 18 degrees is a safe 1.92 dry but a failing 0.96 wet; both are shown, so a subdrain's value is obvious. Translational, drained, no seismic. A screening aid, not a stability analysis.
Formula or tabledriving = gamma_sat H sin(beta) cos(beta); resisting = c' + (gamma_sat - 62.4) H cos^2(beta) tan(phi'); FS = resisting / driving. (c' = 0 gives FS = ((gamma_sat - 62.4)/gamma_sat) tan(phi')/tan(beta))
Source and editionThe infinite-slope stability model with steady slope-parallel seepage on an effective-stress basis, as compiled in Das (Principles of Geotechnical Engineering) and the NAVFAC DM-7 slope-stability references, by name.
Free accessNAVFAC DM-7 is public-domain and free online; the seepage infinite-slope relations are public in the standard geotechnical texts; gamma_w = 62.4 pcf fresh water.
What governsEstimate. AHJ and licensed professional govern.
API field namesbeta_deg, phi_deg, gamma_sat, h_ft, fs_seep, fs_dry, driving_psf
- Steady seepage at the surface the water table is at the slope surface with flow parallel to it (worst case); the friction term uses the buoyant weight gamma_sat - gamma_w while the driving term uses gamma_satinfinite-slope seepage model (Das / NAVFAC)
- Cohesionless halving c' = 0 gives FS = ((gamma_sat - gamma_w)/gamma_sat) tan(phi')/tan(beta), about half the dry value for common soilsinfinite-slope seepage model