Infinite Slope Stability Factor of Safety

For a shallow slide parallel to a long uniform slope, FS = (c' + gamma H cos^2 beta tan phi') / (gamma H sin beta cos beta). A 25 degree cut in c' = 200 psf, phi' = 30 soil holds at FS 1.78; strip the cohesion and the elegant tan phi'/tan beta remains - depth-independent, why dry sand stands exactly at its angle of repose. Translational only, no seepage - a circular Bishop analysis and pore pressure are the geotech's work. A screening aid, not a stability analysis.

driving = gamma H sin(beta) cos(beta); resisting = c' + gamma H cos^2(beta) tan(phi'); FS = resisting / driving. (c' = 0 collapses to FS = tan(phi')/tan(beta))

The infinite-slope stability model -- the factor of safety of a shallow translational slide on a plane parallel to a long uniform slope, with its cohesionless reduction tan(phi')/tan(beta) -- as compiled in Das (Principles of Geotechnical Engineering) and the NAVFAC DM-7 slope-stability references, 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, h_ft, driving_psf, resisting_psf, fs_slope

• Failure mode a shallow translational slide parallel to the surface at depth H; strength-over-stress ratioinfinite-slope model (Das / NAVFAC)
• Cohesionless case c' = 0 gives FS = tan(phi')/tan(beta), independent of depth and unit weight (the angle of repose at FS = 1)infinite-slope model
• No seepage dry slope or water table below the plane; steady-seepage and seismic cases are separatescope of this tile