Infinite Slope Stability Factor of Safety
The screen a site engineer runs before benching a hillside cut: 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.
Formula and source
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.
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