Slope Stability Factor Calculator - Geotechnical

The infinite slope model treats a hillside as a planar layer of soil of uniform thickness resting on a parallel slip plane, long enough that end effects and the stresses on the vertical sides of any column cancel. The factor of safety separates into two additive terms: a cohesion term, c divided by gamma H sin(beta) cos(beta), and a friction term, tan(phi) over tan(beta). The second term gives the classic result that a cohesionless slope is stable whenever beta is less than phi regardless of height, so dry sand rests near its angle of repose of about 30 to 35 degrees. The cohesion term shrinks as the failure depth H grows, which is why shallow slips are common on steep cohesive hillsides while the same material stands in a short vertical cut. Two derived quantities support preliminary design. The dimensionless group gamma H over c is the reciprocal of the stability number used on Taylor charts, which relate slope angle, friction angle and a critical value of that group for homogeneous slopes. The critical height computed here follows the Culmann plane-wedge solution, Hc = 4 c sin(beta) cos(phi) divided by gamma times one minus cos(beta - phi), giving the height at which a cohesive slope reaches limiting equilibrium. The infinite slope form applies only to shallow translational failures where failure depth is small relative to slope length, typically a ratio under about one tenth. Deep rotational slides need Bishop or Spencer circular analyses instead, and none of these expressions capture seepage forces, layered strength profiles, tension cracks or seismic loading.

Systematic slope analysis begins with Karl Culmann, professor at the Zurich Polytechnic, who in his 1866 treatise Die graphische Statik applied graphical statics to a plane failure wedge in a cut and obtained the first closed-form critical height for a cohesive slope. The infinite slope idealisation itself grew from studies of natural hillside soil mantles and talus and was in routine use by the 1930s, when soil mechanics was consolidating as a discipline after Karl Terzaghi published Erdbaumechanik in 1925 and the first International Conference on Soil Mechanics and Foundation Engineering met at Harvard in 1936. Donald W. Taylor of the Massachusetts Institute of Technology gave the approach its most durable design tool in his paper Stability of Earth Slopes, published in the Journal of the Boston Society of Civil Engineers in 1937, where he introduced the dimensionless stability number and the friction-circle charts that let engineers read a required height or angle directly. He expanded the treatment in his 1948 textbook Fundamentals of Soil Mechanics, and Taylor charts remained the standard hand method for homogeneous slopes for decades. Application to real hillsides advanced when Alec Skempton and F. A. DeLory used infinite slope reasoning in 1957 to explain shallow slips in London Clay in terms of long-term pore pressures. Modern highway practice, including the Federal Highway Administration reference manuals on soil slopes and embankments, still uses the method for rapid screening before numerical analysis.