Infinite Slope Stability Factor of Safety (No Seepage)
Infinite Slope Stability Factor of Safety (No Seepage)
The infinite slope model is the standard first check for shallow, planar slides in natural or cut slopes — think a thin layer of soil on a long hillside sliding along a weaker plane beneath it. Because the slope is assumed long relative to the failure depth, edge effects are ignored and the problem reduces to a simple force-balance on a representative soil column. Slopes with a factor of safety only marginally above 1.0 are vulnerable to failure if pore pressures rise during heavy rain — this no-seepage version represents the driest, most favorable case, so real slopes are often re-checked with a seepage or rapid-drawdown condition that lowers the FS further.
The infinite-slope factor of safety is FS = (c + gamma*z*cos^2(beta)*tan(phi)) / (gamma*z*sin(beta)*cos(beta)). where c_soil is soil cohesion, gamma_soil is soil unit weight, z_slope is the vertical depth to the failure plane, beta_slope is the slope angle, and phi_soil is the soil friction angle, with beta and phi in radians.
Inputs
c_soil := 5 kPa=5000 Pa
gamma_soil := 18 kN/m^3=18000 kg/m^2/s^2
z_slope := 3 m=3 m
beta_slope := 0.4363=0.44
phi_soil := 0.5236=0.52
The numerator is the total shear resistance available (cohesion plus friction along the plane), and the denominator is the gravity-driven shear stress trying to cause sliding — their ratio is the factor of safety.
FS_slope := (c_soil + gamma_soil·z_slope·cos(beta_slope)^2·tan(phi_soil))/(gamma_soil·z_slope·sin(beta_slope)·cos(beta_slope))=1.48
Results
A factor of safety of about 1.5 sits right at the threshold most guidance seeks for permanent slopes, while values near 1.0-1.2 signal marginal stability that would likely fail under added rainfall or loading. Because the driving term grows with depth z while cohesion's contribution stays fixed, deeper potential failure surfaces are progressively more dependent on friction alone — a key reason shallow slides are common in cohesive soils during storms.
Assumptions & limitations
- Slope treated as infinitely long — no edge or toe effects.
- Planar failure surface parallel to the slope face.
- No seepage or pore water pressure included (dry condition only).
- Homogeneous soil properties over the full depth z.