Geotechnical Engineering

Infinite Slope Factor of Safety Calculator

Calculate infinite-slope factor of safety from slope angle, soil thickness, unit weight, cohesion, friction angle, and pore-pressure ratio.

Engineering schematic

Infinite-slope stress convention

Static symbolic figure. Enter project values in the calculator fields below.

Long uniform slope at angle beta with a parallel failure plane, vertical soil depth z, a unit slice, weight W, normal force N, downslope shear T, pore pressure u, and shear resistance. — Symbols
β
slope angle
z
vertical soil depth used by the implemented equation
W, N, T
slice weight, normal force, and downslope shear force
u, rᵤ
pore pressure and ratio defined by u = rᵤσₙ
c, φ, γ
cohesion, friction angle, and soil unit weight

Result

Factor of safety: 1.46

Normal stress

295.7

Driving stress

137.89

Pore pressure

59.14

Resisting stress

200.78

Factor of safety

1.46

Step-by-step calculation

Normal stress
$\sigma_n=\gamma z\cos^2\beta=295.7$
Driving shear stress
$\tau_d=\gamma z\sin\beta\cos\beta=137.89$
Pore-water pressure
$u=r_u\sigma_n=59.14$
Factor of safety
$FS=\frac{200.78}{137.89}=1.46$

What this means

The slope is marginal in a screening sense and deserves closer evaluation.

Assumptions

Infinite slope geometry
Planar shallow failure surface
Consistent unit system
No seismic loading

Formula Used

FS=\frac{c+\left(\gamma z\cos^2\beta-u\right)\tan\phi}{\gamma z\sin\beta\cos\beta}

Step-by-Step Example

A 25 degree slope with 3 ft soil thickness, c=75 psf, phi=28 deg, and ru=0.2 has a screening FS near 1.46.

Engineering Notes

Use the model only where a shallow planar failure surface approximately parallel to the ground is credible.
Treat c and phi as parameters for the selected drainage and stress condition; do not mix total-stress cohesion with effective-stress friction casually.
The calculator defines u from ru times the total normal overburden term. Check whether that representation is suitable for the seepage condition.
Run wet-season and parameter sensitivity cases. A single dry factor of safety can conceal groundwater control.
Final slope evaluation may require stratigraphy, noncircular or circular surfaces, seismic loading, external loads, and project-specific target factors of safety.

FAQ

When is the infinite slope model appropriate?

It is most useful for shallow translational screening where the potential failure surface is approximately parallel to a long, uniform ground surface.

How does groundwater affect the result?

Pore pressure reduces effective normal stress and therefore frictional resistance. Wet-season and seepage sensitivity checks are usually more informative than one dry calculation.

Is a factor of safety above 1.0 acceptable?

Not automatically. The target depends on consequence, uncertainty, loading, method, project criteria, and whether the credible failure mechanism was modeled.

Related Engineering Guides

What Is an Infinite Slope Model?Understand the geometry, assumptions, and limits behind the calculation.Infinite Slope Stability ExampleFollow a worked dry and pore-pressure-sensitive screening example.Factor of Safety in Slope StabilityInterpret factor of safety together with model uncertainty and consequence.