Slope Stability Factor Calculator - Geotechnical
Free Slope stability factor geotechnical Calculator for soil & sediment mechanics. Enter variables to compute results with formulas and detailed steps.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
FS = c/(gamma*H*sin(beta)*cos(beta)) + tan(phi)/tan(beta)
The infinite slope factor of safety has two components: a cohesion term that depends on slope geometry and soil weight, and a friction term that is simply the ratio of tangent of friction angle to tangent of slope angle. The stability number Ns = gamma*H/c is a dimensionless group used with Taylor charts. The critical height Hc is the maximum height at which the slope can stand without failure.
Worked Examples
Example 1: Natural Hillside Slope Assessment
Problem:Analyze a 30-degree slope with H = 8 m, c = 20 kPa, phi = 28 degrees, gamma = 18 kN/m3.
Solution:Infinite slope FS = c/(gamma*H*sin(beta)*cos(beta)) + tan(phi)/tan(beta)\n= 20/(18*8*sin30*cos30) + tan28/tan30\n= 20/62.35 + 0.5317/0.5774\n= 0.321 + 0.921 = 1.242
Result:FS = 1.242, marginally stable
Example 2: Cohesionless Sand Slope
Problem:Check stability of a 35-degree dry sand slope with phi = 33 degrees, no cohesion.
Solution:FS (friction only) = tan(33)/tan(35)\n= 0.6494/0.7002 = 0.927\nSlope angle exceeds friction angle, so the slope is unstable.
Result:FS = 0.927, unstable
Frequently Asked Questions
What is the infinite slope method and when is it appropriate?
The infinite slope method analyzes slope stability by assuming the slope extends infinitely in all directions with a uniform thickness of potentially unstable soil. It is most appropriate for shallow planar failures where the depth of the failure surface is small compared to the slope length, such as soil slips on natural hillsides, colluvial deposits, and residual soils. The method is not suitable for deep-seated rotational failures, which require circular arc methods like Bishop or Spencer. It provides a quick, conservative estimate for preliminary slope assessments.
What is the stability number and how is it used in slope design?
The stability number (Ns = gamma * H / c) is a dimensionless parameter introduced by Taylor in 1937 for analyzing homogeneous slopes. It relates the unit weight, slope height, and cohesion into a single value that can be looked up on Taylor stability charts. For a given slope angle and friction angle, these charts provide the critical stability number at which failure occurs. If the actual stability number exceeds the critical value, the slope is expected to fail. This approach allows engineers to quickly determine the maximum safe height for a given slope angle and soil strength.
How does cohesion affect slope stability differently from friction angle?
Cohesion provides a constant shear resistance that is independent of the normal stress, making it most important for steep slopes and near the crest where normal stresses are low. The friction angle provides resistance proportional to the normal stress, so it becomes more significant at greater depths and for gentler slopes. A purely cohesive slope (phi = 0, like soft clay) has a critical height beyond which it cannot stand, while a purely frictional slope (c = 0, like dry sand) is stable at any height as long as the slope angle is less than the friction angle. Most real soils have both components.
What are common causes of slope failure in geotechnical practice?
Water infiltration is the most frequent trigger, raising pore pressures and reducing effective stress along potential failure surfaces. Erosion at the toe of the slope removes support, decreasing the factor of safety. Surcharge loading from construction, stockpiles, or buildings adds driving forces. Earthquake shaking induces additional inertial forces and can trigger liquefaction in saturated loose soils. Weathering gradually degrades the shear strength of exposed materials. Poor drainage design, rapid drawdown of reservoirs, and cutting into natural slopes without adequate retention are common engineering causes.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy