Slope Stability Calculator
Estimate slope stability for your project with our free calculator. Get accurate material quantities, costs, and specifications.
Formula
FOS = c/(gamma*H*cos(beta)*sin(beta)) + tan(phi)/tan(beta)
The infinite slope factor of safety equals the sum of the cohesion component and the friction component. The cohesion component divides the soil cohesion by the product of unit weight, slope height, and the sine and cosine of the slope angle. The friction component is the ratio of the tangent of the friction angle to the tangent of the slope angle. A FOS greater than 1.5 is generally considered stable for permanent slopes.
Worked Examples
Example 1: Highway Cut Slope Analysis
Problem: Analyze stability of a 20 ft high cut slope at 30 degrees with cohesion 200 psf, friction angle 25 degrees, and unit weight 120 pcf.
Solution: Infinite slope FOS:\nCohesion component = 200 / (120 x 20 x cos30 x sin30) = 0.192\nFriction component = tan(25) / tan(30) = 0.808\nFOS = 0.192 + 0.808 = 1.000\nCritical height = 4 x 200 x sin30 x cos25 / (120 x (1-cos5)) = 237.7 ft
Result: FOS = 1.000, marginally stable, requires remediation
Example 2: Embankment Fill Slope
Problem: Check stability of a 15 ft embankment at 45 degrees, cohesion 500 psf, friction 30 degrees, unit weight 125 pcf.
Solution: Infinite slope FOS:\nCohesion component = 500 / (125 x 15 x cos45 x sin45) = 0.533\nFriction component = tan(30) / tan(45) = 0.577\nFOS = 0.533 + 0.577 = 1.110
Result: FOS = 1.110, marginally stable
Frequently Asked Questions
What is the factor of safety for slope stability and what values are acceptable?
The factor of safety (FOS) is the ratio of resisting forces (or moments) to driving forces acting on a slope. A FOS of 1.0 means the slope is at the verge of failure, where driving forces exactly equal resisting forces. Most engineering codes require a minimum FOS of 1.5 for permanent slopes, 1.3 for temporary construction slopes, and 1.25 for slopes where consequences of failure are minor. Critical infrastructure such as dams and bridge abutments may require FOS of 1.75 or higher.
What is the difference between infinite slope and finite slope analysis?
Infinite slope analysis assumes the slope extends indefinitely with a uniform failure surface parallel to the slope face. It is applicable for shallow translational slides where the failure depth is small relative to the slope length. Finite slope analysis considers slopes with defined boundaries and potential circular or non-circular failure surfaces. The Culmann method analyzes planar failure in finite slopes, while methods like Bishop and Spencer analyze circular failure surfaces using slice methods.
How do soil properties affect slope stability?
Two key soil properties govern slope stability: cohesion and internal friction angle. Cohesion provides shear resistance independent of normal stress, which is critical for clay soils and steep slopes. The friction angle provides resistance proportional to the normal force on the failure plane, dominating in granular soils. Saturated conditions reduce effective stress and friction resistance, which is why many slope failures occur during heavy rainfall. Vegetation roots provide additional cohesion of 50 to 300 psf in the root zone.
What are common methods to improve slope stability?
Slope stability can be improved through several methods: reducing the slope angle by excavating material from the top or adding material at the toe, installing drainage systems to lower the water table and reduce pore water pressure, constructing retaining walls or soil nail walls, using geosynthetic reinforcement, planting deep-rooted vegetation for added cohesion, and installing ground anchors or tiebacks. The most cost-effective approach depends on the site conditions, failure mechanism, and required factor of safety increase.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
Is Slope Stability Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.