About Slope Stability Calculator
The slope stability calculator computes the factor of safety against translational sliding of an infinite slope, where the failure surface is a plane parallel to the ground at a vertical depth H. For a dry cohesionless soil the factor of safety simplifies to the classic FoS = tan(phi)/tan(beta), which depends only on the friction angle and the slope angle, not on the unit weight or depth.
For a soil with effective cohesion c the tool uses the general infinite-slope equation FoS = [c + gamma*H*cos^2(beta)*tan(phi)] / [gamma*H*sin(beta)*cos(beta)]. When steady seepage flows parallel to the slope with the water table at the surface, the friction term uses the buoyant unit weight (gamma_sat - gamma_w) to account for pore pressure, while the driving stress uses the total saturated unit weight, capturing the significant loss of stability caused by groundwater.
How It Works
- Choose the case: dry cohesionless, dry c-phi, or c-phi with seepage parallel to the slope.
- Enter the slope angle beta (degrees) and the friction angle phi (degrees).
- For the c-phi cases add the cohesion c (kPa), the failure-plane depth H (m), and the unit weight (gamma for dry, saturated unit weight for seepage).
- The calculator evaluates the appropriate infinite-slope expression and reports the factor of safety along with the cohesion, friction, and driving-stress components.
Worked Example
A long natural slope inclined at beta = 20 deg has c = 10 kPa, phi = 25 deg, and a saturated unit weight of 20 kN/m3, with the potential failure plane at H = 3 m. Under dry conditions the factor of safety is [10 + 18*3*cos^2(20)*tan(25)] / [18*3*sin(20)*cos(20)] = 1.86 using a moist unit weight of 18 kN/m3. With steady seepage parallel to the slope and the water table at the surface, the friction term uses the buoyant unit weight (20 - 9.81) = 10.19 kN/m3 and the driving stress uses 20 kN/m3, dropping the factor of safety to [10 + 10.19*3*cos^2(20)*tan(25)] / [20*3*sin(20)*cos(20)] = 1.17.
Formulas
- Dry cohesionless infinite slope
FoS = tan(phi) / tan(beta)- Dry c-phi infinite slope
FoS = [c + gamma*H*cos^2(beta)*tan(phi)] / [gamma*H*sin(beta)*cos(beta)]- c-phi infinite slope with seepage (water table at surface)
FoS = [c + (gamma_sat - gamma_w)*H*cos^2(beta)*tan(phi)] / [gamma_sat*H*sin(beta)*cos(beta)]- Driving shear stress on the failure plane
tau = gamma * H * sin(beta) * cos(beta)
Standards & References
- Infinite-slope limit-equilibrium method
- Das, Principles of Geotechnical Engineering
- Skempton & DeLory (1957) c'-phi' infinite slope
Frequently Asked Questions
Why does the dry cohesionless factor of safety not depend on depth?
For a cohesionless soil the resisting and driving stresses are both proportional to gamma*H*cos(beta), so the unit weight and depth cancel. The factor of safety reduces to tan(phi)/tan(beta), and the slope is at limiting equilibrium (FoS = 1) when the slope angle equals the friction angle, the angle of repose.
How does seepage reduce the factor of safety?
Seepage parallel to the slope generates pore pressure on the failure plane, reducing the effective normal stress and therefore the frictional resistance. The friction term uses the buoyant unit weight (gamma_sat - gamma_w) while the driving stress still uses the full saturated unit weight, which can roughly halve the factor of safety compared with the dry case.
When is the infinite-slope model appropriate?
It is appropriate for long, planar slopes where the failure surface is shallow relative to the slope length and runs parallel to the ground surface, such as a thin soil mantle over rock. For deep, curved, or circular failure surfaces use a method of slices such as Bishop or Morgenstern-Price instead.
What factor of safety is considered acceptable?
A factor of safety greater than one indicates theoretical stability, but design practice typically requires 1.3 to 1.5 for long-term conditions to allow for uncertainty in strength parameters, pore pressures, and loading. Values near unity warrant detailed investigation.