Equation Pad › Library › Geotechnics › Slopes

Stability of an infinite slope

Factor of safety of a long slope in cohesionless soil, dry and with seepage parallel to the slope. Reference: Infinite slope analysis.

Open this sheet in Equation Pad Browse the Library

Example only. This sheet shows one way to set out the check. It is not endorsed by the bodies that publish the design codes and does not reproduce them. Check every clause, value and assumption against your own copy of the current edition of your references and the codes that apply before you use it, and have the result checked by a competent person. See the disclaimer.

The calculation, line by line

Every line below is typed into Equation Pad exactly as shown; the app typesets it, works out the value with its units and shows checks as TRUE or FALSE. Change any input and everything below it updates.

# Slope
phi := 32 deg
beta := 25 deg
gamma_sat := 20 kN/m^3
gamma_w := 9.81 kN/m^3

# Dry slope
F_dry := tan(phi)/tan(beta) =
F_dry >= 1.3 =

# Seepage parallel to the slope
gamma_b := gamma_sat - gamma_w =
F_seep := gamma_b/gamma_sat*tan(phi)/tan(beta) =
F_seep >= 1.3 =
# FALSE with seepage: the same slope that is stable when dry fails when water flows along it; drainage is needed.

How to use this example

1. Click Open this sheet in Equation Pad. It opens as a new worksheet in your browser; nothing is installed.
2. Change the inputs at the top to those of your project.
3. Check the clauses and coefficients against the code, add your own checks, and save the sheet or export a PDF with your title block.