Sensitivity and probability

How the factor of safety depends on one input, and the probability of failure from uncertain strength.

Start a new project with File › New and click ▶ Run. The factor of safety is 0.984.

1. Sensitivity

Choose Results › Plots › Sensitivity. The first input, the unit weight of M1, is chosen, from 16 to 24 kN/m³ in 9 values. Click Run: cSlope runs the full analysis for each value.

The sensitivity panel with a chart of factor of safety against unit weight — Factor of safety against unit weight, with the line at 1.0.

The factor of safety reaches 1.0 at a unit weight of about 18.5 kN/m³. Choose another input under Vary, such as c or φ, to see which one matters most.

2. Probability of failure

Close the panel and choose Results › Plots › Probabilistic. The panel starts with one variable, the cohesion of M1 (c = 3 kPa, σ = 0.75 kPa). Click + Add variable once to add the unit weight (γ = 20 kN/m³, σ = 1 kN/m³). Both are normally distributed. Choose another property or σ in each row if you like.

Leave Taylor series selected and click Run.

The probabilistic panel with the results of a Taylor series analysis — Taylor series: the standard deviation of the factor of safety, the reliability index and the probability of failure.

With a mean factor of safety below 1.0, the reliability index is negative and the probability of failure is above 50 %. The table at the bottom shows how much each variable changes the factor of safety: here the cohesion matters more than the unit weight.

Monte Carlo gives the same quantities from many random samples, and a histogram of the factor of safety.