Rainfall-Induced Instability of Embankment Slopes: Closed-Form, FORM and Monte Carlo Failure Probabilities for the Infinite-Slope Model, Coupled to a Finite-Element Pore-Pressure Diffusion Solution

For a 1V:2H compacted embankment slope (26.57°) with a slip surface 2 m deep, I compute the failure probability P(FS < 1) of the infinite-slope model in three ways: a closed form for the cohesionless case, FORM, and Monte Carlo with lognormal c′ and φ′. I then couple it to a Galerkin finite-element solution of one-dimensional pore-pressure diffusion. The closed form and Monte Carlo agree to within 0.3%. FORM is accurate when the mean point is safe (β = 3.49, pf = 2.4 × 10⁻⁴ against 2.2 × 10⁻⁴ by Monte Carlo) and loses accuracy near and beyond the critical pore-pressure ratio. The finite-element solver (linear elements, Crank–Nicolson) converges at second order, with error falling from 1.6 × 10⁻³ to 1.0 × 10⁻⁴ kPa as the mesh and time step are halved twice. For an assumed 1 m pressure-head rise at the surface and diffusivity 10⁻⁵ m²/s, P(FS < 1) at 2 m depth rises from 1.9 × 10⁻⁴ to 4.1 × 10⁻² after 10 days and 2.0 × 10⁻¹ after 60 days. A negative c′–φ′ correlation of −0.5 lowers pf by a factor of 2.4 relative to independence. All soil and hydraulic parameters are stated assumptions.