Simulator · Geotechnics
Slope stability
One slope solved by two methods that share no calculation assumption, and the finite element engine checked against published benchmarks. Limit equilibrium assumes a circular surface and searches for it; the finite element model imposes no surface and the failure band forms where plastic strain concentrates. The acceptance criterion was set before the calculation: less than 10 % difference in the factor of safety.
Bishop 1.468 · FEM 1.439 · 2.0 % difference
A · Limit equilibrium
Simplified Bishop, live
Change the geometry or the strength and the browser searches for the critical circle again: 45 upslope outcrop points, 40 downslope and 40 radii per pair, with 60 slices per circle. Only surfaces that daylight inside the model are accepted.
FS = Σ [c′b + W tan φ′] / mα ÷ Σ W sin α, mα = cos α + tan φ′ sin α / FS
Factor of safety
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With this input no admissible surface appears inside the model.
Searching for the critical circle…
B · Finite elements
Strength reduction, no assumed surface
Plane strain with Drucker-Prager matched to Mohr-Coulomb, non-associated flow (ψ = 0), incremental plasticity and the B-bar formulation on 4-node quadrilaterals. Strength is divided by an increasing factor SRF and, for each SRF, self-weight is applied in 16 increments with Newton-Raphson. The factor of safety is the SRF beyond which there is no equilibrium.
C · Benchmark cases
The engine against ACADS
Open full screen ↗Verification of the program on cases with a known answer: a second engine, with 8-node reduced-integration quadrilaterals, on the ACADS 1(a) and 3(a) slopes and a teaching case, with Spencer's critical surface overlaid. On ACADS 1(a) the factor of safety lies between 0.96 and 0.975 against 1.00 for the reference and 0.984 for Spencer.
Model scope and limitations
Constitutive model. The Drucker-Prager match to Mohr-Coulomb is valid only in plane strain. With non-associated flow the tangent matrix is unsymmetric; the continuum tangent is used, which converges more slowly than the consistent one.
Failure criterion. The factor of safety corresponds to non-convergence within 100 iterations at a tolerance of 10⁻³ on the self-weight norm, the usual strength-reduction convention. The value depends on that criterion and on the mesh (sensitivity table).
Hypotheses compared. Bishop assumes a circular surface and a distribution of interslice forces; the finite element model imposes neither. The factors of safety differ by 2.0 %, within the 10 % criterion.
Use of the simulator
Demonstration material, not for design. The calculation notebook and the application of the method to a project are reviewed in a technical meeting.
Book a demonstration