Free engineering tool. Everything is computed in your browser; no input leaves your computer. The results check plasticity solutions and code formulas. They do not replace the design of a foundation by a qualified engineer.
Starting…
| Combination | Vd [kN/m] | φ′d [°] | B′ [m] | Rd exact [kN/m] | Vd/Rd | Rd Annex D [kN/m] | Vd/Rd Annex D |
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The collapse load of a rigid strip footing under a vertical load, on a Mohr-Coulomb soil with c = c′ + k·z, friction φ′ and a water table at any depth (γ above, γ′ below). The soil above the base acts as the surcharge q = effective overburden at base level. The stress field is built with the method of characteristics and refined until qu no longer changes; with an associated flow rule this is the exact plasticity solution.
Type 1: smooth base. Type 2: rough base; a rigid false head under the whole footing. Type 3: rough base; full roughness near the edges.
With a slope beside the footing or a horizontal load, each footing edge gets its own half field and the two are joined on the base (Sokolovskii's construction, constant load inclination along the base). It reproduces Green's exact solution for inclined loads on undrained clay and the closed-form solutions for weightless soil and for clay at the crest of a slope. With soil weight it is a method-of-characteristics solution, not a proven exact one. On a rough base it starts from the smooth-base value; the rough-base estimate scales Martin's exact vertical value by the field's reduction factor. The field's own resultant is generally off-centre; the tool enforces moment equilibrium by using the effective part of the footing whose field resultant passes through your load (Meyerhof's effective width with the field's own pressure distribution; for level ground and a vertical load exactly B′ = B − 2|e|). A water table cannot be combined with a slope.
Exact plasticity assumes dilation ψ = φ′. Real sands dilate less and carry less. With ψ given, the tool also solves the problem for the Davis (1968) reduced strength tan φ* = β tan φ′, c* = β c′, β = cos ψ cos φ′ / (1 − sin ψ sin φ′): an estimate on the safe side, not an exact value. The EN 1997-1 check then uses it.
The check applies the recommended partial factors per combination, the effective width B′ = B − 2e, and puts the code formula of Annex D (same B′ and design strength, no depth factors) beside it.
Stress characteristics after C.M. Martin, ABC v1.0 user manual (Oxford, 2004), ch. 2, rebuilt by EA Suys from the published equations and extended with the water table, the Davis reduction and the EN 1997-1 check. The result is the Richardson value of the three finest meshes.
Checked against Prandtl–Reissner (closed form), the ABC manual tables, Martin (2005) and ABC v1.01 runs: agreement within 0.03 %. Water table: exact limits (at the base and below the mechanism) and second-order convergence.