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Shallow foundation bearing capacity

General bearing-capacity equation (general shear, vertical concentric load) with Prandtl-Reissner factors, a selectable Nγ, and Vesić shape factors.

General shear failure, vertical concentric load. Depth, load-inclination and water-table corrections are NOT applied — add them for final design. Terzaghi's original factors (known to err at low φ) are not used; the modern Prandtl-Reissner Nq/Nc are.

Inputs

Cohesion ckPa

Friction angle φ°

Unit weight γkN/m³

Depth Dfm

Width Bm

Length L (blank=strip)m

Nγ method

Factor of safety

Results

Nc / Nq / Nγ—

sc / sq / sγ—

qu (gross ultimate) [kPa]—

qu (net) [kPa]—

Allowable q (gross/FS) [kPa]—

Citations

EQqu = c·Nc·sc + q·Nq·sq + 0.5·γ·B·Nγ·sγ, q = γ·Df.

NNq = e^(π·tanφ)·tan²(45+φ/2); Nc = (Nq−1)·cotφ; Nγ Vesić 2(Nq+1)tanφ or Meyerhof (Nq−1)tan(1.4φ).

VERIFYFactors verified vs published tables (φ=30: Nq=18.4, Nc=30.1, Nγ=22.4); qu hand-checked (734.5 kPa).

Engine: geotech-f.js v0.1.0 · Method: Prandtl-Reissner + Vesić · Date:

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Preliminary calculation tool. Results are for preliminary sizing and cross-check only. Final design, sealed responsibility, and permit submissions require the full official text of the referenced regulations and the review of a licensed engineer.