Shallow Foundation Bearing Capacity

R/A = c·Nc·s_c·i_c·d_c + q·Nq·s_q·i_q·d_q + 0.5·γ·B·Nγ·s_γ·i_γ (EN 1997-1 Annex D eq.D.1). Nq = e^(π·tan φ)·tan²(45+φ/2); Nc = (Nq−1)/tan φ; Nγ = 2(Nq−1)·tan φ. All factors are applied: shape (s), inclination (i), and depth (d, informational). The effective area A′ = B′ × L′ accounts for eccentric loading via Meyerhof reduction (B′ = B−2·e_B, L′ = L−2·e_L).

Use drained (c′, φ′) for coarse-grained soils (sand, gravel) and fine-grained soils under long-term sustained loading where drainage can occur. Use undrained (cu) for fine-grained soils (clay, silt) under short-term or rapid loading where excess pore pressures cannot dissipate. EN 1997-1 §6.5.2 recommends assessing both conditions for all foundations.

EN 1997-1 recommends DA1 with both Combination 1 (γG=1.35, γQ=1.5; characteristic material) and Combination 2 (γφ=1.25, γc=1.25; factored material). The governing DA is whichever produces the highest utilization. DA2 (γRv=1.4) is used in some NAs as an alternative. DA3 is more conservative and used for extreme conditions. NL NEN 9997-1 mandates DA1. FR NF P94-261 defaults to DA2.

When groundwater is within the influence depth (≈ D + B), the effective unit weight of soil below foundation level is reduced by approximately 10 kN/m³ (γ′ = γ − γw). The overburden term q′ also uses the submerged unit weight. This reduces all three terms in the bearing capacity equation, sometimes significantly.

Sliding resistance check (EN 1997-1 §6.5.3) verifies Hd ≤ Rd,h where Rd,h = (NEd·tan φd + Ad·cd) / γRh. For undrained conditions φd=0, sliding is governed by base adhesion only. Provide shear keys or increase footing dimensions if sliding governs.

The kern is the zone around the centroid where resultant eccentricity does not produce tension under the footing (e ≤ B/6 in each direction for rectangular footings). When eccentricity falls outside the kern, part of the footing lifts off. FrameAI warns when this occurs and applies Meyerhof effective area reduction accordingly.