Bearing Capacity

Bearing capacity is the pressure a soil can carry without shear failure. Learn failure modes, Terzaghi's and Meyerhof's equations, bearing capacity factors, shape and depth factors, water-table effects, factor of safety and safe/allowable bearing pressure.

Push a footing into soil hard enough and the soil beneath shears and bulges out sideways — a bearing capacity failure. Famous examples include the Transcona grain elevator that tilted 27° in 1913.

Engineers compute the ultimate bearing capacity from soil strength, then apply a factor of safety (usually 2.5–3) and also check settlement.

An analogy

Stepping on wet sand in flat shoes versus high heels: the same weight on a smaller area punches in, while a wider footing spreads load and engages more soil.

Failure modes

General shear (dense sand, stiff clay — clear failure surface and heave), local shear (medium dense soils), punching shear (loose soils — footing sinks without heave). Design must also limit settlement, which often governs on sands.

Terzaghi's equation

Three contributions: cohesion (N_c), surcharge from soil above founding level (N_q) and self-weight of soil below (N_γ). The factors rise steeply with φ — for φ = 30°: N_c ≈ 37, N_q ≈ 22.5, N_γ ≈ 20; for φ = 40° they are several times larger.

Water table and eccentricity

A water table at or near the footing base halves the effective unit weight in the N_γ and N_q terms, reducing capacity significantly. Eccentric or inclined loads reduce effective width (B′ = B − 2e) and capacity.

General equations and codes

Meyerhof, Hansen and Vesić add shape, depth and inclination factors; IS 6403 and Eurocode 7 prescribe methods and partial factors. In-situ tests (SPT, CPT, plate load test) provide direct estimates. Allowable pressure = min(shear capacity/FS, pressure for allowable settlement ≈ 25 mm on sand).

Formulas

• Terzaghi (strip): q_u = c N_c + q N_q + ½ γ B N_γ
• Square / circular: q_u = 1.3cN_c + qN_q + 0.4γBN_γ (square), 0.3γBN_γ (circular)
• Net safe bearing capacity: q_ns = (q_u − q) / FS
• Undrained clay (φ = 0): q_u = 5.14 c_u + q (Skempton ≈ 5.7c_u + q for strip in Terzaghi)

Worked example: Strip footing on sand

Given: B = 2 m, D_f = 1.5 m, γ = 18 kN/m³, c = 0, φ = 30°; Terzaghi: N_q = 22.5, N_γ = 19.7

Find: q_u and net safe capacity (FS = 3).

• q = 18 × 1.5 = 27 kPa
• q_u = 27 × 22.5 + 0.5 × 18 × 2 × 19.7 = 607.5 + 354.6 = 962 kPa
• q_ns = (962 − 27)/3 = 312 kPa

Answer: q_u ≈ 962 kPa, q_ns ≈ 312 kPa

Worked example: Square footing, same soil

Given: B = 2 m square

Find: q_u.

• q_u = 27 × 22.5 + 0.4 × 18 × 2 × 19.7 = 607.5 + 283.7 = 891 kPa

Answer: ≈ 891 kPa

Common mistakes

• Wrong: Ignoring the water table. — Right: Use submerged unit weight in the affected terms — capacity can nearly halve.
• Wrong: Designing only for shear failure on sand. — Right: Settlement (≈ 25 mm limit) often controls allowable pressure.

Applications

• Building footings: Isolated, strip and raft foundations sized from safe bearing pressure.
• Tanks & silos: Large uniformly loaded areas checked for bearing and tilt.
• Temporary works: Crane outrigger pads and piling-rig platforms.

Key takeaways

• q_u = cN_c + qN_q + ½γBN_γ (strip).
• Factors grow rapidly with φ.
• Water table and eccentricity reduce capacity.
• Allowable = min(shear/FS, settlement limit).

Going further

• Plate load test: Field test scales settlement/bearing from a small plate — beware scale effects in clay.
• Layered soils: A strong layer over weak soil can punch through — two-layer bearing theories apply.
• Eurocode 7: Uses partial factors on actions and soil parameters (DA1, DA2, DA3) instead of a global FS.