Terzaghi Bearing Capacity: How Shallow Footings Are Sized
Every shallow foundation ultimately rests on a question of soil strength: how much pressure can the ground beneath a footing carry before it fails in shear? Karl Terzaghi's 1943 general shear equation was the first widely adopted answer, and despite decades of refinement by Meyerhof, Hansen, and Vesic, it remains the starting point most engineers reach for when sizing a footing by hand.
Three Failure Mechanisms, Added Together
Terzaghi's equation treats bearing failure as the sum of three independent contributions. The cohesion term (c·Nc) captures the shear strength that comes from the soil particles' own cohesion — significant in clays, essentially zero in clean sands. The surcharge term (q·Nq) accounts for the confining weight of soil beside the footing, which resists the upward heave that would otherwise accompany a bearing failure. The soil-weight term (0.5·γ·B·Nγ) reflects the weight of the failure wedge directly beneath the footing itself, which scales with footing width. Adding all three gives the ultimate bearing capacity — the pressure at which the soil is theoretically on the verge of shear failure.
Why the Bearing Capacity Factors Matter So Much
Nc, Nq, and Nγ are not linear functions of friction angle — they grow exponentially, more than doubling for every 5-10 degrees of additional φ in the 25-40 degree range. That sensitivity is exactly why accurate soil characterization matters more here than almost anywhere else in geotechnical design: an optimistic friction angle assumption doesn't just modestly overstate capacity, it can overstate it by a wide margin. Conservative, lab-verified friction angles are essential inputs, not formalities.
Factor of Safety, Not a Single Number
The ultimate bearing capacity is a theoretical failure threshold, not a design value. Dividing by a factor of safety — typically 2.5 to 3.0 for shallow foundations — produces the allowable bearing pressure a structural engineer actually designs to, building in margin for the natural variability of soil properties, construction tolerances, and the consequences of a bearing failure being far more severe than a modest overload.
What Terzaghi's Original Equation Leaves Out
Terzaghi's general shear factors assume a strip footing, a horizontal ground surface, and a vertical, centered load — conditions that rarely match a real foundation exactly. Later methods add shape factors for square or circular footings, depth factors for embedment effects, and inclination factors for footings carrying combined vertical and lateral load. A Terzaghi-based estimate is a fast, conservative first pass; final bearing capacity for anything beyond a preliminary check should use one of these refined methods together with a project-specific geotechnical investigation.
Open Bearing Capacity Calculator →