Soil Bearing Capacity

What "bearing capacity" means

Stand on dry sand and your foot sinks a little; saturated clay, more; bedrock, not at all. The ground's ability to support a load without shear-failing is its bearing capacity. The number depends on two strength parameters — cohesion c (the stickiness that holds clay together at zero confining pressure) and friction angle φ (the angle at which loose grains start sliding past each other) — plus footing geometry and depth.

Karl Terzaghi formalized the problem in 1943 with an equation that still dominates undergraduate textbooks and most footing design:

q_ult = c·N_c + q·N_q + 0.5·γ·B·N_γ

Three terms in three letters: cohesion contribution, surcharge contribution, and self-weight contribution. The capacity factors N_c, N_q, N_γ are dimensionless functions of the friction angle φ that come from a slip-line solution of the bearing-failure wedge. Tabulated values are universal — every geotechnical engineer knows that for φ = 30°, N_c ≈ 30, N_q ≈ 18, N_γ ≈ 22.

The picture under a failing footing is a wedge of soil pushed straight down, two log-spiral fans flaring out to either side, and two passive wedges lifting at the ground surface:

             building load
                  │
                  ▼
            ┌─────────┐
            │ footing │ ← width B
       ─────┴─────────┴───── ← ground surface
       ↑              ↑       (passive heave)
       │  ╲        ╱  │
       │    ╲    ╱    │
       │     ╲  ╱     │
       │      ╲╱      │      ← wedge driven down
       │     fan      │
       │   ╱     ╲    │
       └──╱─ slip ─╲──┘
       (log-spiral failure surface)

That picture only forms when the ground actually fails. Long before that you see settlement — the soil compresses elastically and consolidates plastically — and that settlement is usually what governs design, not capacity.

Worked example: Terzaghi for cohesive soil

Strip footing 1.5 m wide on saturated clay. Depth of footing D_f = 1 m. Undrained shear strength c = 50 kPa, φ = 0 (clay drains too slowly to mobilize friction). Soil unit weight γ = 18 kN/m³.

For φ = 0, the capacity factors are:

N_c = 5.14
N_q = 1.00
N_γ = 0

Surcharge q at the footing base depth:

q = γ · D_f = 18 · 1 = 18 kPa

Plug into Terzaghi:

q_ult = c·N_c + q·N_q + 0.5·γ·B·N_γ
      = 50·5.14 + 18·1.00 + 0
      = 257 + 18
      = 275 kPa

Apply factor of safety 3:

q_a = q_ult / 3 ≈ 92 kPa

So a 1.5 m wide strip footing at 1 m depth on this clay can carry about 92 kPa, or roughly 138 kN per meter run. A typical 4-storey load-bearing brick wall delivers about 60 kN per meter — comfortably within the limit, with margin for settlement and live-load surge.

For sandy soil the picture flips: c = 0, so only the surcharge and self-weight terms matter. With φ = 30°, N_q = 18, N_γ = 22, and the same footing geometry q_ult = 18·18 + 0.5·18·1.5·22 = 324 + 297 = 621 kPa — over twice the clay's capacity, but very dependent on the density and the settlement that comes with mobilizing it.

In-situ soil tests

Test	What it measures	Typical depth	Soil suitability	Strengths	Limitations
Standard Penetration (SPT)	Blows per 300 mm (N)	0–50 m	Sand, silt, soft rock	Cheap, ubiquitous, sample retrieved	Operator-dependent, ±30% energy variation
Cone Penetration (CPT)	Tip resistance q_c, sleeve friction f_s	0–60 m	Sand, silt, soft clay	Continuous profile, no operator influence	No physical sample, fails in gravel
CPT with pore pressure (CPTu)	q_c, f_s, pore pressure u	0–60 m	All fine-grained soils	Distinguishes drained/undrained	Same gravel limit; expensive equipment
Vane Shear	Undrained shear strength c_u	0–30 m (soft clay)	Soft to medium clay only	Direct strength measurement	Fails in stiff clay, useless in sand
Pressuremeter (PMT)	Stress-strain curve, modulus	0–30 m	Most soils, weak rock	Stress-strain in situ	Slow, costly, requires expert operator
Plate Load Test	Direct q vs settlement	Surface to 5 m	Any soil at depth of plate	Direct settlement reading	Plate ≪ footing — scale effects matter
Dilatometer (DMT)	Lift-off and expansion pressures	0–40 m	Sand, silt, soft clay	Repeatable, modulus and strength	Less common, fewer correlations

Most projects pair SPT with CPT or CPTu — SPT for sample classification, CPT for the continuous profile. Pressuremeter and dilatometer enter for high-value or sensitive structures. Vane shear is the standard test in soft clay where the SPT spoon comes up empty.

Real-world bearing data

• Burj Khalifa (Dubai, 828 m): 3.7 m raft over 192 bored piles 1.5 m diameter, 50 m deep into siltstone–claystone. 500,000 t total; settlement ~50 mm.
• Petronas Towers (Kuala Lumpur): 104 barrette piles 60–115 m deep into Kenny Hill formation. Karstic limestone with cavities — pile depths varied based on bedrock topography.
• Tower of Pisa: 14,500 t founded on 3 m silty sand over 30 m soft Pleistocene clay. Capacity exceeded soon after 1173; peak tilt 5.5°, now stabilized at 3.97°.
• Transcona Grain Elevator (Manitoba, 1913): 5 m raft on 11 m stiff clay over softer clay. Load 36 kPa exceeded undrained capacity within hours of grain loading; structure rotated 27° intact.
• Mexico City buildings: founded on 30+ m of lacustrine clay with c_u as low as 30 kPa. Settlements 50–100 cm per decade; some neighborhoods sunk over 10 m as groundwater is pumped.
• Sound granite: q_a 5–10 MPa, settlement essentially zero. Default for nuclear power plants and dam abutments.

Variants and refinements

• Ultimate vs allowable. q_ult is the failure pressure; q_a = q_ult / FS, with FS commonly 2.5–3 for permanent works, 2 short-term, 1.5 emergency. The 25 mm settlement limit usually governs over the strength limit on stiff sand.
• Net vs gross pressure. Net = gross minus overburden weight removed by excavation. For a deep basement, net can be negative — the structure floats (compensated foundations on Mexico City's clay).
• Strip vs square vs circular footings. Shape factors adjust for confinement: square is ~1.3× strip in cohesive soil, 0.85× in cohesionless. Circular ≈ square for design.
• Drained vs undrained. Sand drains as fast as you load it; use effective-stress φ. Clay loads faster than it drains; use c_u with φ = 0. Long-term behavior may flip: undrained-failing clay can be safe long-term as pore pressures dissipate.
• General vs local vs punching shear. General: defined slip surface in dense sand/stiff clay, sudden. Local: partial slip in medium soil, gradual. Punching: footing pushes into loose/soft soil with no defined surface.
• Pile group action. Stress bulbs overlap so n piles don't give n × single-pile capacity. Group efficiency 0.6–0.9 for friction piles in clay, near 1.0 for end-bearing on rock.

Failure modes

• Bearing capacity exceeded → punching shear. The footing pushes down with no recoverable capacity remaining. Sudden in dense sand and stiff clay, gradual in loose or soft soil. Structure tilts toward the heaviest side and cracks at the foundation level. Transcona, 1913, is the textbook case.
• Excessive total settlement. Even at q_a, primary consolidation in clay produces 50–500 mm of settlement over decades. Floors slope, doors jam, utility lines crack. The Palace of Fine Arts in Mexico City sank ~3 m in the 20th century.
• Differential settlement. One footing settles more than its neighbor; the wall between them cracks diagonally through a window corner. The 50 mm differential limit comes from masonry's tolerance.
• Liquefaction. Saturated loose sand under cyclic loading loses grain contact, pore pressure equals total stress, and the soil flows like a liquid. Bearing capacity drops to near zero. The 1964 Niigata earthquake tipped apartment blocks intact onto their sides.
• Frost heave and thaw weakening. Water expands 9% on freezing, lifting footings; thaw turns the soil temporarily soft. Codes require footings below the frost line — 1.2–1.8 m in northern North America.
• Scour. Bridge piers lose bearing soil to flowing water. The 1987 Schoharie Creek bridge collapse killed 10 people when a flood-scoured pier subsided. Modern designs require scour analysis and rip-rap protection.

Where bearing capacity dominates the design

• Sizing spread footings, mat foundations, and shallow rafts.
• Determining whether shallow foundations work, or piles are required.
• Settlement-controlled design of buildings on compressible soil.
• Bridge piers, abutments, and approach embankments.
• Industrial loads — silos, storage tanks, turbine bases — where eccentric or cyclic loading multiplies the demand.
• Slope stability at the toe, where bearing-type failure interacts with rotational sliding.