Home / Trade / Construction / Terzaghi Bearing Capacity

Terzaghi Bearing Capacity

Calculate safe continuous strip footing foundation capacities utilizing Karl Terzaghi's 1943 geotechnical engineering ultimate limits equations.

Soil Profile & Geometry

Soil Cohesion (c, psf)

Unit Weight (γ, pcf)

Depth of Footing (Df, ft)

Strip Width (B, ft)

Terzaghi Factors

Cohesion (Nc)

Surcharge (Nq)

Weight (Nγ)

🏗️ DIAGNOSTIC LOGIC: If the structural load applied to your footing exceeds the Safe Bearing Capacity, the soil is mathematically guaranteed to undergo shear failure, causing catastrophic foundation settlement.

Safe Bearing Capacity

1,720 PSF

Factored (FS=3.0) structural design limit.

Ultimate Bearing Capacity

5,160 PSF

Exact point of sheer catastrophic soil failure.

Email Link Text/SMS WhatsApp

What is The Physics of Geotechnical Shear Failures?

Karl Terzaghi, the undisputed father of modern soil mechanics, derived the foundational equations for how earth beneath a building supports weight. Terzaghi proved that a concrete foundation doesn't suddenly sink like a stone in water; instead, the extreme pressure creates a microscopic 'wedge' of dirt directly beneath the concrete that physically drives downward. This wedge attempts to force the adjacent dirt sideways and upward. If the localized gravity and internal friction of the surrounding soil are strong enough to resist the wedge, the building stands. If the wedge overcomes the friction, the soil catastrophically 'shears' and the building collapses.

Mathematical Foundation

Terzaghi's Ultimate Bearing Capacity

q_u = (c \times N_c) + (q \times N_q) + (0.5 \times \gamma \times B \times N_\gamma)

q_u

= Ultimate geometric bearing capacity where the soil structurally shears (PSF).

c

= Internal soil cohesion stickiness (PSF).

\gamma

= Bulk unit weight density of the soil (PCF).

B

= Physical width of the concrete strip footing (Feet).

q

= Effective surcharge weight from the soil buried above the footing tip (q = \gamma \times D_f).

N_c, N_q, N_\gamma

= Dimensionless bearing capacity factors derived strictly from the internal friction angle (\phi).

Safe Working Limit

q_{safe} = \frac{q_u}{F_s}

q_{safe}

= The maximum allowable load pressure for architectural design (PSF).

F_s

= Factor of Safety. The industry standard geotechnical requirement is 3.0.

Laws & Principles

The Factor of Safety 3.0 Rule: Because soil is non-homogeneous (it changes density and moisture constantly over time), calculating the true 'Ultimate Capacity' provides a number that guarantees sudden collapse if reached. Therefore, international geotechnical engineering standards strictly mandate dividing the ultimate limit by a massive Factor of Safety (virtually always 3.0) to determine the actual Safe Working Capacity.
The Shallow Footing Limit: Terzaghi's specific classical equation is purely valid for 'shallow' strip footings. Mathematically, a footing is only considered shallow if the burial depth (D_f) is less than or strictly equal to the physical width of the concrete (B). (Depth ≤ Width). For deep piles or drilled piers, different geotechnical theories (like Meyerhof's) must be utilized.
The Water Table Hazard: If the local groundwater table physically rises above the bottom tip of the concrete foundation footing, the effective weight (density) of the submerged soil drops by roughly 50% due to Archimedes' buoyancy. This destroys the N_q and N_gamma friction terms and will slash the total bearing capacity of the soil in half.

Step-by-Step Example Walkthrough

" An architect is designing a brick masonry house. The engineer specs a continuous concrete strip footing 2 feet wide (B) buried 3 feet into the earth (Df). A geotechnical soil boring report indicates the soil weighs 110 pcf with 200 psf of cohesion and an internal friction angle of 20 degrees. Standard Terzaghi charts for 20 degrees provide modifiers: Nc=14.8, Nq=5.6, Nγ=3.2. "

1. Calculate the trench dirt surcharge weight: q = 110 pcf × 3 ft depth = 330 psf.
2. Calculate Cohesion (Term 1): c × Nc = 200 psf × 14.8 = 2,960 psf.
3. Calculate Surcharge (Term 2): q × Nq = 330 psf × 5.6 = 1,848 psf.
4. Calculate Friction Resistance (Term 3): 0.5 × 110 pcf × 2 ft width × 3.2 = 352 psf.
5. Sum up the Ultimate Capacity (q_u): 2,960 + 1,848 + 352 = 5,160 PSF ultimate failure limit.
6. Apply the structural Factor of Safety (Fs = 3.0): 5,160 ÷ 3.0 = 1,720 PSF.

Final Result: The Safe Working Bearing Capacity for this footing configuration is exactly 1,720 pounds per square foot. Since residential building codes often default to assuming 1,500 to 2,000 psf for standard dirt without a test, this geotechnical math validates that a 2-foot wide footing is structurally safe for this specific site.

Quick Answer: What is safe soil bearing capacity?

Safe soil bearing capacity is the maximum amount of structural weight (measured in Pounds per Square Foot or PSF) that building foundations can apply to the ground without causing the soil to shear, shift, or catastrophically settle. Typical residential clay or silt supports around 1,500 PSF, sandy gravel supports around 3,000 PSF, and solid bedrock can support over 10,000 PSF. Engineers determine the ultimate capacity where the dirt mathematically fails, and then divide it by a strict safety factor (usually 3.0) to get the safe working number.

The Terzaghi Components

Term 1: Cohesion Resistance = (Cohesion × N_c)

Term 2: Burial Surcharge Resistance = (Depth × Density × N_q)

Term 3: Width Friction Weight = (0.5 × Density × Width × N_γ)

Note: Adding these three mathematical terms together gives the ultimate destruction limit. The Safe limit is this total divided by 3.

Presumptive Bearing Capacities (IBC)

Soil Classification	Typical Character	Safe Capacity (PSF)
Soft Clay & Silt	Muddy, easily pushed with thumb	1,000 - 1,500
Stiff Clay & Sandy Loam	Hard to dent, typical farm topsoil	2,000 - 2,500
Sand / Gravel Mix	Gritty, drains water instantly	3,000 - 4,000
Sedimentary Rock	Soft sandstone or rippable shale	4,000 - 8,000
Crystalline Bedrock	Solid granite or hard limestone	12,000+
Note: If a geotechnical boring test is not ordered, local building inspectors force architects to use the absolute lowest presumptive values to guarantee safety.

Foundation Failures to Avoid

The Shallow Frost Heave

A contractor builds a retaining wall and pours the concrete footing only 12 inches deep in a northern climate with clay soil. The Terzaghi capacity math works fine on paper. However, in winter, the ground freezes down to 36 inches. The water trapped in the clay turns to solid ice and expands with thousands of pounds of force. It lifts the shallow foundation straight upward, snapping the concrete in half. Foundations must be buried below the local 'frost line,' regardless of bearing capacity.

The Backfill Washout

A foundation is poured for a commercial strip mall. The engineer utilized Terzaghi's Term 2 (Surcharge Weight), relying on 4 feet of dirt being packed heavily over the footing to hold down the soil beneath it. During a rainstorm, poor site drainage washes 3 feet of the dirt away. Without the heavy dirt 'surcharge' pushing down, the soil beneath the footing loses its containment friction and squirts out sideways under the weight of the building. The corner of the strip mall sinks 6 inches.

Geotechnical Best Practices

Do This

✓Widen the footings for safety. If you hit soft, expansive clay during excavation, the easiest and cheapest way to increase the total load capacity of the building is to simply dig the trench wider. Changing a 16-inch wide footing to a 24-inch wide footing drastically drops the PSF pressure placed on the dirt.
✓Order a dynamic cone penetration (DCP) test. Never guess. Pay a lab $500 to come out and drive a metal cone into the trench. They can provide an exact cohesion and friction angle value to plug into the Terzaghi equation, saving you from over-engineering massive amounts of concrete.

Avoid This

✗Don't pour concrete on uncompacted fill. Never dig a hole too deep, throw loose dirt back into it, and pour the footing on top. Terzaghi's math relies on undisturbed native dirt or dirt compacted mechanically in tiny lifts. 'Fluffed' dirt has virtually zero cohesion or friction capacity and will instantly settle.
✗Don't ignore the water table. If you design a foundation assuming the soil is dry, and a heavy rain season causes the water table to rise and submerge your footing, the sudden loss of soil weight via buoyancy will slash your bearing capacity in half. Massive buildings sink because of unexpected water.

Frequently Asked Questions

What is a Strip Footing vs a Square Footing?

A continuous strip footing is a long, narrow ribbon of concrete (like the foundation under the perimeter walls of a house). A square pad footing is a solitary block of concrete designed to support a single point-load, like a heavy steel column. Terzaghi developed slightly different mathematical variations for standard strips versus isolated squares or circular pads.

Why do we divide the capacity by 3?

The Factor of Safety (FS) of 3.0 is a rigid global engineering standard. Unlike structural steel which is manufactured in a controlled factory to exact tolerances, soil is completely natural and unpredictable. A foot away from a core sample, the dirt might change entirely. Cutting the mathematical limit by 66% guarantees that no matter the localized anomalies or future water infiltration, the structure will not shear into the earth.

Does deeper burial increase bearing capacity?

Yes. In the Terzaghi equation, burying the footing deeper (the 'Surcharge' term) piles thousands of pounds of dirt on top of the edges. This heavy blanket of dirt acts like a weighted lid, preventing the compressed soil directly beneath the foundation from escaping upwards. A deeper trench physically pins the failure zone in place.

What soil has the worst bearing capacity?

Organic peat, expansive swamp mud, and uncompacted artificial fill dirt have virtually zero bearing capacity. Buildings placed on these soils will sink continuously or warp dramatically as the organic matter decomposes. These soils must be physically excavated and exported entirely, or the building must be placed on deep steel piles driven all the way down through the bad soil into solid bedrock.