Soil Bearing Capacity Calculator
Estimate soil bearing capacity for your project with our free calculator. Get accurate material quantities, costs, and specifications.
Formula
qu = c*Nc + gamma*Df*Nq + 0.5*gamma*B*Ngamma (Terzaghi)
The Terzaghi bearing capacity equation calculates the ultimate bearing capacity (qu) as the sum of three terms: the cohesion term (c times Nc), the surcharge/depth term (unit weight times foundation depth times Nq), and the width term (0.5 times unit weight times foundation width times Ngamma). The bearing capacity factors Nc, Nq, and Ngamma depend on the soil friction angle. The allowable bearing capacity is the ultimate value divided by the factor of safety (typically 3).
Worked Examples
Example 1: Strip Footing on Sandy Soil
Problem: Calculate the bearing capacity for a 4 ft wide strip footing at 3 ft depth in soil with cohesion 500 psf, friction angle 30 degrees, and unit weight 120 pcf.
Solution: Nq = e^(pi*tan30) x tan^2(60) = 18.40\nNc = (18.40-1)/tan(30) = 30.14\nNgamma = 2(18.40+1)tan(30) = 22.40\nqu = 500(30.14) + 120(3)(18.40) + 0.5(120)(4)(22.40)\nqu = 15,070 + 6,624 + 5,376 = 27,070 psf\nAllowable = 27,070 / 3 = 9,023 psf
Result: Ultimate = 27,070 psf, Allowable = 9,023 psf (FOS=3)
Example 2: Square Footing for Column
Problem: Determine the maximum column load for a 4 ft x 4 ft square footing using the same soil parameters.
Solution: qu_sq = 1.3(500)(30.14) + 120(3)(18.40) + 0.4(120)(4)(22.40)\nqu_sq = 19,591 + 6,624 + 4,301 = 30,516 psf\nAllowable = 30,516 / 3 = 10,172 psf\nMax load = 10,172 x 4 x 4 = 162,752 lbs
Result: Allowable = 10,172 psf, Max column load = 162,752 lbs (81.4 tons)
Frequently Asked Questions
What is soil bearing capacity and why is it important?
Soil bearing capacity is the maximum pressure that the soil beneath a foundation can sustain without experiencing shear failure or excessive settlement. It determines the size of footings and foundations needed to safely support structural loads. If the applied pressure exceeds the bearing capacity, the soil undergoes shear failure, causing the foundation to sink, tilt, or punch through the ground. Bearing capacity depends on soil type, strength parameters, foundation dimensions, and depth of embedment.
What are the Terzaghi bearing capacity factors Nc, Nq, and Ngamma?
The Terzaghi bearing capacity factors are dimensionless parameters that depend on the soil friction angle. Nc is the cohesion factor representing the contribution of soil cohesion to bearing capacity. Nq is the surcharge factor accounting for the overburden pressure from soil above the foundation level. Ngamma is the self-weight factor representing the contribution of soil weight in the failure zone below the foundation. These factors increase dramatically with friction angle, meaning dense granular soils have much higher bearing capacities.
What factor of safety is used for bearing capacity design?
A factor of safety of 3.0 is standard for most bearing capacity design under normal loading conditions. This accounts for variability in soil properties, simplifications in the bearing capacity theory, and uncertainties in the applied loads. For temporary structures, a FOS of 2.0 to 2.5 may be acceptable. When loads include wind or seismic components, many codes allow a one-third increase in allowable bearing pressure. The allowable bearing capacity equals the ultimate bearing capacity divided by the factor of safety.
How does foundation depth affect bearing capacity?
Increasing foundation depth generally increases bearing capacity because the overburden soil above the foundation level provides additional resistance to shear failure through the Nq term. The surcharge effect equals the soil unit weight multiplied by the depth multiplied by Nq. For a soil with friction angle of 30 degrees, doubling the foundation depth from 3 to 6 feet can increase the ultimate bearing capacity by 20 to 30 percent. However, deeper excavation increases construction costs, so the optimal depth balances structural requirements with economy.
What are typical bearing capacity values for different soil types?
Presumptive allowable bearing capacities from building codes provide rough guidance: soft clay 1,000 to 2,000 psf, medium clay 2,000 to 4,000 psf, stiff clay 4,000 to 6,000 psf, loose sand 2,000 to 3,000 psf, medium dense sand 3,000 to 5,000 psf, dense sand 5,000 to 8,000 psf, gravel 6,000 to 12,000 psf, and bedrock 10,000 to 100,000 psf. These are conservative estimates for preliminary design and should be verified with site-specific geotechnical investigation.
How do I calculate the load-bearing capacity of a beam?
Beam capacity depends on material, cross-section dimensions, span length, and support conditions. For a simple rectangular wood beam, bending strength = (F_b x b x d^2) / 6, where F_b is allowable stress, b is width, and d is depth. Always consult a structural engineer for critical applications.