About Bearing Capacity Calculator
The bearing capacity calculator estimates the ultimate and allowable bearing pressure of a shallow foundation using the general (Terzaghi-form) bearing-capacity equation qu = c*Nc + q*Nq + 0.5*gamma*B*Ngamma. It uses the Meyerhof/Reissner bearing-capacity factors, where Nq = e^(pi*tan(phi))*tan^2(45 + phi/2), Nc = (Nq - 1)/tan(phi) reducing to 5.14 for an undrained (phi = 0) clay, and Ngamma = (Nq - 1)*tan(1.4*phi) from the Meyerhof correlation.
Enter the soil cohesion c, the effective friction angle phi, the soil unit weight gamma, the footing width B, the embedment depth Df, and a factor of safety. The tool reports the three bearing-capacity factors, the ultimate bearing capacity, and both the gross allowable (qUlt/FS) and net allowable ((qUlt - q)/FS) values, with classical Terzaghi shape factors applied for square and circular footings.
How It Works
- Choose the footing shape (strip, square, or circular).
- Enter cohesion c (kPa), friction angle phi (degrees), unit weight gamma (kN/m3), width or diameter B (m), embedment depth Df (m), and the factor of safety FS.
- The calculator evaluates the Meyerhof bearing-capacity factors Nc, Nq, and Ngamma for the friction angle.
- It computes the surcharge q = gamma*Df, applies the three-term bearing-capacity equation with Terzaghi shape factors, and divides by FS to obtain the gross and net allowable bearing capacity.
Worked Example
A 2 m wide strip footing is founded at Df = 1.5 m in a soil with c = 20 kPa, phi = 30 deg, and gamma = 18 kN/m3, with a factor of safety FS = 3. The Meyerhof factors are Nc = 30.14, Nq = 18.40, and Ngamma = 15.67. The surcharge is q = gamma*Df = 18 * 1.5 = 27 kPa. The cohesion term is c*Nc = 20 * 30.14 = 602.8 kPa, the surcharge term is q*Nq = 27 * 18.40 = 496.8 kPa, and the self-weight term is 0.5*gamma*B*Ngamma = 0.5 * 18 * 2 * 15.67 = 282.0 kPa, giving qUlt = 1381.6 kPa. The gross allowable bearing capacity is qUlt/FS = 460.6 kPa.
Formulas
- General bearing-capacity equation (strip)
qu = c * Nc + q * Nq + 0.5 * gamma * B * Ngamma- Bearing-capacity factor Nq (Meyerhof/Reissner)
Nq = e^(pi * tan(phi)) * tan^2(45 + phi/2)- Bearing-capacity factor Nc
Nc = (Nq - 1) / tan(phi) [Nc = 5.14 when phi = 0]- Bearing-capacity factor Ngamma (Meyerhof)
Ngamma = (Nq - 1) * tan(1.4 * phi)- Shape factors (Terzaghi) and allowable capacity
strip: 1.0,1.0,1.0 | square: 1.3 c-term, 0.4 gamma B Ngamma | circular: 1.3 c-term, 0.3 gamma B Ngamma | qall = qu/FS, qnet = (qu - q)/FS
Standards & References
- Terzaghi (1943) bearing-capacity theory
- Meyerhof (1963) bearing-capacity factors
- Das, Principles of Foundation Engineering
Frequently Asked Questions
Which bearing-capacity factors does the calculator use?
It uses the Meyerhof/Reissner factors: Nq = e^(pi*tan phi) * tan^2(45 + phi/2), Nc = (Nq - 1)/tan(phi), and the Meyerhof correlation Ngamma = (Nq - 1)*tan(1.4*phi). For phi = 0 these become Nc = 5.14, Nq = 1, and Ngamma = 0.
What is the difference between gross and net allowable bearing capacity?
Gross allowable is the ultimate capacity divided by the factor of safety, qUlt/FS, and includes the existing overburden. Net allowable subtracts the surcharge first, (qUlt - q)/FS, representing the additional pressure the footing can carry above the soil that was removed during excavation.
How are square and circular footings handled?
The calculator applies the classical Terzaghi shape factors. The cohesion term is multiplied by 1.3 for both square and circular footings, the surcharge term is unchanged, and the self-weight term becomes 0.4*gamma*B*Ngamma for square footings and 0.3*gamma*B*Ngamma for circular footings.
Does the calculator account for the water table, eccentricity, or inclined loads?
No. It assumes a concentric vertical load, a horizontal ground surface, and no water table within the influence zone. For submerged soils use a buoyant unit weight, and apply separate depth, inclination, and eccentricity corrections where the loading or geometry requires them.