Soil bearing capacity calculator (Terzaghi and Meyerhof)

Enter a footing, its load and the soil under it. Rischio’s engine works out the ultimate bearing capacity with the general equation, as the studio does, and the page sets Terzaghi’s classic value beside it. It’s free and needs no account.

How it calculates

The engine uses the general bearing capacity equation: Terzaghi’s three terms with the shape, depth and inclination factors that Meyerhof’s approach adds.

• $q$ is the effective vertical stress at the base, and $\gamma'$ the unit weight under it. Both take the water table into account.
• The bearing capacity factors are Reissner’s, Prandtl’s and Vesić’s: $N_q = \tan^2(45° + \phi'/2)\,e^{\pi \tan\phi'}$, $N_c = (N_q - 1)/\tan\phi'$ and $N_\gamma = 2(N_q + 1)\tan\phi'$.
• The shape factors are De Beer’s, the depth factors Hansen’s, and the inclination factors Meyerhof’s and Hanna’s.
• An eccentric load works on Meyerhof’s effective width, $B' = B - 2e$.

The allowable bearing capacity is $q_u/3$. The factor of safety compares $q_u$ with the largest pressure the load puts under the base, $q_{max}$, and asks for 3 or more. The method, with every factor and when it applies, is in the bearing capacity theory of the docs.

Terzaghi’s equation, to compare

Terzaghi’s equation (1943) is where the general one comes from. It was written for a strip footing under a vertical, centred load:

For a square footing, he raised the cohesion term by 1.3 and brought the weight term down to 0.4: $q_u = 1.3\,c' N_c + q N_q + 0.4\,\gamma B N_\gamma$. The calculator takes $N_q$ and $N_c$ in closed form and $N_\gamma$ from a closed-form fit to Terzaghi’s tabulated values, with the same $q$ and $\gamma'$ as the general equation. Terzaghi’s equation has no depth or inclination factors, so for a deep footing or an inclined load the general equation is the one to trust.

How to use it

1. Pick the footing: square, rectangular or strip. A strip’s load goes per metre of its length.
2. Give its width $B$, its length $L$ if it’s rectangular, and how deep its base is, $D_f$.
3. Enter the load at the base: the vertical load and, if there are any, the horizontal load and the moment along the width.
4. Describe the soil (its unit weight, cohesion and friction angle) and the water table, if it’s near.

The results show $q_u$, the allowable capacity, $q_{max}$ and the factor of safety, with every factor of the equation and a drawing of the footing with its contact pressure. To keep the footing, try other loads or get a calculation report with every step, design it in Rischio’s footing tool.

Frequently asked questions

How do you calculate the bearing capacity of soil?

With a bearing capacity equation: Terzaghi’s for a strip under a vertical load, or the general equation for any footing, depth and load. Both add what the soil’s cohesion, the weight of the soil above the base and the soil’s own weight under it can carry before the ground shears.

What is the allowable bearing capacity?

The ultimate bearing capacity divided by a factor of safety, usually 3 for foundations: $q_{all} = q_u/3$. A design also has to keep settlement within limits, which can govern before bearing does.

What is a good soil bearing capacity?

It depends on the soil and on the footing, which is why it’s calculated. As an order of magnitude, the presumptive values of the International Building Code, for use without a geotechnical study, go from 1,500 psf (about 72 kPa) for clays and silts to 2,000 psf (96 kPa) for sands, 3,000 psf (144 kPa) for gravels and 12,000 psf (575 kPa) for crystalline bedrock.

Which soil has the best bearing capacity?

Rock, then dense gravels and sands, then stiff clays. Soft clays, loose sands and organic soils carry the least, and often call for a deep foundation or ground improvement.

What is the difference between Terzaghi’s and Meyerhof’s equations?

Meyerhof’s general equation adds shape, depth and inclination factors to Terzaghi’s three terms, so it covers rectangular footings, deeper bases and inclined or eccentric loads. For a strip footing near the surface under a vertical load, the two come out close.