Soil Bearing Capacity Calculator – Terzaghi & SPT Es

Introduction

The EstiMate Civil Soil Bearing Capacity Calculator calculates the ultimate and allowable bearing capacity of shallow foundations using classical Terzaghi formulation parameters.

Governing Formulas

Ultimate bearing capacity ($ q_u $) for shallow foundations is calculated using Terzaghi's classical formulations:

Strip Footing: $ q_u = c N_c + q N_q + 0.5 \gamma B N_\gamma $
Square Footing: $ q_u = 1.3 c N_c + q N_q + 0.4 \gamma B N_\gamma $
Circular Footing: $ q_u = 1.3 c N_c + q N_q + 0.3 \gamma B N_\gamma $
Allowable Bearing Capacity ($ q_{all} $): $ q_{all} = \frac{q_u}{FS} $ (where $ FS $ is the Factor of Safety, typically between 2.5 and 3.0).

Where:
$ c $ = soil cohesion ($ \text{kN/m}^2 $)
$ q = \gamma D_f $ = effective surcharge at footing base level ($ \text{kN/m}^2 $)
$ D_f $ = depth of foundation ($ \text{m} $)
$ \gamma $ = unit weight of soil ($ \text{kN/m}^3 $)
$ B $ = width of foundation ($ \text{m} $)
$ N_c, N_q, N_\gamma $ = Terzaghi's bearing capacity factors, which are functions of the internal friction angle $ \phi $.

Geotechnical Assumptions

The classical Terzaghi analysis operates under the following key soil mechanics assumptions:

The soil is homogeneous, isotropic, and semi-infinite.
The footing is rigid, shallow ($ D_f \le B $), with a rough base.
The shear failure mode is general shear failure. For local shear failure, cohesion and friction angle must be reduced:
$ c' = \frac{2}{3}c $
$ \phi' = \arctan\left(\frac{2}{3}\tan\phi\right) $
The water table is assumed to be deep below the foundation level (pore water pressure is neglected).

Practical Example Calculation

Consider a square foundation of width $ B = 2.0\text{ m} $ at depth $ D_f = 1.2\text{ m} $. Soil cohesion is $ c = 15\text{ kPa} $, friction angle is $ \phi = 20^\circ $, and unit weight of soil is $ \gamma = 18\text{ kN/m}^3 $. The Factor of Safety is $ FS = 3.0 $:

For $ \phi = 20^\circ $, Terzaghi's factors are approximately $ N_c = 17.7, N_q = 7.4, N_\gamma = 5.0 $:

Surcharge ($q$): $ 18 \times 1.2 = 21.6\text{ kPa} $
Ultimate Bearing Capacity ($q_u$):
$ q_u = (1.3 \times 15 \times 17.7) + (21.6 \times 7.4) + (0.4 \times 18 \times 2.0 \times 5.0) $
$ q_u = 345.15 + 159.84 + 72.0 = 576.99\text{ kPa} $
Allowable Bearing Capacity ($q_{all}$): $ \frac{576.99}{3.0} \approx 192.33\text{ kPa} $

Practical Limitations

Terzaghi bearing capacity formulations have specific limits:

It does not account for groundwater table adjustments, which can cut the bearing capacity of soil by up to 50% if the water table rises to the base of the footing.
It does not account for eccentric or inclined loading (Meyerhof or Vesic equations are required for such cases).
Settlement limits (e.g., limit of 25 mm total settlement) often control design pressure rather than ultimate shear strength.

Standard References

Refer to geotechnical texts and national standards for shallow foundation designs:

Terzaghi, K. Theoretical Soil Mechanics.
IS 6403 – Code of Practice for Determination of Bearing Capacity of Shallow Foundations.