Foundation Types and Bearing Capacity with Terzaghi Worked Example
A foundation transfers the load of a structure safely to the ground. It must satisfy two conditions: the soil must not fail in shear, and the settlement must stay within acceptable limits. Choosing the right type of foundation and sizing it correctly depends on the bearing capacity of the soil. This article describes the common foundation types used in Indian construction, defines the different bearing capacity terms, and works through a footing design on clay using Terzaghi's bearing capacity theory.
Types of Foundations
Foundations are broadly shallow or deep. A shallow foundation has a depth less than or comparable to its width and spreads load near the surface. A deep foundation transfers load to deeper, stronger strata through skin friction and end bearing.
| Type | Category | Where it is used |
|---|---|---|
| Wall (strip) footing | Shallow | Load-bearing brick or stone walls |
| Isolated footing | Shallow | Individual RCC columns on reasonably good soil |
| Combined footing | Shallow | Two columns close together or a column near the property line |
| Strap footing | Shallow | Exterior column connected to an interior footing by a strap beam |
| Raft (mat) foundation | Shallow | Weak soil or heavy loads where footings would cover most of the plan area |
| Pile foundation | Deep | Soft soil at the top, firm stratum at depth, or high water table |
| Well foundation | Deep | Bridge piers in rivers |
General requirements for shallow foundations are covered in IS 1904, the determination of bearing capacity of shallow foundations in IS 6403, and pile foundations in the IS 2911 series.
Bearing Capacity Terms
| Term | Symbol | Meaning |
|---|---|---|
| Ultimate (gross) bearing capacity | qu | Total pressure at the base at which soil fails in shear |
| Net ultimate bearing capacity | qnu | qu minus the overburden pressure γDf already present |
| Net safe bearing capacity | qns | qnu divided by a factor of safety, usually 2.5 to 3 |
| Safe bearing capacity | qs | qns + γDf |
| Allowable bearing pressure | qa | Lower of safe bearing capacity and pressure for permissible settlement |
Terzaghi's Bearing Capacity Equation
Terzaghi analysed a shallow strip footing failing by general shear and expressed the ultimate bearing capacity as the sum of contributions from cohesion, surcharge and soil weight.
Strip footing: qu = c Nc + γ Df Nq + 0.5 γ B Nγ Square footing: qu = 1.3 c Nc + γ Df Nq + 0.4 γ B Nγ Circular: qu = 1.3 c Nc + γ Df Nq + 0.3 γ B Nγ c = cohesion (kN/m²) γ = unit weight of soil (kN/m³) Df = depth of foundation (m) B = width of footing (m) Nc, Nq, Nγ = bearing capacity factors, functions of friction angle φ For purely cohesive soil (φ = 0): Nc = 5.7, Nq = 1, Nγ = 0
For sands, the factors grow rapidly with φ and are read from charts or tables. IS 6403 gives its own set of factors along with shape, depth and inclination factors, so for code-based design use that standard rather than Terzaghi's original values.
Worked Example: Square Footing on Clay
An RCC column carries an axial service load of 600 kN. The soil is saturated clay with undrained cohesion c = 40 kN/m², φ = 0 and unit weight γ = 18 kN/m³. The footing is placed at Df = 1.5 m. Use a factor of safety of 3.
Step 1: Ultimate bearing capacity
qu = 1.3 c Nc + γ Df Nq + 0.4 γ B Nγ = 1.3 x 40 x 5.7 + 18 x 1.5 x 1 + 0 = 296.4 + 27.0 = 323.4 kN/m²
Step 2: Net and safe bearing capacity
qnu = qu - γ Df = 323.4 - 27.0 = 296.4 kN/m² qns = qnu / FS = 296.4 / 3 = 98.8 kN/m² qs = qns + γ Df = 98.8 + 27.0 = 125.8 kN/m²
Since φ = 0 and Nγ = 0, the footing width does not appear in the result, which simplifies sizing. For sandy soil you would assume B, compute qu and iterate.
Step 3: Size of footing
Column load = 600 kN Self weight of footing and backfill (assume 10 %) = 60 kN Total load = 660 kN Area required = 660 / 125.8 = 5.25 m² Side of square footing = √5.25 = 2.29 m Provide 2.3 m x 2.3 m (area 5.29 m²) Actual pressure = 660 / 5.29 = 124.8 kN/m² < 125.8 -> OK
This only checks shear failure of the soil. Consolidation settlement of the clay must also be estimated, and if it exceeds the permissible value the footing must be enlarged or a different foundation chosen. The structural design of the footing (depth for punching and one-way shear, and bottom steel for bending) is then done using factored loads as per IS 456.
Common Mistakes
- Confusing gross and net bearing capacity, especially when comparing with soil report values.
- Ignoring the water table; a high water table reduces the effective unit weight and the bearing capacity in sands.
- Placing footings on filled-up or black cotton soil without investigation.
- Checking only shear failure and forgetting settlement in clays.
Summary
Shallow foundations such as isolated, combined and raft footings suit firm soil near the surface, while piles and wells carry loads to deeper strata. Terzaghi's equation gives the ultimate bearing capacity, which is converted to net safe and safe bearing capacity with a factor of safety. For the clay example, the safe bearing capacity is about 126 kN/m² and a 2.3 m square footing carries the 600 kN column.