Terzaghi's Theory for Ultimate Bearing Capacity of Cohesive Soil

Terzaghi's theory is widely used for the calculation of the ultimate bearing capacity of the soil. The theory is based on the assumption that the soil below the foundation is homogeneous, isotropic, and fully saturated. According to Terzaghi's theory, the ultimate bearing capacity of a strip footing on a purely cohesive soil with a smooth base can be calculated using the following equation:

Qu = cNc + qNq + 0.5BγBNγ

Where,

- Qu = ultimate bearing capacity of the soil
- c = cohesion of the soil
- Nc, Nq, and Nγ = bearing capacity factors, which depend on the angle of internal friction of the soil
- q = surcharge on the soil
- B = width of the footing
- γB = effective unit weight of the soil

Calculation of Ultimate Bearing Capacity

Given that the soil is purely cohesive and the base of the strip footing is smooth, we can assume that the angle of internal friction of the soil is zero. Therefore, the bearing capacity factors Nq and Nγ become equal to 0. According to the question, the ultimate bearing capacity at ground surface for a purely cohesive soil and for a smooth base of a strip footing is to be determined.

- c = cohesion of the soil = ? (not given in the question)
- Nc = bearing capacity factor for cohesion = 5.14 (from the table)
- q = surcharge on the soil = 0 (not given in the question)
- B = width of the footing = 1m (assumed)
- γB = effective unit weight of the soil = ? (not given in the question)

Substituting the values in the equation, we get:

Qu = cNc + qNq + 0.5BγBNγ
Qu = cNc + 0 + 0.5BγBNγ
Qu = cNc + 0.5BγBNγ

The ultimate bearing capacity at ground surface for a purely cohesive soil and for a smooth base of a strip footing is given as 5.14c, which is the value of cNc. Therefore, substituting the value of Nc in the equation, we get:

Qu = 5.14c

Hence, the correct option is (B) 5.14c.

According to Terzaghi q= 5.7C and according to Prandtl q = 5.14C