Terzaghi’s Bearing Capacity Equation:

Terzaghi’s bearing capacity equation is widely used to determine the ultimate bearing capacity of shallow foundations on cohesive soils. According to Terzaghi’s equation, the ultimate bearing capacity (q_u) of a strip footing on cohesive soil can be calculated as:

q_u = cN_c + σ_z'N_q + 0.5γB_qN_γ

Where:
- q_u is the ultimate bearing capacity
- c is the cohesion of the soil
- N_c, N_q, and N_γ are bearing capacity factors
- σ_z' is the effective vertical stress at the depth of the footing
- γ is the unit weight of the soil
- B is the width of the footing

Net Ultimate Bearing Capacity for Strip Footing:

Given that the net ultimate bearing capacity for a strip footing on purely cohesive soil is 100 kPa, it can be assumed that the cohesion (c) of the soil is contributing significantly to the bearing capacity. The net ultimate bearing capacity represents the maximum pressure that can be applied to the soil without causing failure.

Net Ultimate Bearing Capacity for Square Footing:

To calculate the net ultimate bearing capacity for a square footing, we can use Terzaghi's bearing capacity equation with the width of the footing (B) as the dimension. Since a square footing has all sides equal, B represents the length of one side of the square.

By substituting B into the equation, we can determine the net ultimate bearing capacity for the square footing. Assuming all other parameters remain the same, the equation becomes:

q_u = cN_c + σ_z'N_q + 0.5γB_qN_γ

Since the cohesion (c) and the effective vertical stress (σ_z') are the same for both strip and square footings, they will have the same contribution to the bearing capacity. However, the width of the footing (B) will have an impact on the bearing capacity.

Increased Bearing Capacity for Square Footing:

As the width of the footing (B) increases, the bearing capacity of the square footing will be higher compared to the strip footing. This is because the square footing distributes the load over a larger area, resulting in a lower pressure on the soil.

Therefore, if the net ultimate bearing capacity for a strip footing is 100 kPa, the net ultimate bearing capacity for the same soil with a square footing of size B will be greater than 100 kPa. The exact value will depend on the width of the square footing, but it can be estimated to be around 120 kPa.

Conclusion:

In summary, the net ultimate bearing capacity for a square footing on purely cohesive soil will be greater than the net ultimate bearing capacity for a strip footing on the same soil. This is due to the larger contact area of the square footing, which results in a lower pressure