Explanation:

Terzaghi's bearing capacity analysis is used to determine the safe load-carrying capacity of a soil foundation. It is based on the assumption that the soil below the footing is in elastic equilibrium.

Elastic Equilibrium:
In elastic equilibrium, the soil particles return to their original positions after the load is removed. This means that the soil behaves like a spring and deforms under the applied load but returns to its original shape when the load is removed.

Soil Wedge:
The soil wedge immediately below the footing refers to the soil mass that is directly in contact with the footing. It is shaped like a triangular wedge due to the shape of the footing.

Explanation of the Answer:
The correct answer is option 'C' - Elastic Equilibrium. This means that the soil wedge immediately below the footing remains in a state of elastic equilibrium.

- When a load is applied to the footing, the soil wedge deforms and undergoes stress redistribution.
- The soil particles in the wedge compress and displace, causing the wedge to bulge outwards.
- However, since the soil below the footing is assumed to be in elastic equilibrium, it will return to its original shape once the load is removed.
- This assumption is valid as long as the applied load is within the safe bearing capacity of the soil.
- If the load exceeds the bearing capacity, the soil may undergo excessive deformation, leading to failure.

Significance of Elastic Equilibrium:
Assuming elastic equilibrium allows for a simplified analysis of the bearing capacity of the soil. It provides a conservative estimate of the safe load-carrying capacity of the foundation.

Note:
It is important to note that Terzaghi's bearing capacity analysis is a simplified method and does not account for all factors that can affect the bearing capacity of a soil foundation. It provides a conservative estimate and is often used as a preliminary analysis before more detailed and comprehensive analyses are conducted.