Introduction:
Rankine's earth pressure theory is a widely used theory in geotechnical engineering to determine the lateral earth pressure acting on retaining walls. It is based on certain assumptions that help simplify the analysis and provide reasonable estimates of the earth pressure.

Assumption in Rankine's Earth Pressure Theory:
The assumption in Rankine's earth pressure theory is that the soil is in the state of plastic equilibrium during active and passive earth pressure conditions. This means that the soil is assumed to be fully mobilized and the failure surfaces are assumed to be fully developed.

Explanation:
- In Rankine's earth pressure theory, the soil is assumed to behave as a cohesionless material with zero friction angle. This assumption simplifies the analysis and provides conservative results.
- The theory considers two conditions: active earth pressure and passive earth pressure. Active earth pressure occurs when the soil is pushing against the retaining wall, while passive earth pressure occurs when the soil is resisting the movement of the retaining wall.
- During active earth pressure condition, the soil is assumed to be in a state of plastic equilibrium. This means that the soil has reached its maximum shear strength and is fully mobilized. The failure surface is assumed to be a plane surface inclined at an angle of internal friction.
- Similarly, during passive earth pressure condition, the soil is assumed to be in a state of plastic equilibrium. The soil has reached its maximum shear strength and is fully mobilized. The failure surface is assumed to be a plane surface inclined at an angle of internal friction.
- Plastic equilibrium implies that the soil has undergone plastic deformation, and the soil particles have rearranged themselves to achieve a state of equilibrium. This assumption helps in simplifying the analysis and provides reasonable estimates of the lateral earth pressure.
- The assumption of plastic equilibrium is reasonable for sandy and granular soils, which are typically cohesionless and exhibit significant plastic deformation under loading. However, it may not be applicable for cohesive soils, which have a tendency to exhibit elastic behavior.
- Therefore, the correct assumption in Rankine's earth pressure theory is that the soil is in the state of plastic equilibrium during active and passive earth pressure conditions.

Conclusion:
The assumption in Rankine's earth pressure theory is that the soil is in the state of plastic equilibrium during active and passive earth pressure conditions. This assumption simplifies the analysis and provides reasonable estimates of the lateral earth pressure acting on retaining walls. While it is applicable for cohesionless soils, it may not be applicable for cohesive soils, which have a tendency to exhibit elastic behavior.