The coefficient of earth pressure at rest is a fundamental concept in soil mechanics and geotechnical engineering. It refers to the ratio between the lateral stress exerted by soil on a retaining structure and the vertical stress acting on the soil. The coefficient of earth pressure at rest is denoted as K₀.

Understanding the active and passive earth pressures:
Before discussing the coefficient of earth pressure at rest, it is important to understand the concepts of active and passive earth pressures.

- Active earth pressure: It is the lateral pressure exerted by soil on a retaining structure when the soil mass is pushed away from the structure. This typically occurs when the retained soil is loose or has a tendency to expand.

- Passive earth pressure: It is the lateral pressure exerted by soil on a retaining structure when the soil mass is being compressed towards the structure. This typically occurs when the retained soil is dense or has a tendency to contract.

- Coefficient of earth pressure at rest:
The coefficient of earth pressure at rest, K₀, represents the lateral pressure exerted by soil on a retaining structure when the soil is in a state of equilibrium or at rest. It is a measure of the lateral stress ratio and is defined as the ratio of lateral stress to vertical stress (K₀ = σh/σv).

Explanation of the correct answer:
The correct answer is option 'B', which states that the coefficient of earth pressure at rest is greater than the active pressure but less than the passive pressure. This can be explained as follows:

- When the retained soil is in a state of equilibrium or at rest, it exerts a lateral pressure on the retaining structure. This is known as the earth pressure at rest.

- The coefficient of earth pressure at rest, K₀, is greater than the active earth pressure because the lateral stress in the soil when it is at rest is higher than the lateral stress when the soil is being pushed away from the structure (active condition).

- On the other hand, the coefficient of earth pressure at rest is less than the passive earth pressure because the lateral stress in the soil when it is at rest is lower than the lateral stress when the soil is being compressed towards the structure (passive condition).

In summary, the coefficient of earth pressure at rest (K₀) is greater than the active earth pressure but less than the passive earth pressure. This concept is important in the design of retaining structures, such as retaining walls, sheet piles, and bulkheads, as it helps in determining the lateral forces acting on the structures and designing them to withstand the soil pressures.