The correct answer is: A. less than active earth pressure but greater than passive earth pressure.
The coefficient of earth pressure at rest, $K_o$, is a dimensionless number that is used to calculate the lateral earth pressure on a retaining wall. It is defined as the ratio of the lateral earth pressure to the effective overburden pressure.
The active earth pressure is the lateral earth pressure that is exerted by a soil mass when it is moving outward. The passive earth pressure is the lateral earth pressure that is exerted by a soil mass when it is moving inward.
The coefficient of active earth pressure, $K_a$, is always greater than the coefficient of passive earth pressure, $K_p$. This is because the active earth pressure is a result of the soil mass trying to move outward, while the passive earth pressure is a result of the soil mass trying to move inward.
The coefficient of earth pressure at rest, $K_o$, is always less than the coefficient of active earth pressure, $K_a$, but greater than the coefficient of passive earth pressure, $K_p$. This is because the coefficient of earth pressure at rest is a result of the soil mass being in a state of equilibrium.
The following diagram shows the relationship between the coefficient of earth pressure at rest, the coefficient of active earth pressure, and the coefficient of passive earth pressure:
[Diagram of the relationship between the coefficient of earth pressure at rest, the coefficient of active earth pressure, and the coefficient of passive earth pressure]
The coefficient of earth pressure at rest is a very important factor in the design of retaining walls. It is used to calculate the lateral earth pressure that will be exerted on the wall, which is then used to design the wall to withstand that pressure.