For a cantilever retaining wall with a granular backfill, how does the pressure distribution of active earth pressure differ from the at-rest pressure, and what causes this difference?

For a cantilever retaining wall with a granular backfill, the pressure distribution of active earth pressure differs significantly from the at-rest pressure primarily due to the degree of lateral movement allowed for the wall, which in turn affects the mobilization of shear strength within the soil. A cantilever retaining wall is a structure that holds back soil, and granular backfill refers to soil like sand or gravel, which has internal friction but negligible cohesion. At-rest earth pressure (often denoted by the coefficient K₀) is the lateral pressure exerted by the granular backfill when there is absolutely no lateral movement or strain of the retaining wall relative to the soil. In this condition, the soil mass is constrained and cannot expand or contract horizontally. The horizontal stress develops purely as a response to the vertical overburden stress (the weight of the soil above a certain depth) without any lateral yielding. For a granular soil, the coefficient of at-rest earth pressure, K₀, is typically in the range of 0.4 to 0.6, and ....