Earth Pressure Definitions – Active, Passive, and At-Rest Select the correct definition(s) for lateral earth pressure states acting on a retaining structure due to backfill soil.

Introduction / Context:
Retaining wall design hinges on understanding the limiting states of lateral earth pressure. Depending on wall movement relative to the backfill, the soil reaches distinct equilibrium states: active, passive, or at-rest. Correct identification ensures the right pressure coefficients and resultant forces are used in stability checks.

Given Data / Assumptions:

• Homogeneous backfill, level or inclined as context requires.
• Rigid wall exhibiting specific movement modes.
• Drained behavior is assumed for frictional backfills unless stated otherwise.

Concept / Approach:

Active state arises when the wall moves away from the backfill, reducing lateral stress to a minimum consistent with equilibrium. Passive state occurs when the wall pushes into the backfill, raising lateral stress to a maximum. At-rest is the condition with no wall movement, so lateral stress remains at the in-situ value. These distinctions map to well-known coefficients K_a, K_p, and K_0 respectively.

Step-by-Step Solution:

Verification / Alternative check:

Rankine/Coulomb theories quantify K_a and K_p; empirical correlations (e.g., Jaky’s formula) approximate K_0 for at-rest conditions.

Why Other Options Are Wrong:

'None of these' is incorrect because each provided definition matches standard usage; hence 'All of the above' is correct.

Common Pitfalls:

Using K_a where wall cannot move; ignoring wall friction or surcharge effects when computing pressures.

Final Answer:

All of the above