ANS:E - all the above.

1. Backfill is dry, cohesionless, homogeneous, and isotropic: This assumption implies that the soil behind the retaining wall or slope is composed of granular material (such as sand or gravel) without cohesion. Dry conditions are assumed to disregard the effects of pore water pressure. Homogeneous and isotropic assumptions mean that the soil properties, such as density and strength, are uniform in all directions.
2. Slip surface is the plane passing through the heel of the wall: Coulomb's wedge theory assumes that failure occurs along a specific surface, known as the potential slip surface, which passes through the heel of the wall or slope. This simplification allows for the analysis of the forces acting on the wedge of soil above the slip surface.
3. Sliding wedge itself acts as a rigid body, and the value of earth pressure is obtained by considering the limiting equilibrium of the wedge: This assumption treats the soil wedge above the slip surface as a rigid body. It implies that the soil mass moves as a single unit when failure occurs. The theory analyzes the equilibrium conditions at the critical state of failure to determine the stability of the wedge.
4. Position and direction of the resultant earth pressure are known: This assumption implies that the direction and magnitude of the earth pressure acting on the wedge of soil are predetermined or calculable based on the geometry and loading conditions. It allows for the consideration of the resultant forces and moments acting on the wedge during stability analysis.