## Earth Pressure and Stablity requirements

**EARTH PRESSURES AND STABILITY REQUIREMENTS**

**1. Lateral Earth Pressures**

The lateral force due to earth pressure constitutes the main force acting on the retaining wall, tending to make it bend, slide and overturn. The determination of the magnitude and direction of the earth pressure is based on the principles of soil mechanics. In general, the behaviour of lateral earth pressure is analogous to that of a fluid, with the magnitude of the pressure p increasing nearly linearly with increasing depth z for moderate depths below the surface:

where is the unit weight of the earth and C is a coefficient that depends on its physical properties, and also on whether the pressure is active or passive. ‘Active pressure’ (p_{a}) is that which the retained earth exerts on the wall as the earth moves in the same direction as the wall deflects. On the other hand, ‘passive pressure’ (p_{p}) is that which is developed as a resistance when the wall moves and presses against the earth (as on the toe side of the wall). The coefficient to be used is the active pressure coefficient, C_{a}, in the case of active pressure, and the passive pressure coefficient, C_{p}, in the case of passive pressure; the latter (C_{p}) is generally much higher than the former (C_{a}) for the same type of soil.

In the absence of more detailed information, the following expressions for C_{a} and C_{p}, based on Rankine’s theory may be used for cohesionless soils and level backfills

where φ is the angle of shearing resistance (or angle of repose). For a typical granular soil (such as sand), φ ≈ 30o, corresponding to which, C_{a} = 1/3 and C_{p} = 3.0.

When the backfill is sloped, the expression for C_{a} should be modified as follows:

where θ is the angle of inclination of the backfill, i.e., the angle of its surface with respect to the horizontal

The direction of the active pressure, p_{a}, is parallel to the surface of the backfill. The pressure has a maximum value at the heel, and is equal to

where is the height of the backfill, measured vertically above the heel. For the case of a level backfill, θ = 0 and h'= h, and the direction of the lateral pressure is horizontal and normal to the vertical stem. The force, P_{a}, exerted by the active earth pressure, due to a backfill of height h' above the heel, is accordingly obtained from the triangular pressure distribution.

This force has units of kN per m length of the wall, and acts at a height h'/3 above the heel at an inclination θ with the horizontal.

The force, P_{p}, developed by passive pressure on the toe side of the retaining wall is generally small (due to the small height of earth† ) and usually not included in the design calculations, as this is conservative.

**2. Effect of Surcharge on a Level Backfill**

Frequently, gravity loads act on a level backfill due to the construction of buildings and the movement of vehicles near the top of the retaining wall. These additional loads can be assumed to be static and uniformly distributed on top of the backfill, for calculation purposes. This distributed load w_{s} (kN/m^{2}) can be treated as statically equivalent to an additional (fictitious) height, , of soil backfill with unit weight γ_{e}. This additional height of backfill is called surcharge, and is expressed either in terms of height h_{s}, or in terms of the distributed load w_{s }. The presence of the surcharge not only adds to the gravity loading acting on the heel slab, but also increases the lateral pressure on the wall by

The total force due to active pressure acting on the wall is accordingly given by

with the lines of action of P_{a1} and P_{a2} at h/2 and h/3 above the heel