# Concept of Retaining Wall Design: Calculation of Earth Pressure

There different types of retaining walls and their design concept starts with calculation of earth pressures. Earth pressure calculation on retaining walls depends on the depth, pore water pressure and surcharge on retaining walls. Cantilever Retaining Walls:

(a) Cantilever retaining wall without toe projection

(b) Cantilever retaining wall with fillets

Fig: Cantilever Retaining Wall

Counterfort and Buttress Retaining Walls: If the height of the retaining wall exceeds certain limit, the cantilever walls are not economical. Economy can be achieved by providing counterforts which are nothing but vertical beams connected to the stem and the heel slab by reinforcements at regular intervals. The heel slab and the vertical stem are designed as continuous slabs instead of cantilever slabs. If the counterforts are provided in the toe side, the retaining wall is called a buttress wall.

Fig. Counterfort Retaining Wall

Fig: Buttress Retaining Wall

## Surcharge on retaining walls:

A retaining wall which retains earth level upto the top of the retaining wall is a wall without surcharge. If the earth on the earth retained side is not level or the earth carries loads, the earth is said to have surcharge. The pressure exerted by the earth on the retaining wall will be more in this case. The different types of surcharges that may act on a retaining wall are illustrated in fig below.

Fig: Different Types of Surcharges on Retaining Wall

## Earth Pressure on Retaining Wall:

The retained earth exerts horizontal pressure on the retaining wall, which is called the active earth pressure. The resisting pressure applied by the wall on the retained earth is called the passive earth pressure. This earth pressure varies linearly with the dept of retained earth. The pressure at a depth of H on the wall exerted by the earth is given by , where is the coefficient of active earth pressure and w is the density of the earth retained. The total earth pressure up to this depth H is the area of the pressure diagram which is and H acts at a height of H/3 from the bottom. Hence the moment due to the horizontal pressure Where , and is the angle of the repose of the soil.

Fig: Earth Pressure on Retaining Wall

If the earth has a sloping surcharge, sloping at an angle of to the horizontal, then the pressure at a depth of due to earth is and the total earth pressure upto a depth of is . This acts at a height of and parallel to the surface of the ground. Hence the moment about the base is Where

Fig: Earth Pressure due to inclined Backfill on Retaining wall

If the earth has a level surcharge of /unit run, then the pressure is the same at all depths and is equal to and the surcharge pressure at a depth of H is equal to . This acts at H/2 from the bottom. The moment due to this at the bottom (figure below).

Fig: Earth Pressure due to Surcharge on Retaining Wall

If the surcharge is submerged, the submerged earth pressure should be taken into account. Sufficient drainage holes are provided at different levels for the draining of water.