Rankine's Earth Pressure Theory | At Rest, Active and Passive Earth Pressure Formula

Updated: Dec 19, 2020

To analyse the pressure relation between retaining wall and soil mass, the most commonly used theory is Rankine's Earth Pressure Theory. Three conditions are analysed - Wall at rest, Active Earth Pressure and Passive Earth Pressure. Rankine's theory assumes the wall to be smooth and soil cohesionless. This theory is also extended to cohesive soils.

Let us hit the basics first!

Retaining wall and backfill
Retaining wall and backfill

Retaining Wall and Backfill

Every time it is not possible to place the soil until it has great shear strength. Then we construct a wall to keep it in place and will fill the soil back to it. It is called a backfill and the wall is called the retaining wall. If the wall hadn't been there, soil mass could have come out, which implies the soil mass is applying some pressure on the wall, that is called earth pressure. So we should design the retaining wall against the earth pressure.

Design of Retaining Wall

While designing a retaining wall, the following points should be kept in mind.

  • Water does not have shear strength hence the stresses in the vertical and horizontal direction are the same.

  • Whereas the soil has some shear strength and the horizontal stress is a function of vertical stress.

Types of Wall Movement

The wall will attain 3 conditions at any point of time. According to the wall position, earth pressure changes. Three general conditions of the wall are-

  1. The wall does not move or the wall at rest

  2. The wall moves away from the backfill (Active earth pressure condition)

  3. The wall moves towards the backfill (Passive earth pressure condition)

Wall at rest

The wall and base of the wall are rigid, which makes the wall stay at a single place without any movement.

As the wall does not move in any direction, the lateral strains (ratio of change in the area to the original area) is zero.

Active earth pressure

Wall moves away from the backfill

The wall moves in one direction i.e. far from backfill. Wall and its base are not rigid under this case.

Active Earth Pressure, wall moving away from backfill
Active Earth Pressure condition

As the wall moves away from the soil, because of this some of the pressure of soil gets relieved, hence the shear resistance gets mobilized and it is in opposition to the wall movement.

The shear resistance is in the opposite direction, so, the pressure in the horizontal direction gets reduced.

As the wall keeps moving away, we will reach a condition where full shear resistance would be mobilized. After a point, there will not be any further resistance even if the wall moves away.

That horizontal pressure would be the minimum and it is called Active Earth Pressure.

Passive earth pressure

Wall moves towards the backfill

Due to the mass of creating wall and the speed which it moves, the mass of the soil(backfill) tends to move upward.

Passive Earth Pressure, Wall moving towards backfill
Passive Earth Pressure condition

The shear resistance acts in the same direction as horizontal pressure. There will be a situation where the stress can’t be maximum than that, that is the Passive Earth Pressure.

Rankine's Earth Pressure Theory

Rankine's theory was only applicable to uniform cohesionless soil, as originally proposed. But later in 1915 Bell extended the Rankine's theory for cohesive soil as well.

All the soil mass in plasti