A Review of Earth Pressure Theories

 

A Review of Earth pressure Theories

Key words: earth pressure, retaining wall, wedge theory, plastic equilibrium,

Quite often retaining walls are to be constructed in connection with high way embankments, railway embankments, slopes, bridge approaches, tunnels etc to retain the soil. The soil mass exerts pressure in the lateral direction on the concerned structures. To design these structures, the magnitude of earth pressures is to be calculated. There are various theories to find out the magnitudes of earth pressure: Coulomb (1776), Poncelet (1840), Rankine (1860), Culmann (1866), Rebhan (1871), Resal (1910), Bell (1915) and Terzhaghi (1929).

 However the prominent among them are those of Coulomb, Rankine and Terzhaghi which are briefly described here in-

 

          Retaining Wall

Coulomb’s Theory

Coulomb’s theory considers the soil behind the wall as a whole mass. If the wall moves forward due to earth pressure, a rupture plane would develop somewhere between the wall and the surface of repose. The wedge of soil between the back of the wall and the plane of failure is taken for analysis. An analysis of the forces acting on the wedge at incipient failure will reveal the thrust from the lateral earth pressure. The main assumptions of Coulomb’s wedge theory are: The backfill soil is dry, homogeneous, isotropic granular material with no cohesion; the rupture surface is plane passing through the heel of the wall; the sliding wedge acts as a rigid body; the thrust acts on the back of the wall at one-third the height of the wall at an angle of friction between the wall and the backfill.

 Rankine’s Theory                

Rankine’s theory is relatively simple as compared to that of Coulomb. Rankine investigated the stress conditions as associated with the states of plastic equilibrium in a semi-infinite mass of homogeneous, elastic and isotropic soil with its self weight. A mass of soil is said to be in a state of plastic equilibrium if failure is incipient at all points with in the mass.

The important assumptions of his theory are: The soil mass is semi-infinite, homogeneous, dry, cohesionless; the ground surface is plane which may be horizontal or inclined; the face of the wall in contact with the soil is vertical and smooth; the soil mass is stretched or compressed for attaining active or passive states

Terzhaghi’s Theory
In 1929 Terzaghi conducted experiments on the retaining wall and showed the relation of pressure on the wall if wall changes its position i.e. to move inwards to the backfill, outwards of it or remain at its place. There are three types of earth pressures on the basis of the movement of the wall.

1.Earth Pressure at rest

2.Active earth pressure

3.Passive earth pressure

 Pressure at rest:

When the wall is at rest and the material is in its natural state then the pressure applied by material is known as Earth Pressure at Rest.
Active earth pressure:

When the wall moves away from the backfill, there is a decrease in the pressure on the wall and this decrease continues until a minimum value is reached after which there is no reduction in the pressure and the value will become constant.
Passive earth pressure:

When the wall moves towards the backfill, there is an increase in the pressure on the wall and this increase continues until a maximum value is reached after which there is no increase in the pressure and the value will become constant

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