Active and Passive Earth Pressure in Cohesive Soil

A retaining structure is a wall used to maintain the ground surface at different elevation on either

side of it. The following terms are used:

1. Back fill: The material retained by the wall is called back fill.

2. Surcharge: The weight of back fill above the elevation of top of the wall and any other load (may

be due to building, etc.) is called surcharge.

3. Back face and face: The side of wall in contact with back fill is back face and other side face.

4. The slope of back fill above the horizontal is known as surcharge angle.

5. Angle of inclination of the back is the angle made by back face with vertical.

* Earth Pressure as per Rankine’s Theory: The lateral pressure exerted by the soil when the retaining

wall has no movement relative to the back fill is called lateral earth pressure at rest. The lateral

earth pressure when the retaining wall tends to move away from the back fill is called active earth

pressure. This is the minimum earth pressure exerted by the soil when the retaining wall moves

towards the back fill due to any natural cause is known as passive earth pressure.

* Coefficient of earth pressure at rest: It is the ratio of lateral pressure to vertical pressure

sh = Ko gz

By equating lateral strain to zero, it can be shown that

where m is Poisson’s ratio.

Horizontal earth pressure varies linearly from zero at top to maximum value of vertical height H.

Hence, horizontal force per unit length of retaining structure

Since sv at depth z form top surface of earth fill is gz

Table 12.4 Coefficient of earth pressure at rest

Coefficient of active earth pressure for cohesionless soil Ka

is given by

Coefficient of active earth pressure of dry cohesionless soil with top surface inclined at B is given b

In case of cohesive soil:

Active earth pressure at top

Pa = –2c cot a

and at depth z is

Pa = gz cot

2 a – 2c cot a

where g = Dry weight of soil

c = Cohesion

a = 45° + f/2

The variation of pressure is as shown is Fig. 12.9.

Variation of Pa

in cohesive soil

* Coulomb’s earth pressure theory for sand.

Earth pressure theory for sand

It is for finding passive earth pressure P

when wall is smooth (d = 0) and vertical (d = 90°)

same as Rankine’s expression

The value of angle of friction for concrete walls is generally taken as .

* Use Rankine’s formula for R.C.C. retaining walls, i.e., cantilever or counterfort type Use

Coulomb’s formula for masonry gravity walls.