Lateral Earth Pressures

Lateral Support In geotechnical engineering, it is often necessary to prevent lateral soil movements. We have to estimate the lateral soil pressures acting on these structures, to be able to design them.

Tie rod Anchor

Sheet pile

Cantilever Braced excavation Anchored sheet pile retaining wall 2

1 Earth Pressure at Rest

In a homogeneous natural soil deposit,

v’ ’ h X

the ratio h’/v’ is a constant known as coefficient of earth pressure at rest (K0).

Importantly, at K0 state, there are no lateral strains.

Estimating K0

For normally consolidated clays and granular soils,

K0 = 1 – sin ’

For overconsolidated clays,

sin K0,overconsolidated = K0,normally consolidated (OCR)

From elastic analysis,  K  Poisson’s 0 1 ratio

2 Active/Passive Earth Pressures - in granular soils

Wall moves away from soil

Wall moves A towards soil

smooth wall

Let’s look at the soil elements A and B during the wall movement. 5

Active Earth Pressure - in granular soils

v’ = z Initially, there is no lateral movement. v’ z  ’ = K  ’ = K z ’ h 0 v 0 h A As the wall moves away from the soil,

v’ remains the same; and

h’ decreases till failure occurs.

Active state

3 Active Earth Pressure - in granular soils

As the wall moves away from the soil, 

Initially (K0 state) Failure (Active state)

v’  active earth pressure decreasing h’

Active Earth Pressure - in granular soils 

WJM Rankine (1820-1872) 

[h’]active v’ 

[ h ']active  K A v ' Rankine’s coefficient of 1 sin active earth pressure K   tan2 (45  / 2) A 1 sin 8

4 Active Earth Pressure - in granular soils

As the wall moves away from the soil,

h’ decreases till failure occurs.

h’ K0 state v’ z Active ’ h A state

wall movement

Active Earth Pressure - in cohesive soils

Follow the same steps as for granular soils. Only difference is that c  0.

[ h ']active  K A v '2c K A

Everything else the same as for granular soils.

5 Passive Earth Pressure - in granular soils

Initially, soil is in K0 state. As the wall moves towards the soil,

v’ remains the same, and  ’ v  ’ increases till failure occurs. ’ h h B Passive state

Passive Earth Pressure - in granular soils

As the wall moves towards the soil, 

Initially (K0 state) Failure (Passive state)

passive earth pressure

v’ 

increasing h’

6 Passive Earth Pressure - in granular soils 



v’ [h’]passive 

[ h ']passive  KP v ' Rankine’s coefficient of 1 sin passive earth pressure K   tan2 (45  / 2) P 1 sin 13

Passive Earth Pressure - in granular soils

As the wall moves towards the soil,

h’ increases till failure occurs.

h’ Passive state v’ ’ h B

K0 state

wall movement

7 Passive Earth Pressure - in cohesive soils

[ h ']passive  KP v '2c KP

Everything else the same as for granular soils.

8 9 Earth Pressure Distribution - in granular soils

[h’]active

PA and PP are the resultant active and passive thrusts on the wall

[h’]passive H 2 PA=0.5 KAH

h 2 PP=0.5 KPh

KPh KAH 19

Rankine’s Earth Pressure Theory

[ h ']active  K A v '2c K A

[ h ']passive  KP v '2c KP

 Assumes smooth wall

 Applicable only on vertical walls

10 [ h ']active  K A v '2c K A

As given in Figure. σo=0 that z=0 and σo= H at z=H. The pressure distribution shows that at z=0 the active pressure equals indicating a tensile stress that decreases with depth and becomes zero at

a depth z=zc

The depth zc is usually referred to as the depth of tensile crack, because the tensile stress in the soil will eventually cause a crack along the soil– wall interface.

11 Lateral Earth Pressure at Rest At any depth z below the ground surface, the vertical subsurface stress is

the total force per unit length of the wall, P0

12 13 14 Rankine’s Earth Pressure Coefficient for sloped ground

15 A Generalized Case for Rankine Active Pressure -Granular Backfill

16 Coulomb’s coefficients of Earth Pressure

Coulomb’s coefficients of Earth Pressure • Take into consideration  Wall roughness  Inclined walls

Where  : angle between the wall’s back face and the vertical  : angle of friction between the soil and the backside of the wall a : angle of the slope for the backfill behind the wall

17 Lateral Earth Pressure Due to Surcharge

2 p   a  sin a cosa  2   x 