precise data

2. Rankine And Coulombs Theories Of
Lateral Earth Pressure
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3. Lateral earth pressure
Lateral earth pressure is the pressure that soil
exerts in the horizontal direction.

4. Why We Study Lateral Earth
Pressure?
The lateral earth pressure is important because
it affects the consolidation behavior and strength
of the soil and because it is considered in the
design of geotechnical engineering structures
such as retaining walls, basements, tunnels,
deep foundation sand braced excavations.
Earth retaining structures are common in a
manmade environment.

5. Contd..
Lateral earth pressure is a function of
• Type and amount of wall movement
• Shear strength parameter of soil
• Unit weight of soil

6. Lateral Earth Pressure
 There are 3 states of lateral earth pressure
Ko = At Rest
Ka = Active Earth Pressure (wall moves away from soil)
Kp = Passive Earth Pressure (wall moves into soil)
Passive is more like a resistance

7. Definition of key Terms
Coefficient (K)
It is defined as the ratio of the horizontal effective
stress σh to the vertical effective stress σv.
K = σh /σv
Coefficient of earth pressure at rest (Ko):
It is the ratio of horizontal and vertical principal
effective stresses when the retaining wall does not
move at all, i.e. it is “at rest”.

8. Coefficient of earth pressure at rest (Ko)
Ko can be calculated as follows:
Ko = 1 – sin φ for coarse grained soils
Ko = .44 + .42 [PI / 100] for NC soils
Ko (oc) = Ko (NC) (OCR)1/2 for OC soils

9. Active Earth Pressure Coefficient (Ka)
It is the ratio of horizontal and vertical principal
effective stresses when a retaining wall moves
away (by a small amount) from the retained soil.

10. Passive earth pressure coefficient (Kp):
It is the ratio of horizontal and vertical principal
effective stresses when a retaining wall is forced
against a soil mass.

11. Earth Pressure Theories
Two classic Earth pressure theories has been put
forward in the eighteen and nineteen centuries by
Coulomb and Rankine respectively.
 Coulomb’s(1776) Earth Pressure Theory
 Rankine (1857) Earth Pressure Theory

12. Rankine's earth pressure theory
Rankine's theory, developed in 1857, is a stress
field solution that predicts active and passive
earth pressure.
The Rankine theory assumes that there is no
wall friction and the ground and failure surfaces
are straight planes, and that the resultant force
acts parallel to the backfill slope (i.e., no friction
acting between the soil and the backfill)

13. Rankine's earth pressure theory
Note that φ' is the angle of shearing resistance of
the soil and the backfill is inclined at angle β to
the horizontal.
The equations for active and passive lateral
earth pressure coefficients are given in next
slide.

14. Rankine's earth pressure theory

15. Rankine's earth pressure theory

16. Assumptions
Soil is non-cohesive (c = 0) dry, isotropic and
homogenous.
Backfill is horizontal.
Wall is vertical,
Wall friction is neglected.

17. Coulomb's earth pressure theory
Coulomb (1776) first studied the problem of
lateral earth pressures on retaining structures.
He used limit equilibrium theory, which
considers the failing soil block as a free body in
order to determine the limiting horizontal earth
pressure.

18. Coulomb's earth pressure theory
Since the problem is indeterminate, a number of
potential failure surfaces must be analyzed to
identify the critical failure surface (i.e. the
surface that produces the maximum or
minimum thrust on the wall).
Mayniel later extended Coulomb's equations to
account for wall friction, symbolized by δ.
Müller-Breslau further generalized Mayniel's
equations for a non-horizontal backfill and a
non-vertical soil-wall interface.

19. Assumptions
The backfill is a dry, cohesion less,
homogeneous, isotropic soil.
The backfill surface is planar and can be
inclined.
The back of the wall can be inclined to the
vertical.
The failure surface is a plane surface which
passes through the heel of the wall.
The position and the line of action of the earth
pressure are known.

20. Coulomb's earth pressure theory
 The limiting horizontal pressures at failure in
extension or compression are used to determine
the Ka and Kp respectively.

21. Coulomb's earth pressure theory

22. References:
Soil Mechanics & Foundation Eng. – Arora.
Soil Mechanics – V.N.S.Murthy
Müller-Breslau H., (1906) Erddruck auf St
utzmauern, Alfred Kroner, Stuttgart.
Kramer S.L. (1996) Earthquake Geotechnical
Engineering, Prentice Hall, New Jersey