2. WHERE EARTH PRESSURE?
Calculating lateral earth pressure is
necessary in order to design structures such
as:
Retaining Walls
Bridge Abutments
Bulkheads
Temporary Earth Support Systems
Basement Walls 2
4. IN GEOTECHNICAL ENGINEERING,
IT IS OFTEN NECESSARY TO PREVENT LATERAL SOIL
MOVEMENTS
Cantilever
retaining wall
Braced excavation
Anchored sheet pile
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5. DEFINITION OF KEY TERMS
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.
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.
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”. 7
6. LATERAL EARTH PRESSURE - BASIC
CONCEPTS
We will consider the lateral pressure on a vertical wall that
retains soil on one side.
First, we will consider a drained case, i.e. The shear strength
of the soil is governed by its angle of friction φ.
In addition, we will make the following assumptions:
- The interface between the wall and the soil is frictionless.
- The soil surface is horizontal and there are no shear
stresses on horizontal and vertical planes, i.e. The horizontal
and vertical stresses are principal stresses.
- The wall is rigid and extends to an infinite depth in a dry,
homogenous, isotropic soil mass.
- The soil is loose and initially in an at-rest state. 8
7. LATERAL EARTH PRESSURE THEORY
There are two classical earth pressure theories.
They are
1. Coulomb's earth pressure theory.
2. Rankine's earth pressure theory.
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8. THE RANKINE THEORY ASSUMES:
There is no adhesion or friction between the wall
and soil
Lateral pressure is limited to vertical walls
Failure (in the backfill) occurs as a sliding
wedge along an assumed failure plane defined
by φ.
Lateral pressure varies linearly with depth and
the resultant pressure is located one-third of the
height (H) above the base of the wall.
The resultant force is parallel to the backfill
surface.
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9. THE COULOMB THEORY IS SIMILAR TO
RANKINE EXCEPT THAT:
There is friction between the wall and soil and
takes this into account by using a soil-wall
friction angle of δ.
Note that δ ranges from φ/2 to 2φ/3 and δ = 2φ/3
is commonly used.
Lateral pressure is not limited to vertical walls
The resultant force is not necessarily parallel to
the backfill surface because of the soil-wall
friction value δ.
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10. LATERAL EARTH PRESSURE FOR AT
REST CONDITION
If the wall is rigid and does not move with the
pressure exerted on the wall, the soil behind
the wall will be in a state of elastic equilibrium.
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11. LATERAL EARTH PRESSURE FOR AT REST
CONDITION
Element E is subjected to the following pressures.
E
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12. LATERAL EARTH PRESSURE FOR AT REST
CONDITION
If we consider the backfill is homogeneous then v
and h both increase linearly with depth z.
In such a case, the ratio of h to v remains
constant with respect to depth, that is
Where, Ko is called the coefficient of earth pressure for the at rest condition or at
rest earth pressure Coefficient.
The lateral earth pressure h acting on the wall at any depth z may be
expressed as 14
14. COEFFICIENTS OF EARTH PRESSURE FOR AT
REST CONDITION : KO
Type of soil Ip Ko
Loose sand, saturated 0.46
Dense sand, saturated 0.36
Dense sand, dry (e = 0.6) 0.49
Loose sand, dry (e = 0.8) 0.64
Compacted clay 9 0.42
Compacted clay 31 0.60
Organic silty clay, 45 0.57
undisturbed (w{ = 74%)
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15. FACTORS AFFECTING KO
The value of Ko depends upon the relative
density of the sand and the process by
which the deposit was formed.
If this process does not involve artificial
tamping the value of Ko ranges from about
0.40 for loose sand to 0.6 for dense sand.
Tamping the layers may increase it to 0.8.
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23. MOVEMENT REQUIRED TO DEVELOP ACTIVE
EARTH PRESSURE
Soil Type & Condition H Required
H
Sands , Granular soil
Dense 0.001 H to 0.002H
H
loose 0.002 H to 0.004 H
Clays
Stiff/Hard 0.01H to 0.02 H
Soft material 0.02 H to 0.05H
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40. EFFECT OF WATER TABLE ON LATERAL EARTH
PRESSURE
NΦ = tan2 (45+Φ/2)
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41. RANKINE’S THEORY: SPECIAL CASES
σv‘= σv-u
Submergence:
Inclined Backfill:
σh = K aσv ′ + u u= pore water pressure
Inclined but Smooth Back face of wall:
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43. COULOMB'S EARTH PRESSURE THEORY FOR
SAND FOR ACTIVE STATE
Coulomb made the following assumptions in
the development of his theory:
1. The soil is isotropic and homogeneous
2. The rupture surface is a plane surface
3. The failure wedge is a rigid body
4. The pressure surface is a plane surface
5. There is wall friction on the pressure surface
6. Failure is two-dimensional and
7. The soil is cohesionless
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45. PROCEDURE TO DRAW ABC
1. AB is the pressure face
2. The backfill surface BE is a plane inclined at an
angle with the horizontal
3. is the angle made by the pressure face AB with
the horizontal
4. H is the height of the wall
5. AC is the assumed rupture plane surface, and
6. is the angle made by the surface AC with the
horizontal
7. W = yA, where A = area of wedge ABC
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