Lateral earth pressure theories by abhishek sharma

Submitted to : Dr. Sanjeev Naval
Submitted by : Abhishek Sharma 661/15
D.A.V.I.E.T (JAL)

1.INTRODUCTION
In this presentation, we will analyze some typical earth-
retaining structures to determine their stability. The emphases
will be on gaining an understanding of the forces that provoke
failures and methods of analysis of simple earth-retaining structures.
2
When you complete this chapter, you should be able to:
• Understand and determine lateral earth pressures.
• Understand the forces that lead to instability of
earth-retaining structures.
• Determine the stability of simple earth-retaining
structures
2
ABHISHEK SHARMA 661

2.Importance of calculation of lateral earth
pressure ?
Soil is neither a solid nor a liquid, but it exhibits some of the characteristics of both.
One of the characteristics similar to that of a liquid is its tendency to exert a
lateral pressure against any object in contact. In case of water,
pressure is equal in all direction but in case of soil, horizontal pressure
may be less or more than vertical pressure.
3
3
ABHISHEK SHARMA 661

3.EARTH RETAINING STRUCTURES
Structures which are used to hold back a soil mass or
water are called retaining structures.
Retaining walls, sheet pile walls, crib walls, sheeting in excavations,
basement walls etc are examples of earth retaining structures.
4
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ABHISHEK SHARMA 661

Type of Earth Retaining Structures
Earth-retaining structures may be broadly classified as
• Retaining walls and
• Sheet Pile walls
(i) Gravity retaining walls - usually of masonry or mass concrete
(ii) Cantilever walls
(iii) Counterfort walls usually of reinforced concrete.
(iv) Buttress walls
Retaining Walls are further classified as :
5
ABHISHEK SHARMA 661

Gravity Retaining Wall
Gravity walls depend on their weight for stability;
walls up to 2 m height are invariably of this type.
Nowadays Geosynthetics materials are also use as
reinforcement.
6

Cantiliver Retaining Wall
R.C. Cantilever walls have a vertical or inclined stem
monolithic with a base slab. These are considered suitable up
to a height of 7.5 m.
A vertical or inclined stem is used in counter-fort walls,
supported by the base slab as well as by counter-forts with which it is
monolithic.
7

Counterfort & Buttress
Retaining Wall
8
ABHISHEK SHARMA 661

BUTTRESS RETAINING WALL
COUNTERFORT RETAINING WALL
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ABHISHEK SHARMA 661

Sheet pile walls may be further classified
as:
• Cantilever sheet pile walls and
• Anchored sheet pile walls, also called ‗bulkheads‘.
Cantilever sheet pile walls are held in the ground by the
passive resistance of the soil both in front of and behind
them.
Anchored sheet pile wall or bulkhead is fixed at its base
as a cantilever wall but supported by tie-rods near the top,
sometimes using two rows of ties and properly anchored to a
deadman.
THESE ARE ALSO CALLED FLEXIBLE RETAINING WALLS
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ABHISHEK SHARMA 661

SHEET PILE RETAINING WALL
SHEET PILE
RETAINING WALL
WITH ANCHORAGE
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ABHISHEK SHARMA 661

4.STATE OF EQUILIBRIUM
The state of Equilibrium of soil can be divided into two states :
a) State of Elastic Equilibrium
When a small change in stress produces a corresponding
small change in strain or we can say that in this state every point in
given soil mass is not at the verge of failure.
b) State of Plastic Equilibrium
When irreversible strain takes place at a constant stress or we
can say that in this state every point in given soil mass is at the verge of
failure.
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ABHISHEK SHARMA 661

5.LATERAL EARTH PRESSURE
Lateral earth pressure is the force exerted by the soil mass upon an
earth-retaining structure, such as a retaining wall.
There are two distinct kinds of lateral earth pressure; the nature of
each is to be clearly understood.
EARTH PRESSURE AT REST
ACTIVE EARTH PRESSURE
PASSIVE EARTH PRESSURE
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ABHISHEK SHARMA 661

• First, let us consider a retaining wall which holds
back a mass of soil.
• When there is no movement of retaining wall and
soil mass then the pressure exerts by soil on retaining
wall is called earth pressure at rest.
Earth pressure at rest16
ABHISHEK SHARMA 661

The soil exerts a push against the wall by virtue of its
tendency to slip laterally and seek its natural slope or angle of
repose, thus making the wall to move slightly away from the
backfilled soil mass. This kind of pressure is known as the
‗active‘ earth pressure of the soil. The soil, being the actuating
element, is considered to be active and hence the name active
earth pressure.
ACTIVE EARTH PRESSURE17
ABHISHEK SHARMA 661

Let us imagine that in some manner the retaining wall is
caused to move toward the soil. In such a case the retaining
wall or the earth-retaining structure is the actuating element
and the soil provides the resistance which soil develops in
response to movement of the structure toward it is called the
‗passive earth pressure‘, or more appropriately ‗passive
earth resistance‘ which may be very much greater than the
active earth pressure
PASSIVE EARTH PRESSURE18
ABHISHEK SHARMA 661

IMPORTANT NOTE :
In the case of Active pressure,
• the structure tends to move away from the soil
• causing strains in the soil mass, which in turn,
• mobilise shearing stresses;
• these stresses help to support the soil mass and thus
• tend to reduce the pressure exerted by the soil against the
structure
In the case of Passive pressure,
• the structure tends to move towards the soil
• causing strains in the soil mass, which in turn,
• mobilise shearing stresses in opposite direction as in active
case;
• these stresses doesn‘t help to support the soil mass and thus
• tend to increase the pressure exerted by the soil against the
structure19 ABHISHEK SHARMA 661

Logically, therefore, there must be a situation intermediate
between the two (active and passive) when the retaining
structure is perfectly stationary and does not move in either
direction. The pressure which develops in this condition is called
‗earth pressure at rest’.
Its value is
little larger than the limiting value of active pressure,
but is
considerably less than the maximum passive resistance.
20
ABHISHEK SHARMA 661

Very little movement about 0.5% horizontal strain required to
mobilise the ACTIVE PRESSURE.
Larger movements about 2% horizontal strain for dense sands &
15% for loose sands may be require to mobilise full PASSIVE
PRESSURE
(LAMBE AND WHITEMAN 1969)
QUICK NOTE
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ABHISHEK SHARMA 661

In a later sub-section , it will be shown that
the failure planes will be inclined to horizontal at
(45° + φ/2) and (45° – φ/2) in the active and passive cases,
respectively.
This means that the width of the sliding wedge at the top of the
wall will be
H cot (45° + φ/2) and H cot (45° – φ/2) for active and passive cases,
respectively.
H being the height of the wall. For average values of φ, these will be
approximately H/2 and 2H.
The strains mentioned by Lambe and Whitman (1969) will then amount
to a horizontal movement at the top of the wall of 0.0025 H for the
active case and 0.4 H to 0.30 H for the passive case.
22
ABHISHEK SHARMA 661

Terzaghi‘s observation (Terzaghi, 1936)
This agrees fairly well with
that a movement of 0.005 H of the top of the
wall, or even less, is adequate for full
mobilisation of ACTIVE STATE. (In fact,
Terzaghi’s experiments in the 1920’s indicated
that even 0.001 H is adequate for this.
23
ABHISHEK SHARMA 661

The other factors which affect the lateral
earth pressure are
• the nature of soil —cohesive or cohesionless,
• porosity,
• water content and
• unit weight of soil.
The magnitude of the total earth pressure, or to be
more precise, force on the structure, is dependent on the
height of the backfilled soil as also on the nature of
pressure distribution along the height.
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ABHISHEK SHARMA 661

There are two reasons why less strain is required to reach the
active condition than to reach the passive condition.
First, an unloading (the active state) always involves
less strain than a loading (passive state).
Second, the stress change in passing to the active
state is much less than the stress change in passing to
the passive state.
(Lambe and Whitman, 1969).
Q. Why less strain is required to reach mobilised
state in active case than passive case?
25
ABHISHEK SHARMA 661

6. DEFINITIONS OF KEY TERMS
Backfill is the soil retained by the wall.
Active earth pressure coefficient (Ka) is the ratio between the
lateral and vertical principal effective stresses at the limiting
stress state when an earth-retaining structure moves away
(by a small amount) from the backfill (retained soil).
Passive earth pressure coefficient (Kp) is the ratio between the
lateral and vertical principal effective stresses at the limiting
stress state when an earth-retaining structure is forced
against a soil mass.
26
ABHISHEK SHARMA 661

Gravity retaining wall is a massive concrete wall
relying on its mass to resist the lateral forces from the
retained soil mass.
Flexible retaining wall or sheet pile wall is a long,
slender wall relying on passive resistance and
anchors or props for its stability.
Mechanical stabilized earth is a gravity-type retaining
wall in which the soil is reinforced by thin reinforcing
elements (steel, fabric, fibers, etc.).
Continue
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ABHISHEK SHARMA 661

7.LATERAL EARTH PRESSURE AT REST
Earth pressure at rest may be obtained theoretically from the theory
of elasticity applied to an element of soil, remembering that the
lateral strain of the element is zero.
Referring to in next slide
the principal stresses acting on an element of soil situated at a depth z
from the surface in semi-infinite, elastic, homogeneous and isotropic soil
mass are σv and σh as shown.
σv and σh denoting the stresses in the vertical and horizontal directions
respectively.
The soil deforms vertically under its self-weight but is prevented
from deforming laterally because of an infinite extent in all lateral
direction.
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ABHISHEK SHARMA 661

Let Es and v be the modulus of elasticity and
Poisson‘s ratio of the soil respectively.
29
ABHISHEK SHARMA 661

Lateral strain =
But σv = γ. z, where γ is the appropriate unit weight of the soil
depending upon its condition.
Let us denote by K0, which is known as the “Coefficient of earth
pressure at rest” and which is the ratio of the intensity of the earth pressure
at rest to the vertical stress at a specified depth.
∴
∴
It is equal to zero because
earth is at rest and there is
no lateral strain.
σh = K0. γ.z When soil is not consist of any type of moisture
30 ABHISHEK SHARMA 661

σh = K0. γ’.z + γw z When soil is in submerged condition
where γ’ is submerged unit weight of soil
If a structure such as a retaining wall of height H is interposed from the surface and
imagined to be held without yield, the total thrust on the wall unit length P0, is
given by:
This is considered to act at (1/3) H above the base of wall or
(2/3)H from top of wall. As has been indicated in the previous
chapter, choosing an appropriate value for the Poisson’s ratio, ν, is
by no means easy; this is the limitation in arriving at K0
31
ABHISHEK SHARMA 661

Various researchers proposed empirical
relationships for K0.
some of are given below:
FOR OVERCONSOLIDATED SOILS, KO = KO (N.C SOIL) X SQ. ROOT OF O.C.R
WHERE KO(N.C SOIL) IS DETERMINE BY KENNEY EQUATION, AND O.C.R IS
OVERCONSOLIDTATED RATIO.
32 ABHISHEK SHARMA 661

φ′ in these equations represents the effective angle of
friction of the soil
Ip is the plasticity index.
Brooker and Ireland (1965) recommend
Jaky‘s equation for cohesioness soils and
their own equation, given above, for cohesive soils.
However, Alpan (1967) recommends
Jaky‘s equation for cohesionless soils and
Kenney equation for cohesive soils as does Kenney
(1959).
33
ABHISHEK SHARMA 661

Certain values of the coefficient of earth pressure at rest
are suggested for different soils, based on field data,
experimental evidence and experience are given below.
34
ABHISHEK SHARMA 661

8. EARTH PRESSURE THEORIES
A French military engineer, Vauban, set
forth certain rules for the design of
revetments in 1687.
The magnitude of the lateral earth pressure is evaluated
by the application of one or the other of the so-called
‗lateral earth pressure theories‘ or simply ‗earth pressure
theories‘.
Since then, several
investigators have
proposed many
theories of earth
pressure after a lot
of experimental and
theoretical work.
Of all these theories, those given by
Coulomb and Rankine stood the test of time
and are usually referred to as the
―Classical earth pressure theories‖
35
ABHISHEK SHARMA 661

• These theories have been developed originally to apply to
cohesionless soil backfill.
• Later researchers gave necessary modifications to take into
account cohesion, surcharge, submergence, and so on.
• Some have evolved graphical procedures to evaluate the
total thrust on the retaining structure.
ABOUT CLASSICAL EARTH PRESSURE THEORIES
Although Coulomb presented his theory nearly a century
earlier to Rankine‘s theory, Rankine‘s theory will be presented
first due to its relative simplicity.
36
ABHISHEK SHARMA 661

8.1 RANKINE EARTH PRESSURE THEORY
Rankine (1857) developed his
theory of lateral earth
pressure when the backfill
consists of dry, cohesionless
soil. The theory was later
extended by Resal (1910)
and Bell (1915) to be
applicable to cohesive soils.
37
ABHISHEK SHARMA 661
WILLIAM RANKINE (1820–1872)

ASSUMPTIONS:
(i) The soil mass is isotropic, semi infinite, homogeneous, dry and cohesionless.
(ii) The ground surface is a plane which may be horizontal or inclined.
(iii) The face of the wall in contact with the backfill is vertical and smooth.
(This amounts to ignoring the presence of the wall).
(iv) The wall yields about the base sufficiently for the active pressure
conditions to develop; if it is the passive case that is under consideration,
the wall is taken to be pushed sufficiently towards the fill for the passive
resistance to be fully mobilised.
(v) The rupture surface is planar surface which is obtained by
considering the plastic equilibrium of soil.
Thus it is seen that, by neglecting wall friction as also cohesion of
the backfill, the geotechnical engineer errs on the safe side in the
computation of both the active pressure and passive resistance.
38
ABHISHEK SHARMA 661

8.1.1 ACTIVE & PASSIVE RANKINE
Consider the wall shown in Figure below. If the wall remains rigid and no
movement (not even an infinitesimal movement) occurs, then the vertical
and horizontal effective stresses at rest on elements A, at the back wall,
and B, at the front wall, are:
39
ABHISHEK SHARMA 661

Let us now assume a rotation about the bottom of the wall sufficient to
produce slip planes in the soil mass behind and in front of the wall as
shown below.
The soil mass at the back of the wall is causing failure, while the soil
mass at the front of the wall is resisting failure. In the latter, you have
to rotate the wall against the soil to produce failure.
40
ABHISHEK SHARMA 661

41
What happens to the lateral effective stresses on elements
A and B (Figure on slide 39) when the wall is rotated?
The vertical stress will not change on either element, but the
lateral effective stress on
element ‗A‘ will be reduced
for element ‗B‘ will be increased.
We can now plot two additional Mohr‘s circles,
one to represent the stress state of element A (circle A, Figure on slide 42)
other to represent the stress state of element B (circle B, Figure on slide 42).
Both circles are drawn such that the decrease (element A) or increase (element B) in
lateral effective stress is sufficient to bring the soil to the Mohr–Coulomb limiting
stress state.
ABHISHEK SHARMA 661

I = MOHR CIRCLE FOR PRESSURE AT REST
A = MOHR CIRCLE FOR ACTIVE PRESSURE
B = MOHR CIRCLE FOR PASSIVE PRESSURE
σ̍1 = MAJOR PRINCIPAL STRESS
σ̍3 = MINOR PRINCIPAL STRESS
Ko = EARTH PRESSURE COEFFICIENT AT REST
Ka = EARTH PRESSURE COEFFICIENT IN ACTIVE CASE
Kp = EARTH PRESSURE COEFFICIENT IN PASSIVE CASE42 ABHISHEK SHARMA 661

44
Values given in slide 22 & 23
should also be considered
Rotation required to mobilize active and passive resistance.
ABHISHEK SHARMA 661

45
For element A to reach the failure state, the lateral effective
stress must be less than the vertical effective stress,
If the shear stress (Ʈ) induced in a soil is less than the peak or critical
shear strength, then the soil has reserved shear strength, and we can
characterize this reserved shear strength by a factor of safety (FS).
For peak condition in dilating soils:
The ratio of lateral principal effective stress to vertical principal effective
stress at the limiting stress state is given by Equation above for circle A (fig. On
slide 42), is
where Ka is called the active lateral earth pressure coefficient.
ABHISHEK SHARMA 661

46
Similarly, for circle B (fig. on slide 42)
where Kp is the passive earth pressure coefficient.
Relation becomes :
Essential points are:
1. The lateral earth pressures on retaining walls are related directly
to the vertical effective stress through two coefficients. One is the
active earth pressure coefficient,
ABHISHEK SHARMA 661

47
Continue
and the other is the passive earth pressure coefficient,
2. Substantially more movement is required to mobilize the full
passive earth pressure than the full active earth pressure.
3. The lateral earth pressure coefficients developed so far are valid
only for a smooth, vertical wall supporting a homogeneous soil
mass with a horizontal surface.
4. The lateral earth pressure coefficients must be applied only to
principal effective stresses.
ABHISHEK SHARMA 661

48
Some cases :
EFFECT OF SUBMERGENCE:
When the backfill is fully saturated/submerged, the lateral pressure
will be due to two components:
(i) Lateral earth pressure due to submerged unit weight of the backfill
soil; and
(ii) Lateral pressure due to pore water.
σh, is given by:
σh = Ka.γ ′z + γw.z
ABHISHEK SHARMA 661

49
IF THE BACKFILL IS SUBMERGED ONLY TO A PART
OF ITS HEIGHT
The backfill above the water table is considered to be moist. The lateral
pressure above the water table is due to the most unit weight of soil, and that
below the water table is the sum of that due to the submerged unit weight of
the soil and the water pressure
Lateral pressure at the base of wall, = Ka.γ.H2 + Ka.γ ′.H1 + γw .H1
ABHISHEK SHARMA 661
Lateral pressure at the base of wall, = Kp.γ.H2 + Kp.γ ′.H1 + γw .H1

50
EFFECT OF UNIFORM SURCHARGE
The extra loading carried by a retaining structure is known as
‗surcharge‘.
In the case of a wall retaining a backfill with horizontal surface
level with the top of the wall and carrying a uniform surcharge of
intensity q per unit area, the vertical stress at every elevation in the
backfill is considered to increase by q.
σh = Ka.γ.z + Ka.q
ABHISHEK SHARMA 661
σh = Kp.γ.z + Kp.q
Active case
passive case
ABHISHEK SHARMA 661

51
EFFECT OF INCLINED SURCHARGE—SLOPING BACKFILL
Rankine‘s theory for this case is based on the assumption that a
‗conjugate‘ relationship exists between the vertical pressures and
lateral pressures on vertical planes within the soil adjacent to a
retaining wall.
ABHISHEK SHARMA 661

9. Active Earth Pressure of Cohesive
Soil52
σ1 = γz, σ3 = σh
1/Nφ = Ka for a cohesionless soil
For active case
ABHISHEK SHARMA 661

53
At the surface, z = 0 and
The negative values of active pressure up to a depth
equal to half of the so-called ‗critical depth‘
The total active thrust per unit
length of the wall is obtained by
ABHISHEK SHARMA 661

54
For pure clay, φ = 0
The net pressure over depth of 2zc is obviously zero.
The critical depth Hc, is given by
If φ = 0,
ABHISHEK SHARMA 661

10. Passive Earth Pressure of Cohesive
Soil
55
σ3 = γz and σ1 = σhc For passive case
Here, Kp = Nφ
in the usual
notation.
The total passive resistance
per unit length of wall is PP =
ABHISHEK SHARMA 661

11. COULOMB‘S WEDGE THEORY
57
Charles Augustine Coulomb (1776), a
famous French scientist and military
engineer, was the first to try to give a
scientific basis to the hazy and
arbitrary ideas existing in his time
regarding lateral earth pressure on
walls.
Assumptions
1. The backfill soil is considered to be dry, homogeneous
and isotropic; it is elastically underformable but
breakable, granular material, possessing internal friction
but no cohesion.
ABHISHEK SHARMA 661
Charles-Augustin de Coulomb
14 June 1736 – 23 August 1806

58
2. The rupture surface is assumed to be a plane for the sake of
convenience in analysis. It passes through the heel of the wall. It is not
actually a plane, but is curved and this is known to Coulomb.
3. The sliding wedge acts as a rigid body and the value of the earth
thrust is obtained by considering its equilibrium.
4. The position and direction of the earth thrust are assumed to be known.
The thrust acts on the back of the wall at a point one-third of the height
of the wall above the base of the wall and makes an angle δ, with the
normal to the back face of the wall. This is an angle of friction between
the wall and backfill soil and is usually called ‘wall friction’.
5. The problem of determining the earth thrust is solved, on the basis of
two-dimensional case of ‘plane strain’. This is to say that, the retaining
wall is assumed to be of great length and all conditions of the wall and
fill remain constant along the length of the wall. Thus, a unit length of the
wall perpendicular to the plane of the paper is considered.
ABHISHEK SHARMA 661

59
6. When the soil wedge is at incipient failure or the sliding of the wedge
is impending, the theory gives two limiting values of earth pressure, the
least and the greatest (active and passive), compatible with equilibrium.
7. The soil forms a natural slope angle, φ, with the horizontal, without
rupture and sliding. This is called the angle of repose and in the case of
dry cohesionless soil, it is nothing but the angle of internal friction. The
concept of friction was understood by Coulomb.
8. If the wall yields and the rupture of the backfill soil takes place, a soil
wedge is torn off from the rest of the soil mass. In the active case, the soil
wedge slides sideways and downward over the rupture surface, thus
exerting a lateral pressure on the wall. In the case of passive earth
resistance, the soil wedge slides sideways and upward on the rupture
surface due to the forcing of the wall against the fill.
9. The friction is distributed uniformly on the rupture surface.
ABHISHEK SHARMA 661

60
10. The back face of the wall is a plane.
11. The following considerations are employed for the determination of
the active and passive earth pressures:
Active Earth Pressure of Cohesionless Soil
ABHISHEK SHARMA 661

61
The value of Pa so obtained is written as:
For a vertical wall retaining a horizontal backfill for which the angle
of wall friction is equal to φ, Ka reduces to
α = 90°, δ = 0, and β = 0;
ABHISHEK SHARMA 661

62
Passive Earth Pressure of Cohesionless Soil
ABHISHEK SHARMA 661

63
The value of Pp so obtained may be written as
For a vertical wall retaining a horizontal backfill and for which the friction
is equal to φ,
α = 90°, β = 0°, and δ = φ, and Kp reduces to
ABHISHEK SHARMA 661

12. Comparison of Coulomb‘s Theory
with Rankine‘s Theory
64
(i) Coulomb considers a retaining wall and the backfill as a system; he takes
into account the friction between the wall and the backfill, while Rankine
does not.
(ii) The backfill surface may be plane or curved in Coulomb’s theory, but
Rankine’s allows only for a plane surface.
(iii) In Coulomb’s theory, the total earth thrust is first obtained and its
position and direction of the earth pressure are assumed to be known; In
Rankine’s theory, plastic equilibrium inside a semiinfinite soil mass is
considered, pressures evaluated, a retaining wall is imagined to be
interposed later
ABHISHEK SHARMA 661

65
(iv) Coulomb’s theory is more versatile than Rankine’s in that it can take into
account any shape of the backfill surface, break in the wall face or in the
surface of the fill, effect of stratification of the backfill, effect of various
kinds of surcharge on earth pressure, and the effects of cohesion,
adhesion and wall friction.
(v) Rankine’s theory is relatively simple and hence is more commonly used,
while Coulomb’s theory is more rational and versatile although
cumbersome at times; therefore, the use of the latter is called for in
important situations or problems.
ABHISHEK SHARMA 661

66
EXAMPLE 1: A gravity retaining wall retains 12 m of a backfill, γ = 17.7
kN/m3 φ = 25° with a uniform horizontal surface. Assume the wall
interface to be vertical, determine the magnitude and point of
application of the total active pressure. If the water table is a height of 6
m, how far do the magnitude and the point of application of active
pressure changed?
ABHISHEK SHARMA 661

67
(a) Dry cohesionless fill:
H = 12 m φ = 25° γ = 17.7 kN/m3
Active pressure at base of wall = Ka. γH
= 86.2 kN/m2
Total active thrust per metre run of wall
ABHISHEK SHARMA 661

68
This acts at (1/3)H or 4 m above the base of the wall.
(b) Water table at 6 m from surface:
Active pressure at 6 m depth = 0.406 × 17.7 × 6 = 43.1 kN/m2
Active pressure at the base of the wall = Ka(γ. 6 + γ′. 6) + γw .6
= 0.406 (17.7 × 6 + 10 × 6) + 9.81 × 6
= 67.5 + 58.9 = 126.4 kN/m2
(This is obtained by assuming γ above the water table to be
17.7 kN/m2 and the submerged unit weight γ′, in the bottom 6 m
zone, to be 10 kN/m2.
ABHISHEK SHARMA 661

69
Total active thrust per metre run = Area of the pressure distribution
diagram
The height of its point of application above the base is obtained by
taking moments.
Total thrust increase by 120.6 kN and the point of application gets
lowered by 0.38 m.
ABHISHEK SHARMA 661

70
ESE CE 2016 PAPER 2
ABHISHEK SHARMA 661

73
GATE 2018-The 3 m high vertical earth retaining wall retains a dry
grannular backfill with angle of internal friction of 30° and unit weight
20 kN/ m3. If the wall is prevented from yielding (no movement) the total
horizontal thrust (in Kn per unit length) on the wall is
(a) 0 (b) 30
(c) 45 (d) 270
SOLUTION:
As wall does not move, so wall is
at rest.
Coefficient of earth pressure at
rest k0 = 1- sin φ
= 1- sin30O = 0.5
ABHISHEK SHARMA 661

74
= 0.5 X 30 X 3 = 45 kN/m Ans

REFRENCES:
C. VENKATARAMAIAH
GEOTECHNICAL ENGINEERING
THIRD EDITION
(NEW AGE INTERNATIONAL (P) LTD., PUBLISHERS)
MUNI BUDHU
SOIL MECHANICS AND FOUNDATIONS
THIRD EDITION -WILEY (2010)
A.S.R RAO & GOPAL RANJAN
BASIC AND APPLIED SOIL MECHANICS
(NEW AGE INTERNATIONAL (P) LTD., PUBLISHERS)
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ABHISHEK SHARMA 661

Lateral earth pressure theories by abhishek sharma

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