2. IntroductionIntroduction
• Retaining walls are used to retain earth (or other
material) in a vertical position at locations where an
abrupt change in ground level occurs.
• The walls therefore prevents the retained earth from
assuming its natural angle of repose.
3. BackfillBackfill & Surcharge& Surcharge
• The material retained or supported by a retaining
wall is called backfill.
• Backfill may have its top surface horizontal or
inclined.
• The position of the backfill lying above the
horizontal plane at the elevation of top of wall is
called surcharge & its inclination to the horizontal is
called as Surcharge angle.
5. Gravity WallsGravity Walls
• The “gravity wall” resist
the earth pressure
exerted by backfill by its
own self weight (dead
load) .
• It is usually built in
stone masonry, and
occasionally in plain
concrete.
6. Gravity WallsGravity Walls
• The “gravity wall”
provides stability by
virtue of its own weight ,
and therefore, is rather
massive in size.
• It is usually built in
stone masonry, and
occasionally in plain
concrete.
7. Gravity WallGravity Wall• The thickness of wall is also
governed by need to
eliminate or limit the
resulting tensile stress to its
permissible limit .
• Plain concrete gravity walls
are not used for heights
exceeding about 3m, for
obvious economic reasons.
8. Gravity WallGravity Wall• Stress developed is very
low.
• These walls are so
proportioned that no
tension is developed
anywhere and the
resultant of forces
remain within the
middle third of the base.
9. Cantilever WallCantilever Wall
• The “Cantilever wall ” is
the most common type
of retaining structure
and is generally
economical for heights
up to about 8m.
• The structure consists of
vertical stem , and a
base slab, made up of
two distinct regions,
viz., a heel slab and a
toe slab
10. Cantilever WallCantilever Wall
• All three components
behave as one way
cantilever slabs:
• “stem” acts as a vertical
cantilever under the lateral
earth pressure
• “heel slab” acts as a
horizontal cantilever under
the action of weight of the
retained earth (minus soil
pressure acting upwards
from below)
• “toe slab ” acts as a
cantilever under the action
of resulting soil pressure
acting upward.
11. Cantilever WallCantilever Wall
• It resists the horizontal
earth pressure as well
as other vertical
pressure by way of
bending of various
components acting as
cantilevers
• May be L shaped or T
shaped
12. Counterfort WallCounterfort Wall
• Stem and Heel slab are
strengthened by
providing counterforts at
some suitable intervals.
• The stability of the wall is
maintained essentially
by the weight of the
earth on the heel slab
plus the self weight of
the structure.
13. Counterfort WallCounterfort Wall
• For large heights, in a
cantilever retaining wall,
the bending moments
developed in the stem,
heel slab and toe slab
become very large and
require large thickness.
• The bending moments
can be considerably
reduced by introducing
transverse supports,
called counterforts.
14. Counterfort WallCounterfort Wall
• Counterfort wall are
placed at regular
intervals of about1/3 to
½ of the wall height,
interconnecting the
stem with the heel slab.
• The counterforts are
concealed within the
retained earth on the
rear side of the wall.
15. Counterfort WallCounterfort Wall
• This wall is economical for
heights above
(approximately) 7m.
• The counterforts
subdivide the vertical
slab (stem) into
rectangular panels and
support them on two
sides(suspender-style),
and themselves behave
essentially as vertical
cantilever beams of T-
section and varying
depth.
16. Buttress WallButtress Wall
• It is similar to counterfort wall, except
that the transverse stem supports,
Called buttress, are located in the
front side, interconnecting the stem
with the toe slab(and not with heel
slab, as with counterforts)
17. Buttress WallButtress Wall
• Although the buttresses are structurally
more efficient (and more economical)
counterforts, the counterfort wall is
generally preferred to the buttress wall as
it provides free usable space (and better
aesthetics)in front of the wall.
18. Lateral Earth pressureLateral Earth pressure
• The retaining force due to earth pressure
constitutes the main force acting on the retaining
wall, tending to make it bend , slide and
overturn.
• Let pressure p increasing linearly with increasing
depth z below the surface:
P=Cϒez
• Where ϒe is the unit weight of the earth and C is
the coefficient that depends on its physical
properties and also on the pressure is active or
passive.
20. Rankine's TheoryRankine's Theory
Assumptions
•The soil mass is semi-infinite, homogeneous, dry and
cohesionless
•The ground surface is plane which may be horizontal
or inclined.
•The back of the wall is vertical and smooth(No
shearing stresses are developed between the wall
and soil).
•The wall yields about the base and satisfies the
deformation conditions for plastic equilibrium.
22. Dry or moist backfill withDry or moist backfill with
no surchargeno surcharge
23. Dry or moist backfill withDry or moist backfill with
no surcharge (cont.…)no surcharge (cont.…)
24. Effect of surcharge on aEffect of surcharge on a
level backfilllevel backfill
• Gravity loads act on a level backfill due to the
construction of buildings and the movement of
vehicles near the top of retaining wall.
• These additional loads can be assumed to be static
and uniformly distributed on top of the backfill, for
calculation purpose.
• This distributed load ws (kN/m2
) can be treated as
statically equivalent to an additional(fictitious)
height hs=ws / ϒe of soil backfill with unit weight v. this
additional height of backfill is called surcharge, is
expressed either in terms of heights hs or in terms of
the distributed load ws.
26. Submerged BackfillSubmerged Backfill
Lateral pressure is made of two components-
•Lateral Pressure due to water at depth h
Pa=Kaγ’h+γwh
If the water stands to both sides of the wall, the water pressure
need not be considered & net lateral pressure is given by
Pa=Kaγ,
H
30. Backfill with UniformBackfill with Uniform
SurchargeSurcharge
• If the backfill is horizontal and carries surcharge of
uniform intensity w per unit area, the vertical
pressure increment at any depth h will increase by
w. The increase in the lateral pressure at any depth
h is given by,
Pa=Kaγh+Kaw
At the base of the wall, the pressure intensity is ,
Pa=KaγH+Kaw
32. Backfill with slopingBackfill with sloping
SurfaceSurface
β=inclination of sloping surface behind the wall with
the horizontal
=Surcharge Angle
33. Backfill with sloping SurfaceBackfill with sloping Surface
• Assuming, vertical and horizontal stresses are
conjugate. It can be shown that if the stress on a
given plane at a given point is parallel to another
plane, the stress on the latter plane at the same
point must be parallel to the first plane
36. Passive Earth PressurePassive Earth Pressure
• Passive earth pressure is exerted
on a wall when it has a
tendency to move towards the
backfill while supporting an
arch and is subjected to arch
thrust.
• When Due to active pressure
from the right hand side, the
wall moves left. The soil to the
left is thus compressed and in
turn exert passive earth
pressure, resisting such
movement .
40. Methods of Failure ofMethods of Failure of
retaining wallsretaining walls
• Overturning about the toe
• Sliding
• failure of soil due to excessive pressure at toe or
tension at the heel
• Bending failure of stem or base of slab or heel slab
44. • If the wall is found to be unsafe against sliding ,
shear key below the base should be provided. Such
a key develops passive pressure which resists
completely the sliding tendency of the wall. A
factor of safety of 1.5 must be used against sliding.
• In the absence of elaborate tests, the following
values of µ may be adopted:
Soil µ
Coarse grained soil without silt 0.55
Coarse grained soil with silt 0.45
Silt 0.35
47. Bending failureBending failure
• The stem of T shaped
cantilever retaining wall will
bend as cantilever, so that
tensile face will be towards
the backfill.
• The critical section will be at B,
where cracks may occur at
the inner face if it is not
properly reinforced. The heel
slab will have net pressure
acting downwards, and will
bend as cantilever, having
tensile face upwards.
48. Bending failureBending failure
• The critical section at B, where cracks may occur if
it is not reinforced properly at the upper face.
• The net pressure on toe slab will acts upwards, and
hence it must be reinforced at the bottom face.
• The thickness of stem, heel slab and toe slab must
be sufficient to withstand compressive stresses due
to bending.
49. Design principles ofDesign principles of
Cantilever Retaining WallCantilever Retaining Wall
• The design of a cantilever retaining wall consist of
the following –
1. Fixation of base width b
2. Design of stem
3. Design of heel slab
4. Design of toe slab
50. Fixation of base width bFixation of base width b
• The base width b of the
retaining wall should be so
chosen that the resultant of
the forces remain within
middle third, and the ratio
of length of toe slab to the
base width should be such
that the stress p1 at toe does
not exceed the safe
bearing capacity of soil.
56. • Reinforcement is provided towards the inner face of
stem , i.e. towards side of fill. The reinforcement
towards the top of stem can curtailed since B.M.
varies as h3
. Distribution reinforcement is provided
@0.15% of the area of cross section along the
length of retaining wall at inner face.
• Similarly, at the outer face of the stem ,
temperature reinforcement is provided both in
horizontal as well as in vertical direction. At the rate
of 0.15% of the area of cross section.
57. Design of heel slabDesign of heel slab
• The heel slab is also to be designed as a
cantilever . It has both downward pressure
(due to weight of soil and self weight )as well
as upward pressure due to soil reaction.
However , the net pressure is found to act
downward and hence reinforcement is
provided at the upper face BC.
58. Design of toe slabDesign of toe slab
• Neglecting the weight of the soil
above it, the toe slab will bend
upwards as a cantilever due to
upward soil reaction. Hence
reinforcement is placed at the
bottom face.
• Normally , the thickness of both toe
slab and heel slab is kept the same,
determined on the basis of greater of
the cantilever bending moments.
