Retaining walls

Cantilever Retaining
Walls
Submitted by:
Sandeep Singh (90030)
Varun Bhandari (90031)
Simarjit Singh (90035)
Amanpreet Singh (90037)
Kavaldeep Singh (90039)
Lovepreet Singh (90040)
Jaskaran Singh (90041)
Swinderjit Singh (90051)

What is a Retaining wall?
 Retaining wall is a structure used
for maintaining the ground
surfaces at different elevations on
either side of it.

 Retaining walls provide lateral
support to vertical slopes of soil.
They retain soil which would
otherwise collapse into a more
natural shape. The retained soil is
referred to as backfill.

Types of retaining walls:

 Gravity Retaining Walls
 Semi-Gravity Retaining Walls
 Cantilever Retaining Walls
 Counter fort Retaining Walls

Cantilever Retaining Wall:

stem

H2 H1
H
toe
heel
y

shear key
b

Forces acting on the retaining wall:
 Lateral forces: Earth pressure due to backfill and surcharge.
 Vertical forces:
Acting downwards:
Self weight of the retaining wall ;
Weight of soil above heel slab.
Acting upwards:
Force due to soil pressure underneath the base slab.

Earth pressures:
(a) On stem: Earth pressure on
the stem from backfill (active Kaϒh
earth pressure) varies linearly.
According to Rankine’s theory at h
depth ‘h’ below the top of wall
is given by Pa=1/2kaϒH2
pa = kaϒh
H
where ka = Coefficient of active
earth pressure
ka = 1-sinΦ
1+sinΦ H/3
Φ= Angle of internal friction of soil
ϒ= Unit weight of back fill
KaϒH

Incase of backfill with ws
surcharge;
 The surcharge on backfill may be
due to traffic load on top of back
fill or due to a structure near it.
 If ws is the surcharge pressure on
horizontally finished back fill, then
uniform effect of surcharge on
stem is given by;
ps = ka ws

pa

ps

If backfill is sloping;
ὰ
• For sloping black fill, the pressure on
stem is parallel to top surface and is
given by;
pa = k’aϒh

k’a = cosὰ cosὰ - cos2ὰ - cos2Φ
cos ὰ + cos2ὰ - cos2Φ
where,
‘ὰ’ is angle of slope of backfill with
horizontal.(also reffered as surcharge ὰ
angle)
k’ is coeff. Of active earth pressure for
such case.

Stability Conditions:
 A retaining wall must be stable as a whole, and it must have sufficient
strength to resist the forces acting on it.

 In order that the wall may be stable, the following conditions should be
satisfied:

i. The wall must be strong enough to resist the bending moment and
shear force.
ii. The wall should not overturn.
iii. Maximum pressure at base should not exceed the SBC of soil.
iv. The wall should not slide due to lateral pressure.

Design of RCC Cantilever Retaining
walls:
 The depth of foundation depends on the properties of soil. The minimum
depth of foundation is calculated from Rankine’s formula as

ymin = = q0 ka2/ϒ

‘qo’ is SBC of soil.
‘ϒ’ is the unit weight of soil on which footing is resting.
‘ka’ is the coefficient of active earth pressure.

Preliminary Dimensions:
 The tentative proportions of the cantilever retaining wall may be obtained
based on experience and optimization studies.

 Set the preliminary dimensions of retaining wall
 Base width, b = 0.48H to 0.56H
 Toe projection = 0.3 b
 Thickness of base slab = Thickness of stem = H/12
 Top width of stem = 150 mm to 300 mm

Diagrammatic Representation:
.

H PH

0.3b H/3

b

Check for Overturning :
 The lateral loads (earth pressure) causes overturning moment (Mo) about
the toe.
 The weight of backfill, surcharge, self weight of retaining wall cause
stabilizing moment (Ms) about the toe.
 The factor of safety against overturning is given by ;

(Fos)o = Ms/Mo
 The factor of safety should not be less than 1.4.
 As per IS 456-2000 recommendations, only 0.9 times the characteristic
dead load shall be considered
(Fos)o = 0.9Ms/Mo

Check for Sliding :
 The lateral earth pressure on stem tries to slide the retaining wall away
from back fill.
 This lateral force is resisted by frictional force between base slab and the
soil below it.
 Maximum frictional force is given by
F = µΣW
where, ΣW is the total downward load.

 If PH is the total horizontal pressure, then factor of safety against sliding is
given by
(Fos)s = µΣW/PH
 As per IS 456-2000 recommendations, the factor of safety should not less
than 1.4 and only 0.9 times characteristic dead load is to be considered

(Fos)s = 0.9µΣW/PH

Check for Soil Pressure:
 The soil pressure varies .
linearly with more pressure
on toe and less pressure on
the end of heel.

 P1 (max.) < SBC of soil.

 P2(min.) > 0.

P2
P1

Design of stem:
 Calculate the max. factored BM on stem due to lateral earth pressure. This
calculated BM < Mu (lim.).
 If cal.BM > Mu (lim.) ; increase the thickness of base of stem and redesign.
 Accordingly, calculate the area of steel required;

Mu = .87fy Ast d (1 – fy Ast/fck bd)

 Provide bars of app. diameter (Φ) and calculate spacing as:

S = ∏Φ2/4 * 1000
Ast
 Spacing should be min. of the following:
(1) 0.75d (2) 300mm (3) Calculated Spacing
 Provide distribution steel.
 Check for development length and shear.

Design of toe slab:
 Calculate the ultimate BM for 1 metre width of toe slab.

 For calculation of BM,
The weight of soil above toe slab is neglected.
The two forces considered are:
(1) Upward soil pressure;
(2) Downward weight of toe slab.

 Provide reinforcement accordingly.
 Provide distribution steel.
 Check for development length and shear.

Design of heel slab:
 Calculate the ultimate BM for 1 metre width of heel slab.
 For calculation of BM,
The three forces considered are:
(1) Upward soil pressure;
(2) Downward weight of heel slab;
(3) Weight of the soil above heel slab.
 Provide main steel and distribution steel accordingly.
 Apply check for development length and shear.

Retaining walls

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