### DESIGN OF REINFORCED CONCRETE STRUCTURES| CANTILEVER RETAINING WALL DESIGN STEPS

**CANTILEVER RETAINING **

**WALL**

**What is a retaining
wall?**

A Retaining wall is
a structure used to retain Earth or other materials and to maintain ground
surface at different elevations on either side of it.

**The main components of
a retaining wall are :**

Stem

Toe slab

Heel slab

Shear key

**Difference between
cantilever retaining wall and counterfort retaining wall :**

CANTILEVER RETAINING
WALL |
COUNTERFORT
RETAINING WALL |

·
It
consists of Stem, Heel slab, Toe slab and Shear key |
It
consists of stem, Toe slab, Heel slab and Counterforts |

·
Stability
is maintained by weight of retaining wall and weight of earth on heel slab. |
The
vertical stem as well as heel slab act as continuous slab because of
provision of counterforts. |

·
It
resists the horizontal Earth pressure as well as vertical pressure by way of
bending of various components acting as cantilever. |
Counterfort
reduces bending moment in stem and heel slab by providing support to them. |

·
It
is used when the height of wall is up to 6 m. |
It
is used when the height of wall is above 6 m. |

Figure shows the
deflection profile of a cantilever retaining wall

From the figure it is
seen that the tension face of stem is near to the back fill, and the main
reinforcement should be provided on tension face in vertical direction in stem.

For heel slab the top
portion acts as tension face hence main reinforcement is provided on top face
of Heel. For Toe slab bottom portion of the toe slab is the tension face
so main reinforcement is provided at bottom in Toe slab.

** **

These are
the simple steps for the design of a cantilever retaining wall when the
following data has been provided in the question.

**DESIGN STEPS **

**GIVEN DATA : HEIGHT , SBC OF SOIL, Ã¸
, Âµ , Unit weight of soil(****),GRADE OF CONCRETE AND GRADE OF
STEEL **

STEP
1 : CO-EFFICIENT OF EARTH PRESSURE

· Ka = (1-sin∅)/(1+sin∅)

· Kp = (1+sin∅)/(1-sin∅)

STEP 2 : PRELIMINARY DIMENSIONS _{}

·
d_{min
}= {qo/(Î³ )} * ((1-sin∅)/(1+sin∅))2

·
Overall
Height = Given Height + d_{min}

·
Base
Width B = √(3P/2Î³)_{a }Î³_{ } H^{2}

·
Toe
Width = B/3

·
Total
Base Width = B + (B/3)

·
Thickness
of Base Slab = H/12 to H/15

·
Thickness
of Stem at Base

M_{u} = 0.5 K_{a } Î³ h^{2} x (h/3)

M_{u }= 0.138 f_{ck }b
d^{2 }(ii)^{ }

Comparing (i) & (ii)^{ }, value of d is obtained.

D = d + Effective Cover (generally
50mm)

Top width of stem is to be assumed
(generally 0.2m).

Also provide shear key of suitable
size.

STEP 3
: STABILITY CALCULATIONS

Sliding Force P_{ah} = 0.5 K_{a }^{2}

Overturning Moment M_{o
}= 0.5 K_{a }^{2 }x^{ }

LOAD TYPE (col. 1) |
VERTICAL LOAD (col. 2) |
PERPENDICULAR DISTANCE (col. 3) |
MOMENT ABOUT A (KN m) (col. 4) |

W W W W W |
Find the loads and add them ∑W will be obtained |
Distance is measured
from toe |
( col. 2 x col. 3) Adding values of rows 1
to 5 of col. 4 M |

Find _{R }- M_{o}

Find eccentricity , e =

Find Max. Pressure at toe Ïƒ_{max} =

Find Min. Pressure at Heel Ïƒ_{min} =

Find Factor Of Safety against overturning = M_{R }/ M_{o}

Find Factor of Safety against sliding =

STEP 4
: DESIGN OF STEM

·
Find
factored Bending Moment M_{u}
= 0.5 K_{a }^{2} x

·
Find
M_{u}/Bd^{2}
and from SP-16 find p_{t} where
d = D – Effective cover

·
Find
A_{st }= p_{t}Bd/100

·
Provide
suitable dia bars at suitable spacing by the use of Steel Table or SP-16

·
For
Distribution Steel, Find Avg. thickness of stem =

·
Find
A_{st(min)} = 0.12% x 1000 x (Avg. thickness of stem)

·
Provide
suitable dia bars at suitable spacing

·
On
Outer face use 0.06% steel (i.e A_{st(min)} / 2 )bothways.

·
Check
for shear :

Find V_{u} =0.5 K_{a }^{2} x 1.5

Ï„_{v}
= V_{u}/ bd ,
then find p_{t} & by use of Table 19 on pg 73 of IS 456 -2000 find Ï„_{c}
. (If Ï„_{v } < Ï„_{c} hence safe).

STEP 5 : DESIGN OF HEEL SLAB

·
From
Pressure Distribution Below Base diagram find,

·
Pressure
at junction of stem with Heel Slab

·
Pressure
at junction of stem with toe Slab

·
Total
downward pressure on heel slab = weight of backfill + self weight of heel slab

·
Plot
diagram showing Net Pressure on heel

·
Find
factored shear force and Bending Moment

·
Find
M_{u}/Bd^{2}
and from SP-16 find p_{t}

(where d =
Base slab thickness - effective cover)

·
Find
A_{st }= p_{t}Bd/100

Provide suitable dia bars at suitable
spacing on top face of heel

·
For
Distribution Steel

Find A_{st(min)} = 0.12% x
1000 x Base Slab thickness

Provide suitable dia bars at suitable
spacing on bottom face

·
For
crack control use 0.06% steel (i.e A_{st(min)} / 2 )bothways on bottom
face

·
Check
for shear :

Find V_{u} =0.5 K_{a }^{2} x 1.5

Ï„_{v}
= V_{u}/ bd ,
then find p_{t} & by use of Table 19 on pg 73 of IS 456 -2000 find Ï„_{c}
. (If Ï„_{v } < Ï„_{c} hence safe).

STEP 6
: DESIGN OF TOE SLAB

·
Total
downward pressure on toe slab = self weight of toe slab

·
Plot
diagram showing Net Pressure on toe

·
Find
factored shear force and Bending Moment

·
Find
M_{u}/Bd^{2}
and from SP-16 find p_{t}

(where
d = Base slab thickness - effective cover)

·
Find
A_{st }= p_{t}Bd/100

Provide suitable dia bars at suitable
spacing.

Half RF of stem anchored in toe will
serve as toe RF.

·
For
Distribution Steel

Find A_{st(min)} = 0.12% x
1000 x Base Slab thickness

Provide suitable dia bars at suitable
spacing.

STEP 7
: DESIGN OF SHEAR KEY

·
Find
A_{st(min)} =
0.12% x 1000 x D where D is width of shear key

·
Total
A_{st} in key = half of main RF in stem + (A_{st(min)} / 2 value which
found in step 4)

·
If
Total A_{st} in key
> A_{st(min)} (hence O.K)

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