1

Seminar Design Of Cantilever Retaining Walls

With Seismic Analysis

Retaining Wall To hold back the masses of earth or

loose soil where conditions make it impossible to let those masses assume their natural slopes.

To retain earth or such materials to maintain unequal levels on its two faces.

Types of Retaining Wall

Types of Retaining Wall

Parts of Cantilever Retaining Wall

Application Basement

Wing walls and abutments of bridge

Retain slopes in hilly terrain roads

Side walls in bridge approach roads

Lateral Support to embankment

Forces acting on Retaining Wall Lateral earth pressure Self Weight of Retaining Wall Weight of Soil above the base slab Surcharge Soil reaction below base slab Frictional force at the bottom of base

slab

Earth Pressure

Earth Pressure Active and Passive Earth Pressure

Coefficients :1). Rankine Theory:

2). Coulomb Theory:

Earth Pressure Total earth pressure force acting along

the back of the wall is

The total force acts along the back of the wall at a height of H/3 from the base of the wall.

Stability requirements of RW Following conditions must be satisfied

for stability of wall (IS:456-2000). It should not overturn It should not slide It should not subside, i.e Max.

pressure at the toe should not exceed the safe bearing capacity of the soil under working condition

Check against overturningFactor of safety against overturning = MR / MO 1.55 (=1.4/0.9)Where,

MR =Stabilizing moment or restoring moment MO =overturning moment

As per IS:456-2000,0.9 MR 1.4 MO

Check against overturning

Check against overturning

Check against Sliding FOS against sliding =Resisting force to

sliding/Horizontal force causing sliding

= W/Pa 1.55 (=1.4/0.9)

As per IS:456:20001.4 = ( 0.9W)/Pa

Friction W SLIDING OF WALL

Maximum pressure at the toe

T

x1

x2

W1

W2

W3

W4

b/2b/6e

xb

H/3

Pa

W

Hh

Pmax

Pmin.

R

Pressure below the Retaining Wall

Maximum pressure at the toe Let the resultant R due to W and Pa lie at a

distance x from the toe. X = M/W, M = sum of all moments about toe. Eccentricity of the load = e = (b/2-x) b/6

Minimum pressure at heel= >Zero.

For zero pressure, e=b/6, resultant should cut the base within the middle third.

Maximum pressure at toe

= SBC of soil.

be

bW 61Pmin

be

bW 61Pmax

Depth of foundation

Df

Behaviour or structural action

Behaviour or structural action and design of stem, heel and toe slabs are same as that of any cantilever slab.

Design of Cantilever RW

Stem, toe and heel acts as cantilever slabs Stem design: Mu= (ka H3/6) Determine the depth d from Mu = Mu,

lim=Qbd2

Design as balanced section or URS and find steelMu=0.87 fy Ast[d-fyAst/(fckb)]

Design of Heel and Toe

1. Heel slab and toe slab should also be designed as cantilever. For this stability analysis should be performed as explained and determine the maximum bending moments at the junction.

2. Determine the reinforcement. 3. Also check for shear at the junction. 4. Provide enough development length.5. Provide the distribution steel

Design of Stem

Design of Slab

Dynamic Response of Retaining Walls

The dynamic response of even simplest type of retaining wall is quite complex.

Wall movement and pressure depends on the response of the soil underlying the wall, the response of the backfill, the inertial and flexural response of the wall itself, and the nature of the input motions.

Most of the current understanding of the dynamic response of retaining wall has come from the model test and numerical analyses.

Provision of IS 1893:1984 for Calculation of Dynamic Lateral Pressure• As per the provision of IS: 1893:1984 the general

conditions encountered for the design of retaining wall. The active earth pressure exerted against the wall is given by

where,• Pa = active earth pressure• w = unit weight of soil• h = height of wall

 

 

Provision of IS 1893:1984 for Calculation of Dynamic Lateral Pressure

• Two values shall be calculated from above equation, one for 1+αv and the other for 1-αv and

• maximum of the two shall be the design values. The values of the notations shall be taken as:

αv= vertical seismic coefficient its direction being taken consistently throughout

the stability analysis of wall and equal to 2/3 αh Ø= angle of internal friction of soil ƛ=αh/(+-αv) α=angle which earth face of the wall makes with the vertical i=slope of earth fill δ=angle of friction between the wall and earth fill αh= horizontal seismic coefficient

Calculation of Horizontal and Vertical Seismic Coefficient

• Since the relevant code dealing with the provision of seismic design of retaining wall is still under revision the data provided in the IS: 1893:2002 Part I is referred for relevant seismic data.

Where,Z= Zone factorI= Importance factorR= Response reduction factorSa/g= average response acceleration coefficient

 

Problem DefinitionHeight 6 m

SBC 180 kN/m2

18 kN/m3

μ 0.55φ 30δ 20α 90

Zone V

Result Comparison

Retaining Wall4.60

4.80

5.00

5.20

5.40

5.60

5.80

6.00

6.20

6.40

RCC Volume Compar-ision

RWRW+Seismic+CoulombRW+ Seiesmic

RCC

Vol (

m3)

Retaining Wall0

100

200

300

400

500

600

700Reinforcement Comparision

RWRW+Seismic+CoulombRW+Seismic

Stee

l (kg

)

Result Comparison

Reataining Wall0

10000

20000

30000

40000

50000

60000

70000

80000

Cost Comparision

RWRW+Seismic+CoulombRW+Seiesmic

Cost

(Rs

.)

Conclusion Historically, underground facilities have experienced

a lower rate of damage than surface structures. Some underground structures have experienced

significant damage in large earthquakes, that is why its important to do seismic analysis in underground structure.

But, Inclusion of seismic analysis in design results in

increased dimensions & results in costlier structure.

Conclusion Rankine’s design approach is simpler and

gives a more conservative design.

But Coulomb’s design is more practical one since it involves real life scenario – the friction between the wall and the backfill.

The Coulomb’s design approach gives a cost-effective design as compared to Rankine’s design approach.

References Dr.H.J.shah Reinforced Concrete Vol.II By IS 456:2000 Plain And

Reinforced Concrete Code Of Practice By Charotar Publication

Deepankar Choudhury1,*, T. G. Sitharam2 And K. S. Subba Rao2 Seismic Design Of Earth-retaining Structures And Foundations

Shravya Donkada and Devdas Menon Optimal Design Of Reinforced

Concrete Retaining Walls The Indian Concrete Journal April 2012

S.N.Sinha Second Edition Reinforced Concrete Design Mc Grawhill Co. New Delhi.

References N.Krishna Raju & R.N. Pranesh Reinforced Concrete Design By New

Age International Publisher

IS 1893(Part 1):2002 Criteria For Earthquake Resistant Design Of Structures

IS 1893:1984 Criteria for earthquake resistant design of Structures (Fourth Revision)

IS 1893(Part 3) Criteria For Earthquake Resistant Design of Structures (Part 3) Bridges And Retaining Walls