Retaining Wall

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Lateral Earth Pressure Lateral Earth Pressure &&

R t i i g W llR t i i g W llRetaining WallsRetaining Walls

Dr Ir Luthfi Hasan

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Dr. Ir. Luthfi Hasan

LATERAL EARTH PRESSURE & RETAINING WALLS

Contents

K0, active & passive states

Rankine’s earth pressure theory

D i f t i i ll

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Design of retaining walls

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Main References

Das, B.M. (2002). Principles of Geotechnical Engineering 5th edition Geotechnical Engineering, 5th edition, Brooks/Cole Thomson Learning

Das, B.M. (2004). Principles of Foundation Engineering, 5th edition, Brooks/Cole

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Engineering, 5th edition, Brooks/Cole Thomson Learning

Lateral Support

In geotechnical engineering, it is often necessary to prevent lateral soil movementsprevent lateral soil movements.

Tie rod

Anchor

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Cantilever retaining wall

Braced excavation Anchored sheet pile

Sheet pile

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Lateral Support

We have to estimate the lateral soil pressureslateral soil pressureslateral soil pressures acting on th t t t b bl t d i ththese structures, to be able to design them.

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Gravity Retaining wall

Soil nailingReinforced earth wall

Retaining Walls

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Retaining wall-Gabion

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Retaining wall after construction

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Sheet Pile

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Soil Nailing

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Sheet Pile

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Sheet piles marked for driving

Sheet Pile

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Sheet pile wall

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Sheet Pile

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During installation Sheet pile wall

Lateral Support

Reinforced earth wallsReinforced earth wallsReinforced earth walls are increasingly becoming popularReinforced earth wallsReinforced earth wallsReinforced earth walls are increasingly becoming popular.

geosynthetics

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Lateral SupportCrib wallsCrib wallsCrib walls have been used in Queensland.

filled with soil

Interlocking stretchers

and headers

Good drainage & allow plant growth.

Looks good.

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Earth Pressure at Rest In a homogeneous natural soil deposit,

GL

Xσh’σv’

the ratio σh’/σv’ is a constant known as coefficient coefficient coefficient of earth pressure at rest (Kof earth pressure at rest (Kof earth pressure at rest (K )))

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of earth pressure at rest (Kof earth pressure at rest (Kof earth pressure at rest (K000).).).

Importantly, at K0 state, there are no lateral strains.

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Estimating K0

For normally consolidated clays and granular soils, K0 = 1 – sin φ’

For overconsolidated clays,

K0,overconsolidated = K0,normally consolidated OCR0.5

From elastic analysis

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From elastic analysis,

υυ−

=10K Poisson’s

ratio

Active/Passive Earth Pressures

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σv=σ1

σh=σ3

σv=σ3

σh=σ1

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Active/Passive Earth Pressures- in granular soils

Wall movesWall moves away from soil

Wall moves towards soil

A

B

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smooth wall

Let’s look at the soil elements A and B during the wall movement.

Active Earth Pressure- in granular soils

σv’ = γz

A

σv’σh’

z

As the wall moves away from the soil,

Initially, there is no lateral movement.

∴σh’ = K0 σv’ = K0 γz

σ ’ remains the same; and

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σv remains the same; and

σh’ decreases till failure occurs.

Active state

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As the wall moves away from the soil, τ

Initially (K0 state)

Failure (Active state)

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σσv’

decreasing σh’active earth

pressure


τ

σv’[σh’]active σφ

WJM Rankine(1820-1872)

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v[ h ]active

']'[ vAactiveh K σσ =

)2/45(tansin1sin1 2 φ

φφ

−=+−

=AK

Rankine’s coefficient of active earth pressure

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τσ ’

Failure plane is at 45 + φ/2 to horizontal

σ ’[σh’]acti eσ

φ

A

σv

σh’45 + ϕ/2

90+ϕ

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σv[σh ]active


As the wall moves away from the soil,

A

σv’σh’

z

σh’ decreases till failure occurs.

σh’

Active state

K0 state

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wall movement

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Active Earth Pressure- in cohesive soils

Follow the same steps as for granular soils. Only difference is that c ≠ 0.

AvAactiveh KcK 2']'[ −= σσ

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Everything else the same as for granular soils.

Passive Earth Pressure- in granular soils

Initially soil is in K state

B

σv’σh’

Initially, soil is in K0 state.

As the wall moves towards the soil,

σv’ remains the same, and

σh’ increases till failure occurs.

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Passive state

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As the wall moves towards the soil, τ

Initially (K0 state)

Failure (Active state)

passive earth pressure

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σσv’

increasing σh’


τ

σv’ [σh’]passive σφ

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v [ h ]passive

']'[ vPpassiveh K σσ =

)2/45(tansin1sin1 2 φ

φφ

+=−+

=PK

Rankine’s coefficient of passive earth pressure

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τσ ’

Failure plane is at 45 φ/2 to horizontal

’ [σ ’] σφ

A

σv

σh’

90+ϕ

45 - φ/2 to horizontal

45 - ϕ/2

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σv’ [σh ]passive


As the wall moves towards the soil,

B

σv’σh’

σh’ increases till failure occurs.

σh’ Passive state

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wall movement

K0 state

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Passive Earth Pressure- in cohesive soils

Follow the same steps as for granular soils. Only difference is that c ≠ 0.

PvPpassiveh KcK 2']'[ += σσ

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p

Everything else the same as for granular soils.

Earth Pressure Distribution- in granular soils

[σh’]active

P d P th

[σh’]passive H

PA=0.5 KAγH2

PA and PP are the resultant active and passive thrusts on

the wall

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h

KAγHKPγh

PP=0.5 KPγh2

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σh’

Wall movement (not to scale)

Passive state

Active stateK0 state

Rankine’s Earth Pressure Theory

AvAactiveh KcK 2']'[ −= σσ

Assumes smooth wall

PvPpassiveh KcK 2']'[ += σσ

AvAactiveh ][

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Applicable only on vertical walls

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Rankine’s Earth Pressure Theoryβ

φ−β−β coscos 22cos

β

γ

c

φσa

φ−β+β

φβββ=

coscoscoscosK 22a

cos

coscos

φ−β−β

φ−β+ββ=

coscoscoscosK 22

22

pcos

coscos

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β=0 ⎟⎠⎞

⎜⎝⎛ φ

−=2

45tanK 2a

⎟⎠⎞

⎜⎝⎛ φ

+=2

45tanK 2p

Earth pressure distributionq

KHP a2

11 21γ=

ς∇H1

H2

H1.γ.Kaγ

γsat

P1

P2

P

( )HHKP 21a2 q +=

KHHP a213 . γ=

22a

'4 HKP 2

1γ=

22w5 HP 2

1γ=

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2

q.Ka H2.γ’.Ka H2.γw

P3P4 P5

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Retaining Walls - Applications

Road

Train

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highway

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High-rise building

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basement wall

Gravity Retaining Walls

cobbles

cement mortarplain concrete or stone masonry

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They rely on their self weight to support the backfillThey rely on their self weight to support the backfill

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Cantilever Retaining Walls

R i f dReinforced; smaller section

than gravity walls

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They act like vertical cantilever, fixed to the groundThey act like vertical cantilever, fixed to the ground

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Design of Retaining Wall- in granular soils

Analyse the stability of this rigid body with vertical walls (∴Rankine theory valid)

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2 2

3 3

Block no.

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1

toetoe

Wi = weight of block i

xi = horizontal distance of centroid of block i from toe

Retaining Wall-Stability* Sliding* Overturning* B i C it F il* Bearing Capacity Failure* Overall failure

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Retaining Wall-Stability

Sliding Overturning

MR

MR

Sliding Overturning

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Safety against sliding along the base

P.Btan }.W{ PF

A

aiPsliding

c∑ +δ+=

soil-concrete friction angle ≈ 0.5 – 0.7 φ

adhesion ≈ 0.5 – 0.7 c

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2 2

3 3

PA

PA

PP

H

to be greater than 1.5

1PPPP

SStoe

toeR

Rxx

h

PP= 0.5 KPγh2 PA= 0.5 KAγH2

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Safety against overturning about toe

H/3}{3/

A

iiPgoverturnin P

xWhPF ∑+=

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2 2

3 3

PA

PA

PP

H

to be greater than 1.5

1PPPP

SStoe

toeR

Rxx

h

Safety against bearing capacity failure

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2 2

3 3

PA

PA

PPPS

H

h

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PPS

Stoetoe

RRx

x

h

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∑∑

∑−

==WW

Mi

Aii

i

netto H/3 P}xW{x

Safety against bearing capacity failure

xB21e −=

x e

qmaxqmin

⎟⎠⎞

⎜⎝⎛ −= ∑

Be61

BWq i

min

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qmax

qW

B

WWq alli

3

ii

max Be61

B121

2B.e.

B≤⎟

⎠⎞

⎜⎝⎛ +=

⎟⎠⎞

⎜⎝⎛

+= ∑∑∑

⎠⎝ BB

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Calculate the factor of safety with respect to overturning, sliding and bearing capacity failure

Retaining Wall

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