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
Reg : 1.2.500.2.31.09.03.02978
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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Active/Passive Earth Pressures
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Active/Passive Earth Pressures
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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Active Earth Pressure- in granular soils
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
Active Earth Pressure- in granular soils
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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Active Earth Pressure- in granular soils
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
Active Earth Pressure- in granular soils
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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Passive Earth Pressure- in granular soils
As the wall moves towards the soil, τ
Initially (K0 state)
Failure (Active state)
passive earth pressure
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σσv’
increasing σh’
Passive Earth Pressure- in granular soils
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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Passive Earth Pressure- in granular soils
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
Reg : 1.2.500.2.31.09.03.02978
σv’ [σh ]passive
Passive Earth Pressure- in granular soils
As the wall moves towards the soil,
B
σv’σh’
σh’ increases till failure occurs.
σh’ Passive state
Reg : 1.2.500.2.31.09.03.02978
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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Retaining Walls - Applications
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highway
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Retaining Walls - Applications
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)
11
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
11
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 ∑+=
11
2 2
3 3
PA
PA
PP
H
to be greater than 1.5
1PPPP
SStoe
toeR
Rxx
h
Safety against bearing capacity failure
11
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
Reg : 1.2.500.2.31.09.03.02978
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