CE 641 Lecture 3 Strength Characteristics of Reinforced Earth
CE 632 Earth Pressure PPT
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Transcript of CE 632 Earth Pressure PPT
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CE-632Foundation Analysis and DesignDesign
Lateral Earth PressureLateral Earth PressureLateral Earth PressureLateral Earth Pressure
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Foundation Analysis and Design: Dr. Amit Prashant
Lateral Earth PressureLateral Earth PressureLateral Earth PressureLateral Earth PressureLateral earth pressures are a function of type and amount of wall movement shear strength properties weight of soil andwall movement, shear strength properties, weight of soil and drainage
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Foundation Analysis and Design: Dr. Amit Prashant
Lateral Earth PressureLateral Earth PressureLateral Earth PressureLateral Earth PressureLateral Earth pressure is a function of wall movement (or relative lateral movement in the backfill soil)
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Foundation Analysis and Design: Dr. Amit Prashant
Lateral Earth Pressure at RestLateral Earth Pressure at RestCoefficient of earth pressure at rest, o h vK σ σ′ ′=
(No Lateral Movement)p ,
The vertical al stress at any depth, z, is:o h v
v q zσ γ′ ′= +
K′ ′ + u = pore water pressureh o vK uσ σ= + u = pore water pressure
Elastic Solution:
1oK νν
=−
Poisson’s ratio
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Foundation Analysis and Design: Dr. Amit Prashant
Coefficient of Earth Pressure at RestCoefficient of Earth Pressure at RestCoefficient of Earth Pressure at RestCoefficient of Earth Pressure at Rest
For coarse-grained soils (Jaky 1944)For coarse grained soils (Jaky, 1944)K0 = 1 – sin φ’
For fine-grained normally consolidated soils (Massarch 1979)For fine grained, normally consolidated soils (Massarch, 1979)
⎥⎦⎤
⎢⎣⎡+=
100(%)42.044.0 PIKo
Brooker and Ireland, 1965K0 = 0.95 – sin φ’
⎦⎣ 100
0 φ
For overconsolidates clays OCRKK COC )()( = cPOCR =
Mayne and Kulway, 1982K0 = (1 – sin φ’).OCRsin φ’
OCRKK NCoOCo )()( =o
OCR'σ
5
K0 (1 sin φ ).OCR
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Foundation Analysis and Design: Dr. Amit Prashant
Rankine’sRankine’s Theory: Active Earth PressureTheory: Active Earth Pressureyy
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Foundation Analysis and Design: Dr. Amit Prashant
Rankine’sRankine’s Theory: Active Earth PressureTheory: Active Earth Pressureyy
( ) 21 sintan 45K
φ φ′− ′⎛ ⎞⎜ ⎟
( )( )
tan 451 sin 2aK
φ= = −⎜ ⎟′+ ⎝ ⎠
D th f
2c′
Depth of Tension Crack
ca
zKγ
=
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Foundation Analysis and Design: Dr. Amit Prashant
Rankine’sRankine’s Theory: Passive Earth PressureTheory: Passive Earth Pressureyy
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Foundation Analysis and Design: Dr. Amit Prashant
Rankine’sRankine’s Theory: Passive Earth PressureTheory: Passive Earth Pressureyy
( )( )
21 sintan 45K
φ φ′+ ′⎛ ⎞= = +⎜ ⎟⎝ ⎠( )
tan 451 sin 2pK
φ+⎜ ⎟′− ⎝ ⎠
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Foundation Analysis and Design: Dr. Amit Prashant
Rankine’sRankine’s Theory: Special CasesTheory: Special Casesy py p
Submergence:h a vK uσ σ ′= + Pore Pressure
v v uuσ σ′ = −⎡
⎢ =⎣⎣
Inclined Backfill:β
( ) ( ) ( )( ) ( ) ( )
2 2
2 2
cos cos cos
cos cos cosaK
β β φ
β β φ
′− −=
′+ −
1p
a
KK
= Thrust
β( ) ( ) ( )cos cos cosβ β φ+ a β
Inclined but Smooth Back face of wall:
w
β
w PA1 is w
PA1
PA1A AP W P= +
w
PA1PA
β
H1
A1calculated for H1 height
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β
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Foundation Analysis and Design: Dr. Amit Prashant
Rankine’s Theory: Special CasesRankine’s Theory: Special CasesRankine’s Theory: Special CasesRankine’s Theory: Special Casesβ
Inclined Backfill with c‘ φ‘ soil:Thrust
β
Inclined Backfill with c -φ soil:
⎧ ⎫′⎛ ⎞
β
2
2 2
2cos 2 cos sin1 1
cosa
cz
K
β φ φγ
φ
⎧ ⎫′⎛ ⎞ ′ ′+⎪ ⎪⎜ ⎟⎝ ⎠⎪ ⎪
= −⎨ ⎬′ ′ ′⎛ ⎞ ⎛ ⎞⎪ ⎪( )2 2 2 2 2cos
4cos cos cos 4 cos 8 cos cos sinc cz z
φβ β φ φ β φ φ
γ γ′ ′⎛ ⎞ ⎛ ⎞⎪ ⎪′ ′ ′ ′− − + +⎜ ⎟ ⎜ ⎟⎪ ⎪
⎝ ⎠ ⎝ ⎠⎩ ⎭
2
2
2cos 2 cos sin1 1
cz
K
β φ φγ
⎧ ⎫′⎛ ⎞ ′ ′+⎪ ⎪⎜ ⎟⎝ ⎠⎪ ⎪
= −⎨ ⎬
( )2 2
2 2 2 2 2
1cos
4cos cos cos 4 cos 8 cos cos sinpK
c cz z
φβ β φ φ β φ φ
γ γ
⎨ ⎬′ ′ ′⎛ ⎞ ⎛ ⎞⎪ ⎪′ ′ ′ ′+ − + +⎜ ⎟ ⎜ ⎟⎪ ⎪⎝ ⎠ ⎝ ⎠⎩ ⎭ 11
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Foundation Analysis and Design: Dr. Amit Prashant
Coulomb’s Theory: Active Earth PressureCoulomb’s Theory: Active Earth Pressure
Wall Friction:
Coulomb’s theory underestimates Active EPActive EP
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Foundation Analysis and Design: Dr. Amit Prashant
Coulomb’s Theory: Passive Earth PressureCoulomb’s Theory: Passive Earth Pressure
Wall Friction:
Coulomb’s theory overestimates Passive EPPassive EP
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Foundation Analysis and Design: Dr. Amit Prashant
Coulomb’s Theory: SolutionsCoulomb’s Theory: Solutionsyy
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Foundation Analysis and Design: Dr. Amit Prashant
Culmann’sCulmann’s Graphical Method: Active EPGraphical Method: Active EPpp
δ = Wall friction C1C2
C3C4C
B
1
E4E
θE2
E3
E4
E1
D3
D4D
φ'A
D1
D2
φ
ψ =90-θ-δA
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Foundation Analysis and Design: Dr. Amit Prashant
Culmann’sCulmann’s Graphical Method: Passive EPGraphical Method: Passive EPpp
δ = Wall friction C1C2
C3C4
C
E1
f
B
C1 2
E2
E3E4
E
θ
4
A φ'
ψ =90 θ+δ
Ea
PresLi n
AD1 D2
φ'
16
=90-θ+δrth sure ne
D3D4
D
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Foundation Analysis and Design: Dr. Amit Prashant
Seismic Earth Seismic Earth Pressure:byPressure:by MononobeMononobe--Okabe MethodOkabe MethodActive Earth PressureActive Earth Pressure
Wall movement : angle of internal friction of soil
θ b tt l f ll
vk W
β θ: batter angle of wall
δ: angle of friction between the wall and the backfill
hk W
W φ
Failure surface
H
wall and the backfill
β: slope of the backfill top surfaceW φ
α
θAEP
δF
( )1tan
1h
v
kk
ψ −=−
and ( )ψ φ β≤ −
AEα
( )2cosK
φ θ ψ− −=
( )
( ) ( ) ( )( ) ( )
2
2 sin sincos cos cos 1
cos cos
AEKδ φ φ β ψ
ψ θ δ θ ψδ θ ψ β θ
=⎡ ⎤+ − −
+ + +⎢ ⎥+ + −⎢ ⎥⎣ ⎦
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⎣ ⎦
( )21 12AE v AEP H k Kγ= − Assumed to be acting at H/2.
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Foundation Analysis and Design: Dr. Amit Prashant
Seismic Earth Seismic Earth Pressure:byPressure:by MononobeMononobe--Okabe MethodOkabe MethodPassive Earth PressurePassive Earth Pressure
Wall movement
vk W
β
hk W v
Wφ PEP F
Failure surface
H W
PEα
θ
δ
( )1tan
1h
v
kk
ψ −=−
( )ψ φ β≤ +andPEα
( )2cosK
φ θ ψ+ −=
( )v
( ) ( ) ( )( ) ( )
2
2 sin sincos cos cos 1
cos cos
PEKδ φ φ β ψ
ψ θ δ θ ψδ θ ψ β θ
=⎡ ⎤+ + −
− + −⎢ ⎥− + −⎢ ⎥⎣ ⎦
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⎣ ⎦
( )21 12PE v PEP H k Kγ= −