2. Foundation Analysis and Design: Dr. Amit Prashant
Lateral Earth PressureLateral Earth PressureLateral Earth PressureLateral Earth Pressure
Lateral 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
2
3. Foundation Analysis and Design: Dr. Amit Prashant
Lateral Earth PressureLateral Earth PressureLateral Earth PressureLateral Earth Pressure
Lateral Earth pressure is a function of wall movement (or
relative lateral movement in the backfill soil)
3
4. Foundation Analysis and Design: Dr. Amit Prashant
Lateral Earth Pressure at RestLateral Earth Pressure at Rest
Coefficient 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:
1
oK
ν
ν
=
−
Poisson’s
ratio
4
5. 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
PI
Ko
Brooker and Ireland, 1965
K0 = 0.95 – sin φ’
⎦⎣ 100
0 φ
For overconsolidates clays
OCRKK COC )()( = cP
OCR =
Mayne and Kulway, 1982
K0 = (1 – sin φ’).OCRsin φ’
OCRKK NCoOCo )()( =
o
OCR
'σ
5
K0 (1 sin φ ).OCR
6. Foundation Analysis and Design: Dr. Amit Prashant
Rankine’sRankine’s Theory: Active Earth PressureTheory: Active Earth Pressureyy
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7. Foundation Analysis and Design: Dr. Amit Prashant
Rankine’sRankine’s Theory: Active Earth PressureTheory: Active Earth Pressureyy
( ) 21 sin
tan 45K
φ φ′− ′⎛ ⎞
⎜ ⎟
( )
( )
tan 45
1 sin 2
aK
φ
= = −⎜ ⎟′+ ⎝ ⎠
D th f
2c′
Depth of
Tension Crack
c
a
z
Kγ
=
7
8. Foundation Analysis and Design: Dr. Amit Prashant
Rankine’sRankine’s Theory: Passive Earth PressureTheory: Passive Earth Pressureyy
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9. Foundation Analysis and Design: Dr. Amit Prashant
Rankine’sRankine’s Theory: Passive Earth PressureTheory: Passive Earth Pressureyy
( )
( )
21 sin
tan 45K
φ φ′+ ′⎛ ⎞
= = +⎜ ⎟
⎝ ⎠( )
tan 45
1 sin 2
pK
φ
+⎜ ⎟′− ⎝ ⎠
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10. 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 u
u
σ σ′ = −⎡
⎢
=⎣⎣
Inclined Backfill:
β
( ) ( ) ( )
( ) ( ) ( )
2 2
2 2
cos cos cos
cos cos cos
aK
β β φ
β β φ
′− −
=
′+ −
1
p
a
K
K
= Thrust
β( ) ( ) ( )cos cos cosβ β φ+ a β
Inclined but Smooth Back face of wall:
w
β
w PA1 is
w
PA1
PA
1A AP W P= +
w
PA1
PA
β
H1
A1
calculated for
H1 height
10
β
11. Foundation Analysis and Design: Dr. Amit Prashant
Rankine’s Theory: Special CasesRankine’s Theory: Special CasesRankine’s Theory: Special CasesRankine’s Theory: Special Cases
β
Inclined Backfill with c‘ φ‘ soil:
Thrust
β
Inclined Backfill with c -φ soil:
⎧ ⎫′⎛ ⎞
β
2
2 2
2cos 2 cos sin
1
1
cos
a
c
z
K
β φ φ
γ
φ
⎧ ⎫′⎛ ⎞
′ ′+⎪ ⎪⎜ ⎟
⎝ ⎠⎪ ⎪
= −⎨ ⎬
′ ′ ′⎛ ⎞ ⎛ ⎞⎪ ⎪
( )2 2 2 2 2
cos
4cos cos cos 4 cos 8 cos cos sin
c c
z z
φ
β β φ φ β φ φ
γ γ
′ ′⎛ ⎞ ⎛ ⎞⎪ ⎪
′ ′ ′ ′− − + +⎜ ⎟ ⎜ ⎟⎪ ⎪
⎝ ⎠ ⎝ ⎠⎩ ⎭
2
2
2cos 2 cos sin
1
1
c
z
K
β φ φ
γ
⎧ ⎫′⎛ ⎞
′ ′+⎪ ⎪⎜ ⎟
⎝ ⎠⎪ ⎪
= −⎨ ⎬
( )
2 2
2 2 2 2 2
1
cos
4cos cos cos 4 cos 8 cos cos sin
pK
c c
z z
φ
β β φ φ β φ φ
γ γ
⎨ ⎬
′ ′ ′⎛ ⎞ ⎛ ⎞⎪ ⎪
′ ′ ′ ′+ − + +⎜ ⎟ ⎜ ⎟⎪ ⎪
⎝ ⎠ ⎝ ⎠⎩ ⎭ 11
12. 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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13. 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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14. Foundation Analysis and Design: Dr. Amit Prashant
Coulomb’s Theory: SolutionsCoulomb’s Theory: Solutionsyy
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15. Foundation Analysis and Design: Dr. Amit Prashant
Culmann’sCulmann’s Graphical Method: Active EPGraphical Method: Active EPpp
δ = Wall friction C1
C2
C3
C4
C
B
1
E4
E
θ
E2
E3
E4
E1
D3
D4
D
φ'A
D1
D2
φ
ψ =90-θ-δ
A
15
16. Foundation Analysis and Design: Dr. Amit Prashant
Culmann’sCulmann’s Graphical Method: Passive EPGraphical Method: Passive EPpp
δ = Wall friction C1
C2
C3
C4
C
E1
f
B
C1
2
E2
E3
E4
E
θ
4
A φ'
ψ
=90 θ+δ
Ea
Pres
Lin
A
D1
D2
φ'
16
=90-θ+δ
rth
sure
ne
D3
D4
D
17. Foundation Analysis and Design: Dr. Amit Prashant
Seismic EarthSeismic Earth Pressure:byPressure:by MononobeMononobe--Okabe MethodOkabe Method
Active 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
θ
AEP
δ
F
( )
1
tan
1
h
v
k
k
ψ −
=
−
and ( )ψ φ β≤ −
AEα
( )2
cos
K
φ θ ψ− −
=
( )
( )
( ) ( )
( ) ( )
2
2 sin sin
cos cos cos 1
cos cos
AEK
δ φ φ β ψ
ψ θ δ θ ψ
δ θ ψ β θ
=
⎡ ⎤+ − −
+ + +⎢ ⎥
+ + −⎢ ⎥⎣ ⎦
17
⎣ ⎦
( )21
1
2
AE v AEP H k Kγ= − Assumed to be acting at H/2.
18. Foundation Analysis and Design: Dr. Amit Prashant
Seismic EarthSeismic Earth Pressure:byPressure:by MononobeMononobe--Okabe MethodOkabe Method
Passive Earth PressurePassive Earth Pressure
Wall movement
vk W
β
hk W
v
W
φPEP F
Failure surface
H
W
PEα
θ
δ
( )
1
tan
1
h
v
k
k
ψ −
=
−
( )ψ φ β≤ +and
PEα
( )2
cos
K
φ θ ψ+ −
=
( )v
( )
( ) ( )
( ) ( )
2
2 sin sin
cos cos cos 1
cos cos
PEK
δ φ φ β ψ
ψ θ δ θ ψ
δ θ ψ β θ
=
⎡ ⎤+ + −
− + −⎢ ⎥
− + −⎢ ⎥⎣ ⎦
18
⎣ ⎦
( )21
1
2
PE v PEP H k Kγ= −
