CE-632Foundation Analysis and DesignDesign

Lateral Earth PressureLateral Earth PressureLateral Earth PressureLateral Earth Pressure

1

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

2

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)

3

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

4

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

Foundation Analysis and Design: Dr. Amit Prashant

Rankine’sRankine’s Theory: Active Earth PressureTheory: Active Earth Pressureyy

6

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

=

7

Foundation Analysis and Design: Dr. Amit Prashant

Rankine’sRankine’s Theory: Passive Earth PressureTheory: Passive Earth Pressureyy

8

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+⎜ ⎟′− ⎝ ⎠

9

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

10

β

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

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

12

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

13

Foundation Analysis and Design: Dr. Amit Prashant

Coulomb’s Theory: SolutionsCoulomb’s Theory: Solutionsyy

14

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

15

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

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

=⎡ ⎤+ − −

+ + +⎢ ⎥+ + −⎢ ⎥⎣ ⎦

17

⎣ ⎦

( )21 12AE v AEP H k Kγ= − Assumed to be acting at H/2.

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

=⎡ ⎤+ + −

− + −⎢ ⎥− + −⎢ ⎥⎣ ⎦

18

⎣ ⎦

( )21 12PE v PEP H k Kγ= −