CE 632 Earth Pressure PPT

CE-632 Foundation Analysis and Design

Lateral Earth Pressure 1

Foundation Analysis and Design: Dr. Amit Prashant

Lateral Earth Pressure „

Lateral earth pressures are a function of type and amount of wall movement movement, shear strength properties properties, weight of soil and drainage

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Foundation Analysis and Design: Dr. Amit Prashant

Lateral Earth Pressure „

Lateral 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 Rest (No Lateral Movement)

„ „

K o = σ h′ σ v′ The vertical al stress at any depth, z, is: σ v′ = q + γ ′z Coefficient of earth p pressure at rest,,

σ h′ = K oσ v′ + u

u = pore water pressure Elastic Solution: ν Poisson’s Ko = 1 −ν ratio

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Foundation Analysis and Design: Dr. Amit Prashant

Coefficient of Earth Pressure at Rest „

For coarse coarse-grained grained soils (Jaky (Jaky, 1944) K0 = 1 – sin φ’

„

For fine fine-grained grained, normally consolidated soils (Massarch (Massarch, 1979)

⎡ PI (%) ⎤ K o = 0.44 + 0.42 ⎢ ⎥ ⎣ 100 ⎦ „

Brooker and Ireland, 1965 K0 = 0.95 – sin φ’ For overconsolidates clays

K o (OC ) = K o ( NCC ) OCR „

Mayne and Kulway, 1982 K0 = (1 – sin φ’).OCR ).OCRsin φ’

OCR =

Pc σ 'o

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Foundation Analysis and Design: Dr. Amit Prashant

Rankine’s Theory: y Active Earth Pressure

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Foundation Analysis and Design: Dr. Amit Prashant

Rankine’s Theory: y Active Earth Pressure 1 − sin (φ ′ ) φ′ ⎞ 2⎛ Ka = = tan ⎜ 45 − ⎟ 1 + sin (φ ′ ) 2⎠ ⎝ Depth D th off Tension Crack

2c′ zc = γ Ka

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Foundation Analysis and Design: Dr. Amit Prashant

Rankine’s Theory: y Passive Earth Pressure

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Foundation Analysis and Design: Dr. Amit Prashant

Rankine’s Theory: y Passive Earth Pressure

1 + sin (φ ′ ) φ′ ⎞ 2⎛ Kp = = tan ⎜ 45 + ⎟ 1 − sin (φ ′ ) 2⎠ ⎝

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Foundation Analysis and Design: Dr. Amit Prashant

Rankine’s Theory: y Special p Cases σ h = K aσ v′ + u

Submergence:

⎡σ v′ = σ v − u ⎢ ⎣u = Pore Pressure

Inclined Backfill:

Ka =

β

cos ( β ) − cos 2 ( β ) − cos 2 (φ ′ ) cos ( β ) + cos 2 ( β ) − cos 2 (φ ′ )

1 Kp = Ka

Thrust

β

Inclined but Smooth Back face of wall: β w

w PA PA1

PA = W + PA1

PA

PA1

H1

PA1 is calculated for H1 height

β 10

Foundation Analysis and Design: Dr. Amit Prashant

Rankine’s Theory: Special Cases

β

Inclined Backfill with c c‘-φ φ‘ soil: Thrust

β

⎧ ⎫ ⎛ c′ ⎞ 2 ′ ′ 2 cos β 2 cos φ sin φ + ⎪ ⎪ ⎜ ⎟ γ z ⎝ ⎠ ⎪ 1 ⎪ Ka = ⎨ ⎬ −1 2 2 ′ cos φ ⎪ ⎛ c′ ⎞ ⎛ c′ ⎞ 2 ⎪ 2 2 2 2 ′ ′ ′ ′ − − + + 4 cos β cos β cos φ 4 cos φ 8 cos β cos φ sin φ ⎜ ⎟ ⎜ ⎟ ⎪ ⎪ γ z γ z ⎝ ⎠ ⎝ ⎠ ⎩ ⎭

(

)

⎧ ⎫ ⎛ c′ ⎞ 2 ⎪2 cos β + 2 ⎜ ⎟ cos φ ′ sin φ ′ ⎪ γ z ⎝ ⎠ ⎪ 1 ⎪ Kp = ⎨ ⎬ −1 2 cos 2 φ ′ ⎪ ⎛ c′ ⎞ ⎛ c′ ⎞ 2 ⎪ 2 2 2 2 ′ ′ ′ ′ + − + + 4 cos cos cos 4 cos 8 cos cos sin β β φ φ β φ φ ⎜ ⎟ ⎜ ⎟ ⎪ ⎪ γ γ z z ⎝ ⎠ ⎝ ⎠ ⎩ ⎭ 11

(

)

Foundation Analysis and Design: Dr. Amit Prashant

Coulomb’s Theory: Active Earth Pressure „

Wall Friction:

„

Coulomb’s theory underestimates Active EP

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Foundation Analysis and Design: Dr. Amit Prashant

Coulomb’s Theory: Passive Earth Pressure „

Wall Friction:

„

Coulomb’s theory overestimates Passive EP

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Foundation Analysis and Design: Dr. Amit Prashant

Coulomb’s Theory: y Solutions

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Foundation Analysis and Design: Dr. Amit Prashant

Culmann’s Graphical p Method: Active EP δ = Wall friction

C1

C3

C2

C

C4

B E

θ E2

E4

E3

E1

D

D4

D3 D1 A

D2

φ' ψ =90-θ-δ

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Foundation Analysis and Design: Dr. Amit Prashant

Culmann’s Graphical p Method: Passive EP E1

δ = Wall ffriction

C1

C2 E2

B

C

C3

E E 3

C4

E4

θ

φ'

A Earth Pressure ne Lin

ψ

D1

=90 θ+δ =90-

D2 D

D3

D4

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Foundation Analysis and Design: Dr. Amit Prashant

Seismic Earth Pressure:by Mononobe Mononobe--Okabe Method Active Earth Pressure

Ԅ: angle of internal friction of soil

Wall movement

θ batter θ: b tt angle l off wallll

β

δ: angle of friction between the wall and the backfill Failure surface

kv W

kh W H

φ

W

δ PAE

β: slope of the backfill top surface

F

θ

ψ = tan −1 α AE

kh ( 1 − kv )

and

ψ ≤ (φ − β )

cos 2 (φ − θ −ψ )

K AE =

⎡ sin (δ + φ ) sin (φ − β −ψ ) ⎤ cosψ cos θ cos (δ + θ +ψ ) ⎢1 + ⎥ + + − cos (δ θ ψ ) cos ( β θ ) ⎦⎥ ⎢⎣ 1 = γ H 2 ( 1 − kv ) K AE Assumed to be acting at H/2. 2

2

2

PAE

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Foundation Analysis and Design: Dr. Amit Prashant

Seismic Earth Pressure:by Mononobe Mononobe--Okabe Method Passive Earth Pressure Wall movement

β kv W H

PPE

Failure surface

φ

W

δ

kh W

θ

αPE

F

ψ = tan −1

kh ( 1 − kv )

and

ψ ≤ (φ + β )

cos 2 (φ + θ −ψ )

K PE =

⎡ sin (δ + φ ) sin (φ + β −ψ ) ⎤ cosψ cos θ cos (δ − θ +ψ ) ⎢1 − ⎥ − + − cos (δ θ ψ ) cos ( β θ ) ⎦⎥ ⎢⎣ 1 PPE = γ H 2 ( 1 − kv ) K PE 2

2

2

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