CE 632 Earth Pressure PPT

Foundation Analysis and

Design

Design

Lateral Earth Pressure

Lateral Earth Pressure

Lateral Earth Pressure

Lateral Earth Pressure

Lateral Earth Pressure

Lateral Earth Pressure

Lateral Earth Pressure

Lateral Earth Pressure

„

Lateral earth pressures are a function of type and amount of

wall movement shear strength properties weight of soil and

wall movement, shear strength properties, weight of soil and

drainage

Lateral Earth Pressure

Lateral Earth Pressure

Lateral Earth Pressure

Lateral Earth Pressure

„

Lateral Earth pressure is a function of wall movement (or

relative lateral movement in the backfill soil)

Lateral Earth Pressure at Rest

Lateral Earth Pressure at Rest

„

Coefficient of earth pressure at rest,

K

_o

=

σ σ

_h

′

_v

′

(No Lateral Movement)

p

,

„

The vertical al stress at any depth, z, is:

o

h

v

v

q

z

σ

′

= +

γ

′

K

′

′ +

u = pore water pressure

h

K

o

v

u

σ

=

σ

+

u = pore water pressure

Elastic Solution:

1

o

K

ν

ν

=

−

Poisson’s

ratio

4

Coefficient of Earth Pressure at Rest

Coefficient of Earth Pressure at Rest

Coefficient of Earth Pressure at Rest

Coefficient of Earth Pressure at Rest

„

For coarse-grained soils (Jaky 1944)

„

For coarse grained soils (Jaky, 1944)

K

₀

= 1 – sin

φ

’

„

For fine-grained normally consolidated soils (Massarch 1979)

„

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

⎥⎦

⎤

⎢⎣

⎡

+

=

100

(%)

42

.

0

44

.

0

PI

K

_o

„

Brooker and Ireland, 1965

K

₀

= 0.95 – sin

φ

’

⎦

⎣ 100

0

φ

For overconsolidates clays

OCR

K

K

₍

_OC

₎

=

₍

_C

₎

OCR

=

P

c

„

_{Mayne and Kulway, 1982}

K

= (1 – sin

φ

’).OCR

sin

φ

’

OCR

K

K

_o

₍

_OC

₎

=

_o

₍

_NC

₎

o

OCR

'

σ

K

(1 sin

φ

).OCR

Rankine’s

Rankine’s Theory: Active Earth Pressure

Theory: Active Earth Pressure

y

y

Rankine’s

Rankine’s Theory: Active Earth Pressure

Theory: Active Earth Pressure

y

y

( )

2

1 sin

tan

45

K

−

( )

φ

′

⎛

_⎜

φ

′

⎞

_⎟

( )

tan

45

1 sin

2

a

K

φ

=

=

_⎜

−

_⎟

′

+

_⎝

_⎠

D

th f

2c′

Depth of

Tension Crack

c

a

z

K

γ

=

Rankine’s

Rankine’s Theory: Passive Earth Pressure

Theory: Passive Earth Pressure

y

y

Rankine’s

Rankine’s Theory: Passive Earth Pressure

Theory: Passive Earth Pressure

y

y

( )

( )

2

1 sin

tan

45

K

=

+

φ

′

=

⎛

_⎜

+

φ

′

⎞

_⎟

⎝

⎠

( )

tan

45

1 sin

2

p

K

φ

′

⎜

+

⎟

−

_⎝

_⎠

Rankine’s

Rankine’s Theory: Special Cases

Theory: Special Cases

y

y

p

p

Submergence:

h

K

a

v

u

σ

=

σ

′

+

Pore Pressure

v v

u

u

σ

′ =

σ

−

⎡

⎢ =

⎣⎣

Inclined Backfill:

β

( )

( )

( )

( )

( )

( )

2 2 2 2

cos

cos

cos

cos

cos

cos

a

K

β

β

φ

β

β

φ

′

−

−

=

′

+

−

1

p a

K

K

=

Thrust

β

( )

( )

( )

cos

β

+

cos

β

cos

φ

a

β

Inclined but Smooth Back face of wall:

w

β

w

P

A1

is

w

P

_A1

P

_A 1 A A

P

=

W

+

P

w

P

_A1

P

_A

β

H

₁ A1

calculated for

H

₁

height

10

β

Rankine’s Theory: Special Cases

Rankine’s Theory: Special Cases

Rankine’s Theory: Special Cases

Rankine’s Theory: Special Cases

β

Inclined Backfill with c‘

φ‘ soil:

Thrust

β

Inclined Backfill with c -

φ soil:

⎧

⎛

′

⎞

⎫

β

2

2 2

2 cos

2

cos

sin

1

1

cos

a

c

z

K

β

φ

φ

γ

φ

⎧

⎛

′

⎞

_′

_′

⎫

+

⎪

⎜

⎟

⎪

⎝

⎠

⎪

⎪

=

_⎨

_⎬

−

′

_⎪

_⎛

_′

_⎞

_⎛

_′

_⎞

_⎪

(

)

2 2 2 2 2

cos

4 cos

cos

cos

4

c

cos

8

c

cos

cos

sin

z

z

φ

β

β

φ

φ

β

φ

φ

γ

γ

′

′

⎛

⎞

⎛

⎞

⎪

₋

₋

_′

₊

_′

₊

_′

_′

⎪

⎜

⎟

⎜

⎟

⎪

_⎝

_⎠

_⎝

_⎠

⎪

⎩

⎭

2

2 cos

2

cos

sin

1

1

c

z

K

β

φ

φ

γ

⎧

⎛

′

⎞

_′

_′

⎫

+

⎪

⎜

⎟

⎪

⎝

⎠

⎪

⎪

=

_⎨

_⎬

−

1

K

φ

′

⎨

⎬

Coulomb’s Theory: Active Earth Pressure

Coulomb’s Theory: Active Earth Pressure

„

Wall Friction:

„

Coulomb’s

theory

underestimates

Active EP

Active EP

12

Coulomb’s Theory: Passive Earth Pressure

Coulomb’s Theory: Passive Earth Pressure

„

Wall Friction:

„

Coulomb’s

theory

overestimates

Passive EP

Passive EP

Coulomb’s Theory: Solutions

Coulomb’s Theory: Solutions

y

y

Culmann’s

Culmann’s Graphical Method: Active EP

Graphical Method: Active EP

p

p

δ

= Wall friction

_C

1

C

2

C

₃

C

C

4

B

1

E

₄

E

θ

E

₂

E

3

E

₄

E

₁

D

₃

D

₄

D

φ

'

A

D

₁

D

₂

φ

ψ

=90-

θ

-

δ

A

Culmann’s

Culmann’s Graphical Method: Passive EP

Graphical Method: Passive EP

p

p

δ

= Wall friction

_C

1

C

2

C

₃

C

4

C

E

₁

f

B

C

₁ 2

E

₂

E

₃

E

₄

E

θ

4

A

φ

'

ψ

=90

θ

+

δ

Ea

Pres

Li

n

A

D

₁

D

₂

φ

'

16

=90-

θ

+

δ

rth

sure

n

e

D

₃

D

₄

D

Seismic Earth

Seismic Earth Pressure:by

Pressure:by Mononobe

Mononobe--Okabe Method

Okabe Method

Active Earth Pressure

Active Earth Pressure

Wall movement

Ԅ

: angle of internal friction of soil

θ b tt

l

f

ll

v

k W

β

θ: batter angle of wall

δ: angle of friction between the

wall and the backfill

h

k W

W

φ

Failure surface

H

wall and the backfill

β: slope of the backfill top

surface

W

φ

α

θ

AE

P

δ

F

(

)

1

tan

1

h v

k

k

ψ

₌

−

−

and

ψ

≤

(

φ β

−

)

AE

α

(

)

2

cos

K

=

φ θ ψ

− −

(

)

(

)

₍

(

) (

₎

₍

)

₎

2 2

sin

sin

cos cos

cos

1

cos

cos

AE

K

δ φ

φ β ψ

ψ

θ

δ θ ψ

δ θ ψ

β θ

=

⎡

₊

_{− −}

⎤

+ +

⎢

+

⎥

+ +

−

⎢

⎥

⎣

⎦

⎣

⎦

Seismic Earth

Seismic Earth Pressure:by

Pressure:by Mononobe

Mononobe--Okabe Method

Okabe Method

Passive Earth Pressure

Passive Earth Pressure

Wall movement

v

k W

β

h

k W

v

W

φ

PE

P

_F

Failure surface

H

W

PE

α

θ

δ

(

)

1

tan

1

h v

k

k

ψ

₌

−

−

and

ψ

≤

(

φ β

+

)

PE

α

(

)

2

cos

K

=

φ θ ψ

+ −

(

v

)

(

)

₍

(

) (

₎

₍

)

₎

2 2

sin

sin

cos cos

cos

1

cos

cos

PE

K

δ φ

φ β ψ

ψ

θ

δ θ ψ

δ θ ψ

β θ

=

⎡

₊

_{+ −}

⎤

− +

⎢

−

⎥

− +

−

⎢

⎥

⎣

⎦

18

⎣

⎦

(

)

2

1

1

2

PE v PE

P

=

γ

H

−

k K