3) Retaining Structures

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3) Retaining Structures

Types:

① Concrete walls (Rigid walls) - Build wall & Place backfill.

a. Gravity retaining structure b. Cantilevered retaining structure

② Sheet pile walls (Flexible walls) - Construct wall & Excavate.

a. Cantilevered sheet pile walls b. Anchored walls

③ Alternative types of walls

a. Mechanically stabilized backfill systems

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SNU Geotechnical and Geoenvironmental Engineering Lab.

b. Precast modular system

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i) Concrete Walls

Design Condition -

- - -

For concrete walls, facilities for drainage are always provided.

- -

Fig. Example of earth retaining structures with drainage system

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Typical Dimensions

Fig. Approximate dimensions (a) gravity wall; (b)cantilever wall

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a) Gravity Retaining Structures

Rely on weight of concrete for stability.

(1) Forces that act on wall - Rankine

R = W^c + W^s + E^A^R sinβ

Point of application of E^A^R is H/3.

(Theoretically, but for design purpose, 0.4H can be recommended.)

R

E

A

W

c

R S

R

E

p

W

s

x

c

x

s

H/3

β

Q

β

B

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(2) Design Computations (Based on Rankine)

ⓐⓐ

ⓐⓐ Overturning : ΣΣΣ MΣ ^toe

) 5 . 1 3 (

/ H ) (cos E

B ) (sin E x W x W M

. M S .

F _R

A

R A S S C C driving

resisting = + + ≥

= β

β

Stability for overturning can be also checked with eccentricity of the point of applying load. (If e is less than B/6 (soil), B/4 (rock), retaining structure is stable.)

ⓑⓑ

ⓑⓑ Sliding along base

β δ

β E cos

tan R 1 B c cos E

S F

. F S .

F R

A b R

A D

R × +

=

= (≥ 1.5)

β δ

β E cos

E tan R 1 B c cos E

E S

R A

R P b

R A

R

P × + +

+ =

= (≥ 2.0)

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ⓒⓒ

ⓒⓒ Bearing capacity

Vertical pressure distribution on base

Find out eccentricity, e.

( )

*

D R

*

D R

*

D R

net

x 2 B e

R M M

x

M M

R x

M M

M

−

=

−

=

−

=

−

=

∑

∑ ∑ ∑

Pressure distribution on base

for e≤ B/6 )

B e 1 6 1 (

B

sin E W q W

R A s c heel

toe ±

⋅ +

= + β

for e>B/6, )

2 ( sin

3 '_max 4

e B

E W q W

R A s c

− +

= + β

) e 2 B 2( b= 3 − MD

M R

R(=N) x*

e B

q

toe

q

heel

q’max

b

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Bearing Capacity

2 } ) F F N B ) ( F F qN ( ) F F cN {(

B

Q_u _c _cd _ci _q _qd _qi γ ^γ ^γ^d ^γⁱ +

+

=

e 2 B B= −

Df

' q =γ

' N Q

FS = _u (or FS =Q_u /Q_max) (N’ = Normal resultant on base)

Fig. Terms used in bearing capacity equation

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- Embedment factors ; Fcd, Fqd, Fγd (Hansen(1970)) For D_f /B≤1, For D_f /B>1

B D

F_cd =1+0.4 _f / F_cd =1+0.4tan⁻¹(D_f /B)

( )

B

F_qd =1+2tanφ'1−sinφ' ² D^f

( )

_







−  +

= ⁻

B F_qd 1 2tanφ'1 sinφ' ²tan ¹ D^f

d =

F_γ 1 F_γ_d =1

- Inclination factors : Fci, Fqi, FγI 2 ci

qi F 1 90

F 



 





− °

=

= δ

2

1 '

F_γi δ φ

 

= − 

  if δ φ> ', F_γ_i =0

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ⓓⓓ

ⓓⓓ Overall stability

Slope stability analysis for deep seated failure or unfavorable direction of joint

backfill

joint

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b) Cantilevered Retaining Structure

Reinforced concrete walls that use cantilever action for stability

(1) Forces on wall

R

E

A

R

E

P

W

c

W

^s

R H

y

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(2) Design calculation

ⓐ~ⓓ Same procedure as gravity structure

ⓔ Calculate moments and shears in wall

① at stem

. . 0

0

cos

stem

H

b f A

H

V y K dy

M Vdy

γ β

 = ⋅ ⋅ ⋅



 =



∫

② at front











=

−

=

∫

1 1

L

0 L

0

c toe

Vdx M

dx ) d sx q (

V γ

③ at back

( )

{ }











=

+

− +

=

∫

2 2

L

0 L

0

ave soil conc

heel

Vdx M

dx h d

sx q

V γ γ

q

heel

q

toe

s 1

Hstem

d ①

conc⋅ γ

d

L1

②

ave soil

concd γ h

γ +

L 2

③

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ii) Sheet Pile Walls

Cantilevered sheet pile walls (Height < 15 - 20 ft.) Anchored sheetpile

-Failure mode

Deep-seated failure

Rotational failure due to inadequate penetration

Flexural failure of sheet piling

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-Anchorage failure

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a) Cantilevered Sheet pile Walls

Approach

①

② Calculate resultants based on these pressures.

(If the Coulomb method is used, it should be used conservatively for the passive pressure (δ = 0, or use log-spiral failure plane. For cohesive soils, no negative pressures in tension zone.)

③

④ Find Mmax at point of 0 shear and choose the proper type of sheetpile.

⑤

B

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* Example of analysis for cantilevered wall for granular soil.

Find L , 3 P , ₃ P ₄

^K_Pγ_sub^L₃ =

{

γ^L₁ +γ_sub⁽^L₂ +^L₃ ⁾

}

^K_A and,

) K K (

K ) L L

L (

A P sub

A 2 sub 1

3 −

= + γ

γ γ

P₃ =L₄(K_p −K_A)γ_sub

^P₄ =

{

γ^L₁ +γ_sub⁽^L₂ +^L₃ +^L₄ ⁾

}

^K_P −γ_sub⁽^L₃ +^L₄ ⁾^K_A

P L (K K )

) K K ( L )

K K ( L K

) L L

(

A P 4 sub 5

A P 4 sub A

P 3 sub P 2 sub 1

− +

=

− +

+

= γ

γ γ

R

a

P P

3

* A

P P P

P − =

PA P_A^*

4 A

*

P P P

P − =

*

PP sub A

P K )

K

( − γ

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Find the theoretical embedded depth, for the stability of the wall,

∑

^F^H ⁼^ٱ ACDE - ∆EHB + ∆FHG=0

( ) 0

2 1 2

1

5 4 3 4

3 + + =

− PL P P L

R_a and

4 3

4 3 5

2 P P

R L

L P ^a

+

= − ---①

∑

^M^B ⁼^R^a

(

^L⁴⁺^z

)

⁻¹₂^{P L}³ ⁴^⋅^L₃⁴ ⁺¹₂

⁽

^P³⁺^{P L}⁴

⁾

⁵ ^L₃⁵ ⁼⁰ ---② put ① into ②

L₄⁴ +A L₁ ₄³ −A L₂ ²₄ −A L₃ ₄ −A₄ = 0

{ }















−

= +

−

+

= −

2 A P 2 sub

a 5 a 4

2 A P 2 sub

5 A P sub a 3

A P sub

a 2

A P sub

5 1

) K K (

) R 4 P z 6 ( A R

) K K (

P ) K K ( z 2 R A 6

) K K (

R A 8

) K K ( A P

γ γ

γ γ γ

⇒ Find L ₄

⇒ Embedded depth can be determined with D= L₃ +L₄ ⇒ Increase D to 20~40%

Check Mmaxat zero-shear

To find the location of zero shear

(

^L₃ <^z<^D−^L₅

)

( ) 0

2

1 ₂

=

−

− K K z

R_a _P _A γ_sub ⇒ Find z M R_a z z

(

K_P K_A

)

_sub z z

3 1 2

) 1

( ²

max 



 − ⋅

− +

= γ

⇒Section modulus

allow

Mmax

s⁼σ

where σ_allowis allowable flexural stress of sheet pile.

328

A− ⇒ σ_all =170MN/m²



 





−

− 690 A

572

A ⇒ σ_all =210MN/m²

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Fig. Properties of some sheet pile sections

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b) Anchored sheet pile walls (Bulkheads)

Assumption or condition for analysis

- Example of approach for sand

Active

Passive

) H ( P_A

R A

L P

R P

La

z H

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① Calculate net earth pressure distributions against wall

② Calculation point of zero pressure (L ) ₃

3 sub P 3 sub A

A(H) K L K L

P + ⋅γ ⋅ = ⋅γ ⋅

sub A P

A

3 (K K )

) H ( L P

γ

= −

③ Calculate R and its location L_a a and R _P

_P ^P ^A _sub L₄² 2

K

R K − ⋅

= γ

④ To find D,

∑

M_about _tie _rod =0 R_aL_a =R_pL_p

L )

3 l 2 L L L ( 2 L

K K

4 1 3 2 1 2 4 sub A

P − ⋅ + + − +

= γ

⇒ Find L₄ ⇒D=L₃ +L₄

⑤ Compute tie rod tension

T =R_a −R_p(Tie rod force per unit length of wall)

⑥ Calculate M_max in the wall (zero shear occurs at x=l₁+l₂ ~ H)

(z l l ) K 0

2 K 1 ) l l z )(

l l ( T K ) l l 2 ( 1

A 2 2 1 sub A

2 1 2

1 A

2 2

1+ − +γ + − − + γ − − =

γ

⇒ Find z

⇒ We can find M_max

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⑦ Reduce M_max using Rowe’s procedure to account for flexibility of sheeting

- Drained condition (sand) ( ² )

4

in lb EI H

p

ρ= or 10.91 10 ( ² )

4 7

m MN EI

H

p

× −

ρ=

where H = total length of the sheet piling Obtain

max design

M M

R = M from the chart.

- Undrained conditions

Compute S =stability number =_n

) 25 (

.

1 H D

s_u

⋅ −

γ and logρ. Obtain

max design

M M

R = M from the chart.

Fig. Rowe’s moment-reduction coefficients (after Bowles 1982)

log

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⑧ Pick sheet pile section with

a

Md

s⁼ σ ^.

⑨ Add 20~40% to the embedment depth of pile.

⑩A=T/ cosα⋅(Horizontal spacing)

3) Retaining Structures 