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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b. Precast modular system
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
a) Gravity Retaining Structures
Rely on weight of concrete for stability.
(1) Forces that act on wall - Rankine
R = Wc + Ws + EAR sinβ
Point of application of EAR is H/3.
(Theoretically, but for design purpose, 0.4H can be recommended.)
R
E
AW
cR S
R
E
pW
sx
cx
sH/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)
ⓒⓒ
ⓒⓒ 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
toeq
heelq’max
b
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Bearing Capacity
2 } ) F F N B ) ( F F qN ( ) F F cN {(
B
Qu c cd ci q qd qi γ γ γd γi +
+
=
e 2 B B= −
Df
' q =γ
' N Q
FS = u (or FS =Qu /Qmax) (N’ = Normal resultant on base)
Fig. Terms used in bearing capacity equation
Fig. Terms used in bearing capacity equation
- Embedment factors ; Fcd, Fqd, Fγd (Hansen(1970)) For Df /B≤1, For Df /B>1
B D
Fcd =1+0.4 f / Fcd =1+0.4tan−1(Df /B)
( )
B
Fqd =1+2tanφ'1−sinφ' 2 Df
( )
− +
= −
B Fqd 1 2tanφ'1 sinφ' 2tan 1 Df
d =
Fγ 1 Fγd =1
- Inclination factors : Fci, Fqi, FγI 2 ci
qi F 1 90
F
− °
=
= δ
2
1 '
Fγi δ φ
= −
if δ φ> ', Fγi =0
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ⓓⓓ
ⓓⓓ Overall stability
Slope stability analysis for deep seated failure or unfavorable direction of joint
backfill
backfill
joint
b) Cantilevered Retaining Structure
Reinforced concrete walls that use cantilever action for stability
(1) Forces on wall
R
E
AR
E
PW
cW
sR 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
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
heelq
toes 1
Hstem
d ①
conc⋅ γ
d
L1
②
ave soil
concd γ h
γ +
L 2
③
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
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
SNU Geotechnical and Geoenvironmental Engineering Lab.
* Example of analysis for cantilevered wall for granular soil.
Find L , 3 P , 3 P 4
KPγsubL3 =
{
γL1 +γsub(L2 +L3 )}
KA and,) K K (
K ) L L
L (
A P sub
A 2 sub 1
3 −
= + γ
γ γ
P3 =L4(Kp −KA)γsub
P4 =
{
γL1 +γsub(L2 +L3 +L4 )}
KP −γsub(L3 +L4 )KAP 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
γ γ
R
aP P
3
* A
P P P
P − =
PA PA*
4 A
*
P P P
P − =
*
PP sub A
P K )
K
( − γ
Find the theoretical embedded depth, for the stability of the wall,
∑
FH =ٱ ACDE - ∆EHB + ∆FHG=0( ) 0
2 1 2
1
5 4 3 4
3 + + =
− PL P P L
Ra and
4 3
4 3 5
2 P P
R L
L P a
+
= − ---①
∑
MB =Ra(
L4+z)
−12P L3 4⋅L34 +12(
P3+P L4)
5 L35 =0 ---② put ① into ②L44 +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
Ra P A γsub ⇒ Find z M Ra z z
(
KP KA)
sub z z3 1 2
) 1
( 2
max
− ⋅
− +
= γ
⇒Section modulus
allow
Mmax
s=σ
where σallowis allowable flexural stress of sheet pile.
328
A− ⇒ σall =170MN/m2
−
− 690 A
572
A ⇒ σall =210MN/m2
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Fig. Properties of some sheet pile sections
b) Anchored sheet pile walls (Bulkheads)
Assumption or condition for analysis
- Example of approach for sand
Active
Passive
) H ( PA
R A
L P
R P
La
z H
SNU Geotechnical and Geoenvironmental Engineering Lab.
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 La a and R P
P P A sub L42 2
K
R K − ⋅
= γ
④ To find D,
∑
Mabout tie rod =0 RaLa =RpLpL )
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 =Ra −Rp(Tie rod force per unit length of wall)
⑥ Calculate Mmax 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 Mmax
⑦ Reduce Mmax 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
su
⋅ −
γ and logρ. Obtain
max design
M M
R = M from the chart.
Fig. Rowe’s moment-reduction coefficients (after Bowles 1982)
log
log
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)