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CHAPTER 3
ANALYSIS AND DESIGN OF RETAINING STRUCTURES
Learning Outcomes:
At the end of this lecture/week the student would be able
to:
Describe the purpose of retaining wall and its components
(C03-PO4)Understand and discuss different types of retaining earth
structure (C03-PO4)
Perform analysis and design for sheet pile wall (C03-PO4)
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References:
Das,B.M. (2007). Principles of Foundation
Engineering.Thomson
Budhu,M. (2007). Soil Mechanics and Foundations.WILEY
Craig, R.F. (2004). Craigs Soil Mechanics. Taylor &
Francis.
Thomlinson, M.J. (1995). Foundation Design & Construction.
Longman Scientific and Technical
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Retaining Wall
Retaining wall used to prevent the
retained material from assuming its
natural slope:
3 basic components:
Backfill material granular materialReinforcement geotextiles or
metal rodsFacing
3.1Introduction
Facing unit
Earth fill
Reinforcement
Component of ERWall
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3.2Application Areas (BRIDGE WORKS)
Bridge abutment
Bridge abutment,
with piles bankseat
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Application Areas (BRIDGE WORKS)
Bridge abutment and
support to bankseat
Sloping bridge abutment
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Reinforced embankment
in place of viaduct
ADVANTAGES:
Economic May used in poor subsoil Speed of erection high
Application Areas (BRIDGE WORKS)
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Application Areas (DAMS)
Reinforced earth dam
Reinforced soil structure used to raise the height of an
existing dam
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Application Areas (EMBANKMENT)
Reinforced embankment
Material : Geotextile or geogrid
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Geocell mattress used to increase embankment stability
Application Areas (EMBANKMENT)
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Application Areas (FOUNDATION)
Geogrid reinforcement of subsoil beneath embankment
Stone columns formed from geogrid cubes
WEAK SOIL
WEAK SOIL
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Sheet Pile Wall
3.2Sheet Pile
Flexible and are constructed using steel or thin concrete slabs
or
wood.
Two(2) types of sheet pile :
Cantilever sheet pile = used to support height of less than 3
m
= rely on passive soil resistance for their stability
Anchored sheet pile = support deep excavation and waterfront
structures
= rely on combination of anchors and passive soil resistance
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Types of flexible retaining wall
Types of rigid retaining wall
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Cantilever Sheet Pile
3.2.1Cantilever Sheet Pile Wall
Steel sheet piling driven into the ground for temporary works is
commonly used to support the vertical sides of excavation during
construction
To avoid internal proping or external anchoring, it is
preferable if the wall can be designed to act in the cantilever
mode
Following completion of the below ground structure and
backfilling the sheet piles are usually removed
This type of wall should be limited to a maximum height 3-5 m
depending on the soil type and presence of water
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Contiguous or secant bored pile walls and diaphragm wall are
frequently used in cantilever mode for permanent application such
as for retaining structures alongside urban highways, bridge
abutments and for basement walls.
Minimal vibration produced during boring so this method can be
adopted for walls close to existing structures
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3.2.2Analysis of Cantilever Sheet Pile Wall
Cantilever sheet pile wall are analysed by
assuming that rotation occurs at some
point O,just above the base of the wall
By assuming rotation at point O (above the
base) lateral pressure is passive behind
the wall and active in front of the wall
To simply design the passive
resistance, a force R is used at the point of
rotation O and moments about O are taken
for the active and passive thrust, Pa and
Pp
The depth is increased by 20% to 30% to
give embedment design, d
Pressure Distributions
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Anchored Sheet Pile
3.2.2ANCHORED sheet pile wall
Additional support to embedded walls is provided by a row of
tie-backs or props near the top wall.
Tie backs are normally high tensile steel cables or rods,
anchored in the soil some distance behind the wall
Two methods to analyse anchored sheet pile wall:
a) free earth support method (frequently used)
b) fixed earth support method
The design of anchored sheet pile wall addresses:
a) embedded depth
b) Anchor load
c) maximum bending moment
The stability depends due to passive resistance developed in
front
of the wall together with supporting forces in ties and
props.
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3.2.2Free Earth Support Method
Assumption:
Depth of embedment below excavation
level is insufficient to produce fixity at
the lower end of the wall thus base of
wall free to rotate
No passive resistance to backward
movement at bottom
Active and Passive distribution are
static
Stability depends on passive
resistance in front wall
Free Earth Support Method
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Example 1: Cantilever sheet-pile wall
A cantilever sheet-pile wall is to support the side of an
excavation. The depth of excavation is 3 m. The properties of soil
are as follow:
c = 0, =30o, =20 kN/m3
By using FOS on shear strength = 1.4 and
FOS on embedment=1.2, determine:
The safe driving depth
Maximum moment induced in the piling
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Example 2: Anchored sheet pile
(free earth support method)
The anchored sheet pile shown below to be designed by the free
earth support method. The depth of excavation is 9m. The anchor
will be installed at apoint 1.5m below the top of the wall.
Determine the required depth of penetration and the design force
for anchor.
Given: Fs=1.5 ; Fd=1.2 , FT=2.0
c = 0, =28o, =20 kN/m3
1.5 m
T
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CHAPTER 3
ANALYSIS AND DESIGN OF RETAINING STRUCTURES
Learning Outcomes:
At the end of this lecture/week the student would be able
to:
Understand on braced excavation (C03-PO4) Perform analysis and
design forces for struts in braced excavation (C03-PO4)
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Braced Excavation
3.1Introduction
Braced excavation is required when dealing with
construction of basements, bridge piers and abutments
The vertical faces of the cut need to be protected by temporary
bracing system (sheet pile) to avoid failure that may
be accompanied by considerable settlement or by bearing capacity
failure at nearby foundation
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Interlocking sheet piles are driven to the soil before
excavation. As excavation proceeds, struts and wales (horizontal
steel beam) are inserted immediately after reaching the appropriate
depth
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3.2Wall Displacement in Braced Excavation
The wall displacements before the top struts are installed are
usually very small but get larger as the excavation gets deeper
The largest wall displacement occur at the base of the
excavation
Critical design element is when designing loads on struts due to
different lateral load at different depth
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Figure 3.1 : Distribution of displacement for Braced
Excavation
WALL DISPLACEMENT
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LATERAL EARTH PRESSURE DISTRIBUTION
3.3Lateral Earth Pressure
Peck (1969) suggested using design pressure envelopes for
braced
cuts in sand and clay
Lateral Earth Pressure Distribution for course grained soil
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Lateral Earth Pressure Distribution for fine grained soil
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QUESTION
Draw the pressure diagram. Determine the forces on the
struts
for the braced excavation.
(The struts are placed 3 m center to center in the plan)
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SOLUTION:
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CHAPTER 3
ANALYSIS AND DESIGN OF RETAINING STRUCTURES
Learning Outcomes:
At the end of this lecture/week the student would be able
to:
Understand the construction methods for retaining
structures(C03-PO4)
Perform analysis and design for reinforced earth structures
(C03-PO4)
Understand and perform cofferdam design and analysis
(C03-PO4)
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3.1Construction Techniques
Hybrid Systems
Telescope Method
Sliding Method
Concertina Method
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Concertina Method
Originally proposed by Vidal (1966), this method permits
differential settlement within the soil mass by the face structure
closing in a manner similar to a set of bellows or a concertina.
This is the form of construction most frequently used with
geotextiles for steep slopes.
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Telescope Method
In this system the deformations within the soil mass are
accommodated by the facing panels closing and moving forward an
amount equivalent to the internal deformations, Vidal (1978). This
is made possible by the individual facing units being held apart
during construction. Failure to provide a large enough gap can
result in damage to the facing panels.
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Sliding Method
In the sliding method proposed by Jones (1978), differential
settlement and compaction within the soil mass can be accommodated
by permitting the reinforcing elements to slide vertically relative
to the facing. Slideable attachments can be provided by groves,
slots, vertical poles, lugs or bolts. Facings made of discrete
elements, as with the telescope method, can be used as can full
height facings with a range of architectural finishes.
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Hybrid Systems
Reinforcement is used with conventional gravity systems to
produce an
improved composite construction; an example is the tailed
gabion, or
the Norwegian concrete block.
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3.2Construction Tolerances and Serviceability Limit
Table 4.1: Usually accepted tolerances for faces of retaining
walls and abutments.
Location of plane structure 50 mmVerticality 5 mm per metre
height(i.e. 40 mm per 8 m)Bulging (vertical) or Bowing (horizontal)
20 mm in 4.5 m templateSteps at joints 10 mmAlignment along top 15
mm from reference alignment
- Table 4.2 Serviceability limits.Limit on post construction
internal strainsStructureStrain percentBridge
abutments0.5Walls1.0
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3.3Principle of Earth Reinforced Earth
Vertical stress, v = z
Lateral stress, h = Ko v
According to Jacky (1944), for both normally consolidated clays
and compacted soil,
Ko = 1 Sin ,
where = the angle of friction of the soil.
ka = 1- sin
1+sin
kp = 1+ sin
1-sin
z
T
Rankine active earth wedge
Kaz
Pa = active earth force
T = tension force in reinforcement
Pa
H
H/3
45o + /2
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3.4Forces in Reinforcement Strip
ER Wall with pre-cast facing unit
unit in kN
where
therefore,
where zi = depth of strip i below the
ground level
Facing unit
Soil
Reinforcement
Sh
Sv
zi
Ti
Surcharged load, q
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3.4.1The maximum Tension Line
The tensile force in a reinforcement strip varies. It generally
has a low (even a zero) value at the facing unit, reaches a maximum
value a short distance from the facing and then tends towards zero
at the un attached end.
The maximum tension line
Resistant
zone
Profile of maximum tension line
Active
zone
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3.4.2Failure of a reinforcing element
a) Tensile failure (breakage)
The ultimate resistance of a reinforcing element to an axial
tensile stress is equal to the ultimate axial tensile stress that
the material can withstand, fy, time the cross sectional area of
the rectangular strip.
where w = width of reinforcing element
t = thickness of reinforcing element
fy = yield tensile strength of tie material
Rt = fy . w . t
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b) Bond Failure
For a reinforcing element the bond resistance between it and the
soil will be provided by frictional resistance
Frictional resistance,
where w = width of strip
l = length of strip
Fr = 2 zi w l
Note :
Rectangular strip, Fr = 2 zi w l
Round bar (rod), Fr = zi d l ( where d = diameter of bar)
Sheet, Fr = 2 zi l
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3.5Design Criteria
DESIGN PRINCIPLE
ERW
INTERNAL STABILITY
EXTERNAL STABILITY
Tensile FailureBond Failure
Sliding
Overturning
Bearing Capacity
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3.5.1Internal Stability
a) FOS against breakage =
=
=
b) FOS against pull-out =
=
=
where = coefficient of friction soil tie
= 0.5 tan
OR
=
where
=
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c)Determination of thickness
t design =
t corrosion = rate of corrosion x design life
(eg. 0.002mm/yr) x (50 yrs)
t required = t design + t corrosion
t use > t required
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d)Determination of required length of metal strip
lr = length of metal strip within Rankines failure
wedge
le = the effective length of reinforcement
Rankine active wedge
z
H
lr
le
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v
h
v
a
i
S
S
K
T
s
=
q
S
i
v
v
+
=
g
s
h
v
i
a
i
S
S
q
z
K
T
)
(
+
=
g
tie
any
in
force
aximum
m
The
tie
each
of
strength
yield
The
Sh
Sv
v
Ka
t
w
fy
s
Ti
Fr
tie
any
in
force
aximum
m
The
force
friction
aximum
m
The
Ti
Rt
Sh
Sv
v
Ka
l
w
v
s
m
s
2
Sh
Sv
v
Ka
l
w
v
s
j
s
m
tan
2
m
j
j
3
2
w
fy
Sh
Sv
v
Ka
b
FOS
s
)
(
2
45
f
+
o
2
45
f
+
o