ecg503-week-7-lecture-note-chp3.ppt

GEOTECHNICAL ENGINEERING
ECG 503
LECTURE NOTE 07
TOPIC : 3.0 ANALYSIS AND
DESIGN OF RETAINING
STRUCTURES

LEARNING OUTCOMES
Learning outcomes:
At the end of this lecture/week the students would
be able to:
 Understand natural slope and made engineered
soil slope assessment which include rainfall
induced failure and role of suction.

TOPIC TO BE COVERED
 Types of Retaining Structures
 Sheet Pile Wall – Cantilever and
Anchored Sheet Pile

LATERAL EARTH PRESSURE
Introduction & Overview
2.1 Introduction and overview
Retaining structures such as retaining walls, basement
walls, and bulkheads are commonly encountered in
foundation engineering, and they may support slopes
of earth mass.
Proper design and construction of these structures
require a thorough knowledge of the lateral forces that
act between the retaining structures and the soil mass
being retained.

• Retaining walls are used to prevent the
retained material from assuming its
natural slope. Wall structures are
commonly use to support earth are piles.
Retaining walls may be classified
according to how they produce stability
as reinforced earth, gravity wall,
cantilever wall and anchored wall. At
present, the reinforced earth structure is
the most used particularly for roadwork

3 basic components of retaining structure
• Facing unit – not necessary but usually used to
maintain appearance and avoid soil erosion
between the reinforces.
• Reinforcement – strips or rods of metal, strips
or sheets of geotextiles, wire grids, or chain link
fence or geogrids fastened to the facing unit
and extending into the backfill some distance.
• The earth fill – usually select granular material
with than 15% passing the no. 200 sieve.

Types of Retaining Wall
Retaining Wall
Gravity Walls
Embedded walls
Reinforced and anchored earth
The various types of earth-retaining structures
fall into three broad groups.
EARTH RETAINING STRUCTURES

Gravity Walls
Gravity Walls
Masonry walls
Gabion walls
Crib walls
RC walls
Counterfort walls
Buttressed walls

Gravity Walls
Unreinforced masonry wall

Gravity Walls
Gabion wall

Gravity Walls
Crib wall

Gravity Walls
Types of RC
Gravity Walls

Embedded Walls
Embedded walls
Driven sheet-pile walls
Braced or propped walls
Contiguous bored-pile walls
Secant bored-pile walls
Diaphram walls

Embedded Walls
Types of embedded walls

Reinforced and Anchored Earth
Reinforced earth wall
Soil nailing
Ground anchors

Reinforced earth and soil nailing

ecg503-week-7-lecture-note-chp3.ppt

Stability Criteria
Stability of Rigid Walls
Failures of the rigid gravity wall may occur
due to any of the followings:
 Overturning failure
 Sliding failure
 Bearing capacity failure
 Tension failure in joints
 Rotational slip failure
In designing the structures at least the first three of the
design criteria must be analysed and satisfied.

Types of Lateral Pressure
Hydrostatic Pressure and Lateral Thrust
Earth Pressure at Rest
Active Earth Pressure
Passive Earth pressure
States of Equilibrium

Hydrostatic pressure and lateral thrust
Horizontal pressure due to a liquid

Earth pressure at rest
z
σv
σh = Ko σv
A
B
If wall AB remains static –
soil mass will be in a state
of elastic equilibrium –
horizontal strain is zero.
Ratio of horizontal stress to
vertical stress is called
coefficient of earth
pressure at rest, Ko, or
v
h
o
K



z
K
K o
v
o
h 

 

Unit weight of soil = γ


 tan
c
f 


Earth pressure at rest .. cont.

Active earth pressure
z
σv
σh
A
B
Plastic equilibrium in soil
refers to the condition
where every point in a soil
mass is on the verge of
failure.
If wall AB is allowed to move
away from the soil mass
gradually, horizontal stress
will decrease.
This is represented by
Mohr’s circle in the
subsequent slide.


 tan
c
f 


ACTIVE EARTH PRESSURE (RANKINE’S)
(in simple stress field for c=0 soil) – Fig. 1
σX = Ko σz
σz
σz
Ko σz
σx’A
ø

Based on the diagram :
pressure
earth
active
s
Rankine'
of
t
coefficien
Ratio
v
a



a
K
 (Ka is the ratio of the effective stresses)
Therefore :





sin
1
sin
-
1
)
2
(45 -
tan
K 2
v
a
a




It can be shown that :
a
a
2
a
K
2c
-
K
z
)
2
(45 -
tan
2c
-
)
2
(45 -
tan
z








a
a K
2c
-
K
z

z
zo
a
K
2c
-
Active pressure distribution
a
K
2c
-
K
z a


Based on the previous slide, using
similar triangles show that :
a
o
K
c
z

2
 where zo is depth of tension
crack
For pure cohesive soil, i.e. when  = 0 :

c
zo
2


For cohesionless
soil, c = 0
a
a
v
a K
z
K 

 

z
K
z a


Passive Earth Pressure
2.2.4 Passive earth pressure
z
σv
σh
A
B
If the wall is pushed into the
soil mass, the principal
stress σh will increase. On
the verge of failure the
stress condition on the soil
element can be expressed
by Mohr’s circle b.
The lateral earth pressure,
σp, which is the major
principal stress, is called
Rankine’s passive earth
pressure


 tan
c
f 


PASSIVE EARTH PRESSURE (RANKINE’S)
(in simple stress field for c=0 soil) – Fig. 2
σX = Ko σz
σz
σz
Ko σz σx’P
ø

Shear
stress
Normal stress


 tan
c
f 

C
D
D’
O
A σp
Koσv
b
a
σv


c
Mohr’s circle
representing
Rankine’s
passive state.

For cohesionless soil :
Referring to previous slide, it can be shown that :
p
p
2
v
p
K
2c
K
z
)
2
(45
tan
2c
)
2
(45
tan
















sin
1
sin
1
)
2
(45
tan
K 2
p
v
p







For cohesionless soil,
Passive pressure distribution
z
K
z p

p
K
2c
p
p
v
p K
z
K 

 


In conclusion
Earth Pressure
Wall tilt
Passive pressure
At-rest pressure
Active pressure
Earth
Pressure
Wall tilt

Rankine’s Theory
Assumptions :
 Vertical frictionless wall
 Dry homogeneous soil
 Horizontal surface
 Initial work done in 1857
 Develop based on semi infinite “loose granular” soil
mass for which the soil movement is uniform.
 Used stress states of soil mass to determine lateral
pressures on a frictionless wall

Active pressure for cohesionless soil

Effect of a stratified soil
Effect of surcharge

Effect of sloping surface

Active pressure,
Passive pressure,


 cos
'
'
v
a
ha K



 cos
'
'
v
p
hp K

where
)
'
cos
-
(cos
cos
)
'
os
c
-
(cos
-
cos
2
2
2
2








a
K
a
2
2
2
2
p
1
)
'
cos
-
(cos
cos
)
'
os
c
-
(cos
cos
K
K 









and

Tension cracks in cohesive soils

Effect of surcharge (undrained)

Passive resistance in undrained clay

The stability of the retaining wall should be checked against :
(ii) FOS against sliding (recommended FOS = 2.0)
(i) FOS against overturning (recommended FOS = 2.0)
Stability Criteria
moment
Disturbing
moment
Resisting
FOS 
H
w
p
V
R
B
c
P
0.7)
-
(0.5
tan
R
FOS





Stability Analysis
Pp
Ph
∑ V
A
The stability of the retaining wall should
be checked against :
2.3.1 FOS against overturning
(recommended FOS = 2.0)
moment
Disturbing
moment
Resisting
FOS 
.. overturning about A

2.3.2 FOS against sliding
(recommended FOS = 2.0)
Stability Criteria
H
w
p
V
R
B
c
P
0.7)
-
(0.5
tan
R
FOS




Ph
∑ V
Pp
Friction & wall base adhesion









B
6e
B
R
q V
b 1
2.3.3 For base pressure (to be compared against the
bearing capacity of the founding soil. Recommended
FOS = 3.0)
Now, Lever arm of base resultant
Thus eccentricity
R
Moment
x
V


x
-
2
B
e 
Stability Criteria

Stability Analysis
Pp
Ph
∑ V
Base pressure on the founding soil

Stability Analysis
Figure below shows the cross-section of a reinforced concrete
retaining structure. The retained soil behind the structure and
the soil in front of it are cohesionless and has the following
properties:
SOIL 1 : u = 35o, d = 17 kN/m3,
SOIL 2 : u = 30o,  = 25o , d = 18 kN/m3,
sat = 20 kN/m3
The unit weight of concrete is 24 kN/m3. Taking into account the
passive resistance in front of the wall, determine a minimum value
for the width of the wall to satisfy the following design criteria:
Factor of safety against overturning > 2.5
Factor of safety against sliding > 1.5
Maximum base pressure should not exceed 150 kPa
Worked example :

Stability Analysis
SOIL 2
2.0 m
0.5 m
0.6 m
2.9 m
2.0 m
GWT
4.5 m
SOIL 1
SOIL 2
30 kN/m2
4.0 m
THE PROBLEM

Stability Analysis
P1
P3
SOIL 2
2.0 m
0.5 m
0.6 m
2.9 m
2.0 m
GWT
4.5 m
SOIL 1
SOIL 2
30 kN/m2
4.0 m
P2
P4
PP
W41
W3
W2
W1
P5
THE SOLUTION
P6

Stability Analysis
271
.
0
35
sin
1
35
sin
-
1
sin
1
sin
1
o
o
1 







a
K
333
.
0
30
sin
1
30
sin
-
1
sin
1
sin
1
o
o
2 







a
K
00
.
3
30
sin
1
30
sin
1
sin
1
sin
1
o
o
2 








p
K
Determination of the Earth Pressure Coefficients

Stability Analysis
ELEM. FORCE (kN/m) TOTAL
L. ARM
(m)
MOMENT
(kNm/m)
HORIZONTAL
Active
P1 0.271 x 30 x 2 16.26 4.5 73.17
P2 0.333 x 30 x 3.5 34.97 1.75 61.20
P3 0.5 x 0.271 x 17 x 2 x 2 9.21 4.17 38.41
P4 0.333 x 17 x 2 x 3.5 39.63 1.75 69.35
P5 0.5 x .333 x (20-9.81) x 3.5 x 3.5 20.78 1.167 24.25
P6 0.5 x 9.81 x 3.5 x 3.5 60.09 1.167 70.13
SUM 180.94 336.50
Passive
Pp 0.5 x 3 x 18 x 1.5 x 1.5 60.75 0.5 30.38
VERTICAL
W1 0.5 x 4.9 x 24 58.8 1.75 102.90
W2 0.6 x 4.5 x 24 64.8 2.25 145.80
W3 2 x 2.5 x 17 + 2.9 x 2.5 x 20 + 30 x 2.5 305 3.25 991.25
W4 0.9 x 1.5 x 18 24.3 0.75 18.23
SUM 452.9 1288.55

Stability Analysis
OK
is
it
thus
2.5,
moment
Disturbing
moment
Resisting



 83
.
3
50
.
336
55
.
1288
FOS
To check for stability of the retaining wall
(i) FOS against overturning > 2.5
(ii) FOS against sliding > 1.5
1.5
.
.
60.75
x
0.5
25
tan
.
R
P
0.5
tan
R
FOS
o
H
p
V





 34
1
94
180
9
452

Thus it is not OK

Stability Analysis








B
6e
B
R
q V
b 1
2.10
452.9
336.5
-
1288.55
R
Moment
x
V




(iii) For base pressure
Now, Lever arm of base resultant
0.15
2.10
-
2.25
x
-
2
B
e 










4.5
0.15
x
6
4.5
452.9
qb 1
Thus eccentricity
Therefore

Stability Analysis
qb = 120.8 and 80.5 kPa
Since maximum base pressure is less than the bearing pressure of the
soil, the foundation is stable against base pressure failure.
DISTRIBUTION OF BASE PRESSURE
80.5 kPa
120.8 kPa
In conclusion the retaining wall is not safe against sliding. To
overcome this the width of the base may be increased or a
key constructed at the toe.

Group assignment NO. 1:
Form a group of 6 members in each group. Your task is to
write up a case study which involve a dam case failure in
Malaysia and a slope failure in Malaysia. Your report shall
consists of the history of each case, as examples;
amount of dam in Malaysia, their purpose, operation, etc.
Make sure your case study are not the same as others
groups. Penalties will be given accordingly for those who
ignore the warnings.
Date of submission :

Group assignment NO. 2:
Form a group of 6 members in each group. Your task is to
write up a case study which involve a ground
improvement technique. Your shall selected a real project
which will consists of real soil problems and technique to
overcome the problems.
Make sure your case study are not the same as others
groups. Penalties will be given accordingly for those who
ignore the warnings.
Date of submission :

ecg503-week-7-lecture-note-chp3.ppt

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