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.
Component of E.R. Wall
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
EARTH RETAINING STRUCTURES
Gravity Walls
Unreinforced masonry wall
EARTH RETAINING STRUCTURES
Gravity Walls
Gabion wall
EARTH RETAINING STRUCTURES
Gravity Walls
Crib wall
EARTH RETAINING STRUCTURES
Gravity Walls
Types of RC Gravity Walls
EARTH RETAINING STRUCTURES
Embedded Walls
Embedded walls
Driven sheet-pile walls
Braced or propped walls
Contiguous bored-pile walls
Secant bored-pile walls
Diaphram walls
EARTH RETAINING STRUCTURES
Embedded Walls
Types of embedded walls
EARTH RETAINING STRUCTURES
Reinforced and Anchored Earth
Reinforced and anchored earth
Reinforced earth wall
Soil nailing
Ground anchors
EARTH RETAINING STRUCTURES
Reinforced and anchored earth
Reinforced earth and soil nailing
EARTH RETAINING STRUCTURES
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.
EARTH RETAINING STRUCTURES
LATERAL EARTH PRESSURE
Types of Lateral Pressure
Hydrostatic Pressure and Lateral Thrust
Earth Pressure at Rest
Active Earth Pressure
Passive Earth pressure
States of Equilibrium States of Equilibrium
LATERAL EARTH PRESSURE
Types of Lateral Pressure
Hydrostatic pressure and lateral thrust
Horizontal pressure due to a liquid
LATERAL EARTH PRESSURE
Earth Pressure at Rest
Earth pressure at rest
Earth pressure at rest
zσv
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
ho K
z K K ovoh
Unit weight of soil = γ tan c f
LATERAL EARTH PRESSURE
Earth pressure at rest .. cont.
Earth Pressure at Rest
LATERAL EARTH PRESSURE
Active Earth Pressure
Active earth pressure
Earth pressure at rest
zσv
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.
Unit weight of soil = γ tan c f
ACTIVE EARTH PRESSURE (RANKINE’S)(in simple stress field for c=0 soil) – Fig. 1
σX = Ko σz
σz
σzKo σzσx’A
ø
LATERAL EARTH PRESSURE
Based on the diagram :
pressure earthactive sRankine' of tcoefficien Ratiov
a
aK (Ka is the ratio of the effective stresses)
Therefore :
sin 1
sin -1 )
2 (45 -tan K 2
v
aa
It can be shown that :
aa
2a
K 2c -Kz
)2
(45 - tan 2c -)2
(45 -tanz
Active Earth Pressure
LATERAL EARTH PRESSURE
aa K 2c -Kz
z
zo
aK 2c-
Active pressure distribution
Active Earth Pressure
aK 2c-
K z a
LATERAL EARTH PRESSURE
Active pressure distribution
Active Earth Pressure
Based on the previous slide, using similar triangles show that :
a
oK
cz
2
where zo is depth of tension crack
For pure cohesive soil, i.e. when = 0 :
c
zo
2
LATERAL EARTH PRESSURE
For cohesionless soil, c = 0
aava Kz K
z
Active pressure distribution
Active Earth Pressure
K z a
LATERAL EARTH PRESSURE
Passive Earth Pressure
2.2.4 Passive earth pressure
Earth pressure at rest
zσv
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
Unit weight of soil = γ tan c f
PASSIVE EARTH PRESSURE (RANKINE’S)(in simple stress field for c=0 soil) – Fig. 2
σX = Ko σz
σz
σzKo σz σx’Pø
LATERAL EARTH PRESSURE
Sh
ear
stre
ss
Normal stress
tan c f
C
D
D’
OA σpKoσv
b
a
σv
c
Mohr’s circle representing
Rankine’s passive state.
Passive Earth Pressure
LATERAL EARTH PRESSURE
For cohesionless soil :
Referring to previous slide, it can be shown that :
Passive Earth Pressure
pp
2vp
K 2c Kz
)2
(45 tan 2c )2
(45 tan
sin 1
sin 1 )
2 (45 tan K 2
pv
p
LATERAL EARTH PRESSURE
For cohesionless soil,
Passive pressure distribution
Passive Earth Pressure
z
Kz ppK2c
ppvp Kz K
LATERAL EARTH PRESSURE
In conclusion
Earth Pressure
Wall tilt
Passive pressure
At-rest pressure
Active pressure
Ea
rth
P
ress
ure
Wall tilt
LATERAL EARTH PRESSURE
Types of Lateral Pressure
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
LATERAL EARTH PRESSURE
Types of Lateral Pressure
Active pressure for cohesionless soil
LATERAL EARTH PRESSURE
Types of Lateral Pressure
Effect of a stratified soil
Effect of surcharge
LATERAL EARTH PRESSURE
Types of Lateral Pressure
Effect of sloping surface
LATERAL EARTH PRESSURE
Types of Lateral Pressure
Active pressure,
Passive pressure,
cos ''vaha K
cos ''vphp K
where)'cos - (cos cos
)'osc - (cos - cos
22
22
aK
a22
22
p
1
)'cos - (cos cos
)'osc - (cos cos
KK
and
LATERAL EARTH PRESSURE
Types of Lateral Pressure
Tension cracks in cohesive soils
LATERAL EARTH PRESSURE
Types of Lateral Pressure
Effect of surcharge (undrained)
LATERAL EARTH PRESSURE
Types of Lateral Pressure
Passive resistance in undrained clay
LATERAL EARTH PRESSURE
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
momentResisting FOS
H
wpV
R
Bc P 0.7) -(0.5 tan RFOS
LATERAL EARTH PRESSURE
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
momentResisting FOS
.. overturning about A
LATERAL EARTH PRESSURE
2.3.2 FOS against sliding (recommended FOS = 2.0)
Stability Criteria
H
wpV
R
Bc P 0.7) -(0.5 tan RFOS
Ph
∑ V
Pp
Friction & wall base adhesion
LATERAL EARTH PRESSURE
B6e
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
LATERAL EARTH PRESSURE
Stability Analysis
Pp
Ph
∑ V
Base pressure on the founding soil
Stability Analysis
LATERAL EARTH PRESSURE
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 > 2.5Factor of safety against sliding > 1.5Maximum base pressure should not exceed 150 kPa
Worked example :
Stability Analysis
LATERAL EARTH PRESSURE
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
LATERAL EARTH PRESSURE
Stability Analysis
P1P3
SOIL 2
2.0 m
0.5 m
0.6 m
2.9 m
2.0 mGWT
4.5 m
SOIL 1
SOIL 2
30 kN/m2
4.0 m
P2P4
PP
W41
W3
W2
W1
P5
THE SOLUTION
P6
LATERAL EARTH PRESSURE
Stability Analysis
271.035sin1
35sin -1
sin1
sin1o
o
1
aK
333.030sin1
30sin -1
sin1
sin1o
o
2
aK
00.330sin1
30sin 1
sin1
sin1o
o
2
pK
Determination of the Earth Pressure Coefficients
LATERAL EARTH PRESSURE
Stability Analysis
LATERAL EARTH PRESSURE
Stability Analysis
OK is it thus 2.5, moment Disturbingmoment Resisting
83.350.336
55.1288FOS
To check for stability of the retaining wall
(i) FOS against overturning > 2.5
(ii) FOS against sliding > 1.5
1.5 ..
60.75x 0.5 25tan .
R
P0.5 tan RFOS
o
H
pV
34194180
9452
Thus it is not OK
LATERAL EARTH PRESSURE
Stability Analysis
B6e
B
R q V
b 1
2.10 452.9
336.5 - 1288.55
RMoment
xV
(iii) For base pressure
Now, Lever arm of base resultant
0.15 2.10 - 2.25 x - 2B
e
4.50.15 x 6
4.5
452.9 qb 1
Thus eccentricity
Therefore
Stability Analysis
LATERAL EARTH PRESSURE
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 kPa120.8 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 :