GEOTECHNICAL AND FOUNDATION ENGINEERING Lateral Earth Pressure Course Instructor : Syed Zishan Ashiq Week No. 08 May 2015 Mirpur University of Science & Technology Mirpur AJK Department of Civil Engineering
GEOTECHNICAL AND FOUNDATION ENGINEERING
Lateral Earth Pressure
Course Instructor : Syed Zishan Ashiq
Week No. 08
May 2015
Mirpur University of Science & Technology Mirpur AJK Department of Civil Engineering
Learning Objectives
1. Learn about key concepts:
2. Place in context of Mohr Circle analysis
• At rest, active and passive earth pressure
• Lateral earth pressure coefficients
Lateral Earth Pressure
(R.P. Weber)
(R.P. Weber)
??
??
Water Pressure and Soil Pressure
Consider “at-rest” (geostatic) condition Consider hydrostatic condition
Anisotropic
sx
sz
sz sx ≠ sz sx > Isotropic
Earth Pressure Coefficient “At Rest”
sx
sz
K0 = Coefficient of Lateral Earth Pressure at Rest
For normally consolidated soil (Jaky, 1944):
For over-consolidated soil (Meyerhoff, 1976):
In general:
X
Z
Y
Calculate lateral total stress (sx) at z = 5 m if K0 = 0.5
sx
(M. Budhu)
What is a Lateral Earth Pressure?
7
• We can calculate σv’
• Now, calculate σh’ which is the horizontal stress
σh‘/ σv‘ = K
• Therefore, σh‘ = Kσv‘ (σV‘ is what?)
σv’
σh’
H
There are three states of lateral earth pressure
Ko = At Rest
Ka = Active Earth Pressure (wall moves away from soil)
Kp = Passive Earth Pressure (wall moves into soil)
Passive is more like a resistance
σv
σh
z
H
Coefficients of Lateral Earth Pressure
Active and Passive Limit Conditions
Ka = Coefficient of Active Earth Pressure
(Wall Moving Away from Backfill)
Active Failure Condition
movement Active
Failure
Wedge
(45+f/2)
Kp = Coefficient of Passive Earth Pressure
(Wall Moving Toward Backfill)
Passive Failure Condition
movement Passive
Failure
Wedge
(45 -f/2)
movement
Passive Failure
Consider Mohr’s Circles… sx decreases until failure
sx increases until failure
movement
Active
Failure
Active Earth Pressure - in granular soils
As the wall moves away from the soil,
sh’ decreases till failure occurs.
A
sv’
sh’
z
wall movement
sh’
Active state
K0 state
Active Earth Pressure - in cohesive soils
Follow the same steps as for granular soils. Only difference is that c 0.
AvAactiveh KcK 2']'[ ss
Everything else the same as for granular soils.
2
'45tan
'sin1
'sin1
..
'sin1
'sin1''
2 f
f
f
f
fss
a
xz
K
so
Pole Point
45f/2
Active Failure
45f/2
Rankine Active Failure Surface
14
Passive Earth Pressure - in granular soils
B
sv’
sh’
As the wall moves towards the soil,
sh’ increases till failure occurs.
wall movement
sh’
K0 state
Passive state
15
Passive Earth Pressure - in cohesive soils
Follow the same steps as for granular soils. Only difference is that c 0.
PvPpassiveh KcK 2']'[ ss
Everything else the same as for granular soils.
Rankine Passive Failure Surface
2
'45tan
'sin1
'sin1
..
'sin1
'sin1''
2 f
f
f
f
fss
p
zx
K
so
Pole Point
45f/2
Passive Failure
Rankine’s Earth Pressure Theory
i. Assumes smooth wall
ii. Applicable only on vertical walls
PvPpassiveh KcK 2']'[ ss
AvAactiveh KcK 2']'[ ss
Evolution of lateral stress with wall movement…
Active Failure at Ka
Passive Failure at Kp
Stationary (at rest) Movement toward
backfill
Movement away
from backfill
Ka < K0< Kp
Essential Points
1) Coefficient of Lateral Earth Pressure at Rest
2) Active Earth Pressure Coefficient:
3) Passive Earth Pressure Coefficient:
4) Active slip planes at 45˚ + f’/2 to horizontal
5) Passive slip planes at 45˚ - f’/2 to horizontal
6) More wall movement (inward) required for passive failure than active (outward) failure
20
Retaining Walls - Applications
Road
Train
Retaining Walls - Applications
basement wall
High-rise building
Gravity Retaining Walls
cobbles
cement mortar plain concrete or
stone masonry
They rely on their self weight to support the backfill
Cantilever Retaining Walls
They act like vertical cantilever, fixed to the ground
Reinforced; smaller section than gravity walls
Design of Retaining Wall
1
1
2 2
3 3
toe
toe
Wi = weight of block i
xi = horizontal distance of centroid of block i from toe
Block no.
- in granular soils
Analyse the stability of this rigid body with vertical walls (Rankine theory valid)
1
1
2 2
3 3
PA
PA
PP PP S
S toe
toe R
R y y
Safety against sliding along the base
tan }.{
A
iP
slidingP
WPF
H
h
soil-concrete friction
angle 0.5 – 0.7 f
to be greater
than 1.5
PP= 0.5 KPh2 PA= 0.5 KAH2
1
1
2 2
3 3
PA
PA
PP PP S
S toe
toe R
R y y
Safety against overturning about toe
H/3
}{3/
A
iiP
goverturninP
xWhPF
H
h
to be greater
than 1.5
Thank you for listening