lectures in Lateral Earth Pressure_2.ppt

Lateral Earth Pressures
Lateral Earth Pressures
N. Sivakugan
Duration: 18 min

2
SIVA Copyright©2001
Contents
Contents
• Geotechnical applications
• K0, active & passive states
• Rankine’s earth pressure theory
• Design of retaining walls
• A Mini Quiz
A 2-minute break

3
Lateral Support
In geotechnical engineering, it is often necessary to
prevent lateral soil movements.
Cantilever
retaining wall
Braced excavation Anchored sheet pile
Tie rod
Sheet pile
Anchor

4
Lateral Support
We have to estimate the lateral soil pressures
lateral soil pressures acting
on these structures, to be able to design them.
Gravity Retaining
wall
Soil nailing
Reinforced earth wall

5
Soil Nailing

6
Sheet Pile
Sheet piles marked for driving

7
Sheet Pile
Sheet pile wall

8
Sheet Pile
During installation Sheet pile wall

9
Lateral Support
Reinforced earth walls
Reinforced earth walls are increasingly becoming popular.
geosynthetics

10
Lateral Support
Crib walls
Crib walls have been used in Queensland.
Interlocking
stretchers
and headers
filled with
soil
Good drainage & allow plant growth.
Looks good.

11
Earth Pressure at Rest
GL
In a homogeneous natural soil deposit,
X
h’
v’
the ratio h’/v’ is a constant known as coefficient
coefficient
of earth pressure at rest (K
of earth pressure at rest (K0
0).
).
Importantly, at K0 state, there are no lateral
strains.

12
Estimating K0
For normally consolidated clays and granular soils,
K0 = 1 – sin ’
For overconsolidated clays,
K0,overconsolidated = K0,normally consolidated OCR0.5
From elastic analysis,




1
0
K Poisson’s
ratio

13
Active/Passive Earth Pressures
- in granular soils
smooth wall
Wall moves
away from soil
Wall moves
towards soil
A
B
Let’s look at the soil elements A and B during the
wall movement.

14
Active Earth Pressure
- in granular soils
A
v’
h’
z
As the wall moves away from the soil,
Initially, there is no lateral movement.
v’ = z
h’ = K0 v’ = K0 z
v’ remains the same; and
h’ decreases till failure occurs.
Active state

15
- in granular soils


failure envelope
v’
decreasing h’
Initially (K0 state)
Failure (Active state)
active earth
pressure

16
- in granular soils
v’
[h’]active


failure envelope

'
]
'
[ v
A
active
h K 
 
)
2
/
45
(
tan
sin
1
sin
1 2








A
K
Rankine’s coefficient of
active earth pressure
WJM Rankine
(1820-1872)

17
- in granular soils
v’
[h’]active


failure envelope

A
v’
h’
45 + /2
90+
Failure plane is at
45 + /2 to horizontal

18
- in granular soils
A
v’
h’
z
h’ decreases till failure occurs.
wall movement
h’
Active
state
K0 state

19
- in cohesive soils
Follow the same steps as
for granular soils. Only
difference is that c  0.
A
v
A
active
h K
c
K 2
'
]
'
[ 
 

Everything else the same
as for granular soils.

20
Passive Earth Pressure
- in granular soils
B
v’
h’
Initially, soil is in K0 state.
As the wall moves towards the soil,
v’ remains the same, and
h’ increases till failure occurs.
Passive state

21
- in granular soils


failure envelope
v’
Initially (K0 state)
Failure (Active state)
increasing h’
passive earth
pressure

22
- in granular soils
v’ [h’]passive


failure envelope

'
]
'
[ v
P
passive
h K 
 
)
2
/
45
(
tan
sin
1
sin
1 2








P
K
Rankine’s coefficient of
passive earth pressure

23
- in granular soils
v’ [h’]passive


failure envelope

A
v’
h’
90+
Failure plane is at
45 - /2 to horizontal
45 - /2

24
- in granular soils
B
v’
h’
h’ increases till failure occurs.
wall movement
h’
K0 state
Passive state

25
- in cohesive soils
Follow the same steps as
for granular soils. Only
difference is that c  0.
P
v
P
passive
h K
c
K 2
'
]
'
[ 
 

Everything else the same
as for granular soils.

26
Earth Pressure Distribution
- in granular soils
[h’]passive
[h’]active
H
h
KAH
KPh
PA=0.5 KAH2
PP=0.5 KPh2
PA and PP are the
resultant active and
passive thrusts on
the wall

Wall movement
(not to scale)
h’
Passive state
Active state
K0 state

28
Rankine’s Earth Pressure Theory
 Assumes smooth wall
 Applicable only on vertical walls
P
v
P
passive
h K
c
K 2
'
]
'
[ 
 

A
v
A
active
h K
c
K 2
'
]
'
[ 
 


29
Retaining Walls - Applications
Road
Train

30
highway

31
basement wall
High-rise building

32
Gravity Retaining Walls
cobbles
cement mortar
plain concrete or
stone masonry
They rely on their self weight to
support the backfill

33
Cantilever Retaining Walls
They act like vertical cantilever,
fixed to the ground
Reinforced;
smaller section
than gravity
walls

34
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
i
P
sliding
P
W
P
F




H
h
soil-concrete friction
angle  0.5 – 0.7 
to be greater
than 1.5
PP= 0.5 KPh2
PA= 0.5 KAH2

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
i
i
P
g
overturnin
P
x
W
h
P
F



H
h
to be greater
than 1.5

37
Points to Ponder
How does the key help in improving the stability
against sliding?
Shouldn’t we design retaining walls to resist at-rest
(than active) earth pressures since the thrust on the
wall is greater in K0 state (K0 > KA)?

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