Lateral stability (Complete Soil Mech. Undestanding Pakage: ABHAY)

Lateral Earth Pressures
Duration: 18 min N. Sivakugan

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

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

4
Lateral Support
We have to estimate the 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 are increasingly becoming popular.
geosynthetics

10
Lateral Support
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,
v’
X h’
the ratio h’/v’ is a constant known as coefficient
of earth pressure at rest (K0).
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,


K 
Poisson’s
0 1 
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
v’
A
h’
z
v’ = z
Initially, there is no lateral movement.
h’ = K0 v’ = K0 z
As the wall moves away from the soil,
v’ remains the same; and
h’ decreases till failure occurs.
Active state

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

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

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

18
- in granular soils
v’
A
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.
h active A v A [ ' ]  K  '2c K
Everything else the same
as for granular soils.

20
Passive Earth Pressure
- in granular soils
v’
B
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

Initially (K0 state)
Failure (Passive state)
  v’
increasing h’
passive earth
pressure

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

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

24
- in granular soils
v’
B
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.
h passive P v P [ ' ]  K  '2c K
Everything else the same
as for granular soils.

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

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

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

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

34
Design of Retaining Wall
1
- in granular soils
2 2
3 3
1
Block no.
toe
toe
Wi = weight of block i
xi = horizontal distance of centroid of block i from toe
Analyse the stability of this rigid body with
vertical walls (Rankine theory valid)

P W
sliding P
1
P i
2 2
3 3
1
PA
PA
PP
PP
S
toe S
toe
R
y R
y
Safety against sliding along the base
{ }. tan
A
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

F 
P h Wx
overturning P
1
/ 3 { }
P i i
2 2
3 3
1
PA
PA
PP
PP
S
toe S
toe
R
y R
y
Safety against overturning about toe
H/3
A

H
h
to be greater
than 2.0

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)?

Lateral stability (Complete Soil Mech. Undestanding Pakage: ABHAY)

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