Lect 14 lateral_earthpressures

Lateral Earth Pressures
Structures
Retaining Prof. Dr. Mustafa Aytekin

SIVA Copyright©2001
Lateral Support
In geotechnical engineering, it is often necessary to
prevent lateral soil movements.
Tie rod
Anchor
Sheet pile
Cantilever
Braced excavation Anchored sheet pile
2 retaining wall

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

Soil Nailing
4

Sheet Pile
Sheet piles marked for driving
5

Sheet Pile
Sheet pile wall
6

Sheet Pile
During installation Sheet pile wall
7

Lateral Support
Reinforced earth walls are increasingly becoming popular.
geosynthetics
8

Lateral Support
filled with
Crib walls have been used in Queensland. soil
Good drainage & allow plant growth.
Interlocking
stretchers
and Looks good.
headers
9

Earth Pressure at Rest
GL
In a homogeneous natural soil deposit,
v’
h’ X
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.
10

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

Poisson s
0 1 
ratio
11

Active/Passive Earth Pressures
- in granular soils
Wall moves
away from soil
Wall moves A
towards soil
wall
B
smooth Let’s look at the soil elements A and B during the
wall movement. 12

Active Earth Pressure
- in granular soils
v’= z
Initially there is no lateral movement
v’
A
h’
z
Initially, 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
13

- in granular soils

Initially (K0 state)
Failure (Active state)
v’ 
decreasing h’
active earth
pressure
14
p

- in granular soils


WJM Rankine
(1820-1872)
[h’]active v’ 
[ ' ]  K 
' h active A v 1  sin 
2
Rankine’s coefficient of
pressure
 A K active earth 15 tan (45 / 2)
1 sin


 


- in granular soils

v’
’
Failure plane is at
45 + /2 to horizontal
h’ A 45 + /2
 90+
[h’]active v’

16

- in granular soils
h’ decreases till failure occurs.
h’ K state
v’
A
h’
z
h
Active
state
K0 h wall movement
17

- in cohesive soils
Follow the same steps as
for granular soils. Only
difference is that c  0.
[ ' ] K ' 2 K
h active A v A    2c Everything else the same
for soils
18
as granular soils.

Example
19

What is the excavation depth
without a support
24

h active A v A [ ' ]  K  '2c K
25

Solved in the classroom
26

Passive Earth Pressure
- in granular soils
Initially, soil is in K0 state.
As the wall moves towards the soil,
 ’ remains the same and
v’
B
h’
v same, h’ increases till failure occurs.
h Passive state
31

- in granular soils

Initially (K0 state)
Failure (Active state)
passive earth
pressure
v’ 
increasing  ’
32
h

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

- in granular soils

v’
’
Failure plane is at
45 - /2 to horizontal
45 - /2 h’ A
 90+
v’ [h’]passive

34

- in granular soils
h’ increases till failure occurs.
h’ v’
B
h’
h Passive state
h K0 state
wall movement
35

- in cohesive soils
Follow the same steps as
for granular soils. Only
difference is that c  0.
[ ' ] K '2 K
h passive P v P    2c Everything else the same
for soils
36
as granular soils.

SIVA Copyright©2001 Earth Pressure Distribution
- in granular soils
[h’’]active
PA and PP are the
resultant active and
passive thrusts on
the wall
[h’]passive H
P 0 5 K H2
h
PA=0.5 KAPP=0.5 KPh2
K 37 KPh AH

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

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
39

Retaining Walls - Applications
Road
Train
40

highway
41

High-rise building
basement wall
42

Gravity Retaining Walls
cement mortar
l i t
cobbles
plain concrete or
stone masonry
They rely on their self weight to
support the backfill
43

Cantilever Retaining Walls
Reinforced;
smaller section
than gravity
walls
They act like vertical cantilever,
fixed to the ground 44

Design of Retaining Wall
- in granular soils
2 2
1
3 3
Block no.
1
toe
toe
Wi = weight of block i Analyse the stability of this rigid body with
45
y y g y
xi = horizontal distance of centroid of block i from toe
vertical walls (Rankine theory valid)

Safety against sliding along the base
P 
{W
W}. tan soil-concrete friction
P i
sliding P
A
F 
soil angle  0.5 – 0.7 
to be greater
2 2
g
than 1.5
1
PA
3 3
PA
H
PP 1
PP
S
toe S
R
h
toe
y R
y
PP= 0.5 KPh2 PA= 0.5 KAH2

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

Points to Think About
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)?
48

THE END
49

Lect 14 lateral_earthpressures

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