Soil Mechanics − Lateral Earth Pressure
Chih-Ping Lin
National Chiao Tung Univ.
[email protected]
1
Outline
Geotechnical applications
„ K0, active & passive states
„ Rankine’s earth pressure theory
„ Coulomb’s earth pressure theory
„
2
Lateral Support
In geotechnical engineering, it is often necessary to
prevent lateral soil movements.
Tie rod
Anchor
Sheet pile
Cantilever
retaining wall
Braced excavation
Anchored sheet pile
3
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
4
Soil Nailing
5
Sheet Pile
Sheet piles marked for driving
6
Sheet Pile
Sheet pile wall
7
Sheet Pile
During installation
Sheet pile wall
8
Reinforced Earth Wall
Reinforced earth walls are increasingly becoming popular.
geosynthetics
9
Crib Wall
Crib walls have been used in Queensland.
filled with
soil
Good drainage & allow plant growth.
Looks good.
Interlocking
stretchers
and headers
10
Earth Pressure at Rest
In a homogeneous natural soil deposit,
GL
σv’
σh’
X
the ratio σh’/σv’ is a constant known as coefficient
of earth pressure at rest (K0).
σ '
K= h
σv'
Importantly, at K0 state, there are no lateral strains.
11
Estimating K0
For normally consolidated clays and granular soils,
K0 = 1 – sin φ’
For overconsolidated clays,
K0,overconsolidated = K0,normally consolidated OCR0.5
From elastic analysis,
K0 =
υ
1−υ
Poisson’s
ratio
12
Example 12.1
13
Active/Passive Earth Pressures
- in granular soils
Wall moves
away from soil
A
Wall moves
towards soil
B
smooth wall
Let’s look at the soil elements A and B during the
wall movement.
14
Active Earth Pressure
- in granular soils
σv’ = γz
σv’ z
σh’
A
Initially, there is no lateral movement.
∴σh’ = K0 σv’ = K0 γz
As the wall moves away from the soil,
σv’ remains the same; and
σh’ decreases till failure occurs.
Activestate
state
Active
15
Active Earth Pressure
- in granular soils
As the wall moves away from the soil,
τ
ur
fail
e
e
lop
e
v
en
Initially (K0 state)
Failure (Active state)
σv’
active earth
pressure
σ
decreasing σh’
16
Active Earth Pressure
- in granular soils
τ
ure
fail
pe
elo
v
n
e
WJM Rankine
(1820-1872)
φ
σ
σv’
[σh’]active
[σ h ' ]active = K Aσ v '
KA =
Rankine’s coefficient of
active earth pressure
1 − sin φ
= tan 2 (45 − φ / 2)
1 + sin φ
17
Active Earth Pressure
- in granular soils
τ
Failure plane is at
45 + φ/2 to horizontal
45 + ϕ/2
φ
ure
fail
pe
elo
v
n
e
σv’
σh’
A
90+ϕ
[σh’]active
σv’
σ
18
Active Earth Pressure
- in granular soils
As the wall moves away from the soil,
σh’ decreases till failure occurs.
σv’ z
σh’
σh’
K0 state
Active state
A
wall movement
19
Active Earth Pressure
- in cohesive soils
Follow the same steps as
for granular soils. Only
difference is that c ≠ 0.
[σ h ' ]active = K Aσ v '−2c K A
Everything else the same as
for granular soils.
20
Passive Earth Pressure
- in granular soils
Initially, soil is in K0 state.
As the wall moves towards the soil,
σv’ remains the same, and
σv’
σh’
σh’ increases till failure occurs.
B
Passive state
21
Passive Earth Pressure
- in granular soils
As the wall moves towards the soil,
τ
Initially (K0 state)
Failure (Active state)
ur
fail
e
e
lop
e
v
en
σv’
passive earth
pressure
σ
increasing σh’
22
Passive Earth Pressure
- in granular soils
τ
ure
fail
pe
elo
v
n
e
φ
σv’
σ
[σh’]passive
[σ h ' ] passive = K Pσ v '
KP =
1 + sin φ
= tan 2 ( 45 + φ / 2)
1 − sin φ
Rankine’s coefficient of
passive earth pressure
23
Passive Earth Pressure
- in granular soils
τ
Failure plane is at
45 - φ/2 to horizontal
45 - ϕ/2
ure
fail
φ
pe
elo
v
n
e
σv’
σh’
A
90+ϕ
σv’
[σh’]passive
σ
24
Passive Earth Pressure
- in granular soils
As the wall moves towards the soil,
σh’ increases till failure occurs.
σv’
σh’
σh’
Passive state
B
K0 state
wall movement
25
Passive Earth Pressure
- in cohesive soils
Follow the same steps as
for granular soils. Only
difference is that c ≠ 0.
[σ h ' ] passive = K Pσ v '+2c K P
Everything else the same as
for granular soils.
26
Earth Pressure Distribution
- in granular soils
[σh’]active
PA and PP are the
resultant active and
passive thrusts on
the wall
[σh’]passive
H
PA=0.5 KAγH2
h
PP=0.5 KPγh2
KPγh
KAγH
27
σh’
Passive state
Active state
K0 state
Wall movement
(not to scale)
28
Rankine’s Earth Pressure Theory
[σ h ' ]active = K Aσ v '−2c K A
[σ h ' ] passive = K Pσ v '+2c K P
‰ Assumes smooth wall
‰ Applicable only on vertical walls
29
Examples 12.3
30
Examples 12.4
31
Examples 12.5
32
Examples 12.6
33
Rankine’s Theory w/ Sloping Backfill
=0
Ka =
Kp =
cos α − cos 2 α − cos 2 φ '
cos α + cos 2 α − cos 2 φ '
cos α + cos 2 α − cos 2 φ '
cos α − cos 2 α − cos 2 φ '
34
(c)2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
(c)2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.
Coulomb’s Active Pressure
35
Coulomb’s Passive Pressure
36