lateral earth pressures

Lateral Earth PressuresLateral Earth PressuresLateral Earth PressuresLateral Earth Pressures

N. SivakuganDuration: 18 min

2

SIVASIVA Copyright©2001Copyright©2001

ContentsContents

• Geotechnical applications

• K0, active & passive states

• Rankine’s earth pressure theory

• Design of retaining walls• A Mini Quiz

A 2-minute breakA 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 pressureslateral soil pressures acting on these structures, to be able to design them.

Gravity Retaining wall

Soil nailingReinforced 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 wallsReinforced earth walls are increasingly becoming popular.

geosynthetics

10


Lateral Support

Crib wallsCrib 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,

Xh’

v’

the ratio h’/v’ is a constant known as coefficient of earth pressure at rest (Kcoefficient of earth pressure at rest (K00).).

Importantly, at K0 state, there are no lateral strains.

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,

10K

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 stateActive state

15



failure envelope

v’

decreasing h’

Initially (K0 state)

Failure (Active state)


active earth pressure

16



v’[h’]active

failure envelope

']'[ vAactiveh K

)2/45(tansin1

sin1 2

AK

Rankine’s coefficient of active earth pressure

WJM Rankine(1820-1872)

17



v’[h’]activ

e

failure envelope

A

v’

h’45 + /2

90+

Failure plane is at 45 + /2 to horizontal

18



A

v’

h’z


h’ decreases till failure occurs.

wall movement

h’

Active state

K0 state

19


Active Earth Pressure- in cohesive soils

Follow the same steps as for granular soils. Only difference is that c 0.

AvAactiveh KcK 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



failure envelope

v’

Initially (K0 state)

Failure (Active state)


increasing h’

passive earth pressure

22



v’ [h’]passive

failure envelope

']'[ vPpassiveh K

)2/45(tansin1

sin1 2

PK

Rankine’s coefficient of passive earth pressure

23



v’ [h’]passive

failure envelope

A

v’

h’

90+

Failure plane is at 45 - /2 to horizontal

45 - /2

24



B

v’

h’


h’ increases till failure occurs.

wall movement

h’

K0 state

Passive state

25


Passive Earth Pressure- in cohesive soils

Follow the same steps as for granular soils. Only difference is that c 0.

PvPpassiveh KcK 2']'[

Everything else the same as for granular soils.

26


Earth Pressure Distribution- in granular soils

[h’]passive

[h’]active

H

h

KAHKPh

PA=0.5 KAH2

PP=0.5 KPh2

PA and PP are the resultant active and passive thrusts on

the wall

Wall movement (not to scale)

h’

Passive state

Active stateK0 state

28


Rankine’s Earth Pressure Theory

Assumes smooth wall

Applicable only on vertical walls

PvPpassiveh KcK 2']'[

AvAactiveh KcK 2']'[

29


Retaining Walls - Applications

Road

Train

30



highway

31



basement wall

High-rise building

32


Gravity Retaining Walls

cobbles

cement mortarplain concrete or stone masonry

They rely on their self weight to support the backfill

They rely on their self weight to support the backfill

33


Cantilever Retaining Walls

They act like vertical cantilever, fixed to the ground

They act like vertical cantilever, fixed to the ground

Reinforced; smaller section

than gravity walls

34


Design of Retaining Wall

11

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)

11

2 2

3 3

PA

PA

PP

PPS

Stoe

toeR

Ryy

Safety against sliding along the base

tan }.{

A

iPsliding P

WPF

H

h

soil-concrete friction angle 0.5 – 0.7

to be greater than 1.5


PP= 0.5 KPh2PP= 0.5 KPh2 PA= 0.5 KAH2PA= 0.5 KAH2

11

2 2

3 3

PA

PA

PP

PPS

Stoe

toeR

Ryy

Safety against overturning about toe

H/3

}{3/

A

iiPgoverturnin P

xWhPF

H

h



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 earth pressures

Documents

coefficient of earth

lateral earth pressuresn

granular soilsinitially

soil elements

lateral soil pressures

lateral soil movements

granular soilssmooth

rest k0