Duration: 18 min SIVA Copyright©2001 2 Geotechnical applications K 0, active & passive states Rankine’s earth pressure theory Design of retaining walls

Lateral Earth PressuresLateral Earth Pressures

Duration: 18 min

SIVASIVA Copyright©2001Copyright©2001

2

Contents

• 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 pressures acting on these structures, to be able to design them.

Gravity Retaining wall

Soil nailingReinforced earth wall


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Soil Nailing


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Sheet Pile

Sheet piles marked for driving


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Sheet Pile

Sheet pile wall


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Sheet Pile

During installation Sheet pile wall


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Lateral Support

Reinforced earth walls are increasingly becoming popular.

geosynthetics


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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,

Xh’

v’

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,

10K

Poisson’s ratio


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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.


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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


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failure envelope

v’

decreasing h’

Initially (K0 state)

Failure (Active state)


active earth pressure


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v’[h’]active

failure envelope

']'[ vAactiveh K

)2/45(tansin1

sin1 2

AK

Rankine’s coefficient of active earth pressure

WJM Rankine(1820-1872)


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v’[h’]active

failure envelope

A

v’

h’45 + /2

90+

Failure plane is at 45 + /2 to horizontal


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A

v’

h’z


h’ decreases till failure occurs.

wall movement

h’

Active state

K0 state


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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.


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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


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failure envelope

v’

Initially (K0 state)

Failure (Active state)


increasing h’

passive earth pressure


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v’ [h’]passive

failure envelope

']'[ vPpassiveh K

)2/45(tansin1

sin1 2

PK

Rankine’s coefficient of passive earth pressure


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v’ [h’]passive

failure envelope

A

v’

h’

90+

Failure plane is at 45 - /2 to horizontal

45 - /2


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B

v’

h’


h’ increases till failure occurs.

wall movement

h’

K0 state

Passive state


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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.


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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


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Rankine’s Earth Pressure Theory

Assumes smooth wall

Applicable only on vertical walls

PvPpassiveh KcK 2']'[

AvAactiveh KcK 2']'[


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Retaining Walls - Applications

Road

Train


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highway


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basement wall

High-rise building


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Gravity Retaining Walls

cobbles

cement mortarplain concrete or stone masonry

They rely on their self weight to support the backfillThey rely on their self weight to support the backfill


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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


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Design of Retaining Wall

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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)

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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

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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




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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)?

Documents

Duration: 18 min SIVA Copyright©2001 2 Geotechnical applications K 0, active & passive states Rankine’s earth pressure theory Design of retaining walls