3-lateral earth pressures

8/9/2019 3-Lateral Earth Pressures

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Lateral Earth Pressures


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Contents

Geotechnical applications

K0, active & passive states

Rankines earth pressure theory


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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


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Lateral Support

We have to estimate the lateral soil pressuresacting 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 wallsare increasingly becoming popular.

geosynthetics


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Lateral Support

Crib wallshave been used in Queensland.

Interlocking

stretchersand headers

filled with

soil

Good drainage & allow plant growth.

Looks good.


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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 K0state, there are no lateral strains.


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Estimating K0

For normally consolidated clays and granular soils,

K0= 1sin

For overconsolidated clays,K0,overconsolidated= K0,normally consolidatedOCR

0.5

From elastic analysis,

1

0KPoissons

ratio


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Active/Passive Earth Pressures- in granularsoils

smooth wall

Wall moves

away from soil

Wall moves

towards soil

A

B

Lets look at the soil elements A and B during the

wall movement.


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Active Earth Pressure- in granularsoils

A

v

h

z

As the wall moves away from the soil,

Initially, there is no lateral movement.

v= z

h= K

0

v= K

0z

vremains the same; and

hdecreases till failure occurs.

Active state


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v

decreasing h

Initially (K0state)

Failure (Active state)


active earth

pressure


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v[h]active

']'[ vAactiveh K

)2/45(tan

sin1

sin1 2

AK

Rankines coefficient of

active earth pressure

WJM Rankine

(1820-1872)


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v[h]active

A

v

h45 + /2

90+

Failure plane is at

45 + /2 to horizontal


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A

v

h

z


hdecreases till failure occurs.

wall movement

h

Active

state

K0state


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Active Earth Pressure- in cohesivesoils

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 granularsoils

B

v

h

Initially, soil is in K0 state.

As the wall moves towards the soil,

vremains the same, and

hincreases till failure occurs.

Passive state


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v

Initially (K0state)

Failure (Active state)


increasing h

passive earth

pressure


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v [h]passive

']'[ vPpassiveh K

)2/45(tansin1

sin1 2

PK

Rankines coefficient of

passive earth pressure


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v

[h]passive

A

v

h

90+

Failure plane is at

45 - /2 to horizontal

45 - /2


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B

v

h


hincreases till failure occurs.

wall movement

h

K0state

Passive state


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Passive Earth Pressure- in cohesivesoils

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 granularsoils

[h]passive

[h]active

H

h

KAHKPh

PA=0.5 KAH2

PP=0.5 KPh2

PAand PPare the

resultant active and

passive thrusts on

the wall


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Wall movement

(not to scale)

h

Passive state

Active state

K0state


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Rankines 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 backfill


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Cantilever Retaining Walls

They act like vertical cantilever,

fixed to the ground

Reinforced;

smaller section

than gravity

walls


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Design of Retaining Wall

1

1

2 2

3 3

toe

toe

Wi= weight of block i

xi= horizontal distance of centroid of block i from toe

Block no.

- in granularsoils

Analyse the stability of this rigid body with

vertical walls (Rankine theory valid)


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1

2 2

3 3

PA

PA

PPP

P

S

Stoe

toeR

Ryy

Safety against sliding along the base

tan}.{

A

iP

sliding

P

WPF

H

h

soil-concrete friction

angle 0.5 0.7

to be greater

than 1.5

PP= 0.5 KPh2 PA= 0.5 KAH

2

S f i i


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1

2 2

3 3

PA

PA

PPP

P

S

Stoe

toeR

Ryy

Safety against overturning about toe

H/3

}{3/

A

iiP

goverturnin

P

xWhPF

H

h

to be greater

than 2.0


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Points to Ponder

How does the key help in improving the stability

against sliding?

Shouldnt we design retaining walls to resist at-rest

(than active) earth pressures since the thrust on the

wall is greater in K0state (K0> KA)?

3-lateral earth pressures

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