Lecture2(Insitu&InducedStress)

8/13/2019 Lecture2(Insitu&InducedStress)

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Lecture 2

In-situ and Induced Stresses


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In-situ Stresses : Function of the weight of the overlying strata and stresses lockedfrom tectonic origin

Induced Stresses: Resulting from stress re-distribution due to excavation

Some amount of scatter inthe measurements.

Assumed unit weight of the overlyingrock mass =0.027 MN/m3


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h,max

vh,min

Source:

Jinchang

NickelMine, China


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Ratio of the average horizontal stress to the vertical stress is

denoted by k :

where is the Poisson's ratio of the rock mass

Terzaghi

and

Richart

(1952) for zero lateral strain during formation of theoverlying strata

Proved to be inaccurate

k tends to be high at shallow depth and that it decreases at depth

(Brown and

Hoek, 1978,

Herget,1988)

Sheorey

(1994)Develop

elasto-static thermal stress model of the earthConsiders curvature of the crust, variation of elasticconstants, density, thermal expansion coefficients

through the crust and mantle. z (m) is the depth below surface

Eh (GPa) is the average deformation (in horizontal direction)


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Good for approximation

It is recommended that the in situstresses should be measured.


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Source:

Jinchang

NickelMine, China

Hoek and Brown (1978)


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Analysis of induced stresses


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At a distance of say three times the radius from thecentre of the hole, the disturbance to the in situ stress

field is negligible.


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Different PrincipalStress Trajectories(prepared by BoundaryElement Method) fordifferent opening shapesare available in Hoekand Brown (1982)


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Stresses Around a CircularExcavation Independent ofModulus

Kirsch (1898)

( ) ( ){ }

( )

( )k 3 p270and90sidewalltheatand

13k p

180floor theatand0roof theatthen

cos2k 12k 1 p0and

ar opening,theAt

z

00

z

0

0

z

r r

==

==

=

+==

=


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( )

( )k 3 p270and90sidewalltheatand

13k p

180floor theatand

0roof theatand

ar opening,theAt

z

00

z

0

0

==

=

=

=

=

Tension in Roof and Floor when k < 0.33


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Stresses away from opening

At r=3a, induced/applied stress =1

Keep adjacent opening 3 to 4

times the maximum diameteraway


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Biaxial Stress Field in EllipticalOpening

{ }

{ }( ){ }

( ){ }

Catcurvatureof radius

Aatcurvatureof radius12H/ 1k p

12H/W1k pk 2W/ 1 p

k -2W/H1 pstresses boundarytangentialthe

ar opening,theAt

C

A

Cz

zC

Az

zA

==

+=

+=+=

+=

=

The smaller the radius of curvature, thehigher the compressive stress concentration

Sharper end attractsmore stressconcentration thanflatter end


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General Principles:

Opening with sharp corners should be avoided

Optimal shape for an opening in a hydrostatic stress field (k=1)

is a circleFor k not equal to 1, the lowest boundary stresses is from an opening of ovaloidal shape

Example of an optimal opening shape

A

Minimum boundary stress by matching theaxis ratio withthe in situ stressratio

1

2 Lower boundary

stress byincreasing theradius at A


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vh /k =

For Plane Strain Conditions

Radial Displacement, u

Tangential Displacement, v

E = Young Modulus

= Poissons ratio

( ) ( )

+= cos2r

a)-4(1114Gr

u 2

22v

r k k a

( )

= sin2r a

)2-2(114Gr

u 2

22v

k

a


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Since 1990, hydraulic fracturing stress measurements were carried out from:

Route-3 tunnel-project,

Tsing

Yi island

Strategic Sewage Disposal Scheme at Mount Davis and North Point,

Hong Kongisland

Lantau

Fixed Crossing-Tsing

Ma Bridge Anchorage,

Tsing

Yi island

MTR Quarry Bay (Hong Kong island) and Tseung Kwan O

(Kowloon) extension

Additional Treatment and Water Transfer Facilities for the Metropolitan Area and North-

Eastern New Territories

KCR West Rail Central Section extension (New Territories)


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G. Klee, F. Rummel, A.Williams. InternationalJournal of Rock Mechanicsand Mining Sciences 36

(1999) 731-741


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Lecture2(Insitu&InducedStress)