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Tunnels and Induced Stress

EOSC316 Engineering Geoscience

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Tunnels and induced stress

Analysis of stress around underground

cavities Methods employed for tunnelling

Improving rock quality Tunnel monitoring

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Induced stress around a hole

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Stress intensity around flaws

(b) an elliptical hole(a) a circular hole

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How do we analyse the stress

around a hole?

Kirsch solution (1898)

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Kirsch solution

Polar co-ordinates

r

(r, )

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Kirsch solution

r

r

r

r

r

radial stress

tangential stress

shear stress

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Kirsch solution

Stress components at point (r, )

Radial: r = 0.5pz[(1+k)(1-a2/r2)+(1-k)(1-4a2/r2+3a4/r4)cos2]

Tangential:

= 0.5pz[(1+k)(1-a2/r2)-(1-k)(1+3a4/r4)cos2]

Shear:

r = 0.5pz[-(1-k)(1+2a2

/r2

-3a4

/r4

)sin2]

k = horizontal applied stress / vertical applied stress

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Observations from the Kirsch

solution Radial and shear stresses are zero at the

boundary of the opening (r = a) In the roof and the floor (0 and 180

degrees): for k = 0, the stresses are tensional

for k = 0.33, the stresses are zero

for k > 0.33, the stresses around the entireboundary are compressional

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Observations from the Kirsch

solution

Sidewall stresses (90 and 270 degrees)

for k = 0, the stresses are a maximum of 3 x

applied vertical stress for k = 1, stresses are 2 x applied vertical

stress

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Complexities of modelling stress

Shape

Multiple openings 3D effects

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Numerical solutions

Analytical solutions are possible for problems

with simple boundary conditions

Numerical methods must be employed for

complex boundary conditions Boundary methods, boundary of excavation divided

into elements, rock mass represented by continuum

Domain methods, rock mass divided intogeometrically simple elements with assumedproperties

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Tunnelling methods

Drill and blast

Roadheader

Tunnel boringmachine

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Channel tunnel,

Europe, 1992

50 km long, twin bores 7.6 m

diameter

In impermeable chalk marl

low fissure density

UCS 5 9 MPa

Cut by TBM

Lined with pre-fab concrete

segments

Kept 20 m sound rock betweentunnel and seabed

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Improving tunnelling rock quality

Advance ground improvement

Spiling Active support

Rock bolts

Shotcrete

Passive support

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Improving tunnelling rock quality

Rock bolts

Shotcrete

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Underground Research Laboratory,

Canada

To test viability ofhigh level waste at

depth

Max/min stress ratio

~5:1

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Underground Research Laboratory,

Canada

Tunnel alongintermediate principal

stress

Max/min stress ratio

~5:1

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Underground Research Laboratory,

Canada

Sealing experiment AE monitoring

Hydraulic pressure ofup to 4 MPa