Post on 05-Apr-2018
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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