Relation of rock mass characterization and damage V

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Relation of rock mass characterization and damage
Ván P.13 and Vásárhelyi B.23 1RMKI, Dep.
Theor. Phys., Budapest, Hungary, 2Vásárhelyi and
Partner Geotechnical Engng. Ltd. Budapest,
Hungary, 3Montavid Thermodynamic Research Group,
Budapest, Hungary

• Deformation moduli and strength of the rock mass
• Thermo-damage mechanics
• Summary, conclusions and outlook

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Deformation modulus of the rock mass (Erm)
formulas containing the elastic modulus of
intact rock (Ei)
3 Nicholson and Bieniawski (1990) 8 Sonmez
et. al. (2004) Carvalcho (2004)
Zhang and Einstein (2004)
Hoek Diederichs, 2006
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Unconfined compressive strength of the rock mass
(scm) formulas containing the strength of
intact rock (sc)

• Yudhbir et al. (1983) )
• Ramamurthy et al. (1985)
• Kalamaras Bieniawski (1993)
• Hoek et al. (1995)
• Sheorey (1997)

scm/sc exp(7.65((RMR-100)/100)
scm/sc exp((RMR-100)/18.5)
scm/sc exp((RMR-100)/25)
scm/sc exp((RMR-100)/18)
scm/sc exp((RMR-100)/20)
Zhang, 2005
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Using a damage variable - D Intact rock
D0 Fractured rock at the edge of failure D
Dcr rock mass quality measure damage
measure
Intact rock Fractured rock
RMR scales 100 0
Damage scales 0 Dcr
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Deformation modulus exponential form
Equation A
Nicholson Bieniawski (1990) 4.358
Zhang Einstein (2004) 4.440
Sonmez et al. (2004) 2.624
Carvalho (2004) 2.778
3.936 4.167
Hoek-Brown constant for disturbed rock mass
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Uniaxial strength exponential form
Equation B
Yudhbi et al. (1983) 7.650
Ramamurthy et al. (1985) 5.333
Kalamaras Bieniawski (1993) 4.167
Hoek et al. (1995) 5.556
Sheorey (1997) 5.000
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Thermo-damage mechanics I. Thermostatic
potential Helmholtz free energy linear
elasticity damaged rock Energetic
damage Consequence
The energy content of more deformed rock mass is
more reduced by damage.
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Thermo-damage mechanics II. Deformation
modulus exponential, like the empirical
data. Strength thermodynamic stability (Ván
and Vásárhelyi, 2001) (convex free energy,
positive definite second derivative)
exponential, like the empirical data.
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Summary
Equation a
Nicholson Bieniawski (1990) 22.95
Zhang Einstein (2004) 22.52
Sonmez et al. (2004) 38.11 (25.41)
Carvalho (2004) 36.00 (24.00)
a 22.52(25.41)38.11 average 30 (or 23.7,
with disturbed)
Equation b
Yudhbi et al. (1983) 13.07
Ramamurthy et al. (1985) 18.75
Kalamaras Bieniawski (1993) 24.00
Hoek et al. (1995) 18.00
Sheorey (1997) 20.00
b 13.0724.00 average 18.76 (or 20.19, without
Yudhbi)
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Conclusions
Damage model Empirical relations
average
MRModification Ratio
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• Outlook
• Linear elasticity
• damage scalar, vector, tensor,
• Nonideal damage and thermodynamics
• damage evolution
• damage gradients

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Thank you for your attention!
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Thermodinamics - Mechanics
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Conclusions
Damage model Empirical relations
average
MRModification Ratio
Zhang, 2009