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Deformation moduli and strength of the rock mass Thermo-damage mechanics

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

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Deformation moduli and strength of the rock mass Thermo-damage mechanics

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  1. Deformation moduli and strength of the rock mass Thermo-damage mechanics Summary, conclusions and outlook Relation of rock mass characterization and damage Ván P.13and Vásárhelyi B.231RMKI, Dep. Theor. Phys., Budapest, Hungary, 2Vásárhelyi and Partner Geotechnical Engng. Ltd. Budapest, Hungary,3Montavid Thermodynamic Research Group, Budapest, Hungary

  2. 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

  3. 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

  4. Using a damage variable - D Intact rock: D=0 Fractured rock at the edge of failure: D= Dcr rock mass quality measure = damage measure

  5. Deformation modulus: exponential form 3.936 4.167 Hoek-Brown constant for disturbed rock mass:

  6. Uniaxial strength: exponential form

  7. 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.

  8. 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.

  9. Summary a = 22.52…(25.41)…38.11 average: 30 (or 23.7, with disturbed) b = 13.07…24.00 average: 18.76 (or 20.19, without Yudhbi)

  10. Conclusions Damage model: Empirical relations: average: MR=Modification Ratio

  11. Outlook • Linear elasticity: • damage: scalar, vector, tensor, … • Nonideal damage and thermodynamics: • damage evolution • damage gradients

  12. Thank you for your attention!

  13. Impossible world – Second Law is violated Real world – Second Law is valid Ideal world – there is no dissipation Thermodinamics - Mechanics

  14. Conclusions Damage model: Empirical relations: average: MR=Modification Ratio Zhang, 2009

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