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

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

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slide1
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

slide2

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

slide3

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

slide4

Using a damage variable - D

Intact rock: D=0

Fractured rock at the edge of failure: D= Dcr

rock mass quality measure = damage measure

slide5

Deformation modulus: exponential form

3.936

4.167

Hoek-Brown constant

for disturbed rock mass:

slide7

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.

slide8

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.

slide9

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)

slide10

Conclusions

Damage model:

Empirical relations:

average:

MR=Modification Ratio

slide11

Outlook

  • Linear elasticity:
        • damage: scalar, vector, tensor, …
  • Nonideal damage and thermodynamics:
      • damage evolution
      • damage gradients
slide13

Impossible world –

Second Law is violated

Real world –

Second Law is valid

Ideal world –

there is no dissipation

Thermodinamics - Mechanics

slide14

Conclusions

Damage model:

Empirical relations:

average:

MR=Modification Ratio

Zhang, 2009

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