Deformation moduli and strength of the rock mass
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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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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

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


Deformation moduli and strength of the rock mass thermo damage mechanics

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


Deformation moduli and strength of the rock mass thermo damage mechanics

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


Deformation moduli and strength of the rock mass thermo damage mechanics

Using a damage variable - D

Intact rock: D=0

Fractured rock at the edge of failure: D= Dcr

rock mass quality measure = damage measure


Deformation moduli and strength of the rock mass thermo damage mechanics

Deformation modulus: exponential form

3.936

4.167

Hoek-Brown constant

for disturbed rock mass:


Deformation moduli and strength of the rock mass thermo damage mechanics

Uniaxial strength: exponential form


Deformation moduli and strength of the rock mass thermo damage mechanics

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.


Deformation moduli and strength of the rock mass thermo damage mechanics

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.


Deformation moduli and strength of the rock mass thermo damage mechanics

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)


Deformation moduli and strength of the rock mass thermo damage mechanics

Conclusions

Damage model:

Empirical relations:

average:

MR=Modification Ratio


Deformation moduli and strength of the rock mass thermo damage mechanics

  • Outlook

  • Linear elasticity:

    • damage: scalar, vector, tensor, …

  • Nonideal damage and thermodynamics:

    • damage evolution

    • damage gradients


  • Deformation moduli and strength of the rock mass thermo damage mechanics

    Thank you for your attention!


    Deformation moduli and strength of the rock mass thermo damage mechanics

    Impossible world –

    Second Law is violated

    Real world –

    Second Law is valid

    Ideal world –

    there is no dissipation

    Thermodinamics - Mechanics


    Deformation moduli and strength of the rock mass thermo damage mechanics

    Conclusions

    Damage model:

    Empirical relations:

    average:

    MR=Modification Ratio

    Zhang, 2009


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