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

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

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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

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

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

Intact rock: D=0

Fractured rock at the edge of failure: D= Dcr

rock mass quality measure = damage measure

3.936

4.167

Hoek-Brown constant

for disturbed rock mass:

Uniaxial strength: exponential form

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 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.

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)

Damage model:

Empirical relations:

average:

MR=Modification Ratio

• Outlook

• Linear elasticity:

• damage: scalar, vector, tensor, …

• Nonideal damage and thermodynamics:

• damage evolution

• Second Law is violated

Real world –

Second Law is valid

Ideal world –

there is no dissipation

Thermodinamics - Mechanics

Damage model:

Empirical relations:

average:

MR=Modification Ratio

Zhang, 2009