This presentation is the property of its rightful owner.
1 / 14

# 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.

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

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

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 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

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

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 modulus: exponential form

3.936

4.167

Hoek-Brown constant

for disturbed rock mass:

Uniaxial strength: exponential form

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.

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.

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)

Conclusions

Damage model:

Empirical relations:

average:

MR=Modification Ratio

• Outlook

• Linear elasticity:

• damage: scalar, vector, tensor, …

• Nonideal damage and thermodynamics:

• damage evolution

• Thank you for your attention!

Impossible world –

Second Law is violated

Real world –

Second Law is valid

Ideal world –

there is no dissipation

Thermodinamics - Mechanics

Conclusions

Damage model:

Empirical relations:

average:

MR=Modification Ratio

Zhang, 2009