A Creep Damage Model for Rock Mass Based on Internal Variable Theory

Abstract:

The creep damage is discussed within Rice thermodynamic theory with internal state variable (ISV). A viscoelastic-viscoplastic model with damage is derived by giving the complementary energy density function and kinetic equations of ISVs. The viscoelastic equation covers classical component model, and three creep phases with hardening and damage effect can be described by this model. The model parameter cabibration is conducted through uniaxial creep test of analogue material by loading and unloading method. Then intrinsic thermodynamic properties in three creep stages are indicated. The thermodynamic state of material system tends to equilibrate without damage and depart from equilibrate with damage.

• Periodical: Applied Mechanics and Materials (Volume 784)
• Pages: 19-26
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.784.19
• Online since: August 2015
• Authors: Yao Ru Liu*, Long Zhang, Qiang Yang
• Keywords: Creep Damage Model, Equilibrium State, Internal State Variable Theory, Intrinsic Thermodynamic Properties, Three Creep Stage

References

[1] A.A. Fakhimi, C. Fairhurst, A model for the Time-dependent behavior of rock. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 31 (1994) 117-126.

[2] D.F. Malan, Simulating the time-dependent behavior of excavation in hard rock. Rock Mech. Rock Eng. 35 (2002) 225-254.

DOI: 10.1007/s00603-002-0026-0

[3] Z. Hou, Mechanical and hydraulic behavior of rock salt in the excavation disturbed zone around underground facilities. Int. J. Rock Mech. Min. Sci. 40 (2003) 725-738.

DOI: 10.1016/s1365-1609(03)00064-9

[4] G.N. Boukharov, M.W. Chanda, N.G. Boukharov, The three processes of brittle crystalline rock creep. In. J. Rock Mech. Min. Sci & Geomech. Abstr. 32 (1995) 325-335.

DOI: 10.1016/0148-9062(94)00048-8

[5] W.M. Wang, L.J. Sluys, R.D. Borst, Viscoplasticity for instability due to strain softening and strain-rate softeting. Int. J. Numer. Meth. Eng. 40 (1997) 839-3 864.

DOI: 10.1002/(sici)1097-0207(19971030)40:20<3839::aid-nme245>3.0.co;2-6

[6] J.S. Jin, N.D. Cristescu, An elastic/viscoplastic model for transient creep of rock salt. Int. J. Plast. 14 (1998) 85-107.

DOI: 10.1016/s0749-6419(97)00042-9

[7] N. Cristescu, Damge and failure of viscopalstic rock-like material. Int.J. Plast. 2(1986)189-204.

[8] K.S. Chan, S. R. Bodner, A. F. Fossum, D. E. Munson, A damage mechanics treatment of creep failure in rock salt. Int. J. Damage Mech. 6 (1997) 122-152.

DOI: 10.1177/105678959700600201

[9] J. Betten, S. Sklepus, A. Zolochevsky, A creep damage model for initially isotropic materials with different properties in tension and compression. Eng. Fract. Mech. 59 (1998) 623-641.

DOI: 10.1016/s0013-7944(97)00143-4

[10] M.F. Horstemeyer, D.J. Bammann, Historical review of internal state variable theory for inelasticity. Int. J. Plast. 26 (2010) 1310-1334.

DOI: 10.1016/j.ijplas.2010.06.005

[11] J. Lubliner, On the thermodynamic foundations of non-linear solids mechanics. Int. J. Non-Linear Mech. 7 (1972) 237-254.

DOI: 10.1016/0020-7462(72)90048-0

[12] S.W. Park, R.A. Schapery, A viscoelastic constitutive model for particulate composites with growing damage. Int. J. Solids Struct. 34 (1997) 931-947.

DOI: 10.1016/s0020-7683(96)00066-2

[13] H. R. Zhu, L. Sun, A viscoelastic-viscoplastic damage constitutive model for asphalt mixtures based on thermodynamics. Int. J. Plast. 40 (2013) 81-100.

DOI: 10.1016/j.ijplas.2012.07.005

[14] J.L. Chaboche, Thermodynamic formulation of application to the viscoplasticity and viscoelasticity of metal and polymers. Int. J. Solids. Struct. 34 (1997) 2239-2254.

DOI: 10.1016/s0020-7683(96)00162-x

[15] R.A. Schapery, Nonlinear Viscoelastic and Viscoplastic Constitutive Equations Based on Thermodynamics. Mech. Time Depend. Mater. 1 (1997) 209-240.

[16] G. Z. Voyiadjis, A. Zolochevsky, Thermodynamic modeling of creep damage in materials with different properties in tension and compression. Int. J. Solids Struct. 37 (2000) 281- 303.

DOI: 10.1016/s0020-7683(99)00031-1

[21] N.R. Hansen, H.L. Schreyer, A thermodynamically consistent framework for theories of elastoplasticity coupled with damage. Int. J. Solids. Struct. 3 (1994) 359-389.

DOI: 10.1016/0020-7683(94)90112-0

[17] J.R. Rice, Inelastic constitutive relation for solids: an internal- variable theory and its application to metal plasticity. J. Mech. Phys. 19 (1971) 433-455.

DOI: 10.1016/0022-5096(71)90010-x

[18] W.H. Haslach, A non-equilibrium thermodynamic geometric structure for thermoviscoplasticity with maximum dissipation. Int. J. Plast. 18 (2002) 127-153.

DOI: 10.1016/s0749-6419(00)00046-2

[19] Q. Yang, Y. R. Liu, J.Q. Bao, Hamilton's principle of entropy production for creep and relaxation processes. J. Eng. Mater. Technol. 132 (2010) 0110181-0110185.

[20] Q. Yang, X. Chen, W. Y. Zhuo, Microscopic thermodynamic basis of normality structure of inelastic constitutive relations. Mech. Res. Commun. 32 (2005) 590-596.

DOI: 10.1016/j.mechrescom.2005.01.009

[21] H. Ziegler, An Introduction to Thermomechanics. North-Holland, Amsterdam, (1977).

[22] Q. Yang, X. Chen, W. Y. Zhuo, On multiscale significance of Rice's normality structure. Mech. Res. Commun. 33 (2006) 667-673.

[23] L. Zhang, Y.R. Liu, Q. Yang, L.J. Xue, An internal state variable viscoelastic-viscoplastic constitutive equation with damage. Chin.J. Theor. Appl. Mech. 46(2014) 572-581.

[24] M. Aubertin, D.E. Gill, B. Ladanyi, An internal variable model for the creep of rocksalt. Rock Mech. Rock Eng. 24(1991) 81–97.

DOI: 10.1007/bf01032500

[25] L. Zhang, Y.R. Liu, Q. Yang, A Evaluation of reinforcement and analysis of stability of high arch dam based on gaomechanical model testing. Rock Mech. Rock Eng. 48(2015) 572-581.

DOI: 10.1007/s00603-014-0578-9

[26] Y. S. Li, C. C. Xia, Time-dependent tests on intact rocks in uniaxial compression. Int. J. Rock Mech. Min. Sci. 37(2000) 467-475.

DOI: 10.1016/s1365-1609(99)00073-8