Skip to main content
Log in

Thermodynamic aspects of rock friction

  • Published:
Acta Geodaetica et Geophysica Aims and scope Submit manuscript

An Erratum to this article was published on 17 January 2015

Abstract

Rate- and state-dependent friction law for velocity-step tests is analyzed from a thermodynamic point of view. A simple macroscopic non-equilibrium thermodynamic model with a single internal variable reproduces instantaneous jump and relaxation. Velocity weakening appears as a consequence of a plasticity related nonlinear coefficient. Permanent part of displacement corresponds to plastic strain, and relaxation effects are analogous to creep in thermodynamic rheology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Aki K, Richards PG (2002) Quantitative seismology, 2nd edn. University Science Books, Sausalito

    Google Scholar 

  • Baumberger T, Caroli C (2006) Solid friction from stick-slip down to pinning and aging. Adv Phys 55:279–348. doi:10.1080/00018730600732186

    Article  Google Scholar 

  • Bowden FP, Tabor D (1950) The friction and lubrication of solids. Clarendon Press, Oxford

    Google Scholar 

  • Brechet Y, Estrin Y (1994) The effect of strain rate sensitivity on dynamic friction of metals. Scr Metall et Mater 30:1449–1454. doi:10.1016/0956-716X(94)90244-5

    Article  Google Scholar 

  • Cimmelli VA, Jou D, Ruggeri T, Ván P (2014) Conceptual analysis of the entropy principle in continuum physics.

  • de Groot SR, Mazur P (1962) Non-equilibrium thermodynamics. North-Holland Publishing Company, Amsterdam

    Google Scholar 

  • Dieterich JH (1972) Time-dependent friction in rocks. J Geophys Res 77:3690–3697. doi:10.1029/JB077i020p03690

    Article  Google Scholar 

  • Dieterich JH (1978) Time-dependent friction and the mechanics of stick-slip. Pure Appl Geophys 116:790–806. doi:10.1007/BF00876539

    Article  Google Scholar 

  • Dieterich JH (1979) Modeling of rock friction 1. experimental results and constitutive equations. J Geophys Res 84:2161–2168. doi:10.1029/JB084iB05p02161

    Article  Google Scholar 

  • Eyring H (1935) The activated complex in chemical reactions. J Chem Phys 3:107–115. doi:10.1063/1.1749604

    Article  Google Scholar 

  • Eyring H (1936) Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J Chem Phys 4:283–291. doi:10.1063/1.1749836

    Article  Google Scholar 

  • Fülöp T (2008) Rheological circuit diagrams. In: Asszonyi Cs (ed) Material properties of isotropic continua, Pocket Library in Engineering Geology and Rock Mechanics, vol 6, chap 3, BME Publisher, Budapest, pp 93–120 (in Hungarian)

  • Fülöp T, Ván P (2012) Kinematic quantities of finite elastic and plastic deformations. Math Meth Appl Sci 35:1825–1841. doi:10.1002/mma.2558

    Article  Google Scholar 

  • Fülöp T, Asszonyi C, Ván P (2014) Distinguished rheological models in the framework of a thermodynamical internal variable theory

  • Heslot F, Baumberger T, Perrin B, Caroli B, Caroli C (1994) Creep, stick-slip, and dry-friction dynamics: experiments and a heuristic model. Phys Rev E 49:4973–4988. doi:10.1103/PhysRevE.49.4973

    Article  Google Scholar 

  • Houlsby GT, Puzrin AM (2006) Principles of hyperplasticity (An approach to plasticity theory based on thermodynamic principles). Springer, London

    Google Scholar 

  • Kato N, Tullis TE (2001) A composite rate- and state-dependent law for rock friction. Geophys Res Lett 28:1103–1106. doi:10.1029/2000GL012060

    Article  Google Scholar 

  • Kawamura H, Hatano T, Kato N, Biswas S, Chakrabarti BK (2012) Statistical physics of fracture, friction, and earthquakes. Rev Mod Phys 84:839–884. doi:10.1103/RevModPhys.84.839

  • Lin W, Kuwahara Y, Satoh T, Shigematsu N, Kitagawa Y, Kiguchi T, Sato T, Tsukamoto H, Itaba S, Umeda Y, Seki Y, Takahashi M, Matsumoto N, Koizumi N (2010) A case study of 3d stress orientation determination in Shikoku Island and Kii Peninsula, Japan. In: Vrkljan I (ed) Rock engineering in difficult ground conditions (soft rock and karst). Balkema, London, pp 277–282

  • Linker MF, Dieterich JH (1992) Effects of variable normal stress on rock friction. J Geophys Res 97(B4):4923–4940

    Article  Google Scholar 

  • Mair K, Marone C (1999) Friction of simulated fault gouge for a wide range of velocities and normal stresses. J Geophys Res 104(B12):28899–28914

    Article  Google Scholar 

  • Marone C (1998) Laboratory-derived friction laws and their application to seismic faulting. Annu Rev Earth Planet Sci 26:643–696. doi:10.1146/annurev.earth.26.1.643

    Article  Google Scholar 

  • Marone C, Raleigh CB, Scholz CH (1990) Frictional behavior and constitutive modeling of simulated fault gouge. J Geophys Res 95:7007–7025

    Article  Google Scholar 

  • Matolcsi T (2005) Ordinary thermodynamics. Akadémiai Kiadó (Publishing House of the Hungarian Academy of Sciences), Budapest

  • Matsuki K (2008) Anelastic strain recovery compliance of rocks and its application to in situ stress measurement. Int J Rock Mech Min Sci 45:952–965. doi:10.1016/j.ijrmms.2007.10.005

    Article  Google Scholar 

  • Maugin G (1999) The thermomechanics of nonlinear irreversible behaviors: an introduction. World Scientific, Singapore-New Jersey-London-Hong Kong

    Google Scholar 

  • Maugin GA, Muschik W (1994) Thermodynamics with internal variables. part i. Gen concepts. J Non-Equilib Thermodyn 19:217–249. doi:10.1515/jnet.1994.19.3.217

    Google Scholar 

  • Maugin GA, Muschik W (1994) Thermodynamics with internal variables. Part II Applications. J Non-Equilib Thermodyn 19:250–289. doi:10.1515/jnet.1994.19.3.250

    Google Scholar 

  • Nagata K, Nakatani M, Yoshida S (2012) A revised rate- and state-dependent friction law obtained by constraining constitutive and evolution laws separately with laboratory data. J Geophys Res 117:B02314. doi:10.1029/2011JB008818

    Google Scholar 

  • Nakatani M (2001) Conceptual and physical clarification of rate and state friction: frictional sliding as a thermally activated rheology. J Geophys Res 106:13,347–13,380. doi:10.1029/2000JB900453

    Article  Google Scholar 

  • Perrin G, Rice JR, Zheng G (1995) Self-healing slip pulse on a frictional surface. J Mech Phys Solids 43:1461–1495. doi:10.1016/0022-5096(95)00036-I

    Article  Google Scholar 

  • Polrier J-P (1985) Creep of Crystals. Cambridge University Press, New York

    Book  Google Scholar 

  • Putelat T, Dawes JHP, Willis JR (2011) On the microphysical foundations of rate-and-state friction. J Mech Phys Solids 59:1062–1075. doi:10.1016/j.jmps.2011.02.002

    Article  Google Scholar 

  • Ruina A (1983) Slip instability and state variable friction laws. J Geophys Res 88:10359–10370. doi:10.1029/JB088iB12p10359

    Article  Google Scholar 

  • Rusinko A, Rusinko K (2011) Plasticity and Creep of Metals. Springer, Berlin

    Book  Google Scholar 

  • Ván P (2010) Thermodynamics of plasticity. In: Fülöp T (ed) Time and space derivatives in material laws, Pocket Library in Engineering Geology and Rock Mechanics, Vol. 10, BME Publisher, Budapest, pp 15–50 (in Hungarian)

  • Vásárhelyi B (1998) Influence of normal load on joint dilatation rate. Rock Mech Rock Eng 31(2):117–123

    Article  Google Scholar 

  • Vásárhelyi B, Ván P (2006) Shearing test with continuously increasing normal stress. Period Polytech Ser Civil Eng 50(2):171–180

    Google Scholar 

  • Verhás J (1997) Thermodynamics and Rheology. Akadémiai Kiadó and Kluwer Academic Publisher, Budapest

    Google Scholar 

  • Ziegler H (1983) An introduction to thermomechanics, 2nd edn. North-Holland Publishing Company, Amsterdam-New York-Oxford

    Google Scholar 

Download references

Acknowledgments

The authors thank to Tamás Fülöp for valuable discussions. This manuscript was greatly improved by the comments of anonymous reviewers. The work was supported by the Grant Otka K81161 and K104260. N. Mitsui was supported by Canon Foundation in Europe.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Mitsui.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mitsui, N., Ván, P. Thermodynamic aspects of rock friction. Acta Geod Geophys 49, 135–146 (2014). https://doi.org/10.1007/s40328-014-0048-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40328-014-0048-6

Keywords

Navigation