Skip to main content
SpringerLink
Log in

Coupled Thermo-mechanical Behavior of Weakening Geo-Materials

  • Original Paper
  • Published:
Geotechnical and Geological Engineering Aims and scope Submit manuscript

Abstract

In this paper, the overall effective thermo-mechanical properties of limestone samples are estimated using a micro–macro mechanical approach. A mathematical framework is proposed to estimate the overall properties based on local geometrical considerations using Mori–Tanaka’s scheme. In addition, a homogenization-based mathematical formulation is proposed to predict the effective thermal conductivity of composite materials subjected to periodic micro-scale heat fluxes and governed by Fourier’s law and steady state balance equations. Moreover, Coussy’s approach is used to derive the expression of heat capacity. In order to take into account the degradation of heterogeneous rock materials, a damage based numerical model that uses the homogenized thermo-mechanical properties and Griffith’s criterion is proposed. The model is implemented as an external user material subroutine to the multi-purpose finite element software Abaqus, to assess the damage of a limestone rock sample under normal percussion drilling conditions. Moreover, a model parameter identification procedure is performed to calibrate the necessary parameters using a simple indentation test. The obtained results show that the numerical model can reproduce the elastic damaged behavior of rocks, such as limestone, subjected to a simple indentation that mimic the conditions of rock drilling. Finally, the proposed analysis proves that effect of temperature on the overall behavior of limestone can be investigated using multi-physics upscaling.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

References

  • Aboudi J (1991) Mechanics of composite materials: a unified micromechanical approach, vol 93. Elsevier, Amsterdam

    Google Scholar 

  • Asef MR, Najibi AR (2013) The effect of confining pressure on elastic wave velocities and dynamic to static Young’s modulus ratio. Geophysics 78(3):D135–D142. https://doi.org/10.1190/geo2012-0279.1

    Article  Google Scholar 

  • Benveniste Y (1987) A new approach to the application of Mori–Tanaka’s theory in composite materials. Mech Mater 6:147–157

    Article  Google Scholar 

  • Bornert M, Brethau T, Gilormini P (2001) Homogénéisation En Mécanique Des Matériaux 1: Matériaux Aléatoires Elastiques Et Milieux Périodiques. Hermes Science Publications, Paris

    Google Scholar 

  • Budiansky B (1983) Micromechanics. Comput Struct 16(1–4):3–12

    Article  Google Scholar 

  • Chen L, Wang C, Liu J, Liu Y, Liu J, Su R, Wang J (2014) A damage-mechanism based creep model considering temperature effect in granite. Mech Res Commun 56:76–82

    Article  Google Scholar 

  • Christensen RM, Lo KH (1979) Solutions for effective shear properties in three phase sphere and cylinder models. J Mech Phys Solids 27(4):315–330. https://doi.org/10.1016/0022-5096(79)90032-2.

    Article  Google Scholar 

  • Coussy O (2004) Poromechanics. Wiley, Chichester

    Google Scholar 

  • Detournay E, Huang H, Fairhurst C (1998) Normal wedge indentation of rocks by a wedge-shaped tool I: theoretical model. Int J Rock Mech Min Sci Geomech Abstr (submitted)

  • Dormieux L, Kondo D, Ulm F (2006) Microp oromechanics, 1st edn. Wiley, Chichester

    Book  Google Scholar 

  • Eshelby J (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond A Math Phys Sci 241(1226):376–396

    Article  Google Scholar 

  • Gabssi N, Karrech A, Hamdi E (2017) A micromechanical approach for anisotropic rock mass thermo-mechanical properties estimation. Procedia Eng 191:369–377

    Article  Google Scholar 

  • Gabssi N, Souissi S, Hamdi E, Karrech A (2018) Micro-mechanical damage model for geomaterials behavior under indentation. In: TuniRock, Tunisia, DDM, pp 157–162

  • Gaede O, Karrech A, Regenauer-Lieb K (2013) Anisotropic damage mechanics as a novel approach to improve pre- and post-failure borehole stability analysis. Geophys J Int 193(3):1095–1109. https://doi.org/10.1093/gji/ggt045

    Article  Google Scholar 

  • Hamdi E, Romdhane NB, Le Cléac’h JM (2011) A tensile damage model for rocks: application to blast induced damage assessment. Comput Geotech 38(2):133–141. https://doi.org/10.1016/j.compgeo.2010.10.009

    Article  Google Scholar 

  • Hashin Z, Shtrikman S (1962a) A variational approach to the theory of the elastic behaviour of polycrystals. J Mech Phys Solids 10:343–352

    Article  Google Scholar 

  • Hashin Z, Shtrikman S (1962b) On some variational principles in anisotropic and nonhomogeneous elasticity. J Mech Phys Solids 10(42):335–342

    Article  Google Scholar 

  • Hashin Z, Shtrikman S (1963) A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids 11(42):127–140

    Article  Google Scholar 

  • Hill R (1952) The elastic behavior of a crystalline aggregate. Proc Phys Soc Lond 65A:349–354

    Article  Google Scholar 

  • Hill R (1965) Self-cconsistent mechanics of composite materials. J Mech Phys Solids 13:213–222

    Article  Google Scholar 

  • Huang H, Damjanac B, Detournay E (1998) Normal wedge indentation in rocks with lateral confinement. Rock Mech Rock Eng 31(2):81–94

    Article  Google Scholar 

  • Huengens E (1988) Thermal properties of rocks and. Technical report, Reston, Virginia

  • Ihara I (2008) Ultrasonic sensing: fundamentals and its applications to nondestructive evaluation. In: Mukhopadhyay S, Huang R (eds) Sensors. Lecture notes electrical engineering, vol 21. Springer, Berlin

    Chapter  Google Scholar 

  • Karrech A (2013) Non-equilibrium thermodynamics for fully coupled thermal hydraulic mechanical chemical processes. J Mech Phys Solids 61(3):819–837. https://doi.org/10.1016/j.jmps.2012.10.015

    Article  Google Scholar 

  • Karrech A, Schrank C, Freij-Ayoub R, Regenauer-Lieb K (2014) A multi-scaling approach to predict hydraulic damage of poromaterials. Int J Mech Sci 78:1–7. https://doi.org/10.1016/j.ijmecsci.2013.10.010

    Article  Google Scholar 

  • Karrech A, Abbassi F, Basarir H, Attar M (2017) Self-consistent fractal damage of natural geo-materials in finite strain. Mech Mater 104:107–120

    Article  Google Scholar 

  • Lemaitre J (1996) A course on damage mechanics. https://doi.org/10.1007/978-3-642-18255-6_4

  • Liu H, Kou S, Lindqvist P, Tang C (2002) Numerical simulation of the rock fragmentation process induced by indenters. Int J Rock Mech Min Sci 39:491–505

    Article  Google Scholar 

  • Liu J, Karrech A, Regenauer-Lieb K (2014) Combined mechanical and melting damage model for geomaterials. Geophys J Int 198(3):1319–1328. https://doi.org/10.1093/gji/ggu200

    Article  Google Scholar 

  • Mao X, Zhang L, Li T, Liu H (2009) Properties of failure mode and thermal damage for limestone at high temperature. Min Sci Technol 19(3):290–294

    Google Scholar 

  • Motiand T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21:571–574

    Article  Google Scholar 

  • Peters M, Veveakis M, Poulet T, Karrech A, Herwegh M, Regenauer-Lieb K (2015) Boudinage as a material instability of elasto–visco-plastic rocks. J Struct Geol 78:86–102. https://doi.org/10.1016/j.jsg.2015.06.005

    Article  Google Scholar 

  • Poulet T, Karrech A, Regenauer-Lieb K, Fisher L, Schaubs P (2012) Thermal–hydraulic–mechanical–chemical coupling with damage mechanics using escriptrt and abaqus. Tectonophysics 526–529:124–132. https://doi.org/10.1016/j.tecto.2011.12.005

    Article  Google Scholar 

  • Punturo R, Kern H, Cirrincione R, Mazzoleni P, Pezzino A (2005) P- and S-wave velocities and densities in silicate and calcite rocks from the Peloritani Mountains, Sicily (Italy): the effect of pressure, temperature and the direction of wave propagation. Tectonophysics 409(1–4):55–72. https://doi.org/10.1016/j.tecto.2005.08.006

    Article  Google Scholar 

  • Rosenholtz JL, Smith DT (1949) Linear thermal expansion of calcite, var. Iceland spar, and Yule Marble. Am Miner 34:846–854. http://www.minsocam.org/ammin/AM34/AM34_846.pdf

  • Schmidt R, Huddle C (1977) Effect of confining pressure on fracture toughness of Indiana limestone. Int J Rock Mech Min Sci Geomech Abstr 14(5–6):289–293. https://doi.org/10.1016/0148-9062(77)90740-9

    Article  Google Scholar 

  • Schrank C, Fusseis F, Karrech A, Regenauer-Lieb K (2012) Thermal-elastic stresses and the criticality of the continental crust. Geochem Geophys Geosyst 13:Q09005. https://doi.org/10.1029/2012gc004085

    Article  Google Scholar 

  • Somerton W (1992) Heat capacities of rocks. Dev Pet Sci 37(100):8–21. https://doi.org/10.1016/S0376-7361(09)70022-6

    Article  Google Scholar 

  • Souissi S, Hamdi E, Sellami H (2015) Microstructure effect on hard rock damage and fracture during indentation process. Geotech Geol Eng 33(6):1539–1550. https://doi.org/10.1007/s10706-015-9920-6

    Article  Google Scholar 

  • Souissi S, Miled K, Hamdi E, Hedi S (2017) Numerical modelling of rocks damage during indentation process with reference to hard rock drilling. Int J Geomech. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000862

    Article  Google Scholar 

  • Steif PS (1984) Crack extension under compressive loading. Eng Fract Mech 20(3):463–473

    Article  Google Scholar 

  • Wang X, Wang QF, Pei Y, Okan L, Lin S (2018) Dominant cutting parameters affecting the specific energy of selected sandstones when using conical picks and the development of empirical prediction models. Rock Mech Rock Eng 51(10):3111–3128. https://doi.org/10.1007/s00603-018-1522-1

    Article  Google Scholar 

  • Wawersik WR, Brace WF (1971) Post-failure behavior of a granite and diabase. Rock Mech 3(2):61–85. https://doi.org/10.1007/BF01239627

    Article  Google Scholar 

  • Wong TF (1982) Micromechanics of faulting in westerly granite. Int J Rock Mech Min Sci Geomech Abstr 19(2):49–64

    Article  Google Scholar 

  • Zaoui A (1998) Matériaux Hétérogènes Et Composites. France

  • Zaoui A (2002) Continuum micromechanics: survey. J Eng Mech 128:808–816

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LR14ES03 Laboratoire d’Ingénierie Géotechnique, Ecole Nationale d’Ingénieurs de Tunis, Université de Tunis El Manar, 1002, Tunis, Tunisia

    Nesrine Gabssi & Essaieb Hamdi

  2. School of Engineering, The University of Western Australia, 35 Stirling Hwy, Crawley, WA, 6009, Australia

    Ali Karrech

Authors
  1. Nesrine Gabssi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Essaieb Hamdi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ali Karrech
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nesrine Gabssi.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gabssi, N., Hamdi, E. & Karrech, A. Coupled Thermo-mechanical Behavior of Weakening Geo-Materials. Geotech Geol Eng 37, 2675–2692 (2019). https://doi.org/10.1007/s10706-018-00786-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10706-018-00786-w

Keywords

Search

Navigation