DOI QR코드

DOI QR Code

The deformable multilaminate for predicting the Elasto-Plastic behavior of rocks

  • Haeri, Hadi (Department of Mining Engineering, Bafgh Branch, Islamic Azad University) ;
  • Sarfarazi, V. (Department of Mining Engineering, Hamedan University of Technology)
  • Received : 2015.12.17
  • Accepted : 2016.04.01
  • Published : 2016.08.25

Abstract

In this paper, a multilaminate based model have been developed and presented to predict the strain hardening behavior of rock. In this multilaminate model, the stress-strain behavior of a material is obtained by integrating the mechanical response of an infinite number of predefined oriented planes passing through a material point. Essential features such as the variable deformations hypothesis and multilaminate model are discussed. The methodology to be discussed here is modeling of strains on the 13 laminates passing through a point in each loading step. Upon the presented methodology, more attention has been given to hardening in non-linear behaviour of rock in going from the peak to residual strengths. The predictions of the derived stress-strain model are compared to experimental results for marble, sandstone and dense Cambria sand. The comparisons demonstrate the ability of this model to reproduce accurately the mechanical behavior of rocks.

Keywords

References

  1. Antunes, F.V. and Rodrigues, D.M. (2008), "Numerical simulation of plasticity induced crack closure: Identification and discussion of parameters", Eng. Fract. Mech., 75(10), 3101-3120. https://doi.org/10.1016/j.engfracmech.2007.12.009
  2. Batdorf, S.B. and Budiansky, B. (1949), "A mathematical theory of plasticity based on the concept of slip", National Advisory Committee for Aeronautics, TN 1871.
  3. Brewer, R. (1964), Fabric and mineral analysis of soils. Wiley: New York, 129-158.
  4. Brinkgreve, R.B.J., Broere, W. and Waterman, D. (2006), Plaxis, finite element code for soil and rock analyses, Users Manual, PLAXIS b.v., The Netherlands.
  5. Calladine, C.R. (1971), "A microstructural view of the mechanical properties of saturated clay", Geotech., 21(4), 391-415. https://doi.org/10.1680/geot.1971.21.4.391
  6. Caputo, F., Lamanna, G. and Soprano, A. (2013), "On the evaluation of the plastic zone size at the crack tip", Eng. Fract. Mech., 103, 162-173. https://doi.org/10.1016/j.engfracmech.2012.09.030
  7. Chang, C.S. and Hicher, P.Y. (2005), "An elasto-plastic model for granular materials with macrostructural consideration", Int. J. Solid. Struct., 42, 4258-4277. https://doi.org/10.1016/j.ijsolstr.2004.09.021
  8. Christofferson, C., Mehrabadi, M.M, Nemat-Nasser, S.A. (1981), "Macromechanical description of granular behavior", J. Appl. Mech., 48, 339-344. https://doi.org/10.1115/1.3157619
  9. Drucker, D.C. (1959), "A definition of a stable inelastic material", J. Appl. Mech., 26, 101-106.
  10. Fathi, A., Moradian, Z., Rivard, P. and Ballivy, G. (2016), "Shear mechanism of rock joints under pre-peak cyclic loading condition", Int. J. Rock Mech. Min. Sci., 83, 197-210.
  11. Ghadrdan, M., Sadrnejad, S.A. and Shaghaghi, T. (2015), "Numerical evaluation of geomaterials behavior upon multiplane damage model", Comput. Geotech., 68, 1-7. https://doi.org/10.1016/j.compgeo.2015.03.008
  12. Haeri, H. (2015a), "Influence of the inclined edge notches on the shear-fracture behavior in edge-notched beam specimens", Comput. Concrete , 16(4), 605-623, https://doi.org/10.12989/cac.2015.16.4.605
  13. Haeri, H. (2015a), Coupled experimental-numerical fracture mechanics, Lambert academic press, Germany
  14. Haeri, H. (2015b), "Experimental crack analysis of rock-like CSCBD specimens using a higher order DDM", Comput. Concrete, 16(6), 881-896. https://doi.org/10.12989/cac.2015.16.6.881
  15. Haeri, H. (2015c), "Simulating the crack propagation mechanism of pre-cracked concrete specimens under shear loading conditions", Strength Mater., 47(4), 618-632. https://doi.org/10.1007/s11223-015-9698-z
  16. Haeri, H. (2015d), "Propagation mechanism of neighboring cracks in rock-like cylindrical specimens under uniaxial compression", J. Min. Sci., 51(3), 487-496. https://doi.org/10.1134/S1062739115030096
  17. Haeri, H. and Marji, M.F. (2016b), "Simulating the crack propagation and cracks coalescence underneath TBM disc cutters", Arab. J. Geosci., 9(2), 1-10. https://doi.org/10.1007/s12517-015-2098-7
  18. Haeri, H. and Sarfarazi, V. (2016), "The effect of micro pore on the characteristics of crack tip plastic zone in concrete", Comput. Concrete, 17(1), 107-127. https://doi.org/10.12989/cac.2016.17.1.107
  19. Haeri, H., Marji, M.F. and Shahriar, K. (2014c), "Simulating the effect of disc erosion in TBM disc cutters by a semi-infinite DDM", Arab J Geosci., 8(6), 3915-3927 https://doi.org/10.1007/s12517-014-1489-5
  20. Haeri, H., Marji, M.F., Shahriar, K. and Moarefvand, P. (2015), "On the HDD analysis of micro crack initiation, propagation, and coalescence in brittle materials", Arab. J. Geosci., 8(5), 2841-2852. https://doi.org/10.1007/s12517-014-1290-5
  21. Haeri, H., Shahriar, K., Marji, M.F. and Moaref, Vand P. (2014a), "An experimenta and numerical study of crack propagation and cracks coalescence in the pre-cracked rock-like disc specimens under compression", Int. J. Rock Mech. Min. Sci., 67, 20-28.
  22. Haeri, H., Shahriar, K., Marji, M.F. and Moarefvand, P. (2015), "A coupled numerical-experimental study of the breakage process of brittle substances", Arab. J. Geosci., 8(2), 809-825. https://doi.org/10.1007/s12517-013-1165-1
  23. Maier, G. and Hueckel, T. (1979), "Nonassociated and coupled flow rules of elastoplasticity for rock-like materials", Int. J. Rock Mech., Min. Sci. Geomech. Abst., 16, 77-92.
  24. Mandel, J. (1964), "Conditions de Stabilite et Postulat de Drucker", Proceeding of the IUTAM Symposium on rheology and soil mechanics, Kravichenko, J., Sirieys, P.M. (Eds.), Springer-Verlag, Berlin, 58-68.
  25. Mroz, Z. (1963), "Non-associated flow laws in plasticity", J. Mech., 2, 21-42.
  26. Mroz, Z. (1966), "On forms of constitutive laws for elastic-plastic solids", Arch. Mech. Sto., 18, 1-34.
  27. Nakata, Y., Hyodo, M., Murata, H. and Yasufuku, N. (1998), "Flow deformation of sands subjected to principal stress rotation", Soil. Found., 38(2), 115-128. https://doi.org/10.3208/sandf.38.2_115
  28. Nemat-Nasser, S., Mehrabadi, M.M. (1983), "Stress and fabric in granular masses, mechanics of granular materials", New models and constitutive relations (Eds. J.T. Jenkins and M. Satake), 1-8, Elsevier Sci. Pub.
  29. Nemcik, J., Mirzaghorbanali, A. and Aziz, N. (2014), "An Elasto-Plastic constitutive model for rock joints under cyclic loading and constant normal stiffness conditions", Geotech. Geol. Eng., 32(2), 321-335. https://doi.org/10.1007/s10706-013-9716-5
  30. Pande, G.N. and Sharma, K.G. (1983), "Multi-laminate model of clays-a numerical evaluation of the influence of rotation of the principal stress axes", Int. J. Numer. Anal. Method. Geomech., 7(4), 397-418. https://doi.org/10.1002/nag.1610070404
  31. Sadrnejad, S.A. and Pande, G.N. (1989), "A multilaminate model for sands", Proceedings of the 3rd International Symposium on Numerical Models in Geomechanics (NUMOG), Niagara Falls, Canada, Pietruszczak S, Pande GN (eds). Elsevier: London, 17-27.
  32. Samui, P. (2013), "Multivariate Adaptive Regression Spline (Mars) for prediction of elastic modulus of jointed rock mass", Geotech. Geol. Eng., 31(1), 249-253. https://doi.org/10.1007/s10706-012-9584-4
  33. Schadlich, B. and Schweiger, H.F. (2013), "A multilaminate constitutive model accounting for anisotropic small strain stiffness", Int. J. Numer. Anal. Method. Geomech., 37(10), 1337-1362. https://doi.org/10.1002/nag.2089
  34. Scharinger, F. (2007), "A multilaminate model for soil incorporating small strain stiffness", Ph.D. Thesis, Gruppe Geotechnik Graz, Heft 31, Graz University of Technology, Austria.
  35. Scharinger, F. and Schweiger, H.F. (2005), "Undrained response of a double hardening multilaminate model for soils", Proceedings of the 11th International Conference of the International Association of Computer Methods and Advances in Geomechanics (IACMAG), Turin, Italy, Barla G, Barla M (eds). Patron Editore: Bologna, 505-512.
  36. Taylor, G.I. (1958), "Plastic strain in metals", J. Inst. Metal., 62, 307-324 (Reprinted in the Scientific Papers of G. I. Taylor 1. Cambridge University Press: Cambridge, U.K.).
  37. Varadarajan, A., Sharma, K.G, Hashemi, M. Strain (2003), "Softening behaviour of a schistose rock mass under triaxial loading", Technology roadmap for rock mechanics, S. Africa Inst. Min. Metall.
  38. Wang, T.T. and Huang, T.H. (2014), "Anisotropic deformation of a circular tunnel excavated in a rock mass containing sets of ubiquitous joints: Theory analysis and numerical modeling", Rock Mech. Rock Eng., 47(2), 643-657. https://doi.org/10.1007/s00603-013-0405-8
  39. Wiltafsky, C. (2003), "A multilaminate model for normally consolidated clay", Ph.D. Thesis, Gruppe Geotechnik Graz, Heft 18, Graz University of Technology, Austria.
  40. Wu, J.Y. and Xu, S.L. (2011), "An augmented multicrack elastoplastic damage model for tensile cracking", Int. J. Solid. Struct., 48(18), 2511-2528. https://doi.org/10.1016/j.ijsolstr.2011.05.001
  41. Xin, G., Hangong, W., Xingwu, K. and Liangzhou, J. (2010), "Analytic solutions to crack tip plastic zone under various loading conditions", Eur. J. Mech.-A/Solid., 29(4), 738-745. https://doi.org/10.1016/j.euromechsol.2010.03.003
  42. Yi, H., Jingjie, C. and Gang, L. (2010), "A new method of plastic zone size determined based on maximum crack opening displacement", Eng. Fract. Mech., 77(14), 2912-2918. https://doi.org/10.1016/j.engfracmech.2010.06.026
  43. Zienkiewicz, O.C. and Pande, G.N. (1977), "Time-dependent multilaminate model of rocks-a numerical study of deformation and failure of rock masses", Int. J. Numer. Anal. Method. Geomech., 1(3), 219-247. https://doi.org/10.1002/nag.1610010302

Cited by

  1. Experimental and numerical study of shear crack propagation in concrete specimens vol.20, pp.1, 2016, https://doi.org/10.12989/cac.2017.20.1.057
  2. Investigation of ratio of TBM disc spacing to penetration depth in rocks with different tensile strengths using PFC2D vol.20, pp.4, 2016, https://doi.org/10.12989/cac.2017.20.4.429
  3. A review paper about experimental investigations on failure behaviour of non-persistent joint vol.13, pp.4, 2017, https://doi.org/10.12989/gae.2017.13.4.535
  4. Displacement prediction in geotechnical engineering based on evolutionary neural network vol.13, pp.5, 2016, https://doi.org/10.12989/gae.2017.13.5.845
  5. A fracture mechanics simulation of the pre-holed concrete Brazilian discs vol.66, pp.3, 2016, https://doi.org/10.12989/sem.2018.66.3.343
  6. Finite element modeling of contact between an elastic layer and two elastic quarter planes vol.26, pp.2, 2020, https://doi.org/10.12989/cac.2020.26.2.107
  7. Numerical simulation and experimental investigation of the shear mechanical behaviors of non-persistent joint in new shear test condition vol.26, pp.3, 2020, https://doi.org/10.12989/cac.2020.26.3.239
  8. Study of tensile behavior of Y shape non-persistent joint using experimental test and numerical simulation vol.26, pp.6, 2016, https://doi.org/10.12989/cac.2020.26.6.565
  9. Physical test and PFC2D simulation of the failure mechanism of echelon joint under uniaxial compression vol.27, pp.2, 2021, https://doi.org/10.12989/cac.2021.27.2.099
  10. Z shape joints under uniaxial compression vol.12, pp.2, 2016, https://doi.org/10.12989/acc.2021.12.2.105