Modifying Drucker-Prager Criterion for Elastoplastic Porous Rocks Using a Numerical Integration Algorithm

نوع مقاله : مقاله پژوهشی

نویسنده

Dept. of Mining and Metallurgy Engineering, Yazd University, Yazd, Iran

10.22034/anm.2023.20576.1608

چکیده

In the topics related to rock mechanics and geotechnics, elastoplastic criteria are of special importance. This importance makes their numerical implementation necessary. Although most of the existing software in the field of rock mechanics and geotechnics have elastoplastic criteria, the lack of access to their coding core makes it practically impossible for researchers to develop them. Therefore, considering the importance of elastoplastic criteria and the complexity of their implementation, in this study, a suitable scheme was presented to improve the elastoplastic numerical integration algorithm of Darker-Prager criteria. The developed algorithm includes two steps of elastic trial and plastic return-mapping algorithm. In the proposed model, if the elastic trial step is in the elastic domain or on the yield surface, the answer of elasticity is approved. Otherwise, if the trial stress can not confirm the desired conditions in the first step, it is executed by the plastic return-mapping algorithm. This process has been done comprehensively and separately for Drucker-Prager's cone and apex to be able to express the elastoplastic behavior of the material optimally. The presented model was analyzed for the porous rock sample and its validation was confirmed by comparing the numerical results with the laboratory data.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Modifying Drucker-Prager Criterion for Elastoplastic Porous Rocks Using a Numerical Integration Algorithm

نویسنده [English]

  • Manouchehr Sanei
Dept. of Mining and Metallurgy Engineering, Yazd University, Yazd, Iran
چکیده [English]

In the topics related to rock mechanics and geotechnics, elastoplastic criteria are of special importance. This importance makes their numerical implementation necessary. Although most of the existing software in the field of rock mechanics and geotechnics have elastoplastic criteria, the lack of access to their coding core makes it practically impossible for researchers to develop them. Therefore, considering the importance of elastoplastic criteria and the complexity of their implementation, in this study, a suitable scheme was presented to improve the elastoplastic numerical integration algorithm of Darker-Prager criteria. The developed algorithm includes two steps of elastic trial and plastic return-mapping algorithm. In the proposed model, if the elastic trial step is in the elastic domain or on the yield surface, the answer of elasticity is approved. Otherwise, if the trial stress can not confirm the desired conditions in the first step, it is executed by the plastic return-mapping algorithm. This process has been done comprehensively and separately for Drucker-Prager's cone and apex to be able to express the elastoplastic behavior of the material optimally. The presented model was analyzed for the porous rock sample and its validation was confirmed by comparing the numerical results with the laboratory data.

کلیدواژه‌ها [English]

  • Elastoplastic
  • Drucker-Prager
  • Integration algorithm
  • Return mapping
  • Porous Rock

مراجع

[1]                 Rezaiee-Pajand, M., Sharifian, M. and Sharifian, M. (2011). Accurate and approximate integrations of Drucker–Prager plasticity with linear isotropic and kinematic hardening. European Journal of Mechanics - A/Solids, Volume 30(3): 345-361. https://doi.org/10.1016/j.euromechsol.2010.12.001.
[2]                 Borja, Ronaldo I. (2013). Plasticity. Springer Berlin Heidelberg. doi: 10.1007/978-3- 642-38547-6 (cit. on pp. 91, 92).
[3]                 Rezaiee-Pajand, M. and Nasirai, C. (2008). On the integration schemes for Drucker-Prager’s elastoplastic models based on exponential maps. Int. J. Numer. Meth. Eng. 74: 799-826.
[4]                 de Souza Neto E, Peri D, and Owen D.  (2008). Computational methods for plasticity. John Wiley Sons Ltd.
[5]                 Loret, B. and Prevost, J.H. (1986). Accurate numerical solutions for Drucker–Prager elastic–plastic models Comput. Meth. Appl. Mech. Eng.
[6]                 Genna, F. and Pandolfi, A. (1994). Accurate numerical integration of Drucker-Prager’s constitutive equations. Meccanica 29: 239-260.
[7]                 Kobayashi, M., Mukai, M., Takahashi, H., Ohno, N., Kawakami, T. and Ishikawa, T. (2003). Implicit integration and consistent tangent modulus of a time-dependent nonunified constitutive model. Int. J. Numer. Meth. Eng. 58: 1523-1543.
[8]                 Kan, Q.H., Kang, G.Z. and Zhang, J. (2007). A unified visco-plastic constitutive model for uniaxial time-dependent ratchetting and its finite element implementation. Theor. Appl. Fract. Mech. 47: 133-144.
[9]                 Coombs, W.M., Crouch, R.S. and Augarde, C.E. (2010). Reuleaux plasticity: analytical backward Euler stress integration and consistent tangent. Comput. Methods Appl. Mech. Eng. 199: 1733-1743.
[10]              Liu, C.-S. (2004). Internal symmetry groups for the DruckerePrager material model of plasticity and numerical integrating methods. Int. J. Solids Struct. 41: 3771-3791.
[11]              Cecílio D.L., Devloo P.R., Gomes S.M., dos Santos E.R. and Shauer N. (2015). An improved numerical integration algorithm for elastoplastic constitutive equations. Comput Geotech, 64: 1–9.
[12]              Sanei, M., Devloo, P.R.B., Forti, T.L.D., Durán, O. and Santos, E.S.R. (2021a). An innovative scheme to make an initial guess for iterative optimization methods to calibrate material parameters of strain-hardening elastoplastic models. Rock Mech Rock Eng 55(1): 399–421. https:// doi. org/ 10. 1007/ s00603- 021- 02665-y.
[13]              Sanei, M., Devloo, P.R.B., Forti, T.L.D., Durán, O. and Santos, E.S.R. (2019). On data adjustment of an elastoplastic constitutive model using optimization methods. ENAHPE 2019 – Encontro Nacional de Construção de Poços de Petróleo e Gás Serra Negra – SP, 19 a 22 de Agosto de 2019.
[14]              Sanei, M., Durán, O., Devloo, P.R.B. and Santos, E.S.R. (2021b). Analysis of pore collapse and shear-enhanced compaction in hydrocarbon reservoirs using coupled poro-elastoplasticity and permeability. Arab J Geosci. https:// doi. org/ 10. 1007/ s12517- 021- 06754-8.
[15]              Sanei, M., Durán, O., Devloo, P.R.B., Santos, E.S.R. (2022). Evaluation of the impact of strain-dependent permeability on reservoir productivity using iterative coupled reservoir geomechanical modeling. Geomech Geophy Geo Energy Geo Res. https:// doi. org/ 10. 1007/ s40948- 022- 00344-y.
[16]              Sanei, M., Duran, O., Devloo, P.R.B. (2019). Numerical modeling of pore collapse in hydrocarbon reservoirs using a cap plasticity constitutive model. In Proceedings of the 14th International Congress on Rock Mechanics and Rock Engineering, Brazil. ISRM-14CONGRESS-2019-377.
[17]              Durán, O., Sanei, M., Devloo, P.R.B., Santos, E.S.R. (2019). An iterative scheme for poroelasto-plastic to analyze a wellbore during drilling. ENAHPE 2019 – Encontro Nacional de Construção de Poços de Petróleo e Gás Serra Negra – SP, 19 a 22 de Agosto de 2019.
[18]              Sanei, M., Duran, O., Devloo, P.R.B. (2017). Finite element modeling of a nonlinear poromechanic deformation in porous media. In Proceedings of the XXXVIII Iberian Latin American Congress on Computational Methods in Engineering. ABMEC Brazilian Association of Computational Methods in Engineering. https:// doi. org/ 10. 20906/ cps/ cilamce 2017- 0418.
[19]              Duran, O., Sanei, M., Devloo, P.R.B., Santos, E.S.R. (2020). An enhanced sequential fully implicit scheme for reservoir geomechanics. Comput Geosci 24(4): 1557–1587. https:// doi. org/ 10. 1007/ s10596- 020- 09965-2.
[20]              Sanei, M., Duran, O., Devloo, P.R.B., Santos, E.S.R. (2020). An innovative procedure to improve integration algorithm for modified cam-clay plasticity model. Comput Geotech 124: 103604. https://doi.org/10.1016/j.compgeo.2020.103604.
[21]              Heydari, M., Aghakhani Emamqeysi, M.R., Sanei, M. (2022) Finite element analysis of wellbore stability and optimum drilling direction and applying NYZA method for a safe mud weight window. Journal of Analytical and Numerical Methods in Mining Engineering. 10.22034/ANM.2022.2582.
[22]              Rudnicki, John W. (1986). Fluid mass sources and point forces in linear elastic diffusive solids. In: Mechanics of Materials 5(4): 383–393. doi: 10.1016/0167- 6636(86)90042-6.
[23]              Kossa, A. (2011). Exact stress integration schemes for elastoplasticity Ph.D. thesis Budapest University of Technology and Economics.
[24]              Davis, R and Selvadurai, A. (2002). Plasticity and geomechanics. Cambridge University Press.
[25]              Sanei, M., Faramarzi, L., Fahimifar, A., Goli, S., Mehinrad, A., Rahmati, A. (2015). Shear strength of discontinuities in sedimentary rock masses based on direct shear tests. Int. J. Rock Mech. Min. Sci., 75:119-131. https://doi.org/10.1016/j.jksus.2023.102846.
[26]              Sanei, M. (2023). Development of Mohr-Coulomb criterion elastoplastic integration algorithm scheme for rock. Journal of Petroleum Geomechanics. 10.22107/JPG.2023.413537.1209.
[27]              Drucker, D.C. and Prager, W. (1952). Soil Mechanics and Plasticity Analysis of Limit Design. Quart. J. Appl. Math., 10: 157–162.
[28]              Chen, W-F. and Mizuno, E. (1990). Nonlinear Analysis in Soil Mechanics. Theory and Implementation. New York: Elsevier.
[29]              H Yousefian, H Soltanian, MF Marji, A Abdollahipour, Y Pourmazaheri. (2018). Numerical simulation of a wellbore stability in an Iranian oilfield utilizing core data. Journal of Petroleum Science and Engineering 168, 577-592.
[30]              A Abdollahipour, MF Marji. (2020). A thermo-hydromechanical displacement discontinuity method to model fractures in high-pressure, high-temperature environments. Renewable Energy 153, 1488-1503.
[31]              Zhang, C.L. (2016). The stress–strain–permeability behaviour of clay rock during damage and recompaction. In: Journal of Rock Mechanics and Geotechnical Engineering 8(1):  16–26.

فایل ها

سابقه مقاله

  • تاریخ دریافت: 11 شهریور 1402
  • تاریخ بازنگری: 07 آبان 1402
  • تاریخ پذیرش: 10 آبان 1402

هم رسانی

ارجاع به این مقاله

آمار