Determination of Fractured Rock’s Representative Elementary Volume by a Numerical Simulation Method
The present study aims at developing a numerical program called DISSIM which can analyze the homogenization of rock massifs using a new subroutine which calculates Representative Elementary Volume (REV). The DISSIM methodology consists of two steps. The first step involves the modeling of the fractured network in order to provide a surface simulation that represents the real fracture of the examined front. The second step is to numerically model the wave propagation through the simulated fracture network while characterizing the attenuation of vibrations due to the effect of discontinuities. This part allows us to determine in particular the wave propagation velocity through the fractured mass, from which we can determine the homogenized Young's modulus. However, after extensive bibliographic research, it was realized that a third step appeared to be necessary. In fact, it is necessary to look for a representative elementary volume on which we apply the proposed homogenization method. Two types of the representative elementary volume are proposed in this article, the geometric REV and the mechanical REV. The presentation of these two types of REV and the DISSIM methodology are detailed in this paper. Then, this methodology was applied to the study of a real case. The present research provides a method allowing the calculation of both types of REV for fissured rocks. The case study yielded comparable results between the mechanical REV and the geometric REV, which is compatible with previous research studies.
Keywords:representative elementary volume, DISSIM methodology, homogenization, fractured rock, simulated fracture network
J. C. S. Long, J. S. Remer, C. R. Wilson, P. A. Withespoon, “Porous media equivalents for networks of discontinuous fractures”, Water Ressources Research, Vol. 18, No. 3, pp. 645-658, 1982 DOI: https://doi.org/10.1029/WR018i003p00645
A. Pouya, A. Courtois, “Definition de la permeabilite equivalente des massifs fractures par des methodes d‘homogeneisation”, Comptes Rendus Geoscience, Vol. 334, No. 13, pp. 975-979, 2002 (in French) DOI: https://doi.org/10.1016/S1631-0713(02)01839-4
A. Pouya, “Tenseurs de permeabilite equivalente d‘un domaine heterogene fini”, Comptes Rendus Geoscience,Vol. 337, No. 6, pp. 581-588, 2005 (in French) DOI: https://doi.org/10.1016/j.crte.2005.02.002
L. Zhang, L. Xia Q. C. Yu, “Determining the REV for Fracture Rock Mass Based on Seepage Theory”, Geofluids, Vol. 2017, Article ID: 4129240, 2017 DOI: https://doi.org/10.1155/2017/4129240
K. B. Min, L. Jing, “Numerical determination of the equivalent elastic compliance tensor for fractured rock masses using the distinct element method”, International Journal of Rock Mechanics and Mining Sciences,Vol. 40, No. 6, pp. 795-816, 2003 DOI: https://doi.org/10.1016/S1365-1609(03)00038-8
L. Xia, Y. Zheng, Q. Yu, “Estimation of the REV size for blockiness of fractured rock masses”, Computers and Geotechnics, Vol. 76, pp. 83-92, 2016 DOI: https://doi.org/10.1016/j.compgeo.2016.02.016
M. Chalhoub, A. Pouya, “A geometrical approach to estimate the mechanical REV of a fractured rock mass”, 1st Euro Mediterranean Symposium on Advances on Geomaterials and Structures, Hammamet, Tunisia, May 3-5, 2006
K. B. Min, J. Lee, O. Stephansson, “Implications of thermally-induced fracture slip and permeability change on the long-term performance of a deep geological repository”, International Journal of Rock Mechanics and Mining Sciences, Vol. 61, pp. 275-288, 2013 DOI: https://doi.org/10.1016/j.ijrmms.2013.03.009
M. Pierce, P. Cundall, D. Potyondy, D. M. Ivars, “A synthetic rock mass model for jointed rock”, in: Rock Mechanics: Meeting Society's Challenges and Demands, Vol. 1, pp. 341-349, Taylor & Francis Group, 2007 DOI: https://doi.org/10.1201/NOE0415444019-c42
W. S. Dershowitz, H. H. Einstein, “Characterizing rock joint geometry with joint system models”, Rock Mechanics and Rock Engineering, Vol. 21, pp. 21-51, 1988 DOI: https://doi.org/10.1007/BF01019674
W. Zhang, J. P. Chen, C. Liu, R. Huang, M. Li, Y. Zhang, “Determination of Geometrical and Structural Representative Volume Elements at the Baihetan Dam Site”, Rock Mechanics and Rock Engineering, Vol. 45, pp. 409-419, 2012 DOI: https://doi.org/10.1007/s00603-011-0191-0
G. B. Baecher, N. A. Lanney, H. H. Einstein, “Statistical description of rock properties and sampling”, 18th U.S. Symposium on Rock Mechanics, Colorado, USA, June 22-24, 1977
J. Chen, “3-D network numerical modeling technique for random discontinuities of rock mass”, Chinese Journal of Geotechnical Engineering, Vol. 23, No. 4, pp. 397-402, 2001
J. Chen, B. F. Shi, Q. Wang, “Study on the dominant orientations of random fractures of fractured rock masses”, Chinese Journal of Rock Mechanics and Engineering, Vol. 24, No. 2, pp. 241-245, 2005
H. Gasmi, S. Yahyaoui, E. Hamdi, “A new tool for homogenization of jointed rock masses using wave propagation analysis”, 10th International Symposium on Rock Fragmentation by Blasting, New Delhi, India, November 26-29, 2012 DOI: https://doi.org/10.1201/b13759-17
H. Gasmi, E. Hamdi, N. B. Romdhane, “A Numerical homogenization of jointed rock masses using wave propagation simulation”, Rock Mechanics and Rock Engineering, Vol. 47, No. 4, pp. 1393-1409, 2014 DOI: https://doi.org/10.1007/s00603-013-0458-8
K. Esmaieli, J. Hadjigeorgiou, M. Grenon, “Estimating geometrical and mechanical REV based on synthetic rock mass models at Brunswick Mine”, International Journal of Rock Mechanics and Mining Sciences, Vol. 47, No. 6, pp. 915-926, 2010 DOI: https://doi.org/10.1016/j.ijrmms.2010.05.010
How to Cite
MetricsAbstract Views: 433
PDF Downloads: 206
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.