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Numerical Homogenization of Jointed Rock Masses Using Wave Propagation Simulation

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Abstract

Homogenization in fractured rock analyses is essentially based on the calculation of equivalent elastic parameters. In this paper, a new numerical homogenization method that was programmed by means of a MATLAB code, called HLA-Dissim, is presented. The developed approach simulates a discontinuity network of real rock masses based on the International Society of Rock Mechanics (ISRM) scanline field mapping methodology. Then, it evaluates a series of classic joint parameters to characterize density (RQD, specific length of discontinuities). A pulse wave, characterized by its amplitude, central frequency, and duration, is propagated from a source point to a receiver point of the simulated jointed rock mass using a complex recursive method for evaluating the transmission and reflection coefficient for each simulated discontinuity. The seismic parameters, such as delay, velocity, and attenuation, are then calculated. Finally, the equivalent medium model parameters of the rock mass are computed numerically while taking into account the natural discontinuity distribution. This methodology was applied to 17 bench fronts from six aggregate quarries located in Tunisia, Spain, Austria, and Sweden. It allowed characterizing the rock mass discontinuity network, the resulting seismic performance, and the equivalent medium stiffness. The relationship between the equivalent Young’s modulus and rock discontinuity parameters was also analyzed. For these different bench fronts, the proposed numerical approach was also compared to several empirical formulas, based on RQD and fracture density values, published in previous research studies, showing its usefulness and efficiency in estimating rapidly the Young’s modulus of equivalent medium for wave propagation analysis.

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References

  • Amadei B, Savage WZ (1993) Effect of joints on rock mass strength and deformability. In: Hudson JA (ed) Comprehensive rock engineering—principles, practice, and projects, vol 1. Pergamon Press, Oxford

    Google Scholar 

  • Baecher GB, Lanney NA, Einstein HH (1977) Statistical description of rock properties and sampling. In. Proceedings of the 18th US symposium on rock mechanics, Keystone, Colorado, June 1977, p 5C1–5C1–8

  • Bandis SC, Lumdsen AC, Barton NR (1983) Fundamentals of rock joint deformation. Int J Rock Mech Min Sci Geomech Abstr 20(6):249–268

    Article  Google Scholar 

  • Barton N (2002) Some new Q-value correlations to assist in site characterisation and tunnel design. Int J Rock Mech Min Sci 39:185–216

    Article  Google Scholar 

  • Barton N, Lien R, Lunde J (1974) Engineering classification of rock masses for the design of tunnel support. Rock Mech 6:189–236

    Article  Google Scholar 

  • Bieniawski ZT (1973) Engineering classification of jointed rock masses. Trans S Afr Instn Civ Engrs 15(12):335–344

    Google Scholar 

  • Boadu FK (1997) Fractured rock mass characterization parameters and seismic properties: analytical studies. J Appl Geophys 37:1–19

    Article  Google Scholar 

  • Cruden DM (1977) Describing the size of discontinuities. Int J Rock Mech Min Sci Geomech Abstr 14:133–137

    Article  Google Scholar 

  • Deere DU, Hendron AJ, Patton FD, Cording EJ (1967) Design of surface and near surface construction in rock. In: Proceedings of the 8th US symposium on rock mechanics—failure and breakage of rock, Network, p 237–302

  • Dershowitz WS, Herda HH (1992) Interpretation of fracture spacing and intensity. In: Tillerson JR, Wawersik WR (eds) Proceedings of the 33rd US symposium on rock mechanics, Santa Fe, New Mexico, June 1992. Balkema, Rotterdam, p 757–765

  • Gardner WS (1987) Design of drilled piers in the Atlantic Piedmont. In: Smith RE (ed) Foundations and excavations in decomposed rock of the Piedmont Province. Geotechnical Special Publication (GSP), ASCE, no. 9, p 62–86

  • Gasmi H, Hamdi E, Bouden Romdhane N (2008) Influence of the in situ rock mass structure on the blast induced vibrations. In: Proceedings of the international conference on geotechnical engineering (ICGE’08), Hammamet, Tunisia, March 24–26 2008, p 523–532

  • Gasmi H, Yahyaoui S, Hamdi E (2012) A new tool for homogenization of jointed rock masses using wave propagation analysis. In: Proceedings of the 10th international symposium on rock fragmentation by blasting (FRAGBLAST 10), New Delhi, India, November 24–29 2012

  • Gu B, Nihei KT, Myer LR, Pyrak-Nolte LJ (1996a) Fracture interface waves. J Geophys Res 101:827–835

    Article  Google Scholar 

  • Gu B, Suárez-Rivera R, Nihei KT, Myer LR (1996b) Incidence of plane waves upon a fracture. J Geophys Res 101(B11):25337–25346

    Article  Google Scholar 

  • Hamdi E (2008) A fractal description of simulated 3D discontinuity networks. Rock Mech Rock Eng 41(4):587–599

    Article  Google Scholar 

  • Hamdi E, du Mouza J (2005) A methodology for rock mass characterisation and classification to improve blast results. Int J Rock Mech Min Sci 42(2):177–194

    Article  Google Scholar 

  • Hamdi E, Gasmi H, Bouden Romdhane N (2009) Influence of rock mass discontinuity networks on the seismic response parameters. In: Proceedings of the 9th international symposium on rock fragmentation by blasting (FRAGBLAST 9), Granada, Spain, September 13–17 2009, p 589–596

  • Hashemi M, Moghaddas SH, Ajalloeian R (2010) Application of rock mass characterization for determining the mechanical properties of rock mass: a comparative study. Rock Mech Rock Eng 43:305–320

    Article  Google Scholar 

  • Hoek E, Diederichs MS (2006) Empirical estimation of rock mass modulus. Int J Rock Mech Min Sci 43:203–215

    Article  Google Scholar 

  • Hoek E, Carranza-Torres CT, Corkum B (2002) Hoek–Brown failure criterion—2002 edition. In: Bawden HRW, Curran J, Telsenicki M (eds) Proceedings of the 5th North American Rock Mechanics Society (NARMS-TAC 2002) symposium, Mining Innovation and Technology, Toronto, Canada, July 7–10 2002, pp 267–273

  • Hudson JA, Priest SD (1979) Discontinuities and rock mass geometry. Int J Rock Mech Min Sci Geomech Abstr 16:339–362

    Article  Google Scholar 

  • Kayabasi A, Gokceoglu C, Ercanoglu M (2003) Estimating the deformation modulus of rock masses: a comparative study. Int J Rock Mech Min Sci 40:55–63

    Article  Google Scholar 

  • Kendall K, Tabor D (1971) An ultrasonic study of the area of contact between stationary and sliding surfaces. Proc R Soc Lond A 323:321–340

    Article  Google Scholar 

  • Kulhawy FH (1978) Geomechanical model for rock foundation settlement. J Geotech Eng ASCE 104(2):211–227

    Google Scholar 

  • Li JC, Ma GW (2009) Experimental study of stress wave propagation across a filled rock joint. Int J Rock Mech Min Sci 46:471–478

    Article  Google Scholar 

  • Li JC, Ma GW (2010) Analysis of blast wave interaction with a rock joint. Rock Mech Rock Eng 43:777–787

    Article  Google Scholar 

  • Li JC, Ma GW, Zhao J (2010) An equivalent viscoelastic model for rock mass with parallel joints. J Geophys Res 115:B033045

    Google Scholar 

  • Ma GW, An XM (2008) Numerical simulation of blasting-induced rock fractures. Int J Rock Mech Min Sci 45(6):966–975

    Article  Google Scholar 

  • Miller RK (1977) An approximate method of analysis of the transmission of elastic waves through a frictional boundary. J Appl Mech 44(1977):652–656

    Article  Google Scholar 

  • Myer LR, Pyrak-Nolte LJ, Cook NGW (1990) Effects of single fractures on seismic wave propagation. In: Proceedings of the ISRM international symposium on rock joints, Loen, Norway, June 4–6 1990, p 467–473

  • Myer LR, Hopkins D, Peterson JE, Cook NGW (1995) Seismic wave propagation across multiple fractures. In: Myer LR, Cook NGW, Goodman RE, Tsang CF (eds) Fractured and jointed rock masses. Balkema, Rotterdam, pp 105–109

  • Palmström A, Singh R (2001) The deformation modulus of rock masses—comparisons between in situ tests and indirect estimates. Tunn Undergr Sp Tech 16:115–131

    Article  Google Scholar 

  • Perino A, Zhu JB, Li JC, Barla G, Zhao J (2010) Theoretical methods for wave propagation across jointed rock masses. Rock Mech Rock Eng 43:799–809

    Article  Google Scholar 

  • Perino A, Orta R, Barla G (2012) Wave propagation in discontinuous media by the scattering matrix method. Rock Mech Rock Eng 45:901–918

    Google Scholar 

  • Priest SA, Hudson JA (1981) Estimation of discontinuity spacing and trace length using scanline surveys. Int J Rock Mech Min Sci Geomech Abstr 18:183–187

    Article  Google Scholar 

  • Pyrak-Nolte LJ (1996) The seismic response of fractures and the interrelations among fracture properties. Int J Rock Mech Min Sci Geomech Abstr 33(8):787–802

    Article  Google Scholar 

  • Pyrak-Nolte LJ, Meyer LR, Cook NGW (1987) Seismic visibility of fractures. In: Farmer IW et al. (eds) Rock Mechanics: Proceedings of the 28th U.S. Symposium, University of Arizona, Tucson, 29 June–1 July 1987. Balkeman, Rotterdam, Netherlands, pp.47–56

  • Pyrak-Nolte LJ, Myer LR, Cook NGW (1990a) Transmission of seismic waves across single natural fractures. J Geophys Res 95:8617–8638

    Article  Google Scholar 

  • Pyrak-Nolte LJ, Myer LR, Cook NGW (1990b) Anisotropy in seismic velocities and amplitudes from multiple parallel fractures. J Geophys Res 95:11345–11358

    Article  Google Scholar 

  • Resende R, Lamas LN, Lemos JV, Calçada R (2010) Micromechanical modelling of stress waves in rock and rock fractures. Rock Mech Rock Eng 43:741–761

    Article  Google Scholar 

  • Schoenberg M (1980) Elastic wave behavior across linear slip interfaces. J Acoust Soc Am 68(5):1516–1521

    Article  Google Scholar 

  • Schoenberg M (1983) Reflection of elastic waves from periodically stratified media with interfacial slip. Geophys Prospect 31(2):265–292

    Article  Google Scholar 

  • Schoenberg M, Muir F (1989) A calculus for finely layered anisotropic media. Geophysics 54:581–589

    Article  Google Scholar 

  • Schoenberg M, Sayers CM (1995) Seismic anisotropy of fractured rock. Geophysics 60:204–211

    Article  Google Scholar 

  • Sen J, Kazi A (1984) Discontinuity spacing and RQD estimates from finite length scanlines. Int J Rock Mech Min Sci & Geomech Abstr 28:375–382

    Google Scholar 

  • Warburton PM (1980) A stereological interpretation of joint trace data. Int J Rock Mech Min Sci Geomech Abstr 17(4):181–190

    Article  Google Scholar 

  • White JE (1983) Underground sound. Elsevier, New York

    Google Scholar 

  • Zhang L, Einstein HH (2004) Using RQD to estimate the deformation modulus of rock masses. Int J Rock Mech Min Sci 41:337–341

    Article  Google Scholar 

  • Zhao J, Cai JG (2001) Transmission of elastic P-waves across single fractures with a nonlinear normal deformational behavior. Rock Mech Rock Eng 34(1):3–22

    Article  Google Scholar 

  • Zhao XB, Zhao J, Cai JG, Hefny AM (2008) UDEC modelling on wave propagation across fractured rock masses. Comput Geotech 35(1):97–104

    Article  Google Scholar 

  • Zhu JB, Zhao XB, Li JC, Zhao GF, Zhao J (2011) Normally incident wave propagation across a joint set with the virtual wave source method. J Appl Geophys 73(3):283–288

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Geotechnical Engineering Research Unit, University of Tunis El Manar, Ecole Nationale d’Ingénieurs de Tunis, Tunis, Tunisia

    Hatem Gasmi, Essaïeb Hamdi & Nejla Bouden Romdhane

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  1. Hatem Gasmi
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  2. Essaïeb Hamdi
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  3. Nejla Bouden Romdhane
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Correspondence to Essaïeb Hamdi.

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Gasmi, H., Hamdi, E. & Bouden Romdhane, N. Numerical Homogenization of Jointed Rock Masses Using Wave Propagation Simulation. Rock Mech Rock Eng 47, 1393–1409 (2014). https://doi.org/10.1007/s00603-013-0458-8

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