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Effective Elastic Properties of Fractured Rocks: Dynamic vs. Static Considerations

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Abstract

We present a new technique for static computations of effective elastic properties of multiple fractured rocks. This approach is based on the viscoelastic rotated staggered finite-difference (FD) grid wave propagation technique. Our simulations are used to explain discrepancies of some recent numerical studies. The focus is on scale effects of a so-called representative volume element (RVE). From the point of view of classical micromechanics we review different numerical techniques: Static as well as dynamic numerical experiments. We show that the differential effective medium theory (DEM) is capable of producing satisfactory predictions of effective elastic moduli. For non-dilute crack densities this is not the case for the non-interacting approximation (NIA).

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References

  • J. G. Berryman (1992) ArticleTitleSingle-scattering approximations for coefficients in Biot’s equations of poroelasticity Journal of the Acoustical Society of America 91 551–571 Occurrence Handle10.1121/1.402518 Occurrence Handle1992ASAJ...91..551B

    Article  ADS  Google Scholar 

  • B. Budiansky R. J. O’Connell (1976) ArticleTitleElastic moduli of a cracked solid International Journal of Solids and Structures 12 81–97 Occurrence Handle0318.73065 Occurrence Handle10.1016/0020-7683(76)90044-5

    Article  MATH  Google Scholar 

  • T. Dahm T. Becker (1998) ArticleTitleOn the elastic and viscous properties of media containing strongly interacting in-plane cracks Pure and Applied Geophysics 151 1–16 Occurrence Handle10.1007/s000240050102 Occurrence Handle1998PApGe.151....1D

    Article  ADS  Google Scholar 

  • P.M. Davis L. Knopoff (1995) ArticleTitleThe elastic modulus of media containing strongly interacting antiplane cracks Journal of Geophysical Research 100 18.253–18.258 Occurrence Handle1995JGR...10018253D

    ADS  Google Scholar 

  • Grechka V., Kachanov M. (2005). Multiple fractures in rocks: Effective orthotropy and seismic characterization. 75th Ann. Internat. Mtg., Soc. of Expl. Geophys., Expanded Abstracts, page ANI 3.2.

  • V. Grechka M. Kachanov (2006) ArticleTitleEffective elasticity of rocks with closely spaced and intersecting cracks Geophysics 71 IssueID3 D85–D91 Occurrence Handle10.1190/1.2197489

    Article  Google Scholar 

  • R. Hill (1963) ArticleTitleElastic properties of reinforced solids: Some theoretical principles Journal of the Mechanics and Physics of Solids 11 357–372 Occurrence Handle0114.15804 Occurrence Handle10.1016/0022-5096(63)90036-X Occurrence Handle1963JMPSo..11..357H

    Article  MATH  ADS  Google Scholar 

  • M. Kachanov (1992) ArticleTitleEffective elastic properties of cracked solids: critical review of some basic concepts Applied Mechanics Reviews 45 IssueID8 304–335 Occurrence Handle10.1115/1.3119761

    Article  Google Scholar 

  • Krüger O. S., Saenger, E. H., Buske, S., and Shapiro, S. A. (2004). Reflection coefficients of fractured rocks: A numerical study. 74th Ann. Internat. Mtg., Soc. of Expl. Geophys., Expanded Abstracts, page SM1.6.

  • B. Orlowsky E. H. Saenger Y. Guéguen S. A. Shapiro (2003) ArticleTitleEffects of parallel crack distributions on effective elastic properties - a numerical study International Journal of Fractures 124 IssueID3-4 L171–L178 Occurrence Handle10.1023/B:FRAC.0000022563.29991.80

    Article  Google Scholar 

  • M. Ostoja-Starzewski (1999) ArticleTitleScale effects in materials with random distributions of needles and cracks Mechanics of Materials 31 883–893 Occurrence Handle10.1016/S0167-6636(99)00039-3

    Article  Google Scholar 

  • E. H. Saenger O.S. Krüger S.A. Shapiro (2004) ArticleTitleEffective elastic properties of randomly fractured soils: 3D numerical experiments Geophysical Prospecting 52 IssueID3 183–195 Occurrence Handle10.1111/j.1365-2478.2004.00407.x

    Article  Google Scholar 

  • E. H. Saenger S. A. Shapiro (2002) ArticleTitleEffective velocities in fractured media: A numerical study using the rotated staggered finite-difference grid Geophysical Prospecting 50 IssueID2 183–194 Occurrence Handle10.1046/j.1365-2478.2002.00309.x

    Article  Google Scholar 

  • E. H. Saenger S. A. Shapiro Y. Keehm (2005) ArticleTitleSeismic effects of viscous Biot-coupling: Finite difference simulations on micro-scale Geophysical Research Letters 32 L14310 Occurrence Handle10.1029/2005GL023222 Occurrence Handle2005GeoRL..3214310S

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Fachrichtung Geophysik, Freie Universität Berlin, Malteserstr. 74-100, 12249, Berlin, Germany

    Erik H. Saenger, Oliver S. Krüger & Serge A. Shapiro

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  1. Erik H. Saenger
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  2. Oliver S. Krüger
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  3. Serge A. Shapiro
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Correspondence to Erik H. Saenger.

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Saenger, E.H., Krüger, O.S. & Shapiro, S.A. Effective Elastic Properties of Fractured Rocks: Dynamic vs. Static Considerations. Int J Fract 139, 569–576 (2006). https://doi.org/10.1007/s10704-006-0105-4

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  • DOI: https://doi.org/10.1007/s10704-006-0105-4

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