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A Combined Three-Dimensional Geological-Geostatistical-Numerical Model of Underground Excavations in Rock

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Summary.

This paper exploits geological and borehole geotechnical data obtained in the exploratory phase of a tunneling project to investigate in a first place if the kriging interpolation scheme may effectively reproduce the spatial variability of rock mass quality (Rock Mass Rating, RMR) in the vicinity of tunnels. For this purpose a quick solver in Fortran has been developed that performs variography analysis of 3D spatial data, fast kriging estimations of RMR between borehole sampling locations at the centroids of the elements of the numerical model, and model validation. For the purpose of an integrated underground excavation design, a step further is made by incorporating into the 3D mechanical numerical model of the rock mass, the three-dimensional (3D) solid geological model, thus coupling the geology with the ground (geotechnical) model (i.e. each element of the numerical model is assigned a geological material). The mechanical properties of each finite difference cell (or Representative Elementary Volume) of the ground model were then prescribed according to its geological type, the spatial heterogeneity of the rock mass expressed quantitatively with the kriging model, and the upscaling calculations of the mechanical properties of the intact rocks determined in the laboratory, based on the size-effect (strength dependence on size) and Damage Theory. Furthermore, a preliminary numerical simulation of the advance of unsupported tunnels in the model of the heterogeneous rock mass was performed for illustration purposes.

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References

  • E. C. Aifantis (1999) ArticleTitleStrain gradient interpretation of size effects Int. J. Fracture 95 299–314 Occurrence Handle10.1023/A:1018625006804

    Article  Google Scholar 

  • M. Aubertin L. Li R. Simon (2000) ArticleTitleA multiaxial stress criterion for short- and long-term strength of isotropic rock media Int. J. Rock Mech. Min. Sci. 37 1169–1193 Occurrence Handle10.1016/S1365-1609(00)00047-2

    Article  Google Scholar 

  • O. Aydan R. Ulusay T. Kawamoto (1997) ArticleTitleAssessment of rock mass strength for underground excavations Int. J. Rock Mech Min. Sci. 34 IssueID3–4 705

    Google Scholar 

  • N. Barton (2002) ArticleTitleSome new Q-value correlations to assist in site characterization and tunnel design Int. J. Rock Mech. Min. Sci. 39 185–216 Occurrence Handle10.1016/S1365-1609(02)00011-4

    Article  Google Scholar 

  • Z. P. Bazant E.-P. Chen (1997) ArticleTitleScaling of structural failure Appl. Mech. Rev. 50 IssueID10 593–627 Occurrence Handle10.1115/1.3101672

    Article  Google Scholar 

  • Z. P. Bazant F.-B. Lin H. Lippmann (1993) ArticleTitleFracture energy release and size effect in borehole breakout Int. J. Numer. Analyt. Meth. Geomech. 17 1–14 Occurrence Handle10.1002/nag.1610170102

    Article  Google Scholar 

  • J. Bear (1972) Dynamics of fluids in porous media Dover New York

    Google Scholar 

  • Z. T. Bieniawski (1978) ArticleTitleDetermining Rock Mass Deformability: Experience from Case Histories Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 15 237–247 Occurrence Handle10.1016/0148-9062(78)90956-7

    Article  Google Scholar 

  • Bieniawski, Z. T. (1979): The geomechanics classification in rock engineering applications. Proc. 4th ISRM Congress, Montreux Vol. 2, 41–48.

  • Z. T. Bieniawski (1989) Engineering rock mass classifications Wiley New York

    Google Scholar 

  • J.-P. Chiles P. Delfiner (1999) Geostatistics: modeling spatial uncertainty John Wiley & Sons Toronto

    Google Scholar 

  • Exadaktylos, G. E. (2005): Mechanical properties of intact sedimentary and metamorphic rocks, Final Report of DIAS, Project No. DIAS-EVK4-CT2002-00080, http://minelab.mred.tuc.gr/dias.

  • G. E. Exadaktylos I. Vardoulakis (2001) ArticleTitleMicrostructure in linear elasticity and scale effects: a reconsideration of basic rock mechanics and rock fracture mechanics Tectonophysics 335 IssueID1–2 81–110 Occurrence Handle10.1016/S0040-1951(01)00047-6

    Article  Google Scholar 

  • G. A. Fenton E. H. Vanmarcke (1990) ArticleTitleSimulation of random fields via local average subdivision J. Engng. Mech. 116 IssueID8 1733–1749

    Google Scholar 

  • G. Frantziskonis E. C. Aifantis (2002) ArticleTitleOn the stochastic interpretation of gradient-dependent constitutive equations Eur. J. Mech. A/Solid. 21 589–596 Occurrence Handle10.1016/S0997-7538(01)01201-3

    Article  Google Scholar 

  • Griffiths, D. V., Fenton, G. A. (2000): Influence of soil strength spatial variability on the stability of an undrained clay slope by finite elements. Slope Stability 2000, Proc., GeoDenver, ASCE, New York, 184–193.

  • D. V. Griffiths G. A. Fenton (2001) ArticleTitleBearing capacity of spatially random soil: The undrained clay Prandtl problem revisited Geotechnique 51 IssueID4 351–359 Occurrence Handle10.1680/geot.51.4.351.39396

    Article  Google Scholar 

  • D. V. Griffiths G. A. Fenton (2004) ArticleTitleProbabilistic Slope Stability Analysis by Finite Elements J. Geotechnical and Geoenvironmental Engineering 130 IssueID5 507–518 Occurrence Handle10.1061/(ASCE)1090-0241(2004)130:5(507)

    Article  Google Scholar 

  • Hoek, E., Brown, E. T. (1988): The Hoek and Brown failure criterion – a 1988 update. In: Rock Engineering for Underground Excavations: Proceedings of 15th Can. Rock Mechanics Symposium Toronto, 31–38.

  • E. Hoek E. T. Brown (1998) ArticleTitlePractical estimates of rock mass strength Int. J. Rock Mech. Min. Sci. 34 IssueID8 1165–1186 Occurrence Handle10.1016/S0148-9062(97)00305-7

    Article  Google Scholar 

  • Hoek, E., Kaiser, P. K., Bawden, W. F. (1995): Support of underground excavations in hard rock, Balkema Publishers.

  • E. Hoek P. Marinos M. Benissi (1998) ArticleTitleApplicability of the geological strength index (GSI) classification for very weak and sheared rock masses – The case of the Athens Schist formation B. Engng. Geol. Environ. 57 151–160 Occurrence Handle10.1007/s100640050031

    Article  Google Scholar 

  • E. H. Isaaks R. M. Srivastava (1989) Applied geostatistics Oxford University Press New York

    Google Scholar 

  • Itasca Consulting Group Inc. (2002): FLAC3D, Fast Lagrangian analysis of continua in 3 dimensions: user’s guide. Minneapolis, Minnesota USA.

  • A. G. Journel C. H. J. Huijbregts (1978) Mining geostatistics Academic Press London

    Google Scholar 

  • L. M. Kachanov (1986) Introduction to continuum damage mechanics Martinus Nijhoff The Netherlands

    Google Scholar 

  • Kalamaras, G. S., Bieniawski, Z. T. (1995): A rock mass strength for coal seams incorporating the effect of time. In: Fujii, T. (ed.), Proceedings of 8th Congress ISRM, Tokyo, 295–302.

  • K. Kim H. Gao (1995) ArticleTitleProbabilistic approaches to estimating variation in the mechanical properties of rock masses Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 32 IssueID2 111–120 Occurrence Handle10.1016/0148-9062(94)00032-X

    Article  Google Scholar 

  • Kitanidis, P. K. (1997): Introduction to geostatistics, application in hydrogeology. Cambridge Univ. Press, 86–95.

  • J. Lemaitre (1992) A course on damage mechanics Springer Verlag Berlin

    Google Scholar 

  • Matheron, G. (1971): The theory of regionalized variables and its applications. Ecole de Mines, Fontainebleau, France.

  • MATLAB 6.0 (2000): The MathWorks Inc., Natick, Massachusetts, USA.

  • Mitri, H. S., Edrissi, R., Henning, J. (1994): Finite element modeling of cable-bolted stopes in hard rock underground mines. Presented at the SME Annual Meeting, Albuquerque, New Mexico, 14–17 February 1994, 94–116.

  • Negro, A., Queiroz, B. I. P. (2000): Prediction and performance of soft ground tunnels. In geotechnical aspects of underground construction in soft ground, Balkema, Tokyo, Japan, 409–418.

  • G. A. Nicholson Z. T. Bieniawski (1990) ArticleTitleA nonlinear deformation modulus based on rock mass classification Int. J. Min. Geol. Eng. 8 IssueID3 181–202 Occurrence Handle10.1007/BF01554041

    Article  Google Scholar 

  • F. Ouchterlony (1982) ArticleTitleReview of fracture toughness testing of rock Solid Mech. Arch. 7 131–211

    Google Scholar 

  • M. Panet (1993) Understanding deformations in tunnels Comprehensive Rock Engineering NumberInSeries1 Pergamon Press Oxford 663–690

    Google Scholar 

  • J. Planas M. Elices G. V. Guinea F. J. Gomez D. A. Cendon I. Arbilla (2003) ArticleTitleGeneralizations and specializations of cohesive crack models Engng. Fracture Mech. 70 IssueID14 1759–1776 Occurrence Handle10.1016/S0013-7944(03)00123-1

    Article  Google Scholar 

  • Ramamurthy, T. (1986): Stability of rock mass. 8th 1.G.S. Annual Lecture lndn. Geotech. J. 16, 1–74.

  • Ramamurthy, T., Rao, G. V., Rao, K. S. (1985): Strength criterion for rocks. Proc., lndn. Geotech. Conf. Roorkee, Vol. I, 59–64.

  • Rao, K. S. (1984): Strength and deformation behaviour of sandstones. PhD Thesis. IIT Delhi, India.

  • Read, S. A. L., Richards, L. R., Perrin, N. D. (1999): Applicability of the Hoek–Brown failure criterion to New Zealand greywacke rocks. Proceedings of the 9th International Society for Rock Mechanics Congress, Paris, Vol. 2, 655–660.

  • Serafim, L. J., Pereira, P. J. (1983): Consideration on the geomechanical classification of Bieniawski. Proceedings International Symposium Engineering Geology and Underground Construction, Vol. 1, Lisbon, Portugal, 1133–1142.

  • B. Singh M. N. Viladkar N. K. Samadhiya V. K. Mehrotra (1997) ArticleTitleRock mass strength parameters mobilized in tunnels Tunn. Undergr. Sp. Tech. 12 IssueID1 47–54 Occurrence Handle10.1016/S0886-7798(96)00060-0

    Article  Google Scholar 

  • Surpac Vision (2003): Users Reference Manual. Surpac Minex Group Pty Ltd.

  • Trueman, R. (1988): An evaluation of strata support techniques in dual life gateroads. PhD Thesis. University of Wales, Cardiff.

  • C. Tsoutrelis G. E. Exadaktylos (1993) ArticleTitleEffect of rock discontinuities on certain rock strength and fracture energy parameters under uniaxial compression Geotech. Geol. Engng. 11 81–105 Occurrence Handle10.1007/BF00423337

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Dynamic, Tectonic and Applied Geology, Faculty of Geology and Geoenvironment, University of Athens, Greece

    M. Stavropoulou

  2. Department of Mineral Resources Engineering, Technical University of Crete, Chania, Greece

    G. Exadaktylos & G. Saratsis

Authors
  1. M. Stavropoulou
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  2. G. Exadaktylos
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  3. G. Saratsis
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Stavropoulou, M., Exadaktylos, G. & Saratsis, G. A Combined Three-Dimensional Geological-Geostatistical-Numerical Model of Underground Excavations in Rock. Rock Mech. Rock Engng. 40, 213–243 (2007). https://doi.org/10.1007/s00603-006-0125-4

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