Abstract
The mechanical behaviour of Bentheim sandstone, a homogeneous quartz-rich sandstone with porosity of 22.8%, was investigated by triaxial compression tests conducted on dry samples. At confining pressures up to 35 MPa, the failure mode was characterized by a typical brittle deformation regime, as the samples showed dilatancy and failed by strain softening and brittle faulting. Previous studies have shown that the mechanical behaviour and failure mode of brittle porous granular rocks are governed by the time-dependent growth of microcracks. We analyse this process using the “Pore Crack Model” based on fracture mechanics analysis. It is consistent with the microstructure of porous granular rocks since it considers the growth of axial cracks from cylindrical holes in two dimensions. These cracks grow when their stress intensity factors reach the subcritical crack growth limit. Interaction between neighbouring cracks is introduced by calculating the stress intensity factor as the sum of two terms: a component for an isolated crack and an interaction term computed using the method of successive approximations. It depends on crack length, pore radius, pore density, and applied stresses. The simulation of crack growth from cylindrical holes, associated with a failure criterion based on the coalescence of interacting cracks, is used to compare the theoretical stress at the onset of dilatancy and at macroscopic rupture to the experimental determined values. Our approach gives theoretical results in good agreement with experimental data when microstructural parameters consistent with observations are introduced
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ashby, M. F. and Hallam, S. D. (1986), The Failure of Brittle Solids Containing Small Cracks under Compressive Stress States, Acta Metall. 34, 497–510.
Atkinson, B. K. (1984), Subcritical Crack Growth in Geological materials, J. Geophys. Res. 89, 4077–4114.
Atkinson, B. K. and Meredith, P. G., The theory of subcritical crack growth with applications to minerals and rocks. In Fracture Mechanics of Rocks (ed. Atkinson B. K.) (Academic Press, London 1989a).
Atkinson, B. K. and Meredith, P. G., Experimental fracture mechanics data for rocks and minerals, In Fracture Mechanics of Rocks (ed. Atkinson B. K.) (Academic Press, London 1989b) pp. 477–525.
Aubertin, M. and Simon, R. (1997), A Damage Initiation Criterion for Low Porosity Rocks, Int. J. Rock Mech. and Min. Sci. 34, 3–4.
Baud, P. and Reuschlé, T. (1997), A Theoretical Approach to the Propagation of Interacting Cracks, Geophys. J. Int. 130, 460–469.
Costin, L. S. (1983), A Microcrack Model for the Deformation and Failure of Brittle Rock, J. Geophys. Res. 88, 9485–9492.
Horii, H. and Nemat-Nasser, S. (1986), Brittle Failure in Compression: Splitting, Faulting and Brittle-ductile Transition, Phil. Trans. R. Soc. Lond. 319, 337–374.
INGRAFFEA, A. R., Theory of crack initiation and propagation in rock. In Fracture Mechanics of Rocks (ed. Atkinson B. K.) (Academic Press, London 1987) pp. 71–110.
Jaeger, J. C. and CooK, N. G. W., Fundamentals of Rock Mechanics (Chapman and Hall, London 1979).
Klein, E., Baud, P., Reuschlé, T., and Wong, T.F. (2001), Mechanical Behaviour and Failure Mode of Bentheim Sandstone under Triaxial Compression, Phys. Chem. Earth (A). 26, 21–25.
Krantz, R. L. (1979), Crack-crack and Crack-pore Interactions in Stressed Granite, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 16, 37–47.
Lockner, D. A., Byerlee, J. D., Kuksenko, V., Ponomarev, A., and Sidorin, A., Observation of quasistatic fault growth from acoustic emissions. In Fault Mechanics and Transport Properties of Rocks (eds. Evans B. and Wong T.-F.) (Academic Press, San Diego 1992) pp. 1–31.
Martin, J. C. and Serdengecti, S. (1984), Subsidence over Oil and Gas Fields, Geol. Soc. Am. Rev. Eng. Geol. 6, 23–24.
Menendez, B., Zhu, W., and Wong, T.F. (1996), Micromechanics of Brittle Faulting and Cataclastic Flow in Berea Sandstone, J. Struct. Geol. 18, 1–16.
Muskhelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity (N000rdhoff, Groningen 1977).
Paterson, M. S., Experimental Deformation — The Brittle Field (Springer-Verlag, New York 1978).
Read, M. D., Ayling, M. R., Meredith, P. G., and Murrell, S. A. F. (1995), Microcracking During Triaxial Deformation of Porous Rocks Monitored by Changes in Rock Physical Properties. II. Pore Volumometry and Acoustic Emission Measurements on Water-saturated Rocks, Tectonophys. 245, 223–226.
Sammis, C. G. and Ashby, M. F. (1986), The Failure of Brittle Porous Solids under Compressive Stress States, Acta Metall. 34, 511–526.
Schutjens, P. M. T. M., Hausenblas, M., Dijkshoorn, M., and Van Munster, J. G. (1995), The Influence of Intergranular Microcracks on the Petrophysical Properties of Sandstone — Experiments to Quantify effects of core damage, Proc. Int. Symp. Soc. Core Analysts.
Segall, P. and Pollard, D. D. (1980), Mechanics of Discontinous Faults, J. Geophys. Res. 85, 4337–4350.
Shah, R. C., Mechanics of crack growth. In Proc. Eighth Natn. Symp. on Fract. Mech.) (ASTM Spec. Tech., 1976).
Sm, G. C., Handbook of Stress Intensity Factors for Researchers and Engineers (Lehigh Univ., Bethlehem, PA 1973).
Sm, G. C. and Liebowitz, H., Mathematical theories of brittle fracture, In Fracture, an Advanced treatise. (ed. Liebowitz H.) (Academic Press, London 1968).
Sokolnikoff, I. S., Mathematical theory of elasticity (McGraw-Hill, New York 1956).
Teufel, L. W., Rhett, D. W., and Farrell, H. E. (1991), Effect of Reservoir Depletion and Pore Pressure Drawdown on in situ Stress and Deformation in the Ekofish Field, North Sea., Proc. U.S. Rock Mech. Symp. 32, 63–72.
Underwood, E. E., Quantitative Stereology (Addison-Wesley, Reading, 1970).
Veeken, C. A. M., Walters, J. V., Kenter, C. J., and Davis, D. R., Use of plasticity models for predicting borehole stability. In Rocks at Great Depth (eds. Maury V. and Fourmaintaux D.) (Balkema, Rotterdam 1989) pp. 835–844.
Vos, M. W. (1990). Selection of Outcrop Samples for Acoustic Measurements on Reservoir rock, Ph.D. Thesis, Delft University of Technology.
Wiederhorn, S. M., Freiman, S. W., Fuller Jr, E. R., and Simmons, C. J. (1982), Effects of Water and other Dielectrics on Crack Growth, J. Mater. Sci. 17, 3460–3478.
Wong, T.F., David, C., and Zhu, W. (1997), The Transition from Brittle Faulting to Cataclastic Flow in Porous Sandstones: Mechanical Deformation, J. Geophys. Res. 102, 3009–3025.
Wong, T.F., Szeto, H., and Zhang, J. (1992), Effect of Loading Path and Porosity on the Failure Mode of Porous Rocks, Appl. Mech. Rev. 45, 281–293.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Basel AG
About this chapter
Cite this chapter
Klein, E., Reuschlé, T. (2003). A Model for the Mechanical Behaviour of Bentheim Sandstone in the Brittle Regime. In: Kümpel, HJ. (eds) Thermo-Hydro-Mechanical Coupling in Fractured Rock. Pageoph Topical Volumes. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8083-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8083-1_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-0253-5
Online ISBN: 978-3-0348-8083-1
eBook Packages: Springer Book Archive