- Volume 15 Issue 3
DOI QR Code
Applicability of exponential stress-strain models for carbonate rocks
- Palchik, Vyacheslav (Department of Geological and Environmental Sciences, Ben-Gurion University)
- Received : 2017.06.03
- Accepted : 2018.03.23
- Published : 2018.06.30
Stress-strain responses of weak-to-strong carbonate rocks used for tunnel construction were studied. The analysis of applicability of exponential stress-strain models based on Haldane's distribution function is presented. It is revealed that these exponential equations presented in transformed forms allow us to predict stress-strain relationships over the whole pre-failure strain range without mechanical testing of rock samples under compression using a press machine and to avoid measurements of axial failure strains for which relatively large values of compressive stress are required. In this study, only one point measurement (small strain at small stress) using indentation test and uniaxial compressive strength determined by a standard Schmidt hammer are considered as input parameters to predict stress-strain response from zero strain/zero stress up to failure. Observations show good predictive capabilities of transformed stress-stress models for weak-to-strong (
- ASTM. (2001), Standard Test Method for Determination of Rock Hardness by Rebound Hammer Method, ASTM Standards, 04.09. (D5873-00)
- Bogusz, A. and Bukowska, M. (2015), "Stress-strain characteristics as a source of information on the destruction of rocks under the influence of load", J. Sustain. Min., 14(1), 46-54. https://doi.org/10.1016/j.jsm.2015.08.007
- Brown, E.T. (1981), Rock Characterization Testing and Monitoring: ISRM Suggested Methods, Pergamon Press, Oxford, U.K.
- Chen, L.H. and Labuz, J.F. (2006), "Indentation of rock by wedge-shaped tools", Int. J. Rock Mech. Min. Sci., 43(7), 1023-1033. https://doi.org/10.1016/j.ijrmms.2006.03.005
- Ching, L.L., Ta, P.C., Dong, H.Y. and Ching, S.C, (1997), "Stressstrain relationship for granular materials based on hypothesis of best fit", Int. J. Solid. Struct., 34(31-32), 4087-4100. https://doi.org/10.1016/S0020-7683(97)00015-2
- Duncan, J.M. and Chang, C.Y. (1970), "Non-linear analysis of stress and strain in soils", J. Soil Mech. Found. Div., 96, 1629-1653.
- Fairhurst, C.E. and Hudson, J.A. (1999), "Draft IRSM suggested method for the complete stress-strain curve for intact rock in uniaxial compression", Int. J. Rock Mech. Min. Sci., 36(3), 281-289.
- Garaga, A. and Latha, G.M. (2010), "Intelligent prediction of the stress-strain response of intact and jointed rocks", Comput. Geotech., 37(5), 629-637. https://doi.org/10.1016/j.compgeo.2010.04.001
- Gutierrez, M., Kolderup, U.M. and Hoeg, K. (2000), "Model for 3D time-dependent chalk stress-strain behavior", Proceedings of the 6th North Sea Symposium, Brington, UK.
- Haas, C.J. (1989), Static Stress-Strain Relationships, in Physical Properties of Rocks and Minerals, Hemisphere Publishing, Taylor and Francis, London, U.K.
- Habimana, J., Labiouse, V. and Decoeudres, F. (2002), "Geomechanical characterisation of cataclastic rocks: Expirence from the Cleuson-Dixence project", Int. J. Rock Mech. Min. Sci., 39(6), 677-693. https://doi.org/10.1016/S1365-1609(02)00042-4
- Haftani, M., Bohloli, B., Moosavi, M., Nouri, A., Moradi, M. and Maleki Javan, M.R. (2013), "A new method for correlating rock strength to indentation tests", J. Petrol Sci. Eng., 112, 24-31. https://doi.org/10.1016/j.petrol.2013.11.027
- Haldane, J.B.S. (1919), "The combination of linkage values and the calculation of distances between the loci of linked factors", J. Genet., 8(29), 299-309.
- Hazewinkel, M. (2001), Taylor Formula: Encyclopedia of Mathematics, Springer
- Kalyan, B., Murthy, Ch.S.N. and Choudhary, R.P. (2015), "Rock indentation indices as criteria in rock excavation technology-A critical review", Proc. Earth Planet. Sci., 11, 149-158. https://doi.org/10.1016/j.proeps.2015.06.019
- Karaman, K. and Kesimal, A. (2015), "A comparative study of Schmidt hammer test methods for estimating the uniaxial compressive strength of rocks", Bull. Eng. Geol. Environ., 74(2), 507-520. https://doi.org/10.1007/s10064-014-0617-5
- Kodner, R.B. (1963), "Hyperbolic stress-strain response: Cohesive soils", J. Soil Mech. Found. Div., 89(1), 115-143.
- Kumara, J.J. and Hayano, K. (2016), "Importance of particle shape on stress-strain behaviour of crushed stone-sand mixtures", Geomech. Eng., 10(4), 455-470. https://doi.org/10.12989/gae.2016.10.4.455
- Li, Y., Zhang, S. and Zhang, B. (2018). "Dilatation characteristics of the coals with outburst proneness under cyclic loading conditions and the relevant applications", Geomech. Eng., 14(5), 459-466. https://doi.org/10.12989/GAE.2018.14.5.459
- Liu, H.H., Rutqvist, J. and Berryman, J.G. (2009), "On the relationship between stress and elastic strain for porous and fractured rock", Int. J. Rock Mech. Min. Sci., 46(2), 289-296. https://doi.org/10.1016/j.ijrmms.2008.04.005
- Muravskii, G.B. (1996), "On analytical description of stress-strain relationship for rocks and soils", Commun. Num. Meth. Eng., 12(12), 827-834. https://doi.org/10.1002/(SICI)1099-0887(199612)12:12<827::AID-CNM23>3.0.CO;2-0
- Palchik, V. (2006), "Stress-strain model for carbonate rocks based on Haldane's distribution function", Rock Mech. Rock Eng., 39 (3), 215-232. https://doi.org/10.1007/s00603-005-0076-1
- Palchik, V. (2007), "Use of stress-strain model based on Haldane's distribution function for prediction of elastic modulus", Int. J. Rock Mech. Min. Sci., 44(4), 514-524. https://doi.org/10.1016/j.ijrmms.2006.09.003
- Palchik, V. (2012), "Relation between normalized axial stress and failure strain in heterogeneous carbonate rocks exhibiting large axial strains", Rock Mech. Rock Eng., 45(2), 217-224. https://doi.org/10.1007/s00603-011-0172-3
- Palchik, V. (2014), "Use of Descartes folium equation for deriving a relation between total aperture of fractures after uniaxial compression and strain parameters of different rocks exhibiting negative total volumetric strain", Rock Mech. Rock Eng., 47(6), 2075-2086. https://doi.org/10.1007/s00603-013-0510-8
- Palchik, V. and Hatzor, Y.H. (2000), "Correlation between mechanical strength and microstructural parameters of dolomites and limestones in the Judea group-Israel", Isr. J. Earth Sci., 49(2), 65-79. https://doi.org/10.1560/LGVQ-HA9E-P1X7-YRAT
- Puzrin, A.M. and Burland, J.B. (1996), "A logarithmic stress-strain function for rocks and soils", Geotechnique, 46(1), 157-164. https://doi.org/10.1680/geot.1918.104.22.168
- Schmidt, E. (1951), "A non-destructive concrete tester", Concrete, 59, 51-54.
- Shibuya, S. (2002), "A non-linear stress-stiffness model for geomaterials at small to intermediate strains", Geotech. Geol. Eng., 20(4), 333-369. https://doi.org/10.1023/A:1021274500821
- Tatsuoka, F. and Shibuya, S. (1992), "Deformation characteristics of soils and rocks from field and laboratory tests", Proceedings of the 9th Asian Conference on Soil Mechanics and Foundation Engineering, Bangkok, Thailand, December.
- Tharp, T.M. and Scarbrough, M.G. (1994), "Application of hyperbolic stress-strain models for sandstone and shale to fold wavelength in Mexican Ridges Foldbelt", J. Struct. Geol., 16(12), 1603-1618. https://doi.org/10.1016/0191-8141(94)90130-9
- Yadollahia, M.M. and Benli, A. (2017). "Stress-strain behavior of geopolymer under uniaxial compression", Comput. Concrete, 20(4), 381-389.