Influence of Hardening and Softening on Limit Pressure of Cylindrical Cavity Expansion
Publication: International Journal of Geomechanics
Volume 19, Issue 4
Abstract
This paper presents a large strain solution for the problem of cylindrical cavity expansion embedded in hardening–softening, non-associative Mohr-Coulomb material. The solution is obtained by transforming the problem from the original radial domain to the effective stress space in the hardening regime and to the effective plastic strain in the softening regime. The robustness of the solution is demonstrated by tracing the entire loading history of a pressurized cavity embedded in weak sandstones in large expansions and the calculation of the limit pressure beyond which the hole expands without further pressurization. The calculated radial stress profiles are completely smooth at the elastoplastic (EP) and the hardening–softening boundaries. The calculated limit pressure increases with increasing degree of pressure sensitivity, as expected for a stronger material. The limit pressure decreases dramatically as the rate of material softening increases. The elastic perfectly plastic limit-pressure solution, which ignores hardening, is quite close to the value determined from the full EP hardening with the same peak strength. The combination of non-associativity and material softening causes the breakdown of the solution before reaching the limit pressure due to emergence of bifurcation in the form of shear banding and surface instabilities.
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Acknowledgments
The first author would like to thank the A. G. Leventis Foundation for his educational grant.
References
Alonso, E., L. R. Alejano, G. Fdez-Manin, and C. Carranza-Torres. 2003. “Ground response curves for rock masses exhibiting strain-softening behaviour.” Int. J. Numer. Anal. Methods Geomech. 27 (13): 1153–1185. https://doi.org/10.1002/nag.315.
Alsiny, A., I. Vardoulakis, and A. Drescher. 1992. “Deformation localization in cavity inflation experiments on dry sand.” Géotechnique 42 (3): 395–410. https://doi.org/10.1680/geot.1992.42.3.395.
Carter, J. P., J. R. Booker, and S. K. Yeung. 1986. “Cavity expansion in cohesive frictional soils.” Géotechnique 36 (3): 349–358. https://doi.org/10.1680/geot.1986.36.3.349.
Chau, K. T., and J. Rudnicki. 1990. “Bifurcations of compressible pressure-sensitive materials in plane strain tension and compression.” J. Mech. Phys. Solids 38 (6): 875–898. https://doi.org/10.1016/0022-5096(90)90044-5.
Chen, S. L., and Y. N. Abousleiman. 2012. “Exact undrained elasto-plastic solution for cylindrical cavity expansion in modified cam clay soil.” Géotechnique 62 (5): 447–456. https://doi.org/10.1680/geot.11.P.027.
Chen, S. L., and Y. N. Abousleiman. 2013. “Exact drained solution for cylindrical cavity expansion in modified cam clay soil.” Géotechnique 63 (6): 510–517. https://doi.org/10.1680/geot.11.P.088.
Durban, D., and P. Papanastasiou. 1997a. “Cylindrical cavity expansion and contraction in pressure sensitive geomaterials.” Acta Mech. 122 (1–4): 99–122. https://doi.org/10.1007/BF01181993.
Durban, D., and P. Papanastasiou. 1997b. “Elastoplastic response of pressure sensitive solids.” Int. J. Num. Anal. Meth. Geomech. 21 (7): 423–441. https://doi.org/10.1002/(SICI)1096-9853(199707)21:7%3C423::AID-NAG882%3E3.0.CO;2-T.
Gibson, R. E., and W. F. Anderson. 1961. “In situ measurement of soil properties with the pressuremeter.” Civ. Eng. Public Works Rev. 56 (658): 615–618.
Hughes, J. M. O., C. P. Wroth, and D. Windle. 1977. “Pressuremeter tests in sands.” Géotechnique 27 (4): 455–477. https://doi.org/10.1680/geot.1977.27.4.455.
Mántaras, F. M., and F. Schnaid. 2002. “Cylindrical cavity expansion in dilatant cohesive-frictional materials.” Géotechnique 52 (5): 337–348. https://doi.org/10.1680/geot.2002.52.5.337.
Marchi, M., G. Gottardi, and K. Soga. 2014. “Fracturing pressure in clay.” J. Geotech. Geoenviron. Eng. 140 (2): 04013008. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001019.
Palmer, A. C. 1972. “Undrained plane-strain expansion of a cylindrical cavity in clay: A simple interpretation of the pressuremeter test.” Géotechnique 22 (3): 451–457. https://doi.org/10.1680/geot.1972.22.3.451.
Papanastasiou, P., and I. Vardoulakis. 1992. “Numerical treatment of progressive localization in relation to borehole stability.” Int. J. Num. Anal. Meth. Geomech. 16 (6): 389–424. https://doi.org/10.1002/nag.1610160602.
Papanastasiou, P., and I. Vardoulakis. 1989. “Bifurcation analysis of deep boreholes: II. Scale effect.” Int. J. Num. Anal. Meth. Geomech. 13 (2): 183–198. https://doi.org/10.1002/nag.1610130206.
Papanastasiou, P., and D. Durban. 1997. “Elastoplastic analysis of cylindrical cavity problems in geomaterials.” Int. J. Numer. Anal. Methods Geomech. 21 (2): 133–149. https://doi.org/10.1002/(SICI)1096-9853(199702)21:2%3C133::AID-NAG866%3E3.0.CO;2-A.
Papanastasiou, P., M. Thiercelin, J. Cook, and D. Durban. 1995. “The influence of plastic yielding on breakdown pressure in hydraulic fracturing.” In Proc., 35th US Symp. on Rock Mechanics, edited by J. Daemen and R. Schultz, 281–286. Rotterdam, Netherlands: A.A. Balkema.
Randolph, M. F., J. P. Carter, and C. P. Wroth. 1979. “Driven piles in clay—The effects of installation and subsequent consolidation.” Géotechnique 29 (4): 361–393. https://doi.org/10.1680/geot.1979.29.4.361.
Rudnicki, J. W., and J. R. Rice. 1975. “Conditions for the localization of deformation in pressure-sensitive dilatant material.” J. Mech. Phys. Solids 23 (6): 371–394. https://doi.org/10.1016/0022-5096(75)90001-0.
Vardoulakis, I., and P. Papanastasiou. 1988. “Bifurcation analysis of deep boreholes: I. Surface instabilities.” Int. J. Num. Anal. Meth. Geomech. 12 (4): 379–399. https://doi.org/10.1002/nag.1610120404.
Vardoulakis, I., and J. Sulem. 1995. Bifurcation Analysis in Geomechanics. Glasgow, Scotland: Blackie Academic & Professional, an Imprint of Chapman & Hall.
Vrakas, A. 2016. “Relationship between small and large strain solutions for general cavity expansion problems in elasto-plastic soils.” Comput. Geotech. 76 (Jun): 147–153. https://doi.org/10.1016/j.compgeo.2016.03.005.
Yu, H. S. 2000. Cavity expansion methods in geomechanics. Dordrecht, Netherlands: Springer-Science+Business Media.
Yu, H. S., and G. T. Houlsby. 1991. “Finite cavity expansion in dilatant soils: Loading analysis.” Géotechnique 41 (2): 173–183. https://doi.org/10.1680/geot.1991.41.2.173.
Zervos, A., P. Papanastasiou, and I. Vardoulakis. 2001. “Modelling of localisation and scale effect in thick-walled cylinders with gradient elastoplasticity.” Int. J. Solids Struct. 38 (30–31): 5081–5095. https://doi.org/10.1016/S0020-7683(00)00337-1.
Zervos, A., I. Vardoulakis, and P. Papanastasiou. 2007. “Influence of nonassociativity on localization and failure in geomechanics based on gradient elastoplasticity.” Int. J. Geomech. 7 (1): 63–74. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:1(63).
Zhao, C. F., Y. Fei, C. Zhao, and S. H. Jia. 2018. “Analysis of expanded radius and internal expanding pressure for undrained cylindrical cavity expansion.” Int. J. Geomech. 18 (2): 04017139. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001058.
Zou, J. F., and J. M. Du. 2016. “A numerical approach for the quasi-plane strain-softening problem of cylindrical cavity expansion based on the Hoek-Brown failure criterion.” Math. Prob. Eng. 2016: 3698525. https://doi.org/10.1155/2016/3698525.
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© 2019 American Society of Civil Engineers.
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Received: Apr 12, 2018
Accepted: Sep 6, 2018
Published online: Jan 23, 2019
Published in print: Apr 1, 2019
Discussion open until: Jun 23, 2019
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