Unified Solution to Drained Expansion of a Spherical Cavity in Clay and Sand
Publication: International Journal of Geomechanics
Volume 17, Issue 8
Abstract
This paper presents a novel unified solution to drained expansion of a spherical cavity in both clay and sand. The large-strain theory and a critical state model with a unified hardening parameter are used to describe the elastoplastic behavior of the soils after yielding. The elastoplastic constitutive tensor of the critical state model is developed to be a system of first-order differential equations for the drained expansion of a spherical cavity. The problem is formulated as an initial value problem in terms of the Lagrangian scheme by introducing an auxiliary variable and is solved numerically. With the present solution, curves for the expansion pressures, the distributions of stress components, and the stress paths are plotted to illustrate the different expansion responses in clay and sand. The proposed solution not only incorporates the dilatancy and peak strength of dense sand, but it can also reduce to the solution for clay and loose sand when ignoring the dilatancy and peak strength. Therefore, the present solution can be applied to interpret the cone penetration test and the pile installation, as well as to evaluate the pile end bearing capacity in various kinds of soils.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors are grateful for the financial support provided by the National Natural Science Foundation of China (Grant 41272288) for this research work. The anonymous reviewers’ comments have improved the quality of this paper and are also gratefully acknowledged.
References
Bishop, R. F., Hill, R., and Mott, N. F. (1945). “The theory of indentation and hardness tests.” Proc. Phys. Soc., 57(3), 147–159.
Cao, L. F., Teh, C. I., and Chang, M. F. (2001). “Undrained cavity expansion in modified Cam clay I: Theoretical analysis.” Géotechnique, 51(4), 323–334.
Carter, J. P., Booker, J. R., and Yeung, S. K. (1986). “Cavity expansion in cohesive frictional soils.” Géotechnique, 36(3), 349–353.
Chang, M. F., Teh, C. I., and Cao, L. F. (2001). “Undrained cavity expansion in modified Cam clay II: Application to the interpretation of the piezocone test.” Géotechnique, 51(4), 335–350.
Chen, S. L., and Abousleiman, Y. N. (2012). “Exact undrained elasto-plastic solution for cylindrical cavity expansion in modified Cam Clay soil.” Géotechnique, 62(5), 447–456.
Chen, S. L., and Abousleiman, Y. N. (2013). “Exact drained solution for cylindrical cavity expansion in modified Cam Clay soil.” Géotechnique, 63(6), 510–517.
Collins, I. F., Pender, M. J., and Wang, Y. (1992). “Cavity expansion in sands under drained loading conditions.” Int. J. Numer. Anal. Methods Geomech., 16(1), 3–23.
Cudmani, R., and Osinov, V. A. (2001). “The cavity expansion problem for the interpretation of cone penetration and pressuremeter tests.” Can. Geotech. J., 38(3), 622–638.
Frikha, W., and Bouassida, M. (2013). “Cylindrical cavity expansion in elastoplastic medium with a variable potential flow.” Int. J. Geomech., 9–15.
Ghandeharioon, A., Indraratna, B., and Rujikiatkamjorn, C. (2010). “Analysis of soil disturbance associated with mandrel-driven prefabricated vertical drains using an elliptical cavity expansion theory.” Int. J. Geomech., 53–64.
Hill, R. (1950). The mathematical theory of plasticity, Oxford University Press, London.
Khalil, I. (2013). “New pressuremeter test analysis based on critical state mechanics.” Int. J. Geomech., 625–635.
Li, J., Li, L., Sun, D., and Rao, P. (2016a). “Analysis of undrained cylindrical cavity expansion considering three-dimensional strength of soils.” Int. J. Geomech., 04016017.
Li, L., Li, J. P., and Sun, D. A. (2016b). “Anisotropically elasto-plastic solution to undrained cylindrical cavity expansion in K0-consolidated clay.” Comput. Geotech., 73, 83–90.
Mantaras, F. M., and Schnaid, F. (2002). “Cylindrical cavity expansion in dilatant cohesive-frictional materials.” Géotechnique, 52(5), 337–348.
Osinov, V. A., and Cudmani, R. (2001). “Theoretical investigation of the cavity expansion problem based on a hypoplasticity model.” Int. J. Numer. Anal. Methods Geomech., 25(5), 473–495.
Randolph, M. F. (2003). “Science and empiricism in pile foundation design.” Géotechnique, 53(10), 847–875.
Randolph, M. F., Carter, J. P., and Wroth, C. P. (1979). “Driven piles in clay-the effects of installation and subsequent consolidation.” Géotechnique, 29(4), 361–393.
Roy, M., Blanchet, R., and Tavenas, F. (1981). “Behaviour of a sensitive clay during pile driving.” Can. Geotech. J., 18(1), 67–85.
Salgado, R., and Prezzi, M. (2007). “Computation of cavity expansion pressure and penetration resistance in sands.” Int. J. Geomech., 251–265.
Salgado, R., and Randolph, M. F. (2001). “Analysis of cavity expansion in sand.” Int. J. Geomech., 175–192.
Shuttle, D. (2007). “Cylindrical cavity expansion and contraction in Tresca soil.” Géotechnique, 57(3), 305–308.
Shuttle, D., and Jefferies, M. (1998). “Dimensionless and unbiased CPT interpretation in sand.” Int. J. Numer. Anal. Methods Geomech., 22(5), 351–391.
Vesic, A. S. (1977). Design of pile foundations, National Research Council, Washington, DC.
Wood, D. M. (1990). Soil behaviour and critical state soil mechanics, Cambridge University Press, Cambridge, U.K.
Yang, X. L., and Zou, J. F. (2011). “Cavity expansion analysis with non-linear failure criterion.” Proc. Inst. Civ. Eng.Geotech. Eng., 164(1), 41–49.
Yao, Y. P., Sun, D. A., and Luo, T. (2004). “A critical state model for sands dependent on stress and density.” Int. J. Numer. Anal. Methods Geomech., 28(4), 323–337.
Yao, Y. P., Sun, D. A., and Matsuoka, H. (2008). “A unified constitutive model for both clay and sand with hardening parameter independent on stress path.” Comput. Geotech., 35(2), 210–222.
Yu, H., and Carter, J. (2002). “Rigorous similarity solutions for cavity expansion in cohesive-frictional soils.” Int. J. Geomech., 233–258.
Yu, H., Schnaid, F., and Collins, I. (1996). “Analysis of cone pressuremeter tests in sand.” J. Geotech. Eng., 623–632.
Yu, H. S. (2000). Cavity expansion methods in geomechanics, Kluwer Academic, Dordrecht, Netherlands.
Yu, H. S., and Houlsby, G. T. (1991). “Finite cavity expansion in dilatant soils: Loading analysis.” Géotechnique, 41(2), 173–183.
Zareifard, M., and Fahimifar, A. (2014). “Elastic–brittle–plastic analysis of circular deep underwater cavities in a Mohr-Coulomb rock Mass considering seepage forces.” Int. J. Geomech., 04014077.
Zhao, J. D. (2011). “A unified theory for cavity expansion in cohesive-frictional micromorphic media.” Int. J. Solids Struct., 48(9), 1370–1381.
Zhou, H., Liu, H. L., and Kong, G. Q. (2014). “Analytical solution of undrained cylindrical cavity expansion in saturated soil under anisotropic initial stress.” Comput. Geotech., 55, 232–239.
Information & Authors
Information
Published In
Copyright
© 2017 American Society of Civil Engineers.
History
Received: May 16, 2016
Accepted: Dec 20, 2016
Published online: Mar 1, 2017
Published in print: Aug 1, 2017
Discussion open until: Aug 1, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.