A Novel Simple Solution to Cavity Expansion Problem in Crushable Granular Materials Based on Energy Dissipation Method
Publication: International Journal of Geomechanics
Volume 22, Issue 2
Abstract
This study presents an energy dissipation analysis approach for cavity expansion problems in crushable granular materials under the high stress state. By assuming that the energy dissipation generated from cavity expansion is mainly absorbed by the volume strain deformation in the plastic region, the energy conservation equations of the volume changes and energy dissipation in the plastic region during cavity expansion are reconstructed based on the compression failure mechanism. The limit pressure of the cavity expansion under high stresses is obtained based on a new critical state line for the crushable granular materials and the energy dissipation analysis method. The proposed approach is validated by the existed results. The effects of the initial void ratio and stress for the crushable granular materials on limiting expansion pressure of cavity expansion are investigated particularly. The results show that the effect is proved to be significant and must be considered in the analysis of cavity expansion problems, particularly for crushable granular materials at high stress.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the National Key R&D Program of China (Grant No. 2017YFB1201204), the High Speed Railway Joint Fund of National Natural Science Foundation of China (Grant No. U1934208), the Science and Technology Projects of Jiangxi Provincial Department of Transportation (Grant Nos. 2020Z0001 and 2021H0042), the Jiangxi Provincial Natural Science Foundation (Grant No. 20202BABL204067), and the Jiangxi Key Laboratory Foundation (Grant No. 20161BCD40010).
References
Been, K., and M. G. Jefferies. 1985. “A state parameter for sands.” Géotechnique 35 (2): 99–112. https://doi.org/10.1680/geot.1985.35.2.99.
Been, K., M. G. Jefferies, and J. Hachey. 1991. “The critical state of sands.” Géotechnique 41 (3): 365–381. https://doi.org/10.1680/geot.1991.41.3.365.
Cao, L. F., C. I. Teh, and M. F. Chang. 2001. “Undrained cavity expansion in modified Cam-Clay I: Theoretical analysis.” Géotechnique 51 (4): 323–334. https://doi.org/10.1680/geot.2001.51.4.323.
Cao, L. F., C. I. Teh, and M. F. Chang. 2002. “Analysis of undrained cavity expansion in elastoplastic soils with non-linear elasticity.” Int. J. Numer. Anal. Methods Geomech. 26 (1): 25–52. https://doi.org/10.1002/nag.189.
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.
Carter, J. P., and S. K. Yeung. 1985. “Analysis of cylindrical cavity expansion in a strain weakening material.” Comput. Geotech. 1 (3): 161–180. https://doi.org/10.1016/0266-352X(85)90021-7.
Chen, S. L., and Y. N. Abousleiman. 2012. “Exact undrained elastoplastic solution for cylindrical cavity expansion in modified Cam-Clay soil.” Géotechnique 62 (3): 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.
Collins, I. F., M. J. Pender, and W. Yan. 1992. “Cavity expansion in sands under drained loading conditions.” Int. J. Numer. Anal. Methods Geomech. 16 (1): 3–23. https://doi.org/10.1002/nag.1610160103.
Collins, I. F., and J. R. Stimpson. 1994. “Similarity solutions for drained a undrained cavity expansions in soils.” Géotechnique 44 (1): 21–34. https://doi.org/10.1680/geot.1994.44.1.21.
Collins, I. F., and H. S. Yu. 1996. “Undrained cavity expansions in critical state soils.” Int. J. Numer. Anal. Methods Geomech. 20 (7): 489–516. https://doi.org/10.1002/(sici)1096-9853(199607)20:7%3C489::AID-NAG829%3E3.0.CO;2-V.
Jiang, M. J., and Y. G. Sun. 2012. “Cavity expansion analyses of crushable granular materials with state-dependent dilatancy.” Int. J. Numer. Anal. Methods Geomech. 36 (6): 723–742. https://doi.org/10.1002/nag.1027.
Katzir, Z., and M. B. Rubin. 2011. “A simple formula for dynamic spherical cavity expansion in a compressible elastic perfectly plastic material with large deformations.” Math. Mech. Solids 16 (7): 665–681. https://doi.org/10.1177/1081286510387723.
Kolymbas, D., P. Wagner, and A. Blioumi. 2012. “Cavity expansion in cross-anisotropic rock.” Int. J. Numer. Anal. Methods Geomech. 36 (2): 128–139. https://doi.org/10.1002/nag.998.
Konrad, J. M. 1998. “Sand state from cone penetrometer tests: A framework considering grain crushing stress.” Géotechnique 48 (2): 201–215. https://doi.org/10.1680/geot.1998.48.2.201.
Li, J. P., L. Li, and D. A. Sun. 2016b. “Analysis of undrained cylindrical cavity expansion considering three-dimensional strength of soils.” Int. J. Geomech. 16 (5): 04016017. https://doi.org/:10.1061/(ASCE)GM.1943-5622.0000650.
Li, L., J. P. Li, and D. A. Sun. 2016a. “Anisotropically elasto-plastic solution to undrained cylindrical cavity expansion in K0-consolidated clay.” Comput. Geotech. 73 (10): 83–90. https://doi.org/10.1016/j.compgeo.2015.11.022.
Li, X. S., and Y. F. Dafalias. 2000. “Dilatancy for cohesionless soils.” Géotechnique 50 (4): 449–460. https://doi.org/10.1680/geot.2000.50.4.449.
Russell, A. R., and N. Khalili. 2002. “Drained cavity expansion in sands exhibiting particle crushing.” Int. J. Numer. Anal. Methods Geomech. 26 (4): 323–340. https://doi.org/10.1002/nag.203.
Russell, A. R., and N. Khalili. 2004. “A bounding surface plasticity model for sands exhibiting particle crushing.” Can. Geotech. J. 41 (6): 1179–1192. https://doi.org/10.1139/t04-065.
Russell, A. R., and N. Khalili. 2006. “A unified bounding surface plasticity model for unsaturated soils.” Int. J. Numer. Anal. Methods Geomech. 30 (3): 181–212. https://doi.org/10.1002/nag.475.
Russell, A. R., D. Muir Wood, and M. Kikumoto. 2009. “Crushing of particles in idealised granular assemblies.” J. Mech. Phys. Solids 57 (8): 1293–1313. https://doi.org/10.1016/j.jmps.2009.04.009.
Sheng, D., S. Zhang, F. Niu, and G. Cheng. 2014. “A potential new frost heave mechanism in high-speed railway embankments.” Géotechnique 64 (2): 144–154. https://doi.org/10.1680/geot.13.P.042.
Vesic, A. S. 1972. “Expansion of cavities in infinite soil mass.” Primary Care 33 (1): 75–91.
Xiao, Y., and H. Liu. 2016. “Elastoplastic constitutive model for rockfill materials considering particle breakage.” Int. J. Geomech. 17 (1): 04016041. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000681.
Xiao, Y., H. Liu, and Y. Chen. 2014a. “State-dependent constitutive model for rockfill materials.” Int. J. Geomech. 66 (5): 969–970.
Xiao, Y., H. Liu, Y. Chen, and J. Jiang. 2014b. “Bounding surface model for rockfill materials dependent on density and pressure under triaxial stress conditions.” J. Eng. Mech. 140 (4): 04014002. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000702.
Xiao, Y., H. Liu, X. Ding, Y. Chen, J. Jiang, and W. Zhang. 2016a. “Influence of particle breakage on critical state line of rockfill material.” Int. J. Geomech. 16 (1): 04015031. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000538.
Xiao, Y., H. L. Liu, H. Liu, and Y. Sun. 2016b. “Unified plastic modulus in the bounding surface plasticity model.” Sci. China Technol. Sci. 59 (6): 932–940. https://doi.org/10.1007/s11431-016-6016-3.
Yang, H. W., and A. R. Russell. 2015. “Cavity expansion in unsaturated soils exhibiting hydraulic hysteresis considering three drainage conditions.” Int. J. Numer. Anal. Methods Geomech. 39 (18): 1975–2016. https://doi.org/10.1002/nag.2379.
Yang, J., and X. S. Li. 2004. “State-dependent strength of sands from the perspective of unified modeling.” J. Geotech. Geoenviron. Eng. 130 (2): 186–198. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:2(186).
Yeung, A. T., S. K. A. Au, and T. H. Lamo. 2012. “Numerical simulation of pressure-controlled cavity expansion process in clay at constant volumetric expansion rate.” Géotechnique 62 (4): 353–357. https://doi.org/10.1680/geot.9.P.106.
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.
Zhang, J. 1994. “Analysis of spherical cavity expansion in sands by energy conservation and its application.” J. Civ. Eng. 27 (4): 38–45.
Zhang, J. R. 2002. “Problem of spherical cavity expansion in granular soil under high stresses.” J. Rock Mech. Eng. 21 (8): 1209–1214.
Zhang, S., C. X. Tong, X. Li, and D. Sheng. 2015. “A new method for studying the evolution of particle breakage.” Géotechnique 65 (11): 911–922. https://doi.org/10.1680/jgeot.14.P.240.
Zhou, H., G. Kong, P. Li, and H. Liu. 2016. “Flat cavity expansion: Theoretical model and application to the interpretation of the flat dilatometer test.” J. Eng. Mech. 142 (1): 04015058. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000957.
Zhou, H., G. Q. Kong, and H. L. Liu. 2015. “A semi-analytical solution for cylindrical cavity expansion in elastic–perfectly plastic soil under biaxial in situ stress field.” Géotechnique 66 (7): 1–12.
Zhou, H., H. L. Liu, and G. Q. Kong. 2014a. “Influence of shear stress on cylindrical cavity expansion in undrained elastic-perfectly plastic soil.” Géotech. Lett. 4 (3): 203–210. https://doi.org/10.1680/geolett.14.00034.
Zhou, H., H. L. Liu, G. Q. Kong, and Z. Cao. 2014b. “Analytical solution for pressure-controlled elliptical cavity expansion in elastic-perfectly plastic soil.” Géotech. Lett. 4 (2): 72–78. https://doi.org/10.1680/geolett.14.00004.
Zhou, H., H. L. Liu, G. Q. Kong, and X. Huang. 2014c. “Analytical solution of undrained cylindrical cavity expansion in saturated soil under anisotropic initial stress.” Comput. Geotech. 55 (2): 232–239. https://doi.org/10.1016/j.compgeo.2013.09.011.
Zou, J. F. 2007. “Cavity expansion based on the linear and nonlinear failure criteria and it’s engineering applications.” Ph.D. thesis, Dept. of Civil Engineering, Central South Univ.
Zou, J. F., and Z. He. 2016. “Numerical approach for strain-softening rock with axial stress.” Proc. Inst. Civ. Eng.—Geotech. Eng. 169 (3): 276–290. https://doi.org/10.1680/jgeen.15.00097.
Zou, J. F., and S. S. Li. 2015. “Theoretical solution for displacement and stress in strain-softening surrounding rock under hydraulic–mechanical coupling.” Sci. China Technol. Sci. 58 (8): 1401–1413. https://doi.org/10.1007/s11431-015-5885-1.
Zou, J. F., and Y. Su. 2016. “Theoretical solutions of a circular tunnel with the influence of the out-of-plane stress based on the generalized Hoek–Brown failure criterion.” Int. J. Geomech. 16 (3): 06015006. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000547.
Zou, J. F., W. Q. Tong, and J. Zhao. 2012. “Energy dissipation of cavity expansion based on generalized non-linear failure criterion under high stresses.” J. Cent. South Univ. 19 (5): 1419–1424. https://doi.org/10.1007/s11771-012-1158-3.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 22 • Issue 2 • February 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jan 22, 2021
Accepted: Oct 12, 2021
Published online: Dec 13, 2021
Published in print: Feb 1, 2022
Discussion open until: May 13, 2022
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.
Cited by
- Guo-Yao Li, Pin-Qiang Mo, Zhao Lu, Ran Yuan, He Yang, Hai-Sui Yu, Drained Cavity Expansion–Contraction in CASM and Its Application for Pressuremeter Tests in Sands, Journal of Geotechnical and Geoenvironmental Engineering, 10.1061/JGGEFK.GTENG-12417, 150, 9, (2024).
- Chao Li, Pin-Qiang Mo, Energy dissipation analysis for large-strain cylindrical cavity expansion problem in cohesive-frictional soils, Applied Mathematical Modelling, 10.1016/j.apm.2022.07.015, 111, (681-695), (2022).