Abstract
The cavity expansion approach has been a popular tool to interpret a wide range of geotechnical problems over the last several decades. Most previous research focused on the expansion of cylindrical and/or spherical cavities, whereas nonstandard cavities have received much less attention. To address this shortcoming, this paper presents a general theoretical framework for two-dimensional (2D) displacement-controlled undrained noncircular cavity expansion (N-CCE) in undrained soil. The new approach combines strain path method (SPM) concepts and conformal mapping to determine the soil velocity and strain rate fields analytically. The soil displacement and strain subsequently are determined by integrating the soil velocities and strain rates along the strain path using a series of transformed ordinary differential equations. In this study, the modified Cam Clay (MCC) effective stress constitutive model was used to determine the soil stress–strain relationship, and consolidation effects were captured using finite-difference calculations. The proposed methodology was validated by comparing the reduced solution for a circular cavity with traditional circular cavity expansion theory. A parametric analysis subsequently was undertaken to explore the influence of three noncircular cavity shapes on expansion-induced soil deformation mechanisms, shear strains, effective stresses, and pore-water pressure development and consolidation. The proposed solution can be implemented with any critical state–based soil model and can be applied to arbitrary noncircular cavity problems.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The work was supported by the National Natural Science Foundation of China, Grant/Award Nos. 51978105 and 52027812; the Chongqing Science Foundation for Distinguished Young Scholars, Grant/Award No. cstc2021jcyj-jqX0017; and the Chongqing Youth Top Talent Plan, Grant/Award No. cstc2021ycjh-bgzxm0132. The second author is funded by the Royal Academy of Engineering under the Research Fellowship Scheme.
References
Baligh, M. M. 1985. “Strain path method.” J. Geotech. Eng. 111 (9): 1108–1136. https://doi.org/10.1061/(ASCE)0733-9410(1985)111:9(1108).
Basu, D., and R. Salgado. 2008. “Analysis of laterally loaded piles with rectangular cross sections embedded in layered soil.” Int. J. Numer. Anal. Methods Geomech. 32 (7): 721–744. https://doi.org/10.1002/nag.639.
Chen, H., L. Li, J. Li, and D. Sun. 2020. “Elastoplastic solutions for cylindrical cavity expansion in unsaturated soils.” Comput. Geotech. 123 (Jul): 103569. https://doi.org/10.1016/j.compgeo.2020.103569.
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.
Chen, S. L., and K. Liu. 2019. “Undrained cylindrical cavity expansion in anisotropic undrained soils.” Géotechnique 69 (3): 189–202. https://doi.org/10.1680/jgeot.16.P.335.
Collins, I. F., and J. R. Stimpson. 1994. “Similarity solutions for drained and undrained cavity expansions in soils.” Géotechnique 44 (1): 21–34. https://doi.org/10.1680/geot.1994.44.1.21.
Ghandeharioon, A., B. Indraratna, and C. Rujikiatkamjorn. 2010. “Analysis of soil disturbance associated with mandrel-driven prefabricated vertical drains using an elliptical cavity expansion theory.” Int. J. Geomech. 10 (2): 53–64. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000027.
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.
Li, C., J. F. Zou, and S.-G. A. 2019. “Closed-form solution for undrained cavity expansion in anisotropic soil mass based on spatially mobilized plane failure criterion.” Int. J. Geomech. 19 (7): 04019075. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001458.
Liu, H., H. Zhou, and G. Kong. 2014. “XCC pile installation effect in soft soil ground: A simplified analytical model.” Comput. Geotech. 62 (Oct): 268–282. https://doi.org/10.1016/j.compgeo.2014.07.007.
Liu, H., H. Zhou, and G. Kong. 2016. “Upper-bound solution for flat cavity expansion model.” J. Eng. Mech. 142 (7): 04016035. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001084.
Liu, H., H. Zhou, Z. Wang, and X. Li. 2021. “Theoretical solution for cavity expansion in crushable soil.” Int. J. Geomech. 21 (7): 04021098. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002065.
Mantaras, F. M., and F. Schnaid. 2002. “Cylindrical cavity expansion in dilatant cohesive-frictional materials.” Géotechnique 52 (5): 337–348.
Mo, P.-Q., A. M. Marshall, and H.-S. Yu. 2017. “Interpretation of cone penetration test data in layered soils using cavity expansion analysis.” J. Geotech. Geoenviron. Eng. 143 (1): 04016084. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001577.
Muskhelishvili, N. I. 1954. Some basic problems of the mathematical theory of elasticity. Groningen, Netherlands: P. Noordhoff.
Randolph, M. F., and C. P. Wroth. 1979. “An analytical solution for the consolidation around a driven pile.” Int. J. Num. Anal. Methods Geomech. 3 (3): 217–229. https://doi.org/10.1002/nag.1610030302.
Saada, A. S. 2013. Elasticity: Theory and applications. San Diego: Elsevier.
Seo, H., D. Basu, M. Prezzi, and R. Salgado. 2009. “Load-settlement response of rectangular and circular piles in multilayered soil.” J. Geotech. Geoenviron. Eng. 135 (3): 420–430. https://doi.org/10.1061/(ASCE)1090-0241(2009)135:3(420).
Shuttle, D. 2007. “Cylindrical cavity expansion and contraction in Tresca soil.” Géotechnique 57 (3): 305–308. https://doi.org/10.1680/geot.2007.57.3.305.
Sun, G., G. Kong, H. Liu, and A. C. Amenuvor. 2017. “Vibration velocity of X-section cast-in-place concrete (XCC) pile–raft foundation model for a ballastless track.” Can. Geotech. J. 54 (9): 1340–1345. https://doi.org/10.1139/cgj-2015-0623.
Vesic, A. C. 1972. “Expansion of cavities in infinite soil mass.” J. Soil Mech. Found. Div. 98 (3): 265–290.
Wang, C.-L., H. Zhou, H.-L. Liu, and X.-M. Ding. 2022. “Analysis of undrained spherical cavity expansion in modified Cam Clay of finite radial extent.” Eur. J. Environ. Civ. Eng. 26 (3): 952–963. https://doi.org/10.1080/19648189.2019.1687015.
Wood, D. M. 1990. Soil behaviour and undrained soil mechanics. Cambridge, UK: Cambridge University Press.
Yu, H. S., and G. T. Houlsby. 1991. “Finite cavity expansion in dilatants soils: Loading analysis.” Géotechnique 41 (2): 173–183. https://doi.org /10.1680/geot.1991.41.2.173.
Zhou, H. 2017. “Complex variable solution for boundary value problem with X-shaped cavity in plane elasticity and its application.” Appl. Math. Mech. 38 (9): 1329–1346. https://doi.org/10.1007/s10483-017-2235-8.
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, H. L. Liu, and L. Laloui. 2018a. “Similarity solution for cavity expansion in thermoplastic soil.” Int. J. Numer. Anal. Methods Geomech. 42 (2): 274–294. https://doi.org/10.1002/nag.2724.
Zhou, H., H. Liu, G. Kong, and Z. Cao. 2014. “Analytical solution for pressure-controlled elliptical cavity expansion in elastic–perfectly plastic soil.” Geotech. Lett. 4 (2): 72–78. https://doi.org/10.1680/geolett.14.00004.
Zhou, H., H. Liu, M. F. Randolph, G. Kong, and Z. Cao. 2017. “Experimental and analytical study of X-section cast-in-place concrete pile installation effect.” Int. J. Phys. Modell. Geotech. 17 (2): 103–121. https://doi.org/10.1680/jphmg.15.00037.
Zhou, H., H. Liu, and Z. Wang. 2022. “A semi-analytical solution for displacement-controlled elliptical cavity expansion in undrained MCC soil.” Int. J. Numer. Anal. Methods Geomech. 46 (2): 339–373. https://doi.org/10.1002/nag.3302.
Zhou, H., H. Liu, Z. Wang, and X. Ding. 2021a. “A unified and rigorous solution for quasi-static cylindrical cavity expansion in plasticity constitutive models.” Comput. Geotech. 135 (Jul): 104162. https://doi.org/10.1016/j.compgeo.2021.104162.
Zhou, H., H. Liu, Z. Wang, and L. Tong. 2021b. “Analytical solution for cavity expansion in rate-dependent and strain-softening clay and its application for CPT tests.” J. Eng. Mech. 147 (3): 04021004. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001911.
Zhou, H., H. Liu, J. Yuan, and J. Chu. 2019. “Numerical simulation of XCC pile penetration in undrained clay.” Comput. Geotech. 106 (Feb): 18–41. https://doi.org/10.1016/j.compgeo.2018.10.009.
Zhou, H., Z. Wang, H. Liu, H. Shen, and X. Ding. 2021c. “Undrained cylindrical and spherical cavity expansion in elastic–viscoplastic soils.” Can. Geotech. J. 58 (10): 1543–1557. https://doi.org/10.1139/cgj-2020-0193.
Zhou, H., J. Yuan, H. Liu, and G. Kong. 2018b. “Analytical model for evaluating XCC pile shaft capacity in soft soil by incorporating penetration effects.” Soils Found. 58 (5): 1093–1112. https://doi.org/10.1016/j.sandf.2018.04.005.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 148 • Issue 7 • July 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Oct 25, 2021
Accepted: Mar 5, 2022
Published online: May 2, 2022
Published in print: Jul 1, 2022
Discussion open until: Oct 2, 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
- Longyong Tong, Hang Zhou, Hanlong Liu, Xuanming Ding, Failure Envelope of an Underground Rectangular Pipe Gallery in Clay under Pipe–Soil Interactions, International Journal of Geomechanics, 10.1061/(ASCE)GM.1943-5622.0002631, 23, 1, (2023).
- Shaohua Zeng, Hang Zhou, Zengliang Wang, Undrained Solution for Cylindrical Cavity Expansion in Structured Clays Using a Hypoplastic Model, International Journal of Geomechanics, 10.1061/(ASCE)GM.1943-5622.0002629, 23, 1, (2023).
- Renrong Li, Gangqiang Kong, Guangchao Sun, Qing Yang, Thermomechanical Behaviors of an Energy Pile–Raft Foundation under Intermittent Operation with Forced Heat Recharge, International Journal of Geomechanics, 10.1061/(ASCE)GM.1943-5622.0002581, 22, 10, (2022).