Undrained Bearing Capacity of Circular and Square Footings above Centric and Eccentric Three-Dimensional Cavities
Publication: International Journal of Geomechanics
Volume 24, Issue 6
Abstract
Cavities are common subsurface anomalies that have a significant impact on the bearing capacity of footings. While cavities behave three-dimensionally, in previous studies, the analysis of cavities has been limited to two-dimensional plane-strain analysis because of the time-consuming nature and complexity of three-dimensional modeling. However, this study demonstrates that the bearing capacity factor derived from three-dimensional modeling can be up to 10 times higher than that obtained from plane-strain analysis, highlighting the importance of considering three-dimensional effects. The present paper conducted three-dimensional simulations to investigate the impact of spherical cavity on the failure mechanisms and bearing capacity of footings under undrained conditions. An extensive parametric study was performed to investigate the influential parameters, including footing width to cavity dimension ratio (B/D), cover depth ratio (C/D), overburden factor (γD/Su), and void eccentricity ratio (S/D) for both circular or square footings. The results indicate that increasing the overburden factor and void eccentricity ratio leads to a decrease and increase in the bearing capacity of the footing, respectively. Furthermore, changes in other parameters can either increase or decrease the bearing capacity depending on the characteristics of the cavity (size and location) and footing (size and shape). General solutions for the bearing capacity factor are provided for different variations of the dimensionless parameters. This study also examined various failure mechanisms, including both cavity-independent and cavity-dependent failure mechanisms, associated with circular and square footings and influential parameters. These mechanisms are categorized into three zones for cavity-independent failures and four zones for cavity-dependent failures. The changes in the influential parameters including B/D, S/D, γD/Su, and C/D lead to changes in the type of failure mechanism and the size of the failure zones, while the foundation shape does not have a significant effect on the failure mechanism.
Practical Applications
Sinkholes and underground cavities annually contribute to infrastructure damage and financial losses. The 1981 incident in Winter Park, Florida, exemplifies the real-world consequences. Previous investigations have been limited to two-dimensional models due to the time-consuming nature and complexity of three-dimensional modeling, but the real-world nature of cavities in three dimensions requires a more comprehensive understanding. This study directly addresses this need by investigating the impact of three-dimensional cavities on the bearing capacity of circular and square building foundations, also known as footings. This study thoroughly investigated the factors influencing the results, encompassing cavity size, depth, soil weight, and off-center position. It extensively explored potential footing failures, providing detailed discussions. Our findings are presented as easy-to-understand maps and charts covering a broad range of potential scenarios. These visual tools can help engineers and researchers accurately estimate the stability of a building's foundation when a cavity is present underneath. In simpler terms, this research has created a handy tool for professionals to predict the potential danger posed by hidden cavities to buildings and infrastructure. This knowledge can then be applied to ensure safer building practices, potentially saving a significant amount of money and preventing accidents in the future.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and codes that support the findings of this study are available from the corresponding author upon reasonable request.
References
Abbo, A. J., D. W. Wilson, S. W. Sloan, and A. V. Lyamin. 2013. “Undrained stability of wide rectangular tunnels.” Comput. Geotech. 53: 46–59. https://doi.org/10.1016/j.compgeo.2013.04.005.
Al-Rifaiy, I. A. 1991. “Land subsidence in the AI-Dahr residential area in Kuwait: A case history study.” Q. J. Eng. Geol. Hydrogeol. 23 (4): 337–346. https://doi.org/10.1144/GSL.QJEG.1990.023.04.08.
Al-Tabbaa, A., L. Russell, and M. O’Reilly. 1989. “Model tests of footings above shallow cavities.” Ground Eng. 22 (7): 39–42.
Andersland, O. B., and B. Ladanyi. 2003. Frozen ground engineering. Hoboken, NJ: Wiley.
Atkinson, J. H., and D. M. Potts. 1977. “Stability of a shallow circular tunnel in cohesionless soil.” Géotechnique 27 (2): 203–215. https://doi.org/10.1680/geot.1977.27.2.203.
Augarde, C. E., A. V. Lyamin, and S. W. Sloan. 2003. “Prediction of undrained sinkhole collapse.” J. Geotech. Geoenviron. Eng. 129 (3): 197–205. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:3(197).
Azam, G., C. W. Hsieh, and M. Wang. 1991. “Performance of strip footing on stratified soil deposit with void.” J. Geotech. Eng. 117 (5): 753–772. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:5(753).
Azam, G., M. Jao, and M. C. Wang. 1997. “Cavity effect on stability of strip footing in two-layer soils.” Geotech. Eng. 28 (2): 151–164.
Badie, A., and M. C. Wang. 1984. “Stability of spread footing above void in clay.” J. Geotech. Geoenviron. Eng. 110 (11): 1591–1605. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:11(1591).
Baus, R. L., and M. C. Wang. 1983. “Bearing capacity of strip footing above void.” J. Geotech. Eng. 109 (1): 1–14. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(1).
Bell, F. G. 1988. “Subsidence associated with the abstraction of fluids.” Eng. Geol. Underground Movements 5 (1): 363–376.
Brady, B. H., and E. T. Brown. 2006. Rock mechanics for underground mining. London, UK: Springer Science & Business Media.
Brink, A. A. 1984. A brief review of the South African sinkhole problem. Rotterdam, Netherlands: A.A. Balkema, pp. 123–127.
Butterfield, R. 1999. “Dimensional analysis for geotechnical engineers.” Géotechnique 49 (3): 357–366. https://doi.org/10.1680/geot.1999.49.3.357.
Caramanna, G., G. Ciotoli, and S. Nisio. 2008. “A review of natural sinkhole phenomena in Italian plain areas.” Nat. Hazards 45 (2): 145–172. https://doi.org/10.1007/s11069-007-9165-7.
Craig, W. H. 1990. “Collapse of cohesive overburden following removal of support.” Can.Geotech. J. 27 (3): 355–364. https://doi.org/10.1139/t90-046.
Das, B. M., and K. H. Khing. 1994. “Foundation on layered soil with geogrid reinforcement—Effect of a void.” Geotext. Geomembr. 13 (8): 545–553. https://doi.org/10.1016/0266-1144(94)90018-3.
Eason, G., and R. T. Shield. 1960. “The plastic indentation of a semi-infinite solid by a perfectly rough circular punch.” J. Appl. Math. Phys. 11 (1): 33–43.
Fam, M. A., G. Cascante, and M. B. Dusseault. 2002. “Large and small strain properties of sands subjected to local void increase.” J. Geotech. Geoenviron. Eng. 128 (12): 1018–1025. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:12(1018).
Gómez-Ortiz, D., and T. Martín-Crespo. 2012. “Assessing the risk of subsidence of a sinkhole collapse using ground penetrating radar and electrical resistivity tomography.” Eng. Geol. 149–150: 1–12. https://doi.org/10.1016/j.enggeo.2012.07.022.
Gourvenec, S., M. Randolph, and O. Kingsnorth. 2006. “Undrained bearing capacity of square and rectangular footings.” Int. J. Geomech. 6 (3): 147–157. https://doi.org/10.1061/(ASCE)1532-3641(2006)6:3(147).
Kannan, R. C. 1999. “Designing foundations around sinkholes.” Eng. Geol. 52 (1–2): 75–82. https://doi.org/10.1016/S0013-7952(98)00057-X.
Keawsawasvong, S., and B. Ukritchon. 2019. “Undrained stability of a spherical cavity in cohesive soils using finite element limit analysis.” J. Rock Mech. Geotech. Eng. 11 (6): 1274–1285. https://doi.org/10.1016/j.jrmge.2019.07.001.
Kiyosumi, M., O. Kusakabe, and M. Ohuchi. 2011. “Model tests and analyses of bearing capacity of strip footing on stiff ground with voids.” J. Geotech. Geoenviron. Eng. 137 (4): 363–375. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000440.
Kiyosumi, M., O. Kusakabe, M. Ohuchi, and F. Le Peng. 2007. “Yielding pressure of spread footing above multiple voids.” J. Geotech. Geoenviron. Eng. 133 (12): 1522–1531. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:12(1522).
Kohl, M. S. 2001. Subsidence and sinkholes in east Tennessee: A field guide to holes in the ground. Nashville: Division of Geology, Dept. of Environment and Conservation.
Krabbenhoft, K., A. Lyamin, and J. Krabbenhoft. 2019. Optum computational engineering(Optum G2), s.l.: s.n.
Krabbenhoft, K., and A. V. Lyamin. 2012. “Computational Cam clay plasticity using second-order cone programming.” Comput. Methods Appl. Mech. Eng. 209–212: 239–249. https://doi.org/10.1016/j.cma.2011.11.006.
Lard, L. A., C. K. Paull, and B. Hobson. 1995. “Genesis of a submarine sinkhole without subaerial exposure: Straits of Florida.” Geology 23 (10): 949–951.
Lavasan, A. A., A. Talsaz, M. Ghazavi, and T. Schanz. 2016. “Behavior of shallow strip footing on twin voids.” Geotech. Geol. Eng. 34 (6): 1791–1805. https://doi.org/10.1007/s10706-016-9989-6.
Leca, E., and L. Dormieux. 1990. “Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material.” Géotechnique 40 (4): 581–606. https://doi.org/10.1680/geot.1990.40.4.581.
Lee, J. K., S. Jeong, and J. Ko. 2014. “Undrained stability of surface strip footings above voids.” Comput. Geotech. 62: 128–135. https://doi.org/10.1016/j.compgeo.2014.07.009.
Lee, J. K., S. Jeong, and J. Ko. 2015. “Effect of load inclination on the undrained bearing capacity of surface spread footings above voids.” Comput. Geotech. 66: 245–252. https://doi.org/10.1016/j.compgeo.2015.02.003.
Martin, C. 2003. New software for rigorous bearing capacity calculations. London: Thomas Telford.
Michalowski, R. L. 2001. “Upper bound load estimates on square and rectangular footings.” Géotechnique 51 (9): 787–798. https://doi.org/10.1680/geot.2001.51.9.787.
Ono, K., and M. Yamada. 1993. “Analysis of the arching in granular mass.” Géotechnique 43 (1): 105–120. https://doi.org/10.1680/geot.1993.43.1.105.
Prandtl, L. 1920. “Über die Härte plastischer Körper.” In Nachrichten von der gesellschaft der wissenschaften zu göttingen, mathematisch-physikalische klasse, 74–85. Göttingen: Gesellschaft der Wissenschaften zu Göttingen.
Ruth, B. E., T. F. Beggs, and J. D. Degner. 1985. “Predicting sinkhole collapse.” Civ. Eng. ASCE 55 (11): 58–60.
Salgado, R., A. V. Lyamin, S. W. Sloan, and H. S. Yu. 2004. “Two and three-dimensional bearing capacity of foundations in clay.” Géotechnique 54 (5): 297–306. https://doi.org/10.1680/geot.2004.54.5.297.
Samyn, K., Mathieu, F., Bitri, A., Nachbaur, A., and Closset, L. 2014. “Integrated geophysical approach in assessing karst presence and sinkhole susceptibility along flood-protection dykes of the Loire River, Orleans, France.” Eng. Geol. 183: 170–184. https://doi.org/10.1016/j.enggeo.2014.10.013.
Sloan, S. W., and A. Assadi. 1991. “Undrained stability of a square tunnel in a soil whose strength increases linearly with depth.” Comput. Geotech. 12 (4): 321–346. https://doi.org/10.1016/0266-352X(91)90028-E.
Song, K.-I., G.-C. Cho, and S.-B. Chang. 2012. “Identification, remediation, and analysis of karst sinkholes in the longest railroad tunnel in South Korea.” Eng. Geol. 135–136: 92–105. https://doi.org/10.1016/j.enggeo.2012.02.018.
Sowers, G. F. 1996. Building on sinkholes: Design and construction of foundations in karst terrain. New York: American Society of Civil Engineers.
Terzaghi, K. 1943. Theoretical soil mechanics. New York: Wiley.
Than, K. 2010. Sinkhole in Guatemala: Giant could get even bigger [Interview] (June 3, 2010). National Geographic.
Tharp, T. M. 1999. “Mechanics of upward propagation of cover collapse.” Eng. Geol. 52 (1–2): 23–33. https://doi.org/10.1016/S0013-7952(98)00051-9.
Van Baars, S. 2014. “The inclination and shape factors for the bearing capacity of footings.” Soils Found. 54 (5): 985–992. https://doi.org/10.1016/j.sandf.2014.09.004.
Wang, M. C., and A. Badie. 1985. “Effect of underground void on foundation stability.” J. Geotech. Eng. 111 (8): 1008–1019. https://doi.org/10.1061/(ASCE)0733-9410(1985)111:8(1008).
Wang, M. C., and C. W. Hsieh. 1987. “Collapse load of strip footing above circular void.” J. Geotech. Eng. 113 (5): 511–515. https://doi.org/10.1061/(ASCE)0733-9410(1987)113:5(511).
Wilson, D. W., A. J. Abbo, S. W. Sloan, and A. V. Lyamin. 2011. “Undrained stability of a circular tunnel where the shear strength increases linearly with depth.” Can. Geotech. J. 48 (9): 1328–1342. https://doi.org/10.1139/t11-041.
Wilson, W. 1995. Sinkhole and buried sinkhole densities and new sinkhole frequencies of northwest peninsular Florida. Rotterdam, Netherlands: A.A. Balkema.
Wood, L. A., and W. J. Larnach. 1985. The behaviour of footings located above voids. In Proc., 11th Int. Conf. on Soil Mechanics and Foundation Engineering, 12–16. Rotterdam, Netherlands: A.A. Balkema.
Wu, G., H. Zhao, and M. Zhao. 2021. “Undrained stability analysis of strip footings lying on circular voids with spatially random soil.” Comput. Geotech. 133: 104072. https://doi.org/10.1016/j.compgeo.2021.104072.
Zhao, L., S. Huang, Z. Zeng, R. Zhang, G. Tang, and S. Zuo. 2021. “Study on the ultimate bearing capacity of a strip footing influenced by an irregular underlying cavity in karst areas.” Soils Found. 61 (2): 259–270. https://doi.org/10.1016/j.sandf.2020.09.011.
Zhao, L., S. Huang, R. Zhang, and S. Zuo. 2018. “Stability analysis of irregular cavities using upper bound finite element limit analysis method.” Comput. Geotech. 103: 1–12. https://doi.org/10.1016/j.compgeo.2018.06.018.
Zhou, H., G. Zheng, X. He, X. Xu, T. Zhang, and X. Yang. 2018. “Bearing capacity of strip footings on c–φ soils with square voids.” Acta Geotech. 13 (3): 747–755. https://doi.org/10.1007/s11440-018-0630-0.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 24 • Issue 6 • June 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Feb 1, 2023
Accepted: Dec 27, 2023
Published online: Apr 3, 2024
Published in print: Jun 1, 2024
Discussion open until: Sep 3, 2024
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.