On the Eccentrically Loaded Strip Footing Resting Over a Circular Cavity in the Rock Mass: Adaptive Finite-Element Analysis, Observations, and Recommendations
Publication: International Journal of Geomechanics
Volume 23, Issue 2
Abstract
In this study, the effect of an eccentric load on the ultimate bearing capacity (UBC) of a strip footing of width B resting above a circular cavity in the rock mass is investigated using upper -and lower-bound finite-element limit analysis incorporating an adaptive meshing technique. The effect of governing independent variables, such as the diameter of the circular cavity, dc, load eccentricity, e, distance of the cavity from the footing (horizontal, P, and vertical, Q), and rock mass parameters based on the generalized Hoek–Brown (GHB) failure criterion on the reduction of the UBC, is studied using a reduction coefficient, Rc. This study reveals that the influence of the cavity on the UBC is minimal for a cavity beyond a depth of Q/B ≥ 2.5 when e/B ≥ 0.3; and that Q/B ≥ 3 when 0.1 ≤ e/B ≤ 0.2, irrespective of P/B. Similarly, a cavity situated at −2 ≤ P/B ≥ 2 and Q/B ≥ 2 when e/B = 0.3–0.4, and −3.5 ≤ P/B ≥ 3.5 and Q/B ≥ 2.5 when 0.1 ≤ e/B ≤ 0.2, does not show any significant impact on the reduction of the UBC. Dominant potential failure patterns that could cover at least all the representative cases are presented and discussed to strengthen the insight into the possible mechanism of such a footing failure.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The author contributions are as follows. PK: numerical simulations, validation, investigation, analysis and data curation, writing of the original draft, and editing; VBC: conceptualization, methodology, procedural approach, analysis, data curation, review, editing, and supervision.
References
Badie, A., and M. C. Wang. 1984. “Stability of spread footing above void in clay.” J. Geotech. 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: 1–14. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(1).
Carranza-Torres, C. M. 1998. Self-similarity analysis of the elasto-plastic response of underground openings in rock and effects of practical variables. Minneapolis: Univ. of Minnesota.
Ciria, H., J. Peraire, and J. Bonet. 2008. “Mesh adaptive computation of upper and lower bounds in limit analysis.” Int. J. Numer. Methods Eng. 75 (8): 899–944. https://doi.org/10.1002/nme.2275.
Das, B. M., and K. H. Khing. 1994. “Foundation on layered soil with geogrid reinforcement effect of a void.” Geotext. Geomembr. 13: 545–553. https://doi.org/10.1016/0266-1144(94)90018-3.
Davis, T., D. Healy, A. Bubeck, and R. Walker. 2017. “Stress concentrations around voids in three dimensions: The roots of failure.” J. Struct. Geol. 102: 193–207. https://doi.org/10.1016/j.jsg.2017.07.013.
Dunn, D. E., L. J. LaFountain, and R. E. Jackson. 1973. “Porosity dependence and mechanism of brittle fracture in sandstones.” J. Geophys. Res. 78 (14): 2403–2417. https://doi.org/10.1029/JB078i014p02403.
Fenton, G. A., and D. V. Griffiths. 2002. “Probabilistic foundation settlement on spatially random soil.” J. Geotech. Geoenviron. Eng. 128 (5): 381–390. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:5(381).
Fraldi, M., and F. Guarracino. 2010. “Analytical solutions for collapse mechanisms in tunnels with arbitrary cross-sections.” Int. J. Solids Struct. 47 (2): 216–223. https://doi.org/10.1016/j.ijsolstr.2009.09.028.
Griffiths, D. V., G. A. Fenton, and N. Manoharan. 2002. “Bearing capacity of rough rigid strip footing on cohesive soil: Probabilistic study.” J. Geotech. Geoenviron. Eng. 128 (9): 743–755. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:9(743).
Hoek, E., and E. T. Brown. 1980. “Empirical strength criterion for rock masses.” J. Geotech. Eng. Div. 106 (9): 1013–1035. https://doi.org/10.1061/AJGEB6.0001029.
Hoek, E., C. Carranza-Torres, and B. Corkum. 2002. “Hoek–Brown failure criterion—2002 edition.” In Vol. 1 of Proc., North American Rock Mechanics Symposium and 17th Tunneling, 267–273. Toronto: University of Toronto Press.
Imani, M., and A. Fahimifar. 2021. “Effect of load inclination on the bearing capacity of jointed rock foundations.” Geotech. Geol. Eng. 39 (4): 3033–3045. https://doi.org/10.1007/s10706-020-01676-w.
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.
Krabbenhoft, K., A. V. Lyamin, M. Hjiaj, and S. W. Sloan. 2005. “A new discontinuous upper bound limit analysis formulation.” Int. J. Numer. Methods Eng. 63 (7): 1069–1088. https://doi.org/10.1002/nme.1314.
Kumar, P., and V. B. Chauhan. 2022. “Bearing capacity of strip footing resting above a circular void in the rock mass using adaptive finite element method.” Innovative Infrastruct. Solutions 7: 72. https://doi.org/10.1007/s41062-021-00666-y.
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., and J. Kim. 2019. “Stability charts for sustainable infrastructure: Collapse loads of footings on sandy soil with voids.” Sustainability 11 (14): 3966. https://doi.org/10.3390/su11143966.
Lyamin, A. V., and S. W. Sloan. 2002. “Lower bound limit analysis using non-linear programming.” Int. J. Numer. Methods Eng. 55 (5): 573–611. https://doi.org/10.1002/nme.511.
Merifield, R. S., and S. W. Sloan. 2006. “The ultimate pull-out capacity of anchors in frictional soils.” Can. Geotech. J. 43 (8): 852–868. https://doi.org/10.1139/t06-052.
Optum G2. 2020. “Finite element program for geotechnical analysis optum computational engineering.” Accessed July 12, 2022. www.optum.com.
Price, N. J. 1966. Fault and joint development in brittle and semi-brittle rock. Oxford: Pergamon.
Sachpazis, C. I. 1990. “Correlating Schmidt hardness with compressive strength and Young’s modulus of carbonate rocks.” Bull. Int. Assoc. Eng. Geol. 42 (1): 75–83. https://doi.org/10.1007/BF02592622.
Sireesh, S., T. G. Sitharam, and S. K. Dash. 2009. “Bearing capacity of circular footing on geocell–sand mattress overlying clay bed with void.” Geotext. Geomembr. 27 (9): 89–98. https://doi.org/10.1016/j.geotexmem.2008.09.005.
Sloan, S. W. 2013. “Geotechnical stability analysis.” Géotechnique 63 (7): 531–571. https://doi.org/10.1680/geot.12.RL.001.
Ukritchon, B., and S. Keawsawasvong. 2018a. “Lower bound limit analysis of an anisotropic undrained strength criterion using second-order cone programming.” Int. J. Numer. Anal. Methods Geomech. 42 (8): 1016–1033. https://doi.org/10.1002/nag.2781.
Ukritchon, B., and S. Keawsawasvong. 2018b. “Three-dimensional lower bound finite element limit analysis of Hoek-Brown material using semidefinite programming.” Comput. Geotech. 104: 248–270. https://doi.org/10.1016/j.compgeo.2018.09.002.
Ukritchon, B., and S. Keawsawasvong. 2019a. “Stability of retained soils behind underground walls with an opening using lower bound limit analysis and second-order cone programming.” Geotech. Geol. Eng. 37 (3): 1609–1625. https://doi.org/10.1007/s10706-018-0710-9.
Ukritchon, B., and S. Keawsawasvong. 2019b. “Stability of unlined square tunnels in Hoek-Brown rock masses based on lower bound analysis.” Comput. Geotech. 105: 249–264. https://doi.org/10.1016/j.compgeo.2018.10.006.
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).
Wong, L. N. Y., and Z. Wu. 2014. “Application of the numerical manifold method to model progressive failure in rock slopes.” Eng. Fract. Mech. 119 (Mar): 1–20. https://doi.org/10.1016/j.engfracmech.2014.02.022.
Wu, G., M. Zhao, R. Zhang, and G. Liang. 2020a. “Ultimate bearing capacity of eccentrically loaded strip footings above voids in rock masses.” Comput. Geotech. 128: 103819. https://doi.org/10.1016/j.compgeo.2020.103819.
Wu, G., M. Zhao, H. Zhao, and Y. Xiao. 2020b. “Effect of eccentric load on the undrained bearing capacity of strip footings above voids.” Int. J. Geomech. 20 (7): 04020078. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001710.
Wu, Z., and L. N. Y. Wong. 2015. “Modeling the progressive failure in rock slopes based on the fracture mechanics approach using the numerical manifold method.” In Proc., 13th ISRM Int. Congress of Rock Mechanics Innovations in Applied and Theoretical Rock Mechanics. Lisbon, Portugal: International Society for Rock Mechanics.
Xiao, Y., M. Zhao, R. Zhang, H. Zhao, and G. Wu. 2019. “Stability of dual square tunnels in rock masses subjected to surcharge loading.” Tunnelling Underground Space Technol. 92: 103037. https://doi.org/10.1016/j.tust.2019.103037.
Xiao, Y., M. Zhao, and H. Zhao. 2018a. “Undrained stability of strip footing above voids in two-layered clays by finite element limit analysis.” Comput. Geotech. 97: 124–133. https://doi.org/10.1016/j.compgeo.2018.01.005.
Xiao, Y., M. Zhao, H. Zhao, and R. Zhang. 2018b. “Finite element limit analysis of the bearing capacity of strip footing on a rock mass with voids.” Int. J. Geomech. 18 (9): 04018108. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001262.
Zhang, R., G. Chen, J. Zou, L. Zhao, and C. Jiang. 2019. “Study on roof collapse of deep circular cavities in jointed rock masses using adaptive finite element limit analysis.” Comput. Geotech. 111: 42–55. https://doi.org/10.1016/j.compgeo.2019.03.003.
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.
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 23 • Issue 2 • February 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: May 5, 2022
Accepted: Sep 28, 2022
Published online: Nov 22, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 22, 2023
ASCE Technical Topics:
- Analysis (by type)
- Cavitation
- Eccentric loads
- Engineering fundamentals
- Engineering mechanics
- Failure analysis
- Finite element method
- Fluid dynamics
- Fluid mechanics
- Footings
- Foundation design
- Foundations
- Geomechanics
- Geotechnical engineering
- Hydrologic engineering
- Load bearing capacity
- Methodology (by type)
- Numerical methods
- Rock masses
- Rock mechanics
- Shallow foundations
- Static loads
- Statics (mechanics)
- Ultimate loads
- Water and water resources
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.