Bearing Capacity of Foundations over Rock Slopes–Slip Lines and FELA Solutions
Publication: International Journal of Geomechanics
Volume 24, Issue 10
Abstract
The ultimate bearing capacity of a strip footing placed horizontally over the edge of a sloping rock mass has been determined on the basis of the stress characteristics method (SCM) using the generalized Hoek–Brown yield criterion. The effect of footing–rock interface roughness on the results has also been analyzed. The problem has been solved, in addition, with the usage of the adaptive mesh–based finite-element limit analysis (FELA) method. The results are provided in the form of nondimensional bearing capacity factor as a function of different input material parameters for several slope inclinations. After analyzing all the results, an expression on the basis of the regression analysis has also been generated to compute the factor Nσ as a function of different input variables. The bearing capacity obtained from the SCM has been found to lie between the lower and upper bounds of the FELA, and the failure patterns from the two sets of analyses match quite closely with each other for both smooth and rough footings. The results are also found to be in good agreement with the existing solutions from the literature.
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Data Availability Statement
The data that support the findings from this study are available from the corresponding author upon request.
References
Ausilio, E., and P. Zimmaro. 2015. “Displacement-based seismic design of a shallow strip footing positioned near the edge of a rock slope.” Int. J. Rock Mech. Min. Sci. 76: 68–77. https://doi.org/10.1016/J.IJRMMS.2015.02.010.
Bolton, M. D., and C. K. Lau. 1993. “Vertical bearing capacity factors for circular and strip footings on Mohr–Coulomb soil.” Can. Geotech. J. 30 (6): 1024–1033. https://doi.org/10.1139/t93-099.
Cassidy, M. J., and G. T. Houlsby. 2002. “Vertical bearing capacity factors for conical footings on sand.” Géotechnique 52 (9): 687–692. https://doi.org/10.1680/GEOT.2002.52.9.687.
Chen, H.-B., F.-Q. Chen, and Y.-J. Lin. 2022. “Slip-line solution to earth pressure of narrow backfill against retaining walls on yielding foundations.” Int. J. Geomech. 22 (5): 04022051. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002356.
Clausen, J. 2013. “Bearing capacity of circular footings on a Hoek–Brown material.” Int. J. Rock Mech. Min. Sci. 57: 34–41. https://doi.org/10.1016/J.IJRMMS.2012.08.004.
De Buhan, P., and D. Garnier. 1998. “Three dimensional bearing capacity analysis of a foundation near a slope.” Soils Found. 38 (3): 153–163. https://doi.org/10.3208/SANDF.38.3_153.
Ganesh, R., and J. Kumar. 2021. “Ultimate bearing capacity of strip and circular foundations using power type yield criterion using the method of stress characteristics.” Comput. Geotech. 133: 104066. https://doi.org/10.1016/J.COMPGEO.2021.104066.
Ganesh, R., and J. Kumar. 2022. “Seismic bearing capacity of strip foundations with nonlinear power-law yield criterion using the stress characteristics method.” J. Geotech. Geoenviron. Eng. 148 (11): 04022083. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002867.
Hoek, E., C. Carranza-Torres, and C. Brent. 2002. “Hoek-Brown failure criterion-2002 edition.” In Proc., NARMS-TAC Conf., 267–273. Toronto: University of Toronto Press.
Houlsby, G. T., and C. M. Martin. 2003. “Undrained bearing capacity factors for conical footings on clay.” Géotechnique 53 (5): 513–520. https://doi.org/10.1680/GEOT.2003.53.5.513.
Jahanandish, M., and A. Keshavarz. 2005. “Seismic bearing capacity of foundations on reinforced soil slopes.” Geotext. Geomembr. 23 (1): 1–25. https://doi.org/10.1016/j.geotexmem.2004.09.001.
Keshavarz, A., and J. Kumar. 2018. “Bearing capacity of foundations on rock mass using the method of characteristics.” Int. J. Numer. Anal. Methods Geomech. 42 (3): 542–557. https://doi.org/10.1002/nag.2754.
Keshavarz, A., and J. Kumar. 2021. “Bearing capacity of ring foundations over rock media.” J. Geotech. Geoenviron. Eng. 147 (6): 04021027. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002517.
Krabbenhoft, K., A. Lyamin, and J. Krabbenhoft. 2015. “Optum computational engineering (OptumG2).” Computer software. Accessed June 28, 2024. https://optumce.com.
Kumar, J., and V. S. Korada. 2022a. “Seismic bearing capacity of foundations on sloping ground using power-type yield criteria.” Acta Geotech. 18 (2): 711–737. https://doi.org/10.1007/S11440-022-01609-2/TABLES/5.
Kumar, J., and V. S. Korada. 2022b. “Seismic bearing capacity factor Nγ for a rough strip footing on sloping ground.” Comput. Geotech. 152: 105054. https://doi.org/10.1016/J.COMPGEO.2022.105054.
Kumar, J., and V. B. K. Mohan Rao. 2003. “Seismic bearing capacity of foundations on slopes.” Géotechnique 53 (3): 347–361. https://doi.org/10.1680/geot.2003.53.3.347.
Lee, Y.-K., and S. Pietruszczak. 2017. “Analytical representation of Mohr failure envelope approximating the generalized Hoek-Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 100: 90–99. https://doi.org/10.1016/J.IJRMMS.2017.10.021.
Leshchinsky, B., and Y. Xie. 2017. “Bearing capacity for spread footings placed near c′-ϕ′ slopes.” J. Geotech. Geoenviron. Eng. 143 (1): 06016020. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001578.
Li, C., Y. Guan, P. Jiang, and X. Han. 2022. “Oblique bearing capacity of shallow foundations placed near slopes determined by the method of rigorous characteristics.” Géotechnique 72 (10): 922–934. https://doi.org/10.1680/JGEOT.20.P.355.
Maghous, S., Z. Saada, D. Garnier, and V. F. P. Dutra. 2022. “Upper bound kinematic approach to seismic bearing capacity of strip foundations resting near rock slopes.” Eur. J. Environ. Civ. Eng. 26 (9): 3996–4019. https://doi.org/10.1080/19648189.2020.1830179.
Mao, N., T. Al-Bittar, and A.-H. Soubra. 2012. “Probabilistic analysis and design of strip foundations resting on rocks obeying Hoek–Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 49: 45–58. https://doi.org/10.1016/J.IJRMMS.2011.11.005.
Merifield, R. S., A. V. Lyamin, and S. W. Sloan. 2006. “Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek–Brown criterion.” Int. J. Rock Mech. Min. Sci. 43 (6): 920–937. https://doi.org/10.1016/J.IJRMMS.2006.02.001.
Qin, C., and S. C. Chian. 2018. “Seismic ultimate bearing capacity of a Hoek-Brown rock slope using discretization-based kinematic analysis and pseudodynamic methods.” Int. J. Geomech. 18 (6): 04018054. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001147.
Rahaman, O., and J. Kumar. 2022. “Seismic bearing capacity of a strip footing on rock media.” J. Rock Mech. Geotech. Eng. 14 (2): 560–575. https://doi.org/10.1016/J.JRMGE.2021.08.017.
Saada, Z., S. Maghous, and D. Garnier. 2011. “Seismic bearing capacity of shallow foundations near rock slopes using the generalized Hoek-Brown criterion.” Int. J. Numer. Anal. Methods Geomech. 35 (6): 724–748. https://doi.org/10.1002/nag.929.
Santhoshkumar, G., and P. Ghosh. 2020. “Ultimate bearing capacity of skirted foundation on cohesionless soil using slip line theory.” Comput. Geotech. 123: 103573. https://doi.org/10.1016/J.COMPGEO.2020.103573.
Serrano, A., and C. Olalla. 1994. “Ultimate bearing capacity of rock masses.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 31 (2): 93–106. https://doi.org/10.1016/0148-9062(94)92799-5.
Serrano, A., C. Olalla, and J. González. 2000. “Ultimate bearing capacity of rock masses based on the modified Hoek–Brown criterion.” Int. J. Rock Mech. Min. Sci. 37 (6): 1013–1018. https://doi.org/10.1016/S1365-1609(00)00028-9.
Shields, D., N. Chandler, and J. Garnier. 1990. “Bearing capacity of foundations in slopes.” J. Geotech. Eng. 116 (3): 528–537. https://doi.org/10.1061/(ASCE)0733-9410(1990)116:3(528).
Wu, G., H. Zhao, M. Zhao, and L. Duan. 2023. “Ultimate bearing capacity of strip footings lying on Hoek–Brown slopes subjected to eccentric load.” Acta Geotech. 18 (2): 1111–1124. https://doi.org/10.1007/S11440-022-01587-5.
Wu, G., M. Zhao, R. Zhang, and M. Lei. 2021. “Ultimate bearing capacity of strip footings on Hoek–Brown rock slopes using adaptive finite element limit analysis.” Rock Mech. Rock Eng. 54 (3): 1621–1628. https://doi.org/10.1007/S00603-020-02334-6.
Yang, X.-L. 2009. “Seismic bearing capacity of a strip footing on rock slopes.” Can. Geotech. J. 46 (8): 943–954. https://doi.org/10.1139/T09-038.
Yang, X.-L., and J.-H. Yin. 2010. “Slope equivalent Mohr-Coulomb strength parameters for rock masses satisfying the Hoek-Brown criterion.” Rock Mech. Rock Eng. 43 (4): 505–511. https://doi.org/10.1007/S00603-009-0044-2.
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© 2024 American Society of Civil Engineers.
History
Received: Aug 3, 2023
Accepted: Apr 29, 2024
Published online: Aug 7, 2024
Published in print: Oct 1, 2024
Discussion open until: Jan 7, 2025
ASCE Technical Topics:
- Analysis (by type)
- Design (by type)
- Engineering fundamentals
- Finite element method
- Footings
- Foundation design
- Foundations
- Geomechanics
- Geotechnical engineering
- Limit analysis
- Load bearing capacity
- Methodology (by type)
- Numerical analysis
- Numerical methods
- Rock masses
- Rock mechanics
- Shallow foundations
- Slopes
- Structural design
- Structural engineering
- Structural reliability
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