Abstract
This paper presents the computations of vertical bearing capacity factors , , and , of the smooth and rough strip, circular and ring footings resting on soil with a friction angle () ranging from 5° to 45° using a finite element viscoplastic strain method obeying the Mohr-Coulomb yield criterion. The numerical difficulty could be improved to some extent by using the proper magnitude of soil dilation angle () in the analysis of high non-associative flow. The effects of domain and mesh size are presented thoroughly. The factors are calculated individually and found to be in close agreement with the existing solutions. However, differences are also reported and discussed. The magnitude of bearing capacity factors increases with increasing . Moreover, the factors with a rough base are significantly greater than the smooth base at high values of . Moreover, this work also indicates that the shape factors may depend on .
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, and codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This paper has been completed with the financial support of the YUTP Grant with the cost center of 0153AA-E88. Finally, Phuor Ty would like to especially thank his wife, Yin Louchsolida, and his son, Phuor Sopearith, who have provided great support to this work.
References
AFNOR (Association Francaise Normalisation). 1996. Norme XP 1997-1: Calcul géotechnique. Eurocode 7. Paris: AFNOR.
Al-Sanad, H. A., N. F. Ismael, and R. P. Brenner. 1993. “Settlement of circular and ring plates in very dense calcareous sands.” J. Geotech. Eng. 119 (4): 622–638. https://doi.org/10.1061/(ASCE)0733-9410(1993)119:4(622).
Benmebarek, S., M. S. Remadna, N. Benmebarek, and L. Belounar. 2012. “Numerical evaluation of the bearing capacity factor Nγ’ of ring footings.” Comput. Geotech. 44 (Jun): 132–138. https://doi.org/10.1016/j.compgeo.2012.04.004.
Berezantsev, V. G. 1952. Axially symmetric problems of the theory of limiting equilibrium of granular material. Moscow: Gostekhizdat.
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.
Booker, J. R. 1969. Application of theories of plasticity to cohesive frictional soils. Sydney, Australia: Sydney Univ.
Boushehrian, J. H., and N. Hataf. 2003. “Experimental and numerical investigation of the bearing capacity of model circular and ring footings on reinforced sand.” Geotext. Geomembr. 21 (4): 241–256. https://doi.org/10.1016/S0266-1144(03)00029-3.
Caquot, A., and J. Kerisel. 1953. “Sur le terme de surface dans le calcul des fondations en milieu pulvérulent.” In Proc., 3rd Int. Conf. SMFE, 336–337. London: International Society for Soil Mechancis and Geotechnical Engineering.
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.
Chakraborty, D., and J. Kumar. 2014. “Solving axisymmetric stability problems by using upper bound finite elements, limit analysis, and linear optimization.” J. Eng. Mech. 140 (6): 06014004. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000726.
Chen, W. F. 1975. Limit analysis and soil plasticity. Amsterdam, Netherlands: Elsevier.
Chen, W. F., and H. L. Davidson. 1973. “Bearing capacity determination by limit analysis.” J. Soil Mech. Found. Div. 99 (6): 433–449. https://doi.org/10.1061/JSFEAQ.0001887.
Cormeau, I. 1975. “Numerical stability in quasi-static elasto/visco-plasticity.” Int. J. Numer. Methods Eng. 9 (1): 109–127. https://doi.org/10.1002/nme.1620090110.
Cox, A. D., G. Eason, and H. G. Hopkins. 1961. “Axially symmetric plastic deformations in soils.” Philos. Trans. R. Soc. London, Ser. A 254 (1036): 1–45. https://doi.org/10.1098/rsta.1961.0011.
Cox, M. R. B. 2008. “The influence of grain shape on dilatancy.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Arizona.
Demir, A., M. Örnek, M. Laman, and A. Yildiz. 2012. “Analysis of ring footings using field test results.” In Proc., 3rd Int. Conf. of New Developments in Soil Mechanics and Geotechnical Engineering. Nicosia, North Cyprus: Near East Univ.
De Simone, P. 1985. “Bearing capacity of a circular footing on a Coulomb medium.” In Proc., 5th Int. Conf. Numerical Methods Geomechanical, 829–836. Rotterdam, Netherlands: A.A. Balkema.
DTU (Documents Techniques Unifies). 1988. Règles pour le calcul des fondations superficielles, CSTB, Cahiers no 1065. DTU 13.12. Paris: Association Francaise de Normalisation.
Eason, G., and R. T. Shield. 1960. “The plastic indentation of a semi-infinite solid by a perfectly rough circular punch.” Z. Angew. Math. Physik 11 (1): 33–43. https://doi.org/10.1007/BF01591800.
Egorov, K. E. 1958. “Problem of calculating the base under a foundation with a lower surface of ring shape.” NII Osnovanii Soil. Mech. Gosstroiizdat 34.
Egorov, K. E. 1965. “Calculation of bed for foundation with ring footing.” In Vol. 2 of Proc., 6th Int. Conf. on Soil Mechanics and Foundation Engineering, 41–45. Rotterdam, Netherlands: A.A. Balkema.
Egorov, K. E., and A. A. Nichiporovich. 1961. “Research on the deflection of foundations.” In Vol. 1 of Proc., 5th Int. Conf. on Soil Mechanics and Foundation Engineering, 861–866. Rotterdam, Netherlands: A.A. Balkema.
Erickson, H. L., and A. Drescher. 2002. “Bearing capacity of circular footings.” J. Geotech. Geoenviron. Eng. 128 (1): 38–43. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:1(38).
Fischer, K. 1957. “Zur berechnung der setzung von fundamenten in der form einer kreisformigen ringflache.” Der Bauingenieur 32 (5): 172–174.
Frydman, S., and H. J. Burd. 1997. “Numerical studies of bearing-capacity factor Nγ.” J. Geotech. Geoenviron. Eng. 123 (1): 20–29. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:1(20).
Griffiths, D. V. 1982. “Computation of bearing capacity factors using finite elements.” Géotechnique 32 (3): 195–202. https://doi.org/10.1680/geot.1982.32.3.195.
Griffiths, D. V., and I. M. Smith. 2006. Numerical methods for engineers. Boca Raton, FL: CRC Press.
Han, D., X. Xie, L. Zheng, and L. Huang. 2016. “The bearing capacity factor Nγ of strip footings on c–ϕ–γ soil using the method of characteristics.” SpringerPlus 5 (1): 1–17. https://doi.org/10.1186/s40064-016-3084-6.
Hansen, B., N. H. Christensen, and L. L. Karafiath. 1969. “Discussion of ‘Theoretical bearing capacity of very shallow footings’.” J. Soil Mech. Found. Div. 95 (6): 1568–1573. https://doi.org/10.1061/JSFEAQ.0001376.
Hansen, J. B. 1970. “A revised and extended formula for bearing capacity.” Bull. Dan. Geotech. Inst. 28: 5–11.
Hill, R. 1950. “The mathematical theory of plasticity.” In Computational methods for plasticity. New York: Oxford University Press.
Hjiaj, M., A. V. Lyamin, and S. W. Sloan. 2005. “Numerical limit analysis solutions for the bearing capacity factor Nγ.” Int. J. Solids Struct. 42 (5–6): 1681–1704. https://doi.org/10.1016/j.ijsolstr.2004.08.002.
Hosseininia, E. S. 2016. “Bearing capacity factors of ring footings.” Iran. J. Sci. Technol. Trans. Civ. Eng. 40 (2): 121–132. https://doi.org/10.1007/s40996-016-0003-6.
Ismael, N. F. 1996. “Loading tests on circular and ring plates in very dense cemented sands.” J. Geotech. Eng. 122 (4): 281–287. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:4(281).
Kalfa, M., D. Y. A. Massih, and A. H. Soubra. 2008. “Capacité portante des fondations superficielles de forme circulaire.” In Proc., Journées Nationales de Géotechnique et de Géologie de l’Ingénieur, 685–692. Villeurbanne, France: GEOMAS Laboratory.
Keshavarz, A., and J. Kumar. 2017. “Bearing capacity computation for a ring foundation using the stress characteristics method.” Comput. Geotech. 89 (Sep): 33–42. https://doi.org/10.1016/j.compgeo.2017.04.006.
Khatri, V. N., and J. Kumar. 2009. “Bearing capacity factor under condition for piles in clays.” Int. J. Numer. Anal. Methods Geomech. 33 (9): 1203–1225. https://doi.org/10.1002/nag.763.
Kumar, J. 2003. “Nγ for rough strip footing using the method of characteristics.” Can. Geotech. J. 40 (3): 669–674. https://doi.org/10.1139/t03-009.
Kumar, J., and M. Chakraborty. 2014. “Upper-bound axisymmetric limit analysis using the Mohr-Coulomb yield criterion, finite elements, and linear optimization.” J. Eng. Mech. 140 (12): 06014012. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000820.
Kumar, J., and M. Chakraborty. 2015. “Bearing capacity factors for ring foundations.” J. Geotech. Geoenviron. Eng. 141 (10): 06015007. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001345.
Kumar, J., and P. Ghosh. 2005. “Bearing capacity factor Nγ for ring footings using the method of characteristics.” Can. Geotech. J. 42 (5): 1474–1484. https://doi.org/10.1139/t05-051.
Kumar, J., and V. N. Khatri. 2011. “Bearing capacity factors of circular foundations for a general c–ϕ soil using lower bound finite elements limit analysis.” Int. J. Numer. Anal. Methods Geomech. 35 (3): 393–405. https://doi.org/10.1002/nag.900.
Kumar, J., and K. M. Kouzer. 2007. “Effect of footing roughness on bearing capacity factor Nγ.” J. Geotech. Geoenviron. Eng. 133 (5): 502–511. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:5(502).
Kusazakabe, O., H. Suzuki, and A. Nakase. 1986. “An upper bound calculation on bearing capacity of a circular footing on a non-homogeneous clay.” Soils Found. 26 (3): 143–148. https://doi.org/10.3208/sandf1972.26.3_143.
Lee, J. K., S. Jeong, and S. Lee. 2016. “Undrained bearing capacity factors for ring footings in heterogeneous soil.” Comput. Geotech. 75 (May): 103–111. https://doi.org/10.1016/j.compgeo.2016.01.021.
Loukidis, D., and R. Salgado. 2009. “Bearing capacity of strip and circular footings in sand using finite elements.” Comput. Geotech. 36 (5): 871–879. https://doi.org/10.1016/j.compgeo.2009.01.012.
Lyamin, A. V., R. Salgado, S. W. Sloan, and M. Prezzi. 2007. “Two- and three-dimensional bearing capacity of footings in sand.” Géotechnique 57 (8): 647–662. https://doi.org/10.1680/geot.2007.57.8.647.
Manoharan, N., and S. P. Dasgupta. 1995. “Bearing capacity of surface footings by finite elements.” Comput. Struct. 54 (4): 563–586. https://doi.org/10.1016/0045-7949(94)00381-C.
Manoharan, N., and S. P. Dasgupta. 1997. “Collapse load computation for high-friction soil.” Comput. Struct. 62 (4): 681–684. https://doi.org/10.1016/S0045-7949(96)00240-4.
Martin, C. 2005. “Exact bearing capacity calculations using the method of characteristics.” In Vol. 4 of Proc., Int. Association for Computer Methods and Advances in Geomechanics, 441–450. Berlin: Leibniz Association.
Martin, C. M. 2004. User guide for ABC-analysis of bearing capacity. OUEL Rep. No. 2261/03. Oxford, UK: Univ. of Oxford.
Meyerhof, G. G. 1951. “The ultimate bearing capacity of foundations.” Géotechnique 2 (4): 301–332. https://doi.org/10.1680/geot.1951.2.4.301.
Meyerhof, G. G. 1955. “Influence of roughness of base and ground-water conditions on the ultimate bearing capacity of foundations.” Géotechnique 5 (3): 227–242. https://doi.org/10.1680/geot.1955.5.3.227.
Meyerhof, G. G. 1963. “Some recent research on the bearing capacity of foundations.” Can. Geotech. J. 1 (1): 16–26. https://doi.org/10.1139/t63-003.
Michalowski, R. 1997. “An estimate of the influence of soil weight on bearing capacity using limit analysis Michalowski Bearing Capacity N-gamma 1997.” Soils Found. 37 (4): 57–64. https://doi.org/10.3208/sandf.37.4_57.
Milovic, D. M. 1973. “Stresses and displacements produced by a ring foundation.” In Proc., 8th Int. Conf. on Soil Mechanics and Foundation Engineering, 167–171. Rotterdam, Netherlands: A.A. Balkema.
Naylor, D. J., G. N. Pande, B. Simpson, and R. Tabb. 1981. Finite elements in geotechnical engineering. Swansea, UK: Pineridge Press.
Owen, D. R. J., and E. Hinton. 1981. Finite elements in plasticity: Theory and practice. Applied Ocean Research. Swansea, UK: Pineridge Press.
Pande, G. N. 1979. “Visco plastic algorithm for modelling tensile non-linearity in rock and concrete structure.” ADM 33: 39–65.
Pande, G. N., G. Beer, and J. R. Williams. 1990. Numerical methods in rock mechanics. New York: Wiley.
Pande, G. N., and K. G. Sharma. 1979. “On joint/interface elements and associated problems of numerical ill-conditioning.” Int. J. Numer. Anal. Methods Geomech. 3 (3): 293–300. https://doi.org/10.1002/nag.1610030308.
Phuor, T. 2020. “Development and application of three-dimensional finite element interface model for soil-jack-up interaction during preloading.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Universiti Teknologi PETRONAS.
Phuor, T., I. S. H. Harahap, and C. Y. Ng. 2019a. “Calculation of vertical bearing capacity factor of strip footing by FEM.” IOP Conf. Ser.: Mater. Sci. Eng. 513 (1): 012011.
Phuor, T., I. S. H. Harahap, and C. Y. Ng. 2019b. “Computation of vertical bearing capacity factor of strip footing by FEM.” IOP Conf. Ser.: Mater. Sci. Eng. 527 (1): 012017.
Phuor, T., I. S. H. Harahap, and C. Y. Ng. 2022. “Bearing capacity factors for rough conical footing by viscoplasticity finite-element analysis.” Int. J. Geomech. 22 (1): 04021266. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002256.
Phuor, T., I. S. H. Harahap, C. Y. Ng, and M. A. M. Al-Bared. 2021. “Development of the skew boundary condition for soil-structure interaction in three-dimensional finite element analysis.” Comput. Geotech. 137 (Sep): 104264. https://doi.org/10.1016/j.compgeo.2021.104264.
Phuor, T., and G. Yoon. 2022. “Model order reduction for Campbell diagram analysis of shaft-disc-blade system in 3D finite elements.” Struct. Eng. Mech. 81 (4): 411–428. https://doi.org/10.12989/sem.2022.81.4.411.
Potts, D., and L. Zdravkovic. 1999. Finite element analysis in geotechnical engineering: Theory. Technology & Engineering. London: Thomas Telford.
Prandtl, L. 1921. “Hauptaufsätze: Über die Eindringungsfestigkeit (Härte) plastischer baustoffe und die festigkeit von schneiden.” J. Appl. Math. Mech. 1 (1): 15–20.
Reissner H. 1924. “Zum erddruckproblem.” In Proc., 1st Int. Congress of Applied Mechanics, edited by C. B. Biezeno and J. M. Burgers, 295–311. Delft, Nethelands: Waltman.
Remadna, M. S., S. Benmebarek, and N. Benmebarek. 2017. “Numerical evaluation of the bearing capacity factor N’c of circular and ring footings.” Geomech. Geoeng. 12 (1): 1–13. https://doi.org/10.1080/17486025.2016.1153729.
Saha, M. C. 1978. “Ultimate bearing capacity of ring footings on sand.” Master’s thesis, Dept. of Civil Engineering, University of Roorkee.
Shield, R. T. 1955. “On the plastic flow of metals under conditions of axial symmetry.” Proc. R. Soc. London, Ser. A 233 (Dec), 267–287. https://doi.org/10.1098/rspa.1955.0262.
Smith, I. M., D. V. Griffiths, and L. Margetts. 2014. Programming the finite element method. New York: Wiley.
Snodi, L. N. 2011. “Estimation of (Nγ) for strip and circular footings using the method of characteristics.” Diyala J. Eng. Sci. 4 (2): 1–11.
Sokolovskii, V. V. 1966. “Statics of granular media.” J. Appl. Mech. 33 (1): 239. https://doi.org/10.1115/1.3625019.
Soubra, A. H. 1999. “Upper-bound solutions for bearing capacity of foundations.” J. Geotech. Geoenviron. Eng. 125 (1): 59–68. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:1(59).
Terzaghi, K. 1943. Theoretical of soil mechanics. New York: Wiley.
Turgeman, S., and J. Pastor. 1982. “Limit analysis: A linear formulation of the kinematic approach for axisymmetric mechanic problems.” Int. J. Numer. Anal. Methods Geomech. 6 (1): 109–128. https://doi.org/10.1002/nag.1610060108.
Ukritchon, B., A. J. Whittle, and C. Klangvijit. 2003. “Calculations of bearing capacity factor Nγ using numerical limit analyses.” J. Geotech. Geoenviron. Eng. 129 (5): 468–474. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:6(468).
Vermeer, P. A., and R. de Borst. 1984. “Non-associated plasticity for soils, concrete and rock.” Heron 29 (3): 1–64.
Vesic, A. S. 1974. “Analysis of ultimate loads of shallow foundations.” J. Soil Mech. Found. Div. 99 (1): 45–73.
Zhao, L., and J. H. Wang. 2008. “Vertical bearing capacity for ring footings.” Comput. Geotech. 35 (2): 292–304. https://doi.org/10.1016/j.compgeo.2007.05.005.
Zhu, D. Y., C. F. Lee, and H. D. Jiang. 2001. “A numerical study of the bearing capacity factor.” Can. Geotech. J. 38 (5): 1090–1096. https://doi.org/10.1139/t01-023.
Zienkiewicz, O. C., and Y. K. Cheung. 1967. The finite element method in structural and continuum mechanics. New York: McGraw-Hill.
Zienkiewicz, O. C., and I. C. Cormeau. 1974. “Visco-plasticity and plasticity an alternative for finite element solution of material nonlinearities.” Computing methods in applied sciences and engineering, 259–287. Berlin: Springer.
Zienkiewicz, O. C., and P. N. Godbole. 1974. “Flow of plastic and visco-plastic solids with special reference to extrusion and forming processes.” Int. J. Numer. Methods Eng. 8 (1): 1–16. https://doi.org/10.1002/nme.1620080102.
Zienkiewicz, O. C., C. Humpheson, and R. W. Lewis. 1975. “Associated and non-associated visco-plasticity and plasticity in soil mechanics.” Géotechnique 25 (4): 671–689. https://doi.org/10.1680/geot.1975.25.4.671.
Zienkiewicz, O. C., C. Humpheson, and R. W. Lewis. 1977. “Discussion: Associated and non-associated visco-plasticity and plasticity in soil mechanics.” Géotechnique 25 (4): 671–689.
Zienkiewicz, O. C., and G. N. Pande. 1977. “Time-dependent multilaminate model of rocks—A numerical study of deformation and failure of rock masses.” Int. J. Numer. Anal. Methods Geomech. 1 (3): 219–247. https://doi.org/10.1002/nag.1610010302.
Zienkiewicz, O. C., R. L. Taylor, and D. Fox. 2014. The finite element method for solid and structural mechanics. New York: Elsevier.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 148 • Issue 8 • August 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Mar 29, 2021
Accepted: Apr 1, 2022
Published online: Jun 2, 2022
Published in print: Aug 1, 2022
Discussion open until: Nov 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
- Ty Phuor, Avshalom Ganz, Pavel A. Trapper, Bearing capacity factors of cone‐shaped footing in meshfree, International Journal for Numerical and Analytical Methods in Geomechanics, 10.1002/nag.3469, 47, 2, (275-298), (2022).