Prediction of Bearing Capacity of Ring Foundation on Dense Sand with Regard to Stress Level Effect
Publication: International Journal of Geomechanics
Volume 18, Issue 11
Abstract
This paper uses finite-element formulation of the lower bound theorem to determine the bearing capacity of ring foundations on dense sand. The results are validated with the plasticity solutions, numerical analyses, laboratory small-scale model tests, and field plate loading tests available in the literature. The Bolton strength–dilatancy relation is then adopted to consider the dependency of the friction angle on the stress level. For solid circular footings, the present results agree well with centrifuge model tests. However, a considerable discrepancy exists between numerical analyses and centrifuge model tests for the ring foundation, particularly when the radii ratio exceeds 0.5. An alternative method is proposed, in which a resistance ratio of the ring foundation to the solid circular footing with the same size is applied to an approximate equation for the bearing capacity of the solid circular footing regarding the stress level effect. The proposed approach is verified with centrifuge model tests.
Get full access to this article
View all available purchase options and get full access to this article.
References
Al-Sanad, H., N. Ismael, and R. 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).
API (American Petroleum Institute). 2002. Recommended practice for planning, designing, and constructing fixed offshore platforms–Working stress design. API RP 2A. Washington, DC: API.
API (American Petroleum Institute). 2013. Welded steel tanks for oil storage. 12th ed. Washington, DC: API.
Becker, D. B., and K. Y. Lo. 1979. “Settlement and load transfer of ring foundation for tower silos.” Can. Agric. Eng. 21 (2): 97–110.
Benmebarek, S., M. S. Remadna, N. Benmebarek, and L. Belounar. 2012. “Numerical evaluation of bearing capacity factor Nγ′ of ring footings.” Comput. Geotech. 44 (Jun): 132–138. https://doi.org/10.1016/j.compgeo.2012.04.004.
Benmebarek, S., I. Saifi, and N. Benmebarek. 2017. “Undrained vertical bearing capacity factors for ring shallow footings.” Geotech. Geol. Eng. 35 (1): 355–364. https://doi.org/10.1007/s10706-016-0110-y.
Bolton, M. D. 1986. “The strength and dilatancy of sands.” Géotechnique 36 (1): 65–78. https://doi.org/10.1680/geot.1986.36.1.65.
Bolton, M. D., and C. K. Lau. 1989. “Scale effect in the bearing capacity of granular soils.” In Vol. 2 of Proc., 12th Int. Conf. on Soil Mechanics and Foundations Engineering, 895–898. Rotterdam, Netherlands: A.A. Balkema.
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.
Bowles, J. E. 1996. Foundation analysis and design. New Delhi, India: McGraw-Hill.
Bozozuk, M. 1974. “Bearing capacity of clays for tower silos.” Can. Agric. Eng. 16 (1): 13–17.
Cerato, A., and A. Lutenegger. 2007. “Scale effects of shallow foundation bearing capacity on granular material.” J. Geotech. Geoenviron. Eng. 133 (10): 1192–1202. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:10(1192).
Chakraborty, D., and J. Kumar. 2013. “Dependency of Nγ on footing diameter for circular footings.” Soils Found. 53 (1): 173–180. https://doi.org/10.1016/j.sandf.2012.12.013.
Chakraborty, D., and J. Kumar. 2016. “The size effect of a conical footing on Nγ.” Comput. Geotech. 76 (Jun): 212–221. https://doi.org/10.1016/j.compgeo.2016.03.010.
Chen, W. F. 1975. Limit analysis and soil plasticity. Amsterdam, Netherlands: Elsevier.
Choobbasti, A., S. Hesami, A. Najafi, S. Pirzadeh, F. Farrokhzad, and A. Zahmatkesh. 2010. “Numerical evaluation of bearing capacity and settlement of ring footing: Case study of Kazeroon cooling towers.” Int. J. Res. Rev. Appl. Sci. 4 (3): 263–271.
Davis, E. H., and J. R. Booker. 1971. “The bearing capacity of strip footings from the standpoint of plasticity theory.” In Proc., 1st Australia-New Zealand Conf. on Geomechanics, 275–282. Melbourne, Australia: Institution of Engineers.
De Beer, E. E. 1965. “Bearing capacity and settlement of shallow foundations on sand.” In Proc., Symp. on Bearing Capacity and Settlement of Foundations, 15–33. Durham: Duke University.
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, 179–184. Nicosia, Northern Cyprus.
Diaz, E. G. 2013. “Assessment of the range of variation of Nγ from 60 estimation methods for footings on sand.” Can. Geotech. J. 50 (7): 793–800. https://doi.org/10.1139/cgj-2012-0426.
Egorov, K. E. 1958. “Problem of calculating the base under a foundation with a lower surface of ring shape.” [In Russian.] 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 Foundation Engineering, 41–45. Rotterdam, Netherlands: A.A. Balkema.
El Sawwaf, M., and A. Nazir. 2012. “Behavior of eccentrically loaded small-scale ring footings resting on reinforced layered soil.” J. Geotech. Geoenviron. Eng. 138 (3): 376–384. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000593.
Eranti, E., E. Lehtonen, H. Pukkila, and L. Rantala. 2011. “A novel offshore windmill foundation for heavy ice conditions.” In Proc., 30th Int. Conf. on Ocean, Offshore and Arctic Engineering OMAE2011, 957–964. New York: ASME.
Fischer, K. 1957. “Zur Berechnung der Setzung von Fundamenten in der form einer Kreisformigen Ringflache.” [In German.] Der Bauingenieur 32 (5): 172–174.
Fukushima, S., and F. Tatsuoka. 1984. “Strength and deformation characteristics of saturated sand at extremely low pressures.” Soils Found. 24 (4): 30–48. https://doi.org/10.3208/sandf1972.24.4_30.
Gholami, H., and E. S. Hosseininia. 2017. “Bearing capacity factors of ring footings by using the method of characteristics.” Geotech. Geol. Eng. 35 (5): 2137–2146. https://doi.org/10.1007/s10706-017-0233-9.
Graham, J., and J. M. Hovan. 1986. “Stress characteristics for bearing capacity in sand using a critical state model.” Can. Geotech. J. 23 (2): 195–202. https://doi.org/10.1139/t86-029.
Graham, J., and J. Stuart. 1971. “Scale and boundary effects in foundation analysis.” J. Soil Mech. Found. Div. 97 (11): 1533–1548.
Harris, G. M. 1976. “Foundations and earthworks for cylindrical steel storage tanks.” Ground Eng. 9 (5): 24–31.
Hettler, A., and G. Gudehus. 1988. “Influence of the foundation width on the bearing capacity factor.” Soils Found. 28 (4): 81–92. https://doi.org/10.3208/sandf1972.28.4_81.
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.
Hu, P., S. Stanier, M. Cassidy, and D. Wang. 2014. “Predicting peak resistance of spudcan penetrating sand overlying clay.” J. Geotech. Geoenviron. Eng. 140 (2): 04013009. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001016.
Ismael, N. 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).
Jahanandish, M., M. Veiskarami, and A. Ghahramani. 2010. “Effect of stress level on the bearing capacity factor, Nγ, by the ZEL method.” KSCE J. Civil Eng. 14 (5): 709–723. https://doi.org/10.1007/s12205-010-0866-1.
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 Nc under ϕ = 0 condition for piles in clays.” Int. J. Numer. Methods Eng. 33 (9): 1203–1225. https://doi.org/10.1002/nag.763.
Kimura, T., O. Kusakabe, and K. Saitoh. 1985. “Geotechnical model tests of bearing capacity problems in a centrifuge.” Géotechnique 35 (1): 33–45. https://doi.org/10.1680/geot.1985.35.1.33.
Krabbenhøft, K., A. V. Lyamin, and J. Krabbenhøft. 2015. “Optum computational engineering (OptumG2).” http://www.optumce.com.
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. Khatri. 2008a. “Effect of footing width on bearing capacity factor Nγ for smooth strip footings.” J. Geotech. Geoenviron. Eng. 134 (9): 1299–1310. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:9(1299).
Kumar, J., and V. Khatri. 2008b. “Effect of footing width on Nγ.” Can. Geotech. J. 45 (12): 1673–1684. https://doi.org/10.1139/T08-113.
Kusakabe, O., H. Yamaguchi, and A. Morikage. 1991. “Experiment and analysis on the scale effect of Nγ for circular and rectangular footings.” In Proc., Int. Conf. on Centrifuge ’91, 179–186. Rotterdam, Netherlands: Balkema.
Kutter, B., A. Abghari, and J. Cheney. 1988. “Strength parameters for bearing capacity of sand.” J. Geotech. Eng. 114 (4): 491–498. https://doi.org/10.1061/(ASCE)0733-9410(1988)114:4(491).
Laman, M., and A. Yildiz. 2003. “Model studies of ring foundations on geogrid-reinforced sand.” Geosyn. Int. 10 (5): 142–152. https://doi.org/10.1680/gein.2003.10.5.142.
Laman, M., and A. Yildiz. 2007. “Numerical studies of ring foundations on geogrid-reinforced sand.” Geosyn Int. 14 (2): 52–64. https://doi.org/10.1680/gein.2007.14.2.52.
Lau, C. K. 1988. “Scale effects in tests on footings.” Ph.D. thesis, Univ. of Cambridge.
Lau, C. K., and M. D. Bolton. 2011a. “The bearing capacity of footings on granular soils. I: Numerical analysis.” Géotechnique 61 (8): 627–638. https://doi.org/10.1680/geot.7.00206.
Lau, C. K., and M. D. Bolton. 2011b. “The bearing capacity of footings on granular soils. II: Experimental evidence.” Géotechnique 61 (8): 639–650. https://doi.org/10.1680/geot.7.00207.
Lee, J. K., S. S. Jeong, and S. J. Lee. 2016a. “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.
Lee, J. K., S. S. Jeong, and J. Q. Shang. 2016b. “Undrained bearing capacity of ring foundations on two-layered clays.” Ocean Eng. 119 (Jun): 47–57. https://doi.org/10.1016/j.oceaneng.2016.04.019.
Lee, J. W., R. Salgado, and S. Kim. 2005. “Bearing capacity of circular footings under surcharge using state-dependent finite element analysis.” Comput. Geotechnol. 32 (6): 445–457. https://doi.org/10.1016/j.compgeo.2005.07.005.
Lee, K. K., M. F. Randolph, and M. J. Cassidy. 2013. “Bearing capacity on sand overlying clay soils: A simplified conceptual model.” Géotechnique 63 (15): 1285–1297. https://doi.org/10.1680/geot.12.P.176.
Lo, K. Y., and D. B. Becker. 1979. “Pore-pressure response beneath a ring foundation on clay.” Can. Geotech. J. 16 (3): 551–566. https://doi.org/10.1139/t79-060.
Loukidis, D., and R. Salgado. 2011. “Effect of relative density and stress level on the bearing capacity of footings on sand.” Géotechnique 61 (2): 107–119. https://doi.org/10.1680/geot.8.P.150.3771.
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.
Maeda, K., and K. Miura. 1999. “Confining stress dependency of mechanical properties of sands.” Soils Found. 39 (1): 53–67. https://doi.org/10.3208/sandf.39.53.
Makrodimopoulos, A., and C. M. Martin. 2005. “Lower bound limit analysis of cohesive-frictional materials using second-order cone programming.” Int. J. Numer. Methods Eng. 66 (4): 604–634. https://doi.org/10.1002/nme.1567.
Milovic, D. M. 1973. “Stresses and displacements produced by a ring foundation.” In Vol. 3 of Proc., 8th Int. Conf. on Soil Mechanics of Foundation Engineering, 167–171. Rotterdam, Netherlands: A.A. Balkema.
Naseri, M., and E. S. Hosseininia. 2015. “Elastic settlement of ring foundations.” Soils Found. 55 (2): 284–295. https://doi.org/10.1016/j.sandf.2015.02.005.
Okamura, M., A. Mihara, J. Takemura, and J. Kuwano. 2002. “Effects of footing size and aspect ratio on the bearing capacity of sand subjected to eccentric loading.” Soils Found. 42 (4): 43–56. https://doi.org/10.3208/sandf.42.4_43.
Okamura, M., J. Takemura, and T. Kimura. 1997. “Centrifuge model tests on bearing capacity and deformation of sand layer overlying clay.” Soils Found. 37 (1): 73–88. https://doi.org/10.3208/sandf.37.73.
Ostroumov, B. V., and R. E. Khanin. 2007. “Design and construction of a ring foundation for a radio-television tower.” Soil Mech. Found. Eng. 44 (4): 137–142. https://doi.org/10.1007/s11204-007-0025-y.
Ovesen, N. K. 1975. “Centrifugal testing applied to bearing capacity problems of footings on sand.” Géotechnique 25 (2): 394–401. https://doi.org/10.1680/geot.1975.25.2.394.
Perkins, S., and C. Madson. 2000. “Bearing capacity of shallow foundations on sand: A relative density approach.” J. Geotech. Geoenviron. Eng. 126 (6): 521–530. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:6(521).
Remadna, M. S., S. Benmebarek, and N. Benmebarek. 2017. “Numerical evaluation of the bearing capacity factor Nc′ 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.” M.Eng. thesis, Univ. of Roorkee.
Sargazi, O., and E. S. Hosseininia. 2017. “Bearing capacity of ring footings on cohesionless soil under eccentric load.” Comput. Geotech. 92 (Dec): 169–178. https://doi.org/10.1016/j.compgeo.2017.08.003.
Shiraishi, S. 1990. “Variation in bearing capacity factors of dense sand assessed by model loading tests.” Soils Found. 30 (1): 17–26. https://doi.org/10.3208/sandf1972.30.17.
Siddiquee, M. S., T. Tanaka, F. Tatsuoka, K. Tani, and T. Morimoto. 1999. “Numerical simulation of bearing capacity characteristics of strip footing on sand.” Soils Found. 39 (4): 93–109. https://doi.org/10.3208/sandf.39.4_93.
Sloan, S. W. 1988. “Lower bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech. 12 (1): 61–77. https://doi.org/10.1002/nag.1610120105.
Soltani, M., and K. Maekawa. 2015. “Numerical simulation of progressive shear localization and scale effect in cohesionless soil media.” Int. J. Non Linear Mech. 69 (Mar): 1–13. https://doi.org/10.1016/j.ijnonlinmec.2014.10.014.
Tang, C., and K. Phoon. 2017. “Model uncertainty of Eurocode 7 approach for bearing capacity of circular footings on dense sand.” Int. J. Geomech. 17 (3): 04016069. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000737.
Tang, C., K. K. Phoon, and K. C. Toh. 2015. “Effect of footing width on Nγ and failure envelope of eccentrically and obliquely loaded strip footings on sand.” Can. Geotech. J. 52 (6): 694–707. https://doi.org/10.1139/cgj-2013-0378.
Tang, C., K. Phoon, L. Zhang, and D. Li. 2017. “Model uncertainty for predicting the bearing capacity of sand overlying clay.” Int. J. Geomech. 17 (7): 04017015. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000898.
Tang, C., K. Toh, and K. Phoon. 2014. “Axisymmetric lower-bound limit analysis using finite elements and second-order cone programming.” J. Eng. Mech. 140 (2): 268–278. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000669.
Tejchman, J., and I. Herle. 1999. “A ‘class A’ prediction of the bearing capacity of plane strain footings on sand.” Soils Found. 39 (5): 47–60. https://doi.org/10.3208/sandf.39.5_47.
Terzaghi, K. 1943. Theoretical soil mechanics. New York: John Wiley & Sons.
Toyosawa, Y., K. Itoh, N. Kikkawa, J. J. Yang, and F. Liu. 2013. “Influence of model footing diameter and embedded depth on particle size effect in centrifugal bearing capacity tests.” Soils Found. 53 (2): 349–356. https://doi.org/10.1016/j.sandf.2012.11.027.
Ueno, K., K. Miura, O. Kusakabe, and M. Nishimura. 2001. “Reappraisal of size effect of bearing capacity from plastic solution.” J. Geotech. Geoenviron. Eng. 127 (3): 275–281. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:3(275).
Ueno, K., K. Miura, and Y. Maeda. 1998. “Prediction of ultimate bearing capacity of surface footings with regard to size effects.” Soils Found. 38 (3): 165–178. https://doi.org/10.3208/sandf.38.3_165.
Ullah, S. N., S. Stanier, Y. Hu, and D. White. 2017. “Foundation punch-through in clay with sand: Analytical modelling.” Géotechnique 67 (8): 672–690. https://doi.org/10.1680/jgeot.16.P.101.
Veiskarami, M., M. Jahanandish, and A. Ghahramani. 2012. “Stress level based bearing capacity of foundations: Verification of results with 131 case studies.” KSCE J. Civil Eng. 16 (5): 723–732. https://doi.org/10.1007/s12205-012-1473-0.
Vesić, A. 1973. “Bearing capacity of shallow foundations.” In Foundation engineering handbook, edited by H. F. Winterkorn and H. Y. Fang, 121–147. New York: Van Nostrand Reinhold.
White, D. J., K. L. Teh, C. F. Leung, and Y. K. Chow. 2008. “A comparison of the bearing capacity of flat and conical circular foundations on sand.” Géotechnique 58 (10): 781–792. https://doi.org/10.1680/geot.2008.3781.
Yamamoto, N., M. Randolph, and I. Einav. 2009. “Numerical study of the effect of foundation size for a wide range of sands.” J. Geotech. Geoenviron. Eng. 135 (1): 37–45. https://doi.org/10.1061/(ASCE)1090-0241(2009)135:1(37).
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, F., J. Clark, and R. Phillips. 2001. “Scale effect of strip and circular footings resting on dense sand.” J. Geotech. Geoenviron. Eng. 127 (7): 613–621. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:7(613).
Zhu, F. Y. 1998. “Centrifuge modelling and numerical analysis of bearing capacity of ring foundations on sand.” Ph.D. thesis, Memorial Univ. of Newfoundland.
Information & Authors
Information
Published In
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Dec 28, 2017
Accepted: Jun 4, 2018
Published online: Sep 11, 2018
Published in print: Nov 1, 2018
Discussion open until: Feb 11, 2019
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.