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Calculation of Bearing Capacity Factors of Strip Footing Using the Nodebased Smoothed Finite Element Method (NS-FEM)

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Geotechnics for Sustainable Infrastructure Development

Part of the book series: Lecture Notes in Civil Engineering ((LNCE,volume 62))

Abstract

This paper presents an upper bound limit analysis procedure using the node-based smoothed finite element method (NS-FEM) for evaluating bearing capacity factors of strip footing resting on a cohesive-frictional soil. The soil behavior is described as a perfectly plastic Mohr-Coulomb material and it obeys associated flow rule. The smoothed strain field of strip footing problems is approximated by using a smooth function. The commercial software Mosek is employed to deal with the optimization problems which are formulated as well-known second order cone programming. The bearing capacity factors of strip footing and failure mechanisms in both rough and smooth interface are obtained directly from solving the optmization problems. The obtained results using the present method are compared with other numerical results that have been reported in the literature.

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References

  • Bolton, M.D. & Lau, C.K. (1993). Vertical bearing capacity factors for circular and strip footings on Mohr–Coulomb soil. Canadian Geotechnical Journal, 30, pp 1024–1033.

    Google Scholar 

  • Caquot, A. & Kérisel, J. (1953). Sur le terme de surface dans le calcul des fondations en milieu pulve rulents. Proc. of the 3rd Inter. Conf. on Soil Mechanics and Foundation Engineering, Zurich.

    Google Scholar 

  • Chen, J.S, Wu, C.T. & Yoon, S. (2001). A stabilized conforming nodal integration for Galerkin meshfree method. Inter. Journal for Numerical Methods in Engineering, 50, pp 435–466.

    Google Scholar 

  • Cui, X.Y., Li, Z.C., Feng, H. & Feng, S.Z. (2016). Steady and transient heat transfer analysis using a stable node-based smoothed finite element method. Inter. Journal of Thermal Sciences, 110, pp 12–25.

    Google Scholar 

  • Feng, H., Cui, X.Y. & Li, G.Y. (2016). A stable nodal integration method with strain gradient for static and dynamic analysis of solid mechanics. Engineering Analysis with Boundary Elements, 62, pp 78–92.

    Google Scholar 

  • Hansen, J.B. (1970). A revised extended formula for bearing capacity. Bulletin of the Danish Geotechnical Institute, 28, pp 3–11.

    Google Scholar 

  • Hjiaj, M., Lyamin, A.V. & Sloan, S.W. (2005). Numerical limit analysis solutions for the bearing capacity factor Nγ. Inter. Journal of Solids and Structures, 42, pp 1681–1704.

    Google Scholar 

  • Kumar, J. (2003). Nγ for rough strip footing using the method of characteristics. Canadian Geotechnical Journal, 40, pp 669–674.

    Google Scholar 

  • Liu, G.R., Dai, K.Y. & Nguyen-Thoi T. (2007a). A smoothed finite element for mechanics problems. Computer and Mechanics, 39, pp 859–877.

    Google Scholar 

  • Liu, G.R., Nguyen-Thoi T., Dai, K.Y. & Lam, K.Y. (2007b). Theoretical aspects of the smoothed finite element method (SFEM). Inter. Journal for Numerical Methods in Engineering, 71, pp 902–930.

    Google Scholar 

  • Liu, G.R., Nguyen-Thoi T., Nguyen-Xuan H. & Lam, K.Y. (2008). A node based smoothed finite element method (NS-FEM) for upper bound solution to solid mechanics problems. Computer and Structures, 87, pp 14–26.

    Google Scholar 

  • Liu, G.R., Nguyen-Xuan H. & Nguyen-Thoi T. (2010a). A theoretical study of S-FEM models: properties, accuracy and convergence rates. Inter. Journal for Numerical Methods in Engineering, 84, pp 1222–1256.

    Google Scholar 

  • Liu, G.R., Chen, L., Nguyen-Thoi T., Zeng, K.Y. & Zhang, G.Y. (2010b). A novel singular nodebased smoothed finite element method for upper bound solutions of fracture problems. Inter. Journal for Numerical Methods in Engineering, 83, pp 1466–1497.

    Google Scholar 

  • Makrodimopoulos, A. & Martin, C.M. (2006). Upper bound limit analysis using simplex strain elements and second-order cone programming. Inter. Journal for Numerical and Analytical Methods in Geomechanics, 31, pp 835–865.

    Google Scholar 

  • Martin, C.M. (2005). Exact bearing capacity calculations using the method of characteristics. Proc. of the 11th Inter. Conference of IACMAG, Turin, 4, pp 441–450.

    Google Scholar 

  • Meyerhof, G.G. (1963). Some recent research on the bearing capacity of foundations. Canadian Geotechnical Journal, 1, pp 16–26.

    Google Scholar 

  • Mosek. (2009). The MOSEK optimization toolbox for MATLAB manual: http://www.mosek.com, Mosek ApS, Version 5.0 Edition.

  • Nguyen-Xuan H., Rabczuk, T., Nguyen-Thoi T., Tran, T.N. & Nguyen-Thanh N. (2012). Computation of limit and shakedown loads using a node-based smoothed finite element method. Inter. Journal for Numerical Methods in Engineering, 90, pp 287–310.

    Google Scholar 

  • Prandtl, L. (1921). Uber die Eindringungs-festigkeit (Harte) plastischer Baustoffe und die Festigkeit von Schneiden. Zeitschrift fur Angewandte Mathematik und Mechanik, 1, pp 15–20.

    Google Scholar 

  • Reissner, H. (1924). Zum Erddruckproblem. Proc. of the 1st Inter. Congress for Applied Mechanics, Delft, The Netherlands, pp 295–311 (in Germany).

    Google Scholar 

  • Sokolovskii, V.V. (1965). Statics of Soil Media, Pergamon Press.

    Google Scholar 

  • Terzaghi, K. (1943). Theoretical Soil Mechanics. New York: John Wiley & Sons.

    Google Scholar 

  • Ukritchon, B., Whittle, A.W. & Klangvijit, C. (2003). Calculations of bearing capacity factor Nγ using numerical limit analyses. Journal of Geotechnical and Geoenvironmental Engineering, 129, pp 468–474.

    Google Scholar 

  • Vesic, A.S (1973). Analysis of ultimate loads of shallow foundations. J. Soil Mech. and Found. Div. ASCE, 99, pp 45–76.

    Google Scholar 

  • Vo-Minh T., Nguyen-Minh T., Chau-Ngoc A. & Nguyen-Chanh H. (2017). Stability of twin circular tunnels in cohesive-frictional soil using the node-based smoothed finite element method (NS-FEM). Journal of Vibroengineering, 19, pp 520–538.

    Google Scholar 

  • Vo-Minh T., Chau-Ngoc A., Nguyen-Minh T. & Nguyen-Chanh H. (2018). A node-based smoothed finite element method for stability analysis of dual square tunnels in cohesivefrictional soils. Scientia Iranica, 23, pp 1105–1121.

    Google Scholar 

  • Wang, G., Cui, X.Y. & Li, G.Y. (2016). A rotationfree shell formulation using nodal integration for static and dynamic analyses of structures. Inter. Journal for Numerical Methods in Engineering, 105, pp 532–560.

    Google Scholar 

  • Wu, S.C., Liu, G.R., Zhang, H.O., Xu, X. & Li, Z.R. (2009). A node-based smoothed point interpolation method (NS-PIM) for threedimensional heat transfer problems. Inter. Journal of Thermal Sciences, 48, pp 1367–1376.

    Google Scholar 

  • Yoo, J.W., Moran, B. & Chen, J.S. (2004). Stabilized conforming nodal integration in the natural-element method. Inter. Journal for Numerical Methods in Engineering, 60, pp 861–890.

    Google Scholar 

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Correspondence to Thien Vo-Minh .

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Vo-Minh, T. (2020). Calculation of Bearing Capacity Factors of Strip Footing Using the Nodebased Smoothed Finite Element Method (NS-FEM). In: Duc Long, P., Dung, N. (eds) Geotechnics for Sustainable Infrastructure Development. Lecture Notes in Civil Engineering, vol 62. Springer, Singapore. https://doi.org/10.1007/978-981-15-2184-3_147

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  • DOI: https://doi.org/10.1007/978-981-15-2184-3_147

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  • Online ISBN: 978-981-15-2184-3

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