Smoothed Particle Finite-Element Method for Large-Deformation Problems in Geomechanics
Publication: International Journal of Geomechanics
Volume 18, Issue 4
Abstract
This study presents a novel smoothed particle FEM (SPFEM) for large-deformation problems in geomechanics. Within the framework of the particle FEM (PFEM), a strain smoothing technique for nodal integration is incorporated. The problem domain is divided into strain smoothing cells associated with particles, and the equilibrium of the continuum medium is achieved at these strain smoothing cells. The corresponding computational formulations and numerical procedure are given. Compared with the original PFEM, the SPFEM possesses the following advantages: (1) all the field variables are calculated and stored at the particles, and the frequent information transfer between Gauss points and particles, which inevitably introduces error and adds considerable complexity to solution procedures, is avoided; (2) the SPFEM possesses the upper bound property, providing a conservative estimation for problems in geomechanics; and (3) linear elements can be used directly without suffering from the volumetric locking, so special treatment to bypass the volumetric locking is not required. By solving two benchmark examples, the SPFEM has been verified to be a promising numerical method for analyzing large-deformation problems in geomechanics.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The research is supported by the Natural Science Foundation of China (NSFC) (No. 51209237), the Water Conservancy Science and Technology Innovation Project of Guangdong (No. 2017-30), and the Technology Program Funding of Guangzhou (No. 201605030009).
References
Abe, K., Soga, K., and Bandara, S. (2014). “Material point method for coupled hydromechanical problems.” J. Geotech. Geoenviron. Eng., 04013033.
Alonso, E. E., and Zabala, F. (2011). “Progressive failure of Aznalcóllar dam using the material point method.” Géotechnique, 61(9), 795–808.
ANSYS, Inc. (2012). Theory reference—Large deformation analysis, ANSYS user's manual, Version 14.0, Canonsburg, PA.
Bandara, S., and Soga, K. (2015). “Coupling of soil deformation and pore fluid flow using material point method.” Comput. Geotech., 63(Jan), 199–214.
Bathe, K., and Bolourchi, S. (1979). “Large displacement analysis of three-dimensional beam structures.” Int. J. Numer. Methods in Eng., 14(7), 961–986.
Beuth, L. W., Wieckowski, Z., and Vermeer, P. A. (2011). “Solution of quasi–static large–strain problems by the material point method.” Int. J. Numerical Anal. Methods Geomech., 35(13), 1451–1465.
Bishop, A. W., and Morgenstern, N. R. (1960). “Stability coefficients for earth slopes.” Géotechnique, 10(4), 129–147.
Bui, H. H., Fukagawa, R., Sako, K., and Ohno, S. (2008). “Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model.” Int. J. Numer. Anal. Methods Geomech., 32(12), 1537–1570.
Bui, H. H., Fukagawa, R., Sako, K., and Wells, J. C. (2011). “Slope stability analysis and discontinuous slope failure simulation by elastol using elastic–plastic soil constitutive mode.” Géotechnique, 61(7), 565–574.
Burd, H. J. (1986). “A large displacement finite element analysis of a reinforced unpaved road.” Ph.D. thesis, Oxford Univ., Oxford, U.K.
Carbonell, J., Oñate, E., and Suárez, B. (2010). “Modeling of ground excavation with the particle finite–element method.” J. Eng. Mech., 455–463.
Carbonell, J. M., Oñate, E., and Suárez, B. (2013). “Modelling of tunnelling processes and rock cutting tool wear with the particle finite element method.” Comput. Mech., 52(3), 607–629.
Chen, J. S., Wu, C. T., Yoon, S., and You, Y. (2001). “A stabilized conforming nodal integration for Galerkin mesh-free methods.” Int. J. Numer. Methods Eng., 50(2), 435–466.
Chen, W., and Qiu, T. (2012). “Numerical simulations for large deformation of granular materials using smoothed particle hydrodynamics method.” Int. J. Geomech., 127–135.
Cuomo, S., Prime, N., Iannone, A., Dufour, F., Cascini, F., and Darve, F. (2013). “Large deformation FEMLIP drained analysis of a vertical cut.” Acta Geotech., 8(2), 125–136.
da Silva, M. V., Krabbenhoft, K., Lyamin, A. V., and Sloan, S. W. (2011). “Rigid-plastic large-plasticican analysis of geotechnical penetration problems.” Proc., 13th IACMAG Conf., Vol. 1. Univ. of New South Wales, Centre for Infrastructure Engineering and Safety, New South Wales, Australia, 42–47.
Di, Y., Yang, J., and Sato, T. (2007). “An operator-split ALE model for large deformation analysis of geomaterials.” Int. J. Numer. Anal. Methods Geomech., 31(12), 1375–1399.
Griffiths, D. V., and Lane, P. A. (1999). “Slope stability analysis by finite elements.” Géotechnique, 49(3), 387–403.
Huang, Y., and Dai, Z. (2014). “Large deformation and failure simulations for geodisasters using smoothed particle hydrodynamics method.” Eng. Geol., 168(Jan), 86–97.
Kardani, M., Nazem, M., Abbo, A. J., Sheng, D., and Sloan, S. W. (2012). “Refined h-adaptive finite element procedure for large deformation geotechnical problems.” Comput. Mech., 49(1), 21–33.
Kardani, M., Nazem, M., Carter, J., and Abbo, A. (2015). “Efficiency of high-order elements in large-deformation problems of geomechanics.” Int. J. Geomech., 04014101.
Liu, G. R., Dai, K. Y., and Nguyen, T. T. (2007). “A smoothed finite element method for mechanics problems.” Comput. Mech., 39(6), 859–877.
Liu, G. R., Nguyen-Thoi, T., Nguyen-Xuan, H., and Lam, K. Y. (2009). “A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems.” Comput. Struct., 87(1–2), 14–26.
Meyerhof, G. G. (1951). “The ultimate bearing capacity of foundations.” Géotechnique, 2(4), 301–332.
Mohammadi, S., and Taiebat, H. (2015). “H-adaptive updated Lagrangian approach for large-deformation analysis of slope failure.” Int. J. Geomech., 04014092.
Monforte, L., Arroyo, M., Carbonell, J. M., and Gens, A. (2017). “Numerical simulation of undrained insertion problems in geotechnical engineering with the particle finite element method (PFEM).” Comput. Geotech., 82(Feb), 144–156.
Nazem, M., Carter, J. P., Sheng, D., and Sloan, S. W. (2009). “Alternative stress-integration schemes for large-deformation problems of solid mechanics.” Finite Elem. Anal. Des., 45(12), 934–943.
Nazem, M., Sheng, D., and Carter, J. P. (2006). “Stress integration and mesh refinement for large deformation in geomechanics.” Int. J. Numer. Methods Eng., 65(7), 1002–1027.
Nazem, M., Sheng, D., Carter, J. P., and Sloan, S. W. (2008). “Arbitrary Lagrangian-Eulerian method for large-strain consolidation problems.” Int. J. Numer. Anal. Methods Geomech., 32(9), 1023–1050.
Nonoyama, H., Moriguchi, S., Sawada, K., and Yashima, A. (2015). “Slope stability analysis using smoothed particle hydrodynamics (SPH) method.” Soils Found., 55(2), 458–470.
Oñate, E., Celigueta, M. A., Idelsohn, S. R., Salazar, F., and Suárez, B. (2011). “Possibilities of the particle finite element method for fluid-soil-structure interaction problems.” Comput. Mech., 48(3), 307–318.
Oñate, E., Idelsohn, S. R., Celigueta, M. A., and Rossi, R. (2008). “Advances in the particle finite element method for the analysis of fluid–multibody interaction and bed erosion in free surface flows.” Comput. Methods Appl. Mech. Eng., 197(19–20), 1777–1800.
Oñate, E., Idelsohn, S. R., Pin, F. D., and Aubry, R. (2004). “The particle finite element method 16/j.cma.2007.” Int. J. Comput. Methods, 1(2), 267–307.
Pai, P. F., and Palazotto, A. N. (1996). “Large-deformation analysis of flexible beams.” Int. J. Solids Struct., 33(9), 1335–1370.
Pastor, M., et al. (2014). “Application of a SPH depth-integrated model to landslide run-out analysis.” Landslides, 11(5), 793–812.
Prandtl, L. (1921). “H¨auptaufsätze: Uber die Eindringungsfestigkeit (Härte) plastischer Baustoffe und die Festigkeit von Schneiden.” Z. Angew. Math. Mech., 1(1), 15–20.
Salazar, F., Irazábal, J., Larese, A., and Oñate, E. (2016). “Numerical modelling of landslide-generated waves with the particle finite element method (PFEM) and a non-Newtonian flow model.” Int. J. Numer. Anal. Methods Geomech., 40(6), 809–826.
Soga, K., Alonso, E., Yerro, A., Kumar, K., and Bandara, S. (2015). “Trends in large-deformation analysis of landslide mass movements with particular emphasis on the material point method.” Géotechnique, 66(3), 248–273.
Solowski, W. T., and Sloan, S. W. (2015). “Evaluation of material point method for use in geotechnics.” Int. J. Numer. Anal. Methods Geomech., 39(7), 685–701.
Vavourakis, V., Loukidis, D., Charmpis, D. C., and Papanastasiou, P. (2013a). “A robust finite element approach for large deformation elastoplastic plane-strain problems.” Finite Elem. Anal. Des., 77(Dec), 1–15.
Vavourakis, V., Loukidis, D., Charmpis, D. C., and Papanastasiou, P. (2013b). “Assessment of remeshing and remapping strategies for large deformation elastoplastic finite element analysis.” Comput. Struct., 114–115(1), 133–146.
Wang, B., Hicks, M. A., and Vardon, P. J. (2016). “Slope failure analysis using the random material point method.” Géotechnique Lett., 6(2), 113–118.
Yu, H. S. (2000). Cavity expansion methods in geomechanics, Kluwer Academic, Dordrecht, Netherlands.
Yuan, J., and Hicks, M. A. (2013). “Large deformation elastic electro-osmosis consolidation of clays.” Comput. Geotech., 54(Oct), 60–68.
Zhang, W., Dai, B., Liu, Z., and Zhou, C. (2016). “Modeling discontinuous rock mass based on smoothed finite element method.” Comput. Geotech., 79(Oct), 22–30.
Zhang, X., et al. (2013). “Particle finite element analysis of large deformation and granular flow problems.” Comput. Geotech., 54(Oct), 133–142.
Zhang, X., Krabbenhoft, K., and Sheng, D. (2014). “Particle finite element analysis of the granular column collapse problem.” Granular Matter, 16(4), 609–619.
Zhang, X., Krabbenhoft, K., Sheng, D., and Li, W. (2015). “Numerical simulation of a flow-like landslide using the particle finite element method.” Comput. Mech., 55(1), 167–177.
Zhao, G. F. (2014). “Development of the distinct lattice spring model for large deformation analyses.” Int. J. Numer. Anal. Methods Geomech., 38(10), 1078–1100.
Zhao, G. F. (2017). “Developing a four-dimensional lattice spring model for mechanical responses of solids.” Comput. Methods Appl. Mech. Eng., 315(Mar), 881–895.
Zhou, X., and Bi, J. (2016). “3D numerical study on the growth and coalescence of pre-existing flaws in rocklike materials subjected to uniaxial compression.” Int. J. Geomech., 04015096.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 18 • Issue 4 • April 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: May 15, 2017
Accepted: Sep 11, 2017
Published online: Jan 19, 2018
Published in print: Apr 1, 2018
Discussion open until: Jun 19, 2018
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.