-Adaptive Updated Lagrangian Approach for Large-Deformation Analysis of Slope Failure
Publication: International Journal of Geomechanics
Volume 15, Issue 6
Abstract
This paper presents a novel approach to improving our understanding of complicated slope failure mechanisms that can occur in strain-softening material as well as to evaluating the accompanying postfailure deformation of slopes. Three cutting-edge technologies were integrated into one numerical analysis tool: (1) a large-deformation analysis using the updated Lagrangian formulation, (2) a stable numerical algorithm for the solution of progressive failure in strain-softening materials, and (3) an -adaptive mesh refinement algorithm. The significance of this study is mainly in the adoption of a proper numerical discretization for cases of slope failure in which large deformations lead to distortion of the finite-element mesh, unreliable results, and lack of convergence. The -adaptive remeshing technique is used to refine the finite-element mesh around the area of large shear strain, thereby improving the accuracy and convergence of numerical solutions. This study presents a method that can be used to simulate the failure of slopes with highly strain-softening materials that experience large deformations, so that postfailure deformations can be determined. The validity of the method is demonstrated through simulation of the failure and deformation of a highway embankment, and comparing the predicted deformations with the observed record.
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References
Aifantis, E. C. (1984). “On the microstructural origin of certain inelastic models.” J. Eng. Mater. Technol., 106(4), 326–330.
Babuvška, I., and Rheinboldt, W. C. (1978). “Error estimates for adaptive finite element computations.” SIAM J. Numer. Anal., 15(4), 736–754.
Banks, D. C., and Strohm, W. E. (1974). “Calculations of rock slide velocities.” Proc., 3rd Congress ISRM, Vol. 2, International Society of Rock Mechanics, Lisbon, Portugal, 839–847.
Bathe, K.-J., Ramm, E., and Wilson, E. L. (1975). “Finite element formulations for large deformation dynamic analysis.” Int. J. Numer. Methods Eng., 9(2), 353–386.
Bažant, Z. P., Belytschko, T. B., and Chang, T.-P. (1984). “Continuum theory for strain-softening.” J. Eng. Mech., 1666–1692.
Belytschko, T., Fish, J., and Engelmann, B. E. (1988). “A finite element with embedded localization zones.” Comput. Methods Appl. Mech. Eng., 70(1), 59–89.
Belytschko, T., Liu, W. K., and Moran, B. (2000). Nonlinear finite elements for continua and structures, Wiley, Chichester, U.K.
Belytschko, T., and Tabbara, M. (1993). “-Adaptive finite element methods for dynamic problems, with emphasis on localization.” Int. J. Numer. Methods Eng., 36(24), 4245–4265.
Bowles, J. E. (1997). Foundation analysis and design, 5th Ed., McGraw Hill, New York.
Braess, D. (2007). Finite elements theory, fast solvers, and applications in elasticity theory, Cambridge University Press, Cambridge, U.K.
Brinkgreve, R. B. J. (1994). “Geomaterial models and numerical analysis of softening.” Ph.D. thesis, Delft Univ., Delft, Netherlands.
Carter, J. P., and Balaam, N. P. (1995). AFENA users’ manual, Centre for Geotechnical Research, Univ. of Sydney, Sydney, Australia.
Carter, J. P., Booker, J. R., and Davis, E. H. (1977). “Finite deformation of an elasto-plastic soil.” Int. J. Numer. Anal. Methods Geomech., 1(1), 25–43.
Conte, E., Silvestri, F., and Troncone, A. (2010). “Stability analysis of slopes in soils with strain-softening behaviour.” Comput. Geotech., 37(5), 710–722.
Corominas, J. (1996). “The angle of reach as a mobility index for small and large landslides.” Can. Geotech. J., 33(2), 260–271.
Deb, A., Prevost, J. H., and Loret, B. (1996). “Adaptive meshing for dynamic strain localization.” Comput. Methods Appl. Mech. Eng., 137(3–4), 285–306.
De Borst, R. (1991). “Simulation of strain localization: A reappraisal of the Cosserat continuum.” Eng. Comput., 8(4), 317–332.
De Borst, R., Sluys, L. J., Muhlhaus, H.-B., and Pamin, J. (1993). “Fundamental issues in finite analyses of localization of deformation.” Eng. Comput., 10(2), 99–121.
Duncan, J. M. (1996). “State of the art: Limit equilibrium and finite-element analysis of slopes.” J. Geotech. Engrg., 577–596.
Griffiths, D. V., and Lane, P. A. (1999). “Slope stability analysis by finite elements.” Géotechnique, 49(3), 387–403.
Haupt, R. S., and Olson, J. P. (1972). “Case history—Embankment failure on soft varved silt.” Proc., ASCE Specialty Conf. on Performance of Earth and Earth Supported Structures, ASCE, New York, 1–27.
Hu, Y., and Randolph, M. F. (1998a). “A practical numerical approach for large deformation problems in soil.” Int. J. Numer. Anal. Methods Geomech., 22(5), 327–350.
Hu, Y., and Randolph, M. F. (1998b). “-Adaptive FE analysis of elasto-plastic non-homogeneous soil with large deformation.” Comput. Geotech., 23(1–2), 61–83.
Hughes, T. J. R., and Winget, J. (1980). “Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis.” Int. J. Numer. Methods Eng., 15(12), 1862–1867.
Jaumann, G. (1911). “Geschlossenes system physikalischer und chemischer differenzial gesetze.” Sitzungsberichte Akad. Wiss. Wien, 120(IIa), 385–530.
Johnson, C., and Hansbo, P. (1992). “Adaptive finite element methods in computational mechanics.” Comput. Methods Appl. Mech. Eng., 101(1–3), 143–181.
Kardani, M., Nazem, M., Abbo, A. J., Sheng, D., and Sloan, S. W. (2012). “Refined -adaptive finite element procedure for large deformation geotechnical problems.” Comput. Mech., 49(1), 21–33.
Kardani, M., Nazem, M., Sheng, D., and Carter, J. P. (2013). “Large deformation analysis of geomechanics problems by a combined -adaptive finite element method.” Comput. Geotech., 49, 90–99.
Khalili, N., Fell, R., and Tai, K. S. (1996). “A simplified method for estimating failure induced deformation in embankments.” Proc., 7th Int. Symp. on Landslides, K. Senneset, ed., Balkema, Rotterdam, Netherlands, 1263–1268.
Khoei, A. R., Gharehbaghi, S. A., Azami, A. R., and Tabarraie, A. R. (2006). “SUT-DAM: An integrated software environment for multi-disciplinary geotechnical engineering.” Adv. Eng. Softw., 37(11), 728–753.
Khoei, A. R., and Karimi, K. (2008). “An enriched-FEM model for simulation of localization phenomenon in Cosserat continuum theory.” Comput. Mater. Sci., 44(2), 733–749.
Khoei, A. R., and Lewis, R. W. (2002). “-Adaptive finite element analysis for localization phenomena with reference to metal powder forming.” Finite Elem. Anal. Des., 38(6), 503–519.
Khoei, A. R., Lewis, R. W., and Zienkiewicz, O. C. (1997). “Application of the finite element method for localized failure analysis in dynamic loading.” Finite Elem. Anal. Des., 27(1), 121–131.
Khoei, A. R., Tabarraie, A. R., and Gharehbaghi, S. A. (2005). “-Adaptive mesh refinement for shear band localization in elasto-plasticity Cosserat continuum.” Commun. Nonlinear Sci. Numer. Simul., 10(3), 253–286.
Larsson, R., Runesson, K., and Sture, S. (1991). “Finite element simulation of localized plastic deformation.” Arch. Appl. Mech., 61(5), 305–317.
Lee, N.-S., and Bathe, K.-J. (1994). “Error indicators and adaptive remeshing in large deformation finite element analysis.” Finite Elem. Anal. Des., 16(2), 99–139.
Leroueil, S. (2001). “Natural slopes and cuts: Movement and failure mechanisms.” Géotechnique, 51(3), 197–243.
Lewis, R. W., and Khoei, A. R. (2001). “Numerical analysis of strain localization in metal powder-forming processes.” Int. J. Numer. Methods Eng., 52(5–6), 489–501.
Li, L.-Y., and Bettess, P. (1995). “Notes on mesh optimal criteria in adaptive finite element computations.” Commun. Numer. Methods Eng., 11(11), 911–915.
Li, L.-Y., and Bettess, P. (1997). “Adaptive finite element methods: A review.” Appl. Mech. Rev., 50(10), 581–591.
Li, Q., and Ugai, K. (1998). “Comparative study on static and dynamic sliding behaviors of slopes based on small and large deformation theories.” Soils Found., 38(3), 201–207.
Li, S., Yue, Z. Q., Tham, L. G., Lee, C. F., and Yan, S. W. (2005). “Slope failure in underconsolidated soft soils during the development of a port in Tianjin, China. Part 2: Analytical study.” Can. Geotech. J., 42(1), 166–183.
Lo, S. H. (1985). “A new mesh generation scheme for arbitrary planar domains.” Int. J. Numer. Methods Eng., 21(8), 1403–1426.
Löhner, R., Morgan, K., and Zienkiewicz, O. C. (1985). “An adaptive finite element procedure for compressible high speed flows.” Comput. Methods Appl. Mech. Eng., 51(1–3), 441–465.
Loret, B., and Prevost, J. H. (1990). “Dynamic strain localization in elasto-(visco-)plastic solids, Part 1. General formulation and one-dimensional examples.” Comput. Methods Appl. Mech. Eng., 83(3), 247–273.
Mohammadi, S., and Taiebat, H. A. (2011). “Updated Lagrangian analysis of slopes in FEM.” Proc., 14th Pan-American Conf. on Soil Mechanics and Geotechnical Engineering and 64th Canadian Geotechnical Conf. (CD-ROM), A. Drevininka and G. Cascante, eds., Pan-Am CGS 2011 Organizing Committee, Toronto.
Mohammadi, S., and Taiebat, H. A. (2013). “A large deformation analysis for the assessment of failure induced deformations of slopes in strain softening materials.” Comput. Geotech., 49, 279–288.
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.
Oka, F., Adachi, T., and Yashima, A. (1995). “A strain localization analysis using a viscoplastic softening model for clay.” Int. J. Plast., 11(5), 523–545.
Oñate, E., and Bugeda, G. (1993). “Study of mesh optimality criteria in adaptive finite element analysis.” Eng. Comput., 10(4), 307–321.
Ortiz, M., and Quigley, J. J., IV. (1991). “Adaptive mesh refinement in strain localization problems.” Comput. Methods Appl. Mech. Eng., 90(1–3), 781–804.
Pastor, M., Peraire, J., and Zienkiewicz, O. C. (1991). “Adaptive remeshing for shear band localization problems.” Arch. Appl. Mech., 61(1), 30–39.
Peraire, J., Vahdati, M., Morgan, K., and Zienkiewicz, O. C. (1987). “Adaptive remeshing for compressible flow computations.” J. Comput. Phys., 72(2), 449–466.
Pietruszczak, S., and Mróz, Z. (1981). “Finite element analysis of deformation of strain-softening materials.” Int. J. Numer. Methods Eng., 17(3), 327–334.
Pietruszczak, S., and Stolle, D. F. E. (1985). “Deformation of strain softening materials: Part I: Objectivity of finite element solutions based on conventional strain softening formulations.” Comput. Geotech., 1(2), 99–115.
Pietruszczak, S., and Stolle, D. F. E. (1987). “Deformation of strain softening materials Part II: Modelling of strain softening response.” Comput. Geotech., 4(2), 109–123.
Pijaudier-Cabot, G., and Bažant, Z. P. (1987). “Nonlocal damage theory.” J. Eng. Mech., 1512–1533.
Pinsky, P. M., Ortiz, M., and Pister, K. S. (1983). “Numerical integration of rate constitutive equations in finite deformation analysis.” Comput. Methods Appl. Mech. Eng., 40(2), 137–158.
Potts, D. M., Dounias, G. T., and Vaughan, P. R. (1990). “Finite element analysis of progressive failure of Carsington embankment.” Géotechnique, 40(1), 79–101.
Potts, D. M., and Gens, A. (1985). “A critical assessment of methods of correcting for drift from the yield surface in elasto-plastic finite element analysis.” Int. J. Numer. Anal. Methods Geomech., 9(2), 149–159.
Prandtl, L. (1921). “Hauptaufsätze: Über die eindringungsfestigkeit (härte) plastischer baustoffe und die festigkeit von schneiden.” ZAMM., 1(1), 15–20.
Resendiz, D., and Romo, M. P. (1972). “Analysis of embankment deformations.” Proc., ASCE Specialty Conf. on Performance of Earth and Earth Supported Structures, ASCE, New York, 817–836.
Snitbhan, N., and Chen, W.-F. (1978). “Elastic-plastic large deformation analysis of soil slopes.” Comput. Struct., 9(6), 567–577.
Sterpi, D. (1999). “An analysis of geotechnical problems involving strain softening effects.” Int. J. Numer. Anal. Methods Geomech., 23(13), 1427–1454.
Troncone, A. (2005). “Numerical analysis of a landslide in soils with strain-softening behaviour.” Géotechnique, 55(8), 585–596.
Truesdell, C. (1955). “The simplest rate theory of pure elasticity.” Commun. Pure Appl. Math., 8(1), 123–132.
Vardoulakis, I., and Aifantis, E. C. (1989). “Gradient dependent dilatancy and its implications in shear banding and liquefaction.” Ing. Arch., 59(3), 197–208.
Vardoulakis, I., and Sulem, J. (1995). Bifurcation analysis in geomechanics, Taylor & Francis, London.
Wang, S., Zheng, H., Li, C., and Ge, X. (2011). “A finite element implementation of strain-softening rock mass.” Int. J. Rock Mech. Min. Sci., 48(1), 67–76.
Wang, W. M., Sluys, L. J., and De Borst, R. (1997). “Viscoplasticity for instabilities due to strain softening and strain-rate softening.” Int. J. Numer. Methods Eng., 40(20), 3839–3864.
Zienkiewicz, O. C., Huang, M., and Pastor, M. (1995). “Localization problems in plasticity using finite elements with adaptive remeshing.” Int. J. Numer. Anal. Methods Geomech., 19(2), 127–148.
Zienkiewicz, O. C., and Zhu, J. Z. (1987). “A simple error estimator and adaptive procedure for practical engineering analysis.” Int. J. Numer. Methods Eng., 24(2), 337–357.
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Published In
International Journal of Geomechanics
Volume 15 • Issue 6 • December 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Nov 5, 2013
Accepted: Jul 28, 2014
Published online: Sep 2, 2014
Published in print: Dec 1, 2015
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