Abstract
This paper deals with initiation and propagation of landslides, for which suitable numerical models are presented. Concerning the initiation phase, we present a coupled displacement-pore pressure formulation (u-pw) proposed by Zienkiewicz and co-workers. Particular attention is paid to capture of the failure surface where strain localizes. An example is presented where the triggering mechanism is the pore pressure changes induced by rainfall. Once failure has been triggered, propagation is analyzed using an Eulerian formulation of the balance of mass and momentum equations. Two simplified, one-phase models are presented for the two extreme cases of dry granular flows and mudflows. The first model uses a level set algorithm to track the free surface, and is suitable for length scales of 100 m. For longer distances of propagation, we propose a depth integrated model which is discretized using a Taylor-Galerkin technique.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
I. Bab ŬSka: The finite element method with Lagrange multipliersNum. Math. 20pp. 179–192, 1973.
M.A. Biot: General theory of three-dimensional consolidationJ. Appl. Phys. 12pp. 155–164, 1941.
M.A. Biot: Theory of elasticity and consolidation for a porous anisotropic solidJ. Appl. Phys. 26pp. 182–185, 1955.
F. Brezzi: On the existence, uniqueness and approximation of saddle point problems arising from lagrangian multipliersRAIRO8 -R2, pp. 129–151, 1974.
W.F. Chen:Limit Analysis and Soil PlasticityElsevier Science Publishers, Amsterdam, 1975.
A.J. Chorin: Flame advection and propagation algorithmsJ. Com put. Phys . 35pp. 1–11, 1980.
G. Dhatt, D.M. Gao, A. Ben Cheikh: A finite element simulation of metal flow in mouldsInt. J. Num. Meth. Eng.30, pp. 821–831, 1990.
R. Dieterlen, V. Maronnier, M. Picasso, J. Rappaz: Numerical simulation of free surface flows, in: S. IDELSOHN, E. OñATE, E. DVORKIN (eds.):Computational Mechanics. New Trends and ApplicationCIMNE, Barcelona, 1998.
R. Dikau, D. Brundsen, L. Schrott, M.L. Ibsen:Landslide RecognitionJohn Wiley and Sons, New York, 1996.
R. Frenette, D. Eyheramendi, T. Immermann: Numerical modeling of dam-break type problems for Navier-Stokes and granular flows, in: C.-L. CHEN (ed.):Debris-Flow Hazards and Mitigation: Mechanics Prediction and AssessmentASCE, 1997, pp. 586–595.
J.H. Harlow, J.E. Welch: Numerical study of large amplitude free surface motionPhys. Fluids9, pp. 842–851, 1966.
C.W. Hirt, B.D. Nichols: Volume of fluid (VOF) method for the dynamics of free boundariesJ. Comput. Phys.39, pp. 201–225, 1981.
M.G. Katona, O.C. Zienkiewicz: A unified set of single-step algorithms. Part 3: the beta-m method, a generalisation of the Newmark schemeInt. J. Num. Meth. Eng.21, pp. 1345–1359, 1985.
R.W. Lewis, A.S. Usmani, J.T. Cross: Efficient mould filling simulation in castings by an explicit finite element methodInt. J. Num. Meth. Fluids20, pp. 493–506, 1995.
R.L. Lewis, B.A. Schrefler:The Finite Element Method in the Static and Dynamic DeformationandConsolidation of Porous MediaJohn Wiley and Sons, New York, 1998.
M. Medale, M. Jaeger: Numerical simulation of incompressible flows with moving interfacesInt. J. Num. Meth. Fluids24, pp. 615–638, 1997.
W. Noh, P. Woodward: Simple line interface calculation, in: A.I. VOOREN, P.J. ZANBERGEN (eds.):Proc. 5 th Int. Conf. Num. Meth. Fluid DynamicsSpringer-Verlag, Wien, 1976, p. 330.
S. Osher, J.A. Sethian: Fronts propagating with curvature¡ªdependent speed: algorithms based on Hamilton-Jacobi formulationJ. Comput. Phys.79, pp. 12–49, 1988.
M. Pastor, T. Li, J.A. FernÁNdez-Merodo: Stabilized finite elements for harmonic soil dynamics problems near the undrainedincompressible limitSoil Dyn. Earthquake Eng.16, pp. 161–171,1997.
M. Pastor, T. Li, X. Liu, O.C. Zienkiewicz: Stabilized low order finite elements for failure and localization problems in undrained soils and foundationsComp. Meth. Appel. Mech. Eng. 1’74pp. 219–234, 1999.
M. Pastor, O.C. Zienkiewicz, T. LI, X. Liu, M. Huang: Stabilized finite elements with equal order of interpolation for soil dynamics problems, Arch. Comp. Mech. 6, pp. 3–33, 1999.
J. Peraire:A Finite Element Method for Convection Dominated FlowsPh.D. thesis, University of Wales, Swansea, 1986.
J. Peraire, O.C. Zienkiewicz, K. Morgan: Shallow water problems. A general explicit formulationInt. J. Num. Meth. Eng. 22pp. 547–574, 1986.
J. Peraire, M. Vahdati, K. Morgan, O.C. Zienkiewicz: Adaptive remeshing for compressible flow computationsJ. Comput. Phys. ’72pp. 449–466, 1987.
M. Quecedo, M. Pastor: Application of the level set method to the finite element solution of two-phase flows, Int. J. Num. Meth. Eng., 2002, in press.
S.B. Savage, K.-Nutter: The dynamics of avalanches of granular materials from initiation to run out. Part I: analysisActaMechanica 86, pp. 210–223, 1991.
M. Sussman, P. Smereka, S. Osher: A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys. 114, pp. 146–159, 1994.
E. Thompson: Use of pseudo-concentrations to follow creeping viscous flows during transient analysisInt. J. Num. Meth. Fluids 6pp. 749–761, 1986.
S.O. Unverdi, G. Tryggvason: A front-tracking method for viscous, incompressible, multi-fluid flowsJ. Comput. Phys. 100pp. 2537, 1992.
J.S. Wang, H.G. Ni, Y.S. He: Finite-difference TVD scheme for computation of dam-break problemsJ. Hyd. Eng. 126pp. 253–262, 2000.
O.C. Zienkiewicz, C.T. Chang, P. Bettess: Drained, undrained, consolidating dynamic behaviour assumptions in soilsG¨¦otechnique 30pp. 385–395, 1980.
O.C. Zienkiewicz, A.H.C. Chan, M. Pastor, D.K. Paul, T. Shiomi: Static and dynamic behaviour of soils: a rational approach to quantitative solutions. I. Fully saturated problemsProc. R. Soc. Lond. A429pp. 285–309, 1990.
O.C. Zienkiewicz, A.H.C. Chan, M. Pastor, B. Schrefler, T. Shiomi:Computational GeomechanicsJohn Wiley and Sons, New York, 2000.
O.C. Zienkiewicz, M. Huang, M. Pastor: Localization problems in plasticity using finite elements with adaptive remeshingInt. J. Num. Anal. Meth. Geomechs. 19pp. 127–148, 1995.
O.C. ZienkiewiczJ.Rojek, R.L. Taylor, M. Pastor: Triangles and tetrahedra in explicit dynamic codes for solidsInt. J. Num. Meth. Eng. 43pp. 565–583, 1998.
O.C. Zienkiewicz, T.Shiomi: Dynamic behaviour of saturated porous media: the generalised Biot formulation and its numerical solution.Int. J. Num. Anal. Meth. Geomech. 8pp. 71–96, 1984.
O.C. Zienkiewicz, Y.M. Xie, B.A. Schrefler, A. Ledesma, N. Bicanic: Static and dynamic behaviour of soils: a rational approach to quantitative solutions.II.Semi-saturated problemsProc. R. Soc. Lond. A 429pp. 311–321, 1990.
O.C. Zienkiewicz, R.L. Taylor:The Finite Element MethodVol. 2, 4th-edition, McGraw-Hill, New York, 1991.
C. Zoppou, S. Roberts: Catastrophic collapse of water supply reservoirs in urban areasJ.HydraulicEng. 125pp. 686–695, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Pastor, M., Quecedo, M., Fernández-Merodo, J.A., Mira, P., Li, T., Xiaoqing, L. (2002). Numerical Modeling of Initiation and Propagation Phases of Landslides. In: Capriz, G., Ghionna, V.N., Giovine, P. (eds) Modeling and Mechanics of Granular and Porous Materials. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0079-6_11
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0079-6_11
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6603-7
Online ISBN: 978-1-4612-0079-6
eBook Packages: Springer Book Archive