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Depth Averaged Models for Fast Landslide Propagation: Mathematical, Rheological and Numerical Aspects

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Abstract

This paper presents an overview of depth averaged modelling of fast catastrophic landslides where coupling of solid skeleton and pore fluid (air and water) is important. The first goal is to show how Biot–Zienkiewicz models can be applied to develop depth integrated, coupled models. The second objective of the paper is to consider a link which can be established between rheological and constitutive models. Perzyna’s viscoplasticity can be considered a general framework within which rheological models such as Bingham and cohesive frictional fluids can be derived. Among the several alternative numerical models, we will focus here on SPH which has not been widely applied by engineers to model landslide propagation. We propose an improvement, based on combining Finite Difference meshes associated to SPH nodes to describe pore pressure evolution inside the landslide mass. We devote a Section to analyze the performance of the models, considering three sets of tests and examples which allows to assess the model performance and limitations: (i) Problems having an analytical solution, (ii) Small scale laboratory tests, and (iii) Real cases for which we have had access to reliable information.

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Acknowledgments

The authors gratefully acknowledge the economic support provided by the Spanish Ministry MINECO (Projects GEODYN and GEOFLOW). The first author would like to express his gratitude to Dra. Ma. D. Elizalde for the help provided with the documentation at the National Archives (Kew, UK), which allowed the retrieval of information concerning Aberfan flowslide. The authors gratefully acknowledge the support of the Geotechnical Engineering Office, Civil Engineering and Development Department of the Government of the Hong Kong SAR in the provision of the digital terrain models for the Hong Kong landslide cases. Thanks are given to Dr Manzella for the experimental data concerning the granular avalanche experiments.

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Authors and Affiliations

  1. Department of Applied Mathematics, ETS Ingenieros de Caminos, UPM, Madrid, Spain

    M. Pastor, T. Blanc, V. Drempetic, P. Dutto, M. Martin Stickle & J. A. Fernández Merodo

  2. Centro de Estudios y Experimentación de Obras Públicas (CEDEX), Madrid, Spain

    P. Mira

  3. Department of Geotechnical Engineering, Escuela de Ingenieros de Obras Públicas, UPM, Madrid, Spain

    P. Mira

  4. Universidad de Castilla La Mancha, Toledo, Spain

    B. Haddad

  5. Instituto Geológico y Minero de España, IGME, Madrid, Spain

    J. A. Fernández Merodo

  6. Departmento de Ingenieria Vial, Universidad Centroccidental Lissandro Alvarado, Barquisimeto, Venezuela

    Mila Sanchez Morles

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  1. M. Pastor
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Pastor, M., Blanc, T., Haddad, B. et al. Depth Averaged Models for Fast Landslide Propagation: Mathematical, Rheological and Numerical Aspects. Arch Computat Methods Eng 22, 67–104 (2015). https://doi.org/10.1007/s11831-014-9110-3

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