Instabilities in granular materials and application to landslides

Landslides or questions related to slope stability are usually considered in the framework of plastic limit analyses. Recent progress has made it possible to describe some failure modes in the framework of the theories of bifurcation of the strain mode by plastic strain localization and the shear-banding phenomenon. We propose in this paper to reconsider the question of landslide analysis by taking into account an appropriate instability criterion. As soils are strongly non-associated materials, unstable states can be reached strictly inside the plastic limit condition (which defines the set of admissible stresses). In the first part of this paper, we describe the constitutive model. Then Lyapunov's definition of stability allows us to detect unstable stress–strain states from experimental evidence. These unstable states are analysed by considering the sign of the second-order work. The stability analysis, performed for loose and dense sands under plane strain conditions, shows a large domain of instabilities in the stress space. This method is applied to some boundary-value problems by finite elements computations. It is shown finally by examples that such unstable stress–strain states are observed in our FEM modelling of slope problems. Copyright © 2000 John Wiley & Sons, Ltd.

[1]  J. Rice.  Localization of plastic deformation , 1976 .

[2]  R. Nova,et al.  CONTROLLABILITY OF THE INCREMENTAL RESPONSE OF SOIL SPECIMENS SUBJECTED TO ARBITRARY LOADING PROGRAMMES , 1994 .

[3]  Félix Darve,et al.  Constitutive modelling and instabilities of soil behaviour , 1995 .

[4]  Poul V. Lade,et al.  Closure of "Static Instability and Liquefaction of Loose Fine Sandy Slopes" , 1993 .

[5]  A. Liapounoff,et al.  Problème général de la stabilité du mouvement , 1907 .

[6]  J. M. Duncan.  State of the Art: Limit Equilibrium and Finite-Element Analysis of Slopes , 1996 .

[7]  Richard B. Nelson,et al.  INSTABILITY OF GRANULAR MATERIALS WITH NONASSOCIATED FLOW , 1988 .

[8]  J. Rice,et al.  CONDITIONS FOR THE LOCALIZATION OF DEFORMATION IN PRESSURE-SENSITIVE DILATANT MATERIALS , 1975 .

[9]  Robert Charlier,et al.  CLoE, a new rate-type constitutive model for geomaterials theoretical basis and implementation , 1994 .

[10]  Jacques Desrues,et al.  Strain localization measurements in undrained plane-strain biaxial tests on Hostun RF sand , 1999 .

[11]  P. Royis.  Interpolations and one-to-one properties of incremental constitutive laws. A family of incrementally non-linear constitutive laws , 1989 .

[12]  I. Vardoulakis,et al.  Bifurcation Analysis in Geomechanics , 1995 .

[13]  Richard B. Nelson,et al.  Nonassociated Flow and Stability of Granular Materials , 1987 .

[14]  Poul V. Lade,et al.  Instability and Plastic Flow of Soils. I: Experimental Observations , 1990 .

[15]  Wai-Fah Chen.  Limit Analysis and Soil Plasticity , 1975 .

[16]  Adel S. Saada,et al.  Constitutive equations for granular non-cohesive soils , 1989 .

[17]  S. Imposimato,et al.  An investigation on the uniqueness of the incremental response of elastoplastic models for virgin sand , 1998 .

[18]  Donald W. Taylor,et al.  Fundamentals of soil mechanics , 1948 .

[19]  F. Darve.  Liquefaction phenomenon of granular materials and constitutive stability , 1996 .

[20]  R. Nova,et al.  Theoretical investigation of the undrained stability of shallow submerged slopes , 1995 .

[21]  T. Doanh,et al.  Theoretical analysis of strain response envelopes using incrementally non-linear constitutive equations , 1998 .

[22]  Dimitrios Kolymbas,et al.  An outline of hypoplasticity , 1991, Archive of Applied Mechanics.

[23]  Roberto Nova,et al.  Stability problems related to static liquefaction of loose sand , 1994 .