Félix Darve

Three-Dimensional Multiscale Bifurcation Analysis of Granular Media

This paper deals with Hills bifurcation criterion, which is very well suited to describe various failure modes in granular media. The first part of this paper is dedicated to the analytical and numerical investigation of this criterion by considering phenomenological constitutive relations: the incrementally piece-wise linear and nonlinear relations proposed by Darve. The 3D bifurcation domain and 3D cones of unstable directions are given for these two relations. A similar analysis is performed with a micromechanical model in the second part of the article. Finally, a qualitative comparison of the results obtained with these two different approaches leads us to some key conclusions about this material instability criterion, which is studied for the first time for general 3D conditions, by considering these nonconventional constitutive relations.

Micromechanical Formulation of Stress Dilatancy as a Flow Rule in Plasticity of Granular Materials

The paper presents micromechanical formulations of stress dilatancy and their connection to a flow rule in classical elastoplasticity. Dilatancy is inarguably the manifestation of an internal kinematic constraint involving both particle shape and connectivity (texture or fabric) with operative interparticle friction against applied stresses. However, this notion of microstructural dependence is nonexistent in most stress-dilatancy formulations in the literature. We present two different micromechanical approaches that arrive at stress-dilatancy expressions with embedded micromechanical information in the form of a second-order fabric tensor. In connection to stress dilatancy, the underlying nature of the flow rule is next discussed with respect to the dependence of the plastic strain increment vector on the direction of loading (stress increment). It is demonstrated analytically that the flow rule is singular in three-dimensional stress and strain conditions. Finally, the dependencies of dilatancy on fabric are illustrated through various numerical simulations using the micromechanically enriched stress-dilatancy models and a discrete element method.

Granular Materials: Mesoscale Structures and Modeling

Abstract: A straightforward and reliable modeling of granular materials currently remains an open issue. The difficulty lies in the very discrete nature of these materials composed of grains in contact. In this chapter, we explore a new upscaling approach including a mesoscale.

Geometric Degree of Non Conservativeness

Symplectic structure is powerful especially when it is appliedxa0to Hamiltonian systems.We show here how this symplectic structure mayxa0de ne and evaluate an integer index that measures the defect for the system to be Hamiltonian. This defect is called the Geometric Degree of Nonxa0Conservativeness of the system. Darboux theorem on di erential formsxa0is the key result. Linear and non linear frameworks are investigated.

Hierarchy of Failure Modes

The failure of geomaterials as seen presents rich and distinctive deformational features which arise principally from their material responses being dependent on pressure, density and fabric. Following continuous approaches as in the theory of plasticity, these dependencies are described by a non-associated plastic flow rule which provides mathematical sources for material instability, thereby admitting a multiplicity of material responses for the same initial loading conditions. The non-symmetry of the tangent constitutive matrix due to non-associated plasticity initiates different failure indicators during material response history according to a certain hierarchy, leading to various failure modes with or without localized deformations.

Characteristics of Failure in Geomaterials

The basic concepts of material failure are herein presented in this opening chapter as a prelude to a systematic study of failure in engineering materials with a focus on geomaterials. Hence, a cursory but clear description of failure as observed in lab experiments is first given, followed by an in-depth mathematical representation of underlying physical phenomena, which eventually gives way to modern/contemporary theories and concepts relating to the failure analysis of geomaterials.

Failure in Continuum Geomechanics

In this chapter, the concept of failure is formalized starting from an energy approach where a deforming body under external loads is the point of departure. We are prompted with the intriguing question of what is the meaning of the second-order work. It will be shown that the second-order work naturally emerges from an energy balance written from the kinetic energy viewpoint - the well-known kinetic energy theorem. The second-order work is an important concept in solid mechanics that has been the object of numerous publications for the last several decades. However, it has not been fully applied in geomechanics where the notion of failure has not been thoroughly investigated from a mechanical viewpoint.

Soil Erosion as an Instability Problem

Geomaterials are multiphasic systems that are comprised of solids, fluids and gases, including interactions between them. Phenomena such as soil erosion may occur in major hydraulic structures, and their analyses go beyond traditional approaches which are mostly empirical in nature. Internal erosion occurs when particles are dislodged from the solid skeleton due to seepage forces and thereafter transported into the available pore space. Hence, any analysis has to be carried out at the pore and solid scales where notions of instabilities introduced in earlier chapters can be readily applied. Two fundamental types of internal erosion can be distinguished: piping and suffusion. This chapter is concerned only with the latter which corresponds to the transport of fine particles through the pores of the coarse matrix.

Second-Order Work in Boundary Value Problems

As a prelude to analyzing instability issues in boundary value problems, the local second-order work criterion must be generalized into the global setting to address a structural problem. This chapter proposes a robust numerical framework that enables us to assess the stability of a geostructure through the generalized second-order work criterion that replaces the role of a safety factor in traditional engineering analyses based on plastic limit equilibrium methods.

7 – Engineering Applications

: nAll theoretical developments, including illustrative examples pertaining to the lab scale seen in previous chapters, find their true value when they are applied to real engineering boundary value problems. This chapter offers a comprehensive modeling of well-known engineering problems such as slope stability, retaining walls, internal erosion in dykes and multiphysics coupling analyses of heavy oil reservoirs.