Debris flow modeling: A review

A debris flow represents a mixture of sediment particles of various sizes and water flowing down a confined, channel-shaped region (e.g., gully, ravine or valley) down to its end, at which point it becomes unconfined and spreads out into a fan-shaped mass. This review begins with a survey of the literature on the physical-mathematical modeling of debris flows. Next, we discuss the basic aspects of their phenomenology, such as dilatancy, internal friction, fluidization, and particle segregation. The basic characterization of a debris flow as a mixture motivates the application of the continuum thermodynamical theory of mixtures to formulate a model for a debris flow as a viscous fluid-granular solid mixture. A major advantage of such a formulation, which goes beyond the most general models in the literature, e.g., Takahashi (1991), is that it can be used to expose and better understand the assumptions underlying existing models, as well as to derive new, more sophisticated models. Finally, we delve into the issue of how such models have been or can be implemented numerically, as well as general boundary conditions for debris flows.Dedicated to Professor Reint de Boer upon the occasion of his 60^th birthday     

A dynamic theory for magnetizable elastic solids with thermal and electrical conduction

A general dynamical theory of magnetizable, electrically and thermally conducting media is developed for soft ferromagnetic or paramagnetic materials in external electromagnetic fields. The general equations are linearized by assuming infinitesimal strains, linear constitutive equations and that all field variables may be divided into two parts: a "rigid body state" and a "perturbation state". The former is the same as the one in rigid body electrodynamics, and the latter which accounts for electromagnetic interaction with the deformable continuum is coupled with stress and strain through linearized field equations. The theory is developed for general anisotropy but specialized for materials with uniaxial, or higher, symmetry.     

Thermodynamics of polycrystalline materials treated by the theory of mixtures with continuous diversity

The physics of polycrystalline materials is described via microscopic processes such as grain boundary migration, grain growth, grain rotation, polygonization (the bending and breaking of crystallites) and evolution of dislocation density. The importance of taking these processes into account lies in their influence on the macroscopic mechanical behaviour of the material. Constitutive equations to describe such phenomena have been proposed in the literature. The main result of this paper is to give a general and thermodynamically consistent approach for such constitutive equations. The framework of the Theory of Mixtures with Continuous Diversity (TMCD) is used. The inclusion of both orientation and grain-size distributions is presented in this paper for the first time. Their introduction requires the formulation of a new and general constitutive theory that is, therefore, given. The method of Lagrange multipliers used in the context of the entropy principle (Liu, Arch. Rat. Mech. Anal. 46, 131–148 (1972)) provides the restrictions of the second law of thermodynamics on the constitutive equations. The success of this work is that all the main results present in the literature can be incorporated in this framework.     

Important aspects in the formulation of solid–fluid debris-flow models. Part I. Thermodynamic implications

This article points at some critical issues which are connected with the theoretical formulation of the thermodynamics of solid–fluid mixtures of frictional materials. It is our view that a complete thermodynamic exploitation of the second law of thermodynamics is necessary to obtain the proper parameterizations of the constitutive quantities in such theories. These issues are explained in detail in a recently published book by Schneider and Hutter (Solid–Fluid Mixtures of Frictional Materials in Geophysical and Geotechnical Context, 2009), which we wish to advertize with these notes. The model is a saturated mixture of an arbitrary number of solid and fluid constituents which may be compressible or density preserving, which exhibit visco-frictional (visco-hypoplastic) behavior, but are all subject to the same temperature. Mass exchange between the constituents may account for particle size separation and phase changes due to fragmentation and abrasion. Destabilization of a saturated soil mass from the pre- and the post-critical phases of a catastrophic motion from initiation to deposition is modeled by symmetric tensorial variables which are related to the rate independent parts of the constituent stress tensors.