In this chapter, we study erosion and sediment transport from the point of view of the physics of granular media. Situations involving erosion, transport and deposition of particles subjected to fluid flow cover a wide range of applications, from the transport of grains in a pipe to the evolution of landscape on geological scales. We focus in this chapter on the study of erosion and transport of natural sediments under the influence of a water flow (streaming, fluvial erosion, tides, waves and glaciers) or of the wind (dunes, sand invasion, desertification). Besides, we wish to describe sediment transport in the perspective of understanding the geological phenomena that will be discussed in the next chapter. The goal is to propose a description of these phenomena, to model them through basic equations and to explain the dynamical mechanisms at the scale of grains. To do this, we will use the concepts introduced throughout this book.

We begin by briefly outlining the characteristics of the different modes of transport and the most important concepts which allow one to characterize erosion and sediment transport (Section 8.1). We then discuss the nature of the threshold above which a flow may entrain grains into motion (Section 8.2), before presenting the formalism used to describe erosion and transport starting from conservation laws (Section 8.3). Once we have introduced the concepts of saturated transport and saturation transient, we apply them to the different modes of transport: bed load (Section 8.4), aeolian transport (saltation and reptation) (Section 8.5) and turbulent suspension (Section 8.6).

In the previous chapter, we discussed the statics and the elasticity of granular media, when deformations are small and reversible. In this chapter, we address the plasticity of granular media, i.e. irreversible deformations occurring beyond the elastic regime. The two issues associated with plasticity are the following: what is the maximum stress level a granular medium can sustain before being irreversibly deformed and how does the deformation take place beyond the threshold? These questions are covered by soil mechanics, which aims to predict and understand soil stability in nature or during construction in civil engineering. The approaches are mainly based on macroscopic and phenomenological models derived from continuum mechanics. More recently, physicists have been interested in the plasticity of disordered materials, focusing on the microscopic features and trying to understand how rearrangements occur at the grain scale. The link with the continuum models proposed in soil mechanics is still a challenge. In this chapter we will focus on simple macroscopic continuum models, and will only briefly discuss the microscopic properties in a box. The first section (Section 4.1) is dedicated to the phenomenology of plasticity. Several configurations that are used for studying the deformation of a granular medium are described. Section 4.2 is dedicated to the plane shear configuration, for which all the properties of the plasticity of granular media can be introduced using scalar quantities. Tensors, which are necessary to model plasticity, are introduced in Section 4.3. The Mohr–Coulomb model is described and Mohr’s circle used to represent the stress tensor is introduced. In Sections 4.4 and 4.5, we discuss briefly more complex models and unresolved questions. Finally, the plasticity of cohesive materials is presented in Section 4.6.

Definition and examples of granular media

From sand to cereals, from rock avalanches to interplanetary aggregates like Saturn's rings and the asteroid belt (Fig. 1.1), granular media form an extremely vast family, composed of grains with very different shapes and materials, which can span several orders of magnitude in size. However, beyond this great diversity, all these particulate media share fundamental features. They are disordered at the grain level but behave like a solid or a fluid at the macroscopic level, exhibiting phenomena such as arching, avalanches and segregation.

In this book, we shall broadly define a granular medium as a collection of rigid1 macroscopic particles, whose particle size is typically larger than 100 μm (Brown & Richards, 1970; Nedderman, 1992; Guyon & Troadec, 1994; Duran, 1997; Rao & Nott, 2008). As we shall see in Chapter 2, this limitation in size corresponds to a limitation in the type of interaction between the particles (Fig. 1.2). In this book, we will focus on non-Brownian particles that interact mainly by friction and collision. For smaller particles, of diameter between 1 μm and 100 μm, other interactions such as van der Waals forces, humidity and air drag start to play an important role as well. This is the domain of powders. Finally, for even smaller particles, those of diameter below 1 μm, thermal agitation is no longer negligible. The world of colloids then begins (Russel et al., 1989).