The threshold conditions between erosion and sedimentation of a single particle describe incipient motion. The stability of granular material in air is first examined to define the angle of repose in Section 7.1. The following sections cover submerged particles. In Section 7.2, the simplified particle equilibrium conditions on near-horizontal surfaces are discussed for uniform grain sizes, bed sediment mixtures, and cohesive material. The equilibrium of particles under tridimensional moments of forces is detailed in Section 7.3. A simplified force balance is presented in Section 7.4. Two examples of particle stability analysis and stable channel design conclude this chapter.

Angle of repose

The stability of a single particle on a plane horizontal surface is first considered in Figure 7.1a for simple two-dimensional particle shapes. The threshold condition is obtained when the particle center of mass G is vertically above the point of contact C. The critical angle at which motion occurs is called the angle of repose φ and equals 180° divided by the number of sides of the polygons. For instance, the angle of repose φ of an equilateral triangle is φ = 180°/3 = 60°, a square is φ = 180°/4 = 45°, and the angle of repose of a sphere is φ = 180°/∞ = 0°. It is concluded that the angle of repose of particles on a flat surface increases with angularity.

As shown in Figure 7.2, a given particle does not necessarily have a unique value of angle of repose.