Debris Flows and Landslides - River Dynamics and Integrated River Management - page 227

down and accumulate on the bed. Thus, a layer of small particles is seen between the stagnant bed and
the moving particles, as shown in Fig. 4.41. On the other hand, the large particles receive energy from
the small particles and move at a stable velocity and finally move to the head. This fact indicates that the
theory of a dilatant model for the large stones in the head is not correct. In the dilatant theory, large
particles move faster because the dispersive force is proportional to D 2 , large particles are subjected to
large lifting dispersive force and hence rise to the surface of the flow where the velocity is high.
Therefore, large particles move faster and finally concentrate in the debris flow head. This theory is not
correct. Large particles move “faster” and catch up with the head because they move continuously but
small particles stop and fall down after moving for a distance and colliding with large particles.

Fig. 4.41 A layer of small particles between the bed and the moving particles

4.3.2.7 Resistance of Two-phase Debris Flows
The resistance of debris flow is usually represented by Manning's roughness coefficient, n . Figure 4.42
shows Manning's n values for debris flows calculated with the following formula:

1

2/3. 1/2

n h s (4.8)

d

u

d

in which u d is the average velocity, h d is the height of the head of the debris flow. Figure 4.42 shows
Manning's roughness n as a function of the median diameter of the bed gravel. For the same bed material,
the resistance of for debris flow is about 10 times higher than that of normal sediment-laden flow. In
normal sediment-laden flow particles move with the liquid, rolling or moving by saltation over the bed.
In debris flow, particles collide with each other and with the bed so that a supporting force - the so-called
dispersive force is created. The collisions consume a lot of energy and create a great resistance to flow.

Fig. 4.42 Manning's roughness coefficient n as a function of the median diameter of the bed gravel