By simulating the movement processes of different viscous debris flows, a series of experiments has been completed where free surface heights, fluid velocities, pressures, and shear deformations associated with the movement of the fluid were measured. The numerical simulation was carried out to generate the experimental conditions previously described (
Figure 4). The numerical simulation replicated
N = 113,054 particles, particle spacing
dp = 0.0025 m, solid particle density
ρs = 2200 kg/m
3, thickness of solid phase
hs = 0.1 m and thickness of liquid phase
hl = 0.1 m for configuration a and c in
Figure 2. Similar to the tests conducted on the experimental facility, three different viscosity coefficients for the liquid phases (as shown in
Table 1) were selected in the numerical simulation. The inflow conditions were the same as those applied experimentally, and the water level as driving force of the debris flow was kept at 0.2 m for each entire simulation.
Figure 5 represents the free surface values recorded at different times for each of the tests conducted in
Table 1, after the debris flow initiation generated by the release of water upstream. The
x-axis represents the length
L of the debris flow, and the
y-axis represents the height
H of the debris flow. After 0.7 s, the distance reached by the debris flow (considering all the configurations) is within the range 2.48–2.66 m, and the maximum velocity range is 4.65–5.12 m/s. Authors noticed that when the debris flow has similar viscous properties but for the vertical distribution of different particles, the differences in velocities are not so significant and can considered almost negligible in most of the cases. However, the maximum velocity recorded for configuration b (Shown in
Figure 2b correspond to tests 2, 5 and 8 in
Figure 5) is similar to the one recorded for configuration a (Shown in
Figure 2a and corresponding to tests 1, 4, and 7 in
Figure 5), while configuration c (Shown in
Figure 2c and corresponding to tests 3, 6, and 9 in
Figure 5) was characterized by higher values of velocities and elevations measured. By comparing the shapes of head under different vertical distributions, it was found that for the tests conducted in
Table 1, free surface values measured for configuration b fluctuate more than in configuration a and c, demonstrating that this scenario is typical of intermittent debris flows.
Characterization of Intermittent Debris Flow
In order to study the causes of this phenomenon, the characteristics of the fluid movement processes associated to configuration b were analyzed.
Figure 6 shows the evolution of the solid-liquid phase at different locations simulated numerically.
Figure 6a shows that in the horizontal region, most of the particles still retain under the laminar form. When moving into the upstream part of the sloped section, the fluid height decreases and the liquid phase group is stretched, as shown in
Figure 6b. Then, due to the slope, velocity increases while the fluid height decreases, and different layers of liquid and solid particles will appear almost as parallel mixing within the entire width of the debris flow, as shown in
Figure 6c. At this stage, the altering layers interact changing continuously positions demonstrating that mixing processes are taking place and when the mixing is finally completed, the fluctuation amplitude reduce becoming more stable, while the influenced range of the fluctuations can spread over a longer length, as shown in
Figure 6d.
Figure 6e shows the effect of the liquid phase on the height of the debris flow. It is clear that when liquid particles accumulate due to the mixing phenomena (highlighted as circles in
Figure 6e), there is a correspondent decrease of the height of the debris flow (pointed out using arrows in
Figure 6e). This inverse relationship is very interesting especially because it demonstrates how the gathering and accumulation of liquid particles tends to appear towards the bottom side of the debris flow layer.
On this basis, the relationship between the moisture content
ϕ (the amount of liquid particles divided by the amount of solid particles,
), the kinetic energy of particles
Ek and the height of the free surface
(related to the potential energy of particles
Ep) were calculated for the tests conducted for configuration b. As shown in
Figure 7a, the height of the free surface
decreases as the debris flow develops. There is a noticeable correlation between the fluctuation of the free surface associated with the fluctuation of the moisture content. In the regions of
L = 1.00–1.38 m and
L = 1.82−2.04 m, the height of free surface decreases linearly, and in these two regions, the water content remains in the range 0.2–0.65. The points that obviously exceed this threshold are
L = 0.90,
L = 1.52,
L = 1.6,
L = 1.74, and
L = 1.80−1.84, and the height of free surface is different from that of linear decline in these areas or vicinity. When the moisture content is within the range 0.20–0.65, the free surface of the debris flow is characterized by a linear change, but when the moisture content exceeds this range, it generates an impact on the free surface.
From
Figure 7b, it can be seen that there is a more obvious negative correlation between the particles kinetic energy
Ek and the moisture content
ϕ. To almost every peak of the kinetic energy
Ek (highlighted as green circles in
Figure 7b) calculated corresponds a peak of the moisture content
ϕ (highlighted as blue circles in
Figure 7b), which indicates that kinetic energy
Ek and moisture content
ϕ interact directly. However, this effect can only be assigned to small-scale portions of the particle kinetic energy fluctuations. Looking at
Figure 7b, at the location of
L = 1.74 m, the moisture content value corresponds to
ϕ = 0.7619 and it is the maximum value measured in this region, and the corresponding kinetic energy
Ek records its minimum value. But because of the large kinetic energy of the particles recorded in this region, the corresponding kinetic energy
Ek = 5.4848 J is still higher than that recorded at the position of
L = 1.64 m in the adjacent one
Ek = 0.30263 J.
Figure 8 shows the effect of moisture content
ϕ on the kinetic energy
Ek and the height of the free surface
H on a large scale, for configurations a and c. For both configurations, where the solid phase is located at the top and the bottom, the free surface is greatly affected by the magnitude of the moisture content
ϕ, while the kinetic energy
Ek is greatly affected by the derivative of moisture content along the length of the slope
. However, the fluctuation of the moisture content ∆
ϕ along the length
L, especially for configuration a where the solid phase is displayed at the top of the debris flow, is relatively small. So the kinetic energy
Ek and potential energy
Ep curves show relatively large-scale area fluctuations and linear characteristics in comparison to the mixed distribution fluid conditions typical of configuration b.
Finally, the energy conversion curves of fluids with different viscous coefficients were inspected and confronted, as shown in
Figure 9. It was found that the gravitational potential energy (
Ep =
mgH) and the total energy (
E0 =
Ek +
Ep) of fluids decreases at a similar rate. The difference between three fluids is mainly reflected on kinetic energies. When comparing the set of fluids with the smallest density (
ρ = 1400 kg/m
3,
= 0.00004,
= 0.0048, and
= 0.0197), results shows that velocity values increase from
t = 0.0 s up to
t = 0.6 s, reaching almost the highest values, and then the kinetic energy of the three fluids tends to be equal. As the time progresses, the same order appears again in the kinetic energy magnitude arrangement, which is
Ek,ρ = 1400 kg/m
3 >
Ek,ρ = 1500 kg/m
3 >
Ek,ρ = 1600 kg/m
3. This phenomenon is also due to the stronger fluctuation of the less dense fluids and these effects caused by different viscous fluids on debris flow array and collision, and friction forces on debris flow movement, will require further investigation in the future.