Here we present the validation of the fluid dynamic solver presented
in part one of this work
Debris flows are a frequent natural hazard in mountain regions. They
consist of a mixture of water, clay, sand and coarser material
traveling as a partly fluidized mass through steep channels. The mix
of different materials leads to a complex rheological behavior that is
still not well understood. Field observations of debris-flow behavior
and rheology are challenging and still rare, and numerical modeling is
often the approach of choice when assessment of debris-flow behavior
is needed for planning, zoning, and hazard assessment
The object of this study is to illustrate the model's capability to accurately account for the wide range of flow behaviors without recalibration. The key elements of the model concern its sensitivity to water content, gravel- and clay-fraction and clay-mineralogy on the one hand, and the interaction between the three-phase rheology and the complex three-dimensional flow structure on the other. We present the validation and limitations of the model set-up based on simulation results for intermediate and large-scale experiments.
The model is based on an adaptation of the interMixingFoam solver of
the open source Finite Volume Code OpenFOAM
Three different experimental cases were chosen to illustrate how the model represents the sensitivity of the flow and deposition process to water- and clay content, channel curvature and bed roughness based on the calibration of a single free model parameter.
The first two sets of experiments were performed using
intermediate-scale flumes at the Swiss Federal Research Institute WSL,
Switzerland. The first case study includes flume experiments
simulating hillslope debris flows that differ in water content but are
otherwise similar. The flume was wide enough that the flow did not
touch the side-walls. Thus these experiments exclude side-wall effects
that may otherwise dominate the flow behavior of relatively shallow
flows
The second experimental case used for validation was designed to study
the sensitivity of debris flows to channel curvature
While the two sets of experiments described above were performed with
small amounts of sediment, over short times and at a laboratory scale,
we also tested our model against data from full-scale experiments
performed in the USGS experimental debris-flow flume at the
H. J. Andrews Experimental Forest, Oregon
The model setup and performance for all three cases are described in more detail in the following sections.
In our modeling approach, the rheology of the slurry phase depends on
its yield stress, which is known to be exponentially dependent on
water content (e.g.,
All selected experiments were simulated using the same value of
The model adapts to a new water content by calculating a new
Herschel–Bulkley yield stress. However, the free model parameter
Based on the calibrated value of
Enhanced super-elevation due to curvature is characteristic for
viscous debris flows
The experiments were performed by releasing 0.0067
Here, we consider the mixture with the largest clay content
(mixture A,
The measured and simulated surface deflections can be compared to
assess how well the modeled rheology accounts for the increased
super-elevation. Nevertheless one should be aware that in this
experimental setup, a granular front developed, which is in
contradiction to the homogeneous phase distribution in the current
implementation (Fig.
Since it is difficult to upscale from laboratory-scale tests to true
debris flow events, large-scale debris flow experiments are essential
for model validation. The USGS debris-flow flume consists of
a 75
We selected two experimental setups. One focused on the rheology of
the muddy suspension, so we chose an experiment with high content of
loam and a smooth channel bed surface, to reduce the influence of
granular collisions. A material mixture of 5.25 % clay,
12.25 % silt, with 32 % sand and 50.5 % gravel by dry
weight was applied. The water content and density of this test were
determined as 20.6 % of mass and 1920
An important element of our simulation is that we compare the model with the rough channel experiments based on the calibration of the smooth bed experiment that contained 2.5 times more loam and 2.5 % more water in the material mixture. This way we aim to illustrate that the calibrated model can predict the flow process of a different mixture in a channel with different bed roughness. The detailed analysis of the model performance for the rough and smooth channel experiments highlights this in the following.
In test 970722 (numbering as YYMMDD), the channel bed consisted of
smooth concrete. Only video documentation is available
For the rough channel experiments, round bumps of 1.6
The calibrated value of
Flow front position, shape and surface wave patterns (derived from
video recording) were compared to the corresponding simulations
(Figs.
This study represents an attempt to develop a widely applicable modeling framework for debris-flow simulations, based on rather simple constitutive equations describing the two-phase flow rheology and combined with traditional 3-D CFD modeling. Nevertheless the results are surprising, as it appears to be possible to produce accurate front velocities, flow depths and run-out distances after calibration of a single model parameter. Furthermore, the results show that the model can accurately simulate debris flow behaviors that differ by more than one third in travel time or run-out distance without recalibration, just by taking into account the local channel topography and differences in material properties such as clay, sand and gravel composition, as well as water content.
The simulations of the small-scale experiments that focus on water content sensitivity could reproduce the pronounced dependency of the run-out length on water content. The model could to predict flow depth developments over time. Some short-time peak deviations between observations and simulations reached values close to the maximum grain size, possibly resulting from single grain effects. A slight overestimation of the influence of the higher water content led to a run-out over-prediction by 7 % in the model compared to the observation. The deposit of the calibration test case was accurately reproduced by the model, but the run-out of the reduced water content experiment was over-predicted by 21 %. This discrepancy might be reduced with better grid resolutions, because the simulated front for the reduced water content experiment came to a halt at the correct position but was overrun by a second pulse of material, leading to an unrealistic air inclusion within the simulated front. The absence of discrete particles in the model allows the second pulse to pass over the front without any roughness elements. The same limitation by grid resolution and by the absence of particles becomes apparent when looking at the simulated run-out tip of the experiment with increased water content. Due to the large stretching of the material, the flow front depth was represented by less than five grid cells, resulting in an inaccurate velocity profile and shear gradient, and thus leading to an imprecise viscosity. Furthermore, the interface thickness of the Volume Of Fluid approach at such low grid resolutions in relation to flow depth leads to significant air phase concentrations over the whole flow depth of the front. This results in a reduced density and viscosity at the flow front.
The results of the curved channel experiments are encouraging. If the super-elevation of the surface due to channel curvature can be represented with such accuracy for the true flow front volume, other mixtures and the lower channel bend, it would represent strong evidence for an adequately modeled interplay between gravel and slurry rheology. The focus on a mixture of high clay content was due to the fact that our simplified solver cannot account for phase separations due to grain-size sorting. The upper curve was chosen to save computational time. However, the non-Newtonian behavior resulting in increased super-elevation was more pronounced for mixtures with less clay content and slower front velocities at the lower curve. Although we did not consider the experimental flows in the lower curve, we can expect an enhanced influence of the pressure in the model at the lower curve, because the slower flow has a reduced shear gradient compared to the upper curve flows. From the results obtained at the upper curve, we may at least conclude that the model can reproduce enhanced super-elevations and seems to be suitable to predict debris-flow breakouts in curved channels for hazard assessment. The main limitation is that the maximum cross-sectional area of the simulated flow reaches only about 40 % of the area determined from the experiments. We severely underestimate the debris flow volume at the curve due to the simplified release geometry and due to material losses to the walls in the model by the no-slip boundary condition. Therefore, an improved mesh including the reservoir and the box-to-channel reach is necessary before addressing the flow in the lower curve, which is beyond the scope of this paper.
The large-scale experiments at the USGS flume were chosen as examples of flows closest to prototype conditions of the real world, with relatively small uncertainties concerning material composition, flow front velocity or run-out patterns. The experimental flow behavior was well captured by the model. In particular, the model successfully adapted without recalibration to a material mixture containing 2.5 times less loam, combined with a severe change of channel roughness.
For the smooth channel bed, a good representation of the travel time
and front shape on arrival could be achieved. The spreading into the
run-out plane was examined in detail. In both the experiment and the
simulation, the front arrived at the experimental maximum deposit
length at the same time with accordant positions and front shapes at
intermediate time steps. This indicates that the model captures the
deceleration process with high precision. However, the modeled
material front did not come to a halt, but instead continued, such
that the maximal deposit length was over-predicted by about one
third. The reason for this deviation is probably the over-predicted
material volume following the front, which arises from the modeled
flow process as a single surge event. Because the material in this
smooth channel test flowed in two separate surges, less material was
present in the physical experiment to catch up with the front which
led to reduced inertia and deposit length compared to the single surge
model. According to video recordings of the released material in the
reservoir, we infer that the second surge originated from the
reservoir in analogy to the second surge in the rough channel
experiments. Besides run-out distance, the model captures the
different character of the sides of the material front, with one side
smooth and the other side irregular. This is due to the sensitivity of
the debris flow to the slight lateral tilt of the flume of up to
2 % and the detailed run-out pad topography (
A key result of the large-scale tests is the capability of the model to predict the much slower flow-front velocity of the rough channel experiment based on a calibration for a smooth channel and a mixture of 2.5 times higher content of loam. Three experiments of identical setup using the so-called SGM mixture together with a rough channel bed were selected to compare flow front velocities with the simulation. Ensemble-averaged time evolutions of flow depths and basal pressures of twelve such experiments were compared to the model output. The simulated flow depths lie in general within the range of standard deviations of the measurements. However, considering the basal pressures, part of the deviations between experiment and simulation may arise from the pyramid representation of the half-spherical bumps in the rough channel bed, leading in the model results to overestimated pressure peaks and thereby to an exaggerated viscosity by the pressure-dependent gravel rheology. A reduced friction angle therefore improved the modeled flow front velocity, although the effect is not visible in the basal pressure fluctuation. Because grain-size sorting effects and the release mechanism are not accounted for, a single surge flow forms in the simulation, in contrast to the real tests with two surges as in most of the experiments considered. Therefore, when the modeled debris flow reaches the end of the channel, the front composition and volume is not an adequate representation of the experiment. As a consequence we did not model the run-out patterns of the rough channel experiments, in contrast to the smooth channel experiment where less demixing occurred.
On the one hand, it might be possible to obtain better representations
of all SGM experiments with the current model by varying
Among other models applied to the SGM experiments,
Our approach allows the model parameters to be linked to material
properties and local topography. It suggests that one should be able
to develop a model that can be applied to a wide range of debris-flow
simulations, wherever the necessary data on material and site
conditions are available. The purpose was not to gain a perfect
representation of the experiment, but to see how the chosen rheology
represents the sensitivity to water content, channel roughness and
curvature, and fraction of fine material. The new model overcomes
a weak point of debris flow modeling: debris flow models commonly
depend on many free parameters or are simplified by either modeling
the flow from a granular perspective neglecting the interstitial
fluid, or as a viscous continuum without accounting for the granular
component of the flow process. Two-phase approaches, on the other
hand, come along with high numerical costs. In case of two-phase
coupling by drag between grain and fluid, the uncertainty in the drag
between granular and fluid phases brings along parameters that are
difficult to quantify in case of the non-Newtonian suspension and
non-spherical gravel grains. As a consequence, no previous modeling
approach succeeded in predicting debris-flow behavior across such
different experimental settings as those examined here, with
modifications to only a single parameter. Beyond that, our model
succeeded in simulating different material mixtures without
recalibration. However, numerical costs are still high for accurate
results. The application is suitable for situations where the detailed
flow structure is required. While the simulation of the smooth channel
debris flow experiment at the USGS flume required seven hours per
second of flow using 32 processors on the WSL Linux cluster HERA
(consisting of Six Core AMD Opteron 2439 at 2.8
We demonstrated the wide range of applicability of our new numerical
debris-flow model. The model concept follows the strategy of shifting
from requiring user expertise in debris flow model calibration towards
requiring information about the modeled site. The presented
simulations of a wide range of different experiments lead to the
following conclusions:
The material mixture can be characterized based on clay mineral composition, content of clay, silt, sand and gravel, angle of repose of the gravel, and water content. A single free parameter allows calibration to adjust the model to the grid resolution. The model can account for changes in the material mixture without recalibration. The model can account for the sensitivity of the rheology to channel geometry, including the enhanced surface super-elevation of debris flows in curved channels. The sensitivity to surface roughness is captured by the model and it can be varied without recalibration.
The need to calibrate only a single parameter greatly simplifies the model calibration process. This can save significant time while still providing a model of high detail and reliability. Although such a minimally parameterized model may fit the real-world data less well than a highly parameterized model (perhaps because the latter is over-fitted), the time saved in calibration can be used to explore a wider range of material composition and site properties. Because such changes in model setup are translated into consequences for the flow physics by the model, the ensemble of such simulations may mirror how the modeled site would respond to similar changes. Recalibrated models cannot deliver such information. Furthermore, in our model there is less room for the user to make arbitrary parameter settings than in models with several calibration parameters. Thus it may be possible to quantify the model's reliability in a robust and general way, because different users probably apply comparable parameter settings. However, one missing step is the inclusion of phase separation due to grain-size sorting effects, which would not only enable simulation of the granular front but also could enhance the model's capability to perform channel bed erosion by mobilizing gravel deposits. This extension may be included in future versions of the model.
The source-code can be downloaded from the supplement application.zip, please follow the instructions given in the README15.pdf file for installation.
Iso-view sketch of the hill-slope debris-flow flume. Material (b) is released from the reservoir at the top by a sudden vertical removal of a gate (a) and flows down a steep slope (c) followed by a gently inclined run-out plane (d).
Laser measurement and corresponding simulated values of the flow head over time, one meter down-slope of the gate for the experiments with the water contents of 27 % (top) 28.5 % (center) and 30 % (bottom). The laser data were box-averaged over 10 ms.
Simulated deposits for the mixture with 27.0 % (top), 28.5 % (center) and 30 % water content (bottom) without parameter adjustments applying
View from top on the modeled curved channel with release material at the reservoir (b) passing a flap gate (a) into the plane transition box (c). At the restriction (d) the channel profile changes from a rectangle to a half-pipe.
Left: view upstream on modeled channel section 40
Observed and simulated flow front at the end of the channel for a smooth channel bed and high content of loam. The free model parameter
Time-tracking of the run-out process by top camera (upper rows) and iso-perspective camera views (lower rows). The corresponding simulated material is colored by flow velocity and the shape of the simulated run-out is copied into the camera pictures as a dashed line for better comparison.
Perspective selection of the rough channel bed at the experimental site (above) and in the simulation (below). Transverse to the flow, a higher number of bumps was introduced into the model, which allowed to combine simple meshing with a high resolution for transversal flows.
Top view of the modeled flow front, with the transition between air and debris flow material, marked here by the layer with material concentration equal to one third, shown as a free surface. The vertical bar (red) within the white rectangle marks the flow front position presumed as the beginning of the continuous surface, with the purpose to neglect single drops that may spread ahead.
The flow front position over time of the rough-channel SGM mixture simulations, compared to three selected experiments of identical setup using the so-called SGM mixture, a standard mixture of sand, gravel and loam
Snapshots of the flow front of test 000928 (left) 5.6
Comparison of the material surface in test 010913 (left of simulation) and test 030625 (right of simulation) at an intermediate position 7
Comparison of simulated and measured flow heights 32
Comparison of simulated and measured basal normal stresses derived as the average temporal value of three force plates placed in the channel center line at 31.7, 32.3 and 32.9