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Seismic Measurements of Roll Waves in Debris Flows
Fabian Walter1*, Zhen Zhang2, Jordan Aaron1, Brian McArdell1 and Christoph Graf1
1

Swiss Federal Institute for Forest, Snow and Landscape Research WSL, 8903 Birmensdorf, Switzerland
Institute of Mountain Hazards and Environment, Chinese Academy of Sciences, Chendu, China

2Abstract. Accurate debris-flow modelling depends on the ability to simulate surging and pulsing
behaviour. However, our understanding of these phenomena is starved of observational constraints. Here
we propose the use of seismic measurements, which resolve the arrival of coarse-grained roll wave fronts indebris flows at Illgraben, Switzerland. Roll waves likely play a key role in flow pulses but are typically only
observed with point measurements like depth gauges. We compare in-torrent force plate measurements withnear-torrent seismic records and discuss how these data can test existing roll wave theories.

1 Debris flows and roll wave formation
Details of debris-flow dynamics are difficult toconstrain and model. The underlying rheology is still
debated and even the flow behaviour of selected events
is far from understood [1]. Debris flows tend to develop
surges with individual flow pulses moving at different
speeds and potentially overtaking each other toinfluence the overall mass transport and velocity [2, 3].
Channel geometry and roughness, sorting
phenomena and friction likely play a crucial role indebris flow surging behaviour [4]. A related mechanismis the accumulation of a boulder-rich debris-flow front,
which forms as a result of particle segregation andprovides flow resistance for the trailing material leading
to a bulging of the longitudinal surface profile [2].
Non-steady and surging debris-flow dynamics may
also result from instabilities, which are characteristic forshallow, open-channel flows [5]. Perturbations ofspecific wavelengths theoretically grow in an unstablemanner to move downstream at speeds different fromthe particle velocities [4, 6]. As such “roll waves”
overtake each other, they may affect or even control
debris-flow surges. Roll waves are observed as peaks inflow depth within the debris-flow tail. However, point
measurements cannot constrain roll wave dispersion andthe conditions for roll wave formation. Thus, it remains
unclear to what extent roll waves influence debris-flow
dynamics and surging behavior.
Here we present roll wave measurements at
Illgraben, Switzerland, one of Europe’s most active
debris-flow channels. In addition to conventional flow
depth measurements, we present records of impact
forces between debris-flow particles and the underlying
bed. We observe these impacts with geophones and aforce plate and with a near-torrent seismometer. We

discuss the benefit of these impact measurements for ourunderstanding of roll waves within debris flows andexplore future research directions.

2 Debris flows at Illgraben, Switzerland
2.1 Site
Illgraben’s catchment in Southwestern Switzerland
reaches from its highest point at Mount Illhorn (2717 m)
down to 600 m at the estuary with the Rhône River (Fig.
1). Frequent slope failures in the upper catchment
deposit in the channel and re-mobilize as debris flows
during heavy summer precipitation 3-5 times a year [7].

Fig. 1: Illgraben catchment with locations of seismometers(blue triangles) and force plate (yellow bar).

2.2 Measurements
A seasonal seismometer network has been
operational since 2017 monitoring debris flow and slope
failure activity [8]. This supplements in-torrent* Corresponding author: fabian.walter@wsl.ch© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 03031 (2023)
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instrumentation in the lower catchment of Illgraben,consisting of flow depth gauges, Swiss geophone plates
and a force plate (Figure 1) measuring shear and normal
forces between debris flows and the channel bed [9].

roll wave arrival and gently drops until the arrival of thenext one.

Fig. 2: Seismic and flow-depth measurements of roll waves at
Illgraben. Modified from [8].

3 Discussion

2.3 Debris flow seismology

The records in Figure 2 show clear evidence for rollwaves. Higher impact forces at the roll wave front canbe explained with theory predicting transientdensification of coarse-grained material [6]. However,part of the impact force peak ahead of the flow depth
peak likely results from the rapidly changing weight on
the force plate: the quasi-static increase in normal forcechanges rapidly enough to influence the maximum-tominimum force differences. This adds to any increases
in impact forces caused by concentration of coarse
particles.
Seismometer chains along a torrent could be used to
track roll waves within debris flows. Benchmarked withpoint measurements of flow depth as in Figure 2,
seismic measurements could thus provide observationsof roll wave dynamics, which thus far to our knowledge
only exist in the laboratory. This would constrain
propagation velocities of roll waves, independent ofspeeds of their hosting debris flows. Similarly,
distributed seismic sensors would elucidate under which
conditions roll waves are formed and destroyed
allowing to test theoretical dependencies on Froudenumber and channel depth [12, 13]. Importantly, thetracking of roll waves would show if the theoretical limit
for merging and amplification behaviour is reachedwithin typical runout distances of a natural debris flow
[14].
There exist specific technical challenges, which may
limit the potential of seismometer arrays distributed
along a torrent channel. First, seismic point
measurements are sensitive to a range of locations alonga channel, which must be accounted for when allocating
impact force generation to channel sections [15]. The
non-local generation of impact force signals is evident
in Figure 2 showing that in-torrent force platemeasurements resolve the arrival of the roll wave frontbetter than near-torrent seismometers. In the latter case,the impact force increase is smeared out to produce a
regular seemingly sinusoidal fluctuation. The magnitudeof this effect depends on channel-sensor distances,
ground properties and grain sizes within the roll waves,and it may or may not mask the seismic signature of rollwaves at certain channel portions. As an alternative, tilt

High-frequency (> 1 Hz) seismic signals of granularmaterials like debris flows are typically modelled assuperimposed particle impacts onto the channel bed[10]. Assuming instantaneous momentum exchange
during the impact, the frequency signature ischaracterized by the seismic path between impact
location and recording seismometer [11]. This,
however, is difficult to constrain as a result of highly
heterogeneous subsurface structure near debris-flow
channels. In contrast, the force plate measures moreclosely the impact force histories, although some
response of the structural characteristics of the force
plate likely affects the signals, as well.
At Illgraben, station ILL11 (sensor model: Trillium
Compact 120 s) locates within a few meters of thetorrent in the Rhône valley (Fig. 1), some 450 m
upstream of the force plate. The close torrent proximity
minimizes the role of the path effect. Comparisons
between seismic measurements and video footage showthat seismic amplitudes are dominated by the effect ofparticle sizes and flow depth [8]. Consequently, theboulder-rich debris-flow front is seismically the“loudest” flow portion.
Fig. 2 shows a comparison between force plate dataand nearby flow depth measurements as well as seismic
data from ILL11. The force plate time series are thelower quantile (25%) of the maximum-to-median force
differences in non-overlapping bins of 1 s duration. The
seismic data are basal fluctuating forces for each time
window of 10 s calculated using a damped least squares
inversion and the power spectral density (PSD) ofseismic signals between 1 and 30 Hz in discrete time
windows [8]. Throughout the debris flow, the impact
forces measured with seismometer and force plate
correlate with flow depth. Towards the beginning of theflow, the particle size effect amplifies seismic and force
plate measurements compared to flow depth. Note that
whereas flow depth and force plate measurements werenearly co-located, synchronization with the seismometertime series recorded 450 m downstream is subject tolarge uncertainties. In the flow tail, each time series
exhibits regular roll waves. Flow depth steepens at the2E3S Web of Conferences 415, 03031 (2023)
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15. K. Allstadt et al.. J. Geophys. Res.: Earth Surface.

measurements may be able to resolve the added weightof roll waves, similar to what has been observed for thearrival of debris flow fronts [16]. However, it remains tobe shown if this effect can be captured withinstrumentation that is affordable enough to allow forextended sensor chains needed to track the propagationof roll waves along significant portions of a debris flow
channel.

125(9), e2020JF005590.

16. M. Wenner, K. Allstadt, W. Thelen, A Lockhart, J.
Hirschberg, B. W. McArdell & F. Walter. Bull. of theSeism. Soc. of Am. 112(5), 2376-2395.

4 Conclusions
Relatively easy deployments of seismic sensors couldprovide sufficient measuring points along a channel toclarify under which conditions roll waves tend to form.
First comparisons between flow depth, force plates andgeophone measurements are encouraging and suggest
the suitability of this method for longer torrent sections.
Nevertheless, the required number of sensors anddigitizers calls out for low-cost and highly portable
instrumentation, whose suitability has yet to beevaluated. If successful, our distributed seismic
measurements would have important consequences fornumerical models indicating the need to capture flowinstabilities to describe pulsing and surging behaviour ofdebris flows.
Seismic measurements at Illgraben were financed by
WSL and the Canton of Valais.

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