# Solid Concentration as a Main Proxy for Basal Force Fluctuations Generated by Highly Concentrated Sediment Flows

M. Piantini, F. Gimbert, E. Korkolis, R. Rousseau, Hervé Bellot, A. Recking

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## To cite this version:

M. Piantini, F. Gimbert, E. Korkolis, R. Rousseau, Hervé Bellot, et al., Solid Concentration as a Main Proxy for Basal Force Fluctuations Generated by Highly Concentrated Sediment Flows. Geophysical Research Letters, 2023, 50 (1), 10.1029/2022GL100345. [https://doi.org/10.5194/GR-1256](https://doi.org/10.5194/GR-1256)

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# Geophysical Research Letters®

## RESEARCH LETTER

10.1029/2022GL100345

**Key Points:**

* We investigate the force fluctuations generated by highly concentrated sediment flows exhibiting complex changes in internal dynamics

* We observe a unique negative relationship between the solid concentration and the amplitude of force fluctuations

* We suggest solid concentration should be incorporated in seismic models as a key parameter describing particle agitation

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

M. Piantini,
marco.piantini@tiscali.it

**Citation:**

Piantini, M., Gimbert, F., Korkolis, E., Rousseau, R., Bellot, H., & Recking, A. (2023). Solid concentration as a main proxy for basal force fluctuations generated by highly concentrated sediment flows. *Geophysical Research Letters, 50*, e2022GL100345. https://doi.org/10.1029/2022GL100345

Received 7 JUL 2022

Accepted 11 DEC 2022

© 2022. The Authors.
This is an open access article under
the terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

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## Solid Concentration as a Main Proxy for Basal Force Fluctuations Generated by Highly Concentrated Sediment Flows

M. Piantini<fnref n="1" />,<fnref n="2" /> ID, F. Gimbert<fnref n="1" /> ID, E. Korkolis<fnref n="1" /> ID, R. Rousseau<fnref n="2" />, H. Bellot<fnref n="2" />, and A. Recking<fnref n="2" /> ID

**Abstract** Sediment flows generate ground vibrations by exerting force fluctuations on the riverbed. Linking force fluctuations to properties of highly concentrated sediment flows, however, remains particularly challenging due to complexities arising from grain-to-grain interactions. Here, we conduct downscaled flume experiments in which we specifically measure force fluctuations and local seismic vibrations together with flow properties of highly concentrated sediment flows at high spatial and temporal resolution. We observe hysteresis behaviors between force fluctuations amplitude and flow surface elevation and mass that occur during complex changes in internal flow dynamics. By contrast, force fluctuations amplitude exhibits a unique negative relationship with solid concentration. We suggest this is due to the rheology of dense granular flows, where solid concentration is a proxy for particle agitation. We therefore advance that solid concentration should be incorporated in seismic models of such sediment flows as a key parameter describing inter-particle collisions and impacts to the bed.

**Plain Language Summary** During their journey across the landscape, rivers convey varying amounts of sediments. As they are transported, sediments impact the riverbed and generate seismic waves through exerting force fluctuations on the ground. The amplitude of force fluctuations is thought to be linked to the characteristics of the sediment flow such as grain sizes, sediment flux, thickness and velocity. Quantifying those links, however, remains challenging, particularly for highly concentrated sediment flows in which the numerous grains being transported strongly interact with each other. Here, we conduct laboratory experiments with the aim to understand how the generation of force fluctuations by highly concentrated sediment flows is influenced by grain-to-grain interactions, vertical distribution of grain sizes and velocities. Despite apparent complexities in the experimentally reproduced sediment flows, we find that solid concentration is the key parameter describing the amplitude of force fluctuations. We advance that this is due to solid concentration being linked with particle agitation, which tells us about the capability of particles to collide with each other and impact the riverbed. This finding provides grounds for improving theoretical models linking the properties of highly concentrated flows with the generated seismic signal.

## 1. Introduction

Flowing through the landscape, rivers generate high-frequency ground vibrations (>1 Hz) by exerting force fluctuations on their bed (Burtin et al., 2016; Larose et al., 2015). There is well-established evidence that seismic sensors detect ground vibrations from a wide variety of fluvial sediment transport events including very energetic ones (Arattano & Moia, 1999; Burtin et al., 2016; Cook et al., 2018, 2021; McCoy et al., 2013), calling for seismology as an appealing way to remotely monitor sediment transport characteristics and processes.

Through experiments and field observations, numerous efforts have recently been dedicated to investigate the relationships between the amplitude of force fluctuations and the properties of various sediment flows, ranging from bedload to debris flows (Allstadt et al., 2020; Bakker et al., 2020; Cole et al., 2009; Coviello et al., 2018, 2019; Gimbert et al., 2019; Haas et al., 2021; Hsu et al., 2014; McCoy et al., 2013; Zhang Walter, McArdell, Haas et al., 2021). In parallel, physically based mechanistic models have been developed to establish quantitative links between the flow properties and the generated seismic signal (Bachelet et al., 2021; Farin et al., 2019; Gimbert et al., 2019; Lai et al., 2018; Tsai et al., 2012; Zhang Walter, McArdell, Haas et al., 2021). Models concerning bedload transport predict that sediment flux and transported grain sizes are major control parameters, mainly setting the rate and the amplitude of particle impacts against bed roughness elements. These theoretical

<footnote n="1">¹University Grenoble Alpes, CNRS, IRD, Institute for Geosciences and Environmental Research (IGE), Grenoble, France,</footnote>

<footnote n="2">²University Grenoble Alpes, INRAE, CNRS, IRD, IGE, Grenoble, France</footnote>
expectations have been verified through experiments and field observations under relatively low bedload transport rates (Bakker et al., 2020; Gimbert et al., 2019; Lagarde et al., 2021).

However, more complexity arises with highly concentrated sediment flows, for which existing observations reveal not straightforward relationships between flow properties and amplitude of force fluctuations. Coarse granular and debris flows have been shown to generate stronger force fluctuations compared to finer ones (Haas et al., 2021; Hsu et al., 2014; Zhang, Walter, McArdell, Haas, et al., 2021), but the presence of big particles does not necessarily correspond to high force fluctuations, likely depending on their position relative to the bed (Zhang Walter, McArdell, Haas et al., 2021). Hsu et al. (2014) suggest that average sediment flow velocity exerts a primary control on force fluctuations, whereas Allstadt et al. (2020) and Zhang Walter, McArdell, Wenner et al. (2021) observe a rather low correlation. Certain investigations show amplitude of force fluctuations that is positively correlated with flow thickness and mass (McCoy et al., 2013; Zhang Walter, McArdell, Haas et al., 2021), others report poorer correlations when bulk density varies fast (Allstadt et al., 2020), or even negative correlations in the case of mud-saturated debris flows (Hsu et al., 2014). These contrasted results suggest that internal flow dynamics in addition to macro flow properties must be studied in order to better understand observations (Allstadt et al., 2020).

In this view, Piantini et al. (2021) designed laboratory experiments enabling strong changes in the internal flow dynamics of highly concentrated sediment flows, characterized by a wide bimodal grain size distribution enhancing grain sorting processes (Frey & Church, 2009; Iverson et al., 2010; Johnson et al., 2012) and rheological stratification, where the latter is meant as the occurrence of significant variations of flow rheology over depth (Armanini et al., 2005; Manville & White, 2003; MiDi, 2004; Sohn, 1997). They show that these complex processes strongly affect the generated seismic power. In particular, they observe a strong decrease in seismic power associated with the passage of the main body of the sediment flow, which they argue is in contradiction with expectations from theory. They evoke several physical mechanisms as potential drivers of this behavior, but limitations in the experimental instrumentation prevented them from identifying the specific physics controlling the seismic signature, and understanding whether such physics may be described as a function of certain bulk flow properties.

Here, we investigate sediment flows similar to those in (Piantini et al., 2021) but with improved instrumentation composed of a combination of cameras, seismic, and force sensors that allow us to track several in-stream flow properties and their seismic signature at high spatial and temporal resolution. Thanks to this novel set of experiments, we demonstrate that, despite complexities in internal flow dynamics, solid concentration is a good proxy for the amplitude of basal force fluctuations. We suggest that this finding can be explained by the link between solid concentration and particle agitation, which appears to control inter-particle collisions and impacts to the bed when solid concentration is sufficiently high.

## 2. Methods

### 2.1. Experimental Setup and Measurements

We carry out laboratory experiments in a flume composed of a 5-m long and 0.1-m wide straight steep channel (slope of 18%), connected in its upstream part to a 1-m long and on average 0.5-m wide storage area (slope of 0 – 1%) (Figure 1a). The bed and sidewalls of the flume are covered with sediments fixed with silicone. Every run consists in feeding the upstream storage area with constant liquid discharge $Q_l$ ($Q_l \in [0.48; 0.551/s]$) and sediment flux $Q_s$ ($Q_s \in [70; 100 g/s]$) whose values are based on similitude criteria to reproduce typical supercritical and fully turbulent flood conditions in mountain rivers (Froude number $Fr \in [1.63; 1.66]$) and Reynolds number $Re \in [2417; 3525]$; see (Piantini et al., 2021) for overall scaling considerations). We use a bimodal grain size distribution typical of mountain rivers (John Wolcott, 1988; Sklar et al., 2017), with one mode corresponding to sand ($0.5 \text{ mm} < D < 2 \text{ mm}$) and the other to cobbles ($4 \text{ mm} < D < 8 \text{ mm}$), and with $D_{50} = 5 \text{ mm}$ and $D_{84} = 9 \text{ mm}$, where $D_{50}$ and $D_{84}$ are the 50th and 84th percentile particle diameter, respectively.

Seismically relevant quantities are measured through seismic and force sensors. Four Glaser-type KRNBB-PC piezoelectric sensors, which we here refer to as seismic sensors, are mounted on the outside of one of the sidewalls of the channel, using mounting brackets and double-sided adhesive tape (Supporting Information S1). The sensors are connected via an AMP-12BB-J preamplifier to an Elexis Spectrum digitizer with sampling frequency $f_s$ set to 200 kHz. The mean basal force ($\bar{F}$) and force fluctuations are measured by coupling a 0.07-m wide and
<figure><img src="image_4.png" /><figcaption>Figure 1. (a) Sketch of the experimental flume. (b) Side view and (c) top view of a 0.6-m long stretch of the flume including the section equipped with a flow surface elevation sensor, a seismic sensor, and the force sensor. The red dashed square in panel (a) is shown in side view on panel (b). The white dashed square in (c) highlights the area occupied by the steel plate connected to the force sensor.</figcaption></figure>

0.1-m long rectangular steel plate onto the channel bed with two piezoelectric force sensors (model Kistler Typ 9601A21 connected to a Kistler 5073 charge amplifier) measuring the normal and downslope forces exerted by the flow on the plate (using $f_s = 30$ kHz). The plate is mechanically isolated from the rest of the flume to minimize its sensitivity to flume vibrations and is covered by sediments fixed with silicone (Supporting Information S1).

We also monitor several in-stream flow properties simultaneously. We measure the flow surface elevation (h) in three different sections of the channel (Figure 1) by means of three ultrasonic sensors (Banner Q45UR Series, using $f_s = 100$ Hz). We sample and sieve the sediment flux ($Q_s$) by hand at the flume outlet with a frequency of about 1 sample/5 sec. We estimate the in-stream solid concentration as:

$$ \phi(t) = \frac{\rho(t) - \rho_w}{\rho_s - \rho_w} \qquad (1) $$

where $\rho(t)$ is the bulk density, calculated as the ratio between the sediment flow mass and the relative volume, $\rho_s = 2618$ kg/m³ is the sediment density, estimated experimentally for sediments at rest and assumed not to vary significantly during the experiment, and $\rho_w = 1000$ kg/m³ is the density of water (see calculation in Supporting Information S1). We also estimate the macroscopic velocity of the sediment flows ($U_x$) and the downstream velocity of the biggest particles ($u_x$) by combining multiple sets of observations such as particle tracking in videos and time delays in flow surface elevation and seismic measurements (Supporting Information S1). Video recordings are made by means of multiple cameras: a Canon EOS 200D installed perpendicular to the channel bed and covering a stretch of 0.30 m close to the upstream seismic sensor SS1, an inclined webcam (Microsoft HD LifeCam Cinema) offering a wide view on the section with the force sensor FS, and a Canon EOS 100D camera providing a side view on a stretch of 0.10 m close to the downstream seismic sensor SS4 through a window made in the channel sidewall (Figure 1).
## 2.2. Analyzing Seismic and Force Data

We analyze the seismic and normal force fluctuations time series through computing the power spectral density (PSD) using Welch's averaging method (Welch, 1967). Time series are split into 50% overlapping segments of 0.5 s for the seismic signal and 1 s for the force signal. Before force power computation, we apply a band-bass Butterworth filter to the force signal in the frequency range 100–2500 Hz to avoid dealing with strong plate resonances. We focus on this frequency range also because the contribution to seismic vibrations of impacts on the sidewall is particularly noticeable above 2500 Hz (Supporting Information S1), and that of water flow is significant below 100 Hz (Piantini et al., 2021). In the selected frequency range, seismic waves are strongly attenuated with distance, such that the most contributing sources are located within about 1 m around the sensors (Supporting Information S1). We compute the mean force by applying a low pass filter below frequency $f = 1.5$ Hz to the force signal. Force power and flow property time series are smoothed using a 5-s moving window for the results presented in Section 3.3.

## 2.3. Generation and Propagation of the Sediment Flows

The sediment deposit that forms in the storage area is subject to alternating stages of aggradation and erosion, with every erosion generating sediment pulses that propagate in the downstream steep channel (Piantini et al., 2021). The self-triggered destabilizations of the upstream sediment deposit generate a downstream propagating pulse made of three distinct sediment transport phases exhibiting different dynamics and grain size compositions. Phase I (“Front bedload” in Figure 2d) is characterized by a constant and relatively low sediment flux (i.e., similar to that imposed by the boundary conditions to the storage area, $35 < Q_s < 100$ g/s) and a coarse grain size distribution (Figures 2i and 2m). Phase II (“Highly concentrated sediment flow” in Figures 2b and 2c) is characterized by a thick sediment flux ($Q_s > 150$ g/s and $h_{max} \sim 3$ cm) exhibiting a wide grain size distribution made of a varying amount of fines ($D < 2$ mm) (Figures 2i, 2m, 3a, and 3e). Phase III (“Tail bedload” in Figure 2a) is characterized by a low sediment flux similar to phase I ($35 < Q_s < 150$ g/s) although it exhibits a wider grain size distribution with a different content $C$ of big grains ($C_{D>8mm}^{Phase I} = 58\%$ against $C_{D>8mm}^{Phase III} = 27\%$, see Figures 2i and 2m). We investigate four sediment pulses in total, two of them are presented in the main text (referred to here as Exp #1 and Exp #2) and the two others in Supporting Information S1.

# 3. Results

## 3.1. Local In-Stream Dynamics

Phase I is dilute, with $\phi$ ranging from 0.15 to 0.25, and exhibits typical bedload dynamics, that is, grains saltate, roll, and slide in direct contact with the bed (see Movies S1 and S2), with a mean downstream velocity $u_x \approx 0.27$ m/s (Figure 2e). Phase II spans a range of solid concentrations reaching up to $\phi = 0.6$, thus approaching the maximum solid concentration $\phi_{max} = 0.7$ associated with sediments at rest (Supporting Information S1), and exhibits a strong vertical rheological stratification. Surface particles are mainly driven by boundary shear stress (i.e., flowing water) and grain collisions, whereas deeper particles constitute a thick sediment flow and are mainly driven by frictional and enduring contact (see Movies S1 and S2). These dynamics appear similar to that observed for sheetflows on steep slopes (Palucis et al., 2018) and for highly concentrated sediment flows (Armanini et al., 2005; Manville & White, 2003; Sohn, 1997), where a flux of particles driven by shear stress overlays a denser sediment flow that moves *en masse*. A strong increase in fines content occurs during phase II (Figures 2i and 2m), and stands out significantly in the video recordings as clear water becomes brownish and “muddy” when the maximum fines content passes under the cameras (Figure 2b and Movies S1 and S2). These fines further enhance vertical heterogeneities in grain sizes due to sorting processes (Frey & Church, 2009), for which coarse particles are pushed toward the surface carried by a finer matrix (Figure 2b and Movies S1 and S2), drastically modifying the mean downstream surface particle velocity (Figure 2e). When the fines content is low ($C_{D<2mm}^{Phase II} < 10\%$), we estimate a mean downstream surface particle velocity of $u_x \approx 0.17$ m/s, whereas when the content is higher ($C_{D<2mm}^{Phase II} > 35\%$) we have $u_x \approx 0.39$ m/s, to be compared with the average downstream velocity of the underlying thick sediment flow $U_x \approx 0.10$ m/s. We also observe that the maximum values of $\phi$ are always reached when the fines content is maximum (Figures 3a and 3e). Phase III moves back to low values of solid
<figure><img src="image_5.png" /><figcaption>**Figure 2.** General observations. (a to d) Photos from the upstream camera located close to SS1 showing the three different phases of a pulse. (e) Downstream particle velocity associated with each phase of a pulse. The red line in the middle represents the median, the bottom and top of each box the 25th and 75th percentiles, and the whiskers the minimum and maximum measurements. The macroscopic downstream velocity of the sediment flow $U_x$ is shown with the horizontal dotted line. (f and h) and (j and l) Seismic power measured upstream and downstream, respectively, and (g and k) force power. The mean basal force is also shown with the white curve in (g and k). The red squares delimit the time intervals exhibiting the maximum content of fines in phase II. (i and m) Outlet measurements of sediment flux and associated particle diameters (see legend). The vertical black dashed lines delimit the different phases.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 3.</figcaption></figure>
concentration and typical bedload dynamics similar to phase I (see Movies S1 and S2) with a mean downstream particle velocity $u_x \approx 0.30$ m/s.

## 3.2. Force Fluctuations and Seismic Observations

The passage of the highly concentrated sediment flow (phase II, showed between vertical black dashed lines in Figure 2) is reflected by the sharp increase in mean basal force (Figures 2g and 2k). As observed previously by Piantini et al. (2021), phase II is associated with a strong decrease in seismic power compared to phase I and III (Figures 2f, 2h, 2j, and 2l). Here we confirm that such decrease in power also occurs in the force measurements, and we are able to precisely analyze its links with local changes in flow dynamics thanks to the local nature of our measurements (Figures 2g and 2k). The reduction of seismic and force power in fact occurs through two consecutive steps. A first decrease of about 5 dB occurs in the initial stages of phase II under a negligible amount of fines (Figures 2c, 2i, and 2m), and a second and larger decrease of about 10 dB occurs when the maximum fines content passes through the sections closest to the respective seismic and force sensors (see red squares in Figures 2f–2h, 2j–2l, 3a, and 3e). We pick the times with maximum fines content using the cameras and confirm this observation by means of the sampling measurements made at the outlet, since the time delay between maximum sampled fines content and lowest levels of force power corresponds to the travel time of sediments from the force sensor to the outlet (using the estimated downstream velocity $U_x$).

## 3.3. Links Between Force Power and Bulk Flow Properties

In Figure 3, we evaluate the flow surface elevation ($h$), mean basal force ($\bar{F}$), and solid concentration ($\phi$) of phase II as a function of the measured force power. The first seconds of the highly concentrated sediment flows are characterized by weak positive relationships between force power and $h$, $\bar{F}$, and $\phi$ (Figures 3b–3d, and 3f–3h). However, past an inflexion point, the relationship between force power and flow properties becomes negative. In this range, we observe large counter-clockwise hysteresis in the relationships between force power and $h$ and $\bar{F}$, that is, the same values of mean force and flow surface elevation are associated with significantly different force power (5 up to 10 dB differences) (Figures 3b–3c, and 3f–3g). We observe sudden changes in the relationship between force power and $h$ and $\bar{F}$ also at shorter time scales, materialized by the small loop around $t = 35$ s in Exp #2 (Figures 3f and 3g). These complexities arise when the fines content is maximum (Figure 3).

Interestingly, the hysteresis and loops described above are no longer significant when force power is evaluated versus $\phi$, in which case maximum $\phi$ always corresponds to minimum force power (Figures 3d and 3h). Although a small clockwise hysteresis may be distinguished at high values of $\phi$ for the present examples, we do not consider it as noteworthy because it is not systematically observed for other sediment flows (Supporting Information S1).

# 4. Discussion and Conclusions

## 4.1. Existing Theories Unlikely to Explain Our Observations on Phase II

In most current theories (Farin et al., 2019; Lai et al., 2018; Zhang Walter, McDardell, Haas et al., 2021), force fluctuations are considered to be generated by impacts that are bed roughness-controlled, that is, particles impact the bed as they encounter bed roughness elements during their advection. Under this hypothesis, force fluctuations depend on the rate and amplitude of impacts that are mainly set by the average downstream velocity and size of particles, and by their number, which is considered proportional to solid concentration. Changes in these variables can be invoked to explain the 3 dB force power decrease between phase I and phase III (Supporting Information S1). However, the abrupt force power decrease by up to about 15 dB during phase II occurs under similar coarse grain fractions ($C_{D>8\text{mm}}^{\text{Phase II}} = 8\% \pm 2$ for Exp #1 and $C_{D>8\text{mm}}^{\text{Phase II}} = 14\% \pm 2$ for Exp #2), and similar average velocities, otherwise spatial disconnections within phase II would be expected, which is not observed.

**Figure 3.** Flow properties and force power of phase II. (a and e) Force power, $h$, $\bar{F}$, and $\phi$ as a function of time. (b to d) and (f to h) Force power versus flow properties. Panels (c) and (g) also show the flow mass $M$ in a secondary axis, computed through dividing the $\bar{F}$ by the acceleration due to gravity $g$. In panels (d) and (h) $\phi_{max}$ is shown with the horizontal dashed line. Time intervals with maximum fines content are marked in panels (a) and (e) with red vertical lines, and in the scatterplots with red circles. Hysteresis behaviors are highlighted with black curved arrows, while the vanishing of the small loop is highlighted in panel (h) with straight back and forth arrows.
Furthermore, we observe a strong increase in solid concentration rather than a decrease as current theories would require to explain the reduction of force power.

One could hypothesize that the decrease in force power is due to the damping effect of a sediment layer forming at the base of the thick sediment flow, as observed in the presence of static sediment deposit (Kean et al., 2015; McCoy et al., 2013). However, we do not expect this process could primarily explain our observations as by means of a supplementary experiment we observe that a static sediment layer of almost half the total flow surface elevation covering the force plate (worst-case scenario) dampens the force power generated by a particle impact by only 6 dB, which is much smaller than the 15 dB observed in the experiments (Supporting Information S1). The observation that the minimum of force power always corresponds to the maximum fines content might indicate that fines control the reduction of force fluctuations, through carrying big particles in suspension, and thus reducing their impacts to the bed (Piantini et al., 2021) or avoiding their contribution in force chains generation (Zhang Walter, McArdell, Haas et al., 2021). However, since force power significantly decreases even before the fines content becomes relevant, we believe such mechanism potentially occurs at a secondary level.

## 4.2. Solid Concentration Helps Decipher the Amplitude of Force Fluctuations

The key observation yielding further insight into the underlying source of reduced force fluctuations during phase II is the unique negative relationship and suppressed hysteresis and loops behaviors between force power and solid concentration (Figures 3d and 3h). We advance that solid concentration best describes force fluctuations amplitude as being a proxy for particle agitation. The link between solid concentration and particle agitation can be interpreted within the framework of the local $\mu(I)$ rheology of dense granular flows, for which solid concentration is a decreasing function of the dimensionless inertial number $I$ (da Cruz et al., 2005; Forterre & Pouliquen, 2008; MiDi, 2004). This number compares the microscopic time scale of particles rearrangement due to confining pressure $P$ and the macroscopic time scale linked to deformation due to shear rate $\dot{\gamma}$. Under the hypothesis of steady uniform state, and when the fluid has a negligible influence on the rheology, two-phase flows are controlled by the dry inertial number (Cassar et al., 2005; Courrech du Pont et al., 2003; Maurin et al., 2016) expressed as $I_{dry} = \frac{\dot{\gamma}d}{\sqrt{P/\rho_s}}$, where $d$ is the particle diameter. In order to position our experiments within the literature of granular flows, we estimate an average dry inertial number for phase II (the calculation of $I$ is discussed in Supporting Information S1). We obtain $I_{dry} \sim 10^{-1}$, which is in the range of dense granular flows (da Cruz et al., 2005). In this range, a granular flow characterized by a higher $I$ tends to dilate (i.e., relatively low solid concentration) as particles are agitated and inter-particle collisions are more likely to occur, while at a lower $I$ particles are packed (i.e., relatively high solid concentration) and mainly interact with each other through long-lasting contacts. Our experimental setup does not allow us to estimate variations of $I$ in time, but we suggest that solid concentration changes could reflect them. This would be consistent with the recent findings of a positive relationship between the amplitude of acoustic emissions and force fluctuations and the inertial number of dry granular flows (Arran et al., 2021; Bachelet et al., 2021). Macaulay and Rognon (2020) have shown that contact force fluctuations associated with micro-accelerations of the particles within a granular flow increase as the inertial number increase. Since these forces are expected to propagate toward the bed (Bachelet et al., 2021), we suggest that their study supports our hypothesis.

The central role played by solid concentration is further emphasized when comparing our findings with past studies. Allstadt et al. (2020) reported a negative relationship between bulk density and force fluctuations, as presented here, despite observing a positive relationship between flow surface elevation and mass and force fluctuations, which is opposed to our results. Similarly, Zhang Walter, McArdell, Haas et al., 2021 observed a positive relationship between flow surface elevation and mass and force fluctuations, with the two flow properties being negatively correlated with bulk density. This reinforces our interpretation that solid concentration is the parameter controlling force fluctuations, and leads us to suggest that a positive relationship between flow surface elevation and/or mass and force fluctuations holds only when the former are negatively related with solid concentration. This is likely often the case for natural debris flows (Allstadt et al., 2020; Iverson, 1997), but the extent to which it applies to other sediment flows, such as sheetflows or highly concentrated sediment flows, remains to be investigated further. In this sense, we suggest that the $\mu(I)$ rheology may be an appropriate framework to unravel the links between different flow properties for a wide range of dense granular flows with various interstitial fluids [sheetflows (Revil-Baudard & Chauchat, 2013); intense bedload (Maurin et al., 2016); debris flows (Berzi & Jenkins, 2008)].
4.3. Implications for Theoretical Models

In existing theoretical models, in which force fluctuations are considered to be generated by roughness-controlled impacts, solid concentration is only weakly and positively related to the amplitude of force fluctuations, through its control on the number of particles impacting the bed or on the size of force chains (Farin et al., 2019; Zhang Walter, McArdell, Haas et al., 2021). This approach likely holds for phase I, III and the first seconds of phase II. However, we advance that during phase II force fluctuations on the bed switch from being mainly generated by roughness-controlled impacts to being mainly generated by agitation-controlled impacts as sediment flows become denser and reach solid concentrations above about half $\phi_{max}$. A similar inflection point in the relationship between bulk density and force fluctuations was also observed by Allstadt et al. (2020) after the passage of the debris flow fronts. In the case of agitation-controlled impacts, the dependency of the amplitude of force fluctuations on solid concentration is negative and likely much stronger. In our experiments we show that relatively small variations of solid concentration ($\Delta\phi = 0.4 - 0.6$) are sufficient to modulate force power by nearly one to two orders of magnitude, which challenges the consideration that the expected range of variation of solid concentration ($\Delta\phi = 0.4 - 0.8$ for debris flows, following Iverson (1997)) is small enough for solid concentration to be approximated as constant (Farin et al., 2019; Zhang Walter, McArdell, Haas et al., 2021). We therefore propose that theoretical models should incorporate a transition from roughness-controlled impacts to agitation-controlled impacts, where in the agitation-controlled regime the flow satisfies the $\mu(I)$ rheology and in particular the inverse relationship between the inertial number *I* and the solid concentration.

Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

Data Availability Statement

The data analyzed during the current study are available on the Zenodo platform via https://doi.org/10.5281/zenodo.7402495.

References

Allstadt, K. E., Farin, M., Iverson, R. M., Obryk, M. K., Kean, J. W., Tsai, V. C., et al. (2020). Measuring basal force fluctuations of debris flows using seismic recordings and empirical Green's functions. *Journal of Geophysical Research: Earth Surface, 125*(9). https://doi.org/10.1029/2020JF005590

Arattano, M., & Moia, F. (1999). Monitoring the propagation of a debris flow along a torrent. *Hydrological Sciences Journal*, 44(5), 811–823. https://doi.org/10.1080/02626669909492275

Armanini, A., Capart, H., Fraccarollo, L., & Larcher, M. (2005). Rheological stratification in experimental free-surface flows of granular–liquid mixtures. *Journal of Fluid Mechanics*, 532, 269–319. https://doi.org/10.1017/S0022112005004283

Arran, M. I., Mangeney, A., De Rosny, J., Farin, M., Toussaint, R., & Roche, O. (2021). Laboratory landquakes: Insights from experiments into the high-frequency seismic signal generated by geophysical granular flows. *Journal of Geophysical Research: Earth Surface, 126*(5). https://doi.org/10.1029/2021JF006172

Bachelet, V., Mangeney, A., Toussaint, R., DeRosny, J., Farin, M., & Hibert, C. (2021). Acoustic emissions of nearly steady and uniform granular flows: A proxy for flow dynamics and velocity fluctuations. https://doi.org/10.48550/ARXIV.2101.04161

Bakker, M., Gimbert, F., Geay, T., Misset, C., Zanker, S., & Recking, A. (2020). Field application and validation of a seismic bedload transport model. *Journal of Geophysical Research: Earth Surface, 125*(5). https://doi.org/10.1029/2019JF005416

Berzi, D., & Jenkins, J. T. (2008). A theoretical analysis of free-surface flows of saturated granular–liquid mixtures. *Journal of Fluid Mechanics*, 608, 393–410. https://doi.org/10.1017/S0022112008002401

Burtin, A., Hovius, N., & Turowski, J. M. (2016). Seismic monitoring of torrential and fluvial processes. *Earth Surface Dynamics*, 4(2), 285–307. https://doi.org/10.5194/esurf-4-285-2016

Cassar, C., Nicolas, M., & Pouliquen, O. (2005). Submarine granular flows down inclined planes. *Physics of Fluids*, 17(10), 103301. https://doi.org/10.1063/1.2069864

Cole, S. E., Cronin, S. J., Sherburn, S., & Manville, V. (2009). Seismic signals of snow-slurry lahars in motion: 25 September 2007, Mt Ruapehu, New Zealand. *Geophysical Research Letters*, 36(9), L09405. https://doi.org/10.1029/2009GL038030

Cook, K. L., Andermann, C., Gimbert, F., Adhikari, B. R., & Hovius, N. (2018). Glacial lake outburst floods as drivers of fluvial erosion in the Himalaya. *Science*, 362(6410), 53–57. https://doi.org/10.1126/science.aat4981

Cook, K. L., Rekapalli, R., Dietze, M., Pilz, M., Cesca, S., Rao, N. P., et al. (2021). Detection and potential early warning of catastrophic flow events with regional seismic networks. *Science*, 374(6563), 87–92. https://doi.org/10.1126/science.abj1227

Courrech du Pont, S., Gondret, P., Perrin, B., & Rabaud, M. (2003). Granular avalanches in fluids. *Physical Review Letters*, 90(4), 044301. https://doi.org/10.1103/PhysRevLett.90.044301

Coviello, V., Arattano, M., Comiti, F., Macconi, P., & Marchi, L. (2019). Seismic characterization of debris flows: Insights into energy radiation and implications for warning. *Journal of Geophysical Research: Earth Surface*, 124(6), 1440–1463. https://doi.org/10.1029/2018JF004683

Acknowledgments

This research has been supported by
the Agence Nationale de la Recherche
(Grant 17-CE01-0008). We acknowledge
the support of the INRAE Research
Centre of Grenoble for the laboratory and
instrumental equipment. We thank Jeroni
Salens for helping in the installation of
the force sensors, and Zavier Berti for the
scientific discussions. We thank the asso-
ciate editor Victor Tsai, Fabian Walter
and anonymous reviewer for the fruitful
comments on the manuscript.
Coviello, V., Capra, L., Vázquez, R., & Márquez-Ramírez, V. H. (2018). Seismic characterization of hyperconcentrated flows in a volcanic environment: Seismic characterization of hyperconcentrated flows. *Earth Surface Processes and Landforms, 43*(10), 2219–2231. https://doi.org/10.1002/esp.4387

da Cruz, F., Emam, S., Prochnow, M., Roux, J.-N., & Chevoir, F. (2005). Rheophysics of dense granular materials: Discrete simulation of plane shear flows. *Physical Review E, 72*(2), 021309. https://doi.org/10.1103/PhysRevE.72.021309

Farin, M., Tsai, V. C., Lamb, M. P., & Allstadt, K. E. (2019). A physical model of the high-frequency seismic signal generated by debris flows. *Earth Surface Processes and Landforms, 44*(13), 2529–2543. https://doi.org/10.1002/esp.4677

Forterre, Y., & Pouliquen, O. (2008). Flows of dense granular media. *Annual Review of Fluid Mechanics, 40*(1), 1–24. https://doi.org/10.1146/annurev.fluid.40.111406.102142

Frey, P., & Church, M. (2009). How river beds move. *Science, 325*(5947), 1509–1510. https://doi.org/10.1126/science.1178516

Gimbert, F., Fuller, B. M., Lamb, M. P., Tsai, V. C., & Johnson, J. P. L. (2019). Particle transport mechanics and induced seismic noise in steep flume experiments with accelerometer-embedded tracers: Experimental Testing of Seismic Noise Generated by Sediment Transport. *Earth Surface Processes and Landforms, 44*(1), 219–241. https://doi.org/10.1002/esp.4495

Haas, T., Åberg, A. S., Walter, F., & Zhang, Z. (2021). Deciphering seismic and normal-force fluctuation signatures of debris flows: An experimental assessment of effects of flow composition and dynamics. *Earth Surface Processes and Landforms, 516*(11), 2195–2210. https://doi.org/10.1002/esp.5168

Hsu, L., Dietrich, W. E., & Sklar, L. S. (2014). Mean and fluctuating basal forces generated by granular flows: Laboratory observations in a large vertically rotating drum. *Journal of Geophysical Research: Earth Surface, 119*(6), 1283–1309. https://doi.org/10.1002/2013JF003078

Iverson, R. M. (1997). The physics of debris flows. *Reviews of Geophysics, 35*(3), 245–296. https://doi.org/10.1029/97RG00426

Iverson, R. M., Logan, M., LaHusen, R. G., & Berti, M. (2010). The perfect debris flow? Aggregated results from 28 large-scale experiments. *Journal of Geophysical Research, 115*(F3), F03005. https://doi.org/10.1029/2009JF001514

Johnson, C. G., Kokelaar, B. P., Iverson, R. M., Logan, M., LaHusen, R. G., & Gray, J. M. N. T. (2012). Grain-size segregation and levee formation in geophysical mass flows: Levee formation in geophysical flows. *Journal of Geophysical Research, 117*(F1), n/a–n/a. https://doi.org/10.1029/2011jf002185

Kean, J. W., Coe, J. A., Coviello, V., Smith, J. B., McCoy, S. W., & Arattano, M. (2015). Estimating rates of debris flow entrainment from ground vibrations. *Geophysical Research Letters, 42*(15), 6365–6372. https://doi.org/10.1002/2015GL064811

Lagarde, S., Dietze, M., Gimbert, F., Laronne, J. B., Turowski, J. M., & Halfi, E. (2021). Grain-size distribution and propagation effects on seismic signals generated by bedload transport. *Water Resources Research, 57*(4). https://doi.org/10.1029/2020WR028700

Lai, V. H., Tsai, V. C., Lamb, M. P., Ulizio, T. P., & Beer, A. R. (2018). The seismic signature of debris flows: Flow mechanics and early warning at Montecito, California. *Geophysical Research Letters, 45*(11), 5528–5535. https://doi.org/10.1029/2018GL077683

Larose, E., Carrière, S., Voisin, C., Bottelin, P., Baillet, L., Guéguen, P., et al. (2015). Environmental seismology: What can we learn on Earth surface processes with ambient noise? *Journal of Applied Geophysics, 116*, 62–74. https://doi.org/10.1016/j.jappgeo.2015.02.001

Macaulay, M., & Rognon, P. (2020). Two mechanisms of momentum transfer in granular flows. *Physical Review E, 101*(5), 050901. https://doi.org/10.1103/PhysRevE.101.050901

Manville, V., & White, J. D. L. (2003). Incipient granular mass flows at the base of sediment-laden floods, and the roles of flow competence and flow capacity in the deposition of stratified bouldery sands. *Sedimentary Geology, 155*(1–2), 157–173. https://doi.org/10.1016/S0037-0738(02)00294-4

Maurin, R., Chauchat, J., & Frey, P. (2016). Dense granular flow rheology in turbulent bedload transport. *Journal of Fluid Mechanics, 804*, 490–512. https://doi.org/10.1017/jfm.2016.520

McCoy, S. W., Tucker, G. E., Kean, J. W., & Coe, J. A. (2013). Field measurement of basal forces generated by erosive debris flows: Debris flow basal force. *Journal of Geophysical Research: Earth Surface, 118*(2), 589–602. https://doi.org/10.1002/jgrf.20041

MiDi, G. D. R. (2004). On dense granular flows. *The European Physical Journal E, 14*(4), 341–365. https://doi.org/10.1140/epje/i2003-10153-0

Palucis, M. C., Ulizio, T., Fuller, B., & Lamb, M. P. (2018). Intense granular sheetflow in steep streams. *Geophysical Research Letters, 45*(11), 5509–5517. https://doi.org/10.1029/2018GL077526

Piantini, M., Gimbert, F., Bellot, H., & Recking, A. (2021). Triggering and propagation of exogenous sediment pulses in mountain channels: Insights from flume experiments with seismic monitoring. *Earth Surface Dynamics, 9*(6), 1423–1439. https://doi.org/10.5194/esurf-9-1423-2021

Revil-Baudard, T., & Chauchat, J. (2013). A two-phase model for sheet flow regime based on dense granular flow rheology: Granular model for sheet flow regime. *Journal of Geophysical Research: Oceans, 118*(2), 619–634. https://doi.org/10.1029/2012JC008306

Sklar, L. S., Riebe, C. S., Marshall, J. A., Genetti, J., Leclere, S., Lukens, C. L., & Merces, V. (2017). The problem of predicting the size distribution of sediment supplied by hillslopes to rivers. *Geomorphology, 277*, 31–49. https://doi.org/10.1016/j geomorph.2016.05.005

Sohn, Y. K. (1997). On traction-carpet sedimentation. *SEPM Journal of Sedimentary Research, 67*. https://doi.org/10.1306/D42685AE-2B26-11D7-8648000102C1865D

Tsai, V. C., Minchew, B., Lamb, M. P., & Ampuero, J.-P. (2012). A physical model for seismic noise generation from sediment transport in rivers: Seismic noise from sediment transport. *Geophysical Research Letters, 39*(2), n/a-n/a. https://doi.org/10.1029/2011GL050255

Welch, P. (1967). The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms. *IEEE Transactions on Audio and Electroacoustics, 15*(2), 70–73. https://doi.org/10.1109/TAU.1967.1161901

Wolcott, J. (1988). Nonfluvial control of bimodal grain-size distributions in river-bed gravels. *SEPM Journal of Sedimentary Research, 58*. https://doi.org/10.1306/212F8ED6-2B24-11D7-8648000102C1865D

Zhang, Z., Walter, F., McArdell, B. W., Haas, T., Wenner, M., Chmiel, M., & He, S. (2021). Analyzing bulk flow characteristics of debris flows using their high frequency seismic signature. *Journal of Geophysical Research: Solid Earth, 126*(12). https://doi.org/10.1029/2021JB022755

Zhang, Z., Walter, F., McArdell, B. W., Wenner, M., Chmiel, M., de Haas, T., & He, S. (2021). Insights from the particle impact model into the high-frequency seismic signature of debris flows. *Geophysical Research Letters, 48*(1). https://doi.org/10.1029/2020GL088994

## References From the Supporting Information

Chassagne, R., Maurin, R., Chauchat, J., & Frey, P. (2020). Mobility of bidisperse mixtures during bedload transport. *Physical Review Fluids, 5*(11), 114307. https://doi.org/10.1103/PhysRevFluids.5.114307