How debris-flow composition affects bed erosion quantity and mechanisms: An experimental assessment

Understanding erosion and entrainment of material by debris flows is essential for predicting and modelling debris-flow volume growth and hazard potential. Recent advances in field, laboratory and modelling studies have distilled two driving forces behind debris-flow erosion: impact and shear forces. How erosion and these forces depend on debris-flow composition and interact remains unclear. Here, we experimentally investigate the effects of debris-flow composition and volume on erosion processes in a small-scale flume with a loosely packed bed. We quantify the effects of gravel, clay and solid fraction in the debris flow on bed erosion. Erosion increased linearly with gravel fraction and volume, and decreased with increasing solid fraction. Erosion was maximal around a volumetric clay fraction of 0.075 (fraction of the total solid volume). Under varying gravel fractions and flow volumes erosion was positively related to both impact and shear forces, while these forces themselves are also correlated. Results further show that internal dynamics driving the debris flows, quantified by Bagnold and Savage numbers, correlate with erosional processes and quantity. Impact forces became increasingly important for bed erosion with increasing grain size. The experiments with varying clay and solid fractions showed that the abundance and viscosity of the interstitial fluid affect debris-flow dynamics, erosional mechanisms and erosion magnitude. High viscosity of the interstitial fluid inhibits the mobility of the debris flow, the movement of the individual grains and the transfer of momentum to the bed by impacts, and therefore inhibits erosion. High solid content possibly decreases the pore pressures in the debris flow and the transport capacity, inhibiting erosion, despite high shear stresses and impact forces. Our results show that bed erosion quantities and mechanisms may vary between debris flows with contrasting composition, and stress that entrainment models and volume-growth predictions may be substantially improved by including compositional effects.

. If debris flows grow in size their destructive power increases and so does their hazard to mountain communities (Dowling & Santi, 2014;Rickenmann, 1999Rickenmann, , 2005. The erodible power of debris flows, combined with consecutive flow activity, is further suggested to be a primary process in cutting valleys in steep landscapes (Stock & Dietrich, 2003. On a shorter timescale, the erosion, reworking and deposition of sediment by debris flows is a main driver in the evolution of alluvial and debris-flow fans (Beaty, 1963;Blair & McPherson, 1994;De Haas et al., 2014). To minimize debris-flow hazards on Earth and decipher their ability to change landscapes we aim to gain a better understanding of the mechanisms of debris-flow erosion and the parameters that affect it.
Observations from field and experimental studies suggest two driving forces behind debris-flow erosion: (1) basal-shear forces; sliding of the flow along the bed (Frank et al., 2015;Hungr et al., 2005;Mangeney et al., 2007;Takahashi, 1978Takahashi, , 1981; and (2) impact forces; collisions between the grains and the bed (Berger et al., 2011;Hsu et al., 2008;Stock & Dietrich, 2006). Basal-shear force is dependent on the bulk density of the flow, flow thickness, gravity and the slope (e.g., De Haas & Woerkom, 2016). Particle impacts on the bed cause fluctuating basal forces and high-frequency seismic signals (Farin et al., 2019). These impact forces are the direct product of particle diameter and the granular temperature, that is, the velocity fluctuation of the particles relative to the velocity of the flowing mass (Berger et al., 2011;Farin et al.2019;Hsu et al., 2008;Stock & Dietrich, 2006). The magnitude of impact forces is further influenced by debris-flow velocity, flow depth and the velocity structure in the flow (Farin et al., 2019). A third factor influencing the (relative) importance of either two forces is the abundance and viscosity of the interstitial fluid. High abundance and viscosity have been hypothesized to lead to high pore-fluid pressure, which buffers grain interactions and inhibits particle segregation, thus decreasing impact forces (Bagnold, 1954;De Haas et al., 2015;Hsu et al.2008;Iverson, 1997;Iverson et al., 2010;Kaitna et al., 2016;Major, 2000;Major & Iverson, 1999;McCoy et al., 2010;Vallance & Savage, 2000). Others have, however, suggested that as muddy matrices are able to mobilize and transport larger clasts, an increased viscosity of the interstitial fluid may increase impact forces (Hsu et al., 2014). Iverson et al. (2011) showed, by means of large-scale experiments, that besides the abundance of interstitial fluid of the debris flow itself, bed wetness strongly affects erosion. An increase in bed wetness allows for larger positive pore pressures when overridden by a debris flow (also observed by McCoy et al.2012), which increases flow momentum and speed, facilitating progressive erosion of the bed. High pore pressures, and thus a large water content, also increase entrainment by reducing grain-to-grain basal friction (e.g., Iverson et al., 2011;, and at the same time favouring undrained loading and liquefaction (e.g., Hungr et al., 2005;Sassa & hui Wang, 2005).
In addition, some use an equilibrium volumetric sediment concentration to predict whether the debris flow can incorporate and entrain material (e.g., Armanini et al., 2009;Chen & Zhang, 2015) or use a critical flow depth above which erosion occurs (Han et al.2016). Many analytical and empirical models consider erosion as a function of shear forces, but how momentum conservation is incorporated differs greatly (Iverson & Ouyang, 2015). Despite the ability of both empirical and analytical models to predict erosion and entrainment relatively well in specific debris-flow torrents, the need for parameter calibration and the ongoing discussions about analytical models (see, e.g., Iverson & Ouyang, 2015;Kang & Chan, 2018;Pudasaini & Fischer, 2020) indicates the need for a better understanding of debris-flow erosional processes.
Field and laboratory studies have shed light on the possible importance of impact forces on erosion, which is currently not directly incorporated in the earlier discussed models. A field study by Berger et al. (2011) demonstrated that erosion and entrainment of loose material in the Illgraben torrent were associated with the impact of the coarse-grained flow front on the channel bed. They observed erosion before maximum values for flow depth, total normal stress and shear stress, but during the period of largest pressure fluctuations, which are caused by particle collisions with the bed. In contrast to Berger et al. (2011), the study by McCoy et al. (2013) could not find a difference in force fluctuation distribution between granular surges and the more watery intersurge flows. In addition to this contrasting observation, McCoy et al. (2012) could not find a direct link between the magnitude of pressure fluctuations and erosion. They still hypothesized, however, that high-frequency stress fluctuations might facilitate entrainment. Experimental results from a rotating drum show that bedrock erosion increases when inertial stresses, caused by impacts, increase in both dry and wet granular flows (Hsu et al., 2008), and that a larger representative grain size correlates with more erosion (Hsu et al., 2008(Hsu et al., , 2014. Other studies on impacts endorse the correlation between the magnitude of impact forces and particle diameter (De Haas et al., 2021;Farin et al., 2019;He et al., 2016).
However, in the field study by Berger et al. (2011), the link between grain size and erosion could not be distilled as grain size was not recorded and only two debris flows from the same torrent were studied. It can, however, be hypothesized that as the largest clasts occurred at the front of the flow, grain size did affect the inertial stresses. To our knowledge, the effect of inertial stresses, linked to grain size, on the erosion of a loose substrate has not yet been studied directly.
The largely unknown influence of, and interaction between, shear and impact forces on debris-flow erosion suggest that certain boundary conditions, such as flow and bed composition and flow volume, could be affecting erosion and erosional mechanisms. Flow and bed composition are especially difficult to assess in the field (Iverson, 1997;Major & Voight, 1986). The few field studies looking at the influence of flow composition on debris flow dynamics, however, show that the grain composition directly links to debris flow properties (Li et al., 2015;Wang et al.2018) and velocity (Liu et al., 2020). In experiments, the impact of debris flow composition on debris flow dynamics, run-out distance and deposit morphology has been studied (De Haas et al., 2015). De Haas et al. (2015) found that run-out increases with increasing water and clay fractions and that there is an optimum run-out distance when increasing gravel content.
Initially, increasing gravel content increases flow velocity and run-out distance, but increasing gravel further decreases flow velocity and run-out distance. They explained their findings as being the result of the interaction between grain collisional forces, pore-fluid pressure and diffusivity. In addition, rheometric investigations have shown that the behaviour of debris-flow mixtures varied with the concentration of solids, grain-size distributions and ultimately shear rate (Jeong, 2010;Major & Pierson, 1992;O'Brien & Julien, 1988;Phillips & Davies, 1991;Scotto di Santolo et al., 2010). Based on these findings we hypothesize that debris-flow composition will also influence debris-flow erosion and erosional mechanisms-a hypothesis underlined by the work of De Haas and Woerkom (2016). They showed that in experimental debris flows an increase in the water fraction and grain size of the debris flow resulted in an increase in basal-scour depth, and increasing clay content resulted in a decrease in the scour depth-a correlation which they coupled to the dependence of erosion on basal-shear stress. The only exception to this conclusion was their observation on experiments with a very large gravel content, which lacked the relation between basal-shear and erosion. They hypothesized that during these experiments collisional stresses had a relatively large influence on the flow dynamics. Their set-up, however, did not allow for conclusive statements on this. The small-scale flume set-up, with a small grain size relative to flow depth, resulted in an overall small influence of grain collisional stresses, which is in contrast to observations from the field (Berger et al.2011).
Field studies further reveal that maximum flow depth is an important control on the pattern and magnitude of erosion (Schürch et al., 2011), that debris-flow magnitude relates to the balance between erosion and deposition (Chen & Zhang, 2015), and that entrainment is correlated with terrain slope (Baggio et al., 2021;Gregoretti et al., 2019;Reid et al., 2016;Simoni et al., 2020;Theule et al., 2015). Nonetheless, the scatter and uncertainties in these field studies are large and the relations that are found do not provide a process-based explanation of debris-flow erosion. A complicating factor in studying erosion processes in the field, which could explain some of the observed scatter, is the influence and often chaotic nature of the debris flow initiation mechanism, landsliding and other slope failures or grain-bygrain bulking. When landsliding or slope failures trigger debris flows, initial sediment concentration is high, which may limit erosion. In contrast, when grain-by-grain bulking initiates debris flows, erosion starts under the influence of water-dominated flows before transitioning into a debris flow (McGuire et al., 2017), thereby allowing entrainment of large amounts of sediment.
To summarize, there is no consensus on the exact processes and parameters controlling debris-flow erosion. Both impact forces, shear forces and the interaction between the fluid and solid phase in a debris flow likely affect erosion. How these forces and their interactions are affected by boundary conditions, such as debris-flow composition and flow volume, is not well understood. In addition, we need to understand the forces dominating erosion in contrasting flows (e.g., granular vs. viscous) to effectively predict and model debris-flow erosion as a function of their composition.
The objective of our study is to unravel the effects of debris-flow composition on debris-flow erosion and erosional mechanisms. We aim at understanding the mechanisms of debris-flow erosion under different debris-flow compositions, and aim to assess the erosion potential as a function of composition. As correctly assessing debris flow composition in the field has been proven almost impossible (Iverson, 1997;Major & Voight, 1986), and spatiotemporal patterns of water. The erodible bed consisted of sand (98% of solid fraction), kaolinite clay (2% of solid fraction) and water (11% of total weight). The composition of the bed was selected based on preliminary tests in the flume aimed at finding a balance between enabling erosion and not fully removing the bed. We tested the effects of the gravel and clay fractions in the flow, as well as the total solid fraction, including gravel, sand and clay, and the total volume of the debris flow. When increasing the gravel and clay fraction the total solid fraction was kept constant, meaning that the fraction of the other solids was decreased proportionally. Under varying total solid fractions, the relative percentages of gravel, sand and clay were kept constant, but the ratio of solids to water changed. When varying flow volume the composition of the debris flow was kept constant. The intended purpose of the experiments with varying flow volume was to establish the significance of debris-flow composition on erosion relative to the size and flow depth of a debris flow, since we already know from field studies that debris flow size and depth are important controls on erosion magnitude (Chen & Zhang, 2015;Schürch et al.2011). In total, 96 experiments were executed, of which 73 had a flume inclination of 34 (see Supporting Information Table 1). The angle of the flume is steep, but corresponds to the upper reach of debris-flow channels dominated by erosion (Rengers et al., 2021;Simoni et al.2020). In The experiments performed with lower flume angles were performed once. When during or after the experiment the erodible bed in the flume slumped, for reasons unrelated to the passing of the debris flows, the results were discarded and the experiment was repeated.

| Experimental set-up and data analyses
The flume consists of a straight, rectangular channel of 0.3 m wide and 5.4 m long, a mixing tank with a forced-action mixer (Baron E120) and a custom-made release gate ( Figure 1). The flume was tilted at the beginning of every experiment. Mixing of the sediment and water took place for 30 s, during the lifting procedure, and stopped 0.8 s before the gate opened. Our set-up thus differs from earlier experiments on debris flow erosion by Lanzoni et al. (2017), who focused on the influence of the triggering run-off. Our experimental set-up enables us to study debris flow erosion mechanisms and potential of different compositions and volumes independent of the duration and/or volume of the triggering run-off. This provides insights into debris flow erodible mechanisms and potential, beyond the often smaller natural variations in debris flow composition.
In the lower half of the flume the bottom was lowered by 7 cm to create space for an erodible bed with a length of 2.5 m. Along the entire length of the flume the floor was covered with sandpaper to simulate natural channel roughness.
Along the length of the flume five distance sensors were installed (locations are indicated by red lines in Figure 1). Two Baumer OADM 20U2480/S14C distance sensors (at 2.9 and 2.98 m), which are capable of measuring at sub-millimetre accuracy, and three Baumer Erosion of and deposition on top of the erodible bed were captured with a Vialux z-Snapper 3-D scanner, which created a 3-D point cloud with sub-millimetre accuracy from a fringe pattern projector and camera (Hoefling, 2004). A scan of the bed was made before each experiment and after the debris flow had passed. The point clouds were denoised with MATLAB to remove outliers before they were

| Debris flow and bed composition
As discussed above our debris flows were composed of clay (kaolin), sand, angular gravel and water. Our reference experiment had a total mass of 60 kg (0.03 m 3 ), of which 12 kg consisted of water. The sediment mixture of the reference experiment volumetrically comprised 20% gravel (2-16 mm), 75% sand (0.09-2 mm) and 5% clay ($ 2 μ m) (similar to De Haas & Woerkom, 2016;De Haas et al., 2015.
We systematically varied the gravel as a fraction of the total weight from 0 to 0.6 and the clay from 0 and 0.2. We varied the total solid fraction as a fraction of the total volume from 0.43 to 0.75 and the flow mass of the debris flow from 36 to 108 kg (0.018-0.054 m 3 ) (see Table 1 and Supporting Information Table 1. The grain size distributions of the sand and gravel, and the combined distribution for the reference debris flow, can be found in Figure 2. The erodible bed was composed of clay (kaolin), sand and water.
For every experiment $ 90 kg of mixture was prepared for the bed.
This was more than fitted in the bed but made filling and levelling the bed easier. Of this mixture, 89% of the weight consisted of solids and 11% of water. Of the solid fraction, 98% of the weight consisted of sand and 2% consisted of clay. The contents of the bed were thoroughly mixed with a hand-held forced action mixer before being emplaced in the flume. A trowel was used to level the bed at a constant height and replicate the same loose packing in the bed for every experiment. To ascertain that the wetness of the levelled bed was constant, we measured and registered the moisture content of the bed for every run at 12 locations along the length of the flume with an HH2 Moisture Meter and ML3 ThetaProbe (soil moisture accuracy 1%) (see Supporting Information Table 1).

| Characterization of flow characteristics
Basal-shear stress, momentum and seismic energy are used to quantify the forces on the bed. Peak basal shear stress is estimated from simple flow metrics: where ρ is the density of the flow (kg/m 3 ), g is gravitational acceleration (m/s 2 ), H is maximum flow depth (m) just before the erodible bed and S is the channel-bed slope. We approximate flow density as bulk density when perfectly mixed and use maximum flow depth as input for depth. These assumptions introduce small deviations from reality as the flow front generally contains a relatively high solid fraction. The momentum of the flow is defined and calculated as where m is the mass of the debris flow (kg) and u is the debris flow frontal velocity (m/s) just before the erodible bed. Frontal velocity is calculated by using the time until arrival of the flow front at the laser distance sensor at 290 cm, just before the erodible bed. Seismic energy, a measure to quantify the cumulative impact force during the flow, was calculated as the integral of the squared amplitude of the vertical ground velocity of the entire flow (for further details on this procedure see De Haas et al., 2021;Schimmel et al., 2021). Note that shear force, momentum and seismic energy are all recorded and calculated just before the erodible bed. The values therefore represent the conditions in and underneath the debris flow before erosion could occur.
To characterize the dynamics in different flows and objectively compare them, three dimensionless numbers are used: the Bagnold, Savage and friction numbers. These numbers describe the relationship between the forces resisting motion in debris flows: collisional, frictional and viscous forces (Iverson, 1997;Iverson et al., 2010;Parsons et al., 2001). However, as we hypothesize these forces to affect debris-flow erosion, we will use these numbers as indicators for studying the relative importance of these three forces in the erosion process. The Bagnold number defines the ratio between collisional and viscous forces: where δ is the mean grain size of a debris flow mixture (m) (Iverson, 1997), v s is the volumetric solids fraction and γ is the flow shear rate (1=s ): where μ is the interstitial fluid viscosity, which we estimate as (De Haas et al., 2015;Iverson, 1997;Thomas, 1965): where μ w is the dynamic viscosity of pure water (equal to 0.001002 Pa s). According to Iverson (1997), collisional forces dominate at N b > 200. The Savage number describes the ratio between collisional to frictional forces: where ϕ is the internal angle of friction, assumed to be 42 (De Haas et al., 2015;Parsons et al., 2001). For N s > 0:1 collisional forces dominate viscous forces (Iverson, 1997). Lastly, the ratio of frictional to viscous forces is described as follows: For N f > 2000 frictional forces dominate over viscous forces according to cohesionless dry flows from Iverson (1997), but experimental data of wet experimental debris flows of Parsons et al. (2001) and De Haas et al. (2015) suggest that this transition already happens at N f > 100 for the flow body and N f > 250 for the flow front.
2.4 | Scale effects Iverson (1997), Iverson and Denlinger (2001) and Iverson et al. (2010) have argued that small-scale debris-flow experiments suffer from scale effects that influence flow dynamics. They show that small-scale flows experience large effects of yield strength, viscous flow resistance and grain inertia compared to field size debris flows. In addition,

| Correlation of shear and impact forces
In all sets of experiments a significant linear relation exists between vertical seismic energy and maximum shear stress (Figure 9)

| Effects of debris-flow composition and volume on erosion
Our experimental flows clearly show that debris-flow volume and composition influence erosion magnitude (Figure 7). The increase in erosion with debris flow volume shows that our experiments comply with earlier experimental work (Chen & Zhang, 2015;Zheng et al., 2021) and observations from the field (Schürch et al., 2011). Both in these earlier experiments and in field studies, an increase in debris flow volume correlated with an increase in flow depth, which itself correlated with the magnitude of erosion (Schürch et al., 2011;Zheng et al., 2021). In our experiments, an increase in flow volume also resulted, next to an increase in flow depth, in an increase in frontal flow velocity, frontal discharge, momentum, shear stress and seismic energy, all correlating with the increase in erosion (Figure 8d,h,l,p,t).
In addition, the experiments with varying debris flow composition prove that the gravel, clay and total solid content have a significant effect on erosion magnitude. The tested ranges of gravel, clay and solid fraction are slightly larger than observed in nature (Yong et al., 2013), but highlight important trends, mechanisms and tipping points that should be taken into consideration when studying debris flow erosion, bulking and entrainment. Increasing the gravel content results in more erosion (Figure 7a) (as in De Haas & Woerkom, 2016;Egashira et al., 2001). Increasing the total solid content decreases erosion (Figure 7c), in agreement with Egashira et al. (2001), Hungr et al. (2005) and Fagents and Baloga (2006). This finding also corroborates the finding of Egashira et al. (2001), who proposed the existence of an upper sediment concentration limit for debris flows in motion, and the use of equilibrium volumetric solid concentrations in many numerical entrainment models (e.g., Armanini et al., 2009;Chen & Zhang, 2015), preventing models from predicting indefinite erosion. Increasing clay content has a nonlinear effect on erosion (Figure 7b), in contrast to De Haas and Woerkom (2016), who only observed a decrease in erosion due to higher clay fractions. It must, however, be noted that despite De Haas and Woerkom (2016) testing a similar range in volumetric clay fractions as we did, from 1% to 23%, they only tested four clay fractions (1%, 2%, 11% and 23%) of the total volume, whereas we tested more continuously throughout the given range.
In  (Figure 8u). This trend is in agreement with observations on bedrock erosion by debris flows (Hsu et al., 2008(Hsu et al., , 2014Stock & Dietrich, 2006). Our data also indicate that impact forces not only increase with increasing grain size but also with increasing debris-flow volume (Figure 5x) (as earlier concluded by De Haas et al. (2021) and Schimmel et al. (2021), and implied in the assumptions made by

| Influence of the abundance and viscosity of the interstitial fluid on debris-flow dynamics and erosion
Our data show that impact and shear forces are not always able to predict erosion directly. In the experiments where clay and solid fractions are varied, impact and shear forces do not linearly correlate with erosion magnitude. As hypothesized in the Introduction, the viscosity and abundance of the interstitial fluid play a critical role in enabling and amplifying the work of erosional forces (e.g., Bagnold, 1954;Iverson, 1997;Vallance & Savage, 2000).
Our experiments show that in the absence of clay the recorded impact forces are small, and flow velocity and momentum are low (Figure 5b,n,v). This results in net deposition in the flume (Figure 7b), despite a high shear stress due to large flow depths (Figure 5f,r). In the absence of clay the transfer of water and pore pressure from debris flow to the bed happens unhindered, draining the flow and decreasing its capacity to incorporate more sediment. When clay is more abundant (volume fraction 0.05-0.1), the volume and viscosity of interstitial fluid increase, the pore pressures in our debris flows likely increase (as they also did in the experiments of Kaitna et al., 2016), while the transfer of interstitial fluid from debris flow to the bed becomes less unhindered. This allows the debris flow to keep its momentum and transport capacity, while still liquefying the bed.
Under these conditions, the slight increase in clay decreases the angle of internal friction within the debris flow (Hsu et al., 2008), resulting in more mobility (also found by McArdell et al., 2007) Iverson, 1997;Major & Iverson, 1999;McCoy et al., 2010). Under these clay-rich conditions, despite slightly higher shear stresses, erosion completely diminishes ( Figure 7b). Our experiments with varying clay contents seem to comply with contrasting conclusions on the effects of viscosity on debrisflow dynamics from different studies. On the one hand, studies conclude that impact forces decrease when the viscosity of the interstitial fluid increases (e.g., Iverson, 1997;Major & Iverson, 1999;McCoy et al., 2010), whereas others say that impact forces increase with higher clay content (Hsu et al., 2014). We therefore hypothesize that previous studies captured only one half of the nonlinear effect of clay content and interstitial viscosity. Our broad range of tested clay fractions unifies these previously contrasting observations.
The experiments with varying solid content further underline the importance of the abundance of interstitial fluid. When volumetric solid content is increased from 0.4 to 0.6, flow depth, shear stress and seismic energy increase, but erosion decreases (Figures 5g,s,w and 7c). For a further increase in solid content, up to 0.7, flow depth, shear stress and impact forces become smaller, further decreasing erosion and enhancing deposition. If we follow the line of reasoning on transport capacity by Takahashi (1981) and Hungr et al. (2005), we can assume that at these high solid fractions the debris flows are becoming saturated by solids and are not able to incorporate more loose material. In addition, high pore pressures, and thus a larger water content, can aid entrainment by reducing grain-to-grain basal friction (e.g., Iverson et al.2011; and increasing liquefaction (e.g., Hungr et al., 2005;Sassa & hui Wang, 2005).
Our experimental findings on the effects of solid content of the debris flow on erosion are consistent with the hypothesis of Iverson et al. (2011) and Iverson (2012). They stated that a high bed wetness, resulting in high and contrasting pore pressures between the bed and debris flow, is important for promoting entrainment. Their experimental results showed that high pore pressures generated as wet bed sediment are overridden and entrained can result in liquefaction (Iverson, 2012), causing a reduction in grain-to-grain friction, an increase in flow momentum and further erosion (Iverson et al., 2011).
Our results add to their findings by showing that not only bed wetness influences erosion, but water content and the viscosity of the interstitial fluid of the debris flow itself affect erosion and erosional processes of loose sediment, by changing pore pressures and momentum of the flow, influencing the transfer of interstitial fluid from flow to bed and changing the transport capacity of the flow itself. The similarity in observations between Iverson et al. (2011), Iverson (2012 and this study on the effects of water content raises questions on how clay content of the bed affects erosion and whether those effects will be similar to the effects of clay content of the debris flow on erosion.

| Internal debris flow dynamics in relation to erosion
The experiments provide evidence that the internal dynamics of debris flows correspond to the forces, impact and shear, working on the bed underneath a debris flow (Figures 10 and 11 The trends in the Bagnold and Savage numbers, for the experiments in which gravel and clay were varied, also correlate linearly with net change (Figure 11a,b,e,f). This provides evidence that the internal debris-flow dynamics not only correspond to the forces working on the bed but also the actual erosion. More collisional behaviour in the debris flows-that is, higher Bagnold numbers and higher Savage numbers-corresponded to more erosion (Figure 11a,b,e,f). When gravel fraction is increased this is directly linked to the observed increase in seismic energy, and thus impacts on the bed. The linear relation between erosion and Bagnold and Savage numbers for the experiments with varying clay content is, however, more surprising, as the erosion magnitude under varying clay content is nonlinear.
The erosive behaviour of debris flows with varying clay contents is the result of a multitude of different physical mechanisms working on the bed (e.g., impact and shear forces, viscosity of the interstitial fluid, pore pressure transfer, momentum) that are captured by these non-dimensional numbers.
The only erosion-influencing factor that is not captured well by the non-dimensional numbers used in this paper (Bagnold, Savage and friction) is the transport capacity of the flow. When solid fraction is varied, no positive linear relation exists between erosion and these non-dimensional numbers (Figure 11c,g,k). The negative relation between erosion and the Bagnold number when solid content is varied ( Figure 11c) is a direct result of the increase in solid content v s .
The increase in predicted collisional behaviour is, however, baffled by the lack of transport capacity of the flow and the limited transfer of water and pore pressure from the flow to the bed in these sedimentsaturated flows.

| Implications on the prediction and modelling of debris flow erosion and entrainment in the field
Our experimental data show that when debris-flow composition is relatively stable both seismic signals and shear stresses can be used to predict debris-flow erosion, entrainment and volume growth in the field, and that we could use both forces in modelling debris-flow erosion (Figure 8t coarser-grained flow fronts in our experiments due to particle segregation, which enhances impact forces and thus erosion. Our experiments, therefore, enforce earlier hypotheses by Berger et al. (2011) and Stock and Dietrich (2006) stating that most erosion happens underneath the flow front. In contrast, the data from our experiments with a high water content show that even with smaller impact forces large amounts of erosion can occur (Figure 8w), which is in line with (Hungr et al., 2005), who expected that flows with lower sediment concentrations are more erosive. We therefore hypothesize that whether erosion dominantly occurs underneath the flow front, tail or both depends on the interplay between the composition of the debris flow, the erosive forces working on the bed, the efficiency of momentum transfer to the bed and the conditions of the overridden bed.
When the bed conditions are erosion prone-that is, loosely packed wet sediment (Iverson et al., 2011), erosion will occur underneath collision-dominated flow fronts by impact forces and underneath more watery flow fronts and tails by increased pore pressure and liquefaction. Therefore, it becomes clear that debris flow erosion cannot be estimated by the sum of different factors but that the interplay of these factors determines erosion. This has great implications for the modelling of debris-flow erosion. Where the incorporation of an equilibrium sediment concentration by Armanini et al. (2009) is a step in the right direction, their current model does not consider the erosive forces of the debris flow, resulting in unrealistic magnitudes of erosion in some places (Gregoretti et al., 2019). Other models describing debris-flow erosion do incorporate the most important erosive forces, shear and impact, but do not consider the nonlinear effects of clay within the interstitial fluid and the transport capacity of the debris flows. Both these factors influence how, and how effectively, momentum is transferred from the debris flow to the bed.
To summarize our findings and therefore the implications for erosion modelling, we can state that erosion caused by debris flows (E DF ) is a function of impact (F I ) and shear forces (F τ ), and the means and effectiveness of pore pressure transfer between the debris flow and the bed (P DF$B ): in which impact forces are predominantly a function of the grain size (D), the viscosity of the interstitial fluid (μ), flow depth (H) and flow velocity (u): and shear forces are a function of the debris flow density (ρ), flow depth and slope (S), as already defined in Equation (1): in which H itself is also influenced by the composition of the debris flow and its velocity. The means and effectiveness of elevated pore pressure transfer are influenced by the viscosity of the interstitial fluid and the fraction of solids (v s ): As our data show, the interaction between all these parameters is complex, dependent on debris-flow composition, and often nonlinear, especially when clay fraction is varied and water content of the debris flow is limited. The complex interplay between these forces and mechanisms is, nonetheless, also key in accurately describing debrisflow erosion. We therefore recommend incorporating the nonlinear Changes in debris-flow composition as entrainment continues should ideally be accounted for, as well as how bed composition itself affects debris-flow erosion. The importance of the latter has been shown by Iverson et al. (2011), but has to be explored and studied further. An additional complicating factor in the field is the availability of loose sediments (Simoni et al., 2020), a factor not studied in this paper. Solving the erosion functions above is beyond the scope of this paper, as we would also need to include the effects of the conditions of the bed to fully describe erosion of loose sediment by debris flows.

| CONCLUSIONS
We We recommend incorporating the nonlinear effects of the abundance and viscosity of the interstitial fluid on debris flow dynamics and erosional processes in entrainment modelling. Changes in debrisflow composition as entrainment continues should ideally be accounted for, as well as how the bed composition itself affects debris-flow erosion. For erosion and volume prediction in the field we advise to account for the nonlinear effects of interstitial fluid when debris-flow composition differs greatly between events, or when comparing various debris-flow sites. In these cases, data from load cells, distance sensors and pore-pressure sensors could be used to estimate interstitial fluid viscosity and abundance indirectly.
We can also conclude that the forces that dominate internal dynamics of debris flows are similar to those that dictate erosion.
Thereby, dimensionless numbers used to categorize debris flows can also be used as indicators for debris-flow erosion potential and erosional mechanisms when comparing debris flows of different compositions.

Data availability statement
DEMs and raw data from the sensors in the flume are made available via Yoda (online repository of Utrecht University). The data and an instruction on how we processed the raw data can be found under this link: https://public.yoda.uu.nl/geo/UU01/7WFE5C.html. DOI: 10.24416/UU01-7WFE5C.