Experimental Investigation on Scouring v.s. Mass Failure of Unsaturated Soil Bed: Implications for Debris Flow Initiation and Erosion

Scouring and mass failure are two common mechanisms used to describe soil bed erosion, but their combined effects are often not considered. To better understand how these mechanisms compete and under what conditions they prevail, it is essential to consider infiltration and a more realistic unsaturated soil bed. This study investigates soil bed erosion by considering unsaturated soil mechanics, a wetting front, and both erosion mechanisms of scouring and mass failure. Physical experiments were conducted on model water runoff over an unsaturated sand bed to investigate the effects of soil water content and flow velocity on erosion. Experimental results show that current understanding of soil bed erosion can be enhanced by adopting unsaturated soil mechanics and considering the combined effects of scouring and mass failure. The scouring rate is found to be independent of the bed water content because it only affects the uppermost soil particles, which immediately become saturated once water flows over them. Mass failure, on the other hand, is initiated at the wetting front when the rate of infiltration exceeds that of scouring. The depth of mass failure can be described by the net infiltration depth, which is defined as the difference between the infiltration and scouring depths. The net infiltration depth is jointly governed by the soil water content and flow velocity. The crucial role of the coupled effects of the hydro‐mechanical behavior of unsaturated soil in the realistic modeling of soil bed erosion is demonstrated. Outcomes present advancement toward improved hazard assessments of debris flows.


Introduction
Debris flows are mixtures of solid and water that surge downslope under the influence of gravity (Hungr et al., 2001), posing a significant threat to infrastructure in mountainous communities (Froude & Petley, 2018;Hu et al., 2019;Jakob et al., 2012;Ng et al., 2021;Song et al., 2021).Studies by De Haas et al. (2014), Kean et al. (2013), McGuire et al. (2017), and Tang et al. (2019) demonstrated that soil bed material can be eroded by hydrodynamic shear stress exerted by water runoff.As the concentration of eroded bed material increases, runoff eventually develops into debris flows.In addition, hydrodynamic shear stress also plays a crucial role in soil bed erosion underneath the body and tail of debris flows, where fluid stresses are significant compared to solid grain stresses (De Haas et al., 2022;McCoy et al., 2012).
Existing literature (McCoy et al., 2012;McGuire et al., 2017;Ng et al., 2022;Wilcock & McArdell, 1993;Winterwerp et al., 2012) demonstrates that progressive scouring and mass failure are two main mechanisms by which a soil bed is eroded.Scouring occurs when a soil bed is eroded at its surface grain-by-grain by hydrodynamic shear stress (Fraccarollo & Capart, 2002;Shields, 1936).Research in hydraulics (Lim, 2018) has shown that hydrodynamic shear stress exerted on the bed is determined by the flow velocity and can be calculated as follows: where ρ f is the flow density, u is the flow velocity, and C f is the friction factor related to the flow Reynolds number and bed roughness.Equation 1shows that hydrodynamic shear stress increases with the flow velocity.Grain-bygrain scouring of soil particles can be predicted by the Shields number Θ (Shields, 1936), which is formulated based on the force and torque equilibrium of an individual particle, which is assumed to be fully submerged, when eroded by an induced hydrodynamic shear stress: where g is the gravitational acceleration, ρ s and D are the density and characteristic diameter of the soil bed particles.Scouring occurs when the Shields number exceeds a critical value Θ c , and the Θ c increases with slope (Lamb et al., 2008;Prancevic et al., 2014;Shields, 1936).However, the Shields number may not be directly relevant for describing the scouring of unsaturated soil beds, which are more realistic representations of soil beds in the field that are rarely saturated when debris flows occur (McCoy et al., 2012).The presence of air in the interstitial pores of unsaturated soil induces negative pore water pressure (i.e., matric suction) caused by capillary tension (Fredlund & Rahardjo, 1993).The negative pore water pressure provides unsaturated soil with additional shear resistance compared to saturated soil.Hence, the applicability of the critical Shields number for describing the resistance of an unsaturated soil bed against scouring requires evaluation.
Mass failure occurs when a soil bed fails en masse as a block along a failure plane (Ng et al., 2022;Takahashi, 1978).Takahashi (1978) proposed that mass failure of a soil bed is prone to occur in loose saturated soils, where soil is liquefiable under the influence of external loading imposed by a debris flow.While mass failure of a saturated soil bed via liquefaction has been extensively studied, most soil beds are unsaturated when debris flows occur.McCoy et al. (2012) reported the mass failure of unsaturated soil with a water content of less than 6% based on field observations at Chalk Cliff, US.In unsaturated soil beds, large compressibility of the pore air results in the soil skeleton sustaining part of the external loading from the flow (Ng et al., 2017;Skempton, 1954;Yang, 2002).As a result, the pore water pressure cannot easily increase to a critical threshold whereby the effective stress reduces to zero (Xu, 2012).Therefore, it is unlikely that an unsaturated soil bed can be eroded en mass via liquefaction.Evidently, there must be other mechanisms at play that can contribute to the mass failure of unsaturated soil beds.
Both scouring and mass failure of the soil bed were observed by McCoy et al. (2012) at the field observation station at Chalk Cliff, US.During the observation, erosion sensors were installed in the soil bed to monitor the rate and mechanism of soil bed erosion.The measurements by the erosion sensors show that scouring of the soil bed occurred continuously during the passage of the debris flow, while mass failure of the soil bed also occurred but at a lower frequency.McGuire et al. (2017) developed a numerical model to investigate the competing effects between scouring and mass failure on the erosion process.The numerical model is capable of modeling scouring of the channel sediments and has a feature to enable/disable mass failure.The numerical model was calibrated with field measurements of the initiation of a post-wildfire debris flow.The modeling results show that the computed profile of the depth and solid concentration of debris flow matches field measurements only when both scouring and mass failure are considered in the modeling procedure.Mass failure of channel sediments contributes to the formation of the periodic debris flow surges, which are characterized by sharp increases in flow depth and sediment concentrations.
Field measurements by McCoy et al. (2012) reported an abrupt increase in soil water content measured by transducers buried at depths ranging from 75 to 425 mm in an unsaturated bed just before soil bed material was eroded by a debris flow.Measurements indicate the infiltration of water into the bed as erosion occurred.Existing literature (Assouline, 2013;Haverkamp et al., 1990;McCuen et al., 1981) reported that the infiltration rate in the short term is governed by soil sorptivity S: where e i is the depth of infiltration, t is time, ėi is the rate of water infiltration, K is the hydraulic conductivity of the soil bed, Φ is the porosity of the soil, θ is the volumetric bed water content, and H is the matric suction head at the wetting front, below which infiltration is not noticeable.Soil sorptivity S is a parameter that characterizes the capacity of soil to absorb water through capillarity (McCuen et al., 1981).Sorptivity is a constant for soils with the same porosity, water content, hydraulic conductivity and matric suction under the same water pressure gradient between the soil surface and wetting front.Equation 3a is commonly used in the laboratory to determine the sorptivity of soil.In this method, a soil sample is prepared with a specified porosity and matric suction, and the infiltration depth e i over time t is recorded.Then, the relationship between e i and ̅ ̅ t √ is plotted, and the soil sorptivity is determined by examine the slope of the e i ̅ ̅ t √ curve (Assouline, 2013;Haverkamp et al., 1990;McCuen et al., 1981).Equation 3shows that soil sorptivity (Equation 3d) and infiltration rate (Equation 3c) increase with matric suction owing to an increase in the pressure gradient that drives infiltration.Infiltration of flow water results in an increase in the water content of soil near the surface and changes its unsaturated strength.Therefore, considering the effects of flow infiltration on soil bed erosion is a crucial feature to capture, even though it is not considered in existing erosion models (McCoy et al., 2012;McGuire et al., 2017;Ng et al., 2022;Winterwerp et al., 2012).
In this study, the effects of an unsaturated soil bed, runoff infiltration, and the mechanisms of scouring and mass failure are investigated.

Effects of Runoff Infiltration
Infiltration of water not only changes the water content of a soil bed but also its matric suction and strength (Assouline, 2013;Fredlund et al., 1996;Haverkamp et al., 1990;Ng et al., 2003, see Appendix A for details).Figure 1a shows a conceptual diagram of the distribution of water content with depth in a soil bed subjected to infiltration.At the soil bed surface, there is a thin saturated zone with a thickness of only a few grain diameters.(Assouline, 2013;Haverkamp et al., 1990) and (b) the temporal evolution of the infiltration and Scouring depths with a depth of 0 denoting the soil bed surface.The initial soil water content refers to the soil water content before infiltration.
Beneath this zone, the soil water content decreases with depth to a wetting front, beyond which the soil remains unaffected by infiltration (Assouline, 2013;Hillel, 1982;Ravi & Williams, 1998).
Runoff infiltrates and saturates the soil bed surface (Figure 1a), where scouring occurs (i.e., the upper surface of the saturated zone).Therefore, the critical Shields number (Shields, 1936) can be used to describe the resistance of an initially unsaturated soil bed to scouring as the surficial soil particles are saturated by the infiltrated flow.Furthermore, runoff infiltration increases the water content and the unsaturated strength of the soil between the soil bed surface and the wetting front (Appendix A).Consequently, the wetting front is a weak interface with a lower unsaturated strength and resistance to mass failure compared to the soil above it.This weak interface has the least resistance to erosion along the cross-section perpendicular to the slope surface.Therefore, mass failure is prone to initiate at the wetting front when the hydrodynamic shear stress exceeds the unsaturated soil strength at the wetting front.

Scouring
The three-layer erosion model proposed by Iverson (2012) can be recast to quantitatively describe the scouring of soil beds induced by hydrodynamic shear stress.The three-layer model is formulated based on the conservation of momentum.The model proposes that the erosion rate is dictated by the pressure gradient at the interface between the flow and soil bed.Specifically, erosion of soil bed material is governed by the difference between the shear stress exerted by the flow τ h and the resistance of the surficial soil layer to scouring τ s .The momentum conservation of the soil material to be eroded dictates the erosion rate ė of soil bed to be written as: where ρ b is the density of the soil bed and u is the flow velocity.
In the context of soil bed scouring by the hydrodynamic shear stress, the basal shear stress that drives scouring can be calculated using Equation 1.Because the soil near the bed surface is saturated by the runoff infiltration, the resisting mechanism against scouring can be estimated using the critical Shields number Θ c (Prancevic et al., 2014;Shields, 1936): where τ ch is the critical hydrodynamic shear stress that is required to initiate scouring.The eroded soil bed material is assumed to gain the same velocity as that of the flow (Same as the assumption adopted by Iverson (2012)).Thus, the scouring rate can be calculated as: where u is the flow velocity, ės is the scouring rate, which has the same dimension as velocity.
The diameter of a soil particle used in this study, which ranges from 0.1 to 0.3 mm, is small so that the critical hydrodynamic shear stress is negligible compared to the basal hydrodynamic shear stress exerted by the flow.Therefore, it is assumed that all of the impulse exerted by the hydrodynamic shear stress is consumed to accelerate the eroded soil bed material.This assumption is further validated in Section 4. As such, the second term on the right-hand side of Equation 6 can be ignored in the formulation of the scouring rate: where ρ is the ratio of flow density to soil bed bulk density.Equation 7shows that the scouring rate increases with hydrodynamic shear stress and flow velocity.Additionally, scouring is independent of the initial water content of the soil bed because of the saturated zone formed by the runoff infiltration at the bed surface.

Mechanism of Mass Failure
The concepts of infinite slope (Teunissen & Spierenburg, 1995) can be borrowed to interpret the mechanism of mass erosion.Runoff infiltration increases the water content and unsaturated strength of the soil above the wetting front (see Appendix A for details about the effects of water content on the unsaturated soil strength).Therefore, runoff infiltration increases the strength of the soil bed above the wetting front and makes the wetting front a weak interface.As the hydrodynamic stress increases, soil failure is likely to be first initiated at the wetting front.Therefore, unlike scouring, mass erosion of soil bed is less likely to be driven by the pressure gradient at the soilbed interface, and the difference between the hydrodynamic shear stress and the unsaturated soil strength at the wetting front governs whether mass erosion will occur and the amount of mass erosion.
However, the formulation of an analytical expression of mass erosion rate remains challenging.Specifically, the resistance to mass erosion, that is, unsaturated soil strength at the wetting front, varies nonlinearly with the depth of runoff infiltration and soil matric suction (Equation A2).Furthermore, the infiltration depth needs to be calculated using soil sorptivity and matric suction by using the iteration technique (Equations 3a-3d).Therefore, further research using numerical models is required before the quantitative expression of the mass erosion rate can be formulated.Because of the difficulties in the quantitative formulation of the mass erosion rate, a qualitative description of mass erosion is given in this section.
Two conditions are necessary for mass failure of the soil bed to occur.First, a wetting front moves beneath the soil bed surface to form a potential weak interface, where mass failure is prone to occur.Specifically, the runoff infiltration rate must be larger than the scouring rate.As such, the wetting front propagates beneath the soil surface and creates a potential weak interface.The water infiltration rate decreases with water content (Equations 3b and 3c).Therefore, there exists a critical soil water content that governs the occurrence of the mass failure of the soil bed.Above the critical soil water content, the infiltration rate is smaller than the scouring rate, no wetting front is formed, and mass failure does not occur.Second, the hydrodynamic shear stress must be sufficient to initiate soil failure at the wetting front and mobilize the soil block above it.

Net Infiltration Depth Is an Indicator to the Rate of Soil Bed Erosion by Mass Failure
When the soil bed is eroded by mass failure, the distance between the soil surface and the wetting front indicates the amount of soil available to be eroded by mass failure.Figure 1b shows a conceptual diagram of infiltration and scouring depths with time as a wetting front moves into a soil bed.The shaded gray zone represents the change in the distance between the soil surface and the wetting front.The net infiltration depth e ni is defined as the area of the gray zone divided by the time scale T 0 (as shown in Figure 1b): The net infiltration depth describes the average distance between the soil bed surface and the wetting front and quantifies the amount of soil mass available to be eroded en masse.Therefore, the erosion rate of soil bed by mass failure is positively related to the net infiltration depth.

Bilinear Relationship Between the Flow Velocity and the Mass Erosion Rate
The hydrodynamic shear stress exerted by a flow increases with the flow velocity (i.e., Equation 1).However, the net infiltration depth decreases with the flow velocity (Equation 8), and the soil mass available to be eroded via mass erosion decreases with the flow velocity.Consequently, it can be proposed that the soil bed erosion rate due to mass failure exhibits a bilinear relationship with the flow velocity and peaks at a critical flow velocity.Below the critical flow velocity, there is sufficient soil mass above the wetting front, while the hydrodynamic shear stress is insufficient to erode the soil mass.In turn, the mass erosion rate, which can be calculated as the difference between the measured erosion rate and the scouring rate, is governed by the amount of soil mass that the hydrodynamic shear stress can mobilize.The mass failure process is then transport-limited and its rate increases with hydrodynamic shear stress as the flow velocity increases.Above the critical flow velocity, the hydrodynamic shear stress is sufficient to erode all the soil mass above the wetting front and the mass erosion rate is limited by the net infiltration depth.In turn, the mass erosion rate decreases with net infiltration depth as the flow velocity increases, and the mass failure process is supply limited.

Experiment Setup and Test Program
Physical experiments were carried out with a flume (Figure 2), which has a length of 3 m and a width of 0.2 m.The flume adopts a typical configuration for modeling debris flows (De Haas et al., 2015;De Haas & Woerkom, 2016;Ng et al., 2017).A storage container, which has a length of 0.7 m, a width of 0.2 m and a height of 0.4 m, is installed at the upstream end of the flume.To simulate dam break initiation, the material in the storage container was released using a pneumatically controlled gate that was lifted vertically.The channel bed consists of a nonerodible section to accelerate the flow, which then travels over an erodible section of unsaturated soil.The nonerodible section has a length of 1.45 m.The erodible section has a length and depth of 0.85 and 0.072 m, respectively.At the downstream end of the flume, the flow is collected with a tank to ensure that it does not influence the kinematic and dynamic properties of the ensuing flow.
A volume of 0.02 m 3 of water was released from the storage container to simulate runoff, which exerts hydrodynamic shear stress to erode the unsaturated soil bed.Iverson (1997) showed that the viscosity of the fluid component in a debris flow ranges from 0.001 Pa•s to 0.1 Pa•s, and the viscosity of water is 0.001 Pa•s.Thus, the hydrodynamic shear stress exerted by water flow provides a lower bound for the hydrodynamic stress exerted by the liquefied body and tail of debris flow.
The erodible bed was prepared using Toyoura sand, and the particle size ranged from 0.1 to 0.3 mm.The friction angle of Toyoura sand is 31° (Kajiyama et al., 2017).The erodible bed was prepared with a target porosity of 0.47 and target dry density of 1,400 kg/m 3 .The water content of the erodible bed was prepared to change from 5.6% to 34.4%.The modeled slope ranged from 3°to 35°to model the erosion of soil bed on slopes with a broad range.A summary of the test program is given in Table 1.

Instrumentation and Data Processing
A high-speed camera that captures images with a resolution of 1920 by 720 at a frame rate of 1,000 frames per second was installed at the side of the erodible section to capture the flow and erosion kinematics through a clear acrylic sidewall.An ultrasonic sensor was mounted above the bed interface between the non-erodible and erodible sections to measure the flow depth.An ultrasonic sensor with a sampling rate of 2,000 Hz was mounted along the centerline of the flume on the non-erodible bed adjacent to the interface between the non-erodible and erodible sections.The measured flow depth is used to deduce the characteristic depth of the flow.After each experiment, the erosion depth was measured by using a laser sensor.The erosion depth was calculated as the difference in elevation of the soil bed before and after each experiment.The erosion depth was measured at 81 points, which were uniformly distributed over the erodible section.The points formed a 3 × 27 array with a spacing of 30 mm in the flow direction and 50 mm in the transverse direction.
The erosion depth was calculated by averaging the depths at the 81 measurement points.Based on high-speed camera imagery, the erosion rate was calculated by dividing the erosion depth by the erosion duration.
Because the flow depth varied spatiotemporally, a characteristic flow depth was determined by using time-series measurements from the ultrasonic sensor.The characteristic flow depth h f was calculated as an average of the flow depth over the period that erosion occurs (Lamb et al., 2008;Prancevic et al., 2014): where T is the erosion duration.The characteristic flow velocity u is calculated based on mass conservation (Prancevic et al., 2014): where V is the volume of the discharged flow and B is the channel width of the flume.A detailed description of how the erosion depth and erosion duration were deduced is shown in the Supporting Information S1.
The hydrodynamic shear stress τ h exerted on the soil bed was calculated by using Equation 1 based on the friction factor, flow density and the flow velocity.The friction factor C f is determined based on the empirical equation proposed by Lim (2018): where Re is the flow Reynolds number, and n is an empirical factor, the suggested value of which is 0.018 for the soil bed (Lim, 2018).Equation 11is proposed to describe the unsteady open channel flow and is fitted with the laboratory data.The flow Reynolds number Re was calculated as: where ρ f is the density of the model flow and μ is the dynamic viscosity of the model flow.In this study, ρ f = 1,000 kg/m 3 and μ = 1 mPa•s because water flow was used to model the runoff.
The critical hydrodynamic shear stress τ ch , which is required for the initiation of soil bed scouring, was calculated based on Equation 5.The shield number on different slope was determined based on the Shields diagram (Prancevic et al., 2014), and D 50 was adopted as the characteristic particle size of the soil bed in the calculation.The sediment concentration ϑ, which is defined as the ratio of the volume occupied by soil particles within the flow to the total volume of the flow, is estimated as: where e is the total erosion depth, A is the area of the erodible section (0.2*0.85 m 2 ), ρ b is the bulk density of the soil bed, ρ s is the density of the soil particles and V f is the volume of the released flow (0.02 m 3 ).
The soil sorptivity that governs the infiltration of flow water into the soil bed was deduced by the iteration method using Equation 3. Specifically, the matric suction, soil water content, and the matric suction at the wetting front are assumed to be constant in each step during iteration.Then, trial and error is used to determine the total infiltration depth e i and infiltration rate ėi based on Equation 3d.Finally, the relationship between e i and ̅ ̅ t √ can be plotted, and the soil sorptivity is determined as the slope of the e i ̅ ̅ t √ curve.The soil properties required for the calculation of soil sorptivity are summarized in Table 1.

Observed Erosion Mechanisms
The kinematics of the model flow over an erodible bed was captured by using the high-speed camera at the side of the flume.The characteristic flow velocity, flow depth, erosion depth, erosion rate, and erosion duration were obtained by using the methods described in Section 3.2.A summary of the flow and erosion measurements is given in Table 2.  5), which is required to initiate scouring, to the hydrodynamic shear stress exerted by the model flow (Equation 1).The normalized critical shear stress in all experiments was calculated and plotted.
Scouring was observed in all experiments.During scouring, eroded soil at the bed surface was carried away by the flow.Figure 3 shows the normalized critical shear stress based on the experimental measurements.The normalized critical shear stress is defined as the ratio of the critical hydrodynamic shear stress τ ch (Equation 5), which is required to initiate scouring, to the hydrodynamic shear stress exerted by the model flow (Equation 1).Θ c at different slopes were acquired from the diagram reported by Prancevic et al. (2014) and the Θ c increases with slope.The normalized critical shear stress describes the proportion of the exerted impulse that is consumed to initiate scouring.It was observed that less than 2% of the impulse exerted by a model flow was consumed to initiate scouring, which means that nearly all of the exerted impulse was consumed to accelerate the eroded soil particles.The negligible impulse required to initiate scouring is due to the small grain size of the soil used in this study, which also explains why scouring was observed in all experiments.This observation confirms the assumption, which states that the critical hydrodynamic shear stress in the formulation of the scouring rate in Equation 5 is negligible, is valid.Mass failure was only observed in experiments with soil water contents of 5.6% and slopes greater than 5°.
Figure 4 shows a comparison of the erosion processes for soil beds with 5.6% water content and slopes of 5°( Figure 4a), 20°(Figure 4b), and 35°(Figure 4c). Figure 5 shows the images captured in the experiment carried out with 34.4% soil water content and on 25°slope.Mass erosion was not observed in the experiment carried out with 34.4% soil water content.In experiments carried out with 5.6% soil water content, the rate of runoff infiltration was larger than the scouring rate, and the wetting front moved into the soil beds.However, when experiments were conducted with a soil water content of 34.4% and slopes ranging from 5°to 30°, the runoff infiltration rate was smaller than the scouring rate, and the wetting front did not move beneath the soil surface (as shown in Figure 5).Consequently, no weak interface was created within the soil bed, and mass failure did not occur.This phenomenon confirms the validity of the proposed critical soil water content.Specifically, when the soil water content was above the critical value, the soil had low sorptivity, and the infiltration rate was smaller than the scouring rate on the same given slope.As a result, no potential weak interface developed to initiate mass failure.Additionally, as can be observed in Figure 4, the distance between the soil surface and wetting front decreased with slope, which agrees with the prediction of Equation 8.This is because the scouring rate increases with flow velocity while the infiltration rate is not sensitive to the change in flow velocity.Consequently, the net infiltration depth, which is the distance between the soil surface and the wetting front, decreases with flow velocity.
Figure 4b shows a typical observed mass failure process where soil mass failure initiates at the wetting front.The soil mass above the wetting front was lifted upwards by the ensuing flow as a block and then carried downstream.This process agrees with the postulation that the wetting front develops a weak interface where the mass failure of a soil bed is prone to occur.The shift of the controlling variable for mass failure from hydrodynamic shear stress to net infiltration depth as the flow velocity increases can be observed by comparing experiments with 5°( Figure 4a) and 35°(Figure 4c) slopes.The shift of the controlling variable of mass failure roots in the increase in the hydrodynamic shear stress and decrease in net infiltration depth as the flow velocity increases.Specifically, in the 5°slope experiment, mass failure only occurred when the model flow initially overrode the soil bed.However, the net infiltration depth increased with time to a magnitude where the hydrodynamic shear stress was insufficient to mobilize the soil mass above the wetting front.As a result, the wetting front was observed to move deep into the bed (Figure 4a), but mass failure was not observed due to insufficient hydrodynamic shear stress.Hence, mass failure here was a transport-limited process on a 5°slope, where the mass erosion rate was determined by the amount of soil mass that the hydrodynamic shear stress can mobilize.Conversely, on a 35°slope, the hydrodynamic shear stress was capable of eroding all the soil mass above the wetting front.However, the infiltration rate was nearly the same as the scouring rate, and the wetting front was close to the soil bed surface (Figure 4c).Therefore, mass failure was a supply limited process on a 35°slope.The mass erosion rate was determined by the net infiltration depth and the amount of soil mass above the wetting front, that is, the amount of soil available to be eroded by mass failure.
The net infiltration depth can be calculated based on Equations 3 and 8 for each experiment.Figure 6a shows the infiltration depth against the square root of time to deduce the sorptivity of unsaturated soils based on Equation 3. The calculated sorptivity for soil with 5.6% and 34.4% water contents were 13.4 mm/s 0.5 and 4.6 mm/s 0.5 , respectively.The calculated sorptivity shows that the rate of flow water infiltration decreases with soil water content.This trend is because water infiltration is governed by sorptivity in the short term (i.e., in the order of a few seconds).Sorptivity decreases as soil water content increases (Equation 3) (Assouline, 2013;Haverkamp et al., 1990).Consequently, soil sorptivity and infiltration rate decrease with soil water content.Figure 6b shows the temporal change in the runoff infiltration and scouring depths.It is evident from Figure 6b that the net infiltration depth in experiments with 34.4% soil water content is negligible compared to that in experiments with 5.6% soil water content on the same slope.This observation aligns with the fact that the wetting front did not propagate beneath the soil surface, and mass failure of the soil bed was not observed in experiments with 34.4% soil water content.Additionally, Figure 6b shows a plot of the scouring depth and runoff infiltration depth against time.The gray area represents the evolution of the distance between the soil surface and wetting front in the experiment carried out with 5.6% water content on an 8°slope.It is evident from Figure 6b that, with the same soil water content, the height of the gray area, that is, the distance between the soil surface and the wetting front, decreases with the slope because the scouring rate increases with the slope.This means that the soil mass available for erosion by mass failure, that is, the soil mass above the wetting front, decreases with the low velocity.

Effects of Slope and Soil Water Content on the Measured Erosion Rate
Figure 7 shows the correlation between the measured erosion rate and slope.The erosion rate of soil beds with 5.6% and 34.4% water contents increases with slope because the hydrodynamic shear stress that drives soil bed erosion increases with slope in this study.Furthermore, the erosion rate of soil with 5.6% water content is larger than that with 34.4% water content on slopes greater than 5°.This is because mass failure occurs in experiments with 5.6% soil water content and slopes that are greater than 5°.In these experiments, water infiltrates faster than the scouring rate, and the wetting front moves beneath the soil bed surface.This leads to mass failure induced at the wetting front by hydrodynamic shear stress.Mass failure of the soil bed caused an increase in the measured erosion rate.In contrast, the hydrodynamic shear stress is insufficient to induce mass failure at the wetting front in experiments with slopes smaller than 5°.Therefore, mass erosion does not occur although the wetting front is observed to move beneath the bed surface.
For experiments with 34.4% water content, infiltration is slower than the scouring rate because of the low sorptivity (Equation 3).Therefore, no wetting front is observed to move beneath the bed surface, and no interface is formed.Consequently, mass failure is not observed.This confirms the existence of a critical soil water content between 5.6% and 34.4% for Toyoura sand.When the soil water content is below the critical value, the flow infiltrates faster than the scouring rate.Consequently, the wetting front moves beneath the soil bed surface and forms a weak interface where mass failure is prone to initiate.This study demonstrates that runoff infiltration-induced mass failure can enhance soil bed erosion, especially when the soil water content is below a critical value.Both erosion mechanisms of scouring and mass failure should be captured to yield close predictions of soil bed erosion.

Effects of Hydrodynamic Shear Stress on the Measured Erosion Rate
Figure 8 shows the relationship between the hydrodynamic shear stress, which drives soil bed erosion, and the erosion rate of the soil bed.For experiments with soil water contents of 34.4% and 5.6%, when the slope is less than 5°, mass failure was not observed.Therefore, scouring is the only erosion mechanism in these experiments, and the measured erosion rate equals the scouring rate.For experiments carried out on 5°slope, the erosion rate of the soil bed with a water content of 34.4% was lower than that with a water content of 5.6% (Table 2).This is because the hydrodynamic stress was slightly lower in the experiments carried out with 34.4% soil water content than that with 5.6% soil water content.However, the data points obtained in experiments with these two soil water contents collapsed onto a single trendline with a correlation factor of 0.99, which means that scouring of soil with  different water contents can be described with a single fitting equation.This means that the erosion rate of soil with different soil water content is approximately the same if the imposed hydrodynamic shear stresses are the same.Therefore, it can be demonstrated that the scouring rate obtained in these experiments exhibits a linear relationship with the hydrodynamic shear stress.This finding indicates that scouring is independent of soil water content because the soil at the bed surface quickly becomes saturated, regardless of its initial water content, when the flow overrides it.The proposed linear trendline agrees with the prediction that the scouring rate increases linearly with the hydrodynamic shear stress.The linear trendline intersects the origin, implying that the critical shear stress required to initiate soil bed scouring is negligible due to the small size of the soil particles used in this study.
Because the soil near the bed surface is quickly saturated when flow overrides it, the scouring rate is not sensitive to the soil water content, and soil with 5.6% and 34.4% water content exhibit the same scouring rate at the same slope.Consequently, the mass erosion rate can be calculated by subtracting the measured erosion rate of soil with 34.4% water content from that of soil with 5.6% water content at the same slope.A bilinear relationship between the mass erosion rate and the hydrodynamic shear stress exerted by the flow can be observed.Specifically, the mass erosion rate increases with the hydrodynamic shear stress when the slope is less than 20°and decreases with the hydrodynamic shear stress when the slope is larger than 20°.The bilinear relationship indicates that the controlling factor for mass failure changes from hydrodynamic shear stress to net infiltration depth, and the mass failure changes from a transport-limited process to a supply limited process (to be discussed later with Figure 9).

Bilinear Relationship Between the Flow Velocity and Mass Failure
Figure 9 shows that the hydrodynamic shear stress increases with the flow velocity.In contrast, the net infiltration depth decreases with the flow velocity because the scouring rate increases with the flow velocity, while the infiltration rate is not sensitive to the change in the flow velocity.The mass erosion rate increases with the flow velocity until a peak value is reached at a critical flow velocity, after which the mass erosion rate decreases with the flow velocity.The critical flow velocity is between 2.5 m/s and 2.8 m/s.Below the critical flow velocity, the hydrodynamic shear stress is insufficient to erode all the soil mass above the wetting front.The mass erosion rate is determined by the amount of soil mass that the induced hydrodynamic shear stress can mobilize.Therefore, below the critical flow velocity, mass failure is a transport-limited process where the mass erosion rate increases with hydrodynamic shear stress as the flow velocity increases.In contrast, above the critical flow velocity, mass failure is a supply limited process, where the hydrodynamic shear stress is sufficient to erode all the soil mass above the wetting front due to a shallow net infiltration depth.The mass erosion rate is determined by the amount of soil mass above the wetting front, which is governed by the net infiltration depth.This finding shows that the hydrological properties of a soil bed govern its mass failure.A more realistic mechanistic erosion model necessitates the consideration of the coupled hydrological-mechanical behavior of soil.

Discussion
Current mechanistic models (Armanini et al., 2009;Capart & Young, 1998;Egashira et al., 2001;Fraccarollo & Capart, 2002;Hungr, 1995;Iverson, 2012;Liu et al., 2013;Medina et al., 2008;Takahashi, 1978) have provided a solid foundation for understanding soil bed erosion.However, these models assume a saturated soil bed and ignore flow water infiltration, which contradicts that reported from the field by McCoy et al. (2012).This  study demonstrates that considering unsaturated soil, runoff infiltration, and the mechanisms of scouring and mass failure can enhance our current understanding of the soil bed erosion process.
As discussed in Section 2.3, the quantitative analytical description of the mass erosion rate is hindered by the nonlinear dependence of the unsaturated soil strength on the infiltration rate and the matric suction.Furthermore, it is challenging to measure the distribution of the water content of soil between the soil bed surface and the wetting front using laboratory-scale physical experiments, which hinders a more in-depth analysis of the mass failure process.Therefore, further investigation of the mass erosion process should rely on numerical modeling (e.g., Thomas et al., 2021) to solve the highly nonlinear runoff infiltration equation and the mechanical response of unsaturated soil.
Hyperconcentrated flow is defined as the intermediate regime between flood, the sediment concentration of which does not exceed 4%, and debris flow, the sediment concentration of which is larger than 60%.The sediment concentration of the flow in this study ranges from 4.2% to 13%, which is within the range of sediment concentration for hyperconcentrated flows.A water-sand mixture behaves as a Newtonian fluid when the sand concentration is below 35% (Fei, 1983).Therefore, it is reasonable to assume that the eroded sand did not significantly influence the mechanical properties of the flow.
The depth of flow in the field can be up to several meters (Berger et al., 2011;McArdell et al., 2007;McCoy et al., 2012).The difference in flow depth between the model and prototype does not raise scaling issues for the scouring rate (Equation 6), which increases linearly with the flow density and velocity.However, the mass erosion rate is governed by the net infiltration depth, which is governed by soil sorptivity (Equation 3).Sorptivity increases with the water pressure gradient between the soil surface and the wetting front.The water pressure at the soil surface and the water pressure gradient increase with flow depth, resulting in an increase in the net infiltration depth.However, the nonlinear relationship between the water pressure gradient and sorptivity presents a challenge in determining the correlation between the flow depth and net infiltration rate.Further research that investigates scaling issues that arise from mass failure by using largerscale models is warranted.
The rate of flow infiltration decreases as the water content increases, and the critical soil water content is the water content with which the rate of flow infiltration equals that of scouring.Consequently, changes in test conditions that increase the scouring rate, that is, increase in slope and flow velocity, will result in a reduced critical soil water content.The volume of the released flow can also influence the critical soil water content by changing the velocity of the released flow.
This study investigates the erosion of unsaturated sandy beds with particle sizes ranging from 0.1 to 0.3 mm by hydrodynamic shear stress.If the particle size of the bed increases, the capillary phenomenon would be less significant, and matric suction would play a less critical role in contributing to unsaturated soil strength.As a result, runoff infiltration does not significantly strengthen the soil mass above the wetting front, and the wetting front may not act as a weak interface.Consequently, the mechanism of mass failure described in Section 2.3 may contribute less to bed material erosion.When the particle size of the bed material increases to the centimeter scale, the erosion process can be described with the conventional fluvial sediment transport model (Lamb et al., 2008;Prancevic et al., 2014;Shields, 1936).The conventional fluvial sediment transport model uses the Shields number and a slope to determine the erosion mechanisms of the bed sediments.Mass failure occurs when the Shields number and a slope simultaneously exceed their thresholds.Conversely, if the particle size of the soil bed decreases, the infiltration rate and soil mass above the wetting front decrease along with the mass erosion rate.Further research can explore the effects of soil particle size on the soil bed erosion mechanism and identify the soil particle size range in which mass erosion contributes to soil bed erosion.
Further research can be carried out to investigate the mechanism by which the sediment concentration accumulates within runoff.The accumulation of the eroded sediments contributes to the transition of runoff into a debris flow when the sediment concentration exceeds a critical threshold.However, reliable real-time monitoring of the sediment concentration within the flow in both physical experiments and field observations is needed.

Conclusions
In this study, we investigated the effects of an unsaturated soil bed, flow infiltration and different erosion mechanisms on the soil bed erosion.The conclusions may be drawn as follows: 1.In this study, the erosion of an unsaturated soil bed was investigated by considering unsaturated soil mechanics, flow water infiltration, and different erosion mechanisms including scouring and mass failure.A unique set of flume experiments, which examined the effects of soil water content and flow velocity on the erosion of the soil bed, were carried out.This study shows that current understanding of soil bed erosion by hydrodynamic stress can be enhanced by considering unsaturated soil mechanics, flow water infiltration, and different erosion mechanisms.2. Infiltration of flow water creates a saturated zone directly at the bed surface, resulting in the scouring rate being largely insensitive to the initial soil water content.Furthermore, flow water infiltration creates a potential weak interface at the wetting front, where mass failure is prone to initiate.This finding highlights the importance of considering unsaturated soil mechanics and coupled hydrological-mechanical behavior of the soil in predicting soil bed erosion and the volume growth of debris flows.3. The scouring rate increases with the hydrodynamic shear stress and the flow velocity.Mass failure occurs when the flow infiltrates faster than the scouring rate to create a potential weak interface at the wetting front.Furthermore, the hydrodynamic shear stress must be sufficient to initiate soil failure at the wetting front.This finding highlights the necessity of incorporating different erosion mechanisms into debris flow mobility models that aim to depict erosion processes.4. Soil water content governs the mass failure of unsaturated soil beds by changing the flow water infiltration rate and net infiltration depth.An increase in soil water content results in a decrease in flow water infiltration rate and net infiltration depth.Therefore, there exists a critical soil water content, whereby mass failure does not contribute to soil bed erosion above the critical value.An increase in slope or flow velocity, which increases the scouring rate, results in a decrease in the critical soil water content for mass failure to occur.This finding shows that existing studies that do not consider the mass failure mechanism may underestimate the erosion of the soil bed with water content lower than the critical value.5.The mass erosion rate of the soil bed exhibits a bilinear relationship with the flow velocity.There is a critical flow velocity at which the governing factor of mass failure changes from hydrodynamic shear stress to net infiltration depth.A bilinear relationship between mass failure and the flow velocity is discovered.This finding advances state-of-the-art research about soil bed erosion.Due to the highly non-linear relationship between the soil properties and the soil resistance to mass erosion, it remains challenging to formulate an analytical expression for mass erosion rate.Further research can use numerical modeling to formulate a generalizable theoretical framework for soil bed erosion and provide scientists and engineers with a mechanical-based tool to assess soil bed erosion.
atmospheric pressure, and the difference between the atmospheric pressure and the negative pore water pressure is denoted as the matric suction (Fredlund & Rahardjo, 1993).The positive pore water pressure within saturated soil tends to repel adjacent soil particles and reduces the effective stress and the saturated soil strength.However, the negative pore water pressure within unsaturated soil holds adjacent soil particles together and provides additional strength for unsaturated soil.The capillary effects are more significant within soil with lower water content and result in the matric suction decreasing with the soil water content.The strength of unsaturated soil can be expressed as (Fredlund & Rahardjo, 1993): where p a is the pore air pressure, S r is the degree of saturation and κ is a constant.The additional unsaturated soil strength provided by matric suction, that is, the second item on the right side of Equation A2, is determined by the matric suction (p a p w ) and the soil saturation S r , which indicates the contact area between the soil particles and the pore water.
In the extreme cases where the soil is dry or fully saturated, the expression for unsaturated soil strength, that is, Equation A2, degrades to that for saturated soil strength, Equation A1 (Fredlund et al., 1996).Specifically, when the soil is nearly dry, matric suction is infinite, while the contact area between the pore water and soil particles, which is quantified by the degree of saturation, is nearly zero.Consequently, matric suction does not contribute to the unsaturated soil strength, and the second item on the right side of Equation A2 equals 0. Furthermore, when the soil is fully saturated, the pore water pressure is non-negative, and matric suction does not provide additional strength to the soil.When the soil is partially saturated, the matric suction provides additional strength for the soil, and its strength is larger than that of nearly dry soil and fully saturated soil.

Figure 1 .
Figure 1.Conceptual diagram of (a) the distribution of soil water content and unsaturated soil strength with depth between the soil bed surface and wetting front(Assouline, 2013;Haverkamp et al., 1990) and (b) the temporal evolution of the infiltration and Scouring depths with a depth of 0 denoting the soil bed surface.The initial soil water content refers to the soil water content before infiltration.

Figure 2 .
Figure 2. Side view of the experiment setup (Choi & Song, 2023).The figure is reused by the courtesy of Engineering Geology.

Figure 3 .
Figure 3. Variation of the normalized critical shear stress with slope.The normalized critical shear stress is defined as the ratio of the critical hydrodynamic shear stress τ ch (Equation5), which is required to initiate scouring, to the hydrodynamic shear stress exerted by the model flow (Equation1).The normalized critical shear stress in all experiments was calculated and plotted.

Figure 4 .
Figure 4. Comparison of the erosion processes on different slopes: (a) α = 5°; (b) α = 20°; (c) α = 35°; Soil water content is 5.6% in each experiment.t is the time normalized by the erosion duration T. t = 0 denotes the time that a flow arrives at the interface between the non-erodible and erodible sections.

Figure 5 .
Figure 5. Erosion of soil bed with 34.4% soil water content on 25°slope: (a) t = 0.4 s; (b) t = 0.8 s; (c) t = 1.2 s. t = 0 denotes the time that a flow arrives at the interface between the non-erodible and erodible sections.

Figure 6 .
Figure 6.(a) Calculation of the soil sorptivity based on Equation 3; (b) Temporal evolution of scouring depth and infiltration depth with time.

Figure 7 .
Figure 7. Effects of slope on the measured erosion rate of a soil bed with water contents θ of 5.6% and 34.4%.

Figure 9 .
Figure 9. Bilinear relationship between the mass erosion rate and flow velocity, together with the plot of hydrodynamic shear stress and net infiltration depth against the flow velocity.Data plotted are experiments, in which mass erosion was observed, that is, θ = 5.6%, 8°∼ 35°slope.

Table 1
Test Program and Bed Properties In the test ID, "B" denotes soil bed water content, "S" denotes slope and "R" denotes the repeated experiments.
SONG ET AL.

Table 2
Measured Flow Properties and Soil Bed Erosion SONG ET AL.