Growth of Debris Flows by Soil Bed Erosion: Effects of Frictional and Hydrodynamic Shear Stresses

. Debris flows are complex solid-fluid mixtures, which travel downslope under the influence of gravity. The destructive potential of a debris flow is governed by its volume and speed, both of which can be significantly enhanced by the erosion of soil bed material along the flow path. Existing friction-induced erosion theories simplify a debris flow as an equivalent fluid that induces frictional shear stress on a soil bed. Erosion occurs when the frictional stress exceeds the soil strength. Research also shows the importance of hydrodynamic stresses on the erosion of soil beds. However, the mechanism of soil bed failure under the influence of frictional and hydrodynamic shear stresses is not clear. In this extended abstract, some experimental flume test results are presented. The tests simulate the erosion of soil beds by dry sand flow and water flow to evaluate the effects of frictional and hydrodynamic shear stresses imposed on a soil bed, respectively. Findings from this research can be used to improve estimates of erosion of debris flows in mountainous regions, which will strengthen hazard assessments.


Introduction
Debris flows surge downslope under the influence of gravity. They are often reported to cause fatalities and damage infrastructure [1]. The destructive potential of a debris flow is governed by its volume and velocity, which may be enhanced by the erosion of soil bed material [2]. Therefore, understanding the mechanics of soil bed erosion is crucial to improved predictions of the travel distance.
One of the most important aspects of existing theoretical representations of soil bed erosion is identifying the principal driving stress. The commonly adopted depth-average soil bed erosion models [2][3] simplify a debris flow as an equivalent fluid, which induces frictional shear stress at the flow-bed interface. Consequently, bed material fails and is eroded when the interface frictional stress is larger than the strength of the soil. Research [4][5] shows that the hydrodynamic shear stress exerted by the fluid phase of a flow also causes soil bed erosion [5][6].
Research in granular mechanics shows that the frictional shear stress originates from the enduring contact between solid particles, while the hydrodynamic shear stress is caused by a fluid shearing against a surface [6]. Given that debris flows are complex mixtures of fluid and solids [1], the hydrodynamic and frictional shear stresses both play a vital role in erosion. However, the mechanism of soil bed failure under the influence of hydrodynamic and frictional shear stresses remains elusive.
In this extended abstract, details of physical experiments that model soil bed erosion caused by * Corresponding author: cechoi@hku.hk predominately frictional shear stress and hydrodynamic shear stress are described.

Physical modelling of soil bed erosion
Physical modelling was carried out using a flume ( Fig.  1) to compare the soil bed erosion caused by the frictional and hydrodynamic shear stresses. The flume has a length of 2.5 m and a width of 0.2 m. A storage container with a length of 0.5 m, width of 0.2 m and depth of 0.5 m is installed at the upstream end of the flume. Flow material with a volume of 0.02 m 3 is stored in the container for each experiment, and the material is released by triggering the pneumatically-controlled gate. The released material accelerates down the 1.3-mlong rigid section of the channel bed and then erodes the soil prepared in the 0.7-m-long and 0.17-m-deep erodible section of the channel. A thin layer of Toyoura sand is affied to the surface of the rigid section to create a similar roughness as the erodible bed, which consists of Toyoura sand with a volumetric water content of 5%.
Two experiments are carried out with a slope of 30°. One experiment use water as the flow material, which is expected to exert predominantly hydrodynamic shear stress on the soil bed. The other experiment uses dry Toyoura sand as the flow material, which is expected to exert predominantly frictional shear stress on the soil bed. Toyoura sand has a grain size ranging from 0.1 mm to 0.3 mm, which is fine enough to exclude the influence of collisional stresses induced on the soil bed [7].

Instrumentation
An ultrasonic sensor is mounted directly above the interface between the rigid and erodible sections in each experiment. The ultrasonic sensor has a sampling frequency of 2000 Hz and is used to measure the flow depth. A high-speed camera is installed at the side of the flume to capture the flow kinematics on the erodible bed during each experiment. The camera captures images at a rate of 1000 frames per second. The images are analysed using Particle Imaging Velocimetry (PIV) [8] to deduce the velocity fields of the flow.
To measure the erosion depth, 12 erosion columns are installed in the erodible beds (Fig. 2). The erosion columns are washers stringed through a threaded column and the column of washers is prepared to have the same height as the erodible bed before each test. Just before each experiment, the screw columns are removed without disturbing the washers. When the flow overrides the soil bed, the washers near the surface are carried away. Then, the erosion depth can be deduced from the difference in of the columns before and after each experiment. The washers forming the erosion columns are 304 stainless steel, which has a friction coefficient of 0.58 (Bernoulli et al., 2018). The internal frictional coefficient is 0.6, which is slightly higher than that of the washers.

Test results
The profiles of the erosion depth in the two experiments are compared in Fig.3. It is evident that Toyoura sand flow does not erode the soil bed much. The negligible erosion may be from the large shear strength of the soil bed contributed by matric suction. However, significant soil bed erosion is observed in the experiments with water flow. The erosion depth is most obvious near the interface between the rigid and erodible beds. Then, the erosion depth decreases with the distance from the interface between the rigid and erodible beds. The water flow in contact with the soil bed can destroy the matric suction within the soil bed and decrease the soil resistance. Thus, the hydrodynamic shear stress can erode a significant amount of soil bed material. Existing studies on the erosion of soil bed by debris flows rely on an equivalent fluid assumption, which assumes that debris flow imposes frictional shear stress at the flow-bed interface. However, this study shows that an equivalent fluid assumption is highly idealised. Moreover, the infiltration of water into the soil bed is overlooked in current studies. Infiltration changes the matric suction of the soil bed, which affects its shear strength.

Conclusions:
Physical experiments are carried out to compare the erosion caused by flows with predominately frictional and hydrodynamic shear stresses. Some findings can be drawn as follows: (1) Toyoura sand flow, which impose predominately frictional shear stress on a soil bed, barely induces any soil bed erosion. However, significant erosion is observed in the experiments with water flow, which predominately impose hydrodynamic shear stress on the soil bed.
(2) Under the influence of matric suction, the strength of soil bed is larger than the frictional shear stress imposed by the dry sand flow. As such, frictional shear stress is not effective at eroding the soil bed.
(3) Water flow destroys the matric suction within the soil when in contact with the soil bed. The strength of the soil bed decreases, leading to erosion.