The erodible bed model after scouring is captured by a 3D laser scanning device. It is difficult to represent the difference in results for different experimental conditions by directly using the erodible bed model. In this paper, the longitudinal section where the lowest point is located after scouring is extracted from the 3D model as the scour shape for analysis. Figure 3 shows some shapes of the erodible bed after scouring experiments, and the rest can be found as in Supplementary Fig. S1 online. At the end of the flume, the debris flow front collides with the baffle, resulting in scour enhancement and a buildup on the baffle side. Therefore, in the scour shape analysis, only the erodible bed section within 1.8 m is focused on to avoid the influence of the baffle. The experimental results show that there are two states of deposition and scouring on the bed. In the case of deposition, its thickness decreases gradually from the head to the end of the erodible bed (Fig. 3a).
Special attention needs to be paid to scouring, and there are many noteworthy phenomena. The overall feature of the scour shape is that there is a pit at the entrance and a groove at the middle and rear, and the depth of the scouring pit is far greater than that of other positions. With the enhancement of scouring, for example, as shown in Fig. 3b and c, when the density of debris flow is 1.7 g/cm3 and the particle size of sediment is 5–10 mm, the slope of the trough increases from 10° to 19°, the position of the maximum scouring depth will tend to move downward, the scouring pit will continue to expand and the depth of the scouring groove will also gradually increase. When the flume slope increases to 22°, a large number of collapses have occurred in the sediments at the head of the bed, that is, the particularly severe headward erosion has occurred. It can also be found that the scouring initiation points all appear at the head of the erodible bed. Only when headward erosion occurs, the scour initiation point will move significantly forward.
The formation process of depositing and scouring is further analyzed by the video recorded by the high-speed camera. When the debris flow density is high and the grain size of the bed sediment is small, such as the experiment group 16–1.80–1 ~ 2. As shown in Fig. 5a, at this point, the debris flow did not scour the sediment at all but flowed directly down the bed surface, and finally, part of the debris flow deposited up on the erodible bed (Fig. 4). As the grain size of the bed sediment increases, for example, experiment group 16–1.80–5 ~ 10, the contact area between the debris flow and the sediment becomes larger, resulting in an increase in the impact of the debris flow on the sediment, and thus part of the sediment at the bed head is scoured, as shown in Fig. 5b. However, due to the high debris flow density and the high viscosity between the debris flow and the bed sediment, it is difficult for the debris flow to infiltrate, resulting in more debris flow blockage in the area where the bed sediment is scoured. Despite the scouring that occurred during the experiment, the final result of the bed shape still shows full cross-section deposition (Fig. 4). When increasing the slope of the flume, like experiment group 22–1.80–5 ~ 10, as shown in Fig. 5c. The flow rate of the debris flow increases, resulting in a larger pit at the bed head. It is difficult for the debris flow to continue to fill the scoured bed sediment, so the final scour shape is shown in Fig. 4. When reducing the density of the debris flow, for instance, experiment group 22–1.70–5 ~ 10. In Fig. 5d, strong collision and scouring action occurs between the debris flow and sediment at the head of the bed, so a larger pit can be formed at the head of the bed at the beginning, resulting in a change in the direction of the debris flow velocity and continuous downward impact on the pit. Due to impacting the pit, debris flow consumes most of the energy, so the impact capacity of the debris flow behind the pit is substantially reduced. The final scour shape of a pit at the entrance and a groove in the middle and rear is formed (Fig. 4).
Critical scour slope
For a given gully, when the debris flow and sediment conditions are determined, there is a critical slope at which debris flow neither scours nor deposits18,19. What must be known is the situation of neither scouring nor depositing only exists in theory. Neither reality nor experiment can satisfy the theoretical situation. Therefore, it always manifests itself as scouring or deposition on the gully bed, as shown in Fig. 3. However, through experimentation, it is possible to determine a slope at which the bed shape shows the scour. For example, in Fig. 3b, under experimental conditions with a debris flow density of 1.75 g/cm3 and a sediment grain size of 2 ~ 5 mm, the bed shape is full cross-sectional deposition when the flume slope is 13°, while scouring occurred at the head of the flume bed at a flume slope of 16°, so that the critical scour slope can be determined to be in the 13°–16° range. The critical scour slope for each experimental condition is obtained statistically in combination with the scour shape, as shown in Table 3. It can be found that the critical slope increases with the increase of debris flow density and decreases with the increase in grain size of the bed sediment. As analyzed by the scour shape, the higher the density of the debris flow and the smaller the sediment size, the weaker the scouring capacity of the debris flow on the sediment and the easier it is for the debris flow to fill previously the scoured sediment, which means that the gully bed is more likely to appear as a full cross-sectional siltation, resulting in a higher critical scour slope. When the debris flow density is 1.70 g/cm3, the critical scour slope is all less than 13°, so less dense debris flows should be given special consideration in narrow-steep gullies.
The maximum scouring depth
The maximum scouring depth (Hm) is important research data to manifest the erosion intensity of debris flow, and its value is accurately obtained based on 3D laser technology. By this method, the maximum scouring depth is calculated, while statistics the debris flow velocity (U), as shown in Fig. 6. It can be found that Hm decreases with the increase in debris flow density, showing a negative correlation. One reason for this is that when the density of a debris flow decreases, the velocity of the flow decreases accordingly, resulting in a weakening of the scouring dynamics of the debris flow. Besides, the higher the density of a debris flow, the more solids it contains. As the volume fraction of debris flow solids increases, the ability to penetrate the erodible bed decreases, which also leads to a weaker scouring capacity.
However, the contribution of the grain size of the bed sediment (D) to the scouring intensity is the opposite. On the one hand, as the grain size of the bed sediment increases, the pore size increases, resulting in a greater infiltration capacity of the debris flow into the gully bed, which means that the gully bed is more susceptible to scouring by debris flow. On the other hand, the increased particle size of the sediment also increases the roughness of the streambed surface, which can also lead to the gully bed being more susceptible to scouring by debris flows.
Figure 7a shows the relationship between maximum scouring depth and flume slope, and Fig. 7b shows the relationship between debris flow velocity and flume slope. It is clear that the maximum scouring depth increases with increasing slope of the flume. In Fig. 7b, as the slope of the flume increases, the debris flow velocity increases accordingly, resulting in an increase in the scouring capacity of the debris flow. It can also be seen that the debris flow rates are essentially the same for the same debris flow density and slope of the flume, which is an indication of the stability of the experiment to some extent. In addition, the stability of riverbed sediment under large slope is lower, which leads to the formation of scouring, the sediment around the scouring pit is more likely to collapse, forming more serious scouring, even headward erosion. For example, under experimental conditions with ρ of 1.70 g/cm3 and D of 5–10 mm, as the flume slope adjusts from 19° to 22°, the Froude number of the debris flow increases from 5.7 (the flow velocity is 2.82 m/s, the flow depth is 25 mm) to 6.46 (the flow velocity is 3.2 m/s, the flow depth is 25 mm), and the stability of the bed sediments decreases, resulting in a large amount of collapse of the sediment around the flume and the headward erosion has occurs. Here, the maximum scouring depth only increased from 148.04 to 149.97 mm, but the erosion amount increased from 2.06 × 107 to 2.82 × 107 mm3, a significant increase of 36.9%.
As mentioned above, the larger velocity of debris flow on the steep slope is more likely to scour the gully, and the weaker stability of the riverbed sediment on the steep slope leads to the more likely collapse of the riverbed sediment, leading to a significant increase in scouring.