Soil erosion control dams are widely used as part of measures to reduce damage caused by debris flow all over the world. Engineering considerations are needed for proper design of erosion control dams, but in the Republic of Korea, the impact force of debris flow is not fully reflected in the current design criteria of the dam. Against this backdrop, this study was conducted to estimate the impact force of debris flow for the practical purpose of designing erosion control dam. Simulated flume experiments were performed to develop the relationship to estimate the flow velocity as well as the impact force of debris flow. Experimental results showed that increases both in sediment mixture volume and flume slope gradient led to an increase in flow velocity. Especially, it was found that as clay content increased gradually, the flume slope gradient had greater impact on the increase of flow velocity. Also, it was proved that the impact force of debris flow was well fitted to the hydrodynamic model as it showed linear correlation with the flow velocity. Then, the debrisflow velocity model was established based on the factor related to the debrisflow velocity. Finally, the dynamic model to estimate the impact force of debris flow was introduced utilizing correlations between the established debrisflow velocity model and Froude number. Both models which were developed with using statistically significant watershed characteristics succeeded in explaining the experiment results in a more accurate way compared to existing models. Therefore, it is highly expected that these models can be fully utilized to estimate impact force of debris flow which will be required to design erosion control dams in practical use through overcoming their identified limitations.
Debris flow refers to a geological phenomenon in which mixture of sediment and water consisting of various soil particles ranging from fine clay to large boulder rushes down a mountainside at high velocity [
The most common countermeasures against debris flow include structure measure, nonstructure measure, and watershed management. The method of employing soil erosion control dam (ECD) is to block debris flow directly with structure. It is the most applicable as well as effective in urban areas with high population density and intensive land use. To perform the function of ECDs as debrisflow barriers or breaker structures in urban area, dynamic features of debris flow shall be considered in the design of structures. In nations such as Japan and Austria, a number of debris barriers have been constructed to block debris flow directly under the design criteria considering the impact force of debris flow.
Generally, it is difficult to quantitatively measure the impact force of debris flow at the field. Therefore, modeling approach has been employed to calculate the force which utilizes the dynamics of flow characteristics of debris flow and impact force [
In the past, the focus had been placed on the “soil conservation” to restore degraded mountainous areas rather than “disaster prevention” to protect against debris flow directly when ECDs were constructed. Thus, except for static characteristics of sediment pressure and water pressure, dynamic characteristics such as impact force of debris flow were not fully considered in the design of ECDs. Therefore, it is urgent and necessary to establish the estimation of impact force of debris flow applicable to the situation of South Korea and design standard for construction of ECD. The size of debris flow in South Korea is relatively small when compared to that of Australia and Japan with a high frequency of debris flow. Moreover, the construction budget including design per each unit—250 million Korean Won (≈200 thousand USD) per unit—is cheaper. For these reasons, the impact force of debris flow shall be calculated with the costeffective way.
From this point of view, the current study was conducted to suggest that impact force of debris flow be incorporated in designing ECDs. As part of this effort, it was intended not only to estimate the flow velocity of debris flow by using design factors of debris barrier or watershed characteristics but also to develop a model to calculate the impact force based on the flow velocity. We tried to clearly identify the relations between two factors, flow velocity and impact force, by conducting debrisflow flume experiments, and to derive the models to estimate flow velocity and impact force of debris flow, respectively.
Smallsized flume (Figure
Schematic design (a) and photograph (b) of experimental flume and measuring instrument.
To simulate the key feature of debris flow in flume experiment, various mixed sets of clay, sand, and gravel combined with water were employed. The result of field investigation around watersheds of Mt. Umyeon where debris flow event occurred in 2011 was reflected to decide the composition of sediment mixture. SMG [
After considering particle composition of sediment mixture, we chose two factors of “total volume” and “viscosity” among various characteristics of sediment mixtures that could affect to flow velocity and flow depth. A total of nine types of sediment mixture were provided by classifying each factor (total volume and viscosity) into three levels, respectively (Table
Overview of mean (±the standard error of the mean) sediment mixture properties.
Volume index  Viscosity index  Total volume (10^{−3} m^{3})  Weight (kg)  Density (kg m^{−3})  Clay (kg)  Sand (kg)  Gravel (kg)  Water (10^{−3} m^{3}) 

S  A  5.02 ± 0.03  8.40 ± 0.03  1672.38 ± 0.03  1.80 ± 0.03  1.80 ± 0.03  1.80 ± 0.03  3.00 
B  5.04 ± 0.02  8.40 ± 0.02  1667.67 ± 0.02  2.10 ± 0.02  2.10 ± 0.02  1.20 ± 0.02  3.00  
C  5.04 ± 0.03  8.40 ± 0.03  1668.35 ± 0.03  2.40 ± 0.03  2.40 ± 0.03  0.60 ± 0.03  3.00  


M  A  6.74 ± 0.03  11.20 ± 0.03  1661.37 ± 0.03  2.40 ± 0.03  2.40 ± 0.03  2.40 ± 0.03  4.00 
B  6.59 ± 0.07  11.20 ± 0.07  1701.43 ± 0.07  2.80 ± 0.07  2.80 ± 0.07  1.60 ± 0.07  4.00  
C  6.61 ± 0.04  11.20 ± 0.04  1694.24 ± 0.04  3.20 ± 0.04  3.20 ± 0.04  0.80 ± 0.04  4.00  


L  A  8.34 ± 0.02  14.00 ± 0.02  1679.52 ± 0.02  3.00 ± 0.02  3.00 ± 0.02  3.00 ± 0.02  5.00 
B  8.37 ± 0.02  14.00 ± 0.02  1672.15 ± 0.02  3.50 ± 0.02  3.50 ± 0.02  2.00 ± 0.02  5.00  
C  8.36 ± 0.04  14.00 ± 0.04  1675.18 ± 0.04  4.00 ± 0.04  4.00 ± 0.04  1.00 ± 0.04  5.00 
“S, M, and L” mean different volume conditions (about 5.03 × 10^{−3} m^{3}, 6.64 × 10^{−3} m^{3}, and 8.35 × 10^{−3} m^{3}, respectively) and “A, B, and C” mean different clay contents (about 21%, 25%, and 29% of total weight, respectively).
For measurement of flow velocity and impact force of sediment mixtures, flume experiments were repeated three times for every nine types of sediment mixtures with different volumes and clay contents under three conditions of flume gradients, 25°, 30°, and 35°. Whenever we implemented experiments, water and soil of the sediment mixture were fully mixed before it was put into the storage of the flume. Afterwards, they were continuously stirred even just before the storage gate opened to minimize separation. And then, the storage gate was opened to discharge the sediment mixture. The video camera was installed to capture how sediment mixtures were flowing, and the impact force was measured when the sediment mixture reached the plate attached with the load cell at the bottom of the flow path.
Flow characteristics of the sediment mixtures were obtained by using an image analysis method with two cameras (30 fps). The flow velocity was analyzed from the frontview camera image while the flow depth was estimated from the sideview camera image. As the flow velocity, we used velocity of the snout of the sediment mixture just before its impact to the force plate of the flume. Also, maximum depth of the snout of the sediment mixture at 0.1 m away from the force plate was used as flow depth. Load cell (Model MN100L by CAS) and data logger of 80 Hz sampling frequency (Model CI201A by CAS) were used to measure the impact force of the flow.
The experiment results, such as relationships among flow velocity, flow depth, and impact force of sediment mixture, were statistically analyzed to propose relevant models. Statistical analysis on the correlation of flow velocity, impact force, and experimental parameters such as volume and clay contents of sediment mixture and flume slope gradient was conducted by utilizing threeway ANOVA. Furthermore, model parameters for debrisflow impact force model were induced based on the experiment results, and regression analysis was employed to identify the relationship between the coefficient of the model and Froude number (Fr) that represented the flow characteristics. R software ver. 3.3.2 was utilized for such statistical analysis and introducing the model.
We compared Froude numbers between flume experiment and real debris flow events in the previous studies to review reproducibility of the debris flow. The results of flume experiments in the current study showed the Fr of 2.3–9.1. It is hard to compare Fr of the Mt. Umyeon debris flow event in 2011 as we have no measured flow velocity. Fr of debris flow generally ranges from 0 to 3 in the gentle gradient of less than 25° [
As shown in Figure
The change of flow velocity according to clay contents (a) and mixture volume (b) as slope condition changes.
The result of ANOVA of the flow velocity and experimental variables.
Degree of freedom 

 

MR  2  25.49  <0.01 
V  2  17.63  <0.01 
S  2  80.42  <0.01 
MR 
4  1.04  0.39 
MR 
4  1.06  0.38 
V 
4  1.71  0.16 
MR 
8  0.62  0.75 
Residual  75 
“MR” is mixing ratio, “V” is volume, and “S” is channel slope.
It was found that the flow depth of sediment mixture was statistically related to the volume (
The change of flow depth according to clay contents (a) and mixture volume (b) as slope condition changes.
The experiment results showed that flume gradient, volume, and clay content of sediment mixture were statistically significant with the impact force of sediment mixture with the significance level of 99% (ANOVA). Meanwhile, it appeared to be an interaction between the flume gradient and clay content (
Figure
The relationship between impact force and flow behavior. The horizontal axis is flow velocity (a) and flow depth (b). Circle, triangle, and cross symbols mean “S, M, and L” of volume condition. Blue, orange, and gray colors mean “A, B, and C” of viscosity condition.
In previous studies [
Most existing debrisflow velocity models were expressed as the function of channel slope and flow quantity that is represented as flow depth [
Volume constant
Empirical constant
To obtain values of
Equation (
Summary of the result of the comparison of velocity estimation models.
Formula  Coefficient  RMSE  CV  Reference  

Notation (unit)  Value (mean ± standard error)  
Newtonian laminar flow 


0.73 ± 0.03  1.32  0.50  [ 
Dilatant flow 


2044.80 ± 58.08  1.14  0.29  [ 
Newtonian turbulent flow 


0.0221 ± 0.0006  0.62  0.26  [ 
Voellmy flow 


25.57 ± 0.46  0.56  0.18  [ 
This study 


25.60 ± 0.31  0.37  0.12 
The value of each coefficient is expressed as “mean ± standard error.” RMSE is the root mean square error and CV means the coefficient of variance.
The model to calculate the flow velocity of debris flow was assumed as equation (
The relationship between the coefficient of hydrodynamic model for impact force and Froude number. Blue circles show the results of this experiment, and orange diamonds represent data of real debris flow [
Finally, estimation of the debrisflow impact force model after combining equations (
Components of equation (
However, there are limitations which shall be resolved to estimate impact force of debris flow by utilizing equation (
Comprehensively, the model, equation (
This study was preliminary work to suggest that impact force of debris flow shall be considered in designing ECDs in South Korea. As part of this effort, the flume experiments were conducted to develop the model to estimate the impact force of debris flow. Correlations among sediment mixture conditions, flow characteristics, and impact force of the experiments were statistically analyzed, and both models to calculate debrisflow velocity and impact force were introduced successively. Especially, we applied characteristics of soil and topography in South Korea into the models as part of efforts to consider regional conditions of the site where debris flow can occur. Besides, we utilized the design factor of ECDs as input variables of the model to estimate the impact force of debris flow for cost efficiency.
In conclusion, in given conditions of South Korea, the developed model can be applicable enough at a practical level even though there are some clear limitations that shall be resolved by conducting further experiments. It is highly expected that this model can be utilized better at the site with some improvements through additional experiments. If we can obtain sufficient filed observation data on debris flow in the future, the model can be much advanced in practice.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This study was carried out with the support of “R&D Program for Forest Science Technology (Project no. 2017061B101919AB01)” provided by Korea Forest Service (Korea Forestry Promotion Institute).