Determination of the effects of topographic condition on the numerical simulation of debris flow is essential for predicting sediment discharge from large-scale landslides. One such effect is sediment deposition and erosion, which is significant at points where the gradient or width of the debris-flow torrent changes, as pointed out by previous studies. In such cases, variation in the numerical simulation is induced mainly by the erosion rate equations employed by researchers. However, the differential effect of various erosion rate equations has not been examined. This study first revealed the difference in the calculated effects of debris flow on channels with altered inclination and undulations of the bed surface using various erosion rate equations. The effect of each erosion rate equation was examined, and results for the final shape of the channel bed profile were obtained from numerical simulations for cases with and without bed surface undulation. Hydrographs of the lower end of the channel showed significant differences depending on the size of the undulations, even with the same erosion rate equation. These results arise from difference in the responses of the erosion rate equations to steep-slope sections and indicate that the complexity of field topographic conditions affects debris-flow hydrographs. These results also suggest that numerical simulations of debris flow can differ depending on the resolution of the simulation domain.
The shallow water equations are generally used for numerical simulation of debris flows. In this method, the distributions of the flow velocity u and sediment concentration c are vertically averaged. Therefore, the calculation may be inaccurate when the upper and lower layers have different flow directions, as with countergradient flows. We propose a numerical simulation method for calculating the vertical distributions of u and c in debris flows. Our method is based on the moving particle semi-implicit (MPS) method, which was originally used for incompressible viscous fluid flows with free surfaces. Some modifications are necessary to adapt the method for debris flows. We introduce the constitutive equations of Egashira et al. to the MPS method. In Egashira's equations, debris flows are treated as a continuum. Thus, the proportion of gravel in a debris flow is expressed using the variable c. Similarly, each particle has an associated c value in our modified MPS method. In Egashira's sediment concentration equations, the equilibrium vertical distribution of c is obtained by integrating the rate of change of c in the vertical direction from the riverbed. In our method, c values spread among nearby particles, in order to reduce the difference between the equilibrium rate of change c and the actual rate of change of c. Numerical simulations of debris flow are performed. In the equilibrium condition, there is good agreement with the vertical distributions of u and c and those derived from the constitutive equations. In the condition where the riverbed gradient becomes less steep, there is good agreement with experimental results with a very short relaxation time, including those involving the formation of a convex upward deposition shape in the initial deposition process. Results for the initial deposition process are not produced with existing simulation methods that are based on the assumption of local equilibrium of average sediment concentration. However, simulations with a very short relaxation time show that local equilibrium is established as well as in existing methods. This indicates that the assumption of local equilibrium of sediment concentration is correct, and that because it evaluates the local equilibrium of each particle, our model can yield good results.
A simple and effective tree form model is needed for water cycle and rainfall interception studies in forest hydrological research. The purpose of this study is to develop a two-dimensional tree model for Japanese cedar and cypress trees. The model includes a functional relationship between branch lengths and tree height for a single tree. We show that the relationship between them can be modeled by a quadratic curve using the tree form factor with Japanese cedar and cypress trees. The relationship between stand density and the tree form parameter could be expressed by a power equation. In addition, the relationships among leaf area, storage capacity, and branch length could be represented by power equations. Using this model, the storage capacity of the canopy and leaf area index were estimated under different conditions of crown height for Japanese cypress and cedar. The effects of forest management on transpiration and branch storage are suggested by the results.
Toward a novel approach of bedload monitoring in mountainous streams, this study aimed to examine measurements of height and porosity of sediment layer below water surface by applying TDR (Time Domain Reflectometry). A column experiment was conducted to validate accuracies of estimated sediment height and porosity using a commercial probe (0.3 m in length) and a simple probe consisted of a PCV pipe and stainless steel wires (0.9 mm in diameter and 1.0 m in length) and two sets of experimental sand with different grain size distributions. The probes were inserted into a container filled with water. TDR waveforms were then measured during supply of the sand until the probes were totally covered by sediment layer. The waveforms were analyzed and used for calculating height and porosity of sediment layer. Our results indicate that height of sediment layer is estimated better by analyzing a part of waveform corresponding with the probe in the water layer rather than waveform corresponding with the entire probe. Calculated sediment heights agreed well with measured heights for both experimental sands. Small oscillations of TDR waveforms obtained by the simple probe may affect overestimates of porosity. In contrast, calculated porosity by the commercial probe agreed well with measured porosity. A monitoring system with TDR probes scattered in a sand pocket or upstream of a check dam will enable us to investigate temporal change of bedload transport in mountainous streams.
Generally, larger particles concentrate at the frontal part of debris flow under unsaturated-flow conditions. Many studies have explained the mechanisms of this larger-particles concentration with inverse grading : the upper portion of the sedimentary layers having a larger particle in diameter. The reverse-grading mechanism has been explained in terms of the distributed pressure by particle collisions, dynamic sieving, granular convention and the differences in the velocities of the moving particles. However, further explanation is required. In this study, to understand larger-particles concentrations better, experiments were conducted using a conveyor belt and an experimental flume. Particles of two sizes were sieved on the conveyor belt. The results showed that the concentration rate of larger particles converged at a particular value in response to the various experimental conditions. Finally, our results indicated that the concentration of larger particles on the conveyor belt, in the absence of water, was affected by the moving distance, the flow depth, the particle diameter ratio, the riverbed gradient and the internal frictional angle of the particles.
This study presents the results of the observation of the ground vibrations generated by debris flows using a transportable vibration sensor. The transportable vibration sensor used for the observation is similar to the one designed by the Earthquake Research Institute, University of Tokyo. The authors installed the transportable vibration sensor into the Arimura River in Sakurajima, Japan, and observed ground vibrations. The data which is collected from March 2013 to May 2014 illuminated the conditions of eight debris flow events. The data revealed the following : 1) The fluctuation of the hydrograph and the vibration waveform obtained by the transportable vibration sensor are similar, 2) Maximal discharge is proportional to the two-third power of the maximal acceleration, 3) The time periods of increasing and decreasing of the acceleration obtained the transportable and buried type vibration sensors are similar, and 4) During the downward peak discharge of debris flow, the vibration obtained by the sensor indicated predominant frequencies ranging from 20 to 30 Hz. Thus, the estimation of the occurrence and discharge of debris flow using a transportable vibration sensor is considered possible.