THE SURFACE VELOCITY CHARACTERISTICS OF VISCOUS DEBRIS FLOW

Abstract: Some debris flow that the volume concentration of solid is about or over 70% is called ¡°viscous debris flow¡± in China. Due to the importance for understanding the real phenomena of debris flow events, a PIV(Particle Image Velocimetry) method is conducted to analysis the surface velocity of it. With analyzing the recorded data in field, some results were obtained: the Eulerian velocity change in the central part of surges; the surface velocity distribution in cross section; and the surface velocity vector distribution in a surface area. According to these results and the field experiment data, it could be concluded that the structure of debris flow is complex in a surge. And the structures are different in the different scale surges. The surface velocity is fastest in the front of surge, and decrease till the end of the flow. In the front of flow, large-scale surges and small-scale surges flow as the turbulence and the lamina, respectively. And in the rear of flow, both two scales surges could be considered as laminar flow. The end of the flow almost stops in the channel. And this process is relatively slow. It illustrates that the cohesive stress is independent of the velocity gradient dominated the flow. Therefore the value of the cohesive stress is very small.

1 INTRODUCTION

Debris flows are known as the mixtures of bounder, soil, sand, gravel, slurry, clay and water that move down slopes. In response to the various geological, geographical and climatic conditions, some kinds of debris flows occur frequently in mountainous areas of China. Figure 1 shows the distribution of debris flow hazards in China [Dongchuan Observation and Research Station, CAS, 1997]. The flows called ¡°viscous debris flows¡± is characterized that the volume concentration of sediment about over 70% or over, the density about 2.0¡«2.3ton/m³, and the flows with amounts of surges in one event. These events not only often occurred frequently in the southeast of China, but also are reported in Japan [Takahashi, 1999]. These events have been caused serious damage and the loss of many lives, sometimes. For the purpose of mitigation planning to this kind of hazards, it is very important to be clear the mechanism of viscous debris flow.

In the recent years, several models are used to study the mechanism of viscous debris flow. One is the viscous-plastic model (Bingham plastic model), which is popularly used by many Chinese researchers. The typical characteristics of Bingham plastic model is such as ¡°plug flow¡±, but the strong yield stress are doubted through field observation [Takahashi and Arai, 1997]. Takahashi tried to apply dialant fluid model in 1993 and Newtonian viscous flow model in 1997 respectively to explain the behavior of viscous debris flows. However, a quantitative understanding of the mechanism of these flows is still relatively incomplete.

To understand the velocity profile of viscous debris flow, Arai [1998] applied an image analysis method-PIV (Particle Image Velocimetry) method, which is improved in later years, to analyze the surface velocity of viscous debris flow. A viscous debris flow event was recorded by a digital video camera in Jiangjia Gully, Yunnan Province of China. Analyzed results will be obtained as: the Eulerian velocity change of the serial time at the central part of surges, the Eulerian velocity distribution change in the surface cross section and the surface velocity vector distribution and so on. Then these results will be compared with the field experiment results, and the mechanism of viscous debris flow will be discussed.

2 OBSERVED DRANIAGE BASIN

The viscous debris flows are observed in Jiangjia Gully where located in Dongchuan city, Yunnan Province of China. It is a branch of Xiaojiang Basin, which is one of the first class branches of the upstream of Changjiang. Figure 2 shows the basin situation of Jiangjia Gully. The drainage area is 48.6km² and the length of the main channel is 13.9km. In average, debris flow occurred over ten times in this gully annual. There are two types viscous debris flows of intermittence flow and continuous flow according to their movement. Intermittence phenomenon occurred 58 times and continuous flows occurred 2 times from 1994 to 1998. The most discharge of an event is about 2914m³/s, and the fastest velocity arrivals at about 17m/s [Kang, 1999].

On July 24th, 1997, a debris flow occurred in response of a heavy rain in the upstream of Jiangjia Gully. From 16:10 to 19:20, 73 surges flowed down to XiaoJiang River. The observed channel in the middle stream is shown as in photo 1. Seven targets were set along the both bank of the observed channel. According to the measurement with infrared-light distance meter, the length of the channel is about 300m, the width is about 30m, the depth is about 3m and the longitudinal slope angle is about 5 degrees. The grain size distribution of the flow sample is shown in Figure 3.

3 IMAGE ANALYSIS

The mentioned above event was recorded by a digital video camera at the frame rate of 30 frames per second. The resolution of the camera is 640*480 pixels. The recorded video frames are transferred from analog signal into digital signal with an interface board plugged in the computer, then are saved as bitmap files. In order to save the computer memory, the size of every bitmap is 640*380 pixels.

The PIV method is used to measure the surface velocity of debris flow. The distance of one pixel is used to estimate the particle movement distance between two images during a time interval. The surface of debris flow is assumed as a horizontal plane. The calculative parameters are set as following:

Photo 2 shows an example of analyzed image. The points A, B and C are treated as the base points in both photos 1 and 2. To compared with the real coordinates and the image position of targets (T1, T2, T3, T4, T51, T52, T6), shown in Table 1, the correspondent coordinates of these base points in photos 1 and 2 could be calculated. Then the real distances of a pixel in x and y directions is estimated as following:

	Real Coordination (m)			Image position
	x	y	z	px	py
T1	1201.691	3332.975	1363.195	293	108
T2	1126.006	3304.199	1363.434	423	110
T3	1248.813	3246.858	1355.869	244	137
T4	1156.046	3221.838	1356.885	437	136
T51	1282.738	3147.398	1349.991	203	187
T52	1270.335	3143.162	1350.706	238	185
T6	1174.335	3112.100	1353.179	522	181

(4) Due to the image is colorful, the brightness is defined as a function shown as following:

where Y is the brightness of the pixel, r, g and b is red, green and blue value of the pixel, respectively.

In order to make a more accurate measurement, a parabolic approximation fit method is used to obtain the 0.5 pixel position with the maximum correlation coefficient.

4 RESULTS AND DISCUSSIONS

Photos 3 and 4 show examples of the head of the relative large-scale and small-scale debris flow surges, respectively. The analysis results are shown as following:

Fig. 8 The velocity distribution fitting curve in the cross section on 17:42:25 (left part)

Fig. 9 The velocity distribution fitting curve in the cross section on 17:42:25 (right part)

Figures 4 and 5 show the Eulerian velocity change in the center of the debris flow surges, which are respectively shown in photos 3 and 4. The horizontal axis indicates the time, and the vertical axis indicates the surface velocity. According to these results, the surge is very fast in the front part, and become slower and slower in the rear of the surge, then the surface of the flow is looked like stopping in the channel. In the case of surge shown in photo 4, another surge flows following it. And another point could be noticed that the surface velocity is almost same during several seconds.

Figures 6 and 7 illustrate the Eurlian surface velocity distribution change of a cross section. The straight broken lines indicate the critical of the zero velocity in the surface of the flow. And the dot line in the cross section shows as a parabola line. About the detail velocity profiles of the cross section, and some fitting curves are drawn. It could be seen that in the front of the large-scale surge, the surface velocity profile is fitting better to a logarithm curve, shown in Figure 8 and 9. The fitting curve of the surface velocity is a parabola in the rear of surge as shown in Figure 10. In comparably, the surface velocity distributes as a parabola in the front of a small-scale surge, shown in Figure 11.

Figures 12 and 13 show the surface velocity vector distribution of the front of the large-scale and small-scale surges, respectively. The vectors looked turbulent in the front of the large-scale surge, and looked regular in the front of the small-scale surge.

According to these results, a small-scale surge (with small flow depth and relative slower velocity) could be treated as the Newtonian laminar flow. The velocity distribution can be given by

in which

; g = the acceleration due to gravity;

= the channel slope; h = the flow depth; z = the Cartesian coordinate;

= the fluid mass density;

= the dynamic viscosity.

Insertion of the data assumed as that u = 5m/s , h = z = 0.3 m ,

= 5^oand g =9.81 m² /s , gives value for

about 0.0077 m² /s. Reynolds number (

) can be calculated with value of near 155. Therefore, the Reynolds number of large-scale surges (Assumed as h = 2m, u = 10m/s) can be estimated at about 2600.

In 1995, the field experiments were conducted at a small tributary of the Jiangjia Gully, where is located in right-hand side of the trunk gully (Takahashi and Arai, 1997). The average longitudinal angle of this tributary is 13.4^o, the width is about 2m, and the depth is about 0.5m. The results is that mean flow velocity is about 0.2m/s , and mean flow depth is between 0.14 - 0.2m. By using these data, the value for

is about 0.08 m² /s . The Reynolds number is about 0.5.

According to the results obtained herein, it could be yielded that in the front of a large-scale surge, the inertial force dominated the viscous force. The flow is turbulent. In the rear of a large-scale surge, the surface velocity distribution as a laminar, the viscous force is dominant in the flow. At the end of the surge, since the flow almost stops in the channel, the dominant force that is independent to the velocity gradient can be considered as cohesion. However, this process is relatively very slow, it shows that the value of cohesion is very small. And a small-scale surge has a low Reynolds number and a laminar velocity distribution; it is distinct that the viscous force prominent the inertial force. The flow could be treated as a laminar flow.

5 CONCLUSIONS

The PIV method has been used to analysis the surface velocity of the viscous debris flow. The results and the field experiments results suggest that the structure of the debris flow is very complex. Surface velocity profile and Reynolds numbers calculated from field data analyzed herein suggest that debris flow can be treated as laminar when the scale is small. And when the scale is relatively large, debris flows can be treated as turbulence in the front part. In the rear of debris flow, the velocity become slower, and the depth become small, debris flows can be treated as laminar. In the end of the surge, the flows almost stop in the channel. It shows that a very small cohesion dominate the flow.

References

Arai, M. Sawada, T. and Takahashi, T. (1998): An Application of Image Analysis Technique on the Velocity of Debris Flow Observation, Pro. Of 3^rd International conference on Hydro-Science and Engineering, IAHR, 1998, Fie Reservoir. 188, pp1-9.

Dongchuan Observation and Research Station: Chinese Academy of Sciences, 1997, p1

Kang, Z(1999): Generation, Movement and Sedimentation of Viscous Debris Flows, Japan-China Joint Research on the Mechanism and the Countermeasures for the Viscous Debris Flow, 1999, pp30-41.

Takahashi T(1999): Preface, Japan-China Joint Research on the Mechanism and the Countermeasures for the Viscous Debris Flow, 1999, p1.

Takahashi T. and Arai, M. (1997): Mechanism of Viscous Debris Flow, International Symposium on Natural Disaster Prediction and Mitigation, December 1-5, 1997, pp407-414.