NUMERICAL SIMULATION OF MUD FLOW GENERATED IN ATSUMA, HOKKAIDO, JAPANARATA ISHIKAWA(Kyoto University Graduate School of Engineering, Japan), HIROSHI TAKEBAYASHI(Kyoto University, Japan), MASAHARU FUJITA(Kyoto University, Japan)

1. INTRODUCTION

4. DISCUSSION OF SIMULATION RESULTS

On September 6, 2018, "Hokkaido Eastern Iburi Earthquake" (magnitude 6.7) occurred at a depth of about
35 km in the central eastern Hokkaido Iburi district. The damage caused by sediment disaster to humans isenormous. As a countermeasure, we developed a numerical simulation model of sediment disaster. By using
numerical simulation, damage from sediment disaster can be predicted, and simulation results are very usefulfor people evacuation.

Fig. 3 shows the distribution of the maximum flow depth obtained by the simulation in the Yoshino area. As
a result, in both cases, the mud flow reached the house in about 6 seconds and reached the maximum flow
area in about 30 seconds. Therefore, it can be seen that the effect of the earthquake motion was very small.

The basic formulas used in the current numerical simulation model of debris flow and mud flow do notconsider the external force due to earthquake. So, considers the difference in flow characteristics due to thedifferent mudflow locations by comparing the simulation results of the mudflow generated in Takaoka area,
and Yoshino area of Atsuma. In addition, considers the effect of earthquake on the flow characteristics ofmudflow by numerical simulation of mudflow considering acceleration due to earthquake.

2. NUMERICAL SIMULATION MODEL(b) Case2(a) Case1
Fig. 3 Distribution of the maximum depth ofmudflow in Yoshino (unit: m)

However, there were differences in the flow velocity
vectors at each time. Fig. 4 shows the distribution of
the velocity vector after 3 seconds. In Case1, theleftward vector component appears larger than inCase2. In other words, the dynamics of theinstantaneous mudflow are affected by the earthquake,but finally, the effects of the earthquake in eachdirection cancel each other, and the effect of theearthquake is extremely small.

In this study, except for the momentum conservation equations, the basic equations used in the analysis are
the same as the two-dimensional mudflow analysis model of Takebayashi and Fujita (2020). The equation ofmotion of the mudflow considering the seismic acceleration is described as follows in general coordinatesystem. (Only flowing direction.)
𝜕 ℎ𝑈𝜕ℎ𝑈𝜕ℎ𝑈ℎ𝑢𝜕 𝜕𝜉𝜕 𝜕𝜉
+𝑈+𝑉−𝑈+𝑉𝜕t 𝐽𝜕ξ𝐽𝜕η𝐽𝐽𝜕𝜉 𝜕𝑥
𝜕𝜂 𝜕𝑥
1= − 𝑔 − 𝑎𝑧 ℎ𝐽
1 1−
𝜌𝑚 𝐽𝜕𝜉𝜕𝑥𝜕𝜉𝜕𝑥2+2+𝜕𝜉𝜕𝑦𝜕𝜉
𝜕𝑦22ℎ𝑣𝜕 𝜕𝜉𝜕 𝜕𝜉−𝑈+ 𝑉𝐽𝜕𝜉 𝜕𝑦𝜕𝜂 𝜕𝑦𝜕𝑧𝑏 1 𝜕𝜉 𝜕𝜂 𝜕𝜉 𝜕𝜂 𝜕𝑧𝑏ℎ+++ 𝑎𝜉 cos 𝜃𝜕𝜉𝐽 𝜕𝑥 𝜕𝑥 𝜕𝑦 𝜕𝑦 𝜕𝜂𝐽(b) Case2(a) Case1
Fig. 4 Distribution of velocity vector after 3 seconds (unit: m/s)𝜏𝑏𝜉𝜕𝑃 1 𝜕𝜉 𝜕𝜂 𝜕𝜉 𝜕𝜂 𝜕𝑃++−𝜕𝜉𝐽 𝜕𝑥 𝜕𝑥 𝜕𝑦 𝜕𝑦 𝜕𝜂
𝜌𝑚 𝐽

Fig. 1 shows the shape and depth of the slope failure used for the numerical simulation of the Yoshino andTakaoka area. Background image is quoted from GSI. The depth of the slope failure was determined based on
the difference between the DSM measured by drone and the DEM measured by GSI before the disaster.
Fig. 2 shows the temporal changes in seismic acceleration observed by the Japan Meteorological Agency in
Sikanuma, Atsuma. In this analysis, it is assumed that the slope failure occurs when the seismic acceleration isnear the maximum, so occur the slope failure at 8.5 seconds in Fig. 2.
The analysis was performed under 3 conditions. Cases 1 and 2 are Yoshino area and Case 3 is Takaoka area.
Case 1 is an analysis taking into account the earthquake. Case 2 does not consider the earthquake.

Fig. 5 shows the temporal change in thedepth of the mudflow in Case 4. As shownin the figure, it can be seen that themudflows generated from each tributary
merge and flow down the main river slowly.
The time to reach the farmland is 150
seconds, and the flow velocity at the timeof farmland flooding is 3 m/s, which is very
slow compared to the Yoshino.

the time required for themudflow to reach themountain stream exit ismuch longer than Case1,2 ,so it is possible to startevacuation after theearthquake occurs.
(a) After 30s(b) After 150s(c) After 200s
Fig. 5 Temporal change of mud flow depth in Takaoka area in numerical simulation (unit: m)

5. CONCLUSIONS・it was more effective to consider different disaster prevention measures and evacuation methods forparallel slopes and valley topography even in the same Atsuma.
・In addition, the velocity vector of mud flow considering the effect of acceleration due to the Hokkaido
Eastern Iburi Earthquake showed a difference in velocity vector, but no difference in the flow range.
REFERENCES

Fig. 1 Shape and depth of slope failure used in numericalsimulation (unit: m)

Fig. 2 Temporal variation of seismic acceleration
observed at Sikanuma, Atsuma

・Takebayashi H., Fujita, M. (2020). Numerical Simulation of a Debris Flow on the Basis of a Two-Dimensional Continuum Body Model. Geosciences, 10, 45.
・Cabinet Office: About damage situation related to Hokkaido Eastern Iburi Earthquake, 2018.
・Japan Meteorological Agency: Observation information about long-period ground motion, September 6, 2018 Sikanuma, Atsuma.
・Geospatial Information Authority of Japan: Fundamental Geospatial Data site.
・Geospatial Information Authority of Japan: GSI Map