The 15th International Conference on Analysis of Discontinuous Deformation (ICADD15)
23-25 September 2021, Online (Zoom)

Simulation of sediment-related disaster and long-term landform processusing Depth-Integrated Particle Method
Takashi Matsushimaa*a

University of Tsukuba, Tsukuba, Japan* tmatsu@kz.tsukuba.ac.jp
Abstract

Depth-Integrated Particle Method (DIPM) is an efficient numerical method suitable for simulating
sediment-related disaster such as slope failure and subsequent debris flow/mudflow running throughcomplicated topography (Hoang et al. 2009, Nakata and Matsushima 2014, Zhang and Matsushima 2016,2018, Edris and Matsushima 2019). The method deals with the flowing mass as a collection of soilcolumns, and the equation of motion of such soil columns is solved as 2D discrete ‘particles’ moving
along with the surface terrain. The particles are subjected to bottom shear friction calculated by modified
Manning’s formula with a yield stress and particle-wise interaction based on their hydraulic gradient.
Accordingly, the material parameters governing the flow behavior are only two: the Manning’scoefficient, n, and the critical deposition angle, 𝜃𝜃𝑐𝑐𝑐𝑐 related to the yield stress. Also, from the viewpointof numerical method, it is quite similar to Discrete Element Method with very soft particles whose
computational characteristics has been well established.
In the present study, Atami mudflow occurred on July 1st, 2021 was analyzed as a recent case study.
The topography of analyzing domain of about 2300m by 2300m was extracted from Digital map 5m(elevation) published by Geospatial Information Authority of Japan (GSI). According to the publishment
record, the data was taken in 2009, which means that a check dam built in 1999 between the slope failure
location and the densely populated area is reflected in the data, but the landfill soil at the failure site,that was constructed after 2009, is not. The initial slope failure location and the sliding mass volume ofabout 56,000m3 were determined from the information in the Emergency report of GSI (2021).
Manning’s coefficient was set to 0.1 based on the previous studies (Nakata and Matsushima 2014, Edrisand Matsushima 2019), which corresponds to the typical value of natural waterway with irregularbottom surface (see e.g., Chow 1959). A series of simulations were carried out by changing the criticaldeposition angle, 𝜃𝜃𝑐𝑐𝑐𝑐 from 0.0 to 15.0(deg.) as it is unknown and sensitively affected by the soil type
and the water contents. Comparing the disaster observation and the simulation results (Fig.1), we found
the followings:(1) In the cases that 𝜃𝜃𝑐𝑐𝑐𝑐 ≥ 12(deg.) the mudflow does not reach the densely populated area, while itreaches the seacoast when 𝜃𝜃𝑐𝑐𝑐𝑐 ≤ 10.0(deg.). This is consistent with the observation that the averageslope angle in the valley is about 11(deg.) in GSI report (2021).
(2) The maximum flow velocity is about 6.0 to 8.0 (m/s) when it reaches the densely populated area incase that 𝜃𝜃𝑐𝑐𝑐𝑐 = 7.5(deg.), which is in accordance with a SNS video taken at around Aizome bridge.
(3) It is observed that the check dam captured about 6,000 to 7,000m3 mass (Emergency report by Asia
air survey co. ltd., 2021). However, that was not reproduced in the simulation because of the limitationof elevation data.
It should be noted that the above simulations do not consider the erosion of the valley bottom soil
due to the mudflow. In order to incorporate such erosion/ sedimentation process in DIPM, a soil transportmodel of suspended load was implemented based on Lane-Kalinske (1941) model with Garcia andParker (1991) empirical model for dimensionless sediment entrainment rate (Matsushima 2015). In
addition, the model was extended to a multi grainsize model (Fig.2). To demonstrate the performanceof the model, some simple examples of erosion and sedimentation in a uniform slope were simulated(Fig.3). In the simulation, water particles are regularly put on the center of the slope, and they erode thematerial on the slope surface and sedimented in the downstream flat plane forming a alluvial fan-likelandform. This model can be used not only for a single debris flow / mudflow simulation but also a longterm simulation of fluvial landform process.
Keywords: Atami Mudflow, Depth Integrated Particle Method, Long-Term Landform Process

Failure location
check damdensely
populated
areaFig. 1. Observed affected area (left, GSI 2021) and simulation result (right, 𝑛𝑛 = 0.1, 𝜃𝜃𝑐𝑐𝑐𝑐 = 8.0deg.)

average concentration

0.3

D=10µm
D=100µm

0.2

D=1mm
D=10mm

0.1

0.00.010.1110100

flow velocity v (m/s)

1000

10000

Fig. 2. multi grainsize model for the suspended load. Fig. 3 Final alluvial fan-like landform.
References
Hoang, G.Q., Matsushima, T., Yamada, Y., 2009, Debris flow simulation by particle method using PRISMDSM. Proceedings of 6th Geo-Kanto Conference (in Japanese).
Nakata, A.M., Matsushima, T., 2014, Statistical evaluation of damage area due to heavy-rain-induced
landslide, Computer Methods and Recent Advances in Geomechanics (IACMAG), Oka, Murakami,
Uzuoka & Kimoto Eds., Taylor and Francis, 1523-1528.
Zhang, N., Matsushima, T., 2016, Simulation of rainfall-induced debris flow considering material
entrainment, Engineering Geology, 214, 107-115.
Edris, M. A., Matsushima, T., 2019, Evaluation of soil properties of natural slopes from case histories andGIS, Proc. International Conference on Computational Science (ICCS-2019), Singapore, 12p.
Emergency report of GSI, 2021, https://www.gsi.go.jp/BOUSAI/R3_0701_heavyrain.html#10.
Chow, V. T., 1959, Open-Channel Hydraulics, McGraw Hill.
Emergency report by Asia air survey co. ltd., 2021, https://www.ajiko.co.jp/news_detail/1199.
Garcia, M.H., Parker, G., 1991, Entrainment of bed sediment into suspensions, Journal of HydraulicEngineering, ASCE, 114, 4, 414-435.
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meeting of Japanese Geotechnical Society, 2p.