DEVELOPMENT OF NUMERICAL TECHNIQUE
AND FIELD APPLICATION USING INTEGRATEDSIMULATION OF RIVER FLOODING AND
INUNDATION FOR DISASTER PREVENTION AND
MITIGATION

包括型洪水氾濫解析を用いた防災・減災に向けた数値解析技術の開発と現地適用

March 2024
HUA WEIJIAN

Graduate School ofEnvironmental and Life Science(Doctor’s Course)
OKAYAMA UNIVERSITY

Table of Contents
CHAPTER 1
INTRODUCTION ........................................................................... 1
1.1 Background ......................................................................................................... 1
1.2 Previous study ..................................................................................................... 4
1.3 Research Objectives ............................................................................................. 5
1.4 Structure Overview .............................................................................................. 6
References ................................................................................................................. 8
CHAPTER 2OVERVIEW OF NUMERICAL ANALYSIS ................................. 9
2.1 Comprehensive Analysis Model for River Flooding and Inundation ..................... 9
2.2 Two-dimensional shallow water equations ........................................................... 92.3. The Godunov-type finite volume method .......................................................... 10
2.4 Internal boundary conditions and treatment of buildings .................................... 11
References ............................................................................................................... 13
CHAPTER 3
PREDICTION OF LEVEE BREACH DUE TO OVERFLOWUSING FLOOD SIMULATION RESULTS IN MABI DISTRICT OF KURASHIKI
CITY .......................................................................................................................... 15
3.1 Introduction ....................................................................................................... 15
3.2 Detailed description of the disaster event ........................................................... 16
3.2.1 The causes of the disaster ............................................................................ 18
3.2.1.1 The rainfall conditions .............................................................................. 18
3.2.1.2 Water level conditions............................................................................... 18
3.2.1.3 Discharge conditions ................................................................................ 21
3.2.2 Damage Situation ........................................................................................ 21
3.3 Outline of numerical Simulation ........................................................................ 25
3.3.1 Study area.................................................................................................... 25
3.3.2 Simulation conditions .................................................................................. 28
3.4 Causes of levee breach ....................................................................................... 29
3.4.1 Study on the causes of breaches ................................................................... 29
3.4.2 Extraction of physical parameters for breach prediction ............................... 32
3.5 Flood simulation and its verification .................................................................. 33
3.5.1 Flood flow characteristics ............................................................................ 33
3.5.2 Comparison of maximum inundation depth ................................................. 38
3.5.3 Comparison of trace and observed water level at observatories .................... 381

3.6 Levee breach prediction and feasibility assessment ............................................ 41
3.6.1 Considerations for levee breach prediction criterions ................................... 41
3.6.2 Evaluation of levee breach prediction method .............................................. 44
3.7 Conclusion......................................................................................................... 45
References .............................................................................................................. 46
CHAPTER 4
EVALUATION OF BEHAVIOR OF FLOATING LITTER
DURING FLOODING WITH LEVEE BREACH BY USING INUNDATIONANALYSIS ................................................................................................................ 47
4.1 Introduction ....................................................................................................... 47
4.2 Overview of the Research Region ...................................................................... 51
4.3 Flooding Analysis .............................................................................................. 52
4.3.1 Model introduction ...................................................................................... 52
4.3.2 Simulation conditions .................................................................................. 56
4.4 Floating litter analysis ........................................................................................ 58
4.4.1 Model introduction ...................................................................................... 58
4.4.2 Simulation conditions .................................................................................. 59
4.5 Results and discussions ...................................................................................... 60
4.5.1 Verification for flooding simulation and discussions for drainage ................ 60
4.5.1.1 Verification of simulation validity ............................................................. 60
4.5.1.2 Drainage results ........................................................................................ 60
4.5.2 Results and discussions of floating litters ..................................................... 62
4.5.2.1 Trajectory of floats and overall distribution ............................................... 62
4.5.2.2 Characteristics of floats accumulated other than urban area....................... 64
4.6 Conclusion......................................................................................................... 65
References ............................................................................................................... 66
CHAPTER 5
NUMERICAL SIMULATION OF COUPLED DEBRIS FLOWAND INUNDATION DISASTER CONSIDERING MICROTOPOGRAPHY: A
CASE STUDY OF NIIMI CITY, 2019 ..................................................................... 67
5.1 Introduction ....................................................................................................... 67
5.2 Study area description ........................................................................................ 68
5.2.1 Topographical summary............................................................................... 69
5.3. Field observation .............................................................................................. 70
5.3.1 The observation of Imaitani River in Imai district ........................................ 71
5.3.2 The observation of water way in Nishikata district ....................................... 72
2

5.4. Model building ................................................................................................. 72
5.4.1. Introduction for models .............................................................................. 72
5.4.1.1 Governing equations and discretization ..................................................... 72
5.4.1.2 Coupling method ...................................................................................... 74
5.4.2 Simulation conditions .................................................................................. 75
5.4.2.1 Computational mesh and topographic data ................................................ 75
5.4.2.2 Input conditions for reproduction calculation ............................................ 77
5.4.2.3 Case description ....................................................................................... 77
5.5 Results and considerations ................................................................................. 77
5.5.1 Verification of the model accuracy ............................................................... 77
5.5.2 Influences of reproducibility of channel and sediment accumulation by flooding............................................................................................................................. 79
5.6 Conclusion......................................................................................................... 84
References ............................................................................................................... 86
CHAPTER 6
SUMMARY AND CONCLUSIONS ............................................. 873

List of Figures
Fig.1.1 Number of days with daily precipitation exceeding 200 mm annually ....................... 1
Fig.1.2 Inundations in recent years: (a) The inundation at the Kinu River in September 2015,(b) The inundation at the Oda River in July 2018 ..................................................... 2
Fig.1.3 The situations for flooding litters during flooding event (above) and after flooding
event (below) in Mabi distric ................................................................................... 3
Fig.1.4 The situations for debris flow and inland flooding ..................................................... 4
Fig.2.1 Conditions of inner boundaries: (a)levees and (b)building walls. ............................. 11
Fig.2.2 Simplification and redefinition of building footprint pol.......................................... 11
Fig.3.1 Map near the confluence point of the Takahashi River and the Oda River ................ 15
Fig.3.2 Isohyet map of the Takahashi River basin ............................................................... 17
Fig.3.3 Total precipitation in the Takahashi River basin ...................................................... 17
Fig.3.4 Locations of water level observation stations and the peak times of water ............... 19
Fig.3.5 The temporal variation of water levels at observation stations (Water Level: T.P) .... 19
Fig.3.6 Breached locations of the levees along the Oda River and its tributaries .................. 22
Fig.3.7 The situation of the levee breach on the left levee of the Oda River 3.4 km ............. 22
Fig.3.8 The situation of the levee breach on the left levee of the Oda River 6.4 km ............. 22
Fig.3.9 The situation of the levee breaches on both levees near the Suemasa River 0.7 km. . 23
Fig.3.10 The situation of the levee breach on the right levee of the Takama River 0.1km..... 23
Fig.3.11 The situation of the levee breach on the left levee of the Madani River 0.5 km ...... 23
Fig.3.12 The flooding situation on the right levee of the Oda River 2.5km .......................... 24
Fig.3.13 The partial destruction situation on the right levee of the Madani River 0 km ........ 24
Fig.3.14 Numerical domain ................................................................................................ 26
Fig.3.15 Expression of features ........................................................................................... 26
Fig.3.16 Roughness distribution ......................................................................................... 27
Fig.3.17 Boundary conditions for Takahashi River and Oda River ...................................... 27
Fig.3.18 Boundary conditions for tributaries. ...................................................................... 27
Fig.3.19 Breaches of levees ................................................................................................ 28
Fig.3.20 The situation of water levels inside and outside the levee at approximately 3.4 km on
both the left and right levees of Oda River ............................................................. 31
Fig.3.21 Schematic diagram of the water level difference inside and outside the levee after
flooding and the presence or absence of levee breaches .......................................... 32
1

Fig.3.22 Time variation of inundation depth ....................................................................... 34
Fig.3.23 Start time of inundation ........................................................................................ 35
Fig.3.24 Time reached maximum water level ...................................................................... 35
Fig.3.25 Distribution of maximum water depth. ................................................................ 35
Fig.3.26 Comparison between the maximum computed inundation depth and the observed
values .................................................................................................................... 36
Fig.3.27 Comparison of longitudinal water level distribution in Takahashi River and Oda River.............................................................................................................................. 37
Fig.3.28 Comparison of water level changes over time ....................................................... 39
Fig.3.29 Relationship between the occurrence of breaches and the river-landside water level
difference, and levee shape coefficient ................................................................... 41
Fig.3.30 Discriminant analysis results................................................................................. 42
Fig.3.31 Analysis results of the river and landside water levels at the breached site on the leftlevee of the Suna River at 11.2 km (Western Japan Heavy Rainfall in the 2018) ..... 43
Fig.3.32 Analysis results of the internal and external water levels at the breached site on theleft levee of the Kuma River at 55 km using IRIC (the heavy rainfall in July 2020).
.............................................................................................................................. 43
Fig.4.1 Floating litters in rivers: (a) Floating litter accumulated at river weir of the Onga River.
(b) Floating litter accumulated on the Arii Bridge. ................................................. 48
Fig.4.2 The disaster debris in Mabi district in 2018. ............................................................ 49
Fig.4.3 Floating litter at the recession stage in residential area (Komoike sluiceway) .......... 49
Fig.4.4 Orthophoto of study area ........................................................................................ 50
Fig.4.5 Examined sluiceway, S1-S4 .................................................................................... 51
Fig.4.6 Drainage model of sluiceway .................................................................................. 52
Fig.4.7 Drainage operations conducted by pump vehicles ................................................... 53
Fig.4.8 Boundary condition at observation stations ............................................................. 53
Fig.4.9 Observation data of sluiceways(S1-S4) ................................................................... 54
Fig.4.10 The training levee failure at the confluence of the Oda River and Takahashi River 55
Fig.4.11 The training levee failure in numerical simulation ................................................. 56
Fig.4.12 The floats setting areas ......................................................................................... 57
Fig.4.13 Velocity distribution around sluiceway .................................................................. 57
Fig.4.14 Water level comparison at observation stations ..................................................... 58
Fig.4.15 Hydrograph at sluiceways: (a) discharge and water level difference; (b) water level ofurban area side and river side ................................................................................. 59
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Fig.4.16 Initial state of the floating ..................................................................................... 60
Fig.4.17 Track of the float: (a) F1 and F2. (b) F3 and F4 ..................................................... 61
Fig.4.18 Distribution of floats at the final moment of calculation ........................................ 62
Fig.4.19 Number of accumulated floats at the sluiceways ................................................... 63
Fig.4.20 Number of floats which through breach ................................................................ 63
Fig.5.1 Ortho photo of study area ....................................................................................... 68
Fig.5.2 Rainfall conditions on Sep. 3, 2019, in Niimi city ................................................... 68
Fig.5.3 (a) Drainage channels buried by debris flow. (b) Aerial photograph on the disasterarea around the Ohta River .................................................................................... 69
Fig.5.4 (a) Debris flow situation in Imai district. (b) Contour maps derived from 5-meterelevation data and the results obtained through RTK-GPS measurements ............... 70
Fig.5.5 (a) Debris flow situation in Nishikata district. (b) Contour maps derived from 5-meterelevation data and the results obtained through RTK-GPS measurements ............... 71
Fig.5.6 Compute field......................................................................................................... 75
Fig.5.7 Manning coefficient. ............................................................................................... 76
Fig.5.8 The tunnel in urban area ......................................................................................... 76
Fig.5.9 Calculation results of Case 4: (a) sediment height at 18:30 and (b) maximum water
depth ..................................................................................................................... 79
Fig.5.10 Photographs of sediment: (a) north side and (b) south side of the railway .............. 80
Fig.5.11 Photographs of traces: (a) before and (b) after the removal of debris flow.............. 80
Fig.5.12 Trace heights and numerical results: (a) locations of trace, (b) debris flow, and (c)flood flow. ............................................................................................................. 81
Fig.5.13 Riverbed elevations of the Ohta River ................................................................... 81
Fig.5.14 Comparisons of calculation results: (a) water level at downstream of channel, (b) draindischarge, and (c)drain volume .............................................................................. 82
Fig.5.15 Contour map of the difference of the maximum water depth: (a) Case 1 – Case 2, (b)Case 3 – Case 1, and (c) Case 4 – Case 2 ............................................................... 83

3

List of Tables

Table 3.1 The results of the investigation into the factors contributing to the breach conducted by
the levee inspection committee ................................................................................ 25
Table 3.2 Causes of levee breaches .......................................................................................... 30
Table 3.3 Average internal and external water level difference and levee shape coefficient during
overtopping in the Mabi district ............................................................................... 40
Table 4.1 Sluiceway specifications .......................................................................................... 50
Table 4.2 The time when the event of interest occurred ............................................................ 55
Table 4.3 Initial position and number of floats ......................................................................... 57
Table 4.4 Starting and ending position of floats ....................................................................... 61
Table 5.1 Parameters of effective rainfall ................................................................................. 75
Table 5.2 Simulation Cases ..................................................................................................... 78

1

ABSTRACT
In recent years, heavy rains have been increasing, which is considered to be theeffects of global warming, and serious and complex disasters such as landslides andlarge-scale floods inundation are occurring more frequently. In order to develop
disaster prevention and mitigation measures against such increasingly severe andcomplex disasters, it is necessary not only to conduct conventional analysis to predictthe maximum inundation depth, but also to develop highly accurate numerical analysis
that expresses detailed flow conditions. Furthermore, it is required to develop
numerical techniques to extract specific issues from the analysis results.
Therefore, I employed a comprehensive flood analysis model named the"Comprehensive Analysis Model for River Flooding and Inundation" to address theaforementioned issues. This model integrates flood flows, inundation resulting fromlevee overflow, inflow from breached levee sections, and flooding within landsides,
including structures. Two-dimensional shallow water equations were used as thefundamental equations. The entire region, encompassing river channels and landsides,
is discretized using a triangular unstructured mesh, an advantageous method for
reproducing river shapes, roads, buildings, and paddy fields. Based on this method, I
conducted numerical simulations in three aspects: prediction of levee breaches under
overflow conditions; the behavior of floating litters under breach conditions; andinvestigation of the impact of topographical changes induced by debris flow oninundation.
In the study of levee breach prediction, the focus is on the breaches caused by theflood resulting from the heavy rainfall in western Japan in July 2018. A three-day
period of heavy rainfall, exceeding 400 millimeters, occurred due to a stagnant rainyseason front in the Chugoku region of western Japan, particularly in the upper reachesof the Takahashi River. Record-high rainfall in the upstream area led to a prolonged
increase in water levels near the confluence of the Oda River and Takahashi River,causing levee breaches along the Oda River and its tributaries, including the Suemasa
River, Takama River, and Madani River. In 2019, Typhoon No. 19 resulted in 140
breaches in rivers managed nationally and at the prefectural level. Additionally, heavy
rainfall in Kyushu in July 2020 led to two levee breaches along the Kuma River. Given
the recent increase in levee breaches, developing accurate predictions has become acritical engineering challenge. And in past studies, they did not specifically address
1

the risk of breaches triggered by overflow. So, this study drew upon data from the Oda
River Levee Investigation Committee report and the July 2018 Okayama Prefecture
Heavy Rain Disaster Verification Committee report to compile and investigate
information regarding levee breaches and their underlying causes. Furthermore, flood
simulation results conducted by Maeno et al. were utilized to analyze the primaryfactors contributing to levee breaches, with the aim of exploring the feasibility ofpredicting such breaches through a simplified approach. As a result, the time-averaged
water level difference between the river side and the residential side before the levee
broke emerged as a crucial indicator for predicting overflow-induced levee breaches.
In this study, the emphasis was placed on identifying physical quantities influencing
levee breaches and examining the feasibility of predicting breaches through flood
analysis. As a result, the time-averaged water level difference between the river sideand the residential side before the levee broke was revealed as a crucial indicator forpredicting overflow-induced levee breaches.
In the context of the behaviors of floating litter under breach conditions, against the
backdrop of the 2018 Western Japan heavy rainfall impacting the Oda River, the study
investigated the movement of floating litters generated in urban areas due to the floodin the event of a levee breach. During flood events, floating litter typically comprises
various materials: plastic waste, wood, paper, metal waste, fabric, expanded
polystyrene, rubber, and other miscellaneous items. Floating litter flowing into theriver might cause water pollution and ecosystem damage. Furthermore, floating litter
accumulation at bridges and trees in the river can increase water resistance and friction,
leading to the expansion of flood area. To address the issue of floating debris, earlier
studies mainly conducted research in rivers and coastal areas. However, the behaviorof floating litter during external flooding with levee breaches has not been adequately
investigated. To address this, the comprehensive flood analysis model for this study
was enhanced, incorporating drainage from sluiceways and pumps. Additionally, adetailed flood analysis was conducted until the urban area floodwaters werecompletely drained. A simulation of floating litter movement was then performed
based on the flood analysis results. The findings reveal that more than half of thefloating litter generated in the urban area during flooding remains within the residential
area. Approximately one-fifth of the litter flows out through the breached site andenters the river. The proportion of litter flowing out is higher in areas closer to thebreach locations. Furthermore, around 13% of the litter accumulates at drainage gates.
This result provides valuable information for effective flood management and littercontrol in urban areas affected by levee breaches.
2Regarding the impact of topographical changes induced by debris flow oninundation, the focus is on the compound disaster of concentrated heavy rainfall anddebris flow that occurred in Niimi City in 2019. Heavy rainfall of 120 mm/h occurredfrom around 17:00 on September 3, near Niimi city. Multiple slope collapses occurredat around 18:30, creating debris flows that inundated residential areas. In recent years,
debris flows caused by such high-intensity heavy rainfall in a short period of time havefrequently occurred. Effective numerical analysis is required addressing such issues.
Landslide disasters in enclosed areas, such as Niimi City in this event, are believed tohave non-negligible effects on the state of inland water flow. While numerous paststudies have investigated debris flows, flood scenarios that incorporate debris flow
flooding resulting from surface collapse and inland flooding due to localized heavy
rainfall have not been thoroughly examined. To conduct reproducible calculations forsuch compound disasters, establishing a highly accurate simulation model that
integrates both debris flows and inundation flows is crucial. In this study, reproduction
simulations for the disaster were performed using a model that combines a twodimensional debris flow model and an inundation flow model through a one-way
coupling method. The analysis results revealed that sediment accumulation around thedrainage channel not only reduced the drainage flow rate but also significantly
influenced inundation water flow conditions. This suggests that sedimentaccumulation have contributed to an increase in local inundation depth.
As described above, the applications of the "Comprehensive Analysis Model forRiver Flooding and Inundation" facilitated highly advanced numerical simulations offlood disasters under various scenarios. The results obtained from field applications
have proven to be valuable for disaster prevention and mitigation efforts.
Overall, these studies provide in-depth insights into understanding the complexityof flood disasters and underscore the importance of flood analysis models when
considering various factors comprehensively. The findings have practical implications
for enhancing disaster prediction and management strategies, as well as improving
urban flood control and disaster resilience.

3

Acknowledgement
Completing this doctoral dissertation has been a challenging yet immensely
rewarding journey, and there are numerous individuals to whom I owe my deepest
gratitude. In attempting to express my appreciation, I find it necessary to acknowledge
the invaluable support and guidance from various corners.
First and foremost, I would like to extend my sincere thanks to my advisor, Professor
Akoh and Professor Maeno. Your profound expertise, rigorous scholarly approach, andunwavering support have been the guiding lights throughout my academic pursuit.
Your trust in my abilities and insightful mentorship have played a pivotal role inshaping both my research and personal development.
I wish to express my gratitude to my colleagues in the lab, particularly Ms. Liu, Mr.
Mohammed, and Mr. Pan. Their collaboration and support have added depth anddiversity to my research endeavors. I appreciate the support of all the Japanese
students.
To my family, I owe an immeasurable debt of gratitude. Their unwavering support,
understanding, and encouragement have been my anchor throughout this doctoral
journey. I am fortunate to have them by my side.
Finally, to my friends, who provided solace during challenging times and celebrated
with me during moments of triumph, I extend my heartfelt thanks.
To everyone who has contributed to my academic journey, I extend my sincere
appreciation. Your support has been instrumental in the completion of this dissertation,and I consider myself truly fortunate to have such a wealth of support.
With deepest gratitude.

1

CHAPTER 1

INTRODUCTION
1.1 BackgroundIn recent years, with the ongoing trend of global warming in the climate system,
significant changes have occurred. This change is not limited to a specific region but
represents a global trend, driven primarily by the long-term evolution of the global
climate. With rising temperatures and climate system changes, extreme rainfall events
have significantly increased worldwide, bringing more frequent and intense flood risks
to rivers and towns.
Fig.1.1, sourced from the Japan Meteorological Agency (referred to as JMA in
subsequent text and Fig.1.1), illustrates the annual frequency of days with daily
precipitation reaching or exceeding 200 mm over the past few decades. From the

Number of days per 1300 sites(day)figure, it is evident that the annual occurrence of heavy rainfall events has significantly
increased, with a greater rise in the frequency of more intense rainfall events. Since

Trend=23.7(day/10years)

JMA

Year
Fig.1.1 [National AMeDAS] Number of days with daily precipitation exceeding
200 mm annually1).
INTRODUCTION 1

around 1980, the frequency of heavy rainfall events, such as hourly rainfall exceeding
80 mm, three-hour rainfall exceeding 150 mm, and daily rainfall exceeding 300 mm,
has generally doubled.
This shift poses new challenges for the design and management of river water levels
and urban flood control systems. In recent years, there has been a notable increase inheavy rain events, often accompanied by river flooding and urban inundation. For
example, the Kanto-Tohoku Heavy Rainfall in 2015 resulted in levee breaches on theleft levee of the Kinu River at 21 km2) (Fig.1.2(a)), and the Western Japan Heavy
Rainfall in 2018 led to breaches at eight locations, totalling 3.4 km, 6.4 km, and their
tributaries on the Oda River3) (Fig.1.2(b)).
Frequent heavy rainfall not only triggers inundation and levee breaches but also
leads to the generation of disaster waste. Among the disaster waste, floating littersaccompanied inundation and poses a challenge for environmental cleanup. Fig.1.3

The Kinu River in September 2015

The Oda River in July 2018

Fig.1.2 Inundations in recent years: (a) The inundation at the Kinu River in
September 20152), (b) The inundation at the Oda River in July 20183).
2 INTRODUCTION

illustrates the situation of floating litter during and after the inundation caused by the2018 flood in the Mabi district. Moreover, heavy rainfall can also induce debris flow
and inland flooding, as depicted in Fig.1.4, illustrating the consequences of debris flow
and inland flooding entering urban areas in the Ohta area of Niimi City in 2019.
In response to this trend, enhancing societal resilience becomes crucial. Solely
relying on traditional disaster mitigation measures may be insufficient to adapt to theincreasingly changing climate conditions. Therefore, there is an urgent need to deeply
understand the nature of this global trend and take effective measures to address thecontinuously growing disaster risks. This includes formulating more flexible andadaptive disaster mitigation policies and utilizing emerging technologies andinnovative approaches to enhance urban flood control and disaster resilience.

Fig.1.3 The situations for flooding litters during flooding event (above) and after
flooding event (below) in Mabi district.
INTRODUCTION 3

Fig.1.4 The situations for debris flow and inland flooding (Photo provided by the
Okayama Prefectural Office).

1.2 Previous study
In the past, research has been conducted on the compound disasters of levee
breaches, floating litter and compound disasters involving flooding and debris flow.
With regard to the causes of levee breach. Tabata et al.4）estimated the vulnerability
index of levees during the flood in the Kinu River in 2015. Additionally, it examined
the adaptability of the vulnerability index based on actual levee breach locations
during the flood. Furthermore, the study demonstrated that the vulnerability index
could determine the type of levee breach, focusing on breaches caused by seepage inthe levee body. The concept of the vulnerability index was explained based on
dimensional analysis and seepage flow analysis. The study then longitudinallycalculated the vulnerability index for levees in the lower-middle reaches of the Kinu
River, which suffered multiple breaches during the significant flood in September
2015, and validated the method's validity based on actual damage data. Additionally,
to contribute to future levee maintenance, the study clarified the relationship between
the vulnerability index values and the scale and types of damage.
With regard to floating litters. Adachi et al.5）developed a deep learning model using
a virtual image-based approach specifically for detecting river floating litter in fixedpoint camera images and assessed its practical effectiveness. Taking Osaka
Prefecture's Onchi River as an example, the research analysed the discharge
characteristics of river floating litter. By considering precipitation and the number ofsunny days, an estimation equation for the quantity of floating litter was formulated,
4 INTRODUCTION

and the annual transport volume of floating litter was estimated. The study revealed
the presence of a "First Flush" phenomenon during the initial increase in water levels.
Effective river management measures, such as installing oil fences during nondischarge periods, conducting riverbank cleaning activities before discharge events,
and developing floating litter recovery techniques during discharge events, were foundto significantly reduce the discharge of floating litter.
With regard to coupled phenomena of debris flow and inundation disasters. In a
study by Onaka6), the occurrences of debris flows and river flooding during the heavy
rainfall in July 2018 in the Osogoe area of Iwakuni City, Yamaguchi Prefecture were
investigated. Through post-disaster surveys and UAV inspections, this study analyseddebris flows, runoff, and river flooding in the Osogoe area. The results indicate thatthe river flooding in the Osogoe area was primarily caused by the influx of sedimentand debris carried by debris flows. Without the occurrence of debris flows, the riverflooding might not have taken place. Consequently, effective river management isnecessary in areas anticipating direct debris flow entry into the river to prevent thesubstantial influx of sediment and debris.
In this paper, I explored levee breach prediction, the behavior of floating litter underbreach conditions, and the impact of topographic changes caused by debris flow on
inland flooding, using numerical simulation from different perspectives. The specificdiscussions are presented in Chapters 2 to 5.

1.3 Research Objectives
This study utilizes the "River flood flow combined inundation flow model" detailedin Chapter 2 as the base model. It focuses on the compound disasters of the floodcaused by the July 2018 heavy rainfall in Mabi district and compound disasters
involving inland flooding and debris flow caused by the concentrated heavy rainfall in
Niimi City in September 2019. The investigation covers the following aspects.
In the study of the practical application of numerical analysis in predicting levee
breaches resulting from overflow events, we focused on the flood disaster in the Mabi
district in July 2018 as our research subject. Firstly, we conducted a reproduction
simulation of the flooding. Utilizing the results of simulation and taking into accountparameters such as the width of the Oda River levee, water level differences on eitherside of the levee, and other relevant factors, we explored the factors leading to thebreach of the Oda River levee at the breach points.
INTRODUCTION 5

In the study of the flow characteristics of floating litters under levee breachconditions, the flood disaster in the Mabi district in July 2018 was also selected as theresearch subject. Differing from levee breach predictions, a drainage model was
integrated into the “River flood flow combined inundation flow model", accounting
for the drainage conditions of sluiceways and drainage pump vehicles along the Oda
River. The simulation time for the flooding event was extended, and a reproduction
simulation of the flood was conducted. The study explored the characteristics offloating debris under levee breach conditions by combining the results of flood
simulations with a floating model.
In the study of the impact of topographic changes caused by debris flow on inland
flooding, we focused on the flood disaster in the Niimi city in September 2019 as ourresearch subject. Reproduction simulations for the disaster were conducted using amodel that integrates a two-dimensional debris flow model and an inundation flow
model through a one-way coupling method. Through this model, an investigation was
conducted into the impact of topographic changes caused by debris flow on inland
flooding, considering microtopography.
Through this research effort, the aspiration is to offer more effective and intelligent
disaster prevention solutions to society, helping communities and decision-makers
better understand, predict, and reduce the risks of disasters. This endeavour is geared
towards establishing a safer, more sustainable society and laying a solid foundation
for future disaster management.

1.4 Structure Overview
This research is organized into 6 chapters, each dedicated to exploring specificfacets of the study, Chapter 1 is the introduction, and Chapter 6 is the conclusions. The
introductory chapter sets the stage, offering a concise overview of the research's
context, objectives, and previous studies.
Chapter 2 provides a detailed examination of numerical analysis techniques relevant
to river flooding and inundation. Topics covered include the integrated river flood flow
and inundation flow model, 2D shallow water equations, the Godunov-type finite
volume method, and the nuanced treatment of internal boundary conditions andbuildings.
Chapter 3 shifts focus to the practical application of numerical analysis in predicting
levee breaches resulting from overflow events. With the flood disaster in the Mabi
district in July 2018 as the research subject, firstly conducted a reproduction
6 INTRODUCTIONsimulation of the flood. Subsequently, explored the factors leading to the breach of thelevee at the breach points in the Oda River, considering parameters such as the widthof the levee, water level differences on either side of the levee, and other relevant
factors. It introduces the disaster event, encompassing causes like rainfall and waterlevel conditions, and delineates the resulting damage. The chapter then outlines thenumerical simulation, spotlighting the study area and numerical conditions.
Investigative efforts into the causes of levee breaks lead to a detailed presentation anddiscussion of flood disaster reproduction calculations, levee break predictions, andevaluations.
Chapter 4 transitions into the application of numerical analysis in understanding the
behavior of floating litter during flooding with a levee breach. Similar to Chapter 3,
focusing on the flood events that occurred in the Mabi district in July 2018, this chapter
enhanced the comprehensive flood analysis model by incorporating the drainage
effects from sluiceways and pumps, in contrast to the approach taken in the thirdchapter. A simulation of floating litter movement was performed using flood analysis
results. This chapter commences with an introduction, followed by an overview of theresearch region. Subsequent sections delve into flooding and floating litter analyses,
encompassing model introductions, simulation conditions, and comprehensive results
and discussions.
Chapter 5 introduces the application of numerical analysis in understanding thecoupled phenomena of debris flow and inundation disasters, considering
microtopography. In this chapter, the focus is on establishing a highly accurate
simulation model that combines debris flows and inundation flows. The researchsubject is the debris flow and inland flooding that occurred in Niimi City in September
2019. Reproduction simulations for the disaster were conducted using a model that
integrates a two-dimensional debris flow model and an inundation flow model througha one-way coupling method. It begins with an introduction, followed by a descriptionof the study area's topography and a survey of disasters. The chapter covers fieldobservations, model building, simulation conditions, and concludes with results,
considerations, and a comprehensive discussion.

INTRODUCTION 7

References
1）Japan Meteorological Agency: The historical changes in extreme weather events
such as heavy rainfall and extreme heat days. https://www.data.jma.go.jp/cpdinfo/extreme/extreme_p.html.
2）Kanto Regional Development Bureau (MLIT): Regarding the flood damage in the
Kinugawa River during the 'September 2015 Kanto-Tohoku Heavy Rainfall'.
https://www.ktr.mlit.go.jp/ktr_content/content/000634942.pdf
3）Committee for the Investigation of the Oda River Levee on the Takahashi River
System http://www.cgr.mlit.go.jp/eme-rgency/2018/pdf/02odagawahaifu.pdf
4）Tabata, K., Fukuoka, S., Uchibori S. and Uemura, Y. : Study on estimation methodof levee failure risk based on levee vulnerability index. Advances in River
Engineering, Vol. 23, pp. 387-392, 2017.
5）Adachi, T., Kakehi, K. and Nakatani, Y.: Observation of floating debris in rivers
using a deep learning model and analysis of runoff characteristics. JSCE, Ser. B1(Hydraulic Engineering), Vol. 78, No.2, pp. I_937-I_942, 2022.
6）Onaka, N., Akamatsu, Y., Kono, T. and Yamaguchi, K.: Investigation of complex
disaster of debris flow and flood in Higashi River, Shimata River system by theheavy rain in July 2018. JSCE, Ser. B1 (Hydraulic Engineering), Vol.75, No.1, pp.
260-269, 2019.

8 INTRODUCTION

CHAPTER 2OVERVIEW OF NUMERICAL ANALYSIS
2.1 Comprehensive Analysis Model for River Flooding andInundation
This study employs a comprehensive flood analysis model called “Comprehensive
Analysis Model for River Flooding and Inundation”1), integrating flood flows,
inundation resulting from levee overflow, inflow from breached levee sections, andflooding within embanked areas, including structures. Two-dimensional shallow waterflow equations were used as the fundamental equations. The entire region,encompassing river channels and embanked areas, is discretized using a triangular
unstructured grid, which is an advantageous method for reproducing such as river
shapes, roads, buildings, paddy fields. It usually takes a lot of calculation time to
conduct flood flow and inundation simulation for detailed topography. Therefore, inthis study, parallel programming technique using GPGPU was used for higher
efficiency.

2.2 Two-dimensional shallow water equations
Two-dimensional shallow water equations were adopted for numericalsimulations2): a continuity equation for an incompressible fluid and momentum
equations used under the assumption of hydrostatic pressure without horizontal
diffusion terms in Cartesian coordinates. The detail equations in this study are shown
as below.
U E F++
+S = 0(2.1)
t x y

OVERVIEW OF NUMERICAL ANALYSIS 9

uh
vh




h




1
uvh
 
,
U =  uh  , E =  u 2 h + gh 2  , F = 

2


1
2
2
 vh 
v
h
+
gh




 
uvh

2



0




2
2
2 
 z

n
u
u
+
v
b

−
 − gh  −
43



x
h
S=




2
2
2 
 z

n v u +vb−
 − gh  −
43
 y


h




Where, x is x -coordinate in the Japanese rectangular coordinate system (the fifth
system). y is y -coordinate in the Japanese rectangular coordinate system (the fifth
system). U is conserved quantity vector. E is flux vector in x direction. F is flux
vector in y direction. S is a vector of generation and annihilation terms. t is time.
g is gravitational acceleration. zb is elevation. h is water depth. u is velocity inthe x -direction (east-west direction). v is velocity in the y -direction (north-south
direction). n is Manning’s roughness coefficient.

2.3. The Godunov-type finite volume method
The Godunov-type finite volume method3) was used to solve the hyperbolic
differential equations. The spatial domain of integration was covered by a set of
unstructured triangular cells, which are not necessarily aligned with the coordinates.
Therefore, the topography and building footprints were expressed flexibly. The cellaveraged values for water depth, velocity components, and ground surface elevation
were assigned at the centroid of each triangle.
By integrating the equation over each triangular cell and by application of Gauss’s
theorem to the flux integral, a finite-differential equation for time evolution ofvariables was obtained. The method of characteristics was applied to the flux terms.
Roe’s approximate Riemann solver4) was adopted, based on the first-order upwind
approach. In the finite differentiation of the momentum source term induced by groundslope, an upwind approach was also adopted to satisfy the C-property condition foravoiding nonphysical oscillations by ensuring the balance with the flux term in thesteady condition5). The momentum source term induced by bed friction, which was
expressed by Manning’s roughness, was given by the spatial average.
10 OVERVIEW OF NUMERICAL ANALYSIS

2.4 Internal boundary conditions and treatment of buildings
Effects of levees on a flood flow are expressed by imposing the following internal
hydraulic conditions on line segments where the levees are located.
0.35h1 2 gh1 dl

Q=

if h2 / h1  2 / 3

0.91h2 2 g (h1 − h2 )dl otherwise(2.2)

Fig. 2.1 Conditions of inner boundaries: (a)levees and (b)building walls.

Fig. 2.2 Simplification and redefinition of building footprint pol
OVERVIEW OF NUMERICAL ANALYSIS 11

For those expressions, Q is the volumetric flow rate over a unit length of seawall.
In addition, h1 and h2 denote the water depths above the crown at the upstream anddownstream sides respectively (see Fig. 2.1). The first equation and the second
equation respectively represent free overflow and submerged overflow6).
Ordinary BH models exclude building footprints from the calculation area using afree-slip interior boundary condition. In this study, effects of buildings on a flood flow
are expressed by imposing the following internal hydraulic condition on the line
segments of building footprint outlines.
q = C 2g hout − hin (hout + hin ) / 2(2.3)

Therein, q denotes the flow rate across a unit length of the wall; hout andhin respectively represent the water depths immediately outside and inside the wall;(hout + hin ) / 2 denotes the average wetted height of the wall; (hout − hin ) represents thewater surface difference across the wall (see Fig. 2.2); g stands for gravitational
acceleration; and C is a constant representing the wall permeability resulting from
openings such as doors, windows, or cracks and slits caused by wave impacts. Positive
and negative signs denote cases in which hout  hin and hout  hin , respectively. In an
impermeable condition ( C = 0 ), the model is equivalent to the BH model. An exampleof simplification is portrayed in Fig. 2.2.

12 OVERVIEW OF NUMERICAL ANALYSIS

References
1) Maeno, S., Akoh, R., Nihei, Y., Akamatsu, Y. and Yoshida, K.: Flood disastercharacteristics in Mabi district of Kurashiki city due to heavy rain in 2018 andinvestigation of flooding scenario using river flood flow combined inundation flow
model. JSCE, Ser. B1 (Hydraulic Engineering), Vol.75, issue 1, pp. 387-402, 2019.
2) Akoh, R. and Ishikawa, T.: Yhe numerical simulation of runup tsunami in tone
river caused by the 2011 off the pacific coast of Tohoku earthquake. JSCE, Ser.
B1 (Hydraulic Engineering), Vol.68, No.4, pp. I_1543-I_1548, 2012.
3) Godunov, S. K.: A difference method for numerical calculation of discontinuous
solutions of the equations of hydrodynamics. Math. USSR Sb+, Vol. 47, pp. 271–
306, 1959.
4) Roe, P. J.: Approximate Riemann solvers, parameter vectors, and difference
schemes, J. Comput. Phys., Vol. 43, pp. 357–372, 1981.
5) Zhou, J. G., Causon, D. M., Mingham, C. G., and Ingram, D. M.: The surface
gradient method for the treatment of source terms in the shallow-water equations,J. Comput. Phys., Vol. 168, pp. 1–25, 2001.
6) Honma, H.: Coefficient of flow volume on low overflow weir, Civil Engineering,
Journal of Japan Society of Civil Engineers, Vol. 26, pp. 635–645, 1940 (inJapanese).

OVERVIEW OF NUMERICAL ANALYSIS 13

14 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

CHAPTER 3

PREDICTION OF LEVEE BREACH DUETO OVERFLOW USING FLOODSIMULATION RESULTS IN MABI
DISTRICT OF KURASHIKI CITY
3.1 Introduction
During the period from July 5th to July 7th in 2018, heavy rainfall over 400 mm fellwithin three days triggered by the stagnation of the rainy season front in the Chugoku
region of western part of Japan, specifically in the upper reaches of the Takahashi
River1). Two day rainfall in the upstream area was record high. Consequently, the waterlevel near the confluence point of the Oda River and the Takahashi River, as depicted
in Fig.3.1, experienced a prolonged increase due to the influence of backwater flow.

Fig.3.1 Map near the confluence point of the Takahashi River and the Oda River.
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 15

As a result, breaches of levees occurred at various locations not only along the Oda
River, but also its tributaries, as the Suemasa River, the Takama River, and the Madani
River. In addition, heavy rainfall by the Typhoon No. 19 in 2019, a total of 140
breaches occurred in rivers managed at the national and prefectural levels.
Furthermore, heavy rainfall in Kyushu region in July 2020 caused two levee breaches
along the Kuma River. Considering many levee's breaches occurred in recent years,
developing the prediction of levee breaches becomes an essential engineering
challenge.
Research on the mechanism of levee breaches has been clarified by Sekine2) et al.,
who identified the impact of differences in soil structure of the levee on breaches.
Additionally, Maeda3) et al. compared with natural river sections to elucidate thecharacteristics of breaches in the backwater section. In terms of predicting levee
breaches, Tabata4) et al. conducted a longitudinal assessment of the risk of seepage
failure using a levee vulnerability index, identifying locations with a higher risk of
seepage failure. While these studies provide methods for understanding themechanism of levee breaches and assessing the risk of seepage failure, they do not
specifically address the risk of breaches triggered by overflow.
Therefore, this study utilized data from the Oda River Levee Investigation
Committee1) report and the July 2018 Okayama Prefecture Heavy Rain Disaster
Verification Committee report to compile and investigate information on levee
breaches and their causes. In addition, flood simulation results conducted by Maeno
et al. were employed to analyze the primary causes of levee breaches aiming to explore
the possibility of predicting levee breaches through a simplified approach. It isnoteworthy that this study assumes a scenario where breaches occur approximately 3
hours after the start of overflow, and complex phenomena resulting from breaches
which occurs due to reverse overflow, or more than 3 hours after the start of overflow
are not considered. Additionally, the flooded area caused by the flood, as indicated by
the red dashed line in Fig.3.1, is referred to as the "Mabi district" in the following
section.

3.2 Detailed description of the disaster event
Although situation of the flooding occurred in Mabi district was described indetail by Maeno et al.5), for the better understanding of this study, disaster situation ofthere is quoted in the following section.
16 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

Fig.3.2 Isohyet map of the Takahashi River basin

Niimi
Intensity(mm/h)

Upstream of Takahashi River

Accumulated
rainfall (mm)TojoIntensity(mm/h)

Upstream of Nariwa River

Accumulated
rainfall (mm)Ibara
Intensity(mm/h)

Upstream of Oda River

Accumulated
rainfall (mm)Fig.3.3 Total precipitation in the Takahashi River basin.
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 17

3.2.1 The causes of the disaster3.2.1.1 The rainfall conditions6),7),8)
Fig.3.2 displays the cumulative precipitation over the course of three days from
July 5th to July 7th. Additionally, Fig.3.3 illustrates the hourly and cumulative
precipitation at representative locations in the upstream area of the Takahashi Riverbasin during the same period. From these figures, it is evident that the cumulative
precipitation in the upper part basin, particularly in the northwestern part of the
Okayama prefecture, is approximately 350 to 400 mm, while in the southern part ofthe prefecture, such as in Kurashiki City, it is around 300 mm, classified as heavy
rainfall.
Niimi in the upstream areas of the Takahashi River and Tojo in the upper reachesof the right tributary Nariwa River, rain began around noon on July 5th. Relatively
heavy rain up to 20 mm continued until the evening, and the cumulative precipitation
reached around 100 to 150 mm. After a brief pause in the rain on the morning of the
6th, it became active again in the afternoon, with around 20 mm of rain persisting until
around 10 p.m. There was a slight pause in rainfall around midnight, but then another
20 mm or so of precipitation occurred, and cumulative rainfall reached about 400 mm
around noon on July 7th.
On the other hand, in the Ibara area located in the upper reaches of the Oda River,averaging around 5 to 10 mm of rainfall persisted for an extended period from noon
on July 5th to noon on the 6th, and cumulative precipitation reached about 100 mm.
Subsequently, the rainfall intensified again from around 10 p.m. on the 6th to noon on
the 7th, and cumulative precipitation reached approximately 230 mm.
3.2.1.2 Water level conditions7),8)
Fig.3.4 depicts the locations of water level observation station and peak times ofwater levels along the Takahashi River and the Oda River. Additionally, Fig.3.5
illustrates the temporal variations in water levels at each observation point. At the
Hiwa observation point located 14.2 km upstream from the confluence of the
Takahashi River and the Oda River, the water level increased in linked with rainfall inthe upstream region. Initially, on the afternoon of July 5th, the water level rose
following rainfall, but subsequently decreased temporarily as the rain eases. However,
due to rainfall on July 6th, the water level sharply increased from around 18:00 in theevening, and recorded a remarkable increase of 3.76 m in just 3 hours. The water level
18 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW·Fig. 3.4 Locations of water level observation stations and the peak times of water.

Water
level(T.P.m)
水位(m)
36
35
34
33
32
31
30
29
28
27
26
25
24
7/5 00:00 7/5 12:00

Water level(T.P.m)
水位(m)
35.34

水位
氾濫危険水位
避難判断水位Hiwa
日羽
7/6 00:00

Water
level(T.P.m)
水位(m)
8
7
6
5
4
3
2
7/5 00:00 7/5 12:00

Water
level(T.P.m)
水位(m)
17.0
16.0
15.0
14.0
13.0
12.0
11.0
10.0
9.0
8.0
7.0
6.0
5.0
7/5 00:00 7/5 12:00

7/6 12:00

7/7 00:00

7/7 12:00

7/8 00:00

14
13
12
11
10
9
8
7
6
5
4
3
2
7/5 00:00

12.18

水位
氾濫危険水位
避難判断水位

Sakazu酒津
7/5 12:00

7/6 00:00

7/6 12:00

7/7 00:00

7/7 12:00

7/8 00:00

Water
level(T.P.m)
水位(m)

7.45

水位

Funao
船穂
7/6 00:00

7/6 12:00

7/7 00:00

7/7 12:00

7/8 00:00

21
水位
20
氾濫危険水位19
避難判断水位
18
17
16
15
14
7/5 00:00 7/5 12:00 7/6 00:00

20.63

Yakage矢掛

7/6 12:00

7/7 00:00

7/7 12:00

7/8 00:00

15.5

水位

Yagatabashi
矢形橋

7/6 00:00

7/6 12:00

7/7 00:00

7/7 12:00

7/8 00:00

Fig.3.5 The temporal variation of water levels at observation stations(Water Level: T.P).
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 19

continues to rise significantly, surpassing the "Hazardous water level" of 33.22 m
shortly after 21:00. Around 00:30 on July 7th. The peak water level reached 35.34 m
exceeding the "hazardous water level" by over 2 m. After reaching the peak, the waterlevel temporarily drops by approximately 2 m, but increased again around 10:00 on the
7th. During this period, the water level exceeded the hazardous water level for
approximately 17 hours correlating with the ongoing rainfall.
Regarding the Oda River, Yakage observation point, located 13.0 km upstream fromthe confluence point, similar water level rise with the Hiwa station was observed fromthe afternoon of July 5th. However, the water level temporarily decreased by noon on
the 6th. However, the water level rose again from around 7:00 pm, and by 10:00 pm, it
exceeded the hazardous water level of 19.46 m with significant rate, and its peakreached 20.63 m at around 1:50 on July 7th. Yakage Observation also exceeds thehazardous water level for approximately 17 hours. The second peak at Yakage
Observation has a flattened shape, its reason is considered as levee breaches at threelocations along the Oda River and one location at a tributary in the same area. If there
were no breaches, it is estimated that the peak water level would have appeared at aslightly earlier time.
The peak water level at Yagata Bridge on the Oda River, near its confluence site with
the Takahashi River, occurs at 2:30 on July 7th. Although Sakazu station is locateddownstream of confluence site, peak time there is 1:50, it was earlier than that of theconfluence site. This delay is attributed to the influence of backwater due to the rise inwater levels at the confluence site, and it made difficult for receding the water level.
The water level at Sakazu slightly exceeds the hazardous water level, but downstreamof the confluence point, there is no significant damage to facilities during this flood
event.
The Mabi district experienced a substantial and prolonged exceedance of thehazardous water level. The confluence point is located about 13 or 14 km downstream
from both Hiwa observatory of the Takahashi River and Yakage observatory of the Oda
River located nearly equidistant from each station. According to the "fundamental rivermanagement policy", the planned high water discharge at the confluence point of
Takahashi River and Oda River considers the temporal difference in runoff from eachriver basin. However, in this flooding event, flood peaks of both rivers at the confluencesite were almost the same. As a result, the mild riverbed slope of the Oda Riverpromoted backwater effect and maintained elevated water levels for a long period. This
likely led to multiple breaches in the Mabi district.
20 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

3.2.1.3 Discharge conditions1), 9), 10)
In the current flood, the estimated discharges for Hiwa and Sakazu of the Takahashi
River were 6,960 m3/s and 8,900 m3/s, respectively. Additionally, the estimated flowrate at Yakage of the Oda River was 1,250 m3/s. Concerning the Oda River, thedesigned high water discharge is 2,300 m3/s at Yagata Bridge site, whereas target flow
discharge of river development project is 1,500 m3/s. Even when adding the flow fromtributaries to Yakage's discharge, it is presumed that the flow rate was slightly smaller
than the discharge of river development project. On the other hand, for the Takahashi
River, the target discharge of river development project is 8,000 m3/s compared to thedesigned high water discharge of 13,400 m3/s at Funao station. Since there are notributaries between Sakazu and Funao station, it is evident that the flood exceeded thedischarge of river development project by approximately 10%.
3.2.2 Damage Situation1),5),6)
In the Mabi district, as depicted in Fig.3.6, an unprecedented event occurred withbreaches in eight levees within a limited area. This is nearly unprecedented in recent
years, resulting in extensive inundation covering approximately 27% (about 1,200
hectares) of the Mabi district, which encompasses approximately 4,400 hectares. Thiswidespread inundation caused significant damage in the affected area.
In the case of the Oda River, breaches occurred at 3.4 km (Fig.3.7) and 6.4 km(Fig.3.8) on the left levee, resulting in two breaches. Additionally, among the threetributaries of the Oda River, three locations breached for the Suemasa River (Fig.3.9),
two for The Takama River (Fig.3.10), and one for the Madani River (Fig.3.11). The
red triangles indicate overflow without breaching at 2.4 km (Fig.3.12), 3.2 km, 3.4km, and 7.0 km on the right levee of the Oda River, as well as partial breaching at 0km on the right levee of the Madani River (Fig. 3.13). Table 3.1 presents the reasonsfor breaching based on the findings of the Oda River Levee Investigation Committee.
As shown in the table, overflow occurred at all breaching locations except for the leftlevee of the Suemasa River at 0.4 km. At this location, erosion occurred due tooverflow from the Arii Bridge located upstream of the erosion site. Road surface ofthe bridge was about 2 m lower than the levee crown, then a large amount of waterflows out from there and lead to the eventual breach. In terms of local dynamic
hydraulic gradients and levee heavings, all locations except for the left levee at 0.4 kmof the Suemasa River were below the criterion values. Regarding circular slip
criterion, the possibility of circular slip may not be excluded apart from the left levee
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 21

Fig.3.6 Breached locations of the levees along the Oda River and its tributaries.

Fig.3.7 The situation of the levee breach on the left levee of the Oda River 3.4 km.

Oda RiverFig.3.8 The situation of the levee breach on the left levee of the Oda River 6.4 km.
22 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

Fig.3.9 The situation of the levee breaches on both levees near the Suemasa River
0.7 km.

Fig.3.10 The situation of the levee breach on the right levee of the Takama River
0.1km.

Fig.3.11 The situation of the levee breach on the left levee of the Madani River
0.5 km.
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 23

Fig.3.12 The flooding situation on the right levee of the Oda River 2.5km.

Fig.3.13 The partial destruction situation on the right levee of the Madani River0 km.
at 3.4 km of Oda River, but sufficient evidence was not found to confirm theoccurrence of circular slip during the levee survey around the breached sites.
Additionally, for the possibility of riverside levee erosion due to river flow, thevelocities of all breached sites did not exceed 2 m/s, which is insufficient to erode turf
slope protection or revetments. Therefore, erosion is unlikely to be the cause of thebreaches. Furthermore, although the effect of small channel in riverside flood plain or
siphon culvert structures near the breaching sites was investigated, it is clarified thatthe probability of structures being the cause of the breaches is low. Based on theinvestigation results of the causes of breaches mentioned above, the Oda River Levee
Investigation Committee concluded that the main cause was overflow-induced erosion
24 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

Table 3.1 The results of the investigation into the factors contributing to thebreach conducted by the levee inspection committee.

Breach locations

Oda River 3.4km(left levee)
Oda River 6.4km(left levee)

Occurrence of levee
overflow

OccurredOccurred

Suemasa River 0.4km(left levee)

PipingCircular slip
Potential
Local hydrauliccriterion (river side): riverbed erosion
gradient
Ground heaving(flow velocity
criterion: iv=0.5, criterion: G/W = 1.0 or Fsmin=1.4 or below,
not acceptable.
assessment)
ih=0.5or above, not below, not acceptable.
acceptable.
Low riskiv(－), ih(－)
2.00 (OK)
1.67 (OK)(1.0m/s)
Low risk
iv=0.20, ih(－)
1.31（OK）
1.05 (NG)(1.0m/s)Noneiv=0.4(OK),ih=0.62(NG)(－)

1.19 (NG)

Occurrediv(－), ih(－)

1.21 (OK)

1.03 (NG)

Occurred

（－）

（－）

（－）

Takama River 0.1km(right levee)

Occurrediv=0.04 (OK), ih=0.13 (OK)

1.16 (OK)

0.86 (NG)

Safe (0.8m/s)

Takama River 0.0km(left levee)

Occurred

(－)

(－)

(－)

Safe (0.8m/s)

Madani River 0.5km(left levee)

Occurrediv(－), ih=0.30 (OK )1.01 (OK)1.05 (NG)Safe(0.8 m/s)

Suemasa River 0.7km(left levee)
Suemasa River 0.7km(right levee)

Low risk(2.4m/s)
Low risk(2.2m/s)
Low risk(2.2m/s)due to backwater except for the left levee at 0.4 km of the Suemasa River. Additionally,
although failure caused by seepage force could not be confirmed as main factor,
committee reported that the possibility of seepage failure might not be excluded.
Moreover, river water, rainwater, and inland water infiltrates the levee and weaken thelevee, which influenced erosion of the land side slope during overflow process.

3.3 Outline of numerical Simulation
3.3.1 Study area
In this analysis, the domain was divided using a non-structured triangular mesh, as
described in Chapter 2, with a mesh size of 10m. The total number of meshes was
649,669, and the domain is illustrated in Fig.3.14. The analysis domain extends fromthe upstream observation point Hiwa to the downstream observation point Sakazu for
the Takahashi River, and the upstream observation point Yakage for the Oda River of
the Takahashi River's tributary.
The urban area affected by flooding in this study was delineated based on the resultsof field surveys of the flooded area. It mainly encompasses the urban area on bothlevees of Oda River focusing on the severely affected area of Mabi City. The shape ofthree tributaries of the Oda River, namely the Suemasa River (see Fig.3.15a), theTakama River, and the Madani River as well as the tributary of the Takahashi River,
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 25

Takahashi River 27.6km(upstream discharge)

Elevation(T.P.m)Takahashi
River

Mabi
District

Oda River 13.0km(upstream discharge)

Takahashi River 6.4km(downstream water level)

Fig.3.14 Numerical domain.

Suemasa River

Oda River(a) Expression of tributary(b) Expression of buildings

Fig.3.15 Expression of features
the Shinpon River were included for numerical domain and these rivers were also
divided as triangular meshes. About the treatment of buildings, polygons were createdusing the outline data of buildings from the Foundation Map Information released by
the Geospatial Information Authority of Japan11). These building polygons were
26 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

Manning
coefficientFig.3.16 Roughness distribution.
Oda River(Yakage)

Takahashi(Funao)

8
7
6
5
4
3
2
1
0
7/6 12:00

7/7 12:00

7/8 12:00

Water level(T.P.m)

8000
7000
6000
5000
4000
3000
2000
1000
0
7/5 12:00

7/9 12:00

Fig.3.17 Boundary conditions for Takahashi River and Oda River.
70
60
Discharge(m3/s)

Discharge(m3/s)

Takahashi River(Hiwa)

50

Suemasa River
Takama River
Madani River
Shinpon River

40
30
20

10
0
7/5 6:00 7/5 18:00 7/6 6:00 7/6 18:00 7/7 6:00 7/7 18:00 7/8 6:00

Fig.3.18 Boundary conditions for tributaries.
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 27

7/6 23:30-24:00
Suemasa River right levee(0.7km) 7/7 6:30-7:00
7/7 1:00-1:30 Takama River left levee(0.0km)

Suemasa River left levee(0.7km) 7/7 6:30-7:00
Suemasa River left levee(0.4km) 7/7 6:30-7:00

7/6 23:50-24:20

Takama River right levee(0.5km)

Oda River left levee(6.4km) 7/7 1:30-2:00

7/6 23:30-24:00 Madani River right levee(0.0km)

Oda River left levee(3.4km)

7/7 3:00-3:30
7/7 3:20-3:50
7/7 3:40-4:10

7/7 0:30-1:00 Madani River left levee(0.0km)

Fig.3.19 Breaches of levees (the right levee of the Madani River is partiallybreached).
applied to the calculation grid cells that contain them using the translucent building
model proposed in Chapter 2 (Fig.3.15b).

3.3.2 Simulation conditions
The ground elevation in the landside was determined using the 5-meter meshelevation data from the Geospatial Information Authority of Japan measured in
201312). For the river, the average value of ALB data measured in August 2018 withineach analysis mesh was assigned. Regarding the levee crown elevation of the Oda
River, the highest elevation data within the mesh containing the embankment crest was
utilized from the ALB data. However, for the prefectural managed sections of the
Takahashi River and Oda River, regular cross-sectional survey data from 2011 was
employed, and for tributaries, survey data using RTK-GPS was used in combination.
The distribution of the roughness coefficients is depicted in Fig.3.16. The roughness
coefficient of the riverside was based on values used in quasi-two-dimensional nonuniform flow calculation for designed flood by the Ministry of Land, Infrastructure,
Transport and Tourism. Furthermore, in order to express the roughness effect by the
thick tree region, forested zone was firstly identified using aerial photograph, then theresistance of the flood flow was dynamically changed depending on the dragcoefficient of the forest and the water depth there. With respect to the landsideroughness coefficient, a uniform value of 0.025 was used, which corresponds to road
28 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

and cultivated land.
Fig.3.17 illustrates the upstream discharge and downstream water level of
Takahashi River and Oda River. The upstream discharges were calculated using the HQ equation from the Ministry of Land, Infrastructure, Transport and Tourism in 2017.
Fig.3.18 displays the upstream discharges of the tributaries, which was computed
using hydrological data from the RRI13) model by Sayama et al.
Start times of breach were not clarified for all breached sites, in this study, toidentify the time when the levee starts to breach, an analysis was initially conductedunder the specified boundary conditions which the levee remains intact. Fig.3.19
shows the identified levee overflow start times at nine breach positions, including eightbreach locations and a partial breach position on the right levee of Madani River. In
this paper, these nine positions are referred to as levee breach. According to theguidelines of the Flood Inundation Prediction Zone Map Manual14), half of the final
breach length is instantly removed to the landside ground level and then gradually
expand the breach length in the upstream and downstream directions over the next one
hour. However, the breach length of this flood reached tens to hundreds of m, breachstarted position and its expand rate are unclear. Therefore, for simplification, the leveeheight was linearly decreased to the landside ground level. The time required for thebreach was determined as 30 minutes as a result of a trial comparison of observed
riverside and landside water level at sluice gate with numerically obtained waterlevels.
However, the breach width at the 3.4 km left levee of the Oda River is approximately
100 m, which is longer compared to other breach sites. Therefore, breach site wasdivided into three parts, each requiring and each breach occurs in succession with 30
minutes each (see Fig.3.19).

3.4 Causes of levee breach
3.4.1 Study on the causes of breaches7)
Generally, the causes of levee breaches can be categorized into those induced byflow conditions and those arising from the levee itself as shown in Table 3.2. Flow
conditions encompass riverside water level, landside water level, occurrence ofoverflow, flow velocity magnitude, and local flow variations caused by the local
hydraulic structures. Factors related to the levee itself include levee crown width, leveeslope gradient, levee height, and levee materials. The table shows the impact of these
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 29

30 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

Levee shape

Flow conditions

Major classification

Levee material

Levee heightLandside slope of levee

Crown width

Adjacent local hydraulic structures

Flow velocity

OverflowRiverside water levelLandside water level

Individual factors
In the case of high landside water levels, there is a possibility of seepage failure, suchas piping, occurring by permeating through embankments and their foundations.
Despite not experiencing overflow, the embankment along the Yabe River collapsed
during the heavy rainfall in Northern Kyushu in July 2012, suggesting a highlikelihood of seepage failure
When the landside water level is high, there is a possibility of an increase in soil
moisture content, which may weaken the embankment. Additionally, there is a risk of
breaching when flooded landside water flows reversely overflow to the riverside ofthe embankment, as observed in the breaches on the left levee in the Yagake area of
the Oda River in 2018 and in the Kuma River in the Hitoyoshi area in 2020.
The risk of embankment failure increases significantly when the embankment crest is
overtopped, leading to erosion of the back slope. Overtopping is identified as a major
factor for the breaches along the Odagawa River and its tributaries.
There is a possibility of embankment failure due to erosion or scouring ofembankment slopes and foundations caused by high flow velocities, particularly inturbulent river sections.
The embankment may collapse due to localized water level rise, sudden flowchanges, or infiltration around structures, caused by structures such as bridges, gates,
pipes, and weirs.
When the crown width of the embankment is narrow or not paved, there is a higher
risk of embankment failure.
There is a higher risk of embankment failure when the landside slope ofembankment is steep compared to cases where the slope is mild.
A significant difference in elevation between the crest of the embankment and thelandside ground elevation increases the likelihood of embankment failure due tooverflow or seepage force.
There is a possibility of embankment failure when the compaction andembankment material used during construction are not appropriate.

Situations leading to failure

Table 3.2 Causes of levee breaches.

17level(m)Waterlevel(T.p.m)
Water

16
15
14

Water level outside
Water level inside
Embankment height
Elevation inside

13

12
11

10
9
7/6 23:00

7/7 0:00
7/7 1:00
7/7 2:00
Leftleveeside(With
break)
Left(Leveelevee
breach)7/7 3:00

17level(T.p.m)
Waterlevel(m)
Water

16
15

14
13
12

Water level outside
Water level inside
Embankment height
Elevation inside

1110
9
7/6 23:00

7/7 0:00
7/7 1:00
7/7 2:00
Right
levee
(Nonpresenceleveeof levee
breach)Rightside(Without
break)

7/7 3:00

Fig.3.20 The situations of riverside water level and landside water level at
3.4 km on both levees of Oda River.

independent factors on levee breaches. While it would be better to consider all these
independent factors for breach prediction, for the convenience of utilizing flood
simulation results in predicting breaches, it is advisable to use as few factors as
possible to examine the occurrence of breaches. Therefore, in this study, among thesefactors it was judged that the flow velocity and local hydraulic structures were not
likely to be main breach factors in the Mabi district, they were not included as theconsidered factors. Regarding ground materials, it is extremely difficult to get thecharacteristics of the levee materials by conducting a boring survey on all long river
channels in the longitudinal direction. Therefore, this factor was excluded from theconsideration of breach prediction from the viewpoint of simplicity.
As shown in Table 3.1, the overflow is identified as the primary cause of levee
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 31ΔhRiverside

LandsideDiffusive flooding characterized by the overflow of levee, with a prolonged
duration of significant water level differences.
Levee breachΔhRiverside

Landside

Retention flooding with a sudden increase in internal water levels in a shortperiod.
Nonpresence of Levee breachFig.3.21 Schematic diagram of the water level difference inside and outside thelevee after flooding and the presence or absence of levee breaches.
breaches, although not the sole cause, and the possibility of seepage failure cannot be
excluded. Therefore, in terms of flow conditions, riverside water level, landside waterlevel, and overflow were selected as independent factors. Regarding levee shapefactors, the crest width, landside slope, and levee height were selected because they
are easy to get as individual factors.

3.4.2 Extraction of physical parameters for breach prediction
In the preceding section, we extracted individual factors for breach consideration,
including riverside water levels, landside water levels, overflow, levee crest width,
landside levee slope gradient, and levee height. However, for predicting breaches, it ispreferable to determine the occurrence of breaches from as few variables as possible.
Therefore, further narrow down of the factors for considering the cause of the levee
breach was conducted considering the fact that levee did not breach even withoverflow condition.
Fig.3.20 illustrates the temporal changes of the landside and riverside water levels
on the left and right levees when a breach occurred at 3.4 km on the left levee of the
Oda River. From the figure, it can be observed that the right levee's levee height isapproximately 50 cm lower than the left levee, then overflows began earlier and its
32 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

overflow depths was larger. However, when considering the occurrence of breaches,
the left levee where overflow occurred later suffered a breach, while the right levee
where overflow occurred earlier did not breach. The riverside water levels show asimilar trend on both levees, but there is a significant difference in the variation oflandside water levels. This is because, as shown in Fig.3.21, the inundation area in thelandside on the left levee is larger, which caused a diffusive type flooding (upper
image). On the other hand, the inundation area on the right levee side is much smaller
than that of left levee, which induced a rapid increase water levels in landsideresembling a cumulative flooding (lower image). The left levee where a breachoccurred had a larger difference between landside and riverside water level h ,which is considered to promote ongoing erosion of the landside slope, while h of
the right levee decreased in a short time, therefore it is considered that landside slope
erosion hardly occurred. The difference between landside and riverside water levelh includes factors extracted as independent variables, such as riverside water level,
landside water level, and levee height (relative height difference between levee crownand landside ground elevation), which could be a primary factor for predicting
breaches.
Next, regarding individual factors related to levee shape, the levee crown width andlandside levee slope were considered. A larger levee crown width may make it moredifficult for breaches to occur, and a mild rear slope may also contribute to a lower
likelihood of breaches. Therefore, this study introduces a levee shape coefficient thattakes into account the influence of levee crown width and levee slope as a physicalquantity. Although whether paved levee crown may affect the occurrence of breach,
this study does not consider the impact of paving since the levees in the Mabi area arealmost entirely paved.

3.5 Flood simulation and its verification
3.5.1 Flood flow characteristics
Fig.3.22 illustrates the temporal variation of inundation depths in the urban area of
Mabi City. Around 23:00 on July 6th, inundation began through the land lock on theArii Bridge located 0.4 km of the Suesama River. Additionally, inundation due tooverflow occurred in various areas, including the right levee areas near 0.0 km of the
Madani River, 0.1 km of the Takama River, and around 3.0 km on the right levee of
the Oda River.
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 33

Water depth(m)

7/7 1:00

7/7 0:00

7/7 3:00

7/7 7:00

7/7 11:00

7/7 5:00

7/7 9:00

7/7 13:00

Fig.3.22 Time variation of inundation depth.
34 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

Fig.3.23 Start time of inundation.

Time reaching maximum water levelFig.3.24 Time reached maximum water level.
Maximum water depth(m)Fig.3.25 Distribution of maximum water depth.
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 35

6.0

Calculated value(m)

Area1

5.0
4.0
3.0
2.0
1.0
0.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0

Observed value(m)6.0Calculated value(m)Calculated value(m)

6.0

5.0
4.0
3.0
2.0
1.0
0.0

5.0
4.0
3.0

2.0
1.0
0.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Observed value(m)Observed value(m)6.0Calculated value(m)Calculated value(m)

6.0
5.0
4.0
3.0

2.0
1.0
0.0

5.0
4.0
3.0

2.0
1.0
0.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Observed value(m)Observed value(m)Fig.3.26 Comparison between the maximum computed inundation depth and theobserved values.
36 PREDICTION OF LEVEE BREACH DUE TO OVERFLOWAround 01:00 on July 7th, the flooded area of the in the residential area of near the
Oda River began to expand due to the breach of the levees at 0.1 km on right levee of
the Takama River and 0.7 km on right levee of the Suemasa River. Furthermore, partial
breaches at 0.0 km on the right levee of the Madani River and overflow near 3.0 km
on the right levee of Oda River led to inundation depth exceeding 3 m in the the rightlandside of the Oda River.
Between 01:00 and 03:00 on July 7th, rapid expansion of the inundation area in the
upstream region occurred due to breaches at 6.4 km on the left levee of the Oda River.
Additionally, breaches at 0.5 km on the left levee of the Madani River and multiple
locations of overflow on the right levee of the Oda River resulted in a substantial
increase in the inundation area on the right landside.
From 3:00 to 7:00 on July 7th, the breach at 3.4 km on the left levee of the Oda
River led to a sharp increase of inundation depths in the embanked area sandwiched
between the Suemasa River and Takama River. By 05:00, inundation depths had
exceeded 4 m and reached over 5 m by 07:00.

Water level(T.P.m)

30.0
Observed value(left bank)Observed value(right bank)Calculated value(left bank)Calculated value(right bank)

25.0
20.0
15.0
10.0

Takahashi River
5.0
6.0

Water level(T.P.m)

19.0

8.0

10.0

12.0
14.0
16.0
18.0
Distance from river mouth(km)

20.0

22.0

24.0

Observed value(left bank)Observed value(right bank)Calculated value(left bank)Calculated value(right bank)

18.0
17.0
16.0
15.0

Oda River

14.0
0.0

2.0

4.0
Distance from river mouth(km)

6.0

8.0

Fig.3.27 Comparison of longitudinal water level distribution in Takahashi Riverand Oda River.
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 37

Starting at 07:00 on July 7th, the breach at 0.7 km on the left levee of the Suemasa
River caused a continuous expansion ofReferencesation area on the left levee of the
Suemasa River and inundation depths continued to rise by approximately 15:00.
The distribution of the initial inundation depth (10 cm or more) at the starting
moment is shown in Fig.3.23, and the distribution at the time reached the highest waterlevel is depicted in Fig.3.24.
Inundation of National Route 486 traversing the Mabi area from east to west began
flooding due to levee breaches around 0:00 on July 7th.
According to the data from Fig.3.24, peak time of inundated area between the
Suemasa River and the Takama River (central inundation area), where the direct flood
flow from the rivers is considered to be the largest, was 1 hour different from the leftlevee side of the Suemasa River and 2 hours different from the right levee side of the
Takama River.
Specifically, since breaches occurred on both sides near 0.7 km of the Suemasa
River, flooded water in central area moved passing through the breached sites, andentered and expanded the left side area of the Suemasa.

3.5.2 Comparison of maximum inundation depth
Fig. 3.25 shows distribution of maximum water depth. Fig. 3.26 shows the
distribution of calculated and observed maximum inundation depths in different
regions Areas 1 to 5.
From the figures, it can be confirmed that the reproducibility of model is generally
good. Regarding the reproducibility of each region, inundation depths for Area 1 areslightly underestimated, while those for Area 2 are slightly overestimated. This may
be due to the lack of consideration of the reproducibility of the breach velocity at 0.7
km on both levees of the Suemasa River and the washed out effect of surrounding
buildings. And, inundation depths for Areas 4 and 5 are also slightly underestimated.
Regarding Area 4, the calculated water levels of the Oda River are smaller thanobserved values as shown around 5 km in lower Fig.3.27, therefore it is consideredthat the amount of flooding into Area 4 was underestimated. The inundation in Area 5
is caused only by overflow, and its height depends on the reproducibility of the dam's
crest height. The 200 m interval cross-sectional data and 5-meter grid LP datainterpolation used in the study may not provide sufficient reproducibility. Therefore,
the area near 5 km of the Oda River and its right levee in Area 5 is underestimated.

3.5.3 Comparison of trace and observed water level at observatories
38 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

Kamajiri

KomoikeNomiyaYagatabashi
Oda River

Takahashi
River

500 m

Water level(T.P.m)

Water level(T.P.m)

Water level(T.P.m)

Water level(T.P.m)

Water level(T.P.m)

Water level observatory
SakazuSluiceway
17
14

Nomiya Sluiceway

11
8
Observed value
Calculated value

52
7/5 12:00

7/6 0:00

7/6 12:00

7/7 0:00

7/7 12:00

7/8 0:00

17
14

Komoike Sluiceway

11

8
Observed value
Calculated value

52
7/5 12:00

7/6 0:00

7/6 12:00

7/7 0:00

7/7 12:00

7/8 0:00

17
14

Kamejiri Sluiceway

11
8
Observed value
Calculated value

52
7/5 12:00

7/6 0:00

7/6 12:00

7/7 0:00

7/7 12:00

7/8 0:00

14
11

Sakazu Observatory

8
Observed value
Calculated value

52
7/5 12:00

7/6 0:00

7/6 12:00

7/7 0:00

7/7 12:00

7/8 0:00

18

15

Yagatabashi Observatory

12

Observed value
Calculated value

96
7/5 12:00

7/6 0:00

7/6 12:00

7/7 0:00

7/7 12:00

7/8 0:00

Fig.3.28 Comparison of water level changes over time.
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 39

Table 3.3 Average internal and external water level difference and levee
shape coefficient during overtopping in the Mabi district.
Evaluation points

Occurrence Average waterof leveelevel difference
breachΔh(m)Oda River 3.4km(left levee)

Occurred

Oda River 3.4km(right levee)

Levee shapecoefficient(Crown width B ×
Levee slope M)

Crownwidth B(m)

Landside slope gradient M
(1:M)

5.29

8

4

2

Not occurred

2.11

8

4

2

Oda River 6.4km(left levee)

Occurred

3.65

8

4

2

Oda River 2.4km(right levee)

Not occurred

0.76

8

4

2

Oda River 3.2km(right levee)

Not occurred

0.89

8

4

2

Oda River 7.0km(right levee)

Not occurred

3.05

8

4

2

Suemasa River
0.7km(left levee)

Not occurred

2.64

4.5

3

1.5

Suemasa River
0.7km(right levee)

Occurred

3.26

4.5

3

1.5

Takama River
0.1km(right levee)

Occurred

4.70

4.5

3

1.5

Madani River
0.0km(right levee)

Occurred

2.45

4.5

3

1.5

Madani River
0.5km(left levee)

Occurred

3.55

4.5

3

1.5

Madani River
0.5km(right levee)

Not occurred

1.56

4.5

3

1.5

Fig.3.27 depicts a comparison between the longitudinal maximum water levels inevery 200 m for the Takahashi River and the Oda River and the obtained ones fromthe model analysis. For the Takahashi River, the numerical results agree well withthe measured values, therefore the validity of the model is confirmed.
However, concerning the Oda River, although there is an overall good replicability,
the analysis values between 3 km and 6 km slightly underestimate by several tens of
cm. This discrepancy could be attributed to that riverbed heights in the analysis grid
was interpolated using 200-meter interval cross-sectional data, and that the data fromthe Geospatial Information Authority of Japan was not just before the flood event.
In Fig.3.28, the observed water level variations over time for each sluiceway arepresented along with the corresponding simulated results. According to the data fromeach water level observation station, the model-simulated including levee breachresults show in good agreement with the observed values. This indicates that thetiming and conditions of levee breaches used in the analysis as shown in Fig.3.19 are
40 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

Embankment shape coefficient

9
8
7
6
5
4
3
2
1
0

Madani River 0.0km(right side)
Partial failure location

0.0

1.0

Suemasa River
0.7km(left side)
Failure several
hours after overflow

2.0
3.0
4.0
5.0
Average in/out water level difference

6.0

Fig.3.29 Relationship between the occurrence of breaches and the river-landsidewater level difference, and levee shape coefficient.
generally reasonable. Especially, calculated water levels around peak time areconsistent with the observed values.

3.6 Levee breach prediction and feasibility assessment
3.6.1 Considerations for levee breach prediction criterions
Through trial and error based on the results from the previous section 3.4.2, thefollowing three conditions are introduced as criteria for levee breach prediction:(1) Presence of overflow: Overflow occurs in the analysis.
(2) River and land side water level difference: The average river and land side
water level difference within one hour from after the river side water level exceeds
height of 0.2 m lower than the levee crown. However, if the landside water levelexceeds the levee height within one hour, use the average internal-external water level
difference until that time.
(3) Embankment shape coefficient: Shape coefficient is calculated as B×M using
the levee crown width B and land side bank slope ratio 1:M.
Here, taking into account the analytical errors in water level and the need for early
prediction, relative water level difference of river and landside is evaluated from after
exceeding 0.2 m lower water level than the levee crown. B×M is chosen because it isbelieved that the levee width and landside levee slope have a synergistic effect that can
PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 41

Discrimination score

6
Suemasa River
0.7km(left side)
Failure several
hours after overflow

4
2

Coefficient of determination
a=2.2290b=-0.543
c=-2.902-2-4-6
Fig.3.30 Discriminant analysis results.

inhibit levee breach.
Table 3.3 shows various parameters applied to the locations shown in Fig.3.6 using
the conditions mentioned above. However, places such as the left levee at 0.4 km of
Suemasa River and the left levee at 0 km of the Takama River are excluded fromconsideration because factors other than overflow may exist there. Although the rightlevee at 0 km of the Madani River experienced partial damage, it is classified as a levee
breach due to the complete loss of the levee crown. For the left levee at 0.7 km of the
Suemasa River, although overflow occurred around midnight on July 6th, breach did
not occur during initial overflow because the water level temporarily decreased due tothe right levee breach at that time. However, after a few hours later, around 6:00 to
7:00 on July 7, the left levee breached due to reverse flow from the inundated water inright landside. Therefore, in this study, it is assumed that breach did not occur there
during initial over flow.
Table 3.4 Results of the breach estimation for Suna River and Kuma River.
Evaluation
pointsOccurreceof Levee
breachAverage in/out
water level
differenceΔh(m)Levee shape coefficient(Crown width B ×
landside slope gradient
M)

Crown
width B(m)

Landside
gradient M(1:M)

Discrimination
score

Suna River
11.2km(leftlevee)

Occurred

4.87

4.5

3

1.5

5.5

Occurred

Kuma River
55km(leftlevee)

Not
occurred

0.44

9

4.5

2

-6.8

Not occurred

Kuma River
56.4km(Right Not occurred
levee)

2.19

9

4.5

2

-2.9

Not occurred

42 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

Levee
breach堤外地水位
堤内地水位
堤防高
堤内地地盤高

水位(m)

9
8
7
6
5
4
3
2
7/6 23:00

7/7 0:00

7/7 1:00

7/7 2:00

7/7 3:00

Suna River 11.2km left side
Fig.3.31 Analysis results of the river and landside water levels at the breachedsite on the left levee of the Suna River at 11.2 km (Western Japan
Heavy Rainfall in the 2018).

水位（m）

102

100
98
96

堤外地水位
堤内地水位
堤防高
堤内地地盤高94
7/4 4:00 7/4 7:00 7/4 10:00 7/4 13:00 7/4 16:00

Kuma River 55km left side
Fig.3.32 Analysis results of the internal and external water levels at the breachedsite on the left levee of the Kuma River at 55 km using IRIC (the heavy
rainfall in July 2020).

PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 43

With or without breach for evaluation location is shown in Fig.3.29 using parametes
as time-averaged river-landside water level difference and levee shape coefficient.
From the figure, it can be observed that an increase in the average river-landside waterlevel difference makes levee breach more likely, and an increase in the levee shapecoefficient makes breach less likely.

3.6.2 Evaluation of levee breach prediction method
In this study, we conducted a linear discriminant analysis based on the average riverlandside water level difference h and the levee shape coefficient K shown in Table
3.3 to predict the occurrence of levee breach. Fig.3.30 shows the analysis results.
Locations with discriminant score a h bK c greater than 0 predict the occurrenceof breach, while those less than or equal to 0 predict without breach. From the figure,it can be observed that all locations including partially damaged sites were successfully
predicted. However, the left levee at 0.7 km of the Suemasa River was predicted thebreach occurrence, where breach did not occur during initial overflow. Although thissite was judged incorrectly, breach occurred after several hours at this site as describedabove.
Next, this prediction method was applied to two breached rivers. First consideredsite is at 11.2 km on the left levee of the Suna River, left tributary of the Hyakken Riverof the Asahi River basin, it was breached in July 2018 Western Japan Heavy Rainfall(Fig.3.31). Second site is at the left levee at 55 km and right levee at 56.4 km of Kuma
River, these sites were breached during the heavy rain in July 2020 (Fig.3.32).
Although the Kuma River did not breach in the early stages of overflow8), it breachedduring reverse overflow. Table 3.4 shows the results of evaluating the possibility ofbreach due to overflow at these locations using the discriminant coefficients in
Fig.3.30. For the Suna River, since the average river-landside water level difference
was approximately 5 m, which is large enough to predict the actual breach successfully.
For the Kuma River area, the prediction does not indicate breaches due levee overflow,which is consistent with the fact that breached did not occur in the early stages ofoverflow. These results demonstrate the effectiveness of the breach prediction method
based on the river-landside water level difference and the levee shape coefficient
proposed in this study.

44 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

3.7 Conclusion
Obtained main results are as follows:(1) Possibility of levee breach increases in case of a diffusive overflow flooding,where the inundated area is large. Conversely, levee breach becomes hard to occur incase of storage type flooding, where the landside water level rises rapidly.
(2) As the one hour averaged river-landside water level difference increases, levee
becomes more susceptible to breach.
(3) By combining the flood analysis results for the Mabi area with indicators suchas river-landside water level difference and levee shape, a discriminant analysis canaccurately predict the possibility of levee breach during flood overflow.
The simplified levee breach prediction method proposed in this study can identify
locations with a high risk location of levee failure, which aids levee reinforcement
efforts and enhances public awareness of potential crises. However, it should be notedthat the results of this study are specific to rivers experiencing flooding in the Mabiarea. To generalize the prediction method and improve accuracy, further accumulationof validation data is necessary.

PREDICTION OF LEVEE BREACH DUE TO OVERFLOW 45

References
1) Report of the Oda River Levee Investigation Committee, 2020.
2) Sekine, M., Horie, T. and Sato, K.: Study of process of levee breaching. JSCE, Ser.
B1 (Hydraulic Engineering), Vol.74, pp.1057-1062, 2018.
3) Maeda, S., Shimada, T. and Yabe, H.: A study on the levee breech in the backwaterreach based on the investigation of the past cases. Advances in River Engineering，Vol. 25, pp. 547-552, 2019.
4) Tabata, K., Horiuchi, T. and Fukuoka, S.: Estimation of river storage volume andlevee failure risk during a large flood event and consideration of a future river
improvement in the Chikuma river with sequence of valleys and basins. Advancesin River Engineering，Vol. 25, pp.553-558, 2019.
5) Maeno, S., Akoh, R., Nihei, Y., Akamatsu, Y. and Yoshida, K.: Flood disastercharacteristics in Mabi district of Kurashiki City due to heavy rain in 2018 andinvestigation of flooding scenario using river flood flow combined inundation flow
model. JSCE, Ser. B1 (Hydraulic Engineering), Vol. 75, No.1, pp. 387-402, 2019.
6) MLIT ： Flood Inundation Area Mapping Manual (Revised Edition) ， 2014.
https://www.mlit.go.jp/river/shishin_guideline/pdf/manual_kouzuishinsui_1710.p
df7) Report of the Kuma River Levee Investigation Committee, 2021.
8) Okayama Local Meteorological Office：About the heavy rain caused by Typhoon
No. 7 and the stationary front from July 3 to 8, 2018.https://www.jmanet.go.jp/okayama/topix/20180710.pdf (Accessed on March 1, 2019.)
9) MLIT: Overview of flooding in the Chugoku Regional Development Bureau Area
due to heavy rain in July 2018. http://www.cgr.mlit.go.jp/emergency/syussui.htm10) MLIT: Basic policy for River Development in the Takahashi River System. 2007.8.
11) MLIT: River Development Plan for the Takahashi River System. 2018.6.
12) Geospatial Information Authority of Japan: Foundation Map Information
Download Service. https://fgd.gsi.go.jp/download/menu.php (Accessed on August
1,2018.)13) Sayama, T., Ozawa, G., Kawakami, T., Nabesaka, S. and Fukumi, K.: RainfallRunoff-Inundation Analysis of Pakistan Flood 2010 at the Kabul River Basin,
Hydrological Sciences Journal, Vol.57, No.2, pp.298-312, 2012.
14) Okayama Prefecture 'July 2018 Heavy Rain' Disaster Verification Committee
Report. 2019.https://www.bousai.go.jp/fusuigai/suigai_dosyaworking/pdf/okawamahonpen.pdf
46 PREDICTION OF LEVEE BREACH DUE TO OVERFLOW

CHAPTER 4

EVALUATION OF BEHAVIOR OF
FLOATING LITTER DURING FLOODING
WITH LEVEE BREACH BY USINGINUNDATION ANALYSIS
4.1 Introduction
During flood events, the floating litter typically comprises various materials: plastic
waste, wood, paper, metal waste, fabric, expanded polystyrene, rubber, and othermiscellaneous items. Floating litter flowing into the river might cause water pollution
and ecosystem damage. For example, as shown in Fig. 4.1(a), a substantial
accumulation of floating litters was observed at the river mouth weir of the Onga Riverin northern Kyushu after flood event1). Furthermore, the floating litter accumulation atbridges and trees in the river can increase water resistance and friction, leading to
expansion of the flood range2),3),4). As shown in Fig. 4.2(b), a noticeable accumulationof floating debris was observed on the Arii Bridge in Mabi district after the recessionof the flood. Therefore, monitoring the actual situation, sources, and transport
pathways of floating litter and taking corresponding measures is an important task.
Heavy rainfall occurring in western Japan in July 2018 caused severe flooding in Mabi
town, Kurashiki city, Okayama prefecture. According to estimates, the disastergenerated approximately 443,000 tons of waste in Kurashiki city, which is equivalent
to 64% of the annual general waste-processing volume5). As depicted in Fig. 4.2, theflood disaster resulted in extensive damage to housing damage, prompting residents todiscard a substantial amount of waterlogged furniture and appliances. The widespreaddisposal of these items poses significant challenges for both the environmental impact
and post-disaster cleanup efforts. Moreover, the heavy rainfall caused the collection of
EVALUATION OF BEHAVIOR OF FLOATING LITTER 47

(a)※ From MLIT Onga River Office homepage

Fig. 4.1 Floating litters in rivers: (a) Floating litter accumulated at river weir of theOnga River1). (b) Floating litter accumulated on the Arii Bridge.
approximately 1,615 cubic meters of driftwood and other litter from the Seto InlandSea, including Bisan Seto, Bingo Seto, and Hinase, which are located adjacent toOkayama prefecture6). Fig. 4.3 presents some accumulated floating litter around thesluiceway during the inundation. Findings indicate that large amounts of floating litterare generated in residential areas. Therefore, clarifying floating litter behavior during
flood events is extremely important.
To address these issues, several studies have been conducted based on fieldobservations. Nihei and Wakatsuki7) investigated the amounts of floating littertransported during flood events of the Ohori River. The findings clarified that thevolume of floating litter during the rising stage is 10 times greater than that during therecession stage. Moreover, the amount of floating litter depends on the flood scale. In
48 EVALUATION OF BEHAVIOR OF FLOATING LITTERFig. 4.2 The disaster debris in Mabi district in 2018.

Fig. 4.3 Floating litter at the recession stage in residential area
(Komoike sluiceway).
EVALUATION OF BEHAVIOR OF FLOATING LITTER 49

addition, Okano and Andou8) analyzed 7 years of monthly monitoring data acquired in
Tottori prefecture, specifically investigating the influence of river outflow on theamount of floating litter washed ashore. As a study of floating litter behavior using
numerical analysis, the driftwood behavior during flooding has been examined. For
instance, Kato et al.9) conducted numerical simulations to elucidate the behavior ofdriftwood at a driftwood capture facility by combining a quasi-three-dimensional
flood flow model and discrete element method.
In this way, earlier studies mostly addressed floating litter in rivers or coastal areas.
However, as presented in Fig. 4.3, floating litter behavior during external floodingwith levee failure has not been investigated adequately. To examine the behavior offloating litter during such flooding events, it is necessary to consider not only flow
conditions because of levee failures appropriately, but also drainage by sluiceways andpumps.
Therefore, this study aimed at clarifying floating litter characteristics by numericalanalysis applied to data of flooding in Mabi City caused by heavy rains in July 2018.
First, a drainage model incorporating a sluiceway and a pump into the comprehensive
flood analysis model10) was introduced. Furthermore, flood flow and inundation flow
Suemasa River

Nomiya
S1

S2

S3 S4
Takahashi River

Takama River
Yagatabashi
Oda River 3.4km

Oda River
500 m

Madani River

Levee breakbreachBank
Water level observatory
Sluiceway
Drainage pump vehicles

Fig. 4.4 Orthophoto of study area.

Table 4.1 Sluiceway specifications.

50 EVALUATION OF BEHAVIOR OF FLOATING LITTER

SakazuFig. 4.5 Examined sluiceway, S1-S4.
analysis until flood waters in the urban area had drained. Using the obtained results,
we investigated the floating litter behavior was investigated using numericalexperiments with a numerical float model11). The floating litter characteristics were
evaluated quantitatively.

4.2 Overview of the Research Region
For this study, the analytical domain based on an earlier study reported by Maeno
et al.10) was extened. Additionally, drainage pump vehicles and sluiceways areincorporated. Fig. 4.4 portrays the study area and drainage facilities; The red triangles
denote the sluiceway positions situated on the Oda River. And the specifications forsluiceways collected within the field observation. The closely examined four
EVALUATION OF BEHAVIOR OF FLOATING LITTER 51

sluiceways illustrated in Fig. 4.5 are set as S1-S4. Table 4.1 presents the sluiceway
specifications: S1, the largest sluiceway in the study area, is located on the right leveeside of the Suemasa River; S2-S4 are located on the left levee side of the Suemasa
River. Around S2 and S3, accumulation of floating litter was confirmed as presented
in Fig. 4.3. Furthermore, the levee breach points are denoted by white crosses. The
water level observatories are denoted by blue triangles.

4.3 Flooding Analysis
4.3.1 Model introduction
For this study, flooding analysis was conducted using a comprehensive flood
analysis model10). The model was based on two-dimensional shallow water equations.
The governing equations are discretized using finite volume method on a triangularmesh system. In addition, by creating a triangular mesh along buildings and riverlevees and by applying internal boundary conditions, one can examine details of theeffect of building placement and levee breach placement. Chapter 2 provides a moredetailed description of the model.
A drainage model was introduced for this study to assess the sluiceway and pumpvehicle effects. The drainage meshes were set on the urban area side and on the river

River

h2

h1>h Urban area

Flow

River

Flow

h

h1<h

h1

Urban areahFig. 4.6 Drainage model of sluiceway.
52 EVALUATION OF BEHAVIOR OF FLOATING LITTER

h1

Fig. 4.7 Drainage operations conducted by pump vehicles13) (Photo: provided
Ministry of Land, Infrastructure, Transport and Tourism).
side, respectively. Furthermore, it was introduced simply by considering the drainage
discharge as the source term of the continuous equation of each drainage mesh. The
method of calculating the drainage discharge from the sluiceway and the pump vehicle
is presented below.
The drainage discharge from the sluiceway is estimated using the following
equations.
C 2 g h A
2 1
Q = 1
 AR 3 I 2
n( h1  h )( h1  h )(4.1)

Fig. 4.8 Boundary condition at observation stations.
EVALUATION OF BEHAVIOR OF FLOATING LITTER 53

Water level(T.P.m)

0.4

12

0.3

10

0.2

8

0.1

6
7/5 0:00

7/6 0:00

7/7 0:00 7/8 0:00 7/9 0:00
Kanekura Sluiceway(S1)Outer water level

16

T1

T2

0
7/10 0:00

Water level difference

0.5

T3 T4

14

0.4

12

0.3

10

0.2

8

0.1

6

7/6 0:00

Inner water level16

7/7 0:00 7/8 0:00 7/9 0:00
Kamejiri Sluiceway(S2)Outer water level

T1

T2

0
7/10 0:00

Water level difference

1.8

T3 T4

14

1.4

12

1

10

0.6

8
7/5 12:00

0.2
7/6 12:00

Inner water level

18
16
14
12
10
8
6
7/5 0:00

7/7 12:00 7/8 12:00
Komoike Sluiceway(S3)Outer water level
T1

7/6 0:00

T2

Water level
difference(m)

0.5

T3 T4

14

7/5 0:00

Water level(T.P.m)

T2

Water level
difference(m)T1Water level difference

Water level
difference(m)16Inner water level

Water level(T.P.m)

Outer water level

7/9 12:00
Water level difference

T3 T4

7/7 0:00 7/8 0:00 7/9 0:00
NomiyaNomiyaSluiceway(S4)Sluiceway(S4)

1.8
1.5
1.2
0.9
0.6
0.3
0
7/10 0:00

Fig. 4.9 Observation data of sluiceways(S1-S4).

54 EVALUATION OF BEHAVIOR OF FLOATING LITTER

Water level
difference(m)Water level(T.P.m)

Inner water levelTable 4.2 The time when the event of interest occurred.

Therein, Q stands for discharge, C (=0.6) is the discharge coefficient, g represents
the gravity acceleration, A expresses the cross-sectional flow area below the sluiceway,
n is the Manning coefficient, R signifies hydraulic radius and I denotes the hydraulicgradient. Also, h symbolizes the sluiceway height, h1 represents the water level ofurban side, and h2 stands for the water level of the river side, Δh denotes the differencein water levels h1- h2, as illustrated in Fig. 4.6. When h1 exceeds h2, the sluiceway
gates are opened to initiate drainage operations. The sluiceway drainage is categorized
into two types. The first type occurs when h1 is higher than h. The drainage discharge
is calculated based on the water level difference between the urban area side and theriver side of each sluiceway. The second type occurs when h1 is lower than h. The

Oda River
Takahashi River:Position of the
training levee breachFig. 4.10 The training levee failure at the confluence of the Oda River and Takahashi
River15) (Photo provided by ASIA AIR SURVEY CO., LTD.).
EVALUATION OF BEHAVIOR OF FLOATING LITTER 55

Elevation(T.P.m)Takahashi River
Oda River

Levee breachFig. 4.11 The training levee failure in numerical simulation.
drainage discharge is estimated using the formula for normal flow depth.
The drainage discharge from the pump vehicle as shown in Fig. 4.7 was set as aconstant value during the drainage period. Here, the constant value was obtained by
dividing the total drainage discharge by the number of drainage meshes. Furthermore,
the total drainage discharge was found based on the number of dispatched drainage
pump vehicles, as indicated in the data provided by the Chugoku Regional
Development Bureau 12).

4.3.2 Simulation conditions
Reports of earlier studies10) describe the simulation period as 20:00 on July 5, 2018,
through 2:00 on July 8, 2018 (with July 7, 0:00 being the approximate peak time). At
the end of the simulation, the water depth in the Mabi City area ranged from 3-5 m;
the water flow velocity in the urban area was high. Predicting the drifting points offloating litter necessitates analysis until the time when the urban area flooding isalmost resolved by drainage from sluiceways and pumps, not until the time when theriver water level decreases. Therefore, this study extended the flood simulation timefrom 2:00 on July 8 to on 0:00 July 10. Observed discharges and water level data wereused as boundary conditions (see Fig. 4.8). Additionally, the calculation conditions
described in Chapter 3 was adopted, such as the elevation and Manning's coefficient.
Some water level data observed at the sluiceways provided by the Japanese Ministryof Land, Infrastructure, Transport and Tourism (MLIT) are presented in Fig. 4.9. The
gray line in the graph represents the water level difference obtained by subtracting theouter water level from the inner water level. Around 15:00 on July 7, the inner water
56 EVALUATION OF BEHAVIOR OF FLOATING LITTERFig. 4.12 The floats setting areas.
Water depth(m)2018 7/7 20:00
Building
Kamejiri
Sluiceway

Fig. 4.13 Velocity distribution around sluiceway.
Table 4.3 Initial position and number of floats.

EVALUATION OF BEHAVIOR OF FLOATING LITTER 57

level started to exceed the outer water level. At 17:00, the inner water level began todecrease. Based on this observation, it is speculated that the sluiceways were openedat this time. At 15:00 on July 8, the rate of decrease of the inside water level
accelerated. Combined with information provided by the levee investigationcommittee14), we speculate that the drainage pump vehicles started operating at thistime. To ease consideration, the times of T1-T4 shown in Table 4.2 are drawn withblack dashed lines on each figure after Fig. 4.8.
In accordance with Fig. 4.10, during the present flood event the training levee
breached at the confluence of the Oda River and the Takahashi River 15). However,detail records of the exact timing of the breach of training levee and the elevation at
the breach site are unavailable. Therefore, it was assumed that the levee failure occurs
at the same time as the flood peak, 2:00 a.m. on July 7th. Dashed line in Fig. 4.11
illustrates the extent of the breached levee. Breached elevation at the levee was set as
6.0 m which is the same bed level near the Oda River.

4.4 Floating litter analysis
4.4.1 Model introduction
A numerical floating model developed by Akoh et al.11) which estimates the floating
position at each time using results of flood flow analysis was used in this study.
Although their model used a quasi-three-dimensional model to get bottom and surface
velocities, depth averaged velocity using a two-dimensional model described in
Chapter 3 was used in this study. Because the model cannot incorporate collisions
among floats, more advanced models must be used for more detailed studies. However,Fig. 4.14 Water level comparison at observation stations.
58 EVALUATION OF BEHAVIOR OF FLOATING LITTER

the model is regarded as effective enough for simple investigation of the floating litter
movement characteristics.

4.4.2 Simulation conditions
Residential areas are prone to generate floating litter during floods. Therefore, theinitial floats positions were set in the urbanized area, as presented in Fig. 4.12. Within
the flood analysis area, floats were placed on both sides of the densely populated
Takama River, at the left and right levees of the Suemasa River, and in the area near
the levee on the right levee of the Takahashi River, which is located farther away fromthe breach site. Table 4.3 shows the number of floats set up, with one float placed
every 40 m in the urban area. Length of float is 10 cm. Float begins to move when thewater depth becomes larger than submerged float length. Whereas, it stops when thewater depth becomes smaller than its submerged length.
Numerical tracking for the floats covers the period from 0:00 on July 7 to 10:00 on
July 9. This timeframe encompasses the time when the breach occurred until thefloodwater in the urban area almost subsided.

Fig. 4.15 Hydrograph at sluiceways: (a) discharge and water level difference;(b) water level of urban area side and river side.
EVALUATION OF BEHAVIOR OF FLOATING LITTER 59

4.5 Results and discussions
4.5.1 Verification for flooding simulation and discussions for drainage
4.5.1.1 Verification of simulation validity
Fig. 4.13 depicts calculated velocity distribution around sluiceway. In this figure,the white triangle represents the mesh of the sluiceway mentioned earlier. From thefigure, it is evident that the inundated water flows towards the grid of the sluicewaywith swirling. Therefore, it is concluded that the drainage gate model is functioning as
intended.
Fig. 4.14 presents a comparison between observed water levels and calculated
results at observation stations along the Oda River and the Takahashi River. Results
obtained for both rivers show reasonable agreement, indicating a satisfactory degreeof accuracy in the flood analysis. Therefore, it can be inferred that the flood analysis
results are applicable to the calculation of floating litter.
4.5.1.2 Drainage results
Fig. 4.15 (a) portrays the hydrograph of the drainage discharge and of the waterlevel difference between the urban area side and the river side of S1 to S4. Until time
T4, when the pump vehicle’s operations started, the drainage discharge from each

A5
A4

A3

A1

A2
Fig. 4.16 Initial state of the floating.

60 EVALUATION OF BEHAVIOR OF FLOATING LITTERFig. 4.17 Track of the float: (a) F1 and F2. (b) F3 and F4.
Table 4.4 Starting and ending position of floats.

sluiceway was an almost constant value. When the drainage pump vehicles began
pumping, the water depth in the urban area started to decrease more rapidly, leading
to a decline in the discharge volume at S2-S4, which located in the left side of the
Suemasa River. Around midnight on July 9, the water level difference approached 0m; the drainage discharge of S2-S4 also approached 0 m3/s.
However, in the case of S1, the drainage discharge initially exhibited an increasing
trend after time T4. From Fig. 4.15(b), it is evident that the S1 behavior differs fromEVALUATION OF BEHAVIOR OF FLOATING LITTER 61

the other three sluiceways. Until around 4:00 on July 9, the urban area side water level
was higher than that of the river side. By approximately 8:00, the water level of theurban area side became nearly equal to that of the river side. Finally, around 11:30, theinundation on the urban area side was mostly resolved. The drainage discharge from
S1 became 0 m3/s

4.5.2 Results and discussions of floating litters
4.5.2.1 Trajectory of floats and overall distribution
Fig. 4.16 presents the distribution map of floating objects. The initial state of thefloating objects is configured in this way. Fig. 4.17 illustrates the trajectories and timecourse of the float in 4 different cases. The white cross symbols in the figure represent
the locations of several breaches that occurred during the flood analysis, which can bereferenced in Fig. 4.2. Table 4.4 provides information on the starting and ending
positions of the float for each of the 4 cases. The results of F1 and F2 are shown in
Fig. 4.17(a), and That of F3 and F4 are shown in Fig. 4.17(b).
In Fig. 4.17(a), after the breach occurred at 0.1 km from the Takama River breachsite, F1 followed the westward flow of the floodwaters into the urban area.
Subsequently, as floodwater were discharged from the breach, the float followed thefloodwaters and moved out from the breach site of the Takama River. When it reached
3.4 km of the Oda River breach site where the water level of the Oda River was higher,

Fig. 4.18 Distribution of floats at the final moment of calculation.
62 EVALUATION OF BEHAVIOR OF FLOATING LITTERFig. 4.19 Number of accumulated floats at the sluiceways.

Fig. 4.20 Number of floats which through breach.
the float was flushed back into the residential area by floodwaters from the left leveeof the Takama River. After the sluiceways were opened, the floodwaters weredischarged through S1. The float moved along with the floodwaters to the vicinity ofthe sluiceway. After breaches occurred on both the left and right levees of the Suemasa
River, F2 followed the floodwaters and moved to the left levee of the Suemasa River.
Eventually, the float came to a stop at a higher elevation position.
In Fig. 4.17(b), after the breach at the Takama River occurred, F3 followed thefloodwaters and flowed into the Oda River. Because of the earlier breach which
occurred at the Suemasa River, F4 first drifted within the urban area. After the breachat 3.4 km of the Oda River occurred, the floodwaters carried it eastward. After itentered the Suemasa River through the breach site, it ultimately washed into the Seto
Inland Sea.
Fig.4.18 presents the distribution ratio of the ending positions of the floats, withEVALUATION OF BEHAVIOR OF FLOATING LITTER 63

starting positions placed in each area of Fig. 4.12 and Table 4.3. For all areas, over
50% of the floats ended up in the urban area. All floating matter that flowed into the
Oda River and remained in the riverbed originated from A1 and A2, which are locatedalong the river sides of the Takama River. Aside from A5, which is the farthest fromthe breach site, all other areas had over 18% of floats flowing into the Seto Inland Sea.
Particularly, in A2 and A3, located between the Takama River and the Suemasa River,
nearly one-third of the floats are regarded as entering the Seto Inland Sea. The floats
which finally came to stop near the sluiceways originated mostly from A4 and A5
because these two areas are closer to the sluiceways with high discharge rates. Because
only one sluiceway of S1 existed from the confluence of the Suemasa River and Oda
River to 3.4 km on the left levee of the Oda River, fewer than 10% of the floats ended
up in the sluiceways for A2 and A3. Overall, more than 65% of the floats were
deposited in urban areas. However, the findings also suggest that a large proportion of
floats can be deposited near sluiceways and can run off from breach sites.
Floating litters tends to accumulate significantly in sluiceways. During drainage
from sluiceways, as the water level decreases, floating litters are carried by thefloodwater into the river, making them even more challenging to deal with. In responseto this situation, I propose the installation of filtration nets on the landside of thesluiceways specifically designed for floating debris. This measure aims to prevent
floating debris from entering the river.
4.5.2.2 Characteristics of floats accumulated other than urban area
Fig. 4.19 presents the number of floats accumulated at sluiceways of S1-S4. Only a
few floats originated from A1 are observed at sluiceways because it is located most
distantly at the upstream region. Floats from A2 have widely various movements, withprimary accumulation at S1. Because of its distance from the sluiceways, only a few
floats from A5 flowed to S1. Floats from A4 and A5 predominantly collected aroundS2, S3, and S4 within the same vicinity as their initial setup location. Numerous floats
accumulated at S3, which is consistent with the floating litter presented in Fig. 1.
Fig. 4.20 presents analytical results of the number of floats flowing from the breachpoints of Oda River at 3.4 km on the left levee and Suemasa River. Because of theproximities of the breach points of Takama River and Oda River at 3.4 km, thenumbers of floats flowing from both breach points are combined for analysis. It isreadily apparent that the floats moving from the breach point of Oda River at 3.4 km
are more numerous than those from Suemasa River. The majority of floats from A1
and A2 flow out of the breach point of Oda River at 3.4 km. A few floats from A3 also
64 EVALUATION OF BEHAVIOR OF FLOATING LITTER

flow out of this breach point. More floats from A3 flow from the breach point of
Suemasa River. Most of the floats flowing out of the breach point of Suemasa Riveroriginated from A4, but a few originated from A1, A2 and A5, which flows from thisbreach point.
Although the results of the present analysis cannot be compared quantitatively withthe actual situation, the findings clarified the behavior characteristics of floating litter
under external flooding accompanied by levee failure. Findings from this study are
expected to provide knowledge that is applicable to the treatment of floating litter aftera large-scale disaster. The findings suggest the need for measures to prevent theoutflow of floating litter from sluiceways.

4.6 Conclusion
This study applied flood disaster simulation results caused by heavy rains in Mabi
City in 2018 to the movement of floating litter generated in urban areas under breachconditions. The study results are presented as explained hereinafter.
1) Regarding flood analysis, additional calculations were incorporated based onearlier research by considering drainage gates and drainage vehicles. The flood
analysis consistency was found to be high, as evidenced by comparison between
observed values at the locations of flood observations in the Oda River and the
Takahashi River and the calculated values.
2) The final deposition locations were determined from the simulation of floating
litter under breach conditions. More than half of the floating litter generated in urban
areas was found to remain within the urban area, but approximately one-fifth of thefloating litter was observed to flow out through the breached site, to enter the river,and eventually to reach the ocean. This portion of the floating litter is difficult torecover. Countermeasures are required for recovery in the river. Approximately 13%of all litter was found to accumulate in the sluiceway.

EVALUATION OF BEHAVIOR OF FLOATING LITTER 65

References
1) Onga Office of River, Ministry of Land, Infrastructure, Transport and Tourism(MLIT): Illegal dumping of waste. https://www.qsr.mlit.go.jp/onga/activity/
unlawful_dumping.html
2) Ding, Y., Liu, S. and Chen, X.: Floating plastic debris in the Yangtze Estuary andthe East China Sea: Distributions, sources, and implications for river-to-seatransport. Marine Pollution Bulletin, No. 136, pp. 475-480, 2018.
3) Liu, H., Su, L., Zhang, W. and Qi, Y.: Impacts of flood events on the transport offloating microplastics in the Yangtze River Estuary. Journal of Hydrology, No.
569, pp. 463-471, 2019.
4) Ministry of the Environment: Report of comprehensive study on grasping theactual situation of marine litter and efficient collection, 2021.
https://www.env.go.jp/content/ 000123000.pdf
5) Recycling-Oriented Society Promotion Section of Okayama Prefecture: Okayama
Prefecture Action Plan for Disaster Waste Disposal in Relation to the Torrential
Rainstorm Disaster of July 30, 2008 (revised outline). https://www.pref.okayama.jp/uploaded/life/799700_7502073_misc.pdf
6) MLIT: Response to driftwood and other drifting debris from the heavy rainfall in
July 2018. https://www.env.go.jp/co-ntent/900543482.pdf
7) Nihei, Y. and Wakatsuki, N.: Field measurement of floating-litter transport in ariver under flooding conditions, JSCE, Vol.66, No.1, pp. 19-24, 2010.
8) Okano, T. and Andou, S.: Effect of river outflow on beach litter, Journal ofmaterial cycles and waste management, Vol.23, No.5, pp. 232-239, 2012.
9) Kato, K., Sumner, T., Miura, T., Kanno, T., Chiba, K., Inoue, T., and Shimizu, Y.:
Numerical analysis on the behavior of driftwood in driftwood capturing facility.
JSCE, Ser. B1 (Hydraulic Engineering), Vol. 75, issue 2, pp. I_1441-I_1446, 2019.
10) Maeno, S., Akoh, R., Nihei, Y., Akamatsu, Y. and Yoshida, K.: Flood disastercharacteristics in Mabi district of Kurashiki city due to heavy rain in 2018 andinvestigation of flooding scenario using river flood flow combined inundation flow
model. JSCE, Ser. B1 (Hydraulic Engineering), Vol.75, issue 1, pp. 387-402, 2019.
11) Akoh, R., Maeno, S., and Yoshida, K.: Improvement of the Float Measurement
Method for River Discharge Using QUASI-3D Flow Analysis. JSCE, Ser. B1(Hydraulic Engineering), Vol. 73, No. 4, pp. I_517-I_522, 2017.
12) Heavy Rainfall in July, 2018, Chugoku Regional Development Bureau: Records
of Disaster Response" https://www.cgr.mlit.go.jp/photo/h3007gouu_kiroku/index.htm
13) Chugoku Regional Development Bureau, MLIT: July, 2018 Heavy Rain Disaster
Recovery Activities Using Disaster Response Machinery and Equipment.
https://jcmanet.or.jp/bunken/symposiu-m/2019/2019r04.pdf
14) Report of the Oda River Levee breach investigation committee of the Takahashi
River
System,MLIT,
http://www.cgr.mlit.go.jp/emergency/2018/pdf/
02odagawahaifu.pdf
15) ASIA AIR SURVEY CO., LTD.: July,2018 Heavy Rain Aerial Photograph.
https://www.ajiko.co.jp/saigai/2018nishinihongouu/20180708phot-o_come.pdf
66 EVALUATION OF BEHAVIOR OF FLOATING LITTERCHAPTER 5

NUMERICAL SIMULATION OF COUPLEDDEBRIS FLOW AND INUNDATIONDISASTER CONSIDERINGMICROTOPOGRAPHY: A CASE STUDYOF NIIMI CITY, 2019
5.1 Introduction
Record heavy rainfall of 120 mm/h occurred from around 17:00 on September 3,
2019, near Niimi city, Okayama prefecture. Multiple slope collapses occurred ataround 18:30, creating debris flows that inundated residential areas. In recent years,
debris flows caused by such high-intensity heavy rainfall in a short period of time havefrequently occurred. Effective countermeasures using numerical analysis are required.
Therefore, many studies have examined debris flows. For instance, Takebayashi and
Fujita1) conducted a field survey and numerical simulation of debris flows in
Hiroshima prefecture in July 2018. They clarified debris flow characteristics inresidential areas. Onaka et al.2) reported a numerical simulation of debris flows in
Yamaguchi prefecture in July 2018. They used a complex disaster potential map based
on topographic information analysis to identify areas with high risks of complex
disasters caused by debris flows. Nakatani et al.3) examined house and road effects ondebris flow flooding and deposition in alluvial fan areas for a debris flow disaster that
occurred in Hiroshima prefecture in August 2014. They clarified that houses and roads
must be incorporated into debris flow analyses when examining debris flow extent anddamage.
On the other hand, landslide disasters in closed areas such as Niimi city are thought
to have non-negligible effects on the state of inland water flow. However, flood
NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION 67

scenarios incorporating debris flow flooding caused by surface collapse and inland
flooding caused by localized heavy rainfall have not been sufficiently examined.
Therefore, for this study, I combined debris flow analysis and rainfall inundation
analysis to reproduce calculations of a complex inundation disaster that occurred in
Niimi city in September 2019, and I examined local inundation factors.

5.2 Study area description

Verticaldistance
ImaitaniRiver

Crossing
distance

Debris flowstricken region

Niimi Art
Museum

Ohta
River

500m
Fig. 5.1 Ortho photo of study area.

Fig. 5.2 Rainfall conditions on Sep. 3, 2019, in Niimi city.
68 NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION

5.2.1 Topographical summary
Fig.5.1 exhibits an ortho photo of the study area and a black line shows numerical
domain. The region stricken by debris flows including fine sediments such as mud isshown as a red dashed line. This mountainous valley bottom plain has a crossing
distance of about 1700 m, with longitudinal distance of about 1200 m. The terrain
gradient is about 1/100 in the longitudinal direction and about 1/135 in the crossing
direction.
(2) Survey of disasters
Fig. 5.2 shows a hyetograph of rainfall for 10 mins measured at the Niimi
Observation Station. The figure shows that heavy rainfall of over 10 mm per 10 min
occurred during 17:40–19:10. The cumulative rainfall was greater than 160 mm.

Fig. 5.3 (a) Drainage channels buried by debris flow. (b) Aerial
photograph on the disaster area around the Ohta River.
NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION 69

Debris flows caused by surface collapse occurred at around 18:20–18:30 on thesouthern levees of the Imaitani River and the Ohta River, as denoted by △ in Fig.
5.1. Sedimentation was confirmed within the range surrounded by the red frame.
Fig. 5.3 (b) is an aerial photograph of the disaster area around the Ohta River shownin dashed-dotted line in Fig. 5.1. Fig. 5.3 (a) shows the Ohta River at the time of
sediment accumulation. The Ohta River was expected to be buried completely, anddrainage from the box culvert installed at the downstream end was restricted.
Furthermore, the floor of the preschool shown in Fig. 5.3 (b) was inundated, althoughdebris flows did not flow in, because of inland water.

5.3. Field observation

Channel elevation (GSI data)

Measured by RTK-GPS

Road near channel

Road near channel
Elevation(T.P. m)ChannelChannel(b)Fig. 5.4 (a) Debris flow situation in Imai district. (b) Contour maps derived
from 5-meter elevation data and the results obtained through RTK-GPS
measurements.
70 NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION

Channel elevation (GSI data)

Measured by RTK-GPS

Box culvert

Box culvert

ChannelChannelElevation(T.P. m)(b)

Fig. 5.5 (a) Debris flow situation in Nishikata district. (b) Contour maps derived
from 5-meter elevation data and the results obtained through
RTK-GPS measurements.
Since the rivers focused in this study were characterized by narrow widths, and the
5-meter elevation data of GSI did not adequately represent the channels' shape.
Therefore, on-site measurements of the locations and elevation were conducted using
RTK-GPS and Total Station.

5.3.1 The observation of Imaitani River in Imai district
The damage in the vicinity of the Imaitani river is shown in Fig. 5.4(a). Under the
influence of the debris flow, the houses near the mountain were severely damaged
because the debris flow blocked the waterway and prevented normal drainage, thus
the flood water overflowed from the location shown in the figure.
Fig. 5.4(b) illustrates the comparison between the contour maps derived from 5NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION 71

meter elevation data and the results obtained through RTK-GPS and Total Station
measurements. As the RTK-GPS was unable to receive signals at certain measurement
points, Total Station was used as an alternative for measurement. And as shown in Fig.
5.4(b), the black line is formed by connecting points measured during field surveys.
The red dashed box represents the locations of the buildings in Fig. 5.4(a).

5.3.2 The observation of water way in Nishikata district
The Ohta river in the study area is located on the vicinity of the Niimi Art Museum(see Fig.5.1), and the damage condition is shown in the Fig. 5.5(a). A debris flow fromthe nearby mountain blocked the waterway (in Fig. 5.3 (a)), and rainwater in the city
could not be drained smoothly through the drainage channel, making the city flooding
more serious. The debris flow also impacted the houses near the mountain, and thehouses near the waterway were damaged by both the city flooding and the debris flowfrom the mountain.
Fig. 5.5(b) illustrates the comparison between the contour maps derived from 5meter elevation data and the results obtained through RTK-GPS measurements. And
as shown in Fig. 5.5(b), the black line is formed by connecting points measured onsite using RTK-GPS during field surveys. The red dashed box represents the locationsof the buildings in Fig. 5.5(a). And there is a box culvert at the end of channel, we
measured the height and width of box culvert.

5.4. Model building
5.4.1. Introduction for models
5.4.1.1 Governing equations and discretization
For this study, both inundation flow analysis and debris flow analysis were
performed using a two- dimensional horizontal model. Specifically, for inundation
flow analysis, an equation system is used in which the source term based on theeffective rainfall is added to the general shallow water equations. Here, the f1-Rsa
method5) is adopted as the effective rainfall model. This model sets the saturated
rainfall for each land use, with switching of the runoff coefficient to saturated or
unsaturated by comparison with the cumulative rainfall.
For debris flow analysis, I use a two-dimensional model6) which is constructedbased on consideration of two-layer flow: laminar flow and turbulent flow. The
momentum equations and the continuity equation for flows including water and
72 NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION

sediment are the basic equations of this model. They are common to model for
inundation analysis, except for the source term. Furthermore, the continuity equationof sediment and the riverbed fluctuation equation must be resolved to estimate thevariables included in the source term, such as riverbed resistance, pressure, and ratesof erosion and sedimentation. These variables are obtained based on the constitutive
law of coarse-grained soil. and Egashira’s model7) is used.
For this study, the shallow water equations, which are common to both inundation
flow analysis and debris flow analysis, are discretized by the Godunov-type finite
volume method with a triangular mesh system. The literature4),8) provides explanationsof the specific discretization method.
The Egashira’s model used in this study consists of a debris flow continuum, akinematic equation, a continuum of soil and sand, and a continuum of riverbed, after
adjusting the equations in the model to be usable in 2D model are as follows：ch chu chv
+
+
=E
t
x
y

(5.1)

z
hu huu huv
1 P  bx++= − gh b −
−
t
x
y
x  m x  m

(5.2)

z
hu huv hvv
1 P  by++= − gh b −
−
t
x
y
y  m y  m

(5.3)

zb
E
=−
t
c*

(5.4)

In this expression, h is the water depth, u and v are the velocity in x and y directions
respectively, G is the acceleration of gravity，zb is height of ground, c is the average
concentration of debris flow, c＊ is volume concentration of stationary sedimentarylayer, E is erosion rate, P is the pressure, and the hydrostatic pressure approximation
is used.
The relationship between ρ and ρm is shown below：
m = ( −  )c + (5.5)
In the equation, ρ is the density of the fluid and σ is the density of the soil and water.
τbx, τby are the bed shear stress in x- and y-direction, which are expressed in thefollowing equations.
u(5.6)
 bx =  y +  fb (u 2 + v 2 )u 2 + v2v
(5.7)
 by =  y +  fb (u 2 + v 2 )u 2 + v2
NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION 73

τy is the yield stress, and the next equation expresses the relationship.
1/ n

c
 y =   ( −  )cgh cos  tan s c* 

n=5(5.8)

Φs is the angle of internal friction. fb is the friction factor shown below.
fb =

4 
(1 − c)5/3   h 
2    1/3
k
(1
−
e
)
c
+
k
 d
 
f
 
25 
c 2/3   d 


−2

(5.9)

Where d is the representative particle size of the gravel in the debris flow, e is therepulsion coefficient between the gravel, kb, kf are coefficients, kb=0.0828, kf=0.16, andthe equation about the erosion rate E is shown below:E= c* tan( −  e )2
u + v2θ is the slope of the ground in the flow direction shown below:
sin  =

u sin  x + v sin  y
u 2 + v2

(5.10)(5.11)

θx, θy are the slopes of the riverbed in the x and y directions respectively. Then, θe is
the slope when the sediment concentration c in the debris flow is in equilibrium, andthe equation is shown below:

tan  e =( /  − 1)ctan s( /  − 1)c + 1(5.12)

5.4.1.2 Coupling method
For this study, I adopted a one-way coupling method that reflects the analysis resultsof debris flow analysis in flood flow analysis. Specifically, as a first step, debris flow
analysis is performed until an equilibrium state is reached. The obtained debris flow
depth is added to the ground height to create topographical data after the debris flow
occurs. Next, by replacing the topographical data when the debris flow occurs, one canreadily perform the inundation flow analysis while considering the accumulated
sediment because of the debris flow.
This coupling method includes problems, such as the assumption that the
topographical change attributable to the debris flow occur in a sufficiently short timecompared to the change in the inundation flow condition, and that the inundation flow
and the debris flow are not mixed. Although these phenomena must be considered for
74 NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION

high-accuracy simulation, I inferred that the present method has high applicability toactual disasters.

5.4.2 Simulation conditions
5.4.2.1 Computational mesh and topographic data
The computational domain is presented in Fig.5.6. The mesh size is set as 10 m for
mountain areas and 2.5 m for residential areas. The building and channel shapes are
obtained from Geospatial Information Authority of Japan (GSI) website. The
triangular mesh is created so that details of these shapes can be expressed.
Topographical data are created by interpolation using 5 m DEM data from GSI.
However, the use of more detailed topographical data is necessary to express theriverbed elevation of the channel. Therefore, an RTK-GPS survey was conductedaround the channel. The channel topography is created by linear interpolation using

Fig. 5.6 Compute field.

Table 5.1 Parameters of effective rainfall.

NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION 75

the survey data.
Manning’s roughness coefficient is given as 0.06 for mountain areas and as 0.025
for residential areas (see Fig. 5.7), considering that the buildings are represented byimpermeable wall conditions, and the buildings are shown in red polygons in Fig. 5.7.
Fig. 5.8 shows a tunnel at east of the study area (black dotted line rectangle in Fig.
5.7), it must be included in the flood analysis for adequate drainage in the urban area.
Because there are few obstacles on the road as can be seen from the figure, Manning’s
roughness coefficient 0.01 was used there.

Fig. 5.7 Manning coefficient.

Fig. 5.8 The tunnel in urban area.
76 NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATIONAnd the parameters of effective rainfall are shown in Table 5.1.
5.4.2.2 Input conditions for reproduction calculation
For inundation analysis, XRAIN precipitation data from 9/3 17:00 to 21:00 are
given as the rainfall input condition. Furthermore, the drainage flow rate from the box
culvert installed at the downstream end of channel (see Fig. 5.3(b)) is calculated using
the water depth at the downstream end of the channel. If the water level at thedownstream end exceeds the ceiling height of the box culvert, then a fixedvalue(=21.45m3/s) estimated from the box culvert dimensions is used.
Debris flows related to this disaster are reportedly caused by the three slope
collapses shown in Fig. 5.1. However, information could not be obtained for thecollapsed sediment amount and the sediment particle size distribution. Therefore, forthis study, I decided to set the parameters and magnitudes of the landslide of the slope
failure by trial calculation in comparison with the field data described later, referring
to earlier studies9),10),11). The average particle size was set as 20 cm from the fieldsurvey around the Ohta River. The time of notification of evacuation on September 3,
2019, in Niimi city was 18:30, by that time, the debris flow had already occurred.
Therefore, the time of replacement of the topographical data was set as 18:25 for thisstudy.

5.4.2.3 Case description
After reproducibility calculations of this disaster were performed, I investigated theeffects of a) reproducibility of drainage channels and b) topographical changes becauseof debris flow.
Specifically, initial topographical data of two types are created: one in which the
topographical data of the drainage channel were created only with DEM data and theother in which the data were created using RTK-GPS data. For b), two cases were
examined: with and without topographical changes obtained by debris flow analysis.
The calculation cases are presented in Table 5.2.

5.5 Results and considerations
5.5.1 Verification of the model accuracy
In this section, to verify the model validity and calculation conditions, the
NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION 77

Table 5.2 Simulation Cases

calculation results of Case 4 are compared with the actual data.
First, Fig. 5.9(a) portrays a contour map of the sediment height at 18:30, when an
equilibrium state is reached. Comparison with the debris flow-stricken region shownby the dashed line clarifies that the numerical result in the east–west directions agree
well with about 500 m. However, in north–south direction, the debris flow does not
overflow to the railway with a slightly high terrain: it is narrower than the trace region.
Here, as shown in Fig. 5.10, the sediment grain sizes on the north and south sidesof the railway are markedly different. Because this simulation uses the average particle
size of 20 cm, debris flows with small particles are not reproducible, but the range of
sedimentation on the south side is reproduced well.
Fig. 5.9(b) portrays displays a contour map of the maximum water depth, fromwhich it can be confirmed that the inundation depth is greater than 30 cm around thepreschool where inundation on the floor occurred. Simulation results also show thatthe inundation depth becomes greater than 1 m in the north side with the high-density
residential area.
Next, I conducted a comparison with the trace heights measured after the disaster.
Fig. 5.11 portrays photographs taken at the same site before and after removal of
the accumulated sediment. As portrayed in Fig. 5.11(b), trace heights of two types canbe confirmed. The image in Fig. 5.11(a) shows the time of deposition: the lower trace
denotes the debris flow height; the upper trace shows the flood flow.
Trace heights and numerical results are presented in Fig. 5.12: Fig. 5.12 (a) shows
the trace position; Fig. 5.12 (b) depicts debris flows; and Fig. 5.12 (c) shows acomparison of flood flow. Both the debris flow and the inundation flow show good
agreement with observed values. The calculation conditions used for this study can be
regarded as appropriate.
78 NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION

Fig. 5.9 Calculation results of Case 4: (a) sediment height at 18:30 and(b) maximum water depth.

5.5.2 Influences of reproducibility of channel and sedimentaccumulation by flooding
In this section, to clarify effects of the reproducibility of the channel and to consider
NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION 79

Fig. 5.10 Photographs of sediment: (a) north side and (b) south side of the railway.

Fig. 5.11 Photographs of traces: (a) before and (b) after the removalof debris flow.
sediment accumulation on the calculation results of inundation distribution, four casesin Table 2 were used to assess differences in the calculation results.
Fig. 5.13 presents the final calculation results of longitudinal riverbed elevation in thechannel for each case. Fig. 5.14 shows the time variation of (a) water level at thedownstream end of the channel, (b) drainage flow rate, and (c) drain volume. The box
culvert ceiling height at the downstream end of the channel is presented as a dottedline.
Findings from Case 1 and Case 2 in Fig. 5.13 clarify that the riverbed resolution isinadequate when only DEM data are used. Using only those data causes large
differences in the reproducibility of the channel, such as excessive heights over 1.5 m
and a reverse gradient. On the other hand, comparison of Case 3 and Case 4 reveals
that the reproducibility of the channel causes large differences in the amounts of
sediment accumulated in the channel. The findings clarified that the final groundheight is almost the same in both cases. Furthermore, results clarified that in all cases
except Case 2, the riverbed height at the downstream end is about equal to or greaterthan the ceiling of the box culvert.
80 NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION

(b)

(a)

(c)

Fig. 5.12 Trace heights and numerical results: (a) locations of trace, (b) debris flow, and(c) flood flow.

Fig.5.13 Riverbed elevations of the Ohta River.

NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION 81

Fig.5.14 Comparisons of calculation results: (a) water level at downstream of channel,(b) drain discharge, and (c)drain volume.
It can be confirmed from Fig. 5.14(a) and Fig. 5.14(b) that the riverbed height at
the downstream end strongly influences the drainage flow rate. Specifically, if the
reproducibility of the channel is high (Case 2 and Case 4), then a maximum drainage
flow rate of 21 m3/s can be achieved before debris flows occur. Furthermore,comparison of Case 2 and Case 4 in Fig. 5.14(c) shows a difference in drain volume
82 NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION

Maximum water
depth difference (m):Fig.5.15 Contour map of the difference of the maximum water depth:(a) Case 1 – Case 2, (b) Case 3 – Case 1, and (c) Case 4 – Case 2.
NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION 83

of about 60,000 m3 attributable to sediment accumulation. The findings indicate thatthe reproducibility of the channel and the consideration of sedimentation strongly
influence the prediction of the inundation situation at this study site.
Finally, the drainage flow rate and sediment accumulation effects on the inundation
distribution are examined. The contour map of the maximum water depth difference isportrayed in Fig.5.15. Fig.5.15(a) presents the difference of Case 2 – Case 1. The
effects of drainage from the box culvert can affect the eastern side of the channel, withmaximum difference of about 20 cm.
Fig.5.15(b) is the difference of Case 1 – Case 3. As might be clear from Fig.5.15(b), drainage from the box culvert cannot be expressed in either case. Therefore, thisdifference can be regarded as the effect on the inundation distribution attributable todebris flow. As a characteristic of the difference, the water depth has increased by 20
cm or more on the west side of the channel because of the sediment accumulation,
which blocks the flow of flood waters to the east side, suggesting that the debris flow
might have increased flood damage to the eastern side of the channel.
Fig. 5.15(c) portrays the difference of Case 4 – Case 2. This result presents
differences in the inundation distribution attributable to effects of drainage stopping
caused by accumulated sediment in the channel, in addition to effects explained forFig. 5.15(b). Comparison with Fig. 5.15(b) confirms a similar tendency on the westside of the channel. However, the inundation depth on the east side of the channel isincreased about 15 cm. This finding suggests not only that the inundation flow occurs
from the west side to the east side in the city area but also that flood waters from themountain to the city area are shifting to the east side because of accumulation aroundthe channel.
The results presented above clarified the importance of reproducing the channel
shape to get accurate combined flooding simulations that include debris flows andinundation.

5.6 Conclusion
For the debris flow disaster which struck Niimi city in September 2019, a
reproduction calculation was conducted using a combined model with inundation flow
analysis and debris flow analysis. Results obtained from this study are presented asfollows.
1) A one-way coupling model was constructed using the sediment deposition
distribution obtained by debris flow analysis as topographical data for inundation flow
84 NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION

analysis. Comparison of the calculation results with actual data clarified that thepresent model can reproduce both debris flows and inundation flows.
2) Effects of the drainage channel reproducibility and consideration of sedimentdeposition effects on the inundation flow were examined using trial calculations.
Results suggest that sedimentation around the Ohta River decreased drainage volumes,
but it also locally increased the inundation depth.

NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATION 85

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86 NUMERICAL SIMULATION OF COUPLED DEBRIS FLOW AND INUNDATIONCHAPTER 6

SUMMARY AND CONCLUSIONSIn this study, the “River flood flow combined inundation flow model” wasintegrated with other models to explore predictions of levee breaches, the behavior offloating litter under breach conditions, and the impact of topographic changes caused
by debris flow on inland flooding.
In the study of the practical application of numerical analysis in predicting levee
breaches resulting from overflow events. The following conclusions have beenobtained.
⚫
Possibility of levee breach increases in case of a diffusive overflow flooding,where the inundated area is large. Conversely, levee breach becomes hard tooccur in case of storage type flooding, where the landside water level rises⚫

⚫

rapidly.
As the one hour averaged river-landside water level difference increases, levee
becomes more susceptible to breach.
By combining the flood analysis results for the Mabi area with indicators suchas river-landside water level difference and levee shape, a discriminant analysis

can accurately predict the possibility of levee breach during flood overflow.
The simplified levee breach prediction method proposed in this study can identify
locations with a high risk location of levee failure, which aids levee reinforcement
efforts and enhances public awareness of potential crises.
In the study of the practical application of numerical analysis in predicting levee
breaches resulting from overflow events. The following conclusions have beenobtained.
⚫
Regarding flood analysis, additional calculations were incorporated based onearlier research by considering drainage gates and drainage vehicles. The
flood analysis consistency was found to be high, as evidenced by comparison
between observed values at the locations of flood observations in the Oda
River and the Takahashi River and the calculated values.
SUMMARY AND CONCLUSIONS 87

⚫

The final deposition locations were determined from the simulation of
floating litter under breach conditions. More than half of the floating litter
generated in urban areas was found to remain within the urban area, but
approximately one-fifth of the floating litter was observed to flow out
through the breached site, to enter the river, and eventually to reach theocean. This portion of the floating litter is difficult to recover.
Countermeasures are required for recovery in the river. Approximately 13%of all litter was found to accumulate in the sluiceway.
In the study of the impact of geography changes caused by debris flow on inland
flooding. The following conclusions have been obtained.
⚫

⚫

A one-way coupling model was constructed using the sediment deposition
distribution obtained by debris flow analysis as topographical data forinundation flow analysis. Comparison of the calculation results with actual dataclarified that the present model can reproduce both debris flows and inundation
flows.
Effects of the drainage channel reproducibility and consideration of sedimentdeposition effects on the inundation flow were examined using trial
calculations. Results suggest that sedimentation around the Ohta Riverdecreased drainage volumes, but it also locally increased the inundation depth.

These studies, through a comprehensive examination of flood disasters, provide
profound insights into their intricate complexities. They emphasize the pivotal role offlood analysis models, showcasing their importance in integrating a myriad of factors
for a more holistic understanding. The depth of understanding derived from theseinvestigations holds significant implications for practical applications. Particularly, it
contributes to the enhancement of disaster prediction and management strategies. The
findings also play a crucial role in refining urban flood control measures, fostering
greater disaster resilience within communities. Through this multifaceted approach,the research enriches our knowledge of flood dynamics. It also contributes valuable
insights towards creating more effective and adaptive solutions for mitigating theimpacts of such disasters on both a local and global scale.

88 SUMMARY AND CONCLUSION