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Investigating the debris motion during extreme coastal events: experimental and numerical study

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Investigating the debris motion during extreme coastal events: experimental and numerical study

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Content INVESTIGATING THE DEBRIS MOTION DURING EXTREME COASTAL EVENTS:
EXPERIMENTAL AND NUMERICAL STUDY
by
Gizem Ezgi Cinar
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CIVIL ENGINEERING)
August 2024
Copyright 2024 Gizem Ezgi Cinar

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Acknowledgments
First of all, I would like to express my deepest gratitude to my esteemed advisor Prof. Dr. Patrick
Lynett for his endless support and guidance throughout my PhD journey. It has been a great
pleasure and honor to work with him. In this journey filled with many ups and downs, having a
mentor like him has been my greatest fortune. I am grateful for the confidence he has shown in me
and for encouraging me to realize my potential.
I would like to extend my thanks to my dissertation committee members, Prof. Dr. Felipe de Barros
and Prof. Dr. Mitul Luhar for their valuable suggestions and guidance, which made this work
better.
I would also like to thank my previous advisor Prof. Dr. Ahmet Cevdet Yalciner who introduced
me to the academy and opened the door for me to pursue my academic career further. I am grateful
for everything he has done for me, all his support and all the fun times we had in METU.
I am grateful to Dr. Hasan Gokhan Guler, who has always supported and encouraged me since my
master's studies. He helped me without hesitation whenever I needed it and guided me during
challenging times. I count myself a lucky person to have a friend and colleague like him.
I would like to thank my collaborators Adam Keen, Joaquin Pablo MorrisBarra, Sean Duncan,
Pedro Lomonaco, Tim Maddux, and O.H. Hinsdale Wave Research Laboratory staff for their help
with the laboratory experiments and Cagatay Tasci for his support in OpenCV. I would like to
acknowledge the funding provided through the Viterbi and Annenberg fellowships offered by the
University of Southern California. The work presented in this thesis was supported by National
Science Foundation grants CMMI-1661052, OCE-1830056, and ICER-1940315.

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I want to thank my lab mates Zili Zhou, Maile McCann, Behzad Ebrahimi, Willington Renteria,
Jen-Ping Chu, Abigail Stehno and Shoko Sato for sharing the PhD life with me and making the
USCoastal Lab awesome! I also want to thank previous members of our lab Aykut Ayca, Nikos
Kalligeris and Vassilios Skanavis for their support and encouragement. Special thanks to Christine
Hsieh for her guidance and support during challenging times and to Weijian Ding, Bianca Costa,
Raven Althouse, Selin Bac Bilgi and Coskun Bilgi for their friendship and emotional support.
I want to express my sincere thanks to my dear friends both in Turkiye and US for supporting and
cheering for me every step of the way. My dearest friend Ali Karakaya, thank you for not giving
up on me and for your endless efforts to bring me back to Turkiye. What can I say, we are doomed
to love you! My çiçeem Nilsu Atilgan, I’m grateful for all our times filled with laughter and every
memory we built together from high school to the US. I can’t wait to build more! My dear friend
Ali Can Dogan, thank you so much for our friendship and we'll resume our food adventures without
a 6-month break this time. I also want to thank my friends Esat Tavukcu, Izel Bac, Aslihan Esmer
and Akif Altun for all the good times and laughter during my little escapes to home. I love you
guys so much! I feel privileged to have a crew like this. I am also grateful to have a friend like
Simone Frusina who genuinely shaped my life in the US for the better. I know she will always be
there for me with her brightest ideas :) I want to thank Konstantinos Douligeris, my first friend in
LA who introduced me to literally everyone, for his friendship and all the fun times we had
together. Special thanks to Emily Chinn for all the laughter, kindness and being the sunshine!
Last but not least, my girlies Cansu Demir, Elif Bal, Miray Mazlumoglu and Ulas Can, thank you
for your presence in my life and for always believing in me. No matter how far apart we are, I
know our hearts will always find a way to be together.

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The most special gratitude belongs to my family. I am grateful for everything they have done
during my time here. My beloved mom, Sona Cinar, when things get rough and stressful, your
presence is the only thing that would help me calm down. I cannot thank you enough for your
unconditional love, support and encouragement. I’m reminded that I am home whenever I am with
you. My dear dad, Metin Cinar, thank you for making me feel like the luckiest person in the world
for having your unwavering support in every circumstance and for reminding me to be proud of
myself. And my cherished sister, Berfin Su Cinar, I watched you grow up and become this beautiful
and bright person. Thank you for always believing in me and being my biggest supporter. You are
forever loved and forever a part of me. It would be impossible to finish this study without my
family. I owe them everything I achieve.

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Table of Contents
Acknowledgments........................................................................................................................... ii
List of Tables................................................................................................................................. vii
List of Figures.............................................................................................................................. viii
Abstract........................................................................................................................................ xiv
Chapter 1 Introduction ............................................................................................................. 1
1.1 Experimental Debris Studies................................................................................... 3
1.2 Numerical Debris Studies ....................................................................................... 6
1.3 Objectives of Study............................................................................................... 10
Chapter 2 Experimental Study............................................................................................... 13
2.1 Overview............................................................................................................... 13
2.2 Experimental Setup............................................................................................... 15
2.3 Experimental Procedure........................................................................................ 17
2.4 Image Post-processing and Particle Tracking ....................................................... 20
2.4.1 Lens Correction and Image Rectification ................................................. 20
2.4.2 Particle Tracking ....................................................................................... 21
2.5 Results and Discussions........................................................................................ 24
2.5.1 Dispersion Comparison and Trajectories of Particles............................... 25
2.5.2 Distribution of Particles in Structural Array ............................................. 31
2.6 Overall Conclusions from the Experimental Study .............................................. 34
Chapter 3 Numerical Study.................................................................................................... 37
3.1 Hydrodynamic Modeling ...................................................................................... 38
3.1.1 Boussinesq Equations ............................................................................... 38
3.2 Particle Model....................................................................................................... 39
3.2.1 Equations of Particle Motion .................................................................... 39
3.2.1.1 Drag Force ................................................................................. 40
3.2.1.2 Inertia Force ............................................................................... 41
3.2.1.3 Friction Force............................................................................. 41
3.2.1.4 Collision Force........................................................................... 42

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3.2.1.5 Torque Calculation..................................................................... 43
3.2.2 Collision Detection – Separating Axis Theorem....................................... 45
3.2.3 Dispersion ................................................................................................. 48
3.2.3.1 Particle Fluid Interactions.......................................................... 52
Chapter 4 Model Validation ................................................................................................... 54
4.1 Debris Movement over an Unobstructed Beach, Benchmark #1 (Rueben et al.
2015) ............................................................................................................................... 54
4.1.1 Experimental Setup and Parameters ......................................................... 55
4.1.2 Model Comparisons.................................................................................. 58
4.1.2.1 Comparison of C1 Results ......................................................... 60
4.1.2.2 Comparison of C2 Results ......................................................... 63
4.1.2.3 Comparison of C3 Results ......................................................... 65
4.1.2.4 Comparison of C4 Results ......................................................... 69
4.1.2.5 Comparison of C12 Results ....................................................... 72
4.2 Multi-Debris Transport over a Flat Test Bed, Benchmark #2 (Park et al. 2021) .. 75
4.2.1 Experimental Setup and Parameters ......................................................... 76
4.2.2 Model Comparisons.................................................................................. 79
4.2.2.1 Comparison of Case 1 Results................................................... 81
4.2.2.2 Comparison of Case 2 Results................................................... 83
4.2.2.3 Comparison of Case 3 Results................................................... 84
4.3 Conclusions........................................................................................................... 88
Chapter 5 Large-Scale Model Case Study: Crescent City ..................................................... 89
5.1 Test Case 1 - 500 Particles, Initial configuration 10x50....................................... 93
5.1.1 Impact of excluding collision forces on debris dispersion........................ 97
5.2 Test Case 2 - 500 Particles, Initial configuration 20x25..................................... 101
5.3 Test Case 3 - 1000 Particles, Initial configuration 20x50................................... 105
5.4 Conclusions......................................................................................................... 108
Chapter 6 Conclusion and Future Work Recommendations.................................................110
6.1 Conclusions..........................................................................................................110
6.2 Suggested Future Work ........................................................................................112
References....................................................................................................................................114

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List of Tables
Table 2.1: Hydrodynamic conditions and parameters of the experiments.................................... 18
Table 2.2: Total number of particles in each case ......................................................................... 25
Table 2.3: Offshore θ of each different colored debris particle for current only and combined
current + wave cases..................................................................................................................... 31
Table 2.4: Number of particles in each channel and their percentage .......................................... 33
Table 4.1: Description of the Benchmark #2 cases....................................................................... 78
Table 4.2: Comparison of experimental and numerical results for Case 1 ................................... 82
Table 4.3: Comparison of experimental and numerical results for Case 2 ................................... 83
Table 4.4: Comparison of experimental and numerical results for Case 3 ................................... 86

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List of Figures
Figure 2.1: Showing: (a) final positions of debris pieces from Mexico Beach Pier (image ©
Google, Image ©2022 Maxar Technologies); and (b-e) field survey photos for 6, 8, 14 and 24,
respectively (images by Patrick Lynett)........................................................................................ 15
Figure 2.2: Layout of the experimental area that includes the structural array, position of the
debris box, instrumentation bridge, north and south pumps (gray thin rectangles), and four
overhead camera coverages (four different colored rectangles). .................................................. 17
Figure 2.3: Showing: (a) plan view of debris orientation in the debris box; (b) location of
debris box attached to the instrumentation bridge; and (c) instantaneous debris spreading in
current only case. .......................................................................................................................... 19
Figure 2.4: Individual overhead camera views (a), rectified and merged view (b) of the
experimental site for nonstructural cases. Rectified and merged view (c), individual overhead
camera views (d) of the experimental site for structural cases. .................................................... 21
Figure 2.5: Screenshots of how particle tracking worked for each colored debris particle under
different experimental configurations. Particle tracking for (a) DB1 under wave + current
hydrodynamic conditions without structures; (b) DB2 under wave + current hydrodynamic
conditions with structures; and (c) DB3 under current only hydrodynamic conditions without
structures case. .............................................................................................................................. 23
Figure 2.6: Flowchart of the particle tracking algorithm.............................................................. 24
Figure 2.7: Interpolated offshore trajectories of debris particles: (a) without; and (b) with
structural array for current + waves conditions. ........................................................................... 27

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Figure 2.8: MT (dashed lines) and the SD (solid lines) of all particles during combined current
+ wave cases without structures. The colors of the lines represent the corresponding colored
debris particles. ............................................................................................................................. 28
Figure 2.9: No structural case onshore particle trajectories and their mean with SD for (a)
current-only cases; and (b) wave + current cases (shaded areas: light grey represents one
sigma; dark grey represents two sigma)........................................................................................ 30
Figure 2.10: Cross section of the structural area and the nine channels (y = -4, -3, -2, -1, 0,
1, 2, 3, and 4 m) blocks were 0.4 m cubes and each channel between the blocks was 0.6 m
wide............................................................................................................................................... 32
Figure 2.11: Probability density function of particle in channel y = -1 m. Bins represent the
histogram of particles, normal distribution (dashed line), Kernel distribution computed with
pdf parameters, the difference between two distributions and the calculated relative errors. ...... 32
Figure 2.12: Histogram of (a) DB1; (b) DB2; and (c) DB3 particles in each corridor in the ydirection. Solid and dashed bars represent the data at x = 33 and x = 41 m, respectively. This
figure was generated for combined current + wave case in structural array................................. 34
Figure 2.13: Wave breaking and propagation in front of the first raw of structures at different
time frames (t): (a) t = 605.88 s; (b) t = 606.54 s; (c) t = 607.20 s; and (d) t = 607.86 s.............. 34
Figure 3.1: A schematic of rotating rectangular particle and displaced fluid used in the
derivation of a hydrodynamic resistance torque. .......................................................................... 43
Figure 3.2: (a) Four axes that are perpendicular to the edges of the rectangles and (b) Projected
vertices onto Axis 1....................................................................................................................... 46
Figure 3.3: The minimum and maximum scalar values of the rectangles on Axis 1 .................... 47
Figure 4.1: Overview of the testbed and laboratory setup (taken from Rueben et al. 2015)........ 55

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Figure 4.2: Plan view of the experimental basin including the locations of WGs, USWGs and
USWG-ADV pair (Taken from Rueben et al. 2015) .................................................................... 56
Figure 4.3: Initial debris configurations........................................................................................ 57
Figure 4.4: Comparison of water surface elevations at WG2, WG6 and UWG4 and ADV2
with the experimental data: COULWAVE (solid blue, green and black line), Experiment
(dashed blue, green and orange line) ............................................................................................ 59
Figure 4.5: Snapshots from the simulation of C1 ......................................................................... 61
Figure 4.6: Comparison of x distance traveled and corresponding velocity of the debris particle
for C1: Numerical results (solid blue lines), Experimental results (black circles), standard
deviation (dash-dotted grey line) .................................................................................................. 62
Figure 4.7: Snapshots from one of the simulations of C2............................................................. 64
Figure 4.8: Comparison of x and y distance traveled by the debris particle and the
corresponding velocities for C2: Numerical results (solid blue and green lines for x and y
directions, respectively), Experimental results (black and purple circles for x and y directions,
respectively), standard deviation (dash-dotted grey lines) ........................................................... 65
Figure 4.9: Snapshots from one of the simulations of C3............................................................. 67
Figure 4.10: Comparison of x and y distance traveled by the particles centroid for C3:
Numerical results (solid blue and green lines for x and y directions, respectively),
Experimental results (black and purple circles for x and y directions), standard deviation
(dash-dotted grey lines)................................................................................................................. 68
Figure 4.11: Comparison of the velocities of individual debris particles in x and y directions
for C3: Numerical results (solid blue and green lines for x and y directions), Experimental

xi
results (dashed black and purple circles for x and y directions), standard deviation (dash-dotted
grey lines)...................................................................................................................................... 68
Figure 4.12: Snapshots from one of the simulations of C4........................................................... 70
Figure 4.13: Comparison of x and y distance traveled by the particles centroid for C4:
Numerical results (solid blue and green lines for x and y directions, respectively),
Experimental results (black and purple circles for x and y directions), standard deviation
(dash-dotted grey lines)................................................................................................................. 71
Figure 4.14: Comparison of the velocities of individual debris particles in x and y directions
for C4: Numerical results (solid blue and green lines for x and y directions), Experimental
results (black and purple circles for x and y directions), standard deviation (dash-dotted grey
lines).............................................................................................................................................. 72
Figure 4.15: Snapshots from one of the simulations of C12......................................................... 74
Figure 4.16: Comparison of x and y distance traveled by the debris particle and the
corresponding velocities for C2: Numerical results (solid blue and green lines for x and y
directions, respectively), Experimental results (black and purple circles for x and y directions),
standard deviation (dash-dotted grey lines) .................................................................................. 75
Figure 4.17: Overview of the testbed with two debris setups (photo taken from Park et al.
2021) ............................................................................................................................................. 76
Figure 4.18: Plan view of the experimental setup (taken from the Park et al. 2021) ................... 77
Figure 4.19: Initial configurations of debris (a) uniform and (b) random (Photos are taken from
Park et al. 2021) ............................................................................................................................ 78

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Figure 4.20: Comparison of water surface elevations at WG1 and WG9 and WG5 WGh5 and
ADV with the experimental data: COULWAVE (solid blue, green and black line), Experiment
(dashed blue, green and orange line) ............................................................................................ 80
Figure 4.21: Representative final positions of HDPE particles for Case 1: Numerical (orange
dots), Experimental (black dots)................................................................................................... 81
Figure 4.22: Representative final positions of wood particles for Case 2: Numerical (yellow
dots), Experimental (black dots)................................................................................................... 83
Figure 4.23: Sketch of the positional adjustment margin for random configuration (orange
arrows show the possible directions for the particle to move ....................................................... 85
Figure 4.24: Representative final positions of HDPE and wood particles for Case 3: Numerical
(orange dots for HDPE and yellow dots for wood), Experiment (black dots).............................. 86
Figure 5.1: Bathymetric map of the computational domain, red square indicates the initial
position of the debris particles. White and orange dashed lines represent the upper and lower
limits for categorized particle groups based on their final y coordinates. .................................... 91
Figure 5.2: Snapshots from the simulation of Test Case 1 with a closer look at the particles'
initial dispersion. Red, magenta and dark purple represented the initial positions of the
particles categorized in Group 1, Group 2 and Group 3 based on their final y coordinates,
respectively. .................................................................................................................................. 95
Figure 5.3: Snapshots from the simulation of Test Case 1 at various times with a larger area
focus. (Grey lines indicate the paths of the particles.).................................................................. 96
Figure 5.4: Snapshots from the simulation of no collision case with a closer look at the
particles' initial dispersion. Red, magenta and dark purple represented the initial positions of

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the particles categorized in Group 1, Group 2 and Group 3 based on their final y coordinates,
respectively. .................................................................................................................................. 98
Figure 5.5: Snapshots from the simulation of no collision case at various times with a larger
area focus. (Grey lines indicate the paths of the particles.) ........................................................ 100
Figure 5.6: Standard deviation of particle positions through time. Collision disabled (solid
black and green lines for x and y directions, respectively), Collision enabled (solid orange and
blue lines for x and y directions, respectively) ........................................................................... 101
Figure 5.7: Snapshots from the simulation of Test Case 2 with a closer look at the particles'
initial dispersion. Red, magenta and dark purple represented the initial positions of the
particles categorized in Group 1, Group 2 and Group 3 based on their final y coordinates,
respectively. ................................................................................................................................ 103
Figure 5.8: Snapshots from the simulation of Test Case 2 at various times with a larger area
focus. (Grey lines indicate the paths of the particles.)................................................................ 104
Figure 5.9: Snapshots from the simulation of Test Case 3 with a closer look at the particles'
initial dispersion. Red, magenta and dark purple represented the initial positions of the
particles categorized in Group 1, Group 2 and Group 3 based on their final y coordinates,
respectively. ................................................................................................................................ 106
Figure 5.10: Snapshots from the simulation of Test Case 3 at various times with a larger area
focus. (Grey lines indicate the paths of the particles.)................................................................ 107

xiv
Abstract
The aim of this thesis is to investigate debris motion during extreme coastal events through
physical and numerical modeling. Debris impact has an important role in structural damage during
extreme coastal events. Understanding the transport of debris and the characteristic of its motion
is crucial as debris impact depends on debris motion. The experimental part of this study
investigated floating debris dispersion and motion by conducting laboratory experiments that
considered the effects of a structural array or a gridded layout of city-like buildings. Physical model
experiments were conducted for two different hydrodynamic conditions: (1) current only and (2)
current + wave combined cases. Debris was released from a certain height in a repeatable way.
Visual data were collected by four overhead video cameras and a particle tracking algorithm was
implemented to track debris motion. Debris spreading angles (θs) were calculated for each case
and compared with the angles used in the current engineering practice. The presented results aimed
to increase the current knowledge on debris motion and spreading during extreme events, such that
engineers might build more resilient coastal communities.
For the numerical part of the study, COULWAVE, a higher-order depth-integrated hydrodynamic
model that solves Boussinesq-type equations, was combined with a discrete element method for
solving debris motion and collision. The debris motion was modeled by using equations of particle
motion, considering a comprehensive set of forces acting on the particles. A linear spring-dashpot
type collision model is used to calculate collision forces. A random walk model is included to
account for unresolved turbulent mixing and fluid-debris interactions. The one-way coupled debris
model was validated through two debris transport experimental datasets. Model results for water
depth and debris positions compared reasonably well with experimental results. Finally, the
coupled numerical model was applied to investigate the debris motion during a tsunami for

xv
Crescent City. A regional-scale application of the debris transport model demonstrated that the
model could perform well for real-world applications.

1
1.
CHAPTER 1
Introduction
The increasing frequency and intensity of extreme coastal events have drawn significant attention
to their catastrophic impacts on coastal communities, infrastructure, and the environment. Recent
examples of coastal disasters show that flood-born debris has an important role alongside the
hydrodynamic forces to induce catastrophic damage to buildings and infrastructure. Extreme
coastal events, such as tsunamis, hurricanes, storm surges, and flash floods, could lead to
significant debris generation and transport, damaging the infrastructure in coastal communities.
Post-event debris removal is responsible for 27% of the total disaster recovery cost in the US
(FEMA, 2007). Extreme events generate various types and sizes of debris that include construction
materials, cars, trees, piers, docks, and boats. Post-event field surveys have allowed researchers to
collect data from tsunami-affected areas, which indicated that the impact of debris could be a
strong contributor to structural failure (Yeh et al., 2013). Furthermore, Mousavi et al. (2011)
indicated that global warming would lead to intensified hurricanes and accelerated sea level rise.
Their study stated that flooding levels in coastal areas would significantly increase over the next
80 years. Stronger hurricanes and storm surges could affect larger areas and create larger amounts
of debris.
Current knowledge on debris transport dynamics during extreme coastal events, such as
tsunamis, storm surges, and high-magnitude floods is limited because these events are locally rare

2
and unlikely to be directly monitored (Comiti et al., 2016). Post-event surveys can give some
insights into debris transport; however, effective disaster management in coastal areas depends on
a comprehensive understanding of the transport processes and physics. The characteristics of
debris motion are key factors that are needed to classify high-risk areas in these vulnerable
communities. Developing an understanding of debris motion and distribution during a flood event
has a high significance in coastal, hydraulic, and structural engineering (Goseberg et al., 2016).
Because complex violent flows have a great potential to create excessive amounts of debris, a
knowledge of the spatial dispersion of debris could be critical when building resilient communities.
Following the 2011 Tsunami in Eastern Japan, Zhou et al. (2012) identified that the primary
causes of building destruction were the severe tsunami inundation and the impacts from floating
debris. Observations from multiple field studies conducted after disasters suggest that flows
containing debris are significantly more harmful than water waves alone, especially during run-up
events (Yeh et al., 2005; Chock et al., 2012). Recently, there have been notable efforts to explore
the correlation between the impact of debris and the resultant damage to buildings or infrastructure
in the context of tsunamis (Macabuag et al., (2018); Kameshwar et al., 2021). Researchers aim to
develop fragility curves for enhanced risk assessment, incorporating the effects of debris impact.
Current engineering practice in the US follows the ASCE7 standard for estimating debris
impacts during a tsunami, with a method that was developed by Naito et al. (2014) for extreme
loading. Naito et al. (2014) conducted a field survey to investigate debris transport after the 2011
Japan Earthquake and Tsunami and used the recorded data to determine dispersal patterns. They
suggested a conservative estimate for a relationship between the maximum spreading angle (θ) of
flow-captured shipping vessels based on their original location. Most of the debris was contained
in a ± 22.5° spreading sector normal to the shoreline. In this method, a geometric center of the

3
debris source was considered as the origin of the debris to determine the spreading area. In
addition, their study stated that the inundation depth at the initial debris location, building
construction and height, and spacing played a significant role in debris dispersion. Since the
recommended θ was based on one site-specific tsunami event, further investigation,
computational, and experimental research was needed.
Understanding the dynamics of debris transport and its interactions with built and natural
environments is important for improving our ability to mitigate the impacts of extreme coastal
events. Numerical modeling plays a significant role, offering a tool for simulating the complex
interactions between water, debris, and structures. By integrating empirical data, physical laws,
and computational techniques, researchers can create models that predict how debris is generated,
transported, and interacts with various obstacles.
1.1 Experimental Debris Studies
Investigating debris motion in the field is highly challenging because it requires back-tracking
from the impacted area to the source zone. It is difficult to locate the initial position of the debris
as it often spreads widely around the investigation area (Naito et al., 2014). The complexity and
rarity of field events resulted in various experimental works seeking to investigate debris motion.
Several experimental studies were conducted to investigate debris motion under tsunami-like
flows. Nistor et al. (2016) conducted laboratory experiments to study the mechanism of debris
spreading that used a tsunami-like wave and stated that single debris units showed random
dispersion in different trials under identical conditions. Another important indication was that the
debris spreading angle was a function of the total number of debris units and approximated by
linear functions that described the number of debris units at their initial starting location. Goseberg

4
et al. (2016) investigated the interaction between debris with vertical obstacles in the path of debris
propagation. The main conclusion from this research was that the variation in the dispersal of the
debris in the flow was not significantly changed by the presence of obstacles. In addition, they
noted that this needs to be proved in future work that involves additional numbers of repetitions.
Larger or smaller amounts of debris and variations in obstacle arrangements could potentially alter
the spreading angle of dislodged material. Stolle et al. (2017) conducted several experiments to
understand debris configuration on entrainment and transport. They stated that debris
configurations, interdebris spacing, and hydrodynamics could change the debris entrainment. They
detected higher peak velocities when the number of debris was increased.
Advanced laboratory techniques allowed researchers to investigate and evaluate the important
parameters of debris motion by applying accurate debris-tracking methods. The number of debris,
debris orientation, and velocity are some of the variables that current studies have focused on.
Rueben et al. (2015) used optical techniques to analyze tsunami debris movement during several
laboratory experiments. They stated that debris movement was highly repeatable during onshore
motion. However, highly varied debris positions and velocities were observed during offshore
motion. For debris in free translation, increasing the number of debris resulted in decreased peak
velocity. A camera-based object-tracking algorithm to achieve rapid and accurate debris trajectory
tracking in highly turbulent flows was presented by Stolle et al. (2016). Their study stated that the
motion of debris was highly repeatable through conducted tests. When the long axis of the debris
was initially oriented perpendicular to the flow direction; the peak velocity was reached earlier
and faster than in the case of parallel orientation to the flow direction. Higher peak velocity was
observed when they increased the number of debris.

5
Another novel study that was conducted by Stolle et al. (2020) investigated the stochastic
properties of debris motion that focused on lateral spreading and debris velocity through several
laboratory experiments. Their study aimed to implement a probabilistic framework for debris
hazard analysis during extreme coastal events. They concluded that the lateral displacement around
the mean trajectory (MT) of the debris group could be assumed to be Gaussian. As a part of a set
of large-scale experimental studies that were conducted in OSU Hinsdale Laboratory (Corvallis,
OR), Park et al. (2021) investigated tsunami-driven debris advection over a flatbed that used two
different materials for the debris particles to study the density effect along with their initial starting
positions. They stated that the debris group with less density was transported further and showed
less spreading compared with the denser debris group. Moris et al. (2022) investigated the debris
loading on structures that used the same experimental setup presented in this study. The probability
and magnitude of debris impact were evaluated for wave–current flows. These studies showed that
the debris motion could be random and affected by turbulent diffusion. Therefore, a lot of
uncertainties need to be dealt with in the evaluation of debris motion. Nistor et al. (2017) published
a critical review of tsunami-driven debris studies and identified some gaps in the state-of-the-art
research. They highlighted the need for a probabilistic design approach to assess the possibility of
debris loading that occurred based on the random nature of debris motion. Stolle et al. (2018)
conducted several physical experiments that used tsunami-like flow conditions and investigated
the drifted debris motion. Their study showed that the lateral spreading of drifted debris was
statistically distributed with Gaussian distributions and the standard deviations (SDs) were affected
by the longitudinal distance and the total number of debris. Kasaei et al. (2021) conducted several
open-channel experiments on the lateral displacement of debris that considered the effects of the

6
debris release angle and flow velocity. In addition, their study showed that the lateral
displacements of debris followed a Gaussian distribution.
1.2 Numerical Debris Studies
Numerical modeling is essential to evaluating the potential risks and impacts of extreme coastal
events on coastal communities. Such events involve complex interactions between various
physical processes and numerical models, which allow researchers to simulate these processes and
gain predictive insights for preparedness and mitigation strategies. Given the growing awareness
of tsunami-driven debris significant role in building and infrastructure damage, several numerical
studies have been conducted to understand the debris motion and debris effect during extreme
events. The numerical modeling process of debris typically involves the integration of two distinct
models through one of three coupling techniques: solid-to-fluid one-way coupling, fluid-to-solid
one-way coupling, and two-way dynamic coupling (Xiong et al., 2018). The one-way coupling
models do not account for the feedback from the affected phase back to the initiating phase.
Therefore, they are suitable for straightforward scenarios where the dynamics of the solid or fluid
phase are less significant than their interaction. On the other hand, two-way dynamic coupling
approaches consider the interaction between fluid flow and solid objects. In this method, while the
fluid flow influences the movement of solid objects, the movement of solid objects influences and
alters its flow dynamics. Stockstill et al. (2009) developed a one-way fluid-to-solid coupled model
using a two-dimensional (2D) flow solver and a three-dimensional (3D) discrete element model
(DEM) to provide a physics-based method for examining how various floating objects behave
when interacting with river structures. Another critical study conducted by Imamura et al. (2008)
investigated multiple modes of transport, such as siding, rolling, and saltation, by implementing a

7
variable coefficient of friction that adjusts based on ground contact duration. Tomita and Honda
(2010) conducted a study investigating tsunami-drifted bodies and adjusting drag coefficients
based on water depth in developing a one-way coupled model for ships.
Various experimental studies have contributed to the accumulation of knowledge regarding
the fundamental characteristics and variability of debris behavior. Kihara and Kaida (2020) noted
that tsunami inundation events are highly localized and raise questions about the applicability of
existing knowledge and methodologies to regions of varied scales and structural densities. They
conducted a study aiming to develop a numerical method for the probabilistic assessment of debris
impacts on buildings and infrastructures in coastal industrial sites at a local scale. Additionally,
they investigated the effects and importance of the proposed methodology on debris dispersal
simulations for probabilistic evaluations of debris collision. Several studies calculate debris
trajectories considering the hydrodynamic force, impact force between debris and buildings,
impact force among debris, and friction force on the bed under temporal and spatial distributions
of inundation flows. Nojima et al. (2014a) proposed a numerical model to investigate a variety of
motions of debris (shipping vessels, containers, cars, timbers, and tanks). Their model considered
the effects of the draft, drag, and inertia coefficient variation on debris trajectories. Later, an
improved model is used to investigate the impact of friction forces, debris-debris interactions, and
resistant forces on tsunami flow (Nojima et al., 2017). Another study on motion and collision of
solid objects under solitary wave attack was conducted by Guler et al. (2018) using a weakly
coupled numerical model, a two-phase CFD solver coupled with a DEM solver.
A recent study conducted by Koh et al., (2024) proposed a framework coupling a tsunami
flow model and a debris transport model to investigate the multiple debris behavior and their
impact on coastal communities. Their study used a semi-analytic solution for debris transport and

8
provided a case study for the impact of 2500 shipping containers at Honolulu Harbor, Hawaii under
a hypothetical tsunami event. The shape of shipping containers was approximated to a volumeequivalent disc shape. This approach made easier to implement collision detection since there is
only one contact point between the debris particles. Hazard maps including the debris dispersion
ratios, maximum and accumulated impact loading alongside 5% exceedance loading are
introduced as a research outcome.
Ayca and Lynett (2021) proposed a comprehensive model to predict the motion of large
vessels under the influence of strong currents generated by tsunamis. Their approach uses a twoway coupled method to capture the interaction between vessels and flow. Additionally, the model
incorporates a collision solver founded on the conservation of momentum and impulse. Xiong et
al. (2020) proposed a novel two-way coupling method to fully couple a 1D shock-capturing
shallow water equation (SWE) model with a discrete element model (DEM) through buoyancy,
hydrostatic and hydrodynamic forces for investigating complex debris-enriched flow
hydrodynamics. Later, Xiong et al. (2022) extended their work to examine the performance of a
dynamically coupled 2D shock-capturing SWE model and a 3D multi-sphere method-based DEM
model. This advanced two-way coupled SWE-DEM model demonstrated capability in accurately
replicating experimental outcomes such as the flow hydrodynamics, the movement of floating
objects, the timing and intensity of peak impact forces, and the forces' duration and fluctuations
caused by the debris. The study highlighted the significant influence of both the velocity correction
factor and the damping coefficient on the resultant impact forces from the debris. Additionally, the
research acknowledged that various other elements could potentially modify the outcomes of the
simulations, such as the application of depth-averaged velocity for calculating fluid forces on
floating objects, the debris characteristics, and the bed friction in influencing debris trajectory.

9
Chida et al. (2023) conducted a study to investigate the model's applicability to actual topographic
conditions such as ports and urban areas. They improved an existing debris transport model
(STOC-DM) by modifying the modeling of seafloor contact and collisions with buildings to
increase its real-world practicality and applicability.
Recently, several researchers have also attempted to simulate the dynamics of floating
debris using Smoothed Particle Hydrodynamics (SPH) models. Amicarelli et al. (2015) proposed
an SPH framework to investigate the 3D transport of solid objects in free surface flows by
implementing multiple coupling terms for fluid-body and solid-solid interactions in the fluid
dynamics SPH equations, addressing the dynamics of both the main flow and the transported
objects. Their research highlighted the necessity of adopting a statistical approach due to the highly
non-linear nature of solid object transport during flood events. Ren et al. (2014) conducted a study
to investigate the capabilities of a 2D SPH-DEM model in simulating wave-structure interactions,
explicitly focusing on rubble-mound breakwaters and predicting the hydraulic stability of these
structures. Another important study conducted by Canelas et al. (2013) coupled the SPH model
with a DEM; however, the high computational cost required for this coupling makes using the
coupled model impractical for many applications. Nistor et al. (2014) suggested that incorporating
solid deformation and inelastic collision capabilities would significantly improve the model's
applicability in coastal and hydraulic engineering fields. Although SPH and SPH-DEM coupled
models have successfully replicated results from laboratory or small-scale engineering tests, their
broader application to large-scale simulations remains limited. This limitation stems from the
significant computational demands and various unresolved numerical challenges associated with
SPH, which constrain their utility in more extensive scenarios (Nistor et al., 2017; Zhao et al.,
2017).

10
1.3 Objectives of Study
Debris entrainment can drastically alter flow patterns, structural loadings, and impulsive forces;
however, our ability to understand and simulate the motion of debris, which governs the previously
mentioned impacts, is limited. Through experimental and numerical investigations, this study
focuses on the critical and complex problem of debris motion during extreme coastal events.
Although many experimental studies on debris transport and impact have focused on tsunamis and
tsunami-like waves, very few exist on debris transport that consider the combined effect of currents
and waves that occur in extreme storm conditions. Since the driving processes are different for this
combined case, the experimental part of this research aims to study the transport dynamics in
nearshore coastal environments under extreme events, such as storm surges and floods.
Through numerical modeling, high-resolution representations of fluid dynamics and debris
motion are possible. This level of detail provides insights into complex interactions and behaviors
that would be difficult, if not impossible, to observe directly in the real world or through physical
experiments. Therefore, the main objectives of this study are:
1. Develop an understanding of the elements that influence debris dispersal patterns through
experimental and numerical modeling.
2. Investigate the physical mechanism of the interaction between extreme flows and debris
motion through laboratory experiments and provide a unique data set for the combined
effect of currents and waves.
3. Study the effect of a structural array on debris transport and spreading through physical
experiments.

11
4. Numerically model the motion and collision of the debris under tsunami action using an
available Boussinesq hydrodynamic solver one-way coupled with a particle motion solver.
5. Develop a particle motion model that accounts for interactions between debris pieces and
the fluid medium, including buoyancy, drag, and collision effects along with unresolved
flow patterns.
6. Implement collision detection algorithm for rectangular particles.
7. Validate the developed particle model using experimental benchmark data.
8. Demonstrate the capability of the developed model in a large-scale field case to enable
researchers and policymakers to conduct fast, effective, and not computationally expensive
simulations in large-scale areas to predict debris motion.
Debris transport and impact have an important role in structural damage and numerous studies
have investigated the process. This study focuses on the transport of debris and its motion
characteristics through experimental and numerical work hoping to help to better quantify the
debris motion during extreme events, such that engineers might utilize this understanding to
protect life and property in coastal communities.
This thesis is structured in two main parts (experimental and numerical work) in addition
to Chapter 1, which summarized the existing literature on debris transport during extreme coastal
events, including both experimental and numerical work alongside the outlined objectives of the
study, providing a roadmap for the research.
In Chapter 2, the field observations at Mexico Beach after Hurricane Michael are
introduced to serve as a real-world backdrop for the study. Then, the setup of the physical
experiments and procedures are described. This chapter also covers the techniques employed for

12
image post-processing and particle tracking alongside the results and discussion sections of the
experimental results.
In Chapter 3, a detailed description of the coupled numerical model is presented along with
the theoretical background and formulization of the hydrodynamic model, particle model, collision
detection algorithm, methodology used to account for dispersion, and implementation of a simple
random walk model.
Chapter 4 aims to validate the numerical model through two benchmark cases from the
literature on debris motion. Each experiment is described in terms of setup and cases, followed by
comparing the model results with empirical data. This chapter validates the numerical model and
demonstrates its applicability and accuracy in simulating tsunami debris motion.
Chapter 5 presents the results of the numerical simulation of tsunami-driven debris transport
on a large-scale test case for Crescent City. Three distinct simulations were performed to
investigate the parameters that influence debris dispersion characteristics. This chapter provided a
new tool for assessing potential debris hazards on a regional scale.

13
2.
CHAPTER 2
Experimental Study
2.1 Overview
The experiments were motivated by observations at Mexico Beach after the 2018 Hurricane
Michael disaster. Hurricane Michael came onshore in 2018 along the Panhandle coast of Florida.
As it approached the Panhandle, Michael reached Category 5 status with 160 mph (260 km/h) wind
speed with an extremely intense but compact core just before making landfall near Mexico Beach,
Florida. The storm surge at Mexico Beach was approximately 14 ft (4.3 m) with >20 ft (>6 m)
waves (Beven et al. 2018). The most devastating aspect of this hurricane was that many residential
structures were destroyed. One of the reasons for this destruction was that only the first row of
houses that were closest to the ocean was in FEMA’s 100-year flood zone. Therefore, most
homeowners did not need flood insurance and did not do anything to protect their structures from
the flood. Field observations showed that all the destroyed houses had slabs on grade, and
structures were scrapped off their slabs due to the 5–6 ft (1.52–1.82 m) surge depth, 2–3 ft (0.6–
0.9 m) waves and 100 mph (160.9 km/h) winds.
Mexico Beach had a wooden pier that was destroyed during the hurricane. The waves broke
off every offshore pile along with every section of the deck, and some of these pieces of nowdebris were carried inland. Kennedy et al. (2020) published a summary of the post-disaster field
survey at Mexico Beach after Hurricane Michael. When the survey team was out in the field, they

14
noticed that the debris from the pier was unique. The pier piles were uniquely larger in diameter
than other piles in the debris field, and no other infrastructure in the area had components like the
pier deck sections. Therefore, the team could search the area and identify the pieces of debris that
originated from the pier. The locations of all the individual pieces of pier debris that were found
in the Mexico Beach area are shown on a map in Figure 0.1(a). A total of 27 debris pieces were
noted. Some of the photos taken during the site investigation are shown in Figure 0.1(b–e). The
debris was all sourced from the pier that was located in front of debris piece #4. Most of the debris
spread to the northwest, some spread directly inland, and a small fraction spread to the south. This
distribution implied there were combined effects of waves, currents, and wind that affected the
debris transport, with the debris spread to the northwest indicating a directional bias, due to wind
and waves. An immediate observation from the debris pattern was that the dispersion was large.
Recreating this field-observed debris pattern at Mexico Beach could only be approached with a
full hindcast of the waves, current, and wind during the event, an understanding of the wave and
current-driven dispersion was necessary. The primary goal of the OSU experiments that are
discussed in this study was to capture the advection and dispersion of a line source of debris under
combined waves and currents, such that the full hindcast models might calibrate and validate their
debris transport physics.

15
Figure 0.1: Showing: (a) final positions of debris pieces from Mexico Beach Pier (image © Google,
Image ©2022 Maxar Technologies); and (b-e) field survey photos for 6, 8, 14 and 24, respectively
(images by Patrick Lynett).
2.2 Experimental Setup
A series of debris experiments were conducted in the Directional Wave Basin of the Hinsdale
Wave Research Laboratory, at Oregon State University, Oregon, US. The general layout of the
48.8 m long and 26.5 m wide wave basin is shown in Figure 0.2. The bathymetry was initially flat
near the multidirectional piston-type wavemaker (located at x=0 m) to x= 11.3 m. Then, a 1/20
slope 20 m long followed, which was connected to another flat section that was 10 m long and
elevated 1 m from the bottom of the basin. The final flat 10 x 10 m section was meant to represent
a small section of a coastal community, such as Mexico Beach, which in the experiment was
termed the area of interest (AOI). The water depth (h) in the AOI was 10 cm. There were two side
channels to circulate the current. Two pumps were used to create a steady current along the central
channel. The north pump was located closer to the north split wall and the south pump was located
near the south wall.

16
A total of 39 debris particles were placed as a line source at the offshore part of the basin, which
represented debris from a pier. These particles had three different colors - blue (DB1), green
(DB2), and orange (DB3) (13 of each) - which were arranged in three color-uniform groups.
Different colored particles represented the different sections of the debris box. With DB2 in
between, DB1 represented the farthest and DB3 represented the closest to the wavemaker. Each of
the square wooden debris particles had dimensions of 15 cm and were presoaked in water to
increase their weight and ensure that the debris particle weights were constant from trial to trial.
Colored debris particles were placed in a long thin box (Figure 0.2) that was fixed to the
instrumentation bridge. Debris pieces were placed in the debris box with an interblock spacing of
0.6 cm.
An experimental configuration with and without a structural array was considered to
examine the debris motion. Both setups were tested under the hydrodynamic conditions of
combined current and waves. The structural array of 100 idealized buildings (which were simple
concrete cubes with a side length of 0.4 m in this study) was placed in the AOI. The distance
between two buildings in the along-shore direction and cross-shore were 0.6 and 0.4 m,
respectively. The distance between the first row of buildings and the beginning of the overland
flow grid was 1.6 m.
The overland flow grid with a 2-m cell size was painted on the AOI. The grids were used
as reference points for the video cameras. Visual data were collected using four overhead video
cameras that were mounted on a steel frame that was above the AOI. Figure 0.2 shows the four
different camera views that are represented in four different colors with overlapping areas that
cover the AOI. The frame rate and resolution of the four overhead cameras were 29.97 Hz and
1,080 x 1,920 pixels, respectively. The water surface elevation was measured with nine resistance

17
wave gauges in the offshore area and with eight ultrasonic wave gauges in the onshore area, or the
AOI.
Figure 0.2: Layout of the experimental area that includes the structural array, position of the debris
box, instrumentation bridge, north and south pumps (gray thin rectangles), and four overhead
camera coverages (four different colored rectangles).
2.3 Experimental Procedure
The number of trials and the hydrodynamic condition for each different experimental configuration
are given in Table 0.1. All tests were performed using the same water level and wave conditions.
The experiment was scaled at approximately 1/25, which was used to define the wave properties.
During the event, near-shoreline wave heights were estimated to be approximately 5–6 m, which

18
gave scaled wave heights in the experiment of approximately 20 cm. Therefore, random waves
with a significant wave height (Hs) of 0.2 m and wave period (Tp) of 2.25 s were used in the
combined current + wave cases. Each pump took approximately 20 min to stabilize the water level
and current magnitude (at a water level of 110 cm).
Table 0.1: Hydrodynamic conditions and parameters of the experiments
Without Structures With Structures
Experimental
parameters
Current
Only Current + Waves Current
Only Current + Waves
Number of
Repetitions 10 15 3 30
h (m) 1.095 1.095 1.095 1.095
Hs (m)
- 0.2 - 0.2
Tp (sec)
- 2.25 - 2.25
Debris particles were released instantaneously using a false floor in a repeatable way.
Release of the debris was achieved by a trigger that was connected to a cable. The process was
operated manually. The cable was connected to a false floor opening mechanism. When the cable
was pulled from one end by the operator, the false floor opened, and all debris particles dropped
out of the bottom instantaneously. After each trial, numbered debris particles were placed at the
same location in the box. The plan view of the debris orientation in the debris box is shown in
Figure 0.3(a).
This method of debris specimen release led to an initial debris dispersion that was unrelated
to the hydrodynamics. As shown in Figure 0.3(b), the debris box was mounted on the bridge at an
elevation of 1.5 m above the water surface. Therefore, when debris particles impacted the water

19
after release, some chaotic and impact-related spreading occurred immediately. Figure 0.3(c)
shows a snapshot from a current-only case. As soon as the particles were dropped, they
immediately spread away from the line source, and then simply advected linearly onshore with the
current. For cases with waves, the released-related initial spreading was similar to that of the
current only case.
Figure 0.3: Showing: (a) plan view of debris orientation in the debris box; (b) location of debris
box attached to the instrumentation bridge; and (c) instantaneous debris spreading in current only
case.
Investigating debris motion requires the use of hydraulic scale models (Stolle et al. 2018).
Rueben et al. (2015) stated that the formation of turbulent eddies could influence debris spreading.
To eliminate the effects of viscosity in the experimental study, the flow should be fully turbulent.

20
The corresponding Reynold’s number (Re) for the turbulent regime is Re > 12,500 (Te Chow 1959;
Henderson 1966; Munson et al. 2005). In this study, the Re for current only and water + current
cases were approximately 2.4 x 104
and 3.2 x 104
, respectively. Therefore, the Re was in the fully
turbulent regime for both hydrodynamic conditions. Since this study focused on wave-driven
flows, the Froude number (Fr) was not as relevant as in tsunami flows. However, the
corresponding Fr for the current only case was Fr= 0.26 and was calculated to provide a baseline
value for the reader.
2.4 Image Post-processing and Particle Tracking
2.4.1 Lens Correction and Image Rectification
Camera calibration and image analysis were performed by MATLAB. Camera extrinsic, intrinsic,
and lens distortion parameters were obtained from checkerboard images with the Camera
Calibrator app. The app’s default camera calibration settings used a minimum set of camera
parameters. After the lens correction, undistorted collected frames from four different camera
views were synchronized and rectified at a single elevation (Z-value). Rectified images from four
different camera views were merged into a single image for every time step. A MATLAB script
was written to rectify four camera images. The rectification process was performed for every
frame. The images were rectified through fitgeotrans.m, which utilizes the surveyed locations of
the overland grid line intersections on the test section. After the individual camera images were
rectified, they were synchronized and merged. Synchronization was performed manually by
looking for distinct features, such as debris passing a certain line or wave breaking. Therefore,
camera synchronization could include an error margin <0.15 s, which corresponds to four to five

21
numbers of frames. Figure 0.4 shows the rectified and merged camera views for structural and
nonstructural cases.
Figure 0.4: Individual overhead camera views (a), rectified and merged view (b) of the
experimental site for nonstructural cases. Rectified and merged view (c), individual overhead
camera views (d) of the experimental site for structural cases.
2.4.2 Particle Tracking
Before implementing any particle tracking algorithm, an average image was created from
approximately 500 frames before particles showed up in the area of interest to create a background
image. The background image was subtracted from the video images to prevent incorrect detection.
This approach was useful to minimize the glare from water, distinguish between the color-sharing
structures and debris particles, and exclude the overland grid lines when tracking DB3 particles.
Since the lighting changed between trials due to sunlight, the averaged frames were updated to
eliminate glare.
A particle tracking algorithm was implemented that used the open source OpenCV (Bradski
2000) to track the debris particles. Since three different debris colors were used in the experiments,

22
a specific color threshold was only applied for those three colors that used the OpenCV feature
Track Bars in the OpenCV environment. OpenCV captures images in blue–green–red (BGR)
format with integer values in the range of 0–255. However, the hue–saturation–value (HSV) is the
most suitable color model and is preferred over BGR in computer vision and image analysis for
color-based image segmentation due to its intuitiveness to human vision (Cheng et al. 2001). After
converting the BGR image to HSV, color thresholding was implemented with chosen mask
numbers. A binary image was obtained with a black background and a white object. After this step,
an OpenCV function findContours was implemented to obtain the list of found contours, each in
the form of a NumPy array with boundary points of Object and Hierarchy. After finding all the
contours, they were sorted according to their size of contour area, from biggest to smallest. A
threshold was applied for the contour size at this point to prevent incorrect detection. For the
contours that passed the threshold, the coordinates of the appropriate rectangle that was drawn
around each contour were extracted, and the centroid of the contours was calculated.
Color masking was checked and updated, if necessary, for every trial to prevent misleading
results that were caused by light changes and reflections. Figure 0.5(a-c) shows three frames with
detected debris particles for each color. After finding the color mask for the targeted objects, a
boundary for debris entrance was specified. The boundary area for the debris entrance was the area
where the contours were detected for the first time. In addition, the area was used as a boundary
criterion when updating and creating contours. Some challenges when determining the boundary
area, especially for wave–current combined cases, occurred multiple times. Since the wavebreaking zone overlapped the entrance boundary area, detecting the debris particles required some
updated boundary selection. Every trial was checked to make sure that all the debris particles were
detected before entering the AOI. In addition, the detected objects were subjected to a size

23
threshold at this point. If the contour size satisfied the determined criteria and the contour was in
the specific boundary, contours were accepted as target objects to be tracked.
Figure 0.5: Screenshots of how particle tracking worked for each colored debris particle under
different experimental configurations. Particle tracking for (a) DB1 under wave + current
hydrodynamic conditions without structures; (b) DB2 under wave + current hydrodynamic
conditions with structures; and (c) DB3 under current only hydrodynamic conditions without
structures case.
After the particles were detected for the first time, based on the comparison of their
positions in the current frame and the previous one, the Euclidean distance was calculated. The
determined thresholds for Euclidean distance and position change in the x- and y-directions were
applied as update criteria. The workflow of the detection process is shown in Figure 0.6.
Tracking the particles in the combined current + wave case was more complicated than in
the current-only case since particles interacted strongly. Keeping track of the indices on these
individual particles was a challenge due to the image complexity when wave breaking was
involved. However, it was possible with various thresholds and filtering to obtain accurate
trajectories. Every trial was checked manually to confirm that the particles maintained their indices

24
throughout the whole motion. When the changes in the indices were detected, the necessary
updates were performed in the post-processing manually.
Figure 0.6: Flowchart of the particle tracking algorithm.
2.5 Results and Discussions
Debris trajectories and parameters that could affect the motion of debris particles were analyzed
and the results are presented in this section. Particle trajectories were recorded on video that started
on the beach side of the instrument bridge in the AOI, although the particles were released in the
offshore area. The total number of particles in each color with different hydrodynamic conditions

25
is presented in Table 0.2. Uneven current patterns occurred unintentionally due to laboratory
limitations and affected some particles. During the debris particle release, occasionally a particle
would be dispersed a large distance toward the wavemaker, and in some of these cases, the particle
remained offshore. Therefore, each case used slightly different numbers of debris. For combined
current + wave cases, 11 repetitions were included in the analysis without the structural array, and
30 repetitions with the structural array; this difference in trials was driven by facility scheduling
and shared use of the configurations.
Table 0.2: Total number of particles in each case
Number of particles
Without Structures With Structures
Debris color Only Current Current+Waves Only Current Current+Waves
Blue 130 143 44 388
Green 130 143 52 390
Orange 124 143 27 382
All 384 429 123 1160
2.5.1 Dispersion Comparison and Trajectories of Particles
The experimental setup lacked overhead cameras that captured the offshore area that started from
the position where debris particles were first released until just before the overland grid line as
shown in Figure 0.5. However, the particles dispersed significantly until they reached the camera’s
coverage. To predict the trajectories of the particles in this region, an interpolation was performed
that used the initial positions of the particles in the debris box and their corresponding coordinates
at x = 31 m. This approach was applied to the with and without structure cases. The results of the
analysis are shown in Figure 0.7 for the current + wave cases. Dispersion of the particles offshore

26
was controlled by how and where the particles were dropped. Releasing the debris from a high
elevation with free falling caused the particles to immediately disperse when they hit the water
surface. The offshore dispersion of particles with the structural array configuration was higher than
in the trials without the structural array configuration. This increased offshore dispersion with
structures in place was driven by the wave reflection off the array, which led to a more energic
wave field offshore. Using resistance wave gauge data at x = 19.2 m, the increase in Hs at this
location was 6.34%. This was not a proper estimation of the wave reflection coefficient, which
could not be performed with the limited wave gauge data from the experiment; however, this
increase does not indicate that trials with structures had greater wave reflection.

27
Figure 0.7: Interpolated offshore trajectories of debris particles: (a) without; and (b) with structural
array for current + waves conditions.
The mean onshore trajectories for all without structure and wave + current trials across
three different grouped debris particles, which coincided with 143 particles per group, are shown
in Figure 0.8. In addition, spatiotemporal changes in SD were presented. The MT of each colored
debris particle was toward the negative y-direction. This was due to the uneven positioning of the
pumps that caused unsymmetric flow conditions. Of note, the focus of this study was on the
spreading of the particles.

28
Figure 0.8: MT (dashed lines) and the SD (solid lines) of all particles during combined current +
wave cases without structures. The colors of the lines represent the corresponding colored debris
particles.
For all particles, a wider variance around the mean, which was associated with the SD of
the trajectory, was observed as the particles propagated in the x-direction. When the particles
entered the onshore area, their initial positions were offset to y = 0 to separate onshore and offshore
dispersion behavior. The effects of dispersion were more significant for the DB3 particles. This
was because of the physics of the entrainment and advection processes by which the debris was
transported. The DB3 particles followed a slightly different mean path offshore and led to a
different path onshore, where these particles experienced different mean flow and mixing,
compared with the DB1 and DB2 particles. Onshore, DB1 and DB2 particles followed similar
paths with similar dispersion.
The temporal evolution of onshore debris dispersion for the current only and current +
waves combined trials, with no structural array, was compared and shown with SD borders in

29
Figure 0.9. The particles dispersed significantly more when waves were involved. The debris with
no obstructions and free flow path moved parallel to the flow direction. The dispersion remained
small for the current-only cases.
The θs for different colored debris particles were calculated similarly to Nistor et al. (2016)
to better understand the lateral movement and make a comparison with the proposed θ by Naito et
al. (2014).
θ is defined by:
𝜃 = 𝑎𝑟𝑐𝑡𝑎𝑛 (
𝑦𝑓 − 𝑦𝑖
𝑥𝑓 − 𝑥𝑖
) (0.1)
where yf = final y position when x is maximum; yi = initial y position of the debris; xf = maximum
x position of the debris; and xi = initial x position of the debris. The θ was calculated for onshore
and offshore motions (i.e., without structures), which considered the maximum displacement. The
results are given in Table 0.3. For every case, smaller θ was observed than the ±22.5° θ that was
proposed by Naito et al. (2014). Therefore, the large offshore θ for the current only case was a
result of the debris release approach that was used in this study. When debris particles hit the water
surface, the lateral energy of the debris particles dissipates slowly due to the low energy field in
current-only case, leading to large apparent offshore spreading angles. Of note, θ by Naito et al.
(2014) was developed for the tsunami-driven debris started onshore and this study investigated the
wave driven debris motion that started offshore.

30
Figure 0.9: No structural case onshore particle trajectories and their mean with SD for (a) currentonly cases; and (b) wave + current cases (shaded areas: light grey represents one sigma; dark grey
represents two sigma).

31
Table 0.3: Offshore θ of each different colored debris particle for current only and combined
current + wave cases
θ (°)
Onshore Offshore
Debris
color
Only Current Current+Waves Only Current Current+Waves
Blue ±2.55 ±11.49 ±17.34 ±9.4
Green ±1.92 ±10.93 ±14.1 ±7.1
Orange ±1.64 ±13.88 ±14.6 ±7.9
2.5.2 Distribution of Particles in Structural Array
The cross section of the experimental area where the structures were placed is shown in Figure
0.10. The rectangular boxes represented the structures and the gaps between them were referred to
as channels or corridors. Each channel was 0.6 m wide and 8 m long. Particle distributions within
the channels were important to evaluate the risk of debris damage that was caused by impact on
the bounding structures. The distribution of debris particles in channel y = −1 (i.e., contained the
highest number of particles) for different x-positions is shown in Figure 0.11 with the calculated
relative errors. The area under the difference curve where x = 33.5 m was calculated to estimate
the error between the actual and Gaussian distributions. For the rest of the x-locations, the
calculated error was divided by the error at x = 33.5 m and the relative error was introduced.
Particles had more scattered positions when they entered the channel, and their distribution was
much wider. As they moved forward, their distribution became closer to Gaussian, which implied
they had a lower risk of hitting structures. This was a general behavior that was observed in every
channel. However, the majority of the particles entered the mid-channels as given Table 0.4. The
overall distribution of the particles was investigated, and the results were compared for the

32
nonstructural and structural array tests. The particle distribution for both cases had similar errors
and remained close to a Gaussian distribution as the particles propagated inland.
Figure 0.10: Cross section of the structural area and the nine channels (y = -4, -3, -2, -1, 0, 1, 2, 3,
and 4 m) blocks were 0.4 m cubes and each channel between the blocks was 0.6 m wide.
Figure 0.11: Probability density function of particle in channel y = -1 m. Bins represent the
histogram of particles, normal distribution (dashed line), Kernel distribution computed with pdf
parameters, the difference between two distributions and the calculated relative errors.

33
Figure 0.12 shows the difference between the number of particles in each corridor at
different x positions. From this figure, some particles changed their original corridor as they moved
along in the x-direction. In total, 57 particles changed their path. When the total number of particles
in each trial was considered, changing the path was not common behavior. Only 4.9% of the
particles changed their original path. In addition, the recorded videos were examined to determine
the reason for the path change. In total, 87.7% of the particles changed their corridor within 1–2
m after they first entered the structural area. This behavior could be explained by the continuous
wave-breaking effect. Figure 0.13 shows the region where waves started to break and their
propagation inland. Waves started breaking before the structural area and continued to break until
the first row of structures. Combining the effects of wave breaking and reflections from the
structures created a chaotic area between the first three rows of structures, which resulted in path
changes for some particles.
Table 0.4: Number of particles in each channel and their percentage
Channel center coordinate y (m) Number of particles %
-4 12 1.03
-3 39 3.4
-2 156 13.4
-1 400 34.5
0 374 32.2
1 146 12.6
2 43 3.7
3 16 1.4
4 5 0.4

34
Figure 0.12: Histogram of (a) DB1; (b) DB2; and (c) DB3 particles in each corridor in the ydirection. Solid and dashed bars represent the data at x = 33 and x = 41 m, respectively. This figure
was generated for combined current + wave case in structural array.
Figure 0.13: Wave breaking and propagation in front of the first raw of structures at different time
frames (t): (a) t = 605.88 s; (b) t = 606.54 s; (c) t = 607.20 s; and (d) t = 607.86 s.
2.6 Overall Conclusions from the Experimental Study
This part of the thesis presented the results from laboratory experiments that were conducted to
investigate debris motion and dispersion under the combined effects of current and waves. The
physical model experiments were motivated to recreate the Mexico Beach Pier dispersion data that
were collected from the field survey in Mexico Beach, Florida after Hurricane Michael in 2018.
In addition to different hydrodynamic conditions, the effect of a structural array on debris motion

35
and dispersion was investigated. Two pumps that were located in the side channels were used to
create a steady current along the central channel. The debris particles that were used in these
experiments were wooden squares 15 cm long. Each trial was run with 39 debris particles. Debris
particles were released from a certain height that used a false floor in a repeatable way. Four
overhead video cameras were used to collect the visual data, and the particle tracking methodology
was implemented for each frame. Water surface elevation data were collected offshore with nine
resistance wave gauges and onshore with eight ultrasonic wave gauges. Debris spreading was
examined onshore and offshore separately. The following conclusions were drawn based on the
results of this experimental study.
1. For all the tested conditions, debris particles showed wider variance around the mean as
the particles propagated inland. This behavior was consistent with simple particle spreading.
2. The offshore dispersion of particles with the structural array configuration was higher
than in the trials without the structural array configuration. This increased offshore dispersion with
structures in place was driven by wave reflection off the array, which led to a more energic wave
field offshore.
3. The debris with no obstructions and free flow path moved parallel to the flow direction.
When waves were involved, debris particles showed a much larger lateral spreading.
4. Compared with existing findings on θ (Nistor et al. 2016; Goseberg et al. 2016; Stolle et
al. 2019), debris θ was calculated for the onshore and offshore areas. For every case, smaller θ was
observed than the ±22.5° θ that was proposed by Naito et al. (2014).
5. Debris particles entered the structural area in scattered positions with a random nature.
As they move forward between buildings, their distribution approached a Gaussian distribution,
which implied an overall decreasing risk of hitting structures when moving inland.

36
6. A small number of particles changed their original corridor as they move along between
buildings. The combined effects of wave breaking and reflections near the first three rows of
structures were the reason for the corridor change. When the total number of particles was
considered, changing the path was not a common behavior.
This experimental study highlighted the importance of understanding debris motion and
spreading during extreme coastal events. The physical model experiments presented in this study
were limited in terms of hydrodynamic conditions, structural size and configuration, and debris
release mechanism. To better understand debris motion, future studies should consider parameters,
such as different flow hydrodynamics, wave heights, debris type and release methodologies, and
structural configurations.

37
3.
CHAPTER 3
Numerical Study
This study employs a sophisticated one-way coupled model to simulate debris motion under
tsunami-induced hydrodynamics. The model integrates hydrodynamic data from The Cornell
University Long Wave (COULWAVE), a high-order Boussinesq model, to account for the
propagation and evolution of waves. The debris motion is then modeled using particle motion
equations, considering a comprehensive set of forces acting on the particles. These forces include
the bottom friction force, which opposes the particle motion; the inertia force, representing the
resistance to change in motion; the drag force due to the relative fluid-particle velocity; and the
collision force due to interactions between particles.
The interactions between debris particles are modeled using a spring-dashpot system,
which effectively captures the elastic and dissipative aspects of particle collisions. The Separating
Axes Theorem (SAT) is used to detect collisions and compute the corresponding forces. SAT is a
robust approach to detecting potential overlaps between particles, which is essential for accurately
simulating the complex interactions in a debris-filled tsunami flow.
After determining the resultant forces, the equations of motion are solved to update particle
velocities and positions. Additionally, a random walk model is included to account for unresolved
turbulent mixing and fluid-particle interactions. The random walk model is effectively a dispersion
model, approximating physical process that the one-way coupled model does not directly include.

38
The model adds a stochastic component to the particle velocities, aiding the model's ability to
mimic the mixing processes observed in natural tsunami debris motion.
This modeling approach provides a robust framework for simulating tsunami-induced
debris motion, accounting for resolved (deterministic) and unresolved (stochastic) processes. This
chapter presents the Boussinesq equations used for hydrodynamic modeling and setup of the
particle model and describes the different forces included in the force balance. The collision
detection algorithm and the dispersion modeling approach are discussed in detail. The chapter
concludes with an overview of the random walk model approach to include particle-fluid
interactions.
3.1 Hydrodynamic Modeling
3.1.1 Boussinesq Equations
The conservative form of the Boussinesq equations that are weakly dispersive and fully non-linear
have been integrated over depth in a one dimension is as follows (Kim et al., 2009):
𝜕𝐻
𝜕𝑡 +
𝜕𝐻𝑈𝛼
𝜕𝑥 + 𝐷
𝑐 = 0 (0.1)
𝜕𝐻𝑈𝛼
𝜕𝑡 +
𝜕𝐻𝑈𝛼
2
𝜕𝑥 + 𝑔𝐻
𝜕𝜁
𝜕𝑥 + 𝑔𝐻𝐷
𝑥 + 𝑈𝛼𝐷
𝑐 − 𝑅𝑏
𝑥 = 0 (0.2)
where 𝐻 = 𝜁 + ℎ is the total water depth, 𝜁 and ℎ is the water surface elevation the water depth
respectively. 𝑈𝛼 is the velocity at water depth 𝑧𝛼 in the 𝑥 direction. The 𝐷
𝑐
and 𝐷
𝑥
are the higher
order terms that include the bottom turbulence and dispersive properties. The 𝑅𝑏
𝑥
term is the wave
breaking related dissipation term proposed by Lynett (2006). A Finite Volume scheme is used for

39
spatial representation, while a third-order Adams-Bashforth predictor and fourth-order AdamsMoulton corrector scheme is used for time integration. Please refer to Kim et al. (2009) for a
detailed explanation of the hydrodynamic model equations.
3.2 Particle Model
The particle model assumes that debris is represented as a rigid rectangular body and maintains a
horizontal orientation throughout the simulation. The Lagrangian particle tracking model was
developed in MATLAB R2023b. A random walk approach is implemented for the unresolved
turbulent mixing effects on fluid velocity, particle-fluid interactions and wake effects on particle
velocities. A resistance torque approach is also introduced to account for the resistant fluid drag on
rotating particle.
3.2.1 Equations of Particle Motion
Particle motion equations for translational and rotational motion are given by Equations 0.3 and
0.4, respectively. Equation 0.3 is based on Newton’s second law, and the right-hand side of the
equation is the sum of forces acting on the particle, which are represented by the drag force 𝐹𝐷,
the inertia force 𝐹𝐼
, the friction force at the bottom 𝐹𝐹𝑟 and the collision force 𝐹𝐶. The model
calculates the temporal evolution of debris positions and orientations by resolving translational
movements in horizontal (x, y) direction alongside rotational movement around the vertical axis.
𝑚𝑝
𝑑𝑼
𝑑𝑡 = 𝑭𝐷 + 𝑭𝐼 + 𝑭𝐹𝑟 + 𝑭𝐶 (0.3)

40
𝑑𝝎𝑝
𝑑𝑡 = 𝑻⁄𝐼 (0.4)
where 𝑚𝑝 is the particle mass, 𝑈(= 𝑢𝑝, 𝑣𝑝) and 𝜔𝑝 are the linear velocity and the angular velocity
of the particle respectively, 𝑇 is the net torque, and 𝐼 is the moment of inertia of the particle.
The following sections are dedicated to explaining each of the external forces considered in the
final force balance equation (Equation 0.5) given below:
𝑼 =
𝑭𝐷 + 𝑭𝐼 + 𝑭𝐹𝑟 + 𝑭𝐶
𝑚𝑝(1 + 𝐶𝐴)
𝑑𝑡 (0.5)
3.2.1.1 Drag Force
Drag force represents the resistance encountered by the particle moving relative to the fluid. The
drag force in the x and y directions is calculated as follows:
𝐹𝐷𝑥 =
1
2
𝜌𝑓𝐶𝐷𝐴(𝑢𝑓 − 𝑢𝑝)√(𝑢𝑓 − 𝑢𝑝)
2
+ (𝑣𝑓 − 𝑣𝑝)
2
(0.6)
𝐹𝐷𝑦 =
1
2
𝜌𝑓𝐶𝐷𝐴(𝑣𝑓 − 𝑣𝑝)√(𝑢𝑓 − 𝑢𝑝)
2
+ (𝑣𝑓 − 𝑣𝑝)
2
where 𝜌𝑓 is the fluid density, 𝐶𝐷 is the drag coefficient, 𝐴 is the cross-sectional area of the particle
perpendicular to the flow direction, 𝑢𝑝 and 𝑣𝑝 are the particle velocities in x and y directions
respectively and 𝑢𝑓 and 𝑣𝑓 are the fluid velocities in x and y directions respectively at the particle's
position.

41
Flow conditions and the shape of the debris are factors that affects drag coefficient. Goral
et al. (2023) conducted a series of experiments to investigate drag coefficient formulations for both
regular and irregular particle shapes. According to their research drag coefficient remains constant
for rectangular and square prisms. ASCE7 22 states that structural components against the tsunami
overland flow have drag coefficients ranging from approximately 1.2 to 2.5. This study uses the
drag coefficient as a constant representative value, which is referenced in existing literature
(Imamura et al., 2008; Aziz et al., 2008; Takabatake et al., 2021; von Häfen et al. 2021; Koh et al.
2024).
3.2.1.2 Inertia Force
The inertia force accounts for the additional inertia due to the effects of acceleration around the
body as it moves through the fluid and is as follows:
𝑭𝐼 = 𝐶𝐴𝜌𝑓𝑉(𝒂𝑓 − 𝒂𝑝) + (𝜌𝑓𝑉𝒂𝑓) (0.7)
where 𝐶𝐴 is the coefficient of added mass, 𝑉 is the volume of the particle, 𝑎𝑓 is the fluid
acceleration and 𝑎𝑝 is the particle acceleration.
3.2.1.3 Friction Force
The friction force represents the force that opposes motion when a particle is in contact with bottom
surface, whether stationary or moving. The friction force is as follows:

42
𝑭𝐹𝑟 = 𝜇𝑑𝑭𝑁
𝑼𝑝
|𝑼𝑝|
, ℎ𝑑𝑟 ≥ 𝐻𝑙𝑜𝑐
𝑭𝐹𝑟 = 𝜇𝑠𝑭𝑁
𝑼𝑝
|𝑼𝑝|
, ℎ𝑑𝑟 < 𝐻𝑙𝑜𝑐
(0.8)
where 𝜇𝑑 and 𝜇𝑠 are dynamic and static friction coefficients, 𝐹𝑁 is the normal force corresponding
to 𝐹𝑁 = 𝑚𝑝𝑔
ℎ𝑑𝑟−𝐻𝑙𝑜𝑐
ℎ𝑑𝑟
, 𝐻𝑙𝑜𝑐 is the water depth at the particle location, 𝑈𝑝 is the speed of the
particle and ℎ𝑑𝑟 is the height of the particle draft. The friction force is included only when 𝑈𝑝
exceeds some threshold.
3.2.1.4 Collision Force
The collision force represents the particle-particle interaction and is calculated using the spring
and dashpot model. This approach accounts for both elastic and dissipative forces during the
collision. The spring-dashpot model is introduced in a similar way as Tsuji et al. (1992), which
was based on Cundall and Strack (1979), and is given as follows:
𝑭𝐶 = 𝑘𝛿 + 𝑐𝝊𝑟𝑒𝑙 (0.9)
where 𝑘 is the spring constant, reflecting the stiffness of the contact and hence the elastic response
of the collision, 𝛿 is the penetration depth, indicating the overlap between the colliding particles,
𝑐 is the damping coefficient, representing the viscous damping effect that dissipates energy during
the collision and 𝜐𝑟𝑒𝑙 is the relative velocity of the particles along the line of action of the collision
force. Spring and dashpot coefficients are calibrated in the numerical simulations.

43
3.2.1.5 Torque Calculation
The collision response is characterized by calculating the relative velocity of the particles along
the collision normal, enabling the determination of a spring-dashpot force that models the elastic
and damping characteristics of the collision. The components of this force are then utilized to
compute the resultant torque exerted on the particle, taking into account the moment arm, 𝑟,
defined by the vector from the particle's center of mass to the collision point. Cumulative rotational
effects of multiple simultaneous collisions on each particle are effectively captured. The torque
due to the collision force is calculated using Equation 0.10.
𝑻𝑐 = 𝒓 𝑥 𝑭𝑐
(0.10)
The derivation of a hydrodynamic resistance torque on the rotating particle when the flow
is accelerated outward, (see Figure 0.1) is given below:
Figure 0.1: A schematic of rotating rectangular particle and displaced fluid used in the derivation
of a hydrodynamic resistance torque.
𝐴𝑡𝑠 =
1
4
𝑏∆𝑠 (0.11)

44
∀𝑡𝑠=
1
4
𝑏∆𝑠ℎ (0.12)
𝑉 =
∆𝑠
∆𝑡
= 𝜔
𝑏
√2
(0.13)
∆𝑠 = 𝑉∆𝑡 = 𝜔
𝑏
√2
∆𝑡 (0.14)
𝛼 =
∆𝑠
∆𝑡
2
=
𝑉
∆𝑡
=
𝜔𝑏
√2∆𝑡
(0.15)
𝐹 = 𝑚𝛼 = ℂ𝜌𝑓𝑏ℎ∆𝑠𝛼
= ℂ𝜌𝑓𝑏ℎ
𝜔𝑏
√2
∆𝑡
𝜔𝑏
√2∆𝑡
=
ℂ𝜌𝑓𝑏
3ℎ𝜔
2
2
(0.16)
M= 𝐹
𝑏
√2
= ℂ𝜌𝑓𝑏
4ℎ𝜔
2
(0.17)
The final form of a hydrodynamic resistance force on the rotating particle is given in
Equation 0.18.
𝑻𝑟 = 𝐶𝑟𝑚𝜌𝑓𝑏
4ℎ𝝎|𝝎| (0.18)
where 𝑏 is the particle length, ∆𝑠 is the incremental displacement of the particle’s boundary, 𝐴𝑡𝑠
and ∀𝑡𝑠 are the area and volume of triangular section of fluid displaced, ℎ is the draft or flow depth
whichever is smaller, 𝑉 is the linear velocity of the particle, 𝜔 is the angular velocity and 𝐶𝑟𝑚 is
the resistance moment coefficient that needs to be calibrated in the model. This torque is applied
to the opposite direction of the total torque due to collision force.

45
3.2.2 Collision Detection – Separating Axis Theorem
Implementing an accurate collision detection algorithm is one of the fundamental steps to calculate
collision forces. Accurate collision detection ensures that the interactions between the particles are
identified correctly. The SAT is a powerful and commonly used method in computer simulations
to determine if two convex polygons intersect by offering a robust framework for identifying
potential intersections. The theorem states that two convex polygons do not intersect if at least one
line (axis) exists onto which their projections are not overlapping.
Position and velocity information for each particle is extracted, and the vertices of the
particles are calculated using geometric properties such as particle length and width. Then, the
calculated vertices are subjected to a rotation transformation using a rotation matrix 𝑅𝜃 derived
from the particle's orientation angle 𝜃𝑝𝑎𝑟𝑡 . This ensures that the collision detection mechanism is
responsive to dynamic changes in particle orientation.
The Separating Axis Theorem (SAT) requires the examination of projections along axes
normal to the edges of the polygons involved. For rectangles, this means calculating normals to
each of the four edges. However, due to the rectangles' alignment, this simplifies to two unique
axes per rectangle. Therefore, for each pair of particles, the algorithm calculates four axes (two per
particle) that are normal to the edges of the rotated rectangles (Figure 0.2). These axes are essential
for the SAT, as they serve as the reference vectors along which the projections of the particle
vertices are evaluated.

46

Figure 0.2: (a) Four axes that are perpendicular to the edges of the rectangles and (b) Projected
vertices onto Axis 1
The collision detection core logic involves projecting each rotated rectangle's vertices onto
the previously determined axes. For each axis calculated, the vertices are projected onto the axis
and this projection translates the problem into a one-dimensional space where overlap can be easily
assessed (Figure 0.2). Equation 0.19 shows the projection of the upper-right corner of rectangle A
with coordinates (𝐴𝑈𝑅𝑥
, 𝐴𝑈𝑅𝑦
) onto Axis 1 which is represented by the vector
(𝐴𝑥𝑖𝑠 1𝑥 ,𝐴𝑥𝑖𝑠 1𝑦). This projection results in scalar values representing the minimum and
maximum extents of the rectangles along each axis. The overlap between these extents is
calculated for each axis, and the absence of overlap on any axis indicates no collision, leveraging
the principles of SAT (Figure 0.3).

47
𝑃𝑟𝑜𝑗𝐴𝑥𝑖𝑠 1
𝐴𝑈𝑅 =
𝐴𝑈𝑅 . 𝐴𝑥𝑖𝑠 1
‖𝐴𝑥𝑖𝑠 1‖2
𝐴𝑥𝑖𝑠 1
𝐴𝑈𝑅𝑥
∗ 𝐴𝑥𝑖𝑠 1𝑥 + 𝐴𝑈𝑅𝑦
∗ 𝐴𝑥𝑖𝑠 1𝑦 (0.19)
𝐴𝑥𝑖𝑠 1𝑥
2 + 𝐴𝑥𝑖𝑠 1𝑦
2
𝐴𝑥𝑖𝑠 1𝑥 ,
𝐴𝑈𝑅𝑥
∗ 𝐴𝑥𝑖𝑠 1𝑥 + 𝐴𝑈𝑅𝑦
∗ 𝐴𝑥𝑖𝑠 1𝑦
𝐴𝑥𝑖𝑠 1𝑥
2 + 𝐴𝑥𝑖𝑠 1𝑦
2
𝐴𝑥𝑖𝑠 1𝑦
Figure 0.3: The minimum and maximum scalar values of the rectangles on Axis 1
The SAT does not provide the exact collision point directly. Rather, it identifies the axis on
which the two shapes overlap the least. The minimum overlap axis indicates the least distance by
which one shape can be moved to no longer intersect with the other. The collision normal is a
vector that is perpendicular to the axis of minimum penetration and points from one particle to the

48
other. This vector, also called the Minimum Translation Vector (MTV), helps to determine the
direction in applying collision-induced forces.
Once the axis with the minimum overlap is found, the projections of both shapes onto this
axis are calculated. These projections are represented by their scalar values on the axis. To
determine the actual points on the shapes that correspond to these projections, min/max values that
lie on the projection of each shape along the collision normal are calculated. These points could
represent the extremes of the shapes along that axis. Since it is complex to determine the exact
collision points between arbitrary convex polygons, the algorithm uses a practical approximation
method. The collision point is approximated as the mean of the projected points along the axis of
minimum overlap. This heuristic approach is particularly effective when an exact point of collision
is not straightforward to determine due to the overlap being along a line segment rather than a
single point. The mean represents an approximate location between the two sets of projections,
roughly corresponding to the deepest point of intersection.
3.2.3 Dispersion
Dispersion is a critical component to consider when developing numerical models for tsunami
debris motion. In the context of fluid dynamics, dispersion is related to the mechanical mixing of
a fluid mass, which causes the particles to spread. Dispersion, in this context, is not a physical
phenomenon but rather a modeling concept used to account for the hydrodynamic processes that
are not explicitly captured by the flow model. It plays an essential role in hydrodynamic models
by facilitating the mixing of particles, complementing advection.

49
One of the fundamental goals of modeling is to simulate the flow properties of the real-world,
denoted as 𝑢𝑟𝑒𝑎𝑙 as closely as possible. This process involves creating models that approximate
the complexity of real-world phenomena and serve as a tool to understand and predict fluid
behavior. Hydrodynamic models produce a flow field, called 𝑢𝑚𝑜𝑑𝑒𝑙𝑒𝑑, which estimates the actual
flow velocity 𝑢𝑟𝑒𝑎𝑙. The difference between these quantities or the model’s deficit is denoted as
𝑢
′
. The 𝑢
′
represents the aspects of flow dynamics that the model cannot capture due to limitations
in resolution, simplifications such as those made in SWE models, and the exclusion of complex
processes like frequency dispersion, compressibility, wave breaking etc. This relationship can be
expressed as in Equation 0.20. When carried through a typical governing equation derivation, 𝑢
′
lead to stresses in the conservation of momentum equations, which must be then closed with some
other submodel.
𝑢𝑟𝑒𝑎𝑙 = 𝑢𝑚𝑜𝑑𝑒𝑙𝑒𝑑 + 𝑢
′
(0.20)
Modeling of turbulence has a long-standing history in fluid mechanics. Eddy viscosity and
diffusivity coefficients represent the transport of momentum and mass within a fluid that is caused
by turbulence. These coefficients are essential in accounting for mixing potentials of mass and
momentum in areas where the flow is not fully resolved. For instance, in scenarios where coastal
areas are flooded, the model needs to account for transport caused by both unresolved turbulent
mixing and flow changes due to unresolved bathymetric or topographic features. When employing
a numerical model with a 10-m grid resolution, it is expected that smaller topographic and
bathymetric features, which have a local influence on flow dynamics, will remain unresolved. To
account for the influence of these sub-grid scale features dispersion terms are incorporated into the
model. A relevant example can be using a bare-earth digital elevation model in an urban

50
environment. In such cases, the presence of buildings, which are not directly represented in the
grid, requires the inclusion of a dispersion term to simulate the resulting effects on debris transport.
To estimate the transport caused by unresolved turbulent mixing a Taylor Dispersion
model, employing a stochastic component to represent the unresolved turbulent fluctuations, can
be used as in Equation 0.21:
𝑢
′
𝑡𝑢𝑟𝑏 𝑑𝑡 = 𝑟√𝐷𝑡𝑢𝑟𝑏 𝑑𝑡 (0.21)
where r is a random number between -1 and 1, and 𝐷𝑡𝑢𝑟𝑏 is the turbulent dispersion and represents
the mass mixing potential from unresolved flow patterns. The term under the squared root
physically represents the expected area the particle might be spreading into.
When modeling hydrodynamics with bottom friction and breaking effects, the turbulent
dispersion coefficient can be adjusted as in Equation 0.22.
𝐷𝑡𝑢𝑟𝑏 = 𝐶𝐵𝐹𝛿|𝑢
∗
| + 𝐶𝑏𝑟𝑒𝑎𝑘𝑖𝑛𝑔𝜈𝑇𝑏𝑟𝑒𝑎𝑘𝑖𝑛𝑔 (0.22)
where 𝐶𝐵𝐹 and 𝐶𝑏𝑟𝑒𝑎𝑘𝑖𝑛𝑔 are dimensionless coefficients, 𝛿 is the boundary layer thickness (can
take as water depth for long waves), 𝑢
∗
is the bottom shear velocity = 𝛽𝑢′
(can be approximated
as some fraction of the velocity), and 𝜈𝑇𝑏𝑟𝑒𝑎𝑘𝑖𝑛𝑔 is the eddy viscosity from the breaking model. 𝛿,
𝑢
∗
and 𝜈𝑇𝑏𝑟𝑒𝑎𝑘𝑖𝑛𝑔 need to be predicted by the hydrodynamic model.
In addition to turbulent mixing, the transport of debris due to unresolved topographic features can
also be considered (Equation 0.23).

51
𝑢
′
𝑡𝑜𝑝𝑜 𝑑𝑡 = 𝑟√𝐷𝑡𝑜𝑝𝑜 𝑑𝑡 (0.23)
where 𝐷𝑡𝑜𝑝𝑜 = 𝐶𝑡𝑜𝑝𝑜𝛿|𝑢
∗
| and 𝐶𝑡𝑜𝑝𝑜 represents the ‘significance’ of the unresolved topography
features. For fractal topography, 𝐶𝑡𝑜𝑝𝑜 can be set as a function of the resolved topography slope
and/or curvature and for topography with unresolved structures 𝐶𝑡𝑜𝑝𝑜 should be some function of
the structure layout.
The overall transport of debris is calculated by integrating the modeled flow with contributions
from turbulent mixing and topographic features, updating particle positions as in Equations 0.24
and 0.25.
𝑥𝑛𝑒𝑤 = 𝑥𝑜𝑙𝑑 + 𝑢̅ 𝑑𝑡 + 𝑢
′ 𝑑𝑡
𝑦𝑛𝑒𝑤 = 𝑦𝑜𝑙𝑑 + 𝜐̅𝑑𝑡 + 𝜐
′ 𝑑𝑡
(0.24)
where,
𝑢
′ 𝑑𝑡 = 𝑟1√𝐶𝐵𝐹𝐻𝛽|𝑢̅| 𝑑𝑡 + 𝑟2√𝐶𝑡𝑜𝑝𝑜𝐻𝛽|𝑢̅| 𝑑𝑡 + 𝑟3√𝐶𝑏𝑟𝑒𝑎𝑘𝑖𝑛𝑔𝜈𝑇𝑏𝑟𝑒𝑎𝑘𝑖𝑛𝑔 𝑑𝑡 (0.25)
where from theory 𝐶𝐵𝐹 ≅ 0.07 (Elders Model) and 𝛽 = 𝑂(0.1) with large Reynolds number.
However, it is needed to rely on experiments and observations to develop expressions for 𝐶𝑡𝑜𝑝𝑜
and 𝐶𝑏𝑟𝑒𝑎𝑘𝑖𝑛𝑔. 𝐶𝑏𝑟𝑒𝑎𝑘𝑖𝑛𝑔 is assumed in order of 1 with Sc =1 in this model.

52
After calculating drag and inertia forces with the flow velocity including the added dispersion (e.g.
𝐹𝑑𝑟𝑎𝑔 =
1
2
𝐶𝐷𝜌𝑤𝑎𝑡𝑒𝑟𝐴𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 |𝑢̅ + 𝑢
′ − 𝑈|(𝑢̅ + 𝑢
′ − 𝑈)), particle velocity is updated using
Equation 0.26.
𝑈𝑛𝑒𝑤 = 𝑈𝑜𝑙𝑑 +
𝐹𝐷 + 𝐹𝐼 + 𝐹𝐹𝑟 + 𝐹𝐶
𝑚𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 + 𝑚𝑎𝑑𝑑𝑒𝑑
𝑑𝑡 (0.26)
3.2.3.1 Particle Fluid Interactions
When updating the positions of particles in a simulation, a random walk model is used to account
for unresolved debris-fluid interactions and the effects of wakes generated by moving debris. This
wake can affect the flow field around the particle and influence the motion of other particles. While
a random walk model can not capture the physical complexities of debris-fluid dynamics and wake
effects, it can be calibrated to provide a reasonable prediction of their effects, especially in contexts
where overall, or average, behavior is more important than detailed dynamics.
Let 𝑉𝑓𝑙𝑢𝑐 represents stochastic velocity modifications representing unresolved debris-fluid
interactions. 𝑉𝑓𝑙𝑢𝑐 is a function of the strength of the wake. The strength of the wake is controlled
by the velocity of fluid, ability of particles to disrupt the flow (heavy, bigger particles have bigger
wake) and the presence within a particle-generated wake zone. Due to the lack of data to
individually evaluate the impacts of these factors, a single wake strength coefficient has been
utilized to include the effects of these interactions. Fluctuations in particle velocity is described
using Equation 0.27.
𝑉𝑓𝑙𝑢𝑐 = 𝛼𝑈𝑝 (0.27)

53
where 𝑈𝑝 is the particle speed 𝑎 = 𝐶𝑤𝑠𝑟√2 𝑑𝑡, 𝐶𝑤𝑠 is wake strength coefficient, 𝑟 is normally
distributed random number sampled from [-1, 1] and 𝑑𝑡 is the time step. Then, updated particle
velocities (Equations 0.28 and 0.29) are used to calculate the final positions of the particles.
𝑣𝑝 = 𝑣𝑝 + 𝑉𝑓𝑙𝑢𝑐
(0.28)
𝑢𝑝 = 𝑢𝑝√1 − 𝑎
2 (0.29)
Finally, the particle position is updated using Equations 0.30 and 0.31.
𝑥𝑛𝑒𝑤 = 𝑥𝑜𝑙𝑑 + 0.5(𝑢𝑝,𝑛𝑒𝑤 + 𝑢𝑝,𝑜𝑙𝑑) 𝑑𝑡 (0.30)
𝑦𝑛𝑒𝑤 = 𝑦𝑜𝑙𝑑 + 0.5(𝑣𝑝,𝑛𝑒𝑤 + 𝑣𝑝,𝑜𝑙𝑑) 𝑑𝑡 (0.31)

54
4.
CHAPTER 4
Model Validation
The particle model is validated against two laboratory debris studies by comparing the numerical
results with the experimental data. Selected benchmark cases serve the purpose of better
understanding the characteristics of tsunami debris behavior under idealized conditions as well as
the multi debris transport processes considering different density groups. As flow–debris
interactions are ignored in the modeling approach presented here, a flow simulation is performed
first, and simulations of debris motion are then conducted by inputting spatial distributions of
inundation depths and velocities evaluated by the flow simulation at certain intervals; namely, oneway coupled simulations are conducted.
4.1 Debris Movement over an Unobstructed Beach, Benchmark #1 (Rueben et al. 2015)
The experiments chosen for this benchmark were conducted at the O. H. Hinsdale Wave Research
Laboratory at Oregon State University to measure debris movement and tsunami inundation over
an unobstructed beach. A novel image processing technique was used to detect the position and
orientation of debris. Debris was made of plywood rectangular boxes and positioned on a raised
flat section without still water present (Figure 0.1). Debris experiments were conducted using
seven initial configurations considering the three main characteristics including the number of
boxes, the induced rotation, and the segmentation of groups. Five initial configurations were

55
selected to be used in the validation of the particle model. The combination of wire resistance wave
gauges (WGs) and ultrasonic wave gauges (USWGs) was used to capture the free surface
information. The USWG4 was collocated with an acoustic-Doppler velocimeter (ADV2) for the
kinematics trials. Complete details of the experiment can be found in the accompanying journal
paper: Rueben et al. (2015).
Figure 0.1: Overview of the testbed and laboratory setup (taken from Rueben et al. 2015)
4.1.1 Experimental Setup and Parameters
The experiments were conducted in a wave basin that is 48.8 m long, 26.5 m wide and 2.1 m high.
The plan view of the basin can be seen in Figure 0.2. The bathymetry was initially flat near the
multidirectional piston-type wavemaker (located at x = 0 m) to x = 10.0 m. Then, a 1/15 slope 7.5
m long followed, which was connected to another section with a 1/30 slope for another 15 m long.
Finally, the bathymetry ended with a raised flat section starting at x = 32.5 m to x = 43.75 m at
elevation z = 1 m. The bathymetry of the experimental basin is made of impermeable smooth
concrete with a float finish. The estimated roughness height of the bathymetry was estimated to be
0.1 mm – 0.3 mm.

56
Figure 0.2: Plan view of the experimental basin including the locations of WGs, USWGs and
USWG-ADV pair (Taken from Rueben et al. 2015)
In this experiment, debris was made of 12.7 mm thick plywood with a box shape that has a
nominal footprint of 60.0 cm in length and 60.0 cm in width with a height of 40.0 cm. Nominal
dry weights were 14.5 kg (1) per box. The modeled debris in this experiment would correspond
to approximately a standard shipping container. The coefficient of friction between the smooth
concrete basin floor and the wet plywood debris was not measured. However, based on the
literature, it is estimated to be in the range of 0.2 to 0.3 (Gorst et al., 2003).
Figure 0.3 shows the initial debris configurations used in the experiments. These
configurations are designed to study the aspects of the number of debris boxes, the induced

57
rotation, and the segmentation of groups. Path positions and cross-shore velocities for multi box
configurations were presented for the centroid, which is the arithmetic mean of all debris centers.
White rectangles are free to move along the basin and gray rectangle is fixed. Initial configurations
of Config 1(C1), Config 2 (C2), Config 3 (C3), Config 4 (C4) and Config 12 (C12) are selected to
be used for the validation of the particle model. workshop
Figure 0.3: Initial debris configurations.
Experiments were conducted with a constant water depth of 90.56 (0.13) cm with the standard
deviation in parenthesis. The generated wave for this experiment is not a solitary wave. It is a
custom wave meant to maximize the stroke of the wakemaker, while generating a long period
wave. Due to this generation approach, the wave is not permanent, like a solitary wave. The wave
was numerically generated using the time series of incident wave elevation at WG2 to force the
numerical model at x = 2.26 m.

58
4.1.2 Model Comparisons
The COULWAVE model was set up with ∆𝑥 = 0.08 m, ∆𝑡 = 0.0102 s, a standard breaking model,
and solid wall boundary conditions. For the simulations presented, quadratic bottom friction factor
was used as 0.0025. Water surface elevation data at the locations of WG2, WG6, USWG3, and
USWG4 are compared with the COULWAVE, Boussinesq-predicted wave results to ensure that
the generated waves in the model are reasonable in terms of amplitude, period, and arrival time.
Figure 0.4 shows that experimental and numerical results are fairly in good agreement.
Replicating WG data in high accuracy indicates that initial wave generation in the model is
captured very well. Wave amplitudes are represented accurately while the wave propagates inland.
The phase of the model waves is also closely aligned with the experimental data. The arrival time
of the wave is predicted reasonably well. The results for the ADV data seem in good agreement
with the experiment as well. There are small discrepancies between the results that can be
attributed to the hydrodynamic modeling approach i.e. boundary conditions, simplified equations
etc.

59
Figure 0.4: Comparison of water surface elevations at WG2, WG6 and UWG4 and ADV2 with the
experimental data: COULWAVE (solid blue, green and black line), Experiment (dashed blue, green
and orange line)
Rueben et al. (2015) did not specify or recommend any value for the drag coefficient in their
studies. Subsequent literature review reveals that the drag coefficient values used in various
tsunami debris studies range between 1.2 to 3 (Imamura et al., 2008; Nojima et al., 2017; Kihara
and Kaida et al., 2020; von Häfen et al., 2021; Koh et al., 2024). Since drag coefficient is a model
parameter that requires calibration, considering the shape of the debris particles used in the
experiment, there drag coefficient was assumed as 𝐶𝐷 = 1.75. The same consideration is applied
for added mass coefficient as well and was assumed as 𝐶𝑎 = 1. The study did not provide any

60
information on material properties. The stiffness and damping coefficients needed to be calibrated
in the model iteratively and were determined as 𝑘 =1000 N/m and 𝑐 =50 Ns/m. The resistance
torque coefficient is determined in a similar manner and used as 𝐶𝑟𝑚 = 0.5. It was seen that the
wake effect was not very critical for this Benchmark study. C1, C2, and C12 were conducted with
a single debris box, and in C3 and C4, the four debris boxes stayed close enough to each other, not
feeling the effect of each other's wake region that much. The 𝐶𝑤𝑠 implementation was done by
using a step function. A simple approach is used to calculate the number of particles around the
particle in interest and based on the results 𝐶𝑤𝑠 value was updated.
4.1.2.1 Comparison of C1 Results
This case was conducted with one debris box and no obstacles along the flow path. The
configuration was experimentally tested only once. C1 was a baseline for investigating the effect
of increasing the number of debris particles in free translation. Snapshots from one of the numerical
model simulations presenting the debris motion and the wave propagation are given in Figure 0.5.
After the wave arrived, the debris box moved along on a straight line during its motion.
The presented experiment results are from the deterministic trial. However, since the
particle model is stochastic, the model results will be presented in a statistical manner. For this
purpose, the simulations were repeated 100 times for each case. The main cause of uncertainty in
the numerical model is the way debris transport motion is represented. It is important to note it is
assumed here that variations in material properties or discrepancies in initial conditions are factors
that have zero uncertainty. Additionally, the fluid mechanics component of the model is perfectly
repeatable, which means that the observed variability is not a result of the hydrodynamic
calculations.

61
Figure 0.5: Snapshots from the simulation of C1
Figure 0.6 shows the experimental data and the debris motion predictions, focusing on the
x distance traveled by the debris and the corresponding velocity over time. The experimental
results were plotted as black circles for the x direction, the particle model results were plotted as
solid blue lines for the x direction, and the associated standard deviation was plotted as dash-dotted
grey lines. Since velocity and movement in the y direction were negligible in the experiment, the
results were presented only for the x direction. The particle model closely tracks the experimental
data for the x-distance traveled by the debris. This suggests that the model accurately captures the
longitudinal transport dynamics over time. There is a consistent pattern of movement, with the rate
of travel increasing over time as the wave pushes the debris inland. The debris model's prediction
for velocity starts a little after the experimental data. This could be explained by the fact that

62
hydrodynamics used in the model did not consider the particle's existence. However, in the
experiment, the particle’s existence disturbed the flow, and water started to build up on the debris
front face when the wave reached the debris. This created an extra force to push the particle
forward, which led to the increased velocity and particles moving earlier. The accelerating motion
was reasonably well represented. Experimental velocity data was generated by calculating the
derivative of the experimental position data using the forward difference method. Since the
experimental data was sampled roughly every 0.5 seconds, the velocity data can be shifted by dt/2.
The particle model slightly overestimated the experimental peak velocity. This could be due to
missing some physics related to the particle-flow interaction.
Figure 0.6: Comparison of x distance traveled and corresponding velocity of the debris particle for
C1: Numerical results (solid blue lines), Experimental results (black circles), standard deviation
(dash-dotted grey line)

63
4.1.2.2 Comparison of C2 Results
This case consisted of one debris box and one obstacle along the flow path. The configuration was
experimentally tested only once. Figure 4.7 gives snapshots from one of the numerical model
simulations presenting the debris motion and the wave propagation. The particle model effectively
represented the effect of the obstacle on the particle motion, and the rotational motion was
accurately captured.
Figure 0.8 shows the experimental data and the debris motion predictions after 100
iterations, focusing on the x distance traveled by the debris and the corresponding velocity over
time. The experimental results were plotted as black and purple circles for the x and y directions,
the particle model results were plotted as solid blue and green lines for the x and y directions,
respectively, and the associated standard deviation was plotted as dash-dotted grey lines. The
particle model captures the general trend of the debris motion reasonably well. There are small
differences in capturing the peak velocities both in the x and y direction. The possible reason for
that could be the method of handling collision forces. The soft collision model, due to its necessity
to detect overlap before applying collision forces, is unable to completely simulate rigid collisions
as they occur in reality. This leads to a slight delay in the temporal response of the force. Following
the collision with an obstacle, a decrease in velocity in the x-direction is observed, along with the
force experienced due to the collision. This observed small peak reflects the impact of the collision.
At this point, the particle begins to move in the y-direction, accompanied by rotation. Since the
model does not accurately reflect the smooth transition seen in reality by nature, these changes are
perceived as exhibiting some degree of lag.

64
Figure 0.7: Snapshots from one of the simulations of C2

65
Figure 0.8: Comparison of x and y distance traveled by the debris particle and the corresponding
velocities for C2: Numerical results (solid blue and green lines for x and y directions, respectively),
Experimental results (black and purple circles for x and y directions, respectively), standard
deviation (dash-dotted grey lines)
4.1.2.3 Comparison of C3 Results
In this case, there were four individual debris boxes and no obstructions along the flow path. The
configuration was experimentally tested only once. Figure 0.9 presents the snapshots from one of
the 100 numerical model simulations showing the debris motion and wave propagation. When the
wave arrives, particles 1 and 2 collide with particles 3 and 4 immediately. They started propagating
inland and separated from each other.

66
Figure 0.10 shows the experimental data and the debris motion predictions focusing on the
distance traveled by the debris centroid in the x direction. The x and y directions for the particle
model results were plotted as blue and green solid lines, respectively, while the experimental
results were plotted as black and purple circles for the x and y directions, respectively and the
standard deviation is plotted as dash-dotted grey lines. The debris model's prediction for velocity
started a little after the experimental data. The same reasoning described in 4.1.2.1 for this behavior
applies here as well. The agreement in the x-direction for the centroid's motion indicates that the
model reasonably simulates the longitudinal behavior of the debris group, which is essential for
understanding the impact zone in a tsunami event. The slight overestimation is due to the
overestimated x velocities for particles 3 and 4. The lateral movement from the single experimental
trial remains in the standard deviation limits predicted by the model.
Figure 0.11 presents that the velocity graphs for individual particles vary between the
experimental results and the model, showing differences in how individual debris particles
interacted with the local flow conditions and each other. The x-velocity profiles for particles 1 and
2 from the model showed good agreement with the experimental data, capturing the main
characteristics of acceleration and deceleration phases. The model overestimated the x velocities
for particles 3 and 4. These particles are positioned behind particles 1 and 2, which are closer to
the wavemaker. The overestimation of the x velocities suggests that particles 3 and 4 are taking
more energy from the flow than they should. In the actual experiment, particles 3 and 4 are
shadowed and not located in the wake zone, experiencing the flow just around them. When the
flow starts, the particles are immediately adjacent to each other, which causes them to pull together.
However, the model could not capture this behavior without advanced coupling, which can be

67
considered a limitation of the model. Therefore, the outer particles are expected to move too
quickly in the model.
Figure 0.9: Snapshots from one of the simulations of C3

68
Figure 0.10: Comparison of x and y distance traveled by the particles centroid for C3: Numerical
results (solid blue and green lines for x and y directions, respectively), Experimental results (black
and purple circles for x and y directions), standard deviation (dash-dotted grey lines)
Figure 0.11: Comparison of the velocities of individual debris particles in x and y directions for
C3: Numerical results (solid blue and green lines for x and y directions), Experimental results
(dashed black and purple circles for x and y directions), standard deviation (dash-dotted grey lines)

69
4.1.2.4 Comparison of C4 Results
This case consisted of four individual debris boxes and one obstacle along the flow path. The
configuration was experimentally tested six times. Snapshots from one of the numerical model
simulations presenting the debris motion and the wave propagation are given in Figure 0.12. It can
be seen after the wave reached the particles, they started to move and particle 3 collided with the
obstacle. Rotation was introduced due to this collision, and particles interacted with each other
while propagating onshore. When the experiment video was checked, it was seen that particles 2
and 4 formed a column against the obstacle for a while before they started their motion. The mean
experimental results were plotted as black and purple dashed lines for the x and y directions, the
particle model results were plotted as continuous blue and green lines for the x and y directions,
respectively and the associated standard deviation was plotted as dash-dotted grey lines.
Figure 0.13 shows the experimental data and the debris motion predictions, focusing on
the x distance traveled by the debris and the corresponding velocity over time. The experimental
results were plotted as black and purple circles in the x and y directions, the numerical results were
plotted as solid blue and green lines in the x and y directions, respectively, and the associated
standard deviation was plotted as dash-dotted grey lines. The acceleration and deceleration
behavior of the particle group centroid predicted by the numerical model was in good agreement
with the experimental results. Overestimation of the x distance traveled is due to the overestimation
of the x velocity for the individual particles. The displacement in the y direction is captured
reasonably well, and the experimental result remained within the predicted standard deviation
limits.

70
Figure 0.12: Snapshots from one of the simulations of C4
Figure 0.14 presents that the velocity graphs for individual particles vary between the
experimental results and the model, showing differences in how individual debris particles interact
with the local flow conditions, each other, and the obstacle. The time lag in the initial velocity of

71
debris particles 2 and 4 compared to particles 1 and 2 can be explained by forming the column that
is hung up on the obstacle in the experiment. The numerical model did not capture this behavior.
Therefore, particles 3 and 4 experienced a short delay time for starting their motion in the model,
which can be explained by the overlapping requirement for collision detection and force
calculation. The x velocity of particle 3 was overestimated based on the same reasons described in
section 4.1.2.3. When particles are that big and move closer to each other, there is some physics
that the model is missing. Particles are affecting the flow and changing the hydrodynamics in a
way that the model was not able to capture. The local peaks in x velocity of particles 2 and 4 are
due to the collisions they experienced. The velocities in the y direction remained inside the
standard deviation limits.
Figure 0.13: Comparison of x and y distance traveled by the particles centroid for C4: Numerical
results (solid blue and green lines for x and y directions, respectively), Experimental results (black
and purple circles for x and y directions), standard deviation (dash-dotted grey lines)

72
Figure 0.14: Comparison of the velocities of individual debris particles in x and y directions for
C4: Numerical results (solid blue and green lines for x and y directions), Experimental results
(black and purple circles for x and y directions), standard deviation (dash-dotted grey lines)
4.1.2.5 Comparison of C12 Results
This case consisted of one large box and one obstacle along the flow path. The configuration was
experimentally tested only once. Snapshots from one of the numerical model simulations
presenting the debris motion and the wave propagation are given in Figure 0.15. The particle model
effectively captured the obstacle effect by representing the collision. The rotational motion in the
initial stage and the direction of movement from the initial position are similar to the experimental
results.

73
Figure 0.16 shows the experimental data and the debris motion predictions after 100
iterations, focusing on the x distance traveled by the debris and the corresponding velocity over
time. The experimental results were plotted as black and purple circles for the x and y directions,
the particle model results were plotted as solid blue and green lines for the x and y directions,
respectively, and the associated standard deviation was plotted as dash-dotted grey lines. The
model captures the general trend of the debris motion reasonably well. The x and y displacements
were inside the associated standard deviation limits. The acceleration and deceleration behavior of
the particle velocity in the x direction was not captured well by the model. Missing some important
physics between the particle and the flow interaction could be the reason for this. Also, calibrating
the added mass and drag coefficient parameters could improve the accuracy of numerical model
results. The y velocity started with a lag due to the collision handling method. The soft collision
model leads to a slight delay in the temporal response of the force due to the requirement of overlap
detection. After the collision, the particle begins to move in the y-direction, accompanied by
rotation.

74
Figure 0.15: Snapshots from one of the simulations of C12

75
Figure 0.16: Comparison of x and y distance traveled by the debris particle and the corresponding
velocities for C2: Numerical results (solid blue and green lines for x and y directions, respectively),
Experimental results (black and purple circles for x and y directions), standard deviation (dashdotted grey lines)
4.2 Multi-Debris Transport over a Flat Test Bed, Benchmark #2 (Park et al. 2021)
The experiments chosen for this benchmark were conducted at the O. H. Hinsdale Wave Research
Laboratory at Oregon State University. The debris in the experiments consisted of rectangular
pieces made of wood and High-Density Polyethylene (HDPE). Debris specimens were placed on
a raised flat section above the basin floor, with no still water. The position and orientation of
multiple debris samples were detected through optical measurement. Hydrodynamic information
was captured using a combination of WGs, USWGs, and ADVs. For more detailed information
about the experiment, please refer to the accompanying journal paper: Park et al. (2021). The scale

76
and the number of debris specimens can be seen in Figure 0.17. Experiments used debris of
identical size and square box shape. Different colors were used to represent different materials,
with orange representing HDPE and yellow representing wood. Cases used in this benchmark were
conducted without obstacles.
Figure 0.17: Overview of the testbed with two debris setups (photo taken from Park et al. 2021)
4.2.1 Experimental Setup and Parameters
The experiments were conducted at the same basin described in Chapter 2. For general information
on the size and bathymetry of the basin, please refer to Chapter 2.2. Since the back end of the
testbed ends into a drainage basin, the boundary is best modeled as an outgoing boundary rather
than a vertical wall. The bathymetry of the experimental basin is made of impermeable smooth
concrete with a float finish. Figure 0.18 shows the plan view of the wave basin and the
experimental setup with WG, USWG and ADV locations.

77
Figure 0.18: Plan view of the experimental setup (taken from the Park et al. 2021)
In this experiment, two types of debris were used: HDPE and wood. Each debris specimen
has a nominal footprint of 10.2 cm in length and 10.2 cm in width with a height of 5.1 cm. The
mean density of HDPE and wood debris was 987 (11.7) kg/m3 and 648 (17.6) kg/m3, respectively,
with the standard deviation in parenthesis. In this experiment, modeled debris would correspond
to a prototype smaller than a shipping container and larger than a passenger vehicle. The static
friction coefficients of HDPE and wood debris were determined under almost dry and wet
conditions. The average static friction coefficient and its standard deviation given in parenthesis
for HDPE were 𝜇𝑠 = 0.66 (0.07) and for wood were 𝜇𝑠 = 1.28 (0.13). For wet conditions, the
measured static coefficient of HDPE was 0.38 and for wood, it was 0.71. Two different initial
debris configurations were used in selected cases (Figure 0.19). The footprint of the initial debris
configuration kept constant using a 71.4 cm by 56.1 cm frame and debris specimens placed inside.

78
Uniform debris configuration was arranged in 5x4 array, spaced 5.1 cm apart in both x and y
dimensions. Random configuration consisted of debris with irregular orientations and spacing.
Table 0.1 shows the overall description of the cases.
Table 0.1: Description of the Benchmark #2 cases
Case Name Type Number Configuration
Case 1 HDPE 20 Uniform
Case 2 Wood 20 Uniform
Case 3 HDPE + Wood 10 + 10 Random
Figure 0.19: Initial configurations of debris (a) uniform and (b) random (Photos are taken from
Park et al. 2021)
The constant water depth at the wave maker was 0.87 m. Same with the previous benchmark
case, the generated wave for this experiment is not a solitary wave. It is a custom wave meant to
maximize the stroke of the wakemaker, while generating a long period wave. The wave was
generated using the time series of incident wave elevation along the wavemaker paddle to force
the numerical model at X = 0 m. Although, this method may not be ideal in this case as the
wavemaker paddle is moving in time; no wave gauge data was available in the flat section of the
basin near the wavemaker.

79
4.2.2 Model Comparisons
The COULWAVE model was set up with ∆𝑥 = 0.08 m, ∆𝑡 = 0.0102 s, a standard breaking model
and wall boundary conditions. For the simulations presented, the quadratic bottom friction factor
was used as 0.0025. In Figure 0.20, the measured time series of water surface elevation at WG1,
WG9, usWG5, and usWGh5 was compared with the numerical model results. A comparison of
modeled data at these locations was needed to ensure that the generated waves in the model are
reasonable in terms of amplitude, period, and arrival time. It is noted here that the main concern
was to capture the initial wave in this data set. The breakwaters in the side channels and a long
wave generated cause reflected wave energy to arrive at the wave gauges nearly 10 seconds after
the leading wave crest. This resultsin the entire offshore section of the basin experiencing sloshing.
The reflected waves do not have any significant influence on the debris motion. The ADVH5 data
is also plotted; however, due to the bubbly nature of the flow, there is limited available velocity
data at this location. In general, the model appears to capture the general trend of the surface
elevation quite well. There is a good agreement on wave amplitude between experimental and
numerical results. The phase of the model waves is also closely aligned with the experimental data,
indicating that the wave celerity and dispersion are well-represented. The arrival time of the wave
is reasonably predicted. The slight deviations from the experimental measurements might be
related to the hydrodynamic modeling approach i.e the fidelity of the input condition, simplified
equations etc.

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Figure 0.20: Comparison of water surface elevations at WG1 and WG9 and WG5 WGh5 and ADV
with the experimental data: COULWAVE (solid blue, green and black line), Experiment (dashed
blue, green and orange line)
Park et al. (2021) did not specify or recommend any value for the drag coefficient in their
studies. Similar assumptions on coefficients of drag and added mass can be made in here as in
Section 4.1.2. Since the drag coefficient is a model parameter that requires calibration, considering
the shape of the debris particles used in the experiment, it was assumed as 𝐶𝐷 = 1.75. The same
consideration is applied for added mass coefficient as well and was assumed as 𝐶𝑎 = 1. The
information on material properties was not available in the study. The stiffness and damping
coefficients needed to be calibrated in the model iteratively and determined as 𝑘 =4000 N/m and

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𝑐 =40 Ns/m for HDPE and 𝑘 =2000 N/m and 𝑐 =30 Ns/m for wood. Resistant torque coefficient,
𝐶𝑟𝑚 is determined in a similar manner and used as 0.5. Wake strength coefficient, 𝐶𝑤𝑠 was
implemented using a step function. Calculating the number of particles around the particle in
interest determined the value for the parameter.
4.2.2.1 Comparison of Case 1 Results
The particle model aimed to provide a statistical distribution of particle positions rather than a
prediction of a single event. Stochastic model results were obtained after 100 iterations. Figure
0.21 shows the representative final positions of the HDPE debris particles in Case 1 as captured
from one of those iterations. Table 0.2 compares experimental and model data for mean
longitudinal distance, lateral and longitudinal spreading, with associated standard deviations for
each. The mean longitudinal distance traveled was calculated by averaging the positions of debris
in the x direction for each iteration. To quantify the longitudinal and lateral spreading, variances
of the final debris positions in the x and y directions respectively, were calculated.
Figure 0.21: Representative final positions of HDPE particles for Case 1: Numerical (orange dots),
Experimental (black dots)

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Table 0.2: Comparison of experimental and numerical results for Case 1
Case 1
Mean
Longitudinal
Distance (m)
Longitudinal
Spreading
(m)
Lateral
Spreading
(m)
Experiment 3.779 0.451 0.680
Model 3.767  0.039 0.4500.032 0.4150.043
The model captures the system's main dynamics and provides a statistical distribution of
possible outcomes rather than a prediction of a single event but requires calibration of the
parameters. The mean longitudinal distance estimation by the model was very close compared to
the experiment. The experimental result remained within the standard deviation limits. The
longitudinal spreading results were also in good agreement with the experiment results, which
remained in the provided variance. The lateral spreading was underpredicted with a percentage
error of 32%. One possible explanation for this is that the 1D hydrodynamic model used may not
have been able to capture the variations in flow velocity and direction that occurred in the
experiment. Lateral spreading is a complex process that is influenced by the interactions of debris
with flow features such as vortices and eddies, which are inherently multidimensional effects.
Another reason could be the oversimplification of the step function used for 𝐶𝑤𝑠. This
implementation might not reflect the full complexity of particle interactions in the experiment.
Despite this, the model still provided good results for Case 1, with acceptable relative error margins
given the challenging nature of the phenomenon.
Note that experimental results are based on only one trial. Without repeated experiments,
it is difficult to determine the variability inherent in the physical system and the reproducibility of
the results. Any particular trial could be an outlier influenced by uncontrolled variables or unique
conditions that other trials would not capture.

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4.2.2.2 Comparison of Case 2 Results
Similar to Case 1, the stochastic model results were obtained after 100 iterations. Figure 0.22
shows the representative final positions of the wood debris particles in Case 2 as captured from
one of those iterations. Table 0.3 presents the comparison of experimental and model data for mean
longitudinal distance and longitudinal and lateral spreading with associated standard deviations
for each. Note that experimental results are based on a single trial. The mean longitudinal distance
traveled was calculated by averaging the positions of debris in the x direction for each iteration.
To quantify the longitudinal and lateral spreading, variances of the final debris positions in the x
and y directions respectively, were calculated.
Figure 0.22: Representative final positions of wood particles for Case 2: Numerical (yellow dots),
Experimental (black dots)
Table 0.3: Comparison of experimental and numerical results for Case 2
Case 2
Mean
Longitudinal
Distance (m)
Longitudinal
Spreading
(m)
Lateral
Spreading
(m)
Experiment 8.451 0.693 0.598
Model 8.459  0.061 0.637  0.061 0.655  0.077

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The calibrated model performed well in Case 2, providing accurate results. The model's
predicted mean longitudinal distance was very close to the experimental value, indicating that the
model replicates the longitudinal behavior well. The variability in both longitudinal and lateral
motion was also well captured by the model. Although in Case 1, the lateral dispersion was not
accurately captured for HDPE particles, the prediction of the lateral motion for wood particles was
close to the experimental result, which was within the associated standard deviation limits.
4.2.2.3 Comparison of Case 3 Results
For this case, it was challenging to create a random position and random orientation for squaredshaped debris particles inside a designated area without particles overlapping each other. To
achieve something similar to the randomness in the experiment’s initial configuration, using a
uniform array, a limited positional adjustment margin in both the x and y directions has been
defined for each particle position (Figure 0.23). Subsequently, a random orientation was assigned
to these particles. In the physical experiments, one consideration of the random configuration was
to avoid grouping of the same material particles. The determination of whether the particles are
made of HDPE or wood was also made through random assignment. The movement and the impact
of the floating debris may be sensitive to small changes to their initial position and orientation and
influenced by the small change in flow dynamics.

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Figure 0.23: Sketch of the positional adjustment margin for random configuration (orange arrows
show the possible directions for the particle to move
As in Case 1 and Case 2, the stochastic model results were obtained after 100 iterations.
Figure 0.24 shows the representative final positions of the HDPE and wood debris particles in
Case 3, as captured from one of those iterations. The parameters used in Case 3 were derived from
the simulations of Case 1 and Case 2. The main objective is to conduct the Case 3 simulation using
the model parameters that were calibrated from Case 1 and Case 2 then compare the results across
these cases. Table 0.4 presents the comparison of experimental and model data for mean
longitudinal distance and maximum spreading angles for HDPE and wood particles. Note that
experimental results are based on a single trial. The mean longitudinal distance traveled was
calculated by averaging the positions of debris in the x direction for each iteration and different
material debris. The max spreading angle for left (negative y direction) and right (positive y
direction) was calculated for each type by detecting the maximum lateral spreading for each
particle.
The presence of mixed materials can affect turbulent flow dynamics, for example with
denser HDPE potentially affecting the flow more than wood. This can lead to changes in flow
patterns, impacting particle motion. Therefore, the wake strength coefficient was modified for the
wood particles in this case. Since HDPE particles create larger wakes than wood particles, this

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adjustment ensures that wood is more affected by these wakes than HDPE. To address this
difference, the wake strength coefficient in the step function was multiplied by 3 for the wood
particles.
Figure 0.24: Representative final positions of HDPE and wood particles for Case 3: Numerical
(orange dots for HDPE and yellow dots for wood), Experiment (black dots)
Table 0.4: Comparison of experimental and numerical results for Case 3
Case 3
Mean
Longitudinal
Distance (m)
Max Spreading
(Left, )
Max Spreading
(Right, )
HDPE Wood HDPE Wood HDPE Wood
Experiment 4.636 6.643 -16.0 -11.6 13.4 9.2
Model
4.155

0.180
7.378

0.359
-11.19

3.48
-9.65

2.57
10.18

3.44
8.87

2.50
The model slightly underestimated the mean longitudinal distance for HDPE particles with
a percentage error of 6.5%. and the mean longitudinal distance for wood particles was slightly
overestimated by 5.7%. The left max spreading angle for HDPE was underestimated with a
percentage error of 8.3%. The left max spreading angle for wood and right maximum spreading

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angles for HDPE and wood are remained within the standard deviation limits. The observed
differences could be due to several factors, including different material interactions, particle
dynamics, or specific environmental conditions not captured in the model. Moreover, the collision
mechanism could be different between two different materials, and stiffness and damping
coefficients might need to be calibrated specifically.
Additionally, due to their different densities, HDPE and wood particles might have varied
tendencies to cluster, affecting overall dispersion and motion. Clustered particles can disturb the
flow, and the closure method might not be enough to capture the change. Not capturing the
clustering behavior and not coupling the particle-flow interactions can cause some particles to
absorb more energy from the flow than they should. Since the model does not include the particle
fluid coupling, expecting to capture the exact behavior would not be realistic. This leads to
variations in flow patterns and particle trajectories, potentially causing discrepancies in the model
results.
Another thing to consider is the implementation of a simplified step function for the wake
effect, and the threshold value for the distance check can result in inaccuracies. The model might
not fully account for the tendency for particles to cluster or disperse. The step function used to
represent particle wake effects could oversimplify these interactions, leading to an underestimation
of spreading angles. A lack of sufficient data for calibrating coefficients in the step function or
other model components can result in inaccuracies. This limitation restricts the model's ability to
accurately predict particle motion, especially in complex mixed-material scenarios.

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4.3 Conclusions
The objective of this chapter was to validate the developed particle motion model using several
benchmarking test cases. In the first benchmark case, a one-way coupled particle motion model
was implemented to validate the capability of accurately modeling debris translation and rotation
as well as the effects of debris quantity and segmentation of groups. Five different setups were
modeled and results were compared with the experimental data. The model captures the system's
main dynamics and provides a statistical distribution of possible outcomes rather than a prediction
of a single event. Reasonable results were obtained for all the cases. In general, particle
acceleration and deceleration behavior was captured accurately alongside the particle-particle
interactions and rotations due to collisions. In cases that consisted of multiple debris particles,
shadowed particles experienced higher velocities due to some limitations of the model regarding
not capturing flow-particle interactions. The soft collision model slightly delayed the temporal
collision response of the particles in all cases.
In the second benchmark case, the particle model was validated through the simulations of
multi-debris transport. Three different setups were modeled considering different types of particles
and initial configuration and the results were compared with the experimental data. Case 1 and
Case 2 were used to calibrate the model parameters and Case 3 was simulated using the calibrated
parameters. In general, the stochastic numerical model results of the mean longitudinal distance,
longitudinal spreading, and lateral spreading of the particles reasonably agreed with the
experimental data. In Case 3, it was observed that the particles with different masses can affect the
flow differently. The modification in the wake strength coefficient was implemented to account
for different degrees of particle fluid interactions.

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5.
CHAPTER 5
Large-Scale Model Case Study: Crescent City
Located on the Pacific coast in the northwestern part of California, Crescent City is considered the
tsunami capital of the United States. Crescent City has experienced devastating impacts from large
tsunamis, leading to severe destruction of property and casualties. The Great Alaska Earthquake
of March 1964, with a moment magnitude of 9.2, caused a tsunami in Prince William Sound that
left a lasting impact on the surrounding community. Unfortunately, the tsunami claimed twelve
lives in Crescent City and caused more than $15 million in losses related to the disaster (Lander et
al., 1993; Arcas and Uslu, 2010). On November 15, 2006, a powerful earthquake with a magnitude
of 8.3 struck the Kuril Islands, triggering a tsunami that hit Crescent Harbor. The tsunami caused
significant damage to the small boat basin, with estimated costs of up to $5.9 million (Uslu et al.
2007). Crescent City is known to be more vulnerable to tsunamis than any other city along the
West Coast of the United States due to the offshore bathymetry and configuration of the basin.
Since 1938, a total of twenty-four tsunamis have been documented, out of which nine had
amplitudes equal to or greater than 0.5 meters (Dengler and Magoon, 2006). Tsunami waves tend
to get amplified in the area around Crescent City. The observed wave heights in Crescent City
Harbor are typically ten times greater than those measured in other locations along the West Coast.
Tsunami forecasters and emergency managers are likely to benefit from the anticipated wave
heights in Crescent City as they can provide an estimate of the maximum height of tsunami waves
that could hit the western coast of the United States. (Arcas and Uslu, 2010). Due to these reasons,

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Crescent City is considered a high-priority site for tsunami inundation studies and has been
selected to be used as a large-scale test case location in this study.
A deterministic tsunami scenario was simulated using CELERIS (Tavakkol & Lynett,
2017), considering a bathymetry that represents a bare earth condition. The simulation output,
which included flow depth and depth-averaged velocities, was used as an input for the debris
transport model. This chapter aimed to investigate the motion of debris in a large-scale scenario.
Figure 0.1 features the bathymetric map of the hydrodynamic computational domain. For the
numerical modeling of tsunami inundation at Crescent City, tsunami input conditions were adapted
from ASCE 7 (Chock et al., 2011; Chock, 2016) which defines the offshore tsunami amplitude at
the 2500-year return period. At this return period, the tsunami amplitude of offshore Crescent City
was 7.62 m and the period was 15 mins. Wave input was given from the west boundary. The
tsunami model represents the bare-earth surface bathymetry conditions using an 18 m-resolution
mesh grid (901x931). The Manning roughness, n, was set to a constant value of 0.025 in this case
study.
Tsunami-driven debris can include a wide range of items such as boats, ships, vehicles,
shipping containers, and parts of damaged buildings or nonstructural elements (Naito et al., 2014).
Urban areas around harbors are at risk of tsunami waves and debris from marine vessels, vehicles,
and shipping containers in particular. Therefore, the debris type used in the model was determined
to be a typical 20 ft shipping container located just north of the Crescent City harbor. An ISO
standard defines the 20-foot container dimensions with a height, width, and length of 2.591, 2.438,
and 6.096 m, respectively. When fully loaded, this container can weigh up to 28,570 kg and has a
maximum draft of 2.006 m (Koh et al. 2024). The debris weight in the model was set to be 25,000

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kg, and the draft was calculated as 1.682 m. Satellite images were utilized to identify the initial
potential area of the debris sources.
Figure 0.1: Bathymetric map of the computational domain, red square indicates the initial position
of the debris particles. White and orange dashed lines represent the upper and lower limits for
categorized particle groups based on their final y coordinates.
Two initial configurations, one with a 10x50 array (Test Case 1) and another with a 20x25
array (Test Case 2), both consisting of 500 particles, were considered to investigate the debris
motion. Furthermore, two additional simulations were conducted: one using the same
configuration as Test Case 1 but disabling the collision forces to investigate the collision
contribution to dispersion and one with a 20x50 configuration (Test Case 3) consisting of 1000
particles to assess the impact of the number of particles on the system. The model parameters
relevant to the particles were used as follows based on the same discussions in Chapter 4: 𝑘 =

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2*105 N/m and 𝑐 = 30 Ns/m 𝜇𝑠 = 0.65, 𝜇𝑑 = 0.25, 𝐶𝐴 = 1 and 𝐶𝐷 = 1.75. Numerical output was
saved at 10-second intervals, but a finer time step resolution was needed to ensure the accuracy
and stability of the tsunami debris motion simulation. This is accomplished through the application
of linear interpolation between known discrete time points. Specifically, the method involved
determining interpolated values for key parameters, including horizontal and vertical velocity
components, water depth, and other fluid properties, at intermediate times. The finer time step for
the particle motion in all simulations was set to be 0.1 sec, which is found relevant for the present
case after trial simulations.
Although observations from the simulations are presented in details in the forthcoming
sections of the present chapter, the overall behavior of the particles are summarized as follows:
The first wave arrived at approximately 1427 seconds in the area of interest, with an initial flow
direction of northeast. Immediately upon arrival, the particles interacted with each other and
initiated their motion. Following the first wave, another strong current within the first wave arrived
at the dispersed particle locations from the south during the period of 1670 – 1801 seconds due to
the bathymetry and topography impact. The particles propagated towards the north, following the
topography and strong currents. During the period of 2408 - 2800 seconds, the second wave arrived
and affected the dispersed particles. The flow direction started again from the northeast, and
another current followed from the south. Particles continued their motion following the current
patterns. Some of them remained stationary, while some moved further north. The third wave
arrived at 3200 seconds, but it did not reach some of the particles that had already dispersed and
propagated inland and up north. The wave interacted with retreating water, and the particles
followed the currents. The findings suggest that the particles' motion is primarily directed by the
strong currents, which are influenced by the topography of the region.

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For all simulations following the initial dispersion, the debris particles exhibited three
distinguishable groups based on their respective final y-coordinates. Particles with y-coordinates
less than 4700 (below the white dashed line) were classified as Group 1, those between 4700 and
5400 (between the white and orange dashed lines) were placed in Group 2, and particles above
5400 (above the orange dashed line) were categorized as Group 3 (see Figure 5.1). The following
sections summarize the observations from the individual simulations.
5.1 Test Case 1 - 500 Particles, Initial configuration 10x50
In this simulation, a total of 500 particles were positioned in a 10x50 configuration, with their
longer sides extending along the x direction meaning that the initial configuration of the particles
was a long and narrow rectangular formation. Figure 0.2 shows a closer look at the initial
dispersion of the particles for the first 110 seconds. Different particle groups are shown in different
colors (Group 1 as red, Group 2 as magenta and Group 3 as dark purple). The particles in Group 1
predominantly originated from the lower right section of the initial configurations. In contrast, the
particles in Groups 2 and 3 displayed a more heterogeneous distribution. It can be seen that the
wavefront immediately triggered the particle dispersion. Initial dispersion happens more linearly,
with particles primarily spreading outward in the flow direction due to the elongated starting shape.
Particles immediately interacted with each other experiencing collisions. The rotation of the
particles due to collisions was also captured in the model. The overlaps seen in the snapshots are
due to the necessity of the collision detection algorithm.
Figure 0.3 shows the snapshots from the simulation of Test Case 1 at various times in a
larger area to focus on the traditional dispersion behavior. The initial positions of the particles prior
to wave arrival had an influence on their subsequent rapid interaction upon wave impact, resulting
in collisions and dispersion of the particles in both the x and y directions. Therefore, the particles

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experienced rapid elongation in the y direction and were subsequently carried along with the flow.
This initial dispersion had a profound impact on the subsequent particle motion, with some
particles dispersing farther in the y direction during the first few minutes of motion, ultimately
leading to their spread over a large northern area. As the debris particles traveled over time, their
paths were influenced by the background currents. Regions with high velocity gradients seemed
to generate mixing between different debris groups (Group 2 and Group 3), particularly around
eddies. The concentration of particles around the middle right sector appears to correlate with
stronger flow patterns, potentially creating accumulation zones.
At the end of the simulation, 21.4% of the particles remained in Group 1 while Group 2
comprised 60.6% of the particles. The remaining 18% of the particles were categorized into Group
3, which represented the particles that traveled the farthest distance from their initial positions.
The simulation outputs indicate that the direction of flow and topography are the primary factors
influencing the overall particle movement since the tsunami with a 2500-year return period is a
highly strong event.

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Figure 0.2: Snapshots from the simulation of Test Case 1 with a closer look at the particles' initial
dispersion. Red, magenta and dark purple represented the initial positions of the particles
categorized in Group 1, Group 2 and Group 3 based on their final y coordinates, respectively.

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Figure 0.3: Snapshots from the simulation of Test Case 1 at various times with a larger area focus.
(Grey lines indicate the paths of the particles.)

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5.1.1 Impact of excluding collision forces on debris dispersion
Within this case, an additional simulation was conducted to further explore the role of collision
forces in the dispersion of tsunami debris. The collision detection and calculation of collision
forces were disabled to isolate the effect of collision interactions on particle dispersion and overall
dynamics. The aim was to provide a direct comparison of dispersion behaviors with and without
the influence of collisions.
Figure 0.4 shows a closer look at the particles' initial dispersion for the first 110 seconds.
Different particle groups are presented in different colors (Group 1 is shown in red, Group 2 in
magenta, and Group 3 in dark purple). It can be seen that particles started their motion immediately
without affecting each other, leading to an elongated shape as they moved. The spatial plots show
that the exclusion of collision forces led to a more compact particle cloud, suggesting that
collisions significantly contribute to debris spreading. Figure 0.5 shows the snapshots from the
simulation at various times in a larger area to focus on the traditional dispersion behavior. The
results indicated a noticeable reduction in the dispersion of debris particles when collision effects
were excluded. When collision forces are disabled, the decreased dispersion in the x-direction
becomes evident. This suggests that collisions between particles contributed to lateral spreading.
At the end of the simulation, 17% of the particles remained in Group 1 while Group 2
comprised 61.4% of the particles. The remaining 21.6% of the particles were categorized into
Group 3, which represented the particles that traveled the farthest distance from their initial
positions. The increased number of particles traveling far north could be due to the absence of
particle-particle interactions. Disabling collision forces might lead to maintaining higher kinetic
energy levels in the particles as energy is not lost or redistributed through impacts. The energy
transfer enhances dispersion by breaking down particle clusters, leading to a broader spread.

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Disabling collisions could result in smoother trajectories for the particles as they are only
influenced by drag, inertia, and friction forces.
Figure 0.4: Snapshots from the simulation of no collision case with a closer look at the particles'
initial dispersion. Red, magenta and dark purple represented the initial positions of the particles
categorized in Group 1, Group 2 and Group 3 based on their final y coordinates, respectively.
Figure 0.6 shows the normalized standard deviation of debris particles through time to see
the effect of collision on dispersion response. The standard deviation is normalized by the distance
the particles centroid has traveled. The normalized standard deviations of x and y directions for
the collision-disabled particle model results were plotted as blue and red solid lines, respectively,
while the collision-disabled particle model results were plotted as blue and red dashed lines for the
x and y directions, respectively. The results indicated that the considering collision in the particle

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model significantly contributed to the dispersion at the early stages of the particle motion. This is
especially important since the main goals of debris modeling include accurate estimation of debris
damage impact on structures.
It is also interesting to note that the x and y directions respond similarly to the presence of
collisions, although the scale of dispersion is consistently different between the directions. It was
seen that adding collision increased particle dispersion in the y direction and this difference lasted
until the end of the motion. The added early dispersion was ~10% and remained unchanged. When
collision was enabled, the early dispersion in the x direction was almost two times higher than in
the collision-disabled case. This difference lasted until ~3000 seconds, and after that, the
dispersion effect was similar for both cases.

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Figure 0.5: Snapshots from the simulation of no collision case at various times with a larger area
focus. (Grey lines indicate the paths of the particles.)

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Figure 0.6: Standard deviation of particle positions through time. Collision disabled (solid black
and green lines for x and y directions, respectively), Collision enabled (solid orange and blue lines
for x and y directions, respectively)
5.2 Test Case 2 - 500 Particles, Initial configuration 20x25
This test case consisted of a total of 500 particles positioned in a 20x25 configuration, with their
longer sides extending along the x direction, aiming to achieve more of a square-shaped
configuration, denser across both dimensions. This results in a higher initial proximity of particles
across a more uniform field. Figure 0.7 shows a closer look at the initial dispersion of the particles
for the first 110 seconds with different particle groups shown in different colors (Group 1 as red,
Group 2 as magenta and Group 3 as dark purple). The particles in Group 1 again predominantly
originated from the lower right section of the initial configurations. Group 3 particles were initially

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located upper left section of the configuration. The wavefront immediately triggered the dispersion
as in Test Case 1, but the particle patterns were different. With a more compact and square
arrangement, particles disperse outward in a more radial pattern. Collisions happen within the
cluster, and spreading is more uniform due to the near-equal dimensions. The rotation of the
particles due to collisions was captured in the model. The overlaps seen in the snapshots are due
to the necessity of the collision detection algorithm. The different initial configurations impacted
the way particles collide and form clusters. In this test case, the denser and more uniformly packed
particles experienced more frequent internal collisions, potentially altering their dispersion.
Figure 0.8 shows the snapshots from the simulation of Test Case 2 at various times in a
larger area to focus on the traditional dispersion behavior. The clusters retain their compactness
for a longer period, and spreading is influenced by localized turbulence and particle collisions as
well as the flow velocity field. Aggregation is more uniform initially, then gradually breaks down,
leading to a more evenly distributed dispersion over time. Clusters stabilize along certain paths,
which are influenced by the prevailing hydrodynamic patterns. Strong currents and topography of
the area dominated the dispersion characteristics after the initial dispersion of the particles.
At the end of the simulation, 47.2% of the particles remained in Group 1 while Group 2
comprised 44.4% of the particles. The remaining 8.4% of the particles were categorized into Group
3, which represented the particles that traveled the farthest distance from their initial positions.
Compared with the test Case 1 results, it was seen that more particles remained in Group 1
meanwhile less particles remained in Group 3 due to the initial configuration affecting the initial
dispersion of the particles. In both test cases, the amount of propagation towards in x direction was
similar. It can be said that particles also traveled in the y direction in a similar manner to Test Case
1 but the local concentrations of the particles showed difference.

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Figure 0.7: Snapshots from the simulation of Test Case 2 with a closer look at the particles' initial
dispersion. Red, magenta and dark purple represented the initial positions of the particles
categorized in Group 1, Group 2 and Group 3 based on their final y coordinates, respectively.

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Figure 0.8: Snapshots from the simulation of Test Case 2 at various times with a larger area focus.
(Grey lines indicate the paths of the particles.)

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5.3 Test Case 3 - 1000 Particles, Initial configuration 20x50
This test case consisted of the highest particle count results in a very densely packed field initially.
The high concentration makes particle interactions more frequent and complex. Figure 0.9 shows
a closer look at the initial dispersion of the particles for the first 110 seconds with different particle
groups shown in different colors (Group 1 as red, Group 2 as magenta and Group 3 as dark purple).
The particles in Group 1 predominantly originated from the lower right section of the initial
configurations. In contrast, the particles in Groups 2 and 3 displayed a more heterogeneous
distribution. The higher particle count leads to more frequent collisions, influencing the diffusion
pattern. The combination of the initial rectangular shape and high density makes particles highly
reactive to the incoming wave, leading to strong dispersion and subsequent chaotic aggregation.
As time advances from 1487 to 1538 seconds, the debris field becomes more diffuse. Particle
groups are more uniformly distributed over a larger area. However, specific regions still exhibit
higher concentrations, indicating potential aggregation due to local flow dynamics.
Figure 0.10 shows the snapshots from the simulation of Test Case 3 at various times in a
larger area to focus on the traditional dispersion behavior. The particles begin to disperse as soon
as the wavefront reaches them. The initial stages show dense clusters of particles that progressively
spread out with each successive frame as the wave propagates. This dispersion is affected by both
the flow velocity field and the collisions between particles. In the earlier frames, the particles are
highly concentrated, indicating initial grouping and limited spread. However, as the flow develops,
the particles interact through collisions, leading to observable aggregation patterns. This is
particularly evident in regions where particles appear to form temporary clusters or streams, likely
influenced by both hydrodynamic turbulence and particle collisions.

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At the end of the simulation, 31.1% of the particles remained in Group 1 while Group 2
comprised 49.6% of the particles. The remaining 19.3% of the particles were categorized into
Group 3, which represented the particles that traveled the farthest distance from their initial
positions. Compared with the previous cases, it was seen that the Test Case 3 results showed similar
general dispersion characteristics with Test Case 1. The initial configuration of these two cases has
the same number of rows, but Test Case 3 is wider since there are 1000 particles. Therefore, Test
Case 3 showed similar but denser flow paths. Denser configuration more closely mirrors realworld debris fields with varying particle sizes and high counts. Observing how these clusters form
and disperse can inform better predictions of debris impacts and dispersal zones.
Figure 0.9: Snapshots from the simulation of Test Case 3 with a closer look at the particles' initial
dispersion. Red, magenta and dark purple represented the initial positions of the particles
categorized in Group 1, Group 2 and Group 3 based on their final y coordinates, respectively.

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Figure 0.10: Snapshots from the simulation of Test Case 3 at various times with a larger area focus.
(Grey lines indicate the paths of the particles.)

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5.4 Conclusions
In this chapter, the debris transport model is implemented in a large-scale test case, Crescent City,
to evaluate its applicability to field scale. Three distinct simulation cases explore the effects of
collision, varying initial debris configurations and the number of particles on transport behavior.
The first simulation involved 500 particles arranged initially in a 10×50 grid while
investigating the collision effect on debris dispersion. The second simulation featured 500 particles
in a 20×25 grid and the third simulation doubled the particle count to 1,000 with a denser 20×50
configuration. These simulations allowed for an exploration of the impacts of initial dispersion,
particle interactions, and flow dynamics on debris transport. The results indicate that flow currents
strongly influenced debris motion and dictated the paths of all particles. Notably, including
collision, the initial particle configuration and interactions between particles significantly affected
the overall debris dispersion.
In Test Case 1, enabling collision in the particle model contributed to the dispersion at the
early stages of the particle motion in x and y directions with a different scale. Some particles in
Test Case 1 traveled farther north than those in Test Case 2, which was attributed to the initial
positions of debris particles and the nature of debris-debris interactions. In Test Case 3, with a
thicker 1,000-particle arrangement, the debris trajectories and dispersion resembled those in Test
Case 1, though with denser accumulations. The high particle density in Test Case 3 resulted in a
more concentrated and coherent debris field, highlighting the significant influence of initial
particle configuration on debris movement. These findings show the importance of understanding
initial dispersion, debris configuration, and particle-particle interactions when modeling debris
transport in tsunami scenarios. The clustering and aggregation behaviors due to collisions could
become more pronounced because the particles would not receive dynamic flow feedback in real-

109
time. This is especially important in simulations where debris density significantly affects realworld dispersion patterns. The results provide valuable insights for future model refinements,
coastal hazard assessments, and mitigation strategies.

110
6.
CHAPTER 6
Conclusion and Future Work Recommendations
6.1 Conclusions
The major focus of this thesis is the modeling of tsunami-driven debris motion. A one-way coupled
particle motion model was developed and validated against several benchmark studies available
in the literature. The particle model was also tested to see its performance in a large-scale scenario.
In addition, several physical model experiments were carried out to understand the debris motion
during extreme coastal events, specifically focusing on the combined effect of currents and waves.
The physical experimental dataset was provided for future numerical modeling studies.
In the first part of the study, Chapter 2, physical model experiments conducted within the
scope of this study were presented. This experimental study highlighted the importance of
understanding debris motion and spreading during extreme coastal events. The debris spreading
angle was calculated for each case and found to be smaller than the suggested current engineering
practice. Other particular findings can be found in Chapter 2 in an itemized form. This part of the
study was also published in Cinar et al. (2023).
In the second part of this study, Chapters 3, 4, and 5, the development, validation and fieldscale application of the particle motion model were described, respectively. The model integrates
key physical and mechanical properties, such as inertia, drag, friction, and collision, and employs
a robust computational framework to solve the complex interactions between debris particles and

111
the fluid medium. Through statistical analysis of the particle trajectories, it was possible to gain
insights into the dispersion patterns and final resting places of debris under different conditions. A
robust set of data to help quantify the variability and predictability of debris motion was obtained
by running the simulation multiple times. The developed particle model performed reasonably
well, and the results emphasized the importance of accurately modeling fluid-debris interactions
to predict debris pathways and concentrations, highlighting the influence of fluid dynamics on
debris dispersion. Although the detailed sensitivity analysis is not given in this study, it was
observed that the stiffness and damping coefficients of the collision model directly affect the level
of debris deformation and the duration of the collision force. Moreover, added mass and drag
coefficients are also factors that affect the simulation results. The model's applicability to a
regional-scale case was tested. The particle model provided reasonable insights into debris
transport and dispersion during tsunami hazard. The model handled particle-particle interactions
well, and rotations due to interactions seemed reasonable. The observations highlight the role of
collisions in enhancing lateral dispersion, which could be crucial in understanding debris spread
in realistic tsunami scenarios. One-way coupling can simplify calculations but might not fully
capture the effects of dense particle distributions affecting local fluid dynamics; however, this
approach can be acceptable for large-scale simulations since two-way coupling models may
require significantly higher computational time. For large tsunami cases, the overland transport is
advection dominated, and the general locations of the overland debris fields are not likely to be
strongly affected by the dispersion model, although their local concentrations may be.
Using rectangular particles instead of spherical ones offers a unique advantage in capturing
realistic tsunami debris dynamics. Unlike spheres, the rectangular shape creates more complex
interactions with fluid flow. Their flat surfaces and sharp edges cause them to respond differently

112
to hydrodynamic forces, making them prone to lateral sliding and orientation-dependent
movement. Collisions among rectangular debris also exhibit unique mechanics due to their corners
and edges, leading to distinct clustering patterns that better resemble actual debris flows.
As expected, within the range of uncertainty in dispersion coefficients, the debris fields can
have large differences in local debris concentration. By integrating detailed hydrodynamic
modeling with particle dynamics, including collision and dispersion effects, the model offers a
comprehensive and reasonably fast tool for understanding and predicting the behavior of debris in
tsunami events.
6.2 Suggested Future Work
The physical model experiments presented in this study were limited in terms of hydrodynamic
conditions, structural size and configuration, and debris release mechanism. Future studies should
consider parameters such as different flow hydrodynamics, wave heights, debris type and release
methodologies, and structural configurations to better understand debris motion. The observations
showed that collapsed buildings became floating debris and propagated by the tsunami. Future
simulations can consider determining whether destroyed buildings become debris using fragility
functions.
The model's capabilities can be enhanced by identifying the initial locations of potential
debris particles. The particle model can be improved and extended in several ways. The collision
model can be modified to detect a more realistic/exact collision point between convex shapes.
Since debris transport is random by nature, improved hybrid models that combine deterministic
and statistical techniques should be utilized to obtain more realistic modeling results. Physical

113
model experiments should be conducted to understand the effect of different material types (to
identify model parameters regarding collision of the particles) and mass particles on debris
transportation mechanics.
A sensitivity analysis should be performed to identify critical parameters requiring more
precise measurements or more accurate modeling. Implementing Monte Carlo simulations can
provide a comprehensive understanding of the inherent uncertainties in input parameters affecting
debris transport modeling. By generating probabilistic scenarios in this framework, these
simulations can offer more robust predictions of debris accumulation and transport patterns.
Due to computational limitations, the current model employed simplified collision and
transport processes. Detailed topographic effects should be considered to investigate debris motion
to further improve model accuracy. Further research will be required to extend this framework to
different coastal topographies and to evaluate the impact of two-way coupling for more accurate
debris interaction modeling.

114
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Abstract (if available)

Abstract The aim of this thesis is to investigate debris motion during extreme coastal events through physical and numerical modeling. Debris impact has an important role in structural damage during extreme coastal events. Understanding the transport of debris and the characteristic of its motion is crucial as debris impact depends on debris motion. The experimental part of this study investigated floating debris dispersion and motion by conducting laboratory experiments that considered the effects of a structural array or a gridded layout of city-like buildings. Physical model experiments were conducted for two different hydrodynamic conditions: (1) current only and (2) current + wave combined cases. Debris was released from a certain height in a repeatable way. Visual data were collected by four overhead video cameras and a particle tracking algorithm was implemented to track debris motion. Debris spreading angles (θs) were calculated for each case and compared with the angles used in the current engineering practice. The presented results aimed to increase the current knowledge on debris motion and spreading during extreme events, such that engineers might build more resilient coastal communities.
For the numerical part of the study, COULWAVE, a higher-order depth-integrated hydrodynamic model that solves Boussinesq-type equations, was combined with a discrete element method for solving debris motion and collision. The debris motion was modeled by using equations of particle motion, considering a comprehensive set of forces acting on the particles. A linear spring-dashpot type collision model is used to calculate collision forces. A random walk model is included to account for unresolved turbulent mixing and fluid-debris interactions. The one-way coupled debris model was validated through two debris transport experimental datasets. Model results for water depth and debris positions compared reasonably well with experimental results. Finally, the coupled numerical model was applied to investigate the debris motion during a tsunami for Crescent City. A regional-scale application of the debris transport model demonstrated that the model could perform well for real-world applications.

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Creator Cinar, Gizem Ezgi (author)

Core Title Investigating the debris motion during extreme coastal events: experimental and numerical study

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Civil Engineering

Degree Conferral Date 2024-05

Publication Date 07/03/2024

Defense Date 05/28/2024

Publisher Los Angeles, California (original), University of Southern California (original), University of Southern California. Libraries (digital)

Tag debris,debris motion,debris-debris interactions,Experiment,large scale,numerical modeling,OAI-PMH Harvest,tsunami

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Language English

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Advisor Lynett, Patrick (committee chair), de Barros, Felipe (committee member), Luhar, Mitul (committee member)

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