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PROBABILISTIC TSUNAMI HAZARD ASSESSMENT FOR THE UNITED
STATES EAST COAST
BY
TERESA KRAUSE
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
IN
CIVIL AND ENVIRONMENTAL ENGINEERING
UNIVERSITY OF RHODE ISLAND
2011
MASTER OF SCIENCE THESIS
OF
TERESA KRAUSE
APPROVED:
Thesis Committee:
Major Professor Christopher Baxter
Aaron Bradshaw
Stephan Grilli
Nasser H. Zawia
DEAN OF THE GRADUATE SCHOOL
UNIVERSITY OF RHODE ISLAND
2011
ABSTRACT
Public interest in tsunamis has increased dramatically due to the devastating
consequences of recent events in Indonesia (2004) and Japan (2011). Efforts are
underway by both private industry and the United States federal government to
develop probabilistic tsunami hazard assessment (PTHA) for coastal regions. An
important component of a PHTA is understanding the hazard posed by different
tsunami sources. Large magnitude earthquakes are known to be a significant source
of tsunamis, but there is increased awareness that submarine landslides may also
pose a significant tsunami hazard in some regions.
As part of a prior research project, a promising approach to assess the tsunami
hazard from submarine landslides for the northeast U.S. was developed at the
University of Rhode Island in 2006 and 2009 [1–3].
More recently, the National Oceanic and Atmospheric Administration
(NOAA) has funded the National Tsunami Hazard Project (NTHMP) to assess
the tsunami hazard for the entire U.S. East Coast. The objective of this thesis is
to extend the PTHA for the U.S. East Coast from Massachusetts to Florida.
The analysis involves performing Monte Carlo simulations of slope stabil-
ity analyses and then estimating tsunami amplitudes and runup caused by failed
slopes. Transects were taken along the continental slope and pseudo-static slope
stability analyses were performed assuming that the potential failures were induced
by a combination of seismicity and pore pressures. Probabilistic ground motions
were obtained from the U.S. Geological Survey. Once a slope failure was deter-
mined to occur the size of generated tsunami was estimated based on previous
work at the University of Rhode Island [4–6]. The results are presented as esti-
mates of coastal runup for the U.S. East Coast for 100- and 500-year tsunamis,
and areas with higher hazard are identified. These areas should be the target of
more focused study in the future.
The final step in this work is to identify specific landslide candidates along
the coast that may cause high runups. With those properties further modeling can
estimate the tsunami generation and propagation more accurately.
ACKNOWLEDGMENTS
I want to express my gratitude to my major advisor Prof. Christopher
D.P. Baxter and my project PI Prof. Stephan T. Grilli. Both were great teachers
and mentors for me. They gave me the chance to develop and grow with this
project, and I indeed appreciate working with them.
During this year I was lucky to make some very good friends and share my
time with them. They always supported me and gave me the necessary distraction
during my breaks. I also thank my classmates and colleagues who made this year
unforgettable and special.
iv
TABLE OF CONTENTS
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . iv
TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . v
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
CHAPTER
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Recent Landslide Tsunami Research . . . . . . . . . . . . . . . . 2
1.3 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Previous Work at URI . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1 Monte Carlo model . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 Coastline and transects . . . . . . . . . . . . . . . . . . . 10
2.1.2 Input parameters for slope stability model . . . . . . . . 10
2.1.3 Principles of the Monte Carlo approach . . . . . . . . . . 12
2.2 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Results of Previous work . . . . . . . . . . . . . . . . . . . . . . 15
3 Improved Monte Carlo Model . . . . . . . . . . . . . . . . . . . . 17
3.1 Bathymetry and Sediment Properties . . . . . . . . . . . . . . . 17
3.2 Coastline and Transects . . . . . . . . . . . . . . . . . . . . . . 22
v
Page
vi
3.2.1 Coordinate system for investigated area . . . . . . . . . . 22
3.2.2 New Transects and Shoreline . . . . . . . . . . . . . . . . 22
3.3 Changes in Slope Stability Calculations . . . . . . . . . . . . . . 25
3.4 Seismicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.5 Bulk density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.6 Details on parallel implementation . . . . . . . . . . . . . . . . . 36
3.7 Determination of Candidate Landslides Properties for Future Di-rect Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.8 Minimum Number of Runs per Transects . . . . . . . . . . . . . 37
4 Validation of Monte Carlo Results . . . . . . . . . . . . . . . . . 39
4.1 Evaluation of Parallel Processing Implementation and StabilityAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 Comparison of Model Results to Known Failures from GeologicalEvidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Limitations of the Tsunami Runup Estimates . . . . . . . . . . 46
5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.1 East Coast Tsunami Hazard . . . . . . . . . . . . . . . . . . . . 51
5.2 Design Landslides Properties . . . . . . . . . . . . . . . . . . . . 52
6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
APPENDIX
A Tsunami Travel Time and Distance to Breaking . . . . . . . . 58
B Universal Transverse Mercator . . . . . . . . . . . . . . . . . . . 60
C Main Monte Carlo Analysis . . . . . . . . . . . . . . . . . . . . . 61
Page
vii
D Slope Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . 77
E Tsunami Codes and other Supporting Subroutines . . . . . . 91
F Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 104
G Evaluation Subroutines . . . . . . . . . . . . . . . . . . . . . . . . 108
H Validation of Input parameters and runup . . . . . . . . . . . . 127
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
LIST OF TABLES
Table Page
1 Landslide properties leading to hazardous runups on the U.S.East Coast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
viii
LIST OF FIGURES
Figure Page
1 Cross section through the continental shelf and slope. . . . . . 2
2 Distribution of the open-sloped sourced and canyon sourcedlandslides. The shelf egde and base of slope are representedby the black lines [7]. . . . . . . . . . . . . . . . . . . . . . . . 3
3 Failure scar volumes along the U.S. East Coast. [8] . . . . . . . 4
4 Location of the Currituck landslide (a) study area (b) The Cur-rituck slide looking towards the southwest (c) and (d) schematicviews of the Currituck slide [9]. . . . . . . . . . . . . . . . . . . 6
5 Number of submarine landslides on the atlantic ocean marginsince the last glacial peak and the corresponding chance in sealevel [10]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
6 Study area with transects (blue lines) and shore line (coastalpoints, red line) used in Taylor 2008 [2]. . . . . . . . . . . . . . 11
7 Flowchart of Monte Carlo model used in Taylor 2008 [2] showingdistributions of input and output data . . . . . . . . . . . . . . 13
8 Wave height for 1-percent-annual-chance and 0.2-percent-annual-chance design tsunamis. The x-axis are coastal pointsranging from Massachusetts(100) to New Jersey(800) [2]. . . . 16
9 Surficial Sediment Distribution of the Southeast U.S. Coast [11]. 18
10 U.S. Southeastern Coast and bathymetry (ETOPO1 dataset). . 19
11 Shallow Bathymetry and Topography of the U.S. mid-Atlantic. 20
12 GLORIA Bathymetry Contours U.S. East Coast . . . . . . . . 21
13 Transverse Mercator projection [12]. . . . . . . . . . . . . . . . 23
14 Newly chosen transects to characterize the seabed of the U.S.East Coast. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
15 Shore line with coastal points assigned to each state. . . . . . . 25
ix
Figure Page
x
16 Slope stability analysis flowchart used by Taylor (2008) [2] . . . 26
17 Slope stability analysis flowchart used in this work. . . . . . . 29
18 2nd degree polynomial fit to the natural log of PHA and thenatural log of the probability of exceedance 1
λ. . . . . . . . . . 31
19 Correction of 2nd degree polynomial fit for small peak groundaccelerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
20 Corrected 2nd degree polynomial fit. . . . . . . . . . . . . . . . 32
21 3rd degree polynomial fit. . . . . . . . . . . . . . . . . . . . . . 33
22 Close up of 3rd degree polynomial fit. . . . . . . . . . . . . . . 33
23 ODP holes with bulk density information used in this study. . 35
24 Curve fitting of bulk density from ODP hole 995. . . . . . . . . 36
25 Runup on the upper east coast calculated with and withoutmulticore processing. . . . . . . . . . . . . . . . . . . . . . . . 40
26 Runup on the upper east coast calculated with Taylor (2009) [2]and with the modified stability analysis. . . . . . . . . . . . . . 41
27 Failure Distribution of translational and rotational failures forMCS (100 and 500-year PHA) and observed failures [13]. . . . 43
28 Frequency distribution of failure slope angles for MCS comparedto observed failures [13]. . . . . . . . . . . . . . . . . . . . . . 44
29 Frequency distribution of failure volume for MCS compared withobserved failures [8] . . . . . . . . . . . . . . . . . . . . . . . . 45
30 Frequency distribution of failure area for MCS compared withobserved failures [8] . . . . . . . . . . . . . . . . . . . . . . . . 45
31 Transects with failure slope angles bigger than 30degree. X-axisnumber of transects from north to south. . . . . . . . . . . . . 47
32 Abbreviated data set for Coastal Point 1200 corresponding to atsunamigenic slope failure of a return period of 5,800 years . . . 50
Figure Page
xi
33 MCS runup for 100 and 500year tsunami events. The x-axis isthe index of studied coastal points, numbered N-S. . . . . . . . 51
34 Failure area of landslide causing a 500-year runup on the U.S.East Coast. The x-axis is the index of studied coastal points,numbered N-S. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
35 Failure volume of landslide causing a 500-year runup on the U.S.East Coast. The x-axis is the index of studied coastal points,numbered N-S. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
36 Failure slope angle of landslide causing a 500-year runup on theU.S. East Coast. The x-axis is the index of studied coastalpoints, numbered N-S. . . . . . . . . . . . . . . . . . . . . . . . 55
A.37 Average Tsunami breaking distance from shore for each coastalpoint. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
A.38 Average tsunami arrival time for each coastal point . . . . . . . 59
B.39 UTM zones across the United States. . . . . . . . . . . . . . . 60
H.40 Cumulative frequency distribution compared to log-normal dis-tribution fit (R2=0.9762) of the randomly generated slide depthinput parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . 127
H.41 Cumulative frequency distribution compared to log-normal dis-tribution fit (R2=0.6012) of the randomly generated slide lengthinput parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . 128
H.42 Cumulative frequency distribution compared to normal distri-bution fit (R2=0.9358) of the randomly generated slide densityinput parameter for the northern 45 transect. . . . . . . . . . . 128
H.43 Cumulative frequency distribution compared to normal distri-bution fit (R2=0.9735) of the randomly generated slide densityinput parameter for the southern 46 transect. . . . . . . . . . . 129
H.44 Cumulative frequency distribution compared to log-normal dis-tribution fit (R2=0.7207) of the calculated runup at coastalpoint 700. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Figure Page
xii
H.45 Coefficient of determination R2 for a log-normal distribution fitto the cumulative frequency distribution of runup values at each
coastal point (R2
=0.4664). . . . . . . . . . . . . . . . . . . . . 130
CHAPTER 1
Introduction
1.1 Overview
The devastating tsunami in March 2011 in Japan illustrates once more the
consequences of this natural hazard for people, environment, and industry. Even
in a technologically advanced country with a long history of dealing with tsunamis,
the March tsunami caused thousands of fatalities and will affect Japan for a long
time. This event has caused an increasing interest in assessing the tsunami hazards
in other heavily populated areas. In contrast to Japan, which is located to the west
of a large subduction zone, submarine landslides are the probable source of tsunami
hazards for the U.S. East Coast [7, 8]. The assessment of the landslides tsunamis
is especially difficult due to the lack of historical records, uncertainty about the
triggering mechanisms, and reoccurrence of such events.
The National Oceanic and Atmospheric Administration (NOAA) was directed
through the National Tsunami Hazard Mitigation Program (NTHMP) to reduce
the impact of tsunamis through hazard assessment, warning guidance, and miti-
gation. Within this project, the University of Rhode Island has been contracted
with the University of Delaware to assess the tsunami hazard for the U.S. East
Coast.
Previous work by Taylor (2008) [2] and Grilli et al. (2009) [3] developed and
refined a probabilistic model to assess the tsunami hazard of the upper U.S. East
Coast. That work identified regions of higher tsunami hazard along New Jersey
coast and Long Island, New York. However, this model is limited to the upper
east coast region of the U.S. from Massachusetts to New Jersey.
1
1.2 Recent Landslide Tsunami Research
Tsunami landslides have been studied extensively during the last decade [3,8,
14,15]. Historic landslides in the U.S. Atlantic have been evaluated recently by the
U.S. Geological Survey [7, 8]. Large individual landslides, such as the Currituck
landslide offshore North Carolina, were studied by Geist et al. [16] and Locat et
al. [9]. Grilli et al. [3] and ten Brink et al. [14] have developed strategies and
models to quantify the hazard for the U.S. East coast.
Geological studies of historic landslides at the Atlantic margin show that there
exist two kinds of landslides with major morphological differences: landslides that
occur on the open slope and landslides in canyons (Fig. 1; Fig. 2). Canyon-
sourced landslides have their headwall scarp on the upper slope while open slope-
sourced begin at the lower slope or upper rise. The main difference between those
categories is the volume of the soil that is involved in failures in these regions.
Open-slope failures have a higher volume than the canyon-sourced ones. A higher
displaced volume generally results in a larger wave so that the investigation of
volume distribution along the U.S. East Coast becomes important for assessing
the hazard.
Figure 1. Cross section through the continental shelf and slope.
Chaytor et al. [8] studied the size distribution of landslides at the U.S. Atlantic
2
Figure 2. Distribution of the open-sloped sourced and canyon sourced landslides.The shelf egde and base of slope are represented by the black lines [7].
margin. In his work he identified 106 landslides from the end of Georges Bank
to the Blake Spur off the coast of Florida. The landslide volume follows a log-
normal distribution between 0.002 and 179 km3. The biggest landslides were in
the southern New England, southern Virginia region, and at the Carolina trough
area with volumes over 100km3. However, the mean volume is approximately 0.86
km3 which indicates that most landslides have a volume around 1 km3. Fig. 3
shows the failure scars along the U.S. Atlantic margin color-coded by their volume.
There is also evidence that large failures were caused by multiple small failures.
Therefore single events of large soil mass failures are unlikely but can not be ruled
out.
The most significant triggering mechanism for submarine landslides is often
3
Figure 3. Failure scar volumes along the U.S. East Coast. [8]
4
assumed to be seismic activity [10, 14]. However, the sediments and slopes are
influenced by several other aspects like oversteepening of canyon slopes and disso-
ciation of gas hydrates.The biggest influence on submarine landslides is the glacial
cycle which effects are very complex [10]. During glaciation, the load on the crust
is increased, ice erodes geologic material, and the sea level is decreased. The lower
sea level leads to more unstable shelf edges. At the same time the eroded material
increases the thickness and the pressure on the sediments of the continental shelf.
With melting ice sheets, readjustments in crustal stresses cause a higher seismic
activity. The entire glacial cycle supports the development of submarine landslides.
The Currituck slide (Fig. 4) is one example of a well analyzed past landslide
[9]. It had a volume of approximately 165 km3 off of North Carolina. Previous
work has suggested that the slide failed during a period of lower sea level and
occurred between 24,000 and 50,000 years ago. It failed as a single event with
the main acceleration completed within 10 minutes. It was likely triggered by an
extreme event like an earthquake during which the pore pressure was increased
suddenly. Geist et al. [16] modeled the Currituck slide with a wave modeling
package called COULWAVE and, considering a volume of 165 km3, this landslide
could have caused a runup between 2.35 and 8.8m.
A few studies have been conducted to quantify the probabilistic tsunami haz-
ard for the U.S. East Coast. Geist and Parson [15] estimated the probability of
earthquake and landslide tsunamis sources in the Atlantic. The investigation of
landslide tsunamis was split into purely empirical methods linking tsunamis di-
rectly to earthquake ground motions. In his empirical approach he assumes that
the recurrence of landslides follows a nonstationary Poisson distribution depending
on the glacial cycle.
Regarding Geists’ consideration of landslides in connection with earthquake
5
Figure 4. Location of the Currituck landslide (a) study area (b) The Currituckslide looking towards the southwest (c) and (d) schematic views of the Currituckslide [9].
6
motion, he found that the probability of failure can be determined from known
topography, geology, shear strength, and seismic shaking. However, in almost all
cases the shear strength is unknown due to limited sample taking and testing of
the sea bed sediments. Therefore, to quantify the failure probability, Geist used
empirical relationships between earthquake magnitude and landslide statistics.
Geist and Parsons concluded that landslide tsunamis have a high level of
uncertainty and further analyses are essential, and that a probabilistic approach
is the most promising hazard assessment approach due to this lack of information.
The recurrence interval of landslides was used by Geist and Parsons and is
critically important to assess the tsunami hazard of landslides. Lee [10] reported
that the frequency of landslides tsunamis occurrence has decreased since the end
of the last glacial cycle.
Fig. 5 shows the timing of submarine landslides on the Atlantic margin over
the past 20,000 years. It suggests that the frequency of landslides has decreased
with time and increasing sea level. Within the last 5,000 years the number of
landslide is 1.7-3.5 times less than directly after the glacial peak.
ten Brink et al. [14] assessed the tsunami hazard by determining the size and
recurrence interval for landslides from the size and recurrence interval of earth-
quakes. The minimum earthquake magnitude needed to create a tsunamigenic
landslide was estimated. Furthermore, the probable distance from earthquake
source to the soil movement was estimated since the effect from an earthquake
decreases with distance and increases with slope angle. For his research he used
slope stabilty analysis, subaerial observation of distance from earthquake to lique-
faction, and observed failure areas of subaerial landslides. The simulated failure
properties were validated using the Grand Banks landslide and tsunami case study
from 1929.
7
Figure 5. Number of submarine landslides on the atlantic ocean margin since thelast glacial peak and the corresponding chance in sea level [10].
The results suggested that a magnitude 7.5 earthquake must occur within
100km of the continental slope to cause a devastating tsunami landslide. Also
when the earthquake is directly on the slope it needs to be at least a magnitude
5.5 for a significant tsunami.
1.3 Thesis Objectives
Grilli et al. [3] developed a probabilistic tsunami hazard analysis approach to
estimate the tsunami hazard for the U.S. East Coast. That model was applied to
the northeast U.S., and extend this research will extend it to the remaining regions
of the east coast from New Jersey to Florida. the objective is to calculate runups
and tsunami travel times and identify regions along the entire U.S. East Coast
with potentially higher tsunami hazard.
Another aim of this work is to determine design landslide events for specific
return periods that can be used for further deterministic modeling. Previous re-
search at URI focused only on estimating coastal runups and travel times in a
8
probabilistic framework. An important finding of this work is to highlight areas
where more detailed deterministic modeling should be performed. Information
about representative submarine landslides (location, volume, water depth, etc.)
will be compiled for such modeling efforts in the future.
Chapter 2 presents a review of the Monte Carlo model developed in 2006,
2008 and 2009. It focuses on a broad overview since the details are well explained
in Maretzki (2006) and Taylor (2008) [1, 2]. Chapter 3 presents the details about
changes in the model that were implemented in this research to apply it to the
U.S. East Coast. Those changes affect the stability analysis, the seismicity data,
the bulk density and other aspects of the model. Chapter 4 presents the validation
of the revised model by comparison the model results with landslide statistics for
the region. Chapter 5 presents the results and some conclusions from the study
are presented in Chapter 6.
9
CHAPTER 2
Previous Work at URI
2.1 Monte Carlo model
The model used in this work was developed by Maretzki (2006) and enhanced
by Taylor (2008). This chapter gives an overview of the work implemented in 2009.
The following section presents a description of the model, which includes an
overview of how the transects, coastline, input parameters, and seismic data are
generated. The statistical analysis is also presented with the results from the
simulations in 2009.
2.1.1 Coastline and transects
The coastline of the northeast U.S. was represented in the model by a series
of 900 coastal points (Fig. 6). This was done to simplify the topography of
the coastline. Runup estimates were made only at these coastal points. The
continental slope was represented by a series of 45 transects, which were chosen
by hand to provide 2 dimensional slope information for the slope stability model.
The bathymetry and topography data used to generate the coastal points and
transects were obtained from National Geophysical Data Center (NGDC) and and
were imported in the geographical information system ArcGIS.
2.1.2 Input parameters for slope stability model
Input parameters for the slope stability analyses are the slope geometry, sed-
iment distribution, bulk density, excess pore pressure, and seismicity. The un-
certainty of each of these parameters is very high so that no discrete values can
be assigned for the stability analyses. Within a Monte Carlo model the values
are chosen accordingly to distributions. The effective stress friction angle and the
bulk density follow a normal distribution while the depth of failure and the failure
10
Figure 6. Study area with transects (blue lines) and shore line (coastal points, redline) used in Taylor 2008 [2].
11
thickness are lognormally distributed. Fig. 7 shows the flow chart for the Monte
Carlo model and all the input parameters with their distributions.
2.1.3 Principles of the Monte Carlo approach
The tsunami hazard in the study area is assessed using a Monte Carlo ap-
proach, in which distributions of parameters are used to perform thousands of
analyses and then the results are themselves presented in a statistical framework.
A flow chart of the Monte carlo model used in this study is shown in Figure 7.
The main part of the model is the slope stability analysis where candidate slip
surfaces along the 45 transects are evaluated for stability against seismic loads
(via a pseudostatic coefficient) and excess pore pressure. Two failure modes are
considered: rotational and translational. They are calculated with the modified
Bishops’ method and the infinite slope method, respectively. Both methods are
limit equilibrium approaches and described in Nowak and Collins [17].
When the slope stability analysis indicates a failure, an estimate of the initial
amplitude of the resulting surface wave created is made using an empirical approach
developed by Grilli and Watts [6]. An approximate estimate of the resulting runup
is made using the correspondence principle [6], which states that the amplitude of
the tsunami wave on shore is roughly equal to the initial generated wave amplitude
above the center of soil mass failure. The approximation neglects any energy
dissipation due to wave breaking as the tsunami approaches the shoreline.
Once the initial amplitude of the tsunami is calculated, the travel time to
the coast is estimated using a simplified bathymetry and linear wave theory. The
propagation of the tsunami is assumed to be in the direction of the transect with
a ±5◦ spread distributed normally. Information about the runups at each coastal
point are collected for statistical analysis.
12
Figure 7. Flowchart of Monte Carlo model used in Taylor 2008 [2] showingdistributions of input and output data
13
2.2 Statistical Analysis
The results of the Monte Carlo simulations require statistical analysis to asso-
ciate values of runup with return periods. A return period Y is statistically defined
as the time period in which the magnitude of an event is equaled or exceeded once.
Its reciprocal is the probability of exceedance λ in any given year.
Return periods for tsunami events are estimated from the probability of slope
failure and annual probability of exceedance of the ground motion that triggered
them.
SMF =1
nN· PPHA
(1)
with
SMF = return period of tsunamigenic slope failure
n = number of tsunamigenic slope failures
N = total number of simulations
PPHA = annual probability of exceedance of a peak horizontal ground
acceleration
nN
= probability of slope failure
To determine the hazard for the coast in terms of specific runup values for
certain return periods of tsunamis the principles of the Federal Emergency Man-
agement Agency (FEMA) are used. FEMA assigns the 1 percentile point of all
descending runup values to the highest possible tsunami return period calculated
in that area [18].
This work determines 100- and 500-year tsunami runups for the U.S. East
Coast. After Equation 2, each coastal point is assigned with two runup values for
a 100-year and 500-year tsunami event, respectively. Accordingly, the results of
14
the statistical analysis are diagrams of runup and shoreline.
m =Pz
PSMF · 100·M (2)
with
m = index of runup belonging to an event with the the annual
probability of exceedance PZ
M = total number of runups on one coastal point
Pz = annual probability of tsunami
(1% for 100-year, 0.2% for 500-year event)
PSMF = annual probability of tsunamigenic soil mass failure
2.3 Results of Previous work
Fig. 8 shows the coastal inundation of a 100 and 500 year tsunami event [2].
These results suggested that there is an elevated tsunami hazard for Long Island,
NY and New Jersey Coast in case of a 500 year tsunami event.
15
Figure 8. Wave height for 1-percent-annual-chance and 0.2-percent-annual-chancedesign tsunamis. The x-axis are coastal points ranging from Massachusetts(100)to New Jersey(800) [2].
16
CHAPTER 3
Improved Monte Carlo Model
This chapter presents an overview of changes made to the Monte Carlo model
in this research to extend of the model to the entire U.S. East Coast. Changes
to the model included a change in the pseudostatic slope stability algorithm and
parallelization of the Matlab code. Extension of the model required new seismic
sediment, and bathymetry data.
3.1 Bathymetry and Sediment Properties
The slope stability model requires information about the sediment (i.e. den-
sity, strength), the geometry of the slope (i.e. bathymetry), and the seismic coeffi-
cient (i.e. peak horizontal ground acceleration). Sediment data was obtained from
the Continental Margin Sediment Distribution (CONMAPS) dataset [11], which is
a compilation surficial sediment distributions of the U.S. East Coast Continental
Margin, as shown in Fig. 9. As part of CONMAP , thousands of sediment sam-
ples were obtained for grain size analysis. The data file contains polygons which
contain attributes of the sediment type. Several sediment types in one area are
possible, but just the dominant surficial sediment type is saved. The sediments
were classified using the Wentworth grain-size scale and the Shepard scheme of
sediment classification.
Bathymetry data was obtained from the National Geophysical Data Center
(NGDC). Figure 10 shows the bathymetry and the simplified shoreline for the U.S.
East Coast from Virginia to Florida. It is a global relief model from Earth’s surface
including land TOPOgraphy and ocean bathymetry (ETOPO1). It was built from
various global and local data sets and has a resolution of 1 arc-minute.
Raster data is also available from the National Geophysical Data Center for
17
72° 0’0"W 74° 0’0"W 76° 0’0"W 78° 0’0"W 80° 0’0"W 82° 0’0"W 38° 0’0"N36° 0’0"N34° 0’0"N 32° 0’0"N 30° 0’0"N
28° 0’0"N 0 140 280 420 56070Kilometer sLegendconm apsg
SE D IME N T
bedrock
clay
clay-silt/ sand
gravel
gravel-sand
sand
sand-clay/silt
sand-silt/clay
sand/silt/clayFig ure 9 . Surficia lSediment Distributio n o f the So uthea st U.S. Co a st [1 1 ].1 8
72° 0’0"W74° 0’0"W76° 0’0"W78° 0’0"W80° 0’0"W82° 0’0"W
38° 0’0"N
36° 0’0"N
34° 0’0"N
32° 0’0"N
30° 0’0"N
28° 0’0"N
0 140 280 420 56070Kilometers
Figure 10. U.S. Southeastern Coast and bathymetry (ETOPO1 dataset).
19
the shallow coastal in a higher resolution than the ETOPO1 data. Figure 11 shows
raster data for North Carolina and Virginia. This includes information from the
U.S. National Ocean Service Hydrographic Database, the U.S. Geological Survey
(USGS), the Monterey Bay Aquarium Research Institute, and the U.S. Army Corps
of Engineers [19]. The raster has a resolution of 3 arc-seconds which is equal to
90m.
The bathymetry data was processed with the aim of combining coarse and
fine raster into one file. The NGDC homepage limits the amount of downloadable
data of the fine coastal relief model. Therefore the fine raster from the U.S. East
Coast had to be split into three areas which were merged in ArcGIS afterwards.
Figure 11. Shallow Bathymetry and Topography of the U.S. mid-Atlantic.
Additionally, Figure 12 shows bathymetry contours saved as polylines in a
shapefile which is readable and writable by ArcGIS. The height difference between
two contour lines is 250m starting at -250m at the shallowest area up to -5000m
at the deepest. The dataset was created with a Geological LOng Range-Inclined
Asdic (GLORIA) side sonar system for the deep water parts (over 400m) starting
in the U.S. Exclusive Economic Zone in 1984 [20]. This system produces digital
20
image maps of the seafloor from reflected sound waves. More information about
the GLORIA system can be found in Somers et al. (1978) [21]. The results were
published in atlas form in 1991. The contour lines, however, are mostly manually
digitized from several published and unpublished maps. The raster are the basis
for the water depth information of the Monte-Carlo simulation. The contour lines
are helpful for choosing transects since lines present features like canyons and steep
slopes better than a grid.
72° 0’0"W74° 0’0"W76° 0’0"W78° 0’0"W80° 0’0"W82° 0’0"W
38° 0’0"N
36° 0’0"N
34° 0’0"N
32° 0’0"N
30° 0’0"N
28° 0’0"N
0 140 280 420 56070Kilometers
Figure 12. GLORIA Bathymetry Contours U.S. East Coast
21
3.2 Coastline and Transects
The study area is represented in the Monte Carlo model by transects that
cross the continental slope and coastal points which represents the coastline. In
order to create new transects and a shoreline the coordinate system within the
bathymetry and topography has to be adapted.
3.2.1 Coordinate system for investigated area
For coastal points and transects in the new study region, the transverse mer-
cator (TM) projection was used. The TM coordinate system can be created and
applied in ArcGIS. The line of tangency (line at which the cylinder of the earth’s
diameter touches the earth surface) is the center of the investigated area. The
longitudinal extension of that region is maximum 6 degrees which equals one zone
UTM zone and ensures a reasonable accuracy.
TM coordinate system is a cylindrical projected coordinate system as seen in
Fig. 13. All coordinates using this projection are positive to simplify calculations.
The line where the cylindrical projection touches the earth surface is called natural
origin or central meridian. Distances are most accurate close to the origin and
bias when being further away. To ensure a reasonable accuracy the distance of the
coordinate system in longitude should not be larger than 15◦.
3.2.2 New Transects and Shoreline
The transects chosen to represent the U.S. East coast in this study are shown
in Fig. 14. Judgement was used to place the transects over relevant features on the
slope, such as canyons. The length of the transects and spacing between transects
was consistent with the transects chosen by Taylor (2008). The numbering of the
coastal points and the transects is from north to south. The blake nose feature
off of Florida (see the prominent bathymetric feature at 30◦N in Fig. 12) is not
22
Figure 13. Transverse Mercator projection [12].
studied due to hard carbonic sediments there that makes this region very stable
(Jason Chaytor, personal communication, 2011).
The shoreline is represented by coastal points along the marked line in Fig. 15
with a distance of 800m between each point. The coastal points can be assigned
to the states to make the hazard assessment for the United States easier.
23
Figure 14. Newly chosen transects to characterize the seabed of the U.S. EastCoast.
24
Figure 15. Shore line with coastal points assigned to each state.
3.3 Changes in Slope Stability Calculations
Fig. 16 shows the flowchart for the slope stability model developed by Taylor
(2008) [2]. For a given transect, 15,000 slip surfaces are evaluated for seismic slope
stability. For each slip surface (step C), sediment properties are generated (step D)
and a peak horizontal ground acceleration (PHA) corresponding to a return period
of 50 years is applied (step E). If the slip surface is stable the PHA is increased
incrementally until either the slope fails or a PHA corresponding to a return period
of 750 years is exceeded.
In this work another method to determine the peak ground acceleration for
failure (FOS ≤ 1) is implemented. It can be directly calculated in the Bishops and
Infinite slope method as seen in developing Eq. 4 and Eq. 3 from Taylor 2008 [2],
respectively. This method speeds up the computation time by eliminating a FOR-
loop in the code.
25
Figure 16. Slope stability analysis flowchart used by Taylor (2008) [2]
26
FS =(γ − 1) · (1− Ru)− k · γ · tan β
(γ − 1) · tanβ + k · γ· tanφ
forFS = 1
k =(γ − 1) · (1− Ru) · tanφ− (γ − 1) · tanβ
γ · (1 + tanβ · tanφ)
(3)
with
γ = sediment specific density ρSρW
Ru = stress reduction factor to encompass excess pore water pressure
k = seismic coefficient
β = slope angle of failure
φ = effective friction angle
FS =
I∑
i=1
Sui∆li
I∑
i=1
(W ′
i sinαi + kWi(cosαi −hi
2r))
=
I∑
i=1
Sui∆li
I∑
i=1
(W ′
i sinαi) + kI∑
i=1
(Wi(cosαi −hi
2r))
forFS = 1
k =
I∑
i=1
Sui∆li −I∑
i=1
W ′
i sinαi
I∑
i=1
(Wi(cosαi −hi
2r))
(4)
27
with
i = 1..I = failure slices
Sui = undrained shear strength of the sediment of each slice
∆li = width of slice
k = seismic coefficient
hi = average slice height
αi = failure plane angle at the base of each slice
FOS = factor of safety
r = failure circle radius
W ′
i = buoyant weight
The new flowchart for the Monte Carlo model is presented in Fig. 17. Note
that in this analysis the seismic coefficient k is equal to the PHA since it is as-
sumed that reducing and amplifying effects on the PHA cancel each other out. This
assumption is made due to the lack of information about the sediment stratigra-
phy, depth to bedrock and sediment properties needed for a proper site response
analysis.
28
Figure 17. Slope stability analysis flowchart used in this work.
29
3.4 Seismicity
The primary triggering mechanism for the slope stability model is seismicity
data from the U.S. Geological Survey (USGS). The USGS National Seismic Hazard
Mapping project developed maps to correlate peak horizontal ground motions to
its annual probability of exceedance [22]. This data is available online as grid data
of PHA for various probabilities of exceedance at a spatial resolution of 1 degree for
the entire U.S. and coastal regions. At each location, up to 19 values of PHA are
provided for probabilities of exceedance 1
λranging from 0 to 0.0096 are provided.
These data are interpolated with different curve fits to reduce the size of
the file and to create continuous information about seismicity for return periods of
interest in this study (50 to 750 years). In Taylor (2008) and Grilli et al. 2009 [2,3]
the independent variable of the curve fits was not the peak ground acceleration but
the recurrence period. This was useful because the return period was increased
stepwise until failure. With any increment of the return period a new peak ground
acceleration was determined to calculate the slope stability. In the latest model
version the peak ground acceleration for a failing slope is calculated (see section
3.3) and the associated recurrence period has to be determined.
The change of the independent variable leads to a change of the type of curve
fit. Taylor (2008) used a curve fit based on the double logarithm of the probabil-
ity of exceedence and a single logarithm of the peak ground acceleration. When
changing the independent variables no double logarithms of data is possible due
to the range of values and that the logarithm of a negative number is not defined.
Hence, just single logarithmic data could be curve fitted.
The curve fit uses the least squares method to compare the accuracy easily.
The first curve fit evaluated was a 2nd degree polynomial with an accuracy (R2
value) of 0.9984 for the data set (Fig. 18). However, the quadratic curve fit has
30
to be corrected for small accelerations (Fig. 19) due to the peak of the hyperbola.
For PHA values smaller than the peak of the curve, the y values are flipped over
(Fig. 20).
Figure 18. 2nd degree polynomial fit to the natural log of PHA and the naturallog of the probability of exceedance 1
λ.
The other considered curve fit is a 3rd degree polynomial (Fig. 21 and
22) which has a higher accuracy compared to the second degree polynomial
(R2=0.9991). Also no corrections are necessary.
The Monte Carlo model was run for the Upper East Coast with both curve
fits to compare which is the most suitable. These results are shown in Chapter 4
(Fig 26), and it was decided to use the 2nd degree polynomial with the “flip over
correction” for small values of PHA.
31
Figure 19. Correction of 2nd degree polynomial fit for small peak ground acceler-ations.
Figure 20. Corrected 2nd degree polynomial fit.
32
Figure 21. 3rd degree polynomial fit.
Figure 22. Close up of 3rd degree polynomial fit.
33
3.5 Bulk density
Taylor (2008) used a bulk density profile from a borehole off the coast of New
York performed as part of the Ocean Drilling Project (leg 174, hole 1073) for use
in the slope stability analyses. The location of this borehole is shown in Fig. 23.
This data was used in this study for the first 45 transects from Massachusetts to
New Jersey. For the southern 46 transects, bulk density data was obtained from
ODP leg 164, hole 994, 995 and 997. This data is shown in Fig. 24 along with a
logarithmic curve fit.
In addition to leg 174 hole 1073, bulk density information could be found in
leg 164 hole 994, 995, and 997, see Fig. 23. The data processing was analog to
Maretzki (2006), Taylor (2008), Grilli et al.(2009). The data points obtained from
the Ocean Drilling Program are curve fitted, see Fig. 24. The density behavior
with depth is then averaged by integrating the fitted curve. Result of this is a two
parametric expression with the depth as independent variable.
The two legs with bulk density information are off of South Carolina and New
Jersey. The information cannot be combined due to the large geographical distance
between the two legs. When running the entire east coast, the first 45 transects
are assigned to the bulk density information from Taylor, 2009 [2]. The new bulk
density information is then used for the remaining 46 transects.
34
Figure 23. ODP holes with bulk density information used in this study.
35
Figure 24. Curve fitting of bulk density from ODP hole 995.
3.6 Details on parallel implementation
The model was parallelized with the Parallel Computing Toolbox fromMatlab.
It uses the single instruction multiple data (SIMD) approach to start the same
code sequence on several data sets. This toolbox allows for the creation of up to
eight worker threads that execute the code at the same time. In our work each
worker uses one central processing unit (CPU) and shares the memory with the
remaining workers. It is also possible to use this toolbox to work with graphic
processing units (GPUs) and computer clusters. For-loops and special array types
can be parallelized easily without the need of additional communication between
the loops like usually done by a Message Passing Interface (MPI).
In the implemented Monte Carlo model several for-loops are used to run the
stability calculation and to create and analyze the runup. The system was accel-
erated up to 8 times by meeting all requirements for parallel for-loops.
36
3.7 Determination of Candidate Landslides Properties for Future Di-
rect Modeling
One objective of this work is to identify specific locations and properties of
potential tsunamigenic landslides that could be used as sources for more advanced
hydrodynamic modeling in the future. There are a number of ways to accomplish
this, including site specific slope stability analyses using traditional limit equilib-
rium or finite element approaches. This approach, however, requires more detailed
information about the sediment properties with depth than is available for most of
the study area. Therefore, in this study, the results of the Monte Carlo simulations
were used to identify possible sources for deterministic modeling.
To accomplish this, runup data at each coastal point for a given probability of
exceedance, 1
Z, was identified. The magnitude of this runup could be attributed to
more than one predicted submarine soil mass failure on nearby transects. Therefore
the properties of these failures (length, width, volume) were averaged depending
on the type of mass failure (rotational or translational). Also, the coordinates of
the affected transects and the depth of failure are averaged to localize the design
landslide for further investigations.
3.8 Minimum Number of Runs per Transects
In a probabilistic model results vary slightly from simulation to simulation.
The larger the number of simulations the more likely the system converges towards
one repeatable solution. To ensure convergence of the model it is important to use
a high number of simulations. Convergence can be quantified by a coefficient of
variation and the highest accurately predictable probability of exceedance of an
tsunamigenic event. If a higher annual-probability is calculated then assumed, the
number of simulations has to be increased to ensure convergence and accuracy.
Equation 6 shows how to calculate the minimum number of required simulations
37
depending on the highest probability of exceedance that can be reached and the
coefficient of variation.
N =1− Pmax
CoV 2 · Pmax
(5)
with
N = total number of simulations
Pmax = maximum annual-probability that can be estimated by the MC-model
CoV = coefficient of variation
The coefficient of variation is assumed to be sufficient at 10%, according to
Taylor and Nowak [2, 17]. It is also assumed that the probability of exceedance is
maximum 0.015% (7000-years event). The total number of runs is therefore
N =1− 0.00015
0.12 · 0.00015= 399900. (6)
Each transect has to have at least 399900/91 = 4500 runs. In this work 15,000
simulations are done so convergence and accuracy are ensured when the probability
of exceedance stays under 0.015%.
38
CHAPTER 4
Validation of Monte Carlo Results
Any modeling effort must have a validation stage to evaluate or calibrate the
model against known data. In this study, validation involved three stages. The
first validation for the Monte Carlo model involved evaluating the distributions
of relevant parameters at the end of the simulations and comparing them to the
assumed distributions. For example, values of effective stress friction angle, are
assumed to be normally distributed, and thus the final distribution of φ′ outputed
by the model can be checked to see that the model is behaving as intended. This
validation effort was performed similar to Maretzki (2006) and Taylor (2008) and
is presented in Appendix H.
A second validation is to compare the results of the model modified in this
study with results of the Taylor (2008) model. The third validation approach is
to compare landslide statistics (area, volume) from the model with geological data
from the region. This third approach is, in fact, used to calibrate the model such
that the results of the Monte Carlo simulations compare well to existing evidence
of submarine mass failures in the study area.
Validation of the model was performed in this study with 15,000 simulations
per transect to ensure convergence of the model and to be able to capture events
with high return periods. It will be shown that the distributions of landslides from
the Monte Carlo model are reasonable for the study area.
Three specific aspects of this model were checked as part of the validation:
the modification to the slope stability calculation, the parallel implementation,
and the slope failure properties. The stability calculation and the parallelization
should not change the results of the model but only enhance the processing speed.
39
4.1 Evaluation of Parallel Processing Implementation and Stability Al-
gorithm
As mentioned previously, the source code was modified to allow for parallel
processing. The effects of those changes are evaluated by comparing 100-year and
500-year runups for the Massachusetts to New Jersey region with the results from
Taylor (2008) [2]. The parallel processing is not expected to change the results
since the model calculations and parameters are independent. However, results
of Monte Carlo models do vary due to the stochastic nature of those approaches.
This comparison is shown in Fig. 25. The runup magnitudes and locations match
reasonably well considering the expected variability.
100 200 300 400 500 600 700 8000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Coastline Upper East Coast[−]
Run
up [m
]
100−year tsunami (Taylor 2008)500−year tsunami (Taylor 2008) 100−year tsunami; parallel 500−year tsunami; parallel
Figure 25. Runup on the upper east coast calculated with and without multicoreprocessing.
Modifications to the stability calculations and in the seismic curve fit should
not have a significant influence on the results of the analysis. Fig. 26 shows the
runup results from Taylor 2008 (dashed lines) and recent runups (solid line) for a
40
100 and 500-year tsunami. The regions of higher hazard between coastal points
450-550 and 650-750 are recognizable and the magnitude of the maximum runup
at the coastal point 710 matches well. However, the new stability calculation leads
to runup magnitudes with a maximum about 0.5 meters smaller then in Taylor
(2008). This is still acceptable to identify regions of higher hazard. Also, the
results vary slightly due to the stochastic nature of a Monte Carlo model.
100 200 300 400 500 600 700 8000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Coastline Upper East Coast[−]
Run
up [m
]
100−year tsunami (Taylor 2008)500−year tsunami (Taylor 2008)100−year tsunami500−year tsunam
Figure 26. Runup on the upper east coast calculated with Taylor (2009) [2] andwith the modified stability analysis.
4.2 Comparison of Model Results to Known Failures from Geological
Evidence
For the comparison of observed landslides with the simulated landslides, the
model was run including the transects along the Upper East Coast studied in Taylor
(2008) and Grilli et al (2009) [2, 3]. In this way, the number of failures and their
volume distribution represent the entire east coast. Published data about historic
landslides typically considers the entire east coast which makes the comparison
between historic and simulated data easier.
41
Historic landslides at the U.S. Atlantic continental margin were studied by
Chaytor et al. [8]. His study investigated landslide failure scars to determine
the failure area and volume distribution. The bathymetry for this purpose was
assessed with a digital elevation model and a resolution of 100m. In his work, it
was found that the volume distribution follows a log-normal distribution between
0.002 and 179 km3. However, the mean volume is 0.86km3 since large landslides
are distributed just infrequently along the margin.
As mentioned previously, parameters within the model can be adjusted so
that the Monte Carlo results match more closely with geologic evidence. One such
parameter is the standard deviation of the landslide length that was increased to
change the volume distribution. Another is the stress reduction factor to integrate
excess pore pressure into the model. Excess pore pressure in the sediments can be
caused by rapid sedimentation or drainage layers transferring overpressures. Due
to the lack of determination methods for excess pore pressure an empirical param-
eter ε was introduced in Taylor (2008) [2]. The excess pore pressure parameter,
Ru, is calculated using ε that were found to be 0.15 and 0.65 for rotational and
translational failures.
The volume, area, slope angle and distribution failure types were compared
with observed landslides (Fig. 27 - 30). Fig. 27 illustrates the number of observed
and simulated rotational and translational slope failures along the United States
East coast. There are slightly more translational failures in the study region which
is also shown in the Monte Carlo simulations. Also the failure slope angle distribu-
tion (Fig. 28) as well as the failure volume distribution (Fig. 29) look reasonable
compared to observed failures. However, the failure area does not match well as
shown in Fig. 30. This phenomenon was also observed in the simulations of Monte
Carlo model in 2008. However, Booth at al. [13] expressed that the mean slide area
42
may be smaller than observed. It was also stated in recent tsunami research [16]
that the volume is more important for tsunami generation than area. Generally
speaking, the most important parameters of the simulations match well with the
observed values for the East Coast.
Translational Rotational0
10
20
30
40
50
60
70
Tot
al F
ailu
res
[%]
MCS 100 yearsMCS 500 yearsBooth et al. 1993
Figure 27. Failure Distribution of translational and rotational failures for MCS(100 and 500-year PHA) and observed failures [13].
43
0 5 10 15 20 25 30 350
2
4
6
8
10
12
14
16
18
20
Slope angle [deg.]
Fai
lure
s [%
]
MCS 100 yearsMCS 500 yearsBooth 1993
Figure 28. Frequency distribution of failure slope angles for MCS compared toobserved failures [13].
44
<0.1 0.1−0.5 0.5−1 1−5 5−100
5
10
15
20
25
30
35
40
45
50
V [km3]
Fai
lure
s [%
]
MCS 100 years MCS 500 yearsChaytor et al. 2009
Figure 29. Frequency distribution of failure volume for MCS compared with ob-served failures [8]
<1 1−10 10−100 100−1000 >10000
10
20
30
40
50
60
70
A [km2]
Fai
lure
s [%
]
MCS 100 years MCS 500 yearsChaytor et al. 2009
Figure 30. Frequency distribution of failure area for MCS compared with observedfailures [8]
45
4.3 Limitations of the Tsunami Runup Estimates
Before presentation of the results in Chapter 5, it is important to highlight a
limitation of the tsunami model regarding the steepness of the continental slope.
The calculation of the initial amplitude of the tsunami is a function of several
parameters including the slope angle. The characteristic height equation developed
by Grilli and Watts (2005) [23] has a limiting slope angle of 30 degrees, beyond
which it is not applicable.
The slope angle exceeds 30 degrees in some regions of the study area like the
Carolina Trough This affects the runup estimates for 4 transects off the North
Carolina coast, as shown in Fig. 31. Runups from these 4 transects should be
discounted because of unreasonably high estimates.
Another limitation of the runup calculations is that it is assumed that the
runup on shore is roughly equal to the initial amplitude of the tsunami. This
“correspondence principle” does not take into account energy dissipation due to
wave breaking or shoaling. Portions of the continental shelf south of North Carolina
are quite shallow and wave breaking during an actual tsunami would result in
smaller runups than what is predicted in the model.
46
0 20 40 60 80 1000
0.5
1
1.5
2
2.5
3
Transects N−S
Slo
pe F
ailu
res
with
an
angl
e of
hig
her
than
30
degr
ee [%
]
74° 0’0"W76° 0’0"W78° 0’0"W80° 0’0"W
38° 0’0"N
36° 0’0"N
34° 0’0"N
32° 0’0"N
30° 0’0"N
0 110 220 330 44055Kilometers
Figure 31. Transects with failure slope angles bigger than 30degree. X-axis numberof transects from north to south.
47
CHAPTER 5
Results
This chapter presents the results of the Monte Carlo simulation for the east
coast study area from Massachusetts to the Blake Nose off the coast of Florida.
15,000 slope stability analyses were performed for each of the 91 transects, for a
total number, N, of 1,365,000 simulations. There were n=117,390 slip surfaces that
failed for earthquake return periods smaller than 500 years and generated a wave
with an amplitude of > 2cm. This leads to a probability of tsunamigenic slope
failure caused by a combination of seismic loading and excess pore pressure of
Pf =n
N= 8.6%.
This slope failure probability corresponds to an earthquake return period of 500-
years which implies that there is an 8.6% chance of a tsunamigenic landslide oc-
curring within 500 years.The annual probability that a 500-year earthquake occurs
and triggers a tsunamigenic landslide is expressed by the joint probability PSMF .
PSMF = PPHA · Pf = 0.002 · 0.086 = 0.000172
Taylor (2008) estimated a PSMF of 0.03% annual probability of exceedance.
This is slightly higher than the 0.0172% annual probability of exceedance estimated
for the entire east coast. This decrease in PSMF may be due to the general stability
of the southeastern continental slope and lower seismicity offshore in this region.
The return period of a tsunamigenic landslide is 5814 ∼ 5800-years. Therefore,
the runup data at each coastal point contains up to a 5800-year tsunami event. For
each coastal point, the runups are sorted in descending order and the runup values
corresponding to a 100 and 500-year tsunami are determined using Equation 2 of
Chapter 2.2.
48
The runups on coastal point 1200 in north Virginia are shown in Fig. 32. The
design tsunami for a return period of ∼ 5800-years is 5.97m. The runup index
m for a 100- and 500-year tsunami event at coastal point 1200 is 334 and 67,
respectively (Equ. 7 and 8). These indices lead to runup values of 0.1m and 1.29m
for a 100- and 500-year tsunami at coastal point 1200. The runup for 100- and
500-year tsunamis for all coastal points are determined this way which leads to a
tsunami runup on the U.S. East Coast shown in Fig. 33.
m100 =Pz
PSMF · 100·M =
0.01
0.000172 · 100· 568 = 333.98 (7)
m500 =Pz
PSMF · 100·M =
0.002
0.000172 · 100· 568 = 66.79 (8)
49
Figure 32. Abbreviated data set for Coastal Point 1200 corresponding to a tsunami-genic slope failure of a return period of 5,800 years
50
500 1000 1500 2000 25000
0.5
1
1.5
2
2.5
3
3.5
4
Coastline East Coast[−]
Run
up [m
]
100 year tsunami500 year tsunami
Figure 33. MCS runup for 100 and 500year tsunami events. The x-axis is theindex of studied coastal points, numbered N-S.
5.1 East Coast Tsunami Hazard
The runup on South Carolina, Georgia, and Florida (coastal points 1800 to
2800) is significantly smaller than the runup compared to the remaining region
considering 100- and 500-year tsunami events. The following regions show a slightly
higher inundation which points to a hazard in those regions:
1. Long Island, New York (coastal points 500-550)
2. New Jersey coast (coastal points 650-750)
3. south New Jersey/north Delaware (coastal points 800-840),
4. Virginia (coastal points 1000-1200),
5. North Carolina - north Cape Hatteras (coastal points 1300-1350), and
51
6. North Carolina - south Cape Hatteras (coastal points around 1400).
It can be observed that the runup magnitude of a 100-year tsunami event for
the upper East Coast has changed comparing recent results with the results from
Taylor (2008). Fig. 26 and Fig. 33 show that the 100-year runup has decreased
by a almost a factor of 2. One reason for that could be the influence of the pore
pressure coefficient that was adjusted within the validation process and is therefore
not the same as in the work in 2008. However, a clear reason can not be stated.
The runup of a wave also depends on its point of breaking. After breaking
the wave loses energy which leads to a smaller runup on the coast. A point of
breaking far off the coast decreases the wave height and therefore the hazard. The
hazard is also influenced by the travel time of a wave until it hits the coast. A
long travel time means more time for warnings and for people to get prepared for
the approaching wave. Both travel time and distance from shore to breaking are
calculated and presented in Appendix A.
5.2 Design Landslides Properties
Slope failure properties are assigned to each 500-year tsunami runup value
on the coastal points. Due to the differences in appearance the landslides are di-
vided into their two major categories (translational and rotational slope failures)
to determine their volume and location. Fig. 34 to 36 show the design landslide pa-
rameters and the landslide properties of the most hazardous regions are presented
in Table. 1.
For example, coastal point 1300 is in North Carolina, north of Cape Hatteras,
and a 500-year translational landslide affecting that point has a volume of 1.7km3,
a width of 1.83km, a length of 5.516km, a thickness of 0.2393km, at a water depth
of 745m with coordinates of 35.5722/-74.805 (latitude/longitude). However, there
is no simulated rotational landslide causing a 500-year tsunami runup.
52
Coastal Point Location description water depth length width thickness volumelat/long m km km km km3
Translational
Failure 820 38.164/-73.614 south NJ 1111 8.37 3.75 0.4538 10.1146
1100 - - - - - - -
1300 35.5722/-74.805 north Cape Hatteras 745.5 5.516 1.83 0.2393 1.7009
1400 34.8245/-75.30 south Cape Hatteras 1391.3 11.88 3.41 0.3171 7.8907
Rotational
Failure 820 38.1553/-73.6967 south NJ 523 10.99 2.52 0.3394 7.6696
1100 36.899/-74.5042 Virginia 1292 18.41 5.07 0.4096 30.0414
1300 - - - - - - -
1400 - - - - - - -
Table 1. Landslide properties leading to hazardous runups on the U.S. East Coast
53
500 1000 1500 2000 25000
100
200
300
400
500
600
700
Coastline N−S
Are
a of
rot
atio
nal d
esig
n la
ndsl
ides
[km
2]
500 1000 1500 2000 25000
100
200
300
400
500
600
700
800
Coastline N−SA
rea
of tr
ansl
atio
nal d
esig
n la
ndsl
ides
[km
2]
Figure 34. Failure area of landslide causing a 500-year runup on the U.S. EastCoast. The x-axis is the index of studied coastal points, numbered N-S.
500 1000 1500 2000 25000
50
100
150
200
250
300
Coastline N−S
Vol
ume
of r
otat
iona
l des
ign
land
slid
es [k
m3]
500 1000 1500 2000 25000
50
100
150
200
250
300
350
Coastline N−S
Vol
ume
of tr
ansl
atio
nal d
esig
n la
ndsl
ides
[km
3]
Figure 35. Failure volume of landslide causing a 500-year runup on the U.S. EastCoast. The x-axis is the index of studied coastal points, numbered N-S.
54
500 1000 1500 2000 25000
5
10
15
20
25
30
C
o
a
s
t
l
i
n
e
N
−
S
S
l
o
p
e
a
n
g
l
e
o
f
r
o
t
a
t
i
o
n
a
l
d
e
s
i
g
n
l
a
n
d
s
l
i
d
e
s
[
d
e
g
r
e
e
]
CHAPTER 6
Conclusion
The objective of this thesis was to perform a probabilistic tsunami hazard
assessment for the U.S. East Coast from Massachusetts to central Florida. This
was accomplished by performing Monte Carlo simulations of pseudostatic slope
stability analyses, estimating the initial tsunami and runup generated from the
submarine mass failure, compiling runup data for 3210 coastal points, and then
performing statistical analyses to estimate a 100-year and 500-year tsunami runup
at each coastal point.
The model was originally developed by Maretzki (2006) and Taylor (2008)
and published in Grilli et al. (2009). Changes were made to the Matlab code to
extend the model for the entire east coast to be able to incorporate the bathymetry
data and make the slope stability algorithm more efficient. In addition, the code
was changed to allow for parallel processing which decreased computation time
significantly.
The model validation was based on three aspects: input parameter distribu-
tions, effects of modified model, and landslide properties. The input parameter
distributions were validated thoroughly in Taylor (2008). The runups of the modi-
fied model were compared with runup values from Taylor (2008) and the simulated
landslide properties were compared with historic submarine landslide observations.
It was shown that neither the parallelization nor the change of the stability algo-
rithm had major influences on the runup magnitude or shape. Also the landslide
properties matched with historic values.
The probability of a tsunamigenic slope failure for the entire east coast when
assuming a 500-year earthquake event is 8.6%. There the probability that an
56
earthquake occurs which causes that tsunamigenic landslide is the joint probability
of 0.0172%. This implies that the highest return period of possible tsunami events
on each coastal point is 1
0.000172= 5, 800 years. These statistical values and the
statistical analysis from FEMA lead to an inundation level for the U.S. East Coast
from tsunamis with a return period of 100- and 500-years.
The highest runups appear north of South Carolina with magnitudes about
2.40m to 3.5m. Regions with higher inundation compared to the remaining coast-
line are identified along Long Island, New York (2.70m) and New Jersey coast
(3.50m). These regions were already identified in Taylor (2008). Also Virginia
coast and parts of North Carolina show a higher inundation level (around 2.5m).
Regions with a higher runup point to the potential hazardous regions of the U.S.
East Coast.
Finally, the landslide properties causing the 500-year tsunami runups are de-
termined. The landslide width, thickness, length, volume, and location are used
for future deterministic modeling.
57
APPENDIX A
Tsunami Travel Time and Distance to Breaking
The distance from the shoreline to where the tsunami breaks is illustrated in
Fig. A.37. When the wave breaks further offshore it loses energy when approaching
the coast so that the hazard of the wave impact is smaller.
Fig. A.38 shows the estimated times a tsunami needs from generation to
approaching the shoreline.
0 500 1000 1500 2000 2500 3000 3500 40000
500
1000
1500
2000
2500
0 500 1000 1500 2000 2500 3000 3500 40000
50
100
150
200
250
300
350
400
Coastline numbered N−S[−]
Tra
velti
me
[min
]
Figure A.38. Average tsunami arrival time for each coastal point
59
APPENDIX B
Universal Transverse Mercator
The UTM coordinate system is one example of a TM coordinate system with
world wide coverage. It divides the earth into 60 zones with a width of 6◦ each.
The U.S. East Coast is represented by UTM zone 17 and 18 (see Fig. B.39) but
just zone 18 was investigated in Taylor (2008) [2, 3]. In geodesy practice it is not
recommended to work with data from different UTM zones. Therefore the former
used universal transverse mercator (UTM) coordinate system is not applicable for
use within the entire U.S. East Coast.
Figure B.39. UTM zones across the United States.
60
APPENDIX C
Main Monte Carlo Analysis
function carlo v5% This program is written in MATLAB format and will be compile d.%% parallel programming toolbox:% when working at URI, 1 toolbox licence is included (if one
computer at URI% uses it it's not accessible for a 2nd)% −for loading the toolbox: type 'matlabpool' in command line a nd
execute% − if an error occurs the license is not available beacuse someo ne
else% uses it% − with using parfor, no global variables are possible%% − SIG L%%
*************************************************** ********************
% Project: FM Global Tsunami Hazard Mapping%
*************************************************** ********************
%close all; clear all;THETA1 = cputime;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%choosenmbCP=3510; %2610;nmbTS=91; %91;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%nmbRuns=0;%GE = 9.81; % gravitational
accelerationD2R = pi/180; % conversion degrees to
radsR2D = 180/pi; % conversion radians to
degsRHOW = 1027; % density of water% (global parameters)%L LIMS = zeros(2,3);L LIMS(1,1) = 1000; % minimum length for
type 1 % Infinite Slope;
61
L LIMS(1,2) = 5000; %3500 area bissel kleiner, volumenauch % median length for type 1
L LIMS(1,3) = 50000; % maximum length fortype 1
L LIMS(2,1) = 1000; % minimum length fortype 2
L LIMS(2,2) = 2000; % median length for type2
L LIMS(2,3) = 4000; % maximum length fortype 2
% (for log −normal lengths distribution)%LOGND = 0.55; % specify median depth
at% quarter of depth
range% (explanation: depth range ˜120 to 2500;)% (only very few in greater depths acc. to Booth)%SIG D = 0.5;SIG L = 1; %0.55%change by krause% (norm. data and a 0.5 stand. dev. are used for both distribut ions
;% normalizations are done with median depths and lengths)
%% Get user input.fprintf(1, 'This program is running Monte Carlo simulations for the US
East Coast. \n' );fprintf(1, 'If results for a certain recurrence period already exist, \
n' );fprintf(1, 'the relevant folder and all subdirectories will be deleted
, \n' );fprintf(1, 'unless it has been removed prior to computations. \n\n' );fprintf(1, 'Maximum input for both Monte Carlo runs and recurrence
period should not \n' );fprintf(1, 'exceed 100,000, as this will result in unmanageable
amounts of data. \n\n' );% PSNUM = input('How many recurrence periods are to be invest igated
?\n');% while PSNUM > 5% disp('Please choose 5 at maximum!');% PSNUM = input('How many recurrence periods are to be
investigated? \n');% endPSNUM = 2;INPUT = zeros(2,PSNUM);for n = 1:PSNUM
fprintf(1, 'For period No. %1i: \n' ,n);INPUT(1,n) = input( 'Enter The earthquake period. \n' );while (INPUT(1,n) == 0) | | (INPUT(1,n) > 100000)
62
disp( 'Invalid entry!' );INPUT(1,n) = input( 'Please try again! \n' );
endend
INPUT(2,:) = input( 'How many runs on this one? [mutiples of 1000 only!] \n' );
while (INPUT(2,n) == 0) | | (INPUT(2,n) > 100000)disp( 'Invalid entry!' );INPUT(2,:) = input( 'Please try again! \n' );
endfprintf(1, 'The following data is used for calculations \n' );fprintf(1, '(1st column >> period; 2nd column >> runs): \n' );disp(INPUT');ESTIM = sum(INPUT(2,:))/7;fprintf(1, 'Estimated Runtime [s]: %7.0f \n' ,ESTIM);T ALL = INPUT(1,:);RUNS = INPUT(2,:);nmbRUNSperTS=INPUT(2,1);nmbRuns = nmbTS* INPUT(2,1); %nmbRuns = global variable for number of
runs
% Open min/max depth file and check for number of regions.bla2 = load( 'datafiles/subm ex' );DS EX = bla2.DS EX;MAXEL = nmbTS;%old length(DS EX);%now: independent of how many
transects are saved in that file%% Open sedimentation rates file.bla = load( 'datafiles/sedrates' );SRDAT = bla.SRDAT;MAXSR = length(SRDAT);%% Open soil data file.bla = load( 'datafiles/soil data' );SOILS = bla.SOILS;
bla=load( 'datafiles/soil data Hole1073' );SOILS 1073=bla.SOILS 1073;
%% Open seismicity file.bla = load( 'datafiles/seismicity' );E DAT = bla.E DAT;%% Open shoreline file.bla4=load( 'datafiles/shoreline' );SHORE=bla4.SHORE;MAXSH = nmbCP;%length(SHORE);%% Check for number of time periods.MAXTP = length(T ALL);
63
%% Define maximum matrix dimensions.MAXMT = 1000;%%% Loop over user −specified time periods.% Define file output for every loop.for i = 1:MAXTP
fname1 = int2str(T ALL(i));mkdir([ 'results' fname1 ]);mkdir([ 'results' fname1 '/distributions' ]);mkdir([ 'results' fname1 '/temp' ]);mkdir([ 'results' fname1 '/volume' ]);MATNUM = RUNS(i)/MAXMT;for m = 1:ceil(MATNUM)
for ts = 1:nmbTStrn = int2str(ts);APP = m−1;if (APP < 10)
matnum = [ '000' int2str(APP) ];elseif (APP > 9) && (APP < 100)
matnum = [ '00' int2str(APP) ];elseif (APP > 99) && (APP < 1000)
matnum = [ '0' int2str(APP) ];else
matnum = int2str(APP);endif (m < MATNUM)
DISTR = zeros(MAXMT,MAXSH);save([ 'results' fname1 '/temp/' trn 'distr' matnum '
.mat' ], 'DISTR' );Hb = zeros(MAXMT,MAXSH);save([ 'results' fname1 '/temp/' trn 'Hb' matnum '.mat
' ], 'Hb' );else
ENTRS = RUNS(i) − APP* MAXMT;DISTR = zeros(ENTRS,MAXSH);save([ 'results' fname1 '/temp/' trn 'distr' matnum '
.mat' ], 'DISTR' );Hb = zeros(ENTRS,MAXSH);save([ 'results' fname1 '/temp/' trn 'Hb' matnum '.mat
' ], 'Hb' );endclear DISTR; clear Hb;
endend
end
disp( 'Check folders [Press ENTER to continue]' );pause
64
% Create Coastal Travel time Matrix
%POINTS1() = zeros(nmbCP,12);% for i2 = 1:nmbCP% POINTS1(i2,1) = i2;% end
% Loop over transect files.% Open transect files.parfor j = 1:MAXEL
phartn=zeros(nmbRUNSperTS,4) ;volume=zeros(nmbRUNSperTS,2);
POINTS = zeros(nmbCP,7);for i2 = 1:nmbCP
POINTS(i2,1) = i2;enddisp( 'Transect:' );disp(j);disp( 'Trial:' );disp(T ALL(i));
if j < 10fname2 = [ '000' int2str(j) ];
elseif j > 9 && j < 100fname2 = [ '00' int2str(j) ];
elseif j > 99 && j < 1000fname2 = [ '0' int2str(j) ];
elsefname2 = int2str(j);
end
bla = load([ 'datafiles/transect' fname2 ]);TS = bla.TS;% Create matrix with dimensions (x Runs) x MAXSH. When full (
specified% above as MAXMT), contents are flushed to .mat −files. This way
, long% computation times and errors due to exceedingly large matr ix
dimensions% are avoided.RESULTSmax = zeros(0,MAXSH);RESULTSmin = zeros(0,MAXSH);Hb max = zeros(0,MAXSH);Hb min = zeros(0,MAXSH);%% Calculate transect direction on UTM system.% Set zero angle vector orthogonal to transect direction.% ANG is always PI/2 then.DUTMX = TS(1,7) −TS(length(TS),7);DUTMY = TS(1,6) −TS(length(TS),6);
65
ZERO = [DUTMY−DUTMX];%% Calculate index of minimum and maximum depth points.% Cut transect file at those end points.[T1,IND 1] = min(abs(TS(:,3) −DS EX(j,2))); %#ok[T2,IND 2] = min(abs(TS(:,3) −DS EX(j,3))); %#okTS = TS(IND 1:IND 2,:);SIZETS = length(TS);%% Create RAW DATA file:fiddata = fopen([ 'results' fname1 '/Data ' num2str(j) '.txt' ], 'w'
);fidtsun = fopen([ 'results' fname1 '/Tsunami ' num2str(j) '.txt' ],
'w' );% HEADER for fiddata: RUN / LNGTH / WDTH / THCK / DPTH / SLP /
DNSTY / F.S. / Pf / SMF / FTYPE / TSUN%MCTR = 0; n=1;% Loop over runs.% Collect all necessary data for calculations.for k = 1:RUNS(i)
volume(k,1)=k;vol=0;
%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
% Removal of negatively generated slope angles. Negativeangles are
% assumed to be stable as the failure would have to beupslope.
SLP=−1;while SLP <= 0
%% Randomly define depth and length of failure surface.FOUND = 0;while FOUND == 0
% Depth.DPTHI = 0;d=0;while DPTHI == 0
CHI 1A = rand(1);CHI 1B = rand(1);DPTHI = (DS EX(j,3) −DS EX(j,2)) * CHI 1A +
DS EX(j,2);MEDD = (DS EX(j,2) + LOGND * (DS EX(j,3) −
DS EX(j,2)));NORMD = DPTHI / MED D;PROBD = exp( −((log(NORM D)/SIG D)ˆ2)/2)/(
NORMD* SIG D* sqrt(2 * pi));d=d+1;if (d >1000) disp( 'loop over 1000 times − 1' ); end
66
if CHI 1B > PROBDDPTHI = 0;
endend% Find Index, Soil Type, Failure Type.[DD,IND D] = min(abs(TS(:,3) −DPTHI)); %#okS TYP = TS(IND D,9);FIND = fsoil(S TYP); %hierentscheided sich der
fehlertyp% −−−−−FAIL = SOILS(FIND,3);% Length.LGTH I = 0;
while LGTH I == 0CHI 1C = rand(1);CHI 1D = rand(1);LGTH I = (L LIMS(FAIL,3) −L LIMS(FAIL,1)) *
CHI 1C + L LIMS(FAIL,1);NORML = LGTH I / L LIMS(FAIL,2); %10 000 =
natural upper limit (guessed)
PROBL = exp( −((log(NORM L)/SIG L)ˆ2)/2)/(NORML* SIG L* sqrt(2 * pi)); %gauss
if CHI 1D > PROBLLGTH I = 0;
endend% Check distances to top and bottom; if no
overstepping, find start and% end indices; else, return to start of while loop.DST TP = sqrt((TS(IND D,2) − TS(1,2) )ˆ2 + (
TS(IND D,3) − TS(1,3) )ˆ2);DST BT = sqrt((TS(IND D,2) − TS(SIZETS,2))ˆ2 + (
TS(IND D,3) − TS(SIZETS,3))ˆ2);if ((LGTH I/2) > DST TP) | | ((LGTH I/2) > DST BT)
FOUND = 0;else
[TP,IND S] = min(abs(sqrt((TS(IND D,2) − TS(1:IND D,2) ).ˆ2 + (TS(IND D,3) − TS(1:IND D,3) ).ˆ2) − LGTH I/2)); %#ok
[BT,IND E] = min(abs(sqrt((TS(IND D,2) − TS(IND D:SIZETS,2)).ˆ2 + (TS(IND D,3) − TS(IND D:SIZETS,3)).ˆ2) − LGTH I/2)); %#ok
IND E = IND E + IND D − 1;FOUND = 1;
endend% Extract matrix between start and end point.% Calculate length of failure region.% Get longitude, latitude, PHA of subregion.
67
LGTH = sqrt( (TS(IND E,2) − TS(IND S,2))ˆ2 + (TS(IND E,3) − TS(IND S,3))ˆ2 );
LAT = (TS(IND S,4) + TS(IND E,4))/2;LON = (TS(IND S,5) + TS(IND E,5))/2;
% Sedimentation rates and excess pore pressures: onlyimportant in river
% deltas!SEDR = fsedr(LAT,LON,SRDAT,MAXSR);% −−−−−% Determine the slope of the failure regionSLP = atan( (TS(IND S,3) − TS(IND E,3)) / (TS(IND E
,2) − TS(IND S,2)) );
% slpdeg=SLP * R2D;% if slpdeg >30% nmbSlopeAngleTooHigh=nmbSlopeAngleTooHigh+1;% SLP=30* D2R;% end
%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
% End of negative slope removalend
%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
%% Start of stability calculations.TS SS = TS(IND S:IND E,:);CHI 2B = rand(1);CHI 2C = rand(1);GOON = 0;
% Calculation of Slope Stability.% In failure case, output of Tsunami source data as
described above.% Tsunami propagation direction is angle of deflection from
main transect% direction.%
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
if FAIL == 1 % Infinite Slope; Force EquilibriumTHI = 0;while (THI < 10) | | (THI > 600)
CHI 2A = rand(1);THI = (CHI 2A* 3+ 1) * LGTH/100;
68
if (THI <10) THI=10; endend
if 1<=j && j <=45[STAB,RTN f,TSUN,Ru,PHA,PHI,FS] = fstab1c(TS SS,FIND,
SOILS 1073,LGTH,SLP,THI,SEDR,LAT,LON,E DAT);else
[STAB,RTN f,TSUN,Ru,PHA,PHI,FS] = fstab1c(TS SS,FIND,SOILS,LGTH,SLP,THI,SEDR,LAT,LON,E DAT);
end% −−−−−−COHR = 0;TSUN(10) = (CHI 2B* 10+20) * LGTH/100;
if STAB <= 1LMBDN = sqrt((( −TSUN(5)) * TSUN(6) * pi * ((TSUN(9)+1))
ˆ2)/(2 * sin(TSUN(8)) * (TSUN(9) −1)));SPR = TSUN(10) / (TSUN(10) + LMBDN);DST = 0.5 * pi * TSUN(6) * (TSUN(9)+1);ETA 01A = (0.0574 −0.0431 * sin(TSUN(8))) * (TSUN(7)/TSUN
(6));ETA 01B = ((TSUN(6) * sin(TSUN(8)))/( −TSUN(5)))ˆ1.25;ETA 01C = (1 − exp( −2.2 * (TSUN(9) −1)));ETA 0 = SPR * DST * ETA 01A * ETA 01B * ETA 01C;GOON = 1;
%if (isreal(ETA 0) <= 0.02) | | (abs(TSUN(5)) < 500)if (isreal(ETA 0) == 0) | | (ETA 0 <= 0.02) | | (abs(
TSUN(5)) < 500)ETA 0 = 0;GOON = 0;
elsevol=TSUN(11);
end
elseGOON = 0; ETA 0 = 0;
end%
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
elseif FAIL == 2 % Circular Shape; Bishop's Simpl.M.THI = 0;while (THI < 70) | | (THI > 600)
CHI 2A = rand(1);THI = (CHI 2A* 13+ 7) * LGTH/100;
69
if (THI >800) THI=800; %disp('1 bigger than 800');endif (THI <70) THI=70; end
end
if 1<=j && j <=45[STAB,RTN f,TSUN,Ru,PHA,COH R,FS] = fstab2a(TS SS,
FIND,SOILS 1073,LGTH,SLP,THI,SEDR,LAT,LON,E DAT);else
[STAB,RTN f,TSUN,Ru,PHA,COH R,FS] = fstab2a(TS SS,FIND,SOILS,LGTH,SLP,THI,SEDR,LAT,LON,E DAT);
end% −−−−−−PHI = 0;TSUN(10) = (CHI 2B* 40+80) * LGTH/100;TSUN(12) = (CHI 2C* 42+10)/100;if STAB <= 1
LMBDN = sqrt((TSUN(11) * ( −TSUN(5)) * (TSUN(9)+1)/(TSUN(9)−1)));
SPR = TSUN(10) / (TSUN(10) + LMBDN);DST = (TSUN(11) * TSUN(12))/2;ETA 02A = (0.131/sin(TSUN(8))) * (TSUN(7)/TSUN(6));ETA 02B = (TSUN(6) * sin(TSUN(8))/( −TSUN(5)))ˆ1.25;ETA 02C = ((TSUN(6)/TSUN(11))ˆ0.63) * (TSUN(12)ˆ0.39
);ETA 02D = (1.47 − 0.35 * (TSUN(9) −1)) * (TSUN(9) −1);ETA 0 = SPR * DST * ETA 02A * ETA 02B * ETA 02C *
ETA 02D;GOON = 1;
if (isreal(ETA 0) == 0) | | (ETA 0 <= 0.02) | | (abs(TSUN(5)) < 500)ETA 0 = 0;GOON = 0;
elsevol=TSUN(13);
end
elseGOON = 0; ETA 0 = 0;
end%
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
end
C EXP = 0;%% If a tsunami (amplitude >0.02m) occurs, calculations go
on.
70
% disp(GO ON);if (GO ON == 1) %&& SLP* R2D<30
% Exposed coastal region and the related runup must becalculated.
% 95% of the tsunamis are deflected within a range of−10 to +10 , which
% means the are within 1.95996 standard deviations;% Spreading angle set to 10 , can always be changed.CHI 3 = randn(1);DEFL = CHI 3* (pi/18)/1.95996;PROP = pi/2 + DEFL;SPRD = pi/18;%% Compute Shoreline Points to be hit.C EXP = fshore(ZERO,PROP,SPRD,MAXSH,SHORE,TSUN);% −−−−−−%if numel(C EXP) == 0
vol= −130;C EXP=0;RN UP =[];%break
else
% Calculate Runup as a function of angle (use Gausscurve).
RN UP = frunup(C EXP,SPRD,ETA 0);% −−−−−−%% Calculate the Tsunami Travel Time:[POINTS,Hbw] = ftimeb(fname2, RN UP, C EXP, IND S,
POINTS,SHORE,nmbCP);
%name=['results', num2str(fname1), '/temp/travel00',num2str(j),' run00',num2str(k),'.mat'];
%fsaveMatHB(name,POINTS);
endelse
RN UP =[]; C EXP =0;end
for index=1:length(T ALL)% EDIT KRISCHANfname1b= int2str(max(T ALL));fname1a = int2str(min(T ALL));test = isempty(RN UP);
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full = k/(n * MAXMT);if index == 1
in = 1;else
in = 0;end
if (RTN f <= max(T ALL)) && (test == 0)
% Compare runups to output datafile and replacemaximum runup if
% necessary and avg. runup everytime new data isinserted.
HITS = length(RN UP);STAPT = RNUP(1,1);ENDPT = STAPT + HITS−1;% Write Data in RESULTS matrix and flush if filled
up; saves a lot of% computation time. (see documentation)RESULTSmax(length(RESULTS max(:,1))+in,STAPT:ENDPT)
= RN UP(:,4);Hb max(length(Hb max(:,1))+in,:) = Hbw;
else
RESULTSmax(length(RESULTS max(:,1))+in,:) = 0;Hb max(length(Hb max(:,1))+in,:) = 0;
end
if (RTN f <= min(T ALL)) && (test == 0)
% Compare runups to output datafile and replacemaximum runup if
% necessary and avg. runup everytime new data isinserted.
HITS = length(RN UP);STAPT = RNUP(1,1);ENDPT = STAPT + HITS−1;% Write Data in RESULTS matrix and flush if filled
up;RESULTSmin(length(RESULTS min(:,1))+in,STAPT:ENDPT)
= RN UP(:,4);Hb min(length(Hb min(:,1))+in,:) = Hbw;
else
RESULTSmin(length(RESULTS min(:,1))+in,:) = 0;Hb min(length(Hb min(:,1))+in,:) = 0;
end
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if full == 1trsct = int2str(j);if (MCTR < 10)
matnum = [ '000' int2str(MCTR) ];elseif (MCTR > 9) && (MCTR < 100)
matnum = [ '00' int2str(MCTR) ];elseif (MCTR > 99) && (MCTR < 1000)
matnum = [ '0' int2str(MCTR) ];else
matnum = int2str(MCTR);end
DISTR = RESULTSmax;name1=[ 'results' , num2str(fname1b), '/temp/' ,
num2str(trsct), 'distr' , num2str(matnum), '.mat'];
fsaveMatDistr(name1,RESULTS max);DISTR = [];
Hb = Hb max;name2=[ 'results' , num2str(fname1b), '/temp/' , num2str
(trsct) , 'Hb' , num2str(matnum) , '.mat' ];fsaveMatHB(name2,Hb max);Hb = [];
DISTR = RESULTSmin;name3=[ 'results' , num2str(fname1a), '/temp/' , num2str
(trsct) , 'distr' , num2str(matnum), '.mat' ];fsaveMatDistr(name3,RESULTS min);DISTR = [];
Hb = Hb min;name4=[ 'results' ,num2str(fname1a) , '/temp/' , num2str(
trsct) , 'Hb' , num2str(matnum) , '.mat' ];fsaveMatHB(name4,Hb min);Hb = [];
endendif full == 1
RESULTSmax = zeros(0,MAXSH); RESULTS min = zeros(0,MAXSH);
MCTR = MCTR+1; n = n + 1;Hb max = zeros(0,MAXSH); Hb min = zeros(0,MAXSH);
end
tsunami=zeros(1,17);tsunami(1)=j; tsunami(2)=k;ii=length(TSUN);for op=1:ii
tsunami(op+2)=TSUN(op);endii=length(C EXP);
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tsunami(15)=C EXP(1);tsunami(16)=C EXP(ii);tsunami(17)=ETA 0;info = zeros(1,18);info = [j k LGTH TSUN(10) TSUN(7) −TSUN(5) ceil(SLP * R2D) (
TSUN(9) * RHOW) Ru PHA PHI COHR RTNf FS FAIL TSUN(1)TSUN(2) vol];
fprintf(fiddata, '%1.0f %4.0f %8.4f %8.4f %8.4f %8.4f%8.1f %8.4f %6.4f %6.4f %6.2f %6.4f %6.0f
%6.4f %6.0f %8.4f %8.4f %8.4f \r' ,info);fprintf(fidtsun, '%1.0f %4.0f %6.4f %6.4f %6.4f %6.4f
%6.4f %6.4f %6.4f %6.4f %6.4f %6.4f %6.4f%6.4f %6.0f %6.0f %6.4f \r' ,tsunami);
%
volume(k,2)=vol;% End of loop over runs.
end
%save volume to mat filevolume = sort((volume(:,2)), 'descend' );index=num2str(j);name=[ 'results500/volume/volume' , index, '.mat' ];fsaveMatHB(name,volume);
fclose(fiddata);fclose(fidtsun);MCTR = 0;
%save POINTS for traveltime 500index=num2str(j);name=[ 'results500/points' , index, '.mat' ];fsaveMatHB(name,POINTS);% End of loop over transects.
end
% Output File for Tsunami Travel Time(seperate function):% krause 12 7
POINTSall = zeros(nmbCP,12);
for o=1:MAXEL%go over all transectsname=[ 'results500/points' , num2str(o), '.mat' ];bla=load(name);point=bla.Hb;POINTSall=Adaptedftimeb(point,POINTSall,nmbCP);
end
%average the POINTSall filefor b = 1:nmbCP
if POINTSall(b,3)==0POINTSall(b,8) = POINTSall(b,8);POINTSall(b,9) = POINTSall(b,9);
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POINTSall(b,10) = POINTSall(b,10);POINTSall(b,11) = POINTSall(b,11);POINTSall(b,12) = POINTSall(b,12);
elsePOINTSall(b,8) = POINTSall(b,2)/POINTSall(b,3); % Ave
Arrival Time [min]POINTSall(b,9) = POINTSall(b,4)/POINTSall(b,3); % Ave Time
to Breaker [min]POINTSall(b,10) = POINTSall(b,5)/POINTSall(b,3); % Ave Time
from breaker to shore [min]POINTSall(b,11) = POINTSall(b,6)/POINTSall(b,3); % Ave
Total Distance [km]POINTSall(b,12) = POINTSall(b,7)/POINTSall(b,3); % Ave
distance from Shore to breaker [m]end
end
foutput(POINTSall, fname1,nmbCP);
% Prepare everything for a decent output file.%% More output files could be generated easily, depending on w hat
kind of% information is required.disp( 'Runtime [s]:' );THETA2 = cputime;RUNTIME = THETA2− THETA1;disp(RUNTIME);pause(2);%%% Finally, the .mat −files containing the whole output need to be
changed% to runup probability distributions for each coastpoint.fprintf(1, 'The simulations are completed. The obtained data is now
being \n' );fprintf(1, 'processed to generate probability distributions for each
coastpoint. \n' );fprintf(1, 'This might take a while, your patience is appreciated. \n\n
' );%ESTIM = sum(INPUT(2,:))/11;fprintf(1, 'Estimated Runtime [s]: %7.0f \n' ,ESTIM);%THETA1 = cputime;
%start staistical analysisstat newJoint(nmbTS, nmbCP,nmbRUNSperTS)%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp( 'Runtime [s]:' );
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THETA2 = cputime;RUNTIME = THETA2− THETA1;disp(RUNTIME);disp( '' );disp( 'Press ENTER to exit' );pause;
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APPENDIX D
Slope Stability Analysis
fstab1c.m
function [STAB1,RTN,TSUN,Ru,PHA,PHI,FOS] = fstab1c(TS SS,FIND,SOILS,LGTH,SLP,THI,SEDR,LAT,LON,E DAT)
phaT=0;rtnT=0;
% Function Written 5/18/08 by Oliver Taylor% edited by Krause 23 April 2011
%
*************************************************** *************************
% INFINITE SLOPE METHOD%
*************************************************** *************************
D2R = pi/180; % conversion degrees torads
R2D = 180/pi; % conversion radians todegs
RHOW = 1027; % density of water
%
*************************************************** *****************
%slpOriginal=0;FOS =10;% Create local coordinate system, where x(STA) = 0; y −values stay
samePTS = length(TS SS(:,1));LOC = TSSS;LOC(:,2) = TS SS(:,2) − TS SS(1,2);%
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% Create linear equation which starts at STA and ends at END an dcheck
% which one of the points in between exhibits the highest vert ical% distance from that lineMAXDY = max(LOC(:,3) − (LOC(1,3) − (tan(SLP)) * LOC(:,2)));MAXH = THI/cos(SLP);H EDG = MAXH − MAXDY;if H EDG< 0
H EDG = 0;end%DPTH = mean(LOC(:,3));% Exceedingly improbable, but in very few cases, SLP was == 0; to
avoid% division by zero and thus errors, slightly change value (to 0.01
degs).if SLP == 0
SLP = 0.001745;end
slope=SLP * R2D;%%CHIF2 = rand(1);PHI = CHIF2 * (SOILS(FIND,9) −SOILS(FIND,8)) + SOILS(FIND,8);% Determination of the excess pore pressure:
r = 0.9909 − (0.0328 * slope)+ (0.0003 * PHI); % 99.0% of the Rurequired for failure for phi' = 28
R = (0.9008 − (0.0299 * slope)); % 90.0% of the Ru required forfailure for phi' = 28
a=−10;fudge=0.6; %0.7;%0.5;0.7;while a>=1 | | a<=−1
a=((randn(1) * .5)/1.95996)+fudge;end
if slope >= 10;Ru = 0;
elseif slope <=0Ru = 0;
elseRu = R + ((r −R)* a);
end% Definition of slices;% Slices should be about equally wide >>> use 3 points for one
slice,% unless there will remain few points >>> use 4 points for some;% End point of slice i is starting point for slice i+1
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SL QU = (PTS − 1)/2;NUMSL = floor(SL QU);GR SL = 2* (SL QU − NUMSL);SM SL = NUMSL− GRSL;%% Define geometry matrix (linked to local coordinates LOC);% X1 Y1 X2 Y2 X3 Y3 X4 Y4 SRF BOT AVGH WID VOL RHOB
RHOS% EXC% (for each slice; start from top left and go counterclockwis e)POS = zeros(4,1);RHOAV = 0;GEOM1 = zeros(SM SL,16);for i = 1:SM SL
IND S = (i −1) * 2 + 1;IND M = (i −1) * 2 + 2;IND E = (i −1) * 2 + 3;GEOM1(i,1) = LOC(IND S,2);GEOM1(i,2) = LOC(IND S,3);GEOM1(i,3) = LOC(IND S,2);GEOM1(i,4) = LOC(1,3) − H EDG− ((tan(SLP)) * LOC(IND S,2));GEOM1(i,5) = LOC(IND E,2);GEOM1(i,6) = LOC(1,3) − H EDG− ((tan(SLP)) * LOC(IND E,2));GEOM1(i,7) = LOC(IND E,2);GEOM1(i,8) = LOC(IND E,3);GEOM1(i,9) = mean(LOC(IND S:IND E,3)); % avg. srf.
dpth.GEOM1(i,10) = (GEOM1(i,4) + GEOM1(i,6))/2; % avg. btm.
dpth.if GEOM1(i,9) > GEOM1(i,10)
GEOM1(i,11) = GEOM1(i,9) − GEOM1(i,10); % heightelse
GEOM1(i,11) = 0;endGEOM1(i,12) = GEOM1(i,7) − GEOM1(i,1); % widthGEOM1(i,13) = GEOM1(i,11) * GEOM1(i,12); % volumeif GEOM1(i,11) > 0
GEOM1(i,14) = (SOILS(FIND,6)) * log(GEOM1(i,11)) + SOILS(FIND,7);
elseGEOM1(i,14) = SOILS(FIND,7);
endCHIF1 = randn(1);GEOM1(i,14) = (1+CHIF1 * (0.05/1.95996)) * GEOM1(i,14); % avg. bulk
dens.GEOM1(i,15) = GEOM1(i,14) − RHOW; % sbm. avg.
dens.GEOM1(i,16) = 0; % exc. pore
pres.POS(1) = POS(1) + (LOC(IND M,4)) * (GEOM1(i,13)); % LatPOS(2) = POS(2) + (LOC(IND M,5)) * (GEOM1(i,13)); % LonPOS(3) = POS(3) + (LOC(IND M,6)) * (GEOM1(i,13)); % UTMY
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POS(4) = POS(4) + (LOC(IND M,7)) * (GEOM1(i,13)); % UTMXRHOAV = RHOAV + (GEOM1(i,14) * (GEOM1(i,13))); % add. avg.
dens.endGEOM2 = zeros(GR SL,16);% For slices this thin, there will always only be one slice at t he
most% (if at all) exhibiting 4 points. However, if for computatio n
reasons% the slice width can or has to be made larger, the program
structure for% that already exists here. (There will only be a few numbers t hat
need% to be changed here.)for j = 1:GR SL
IND S = SMSL* 2 + (j −1) * 3 + 1;IND M = SMSL* 2 + (j −1) * 3 + 2;IND E = SMSL* 2 + (j −1) * 3 + 4;GEOM2(j,1) = LOC(IND S,2);GEOM2(j,2) = LOC(IND S,3);GEOM2(j,3) = LOC(IND S,2);GEOM2(j,4) = LOC(1,3) − H EDG− ((tan(SLP)) * LOC(IND S,2));GEOM2(j,5) = LOC(IND E,2);GEOM2(j,6) = LOC(1,3) − H EDG− ((tan(SLP)) * LOC(IND E,2));GEOM2(j,7) = LOC(IND E,2);GEOM2(j,8) = LOC(IND E,3);GEOM2(j,9) = mean(LOC(IND S:IND E,3)); % avg. srf.
dpth.GEOM2(j,10) = (GEOM2(j,4) + GEOM2(j,6))/2; % avg. btm.
dpth.if GEOM2(j,9) > GEOM2(j,10)
GEOM2(j,11) = GEOM2(j,9) − GEOM2(j,10); % heightelse
GEOM2(j,11) = 0;endGEOM2(j,12) = GEOM2(j,7) − GEOM2(j,1); % widthGEOM2(j,13) = GEOM2(j,11) * GEOM2(j,12); % volumeif GEOM2(j,11) > 0
GEOM2(j,14) = (SOILS(FIND,6)) * log(GEOM2(j,11)) + SOILS(FIND,7);
elseGEOM2(j,14) = SOILS(FIND,7);
endCHIF1 = randn(1);GEOM2(j,14) = (1+CHIF1 * (0.05/1.95996)) * GEOM2(j,14); % avg. bulk
dens.GEOM2(j,15) = GEOM2(j,14) − RHOW; % sbm. avg.
dens.GEOM2(j,16) = 0; % exc. pore
pres.POS(1) = POS(1) + (LOC(IND M,4)) * (GEOM2(j,13)); % LatPOS(2) = POS(2) + (LOC(IND M,5)) * (GEOM2(j,13)); % Lon
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POS(3) = POS(3) + (LOC(IND M,6)) * (GEOM2(j,13)); % UTMYPOS(4) = POS(4) + (LOC(IND M,7)) * (GEOM2(j,13)); % UTMXRHOAV = RHOAV + (GEOM2(j,14) * (GEOM2(j,13))); % add. avg.
dens.end%GEOM = zeros(NUMSL,16);GEOM(1:SMSL,:) = GEOM1;GEOM((SMSL+1):NUMSL,:) = GEOM2;VOL = sum(GEOM(:,13));%% In a very few exceptional cases, the seafloor surface is so% inhomogeneous that one peak exceeds all other points on the slope
by% more than the initially obtained random thickness. This le ads to
a% volume of zero and hence to an unuseful output in that single
run. In% those cases, no tsunami is assumed to be generated.if VOL ˜= 0
TSUN = zeros(11,1);TSUN(11)=VOL; % volumeTSUN(1) = POS(1)/VOL; % LatTSUN(2) = POS(2)/VOL; % LonTSUN(3) = POS(3)/VOL; % UTMYTSUN(4) = POS(4)/VOL; % UTMXTSUN(5) = DPTH; % DepthTSUN(6) = LGTH; % LengthTSUN(7) = (VOL/LGTH + THI)/2; % ThicknessTSUN(8) = SLP; % SlopeTSUN(9) = (RHOAV/VOL) / RHO W; % Average relative
density% Start of stability calculation%gamma = TSUN(9);%
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
% Taylor% Determine the factor of safety for the psuedodynamic analy sis%% FOS = 10; n = 50; RTN = n;% while (FOS > 1)% RTN = n;% if RTN>750% break% end% PHA = fseisT(n,LAT,LON,E DAT);%% FOS = ((((gamma−1) * (1 −Ru)) − PHA* gamma* tan(SLP)) / ...% (((gamma−1) * tan(SLP)) + (PHA * gamma))) * tan(PHI);% STAB1 = FOS;
81
% n = n + 10;% end%% phaT=PHA;% rtnT=RTN;%%% RTN = 5000;% FOS = 5000;% PHA = 0;
% KrauseA=gamma−1;B=1−Ru;
%PHA=((tan(PHI) * (gamma−1) * (1 −Ru)) −(gamma−1) * tan(SLP))/((tan(PHI) *gamma* tan(SLP))+gamma);
PHA=(A* B* tan(PHI) −A* tan(SLP))/(gamma+gamma * tan(PHI) * tan(SLP));
probExceedance = fseis(PHA,LAT,LON,E DAT); %curvefit
rtnPeriod = 1 ./ probExceedance;
%round return period: at least 50, maximum 750, in between st epsof 10
if (rtnPeriod <750)if (rtnPeriod < 50)
RTN=50;FOS=1;
elsertnPeriodRound=10 * ceil(rtnPeriod/10);RTN=rtnPeriodRound;FOS=1;
endelse
%assumed to be stableRTN = 5000;FOS = 5000;PHA = 0;
PROB = 0;STAB1 = 2000;
TSUN = [];
PHI = 0;
end
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STAB1 = FOS;
elsePROB = 0;STAB1 = 2000;RTN = 5000;TSUN = [];PHA = 0;PHI = 0;
end%
%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
fstab2a.m
function [STAB3,RTN,TSUN,Ru,PHA,COH R,FOS] = fstab2a(TS SS,FIND,SOILS,LGTH,SLP,THI,SEDR,LAT,LON,E DAT)
phaT=0;rtnT=0;
%%
*************************************************** *************************
% BISHOPS METHOD%
*************************************************** *************************
% edited by Krause April 23 2011% instead of increasing PHA till slope fails, calculate PHA f or
failing% slope (factor of safety = 1)%
*************************************************** *************************
%global GE;GE= 9.81;%global RHO W;RHOW = 1027; % density of water
%global R2D;%global D2R;D2R = pi/180; % conversion degrees to
radsR2D = 180/pi; % conversion radians to
degs%
83
%
*************************************************** *****************
FOS = 10;slpOriginal=0;%
fudge=0.15; %0.55;%0.45;%0.35;0.15;r = 1.01 − (0.09 * (SLP * R2D)); % Ru required for failure for Su
/sig p = 0.1 (Locat et al. 2003)a = −1;if r <=0
Ru = 0;else
while (a >=r) | (a <=0)a=(abs((randn(1) * .5)/1.95996))+fudge * r;
endRu = (a);
end%% create local coordinate system, where x(STA) = 0; y −values stay
samePTS = length(TS SS(:,1));LOC = TSSS;LOC(:,2) = TS SS(:,2) − TS SS(1,2);%% Exceedingly improbable, but in very few cases, SLP was == 0; to
avoid% division by zero and thus errors, slightly change value (to 0.01
degs).if SLP == 0
SLP = 0.001745;end
slope=SLP * R2D;
%% SEGM(X,Y) is centered between start and end point% SEGS(X,Y) is extension of building line to point where X = 0SEGM(1) = LOC(PTS,2)/2;SEGM(2) = (LOC(1,3) + LOC(PTS,3))/2;BETA = pi/2 − SLP;SEGS(1) = 0;SEGS(2) = SEGM(2) − SEGM(1)* tan(BETA);%% Linear equation: Y = SEGS(2) + X * tan(BETA) for building line;% Find closest point to this linear equation;
84
% Ignore first point to avoid division by zero; add one to inde xthen
[DEL B,IND] = min(abs(BETA − atan((LOC(2:PTS,3) −SEGS(2))./LOC(2:PTS,2)))); %#ok
IND = IND+1;%DPTH = LOC(IND,3);LATI = LOC(IND,4);LONI = LOC(IND,5);UTMYI = LOC(IND,6);UTMXI = LOC(IND,7);%% Calculate height of circle segment (distance to center of c ircle% segment 'minus' distance to nearby slope surface)THI D = sqrt((SEGM(2) −SEGS(2))ˆ2 + (SEGM(1))ˆ2) − sqrt((LOC(IND,3) −
SEGS(2))ˆ2 + (LOC(IND,2))ˆ2);SEGH = THI + THI D;%% In one particular run, the exceptional case of SEGH = 0 occur red,
which% is corresponding to a linear failure plane with radius = inf ; in
this% case, SEGH is being increased slightly to avoid division by zero.if SEGH == 0
SEGH = 10;end%% Calculate radius of slip circle and position of rotation ce nterRADS = (SEGH/2) + (LGTHˆ2 / (8 * SEGH));SEGC(1) = SEGM(1) + (RADS − SEGH)* cos(BETA);SEGC(2) = SEGM(2) + (RADS − SEGH)* sin(BETA);%% Circle equation to find any point on the slip surface:% (X − SEGC(1))ˆ2 + (Y − SEGC(2))ˆ2 = RADSˆ2% (usually, X is known, Y is calculated)% ATTENTION! >>> When solving for X or Y, there are two solutions% (quadratic equation)%%% Definition of slices;% slices should be about equally wide >>> use 3 points for one
slice,% unless there will remain few points >>> use 4 points for some% End point of slice i is starting point for slice i+1SL QU = (PTS − 1)/2;NUMSL = floor(SL QU);GR SL = 2* (SL QU − NUMSL);SM SL = NUMSL− GRSL;%% Define geometry matrix (linked to local coordinates LOC);% X1 Y1 X2 Y2 X3 Y3 X4 Y4 SRF BOT AVGH WID VOL ANGB
DEL L
85
% RHOB RHOS EXC% (for each slice; start from top left and go counterclockwis e)RHOAV = 0;GEOM1 = zeros(SM SL,18);for i = 1:SM SL
IND S = (i −1) * 2 + 1;IND E = (i −1) * 2 + 3;GEOM1(i,1) = LOC(IND S,2);GEOM1(i,2) = LOC(IND S,3);GEOM1(i,3) = LOC(IND S,2);GEOM1(i,4) = −sqrt(RADSˆ2 − (GEOM1(i,3) − SEGC(1))ˆ2) + SEGC(2);GEOM1(i,5) = LOC(IND E,2);GEOM1(i,6) = −sqrt(RADSˆ2 − (GEOM1(i,5) − SEGC(1))ˆ2) + SEGC(2);GEOM1(i,7) = LOC(IND E,2);GEOM1(i,8) = LOC(IND E,3);GEOM1(i,9) = mean(LOC(IND S:IND E,3)); % avg. srf.
dpth.GEOM1(i,10) = (GEOM1(i,4) + GEOM1(i,6))/2; % avg. btm.
dpth.if GEOM1(i,9) > GEOM1(i,10)
GEOM1(i,11) = GEOM1(i,9) − GEOM1(i,10); % heightelse
GEOM1(i,11) = 0;endGEOM1(i,12) = GEOM1(i,7) − GEOM1(i,1); % widthGEOM1(i,13) = GEOM1(i,11) * GEOM1(i,12); % volumeGEOM1(i,14) = atan((GEOM1(i,4) −GEOM1(i,6))/GEOM1(i,12));% % slice
base ang.GEOM1(i,15) = sqrt((GEOM1(i,4) −GEOM1(i,6))ˆ2 + (GEOM1(i,12))ˆ2);% % Slice
base lgt.if GEOM1(i,11) > 0
GEOM1(i,16) = (SOILS(FIND,6)) * log(GEOM1(i,11)) + SOILS(FIND,7);
elseGEOM1(i,16) = SOILS(FIND,7);
endCHIF1 = randn(1);GEOM1(i,16) = (1+CHIF1 * (0.05/1.95996)) * GEOM1(i,16); % avg. bulk
dens.GEOM1(i,17) = GEOM1(i,16) − RHOW; % sbm. avg.
dens.GEOM1(i,18) = GEOM1(i,11) * SEDR* 0; % exc. pore
pres.RHOAV = RHOAV + (GEOM1(i,16) * (GEOM1(i,13))); % add. avg.
dens.endGEOM2 = zeros(GR SL,18);% For slices this thin, there will always only be one slice at t he
most
86
% (if at all) exhibiting 4 points. However, if for computatio nreasons
% the slice width can or has to be made larger, the programstructure for
% that already exists here. (There will only be a few numbers t hatneed
% to be changed here.)for j = 1:GR SL
IND S = SMSL* 2 + (j −1) * 3 + 1;IND E = SMSL* 2 + (j −1) * 3 + 4;GEOM2(j,1) = LOC(IND S,2);GEOM2(j,2) = LOC(IND S,3);GEOM2(j,3) = LOC(IND S,2);GEOM2(j,4) = −sqrt(RADSˆ2 − (GEOM2(j,3) − SEGC(1))ˆ2) + SEGC(2);GEOM2(j,5) = LOC(IND E,2);GEOM2(j,6) = −sqrt(RADSˆ2 − (GEOM2(j,5) − SEGC(1))ˆ2) + SEGC(2);GEOM2(j,7) = LOC(IND E,2);GEOM2(j,8) = LOC(IND E,3);GEOM2(j,9) = mean(LOC(IND S:IND E,3)); % avg. srf.
dpth.GEOM2(j,10) = (GEOM2(j,4) + GEOM2(j,6))/2; % avg. btm.
dpth.if GEOM2(j,9) > GEOM2(j,10)
GEOM2(j,11) = GEOM2(j,9) − GEOM2(j,10); % heightelse
GEOM2(j,11) = 0;endGEOM2(j,12) = GEOM2(j,7) − GEOM2(j,1); % widthGEOM2(j,13) = GEOM2(j,11) * GEOM2(j,12); % volumeGEOM2(j,14) = atan((GEOM2(j,4) −GEOM2(j,6))/GEOM2(j,12));% % slice
base ang.GEOM2(j,15) = sqrt((GEOM2(j,4) −GEOM2(j,6))ˆ2 + (GEOM2(j,12))ˆ2);% % Slice
base lgt.if GEOM2(j,11) > 0
GEOM2(j,16) = (SOILS(FIND,6)) * log(GEOM2(j,11)) + SOILS(FIND,7);
elseGEOM2(j,16) = SOILS(FIND,7);
endCHIF1 = randn(1);GEOM2(j,16) = (1+CHIF1 * (0.05/1.95996)) * GEOM2(j,16); % avg. bulk
dens.GEOM2(j,17) = GEOM2(j,16) − RHOW; % sbm. avg.
dens.GEOM2(j,18) = GEOM2(j,11) * SEDR* 0; % exc. pore
pres.RHOAV = RHOAV + (GEOM2(j,16) * (GEOM2(j,13))); % add. avg.
dens.end%
87
GEOM = zeros(NUMSL,18);GEOM(1:SMSL,:) = GEOM1;GEOM((SMSL+1):NUMSL,:) = GEOM2;VOL = sum(GEOM(:,13));%% In a very few exceptional cases, the seafloor surface is so% inhomogeneous that the failure plane is located above the
seafloor% surface. This leads to a volume of zero and hence to an unusef ul
output% in that single run. In those cases, no tsunami is assumed to b e% generated.if VOL ˜= 0
TSUN = zeros(13,1);TSUN(13) = VOL; % VolTSUN(1) = LATI; % LatTSUN(2) = LONI; % LonTSUN(3) = UTMYI; % UTMYTSUN(4) = UTMXI; % UTMXTSUN(5) = DPTH; % DepthTSUN(6) = LGTH; % LengthTSUN(7) = THI * VOL/((RADSˆ2) * (acos(1 − SEGH/RADS)) − (RADS − SEGH
) * (sqrt(2 * RADS* SEGH− SEGHˆ2)));% % ThicknessTSUN(8) = SLP; % SlopeTSUN(9) = (RHOAV/VOL) / RHO W; % Average WeightTSUN(11) = RADS; % Radius%% Start of stability calculations%CHIF2 = rand(1);COHR = CHIF2* (SOILS(FIND,11) − SOILS(FIND,10)) + SOILS(FIND,10);%%%Taylors way% increase returnperiod and therefore pha until fails% FOS = 10; n = 50; RTN = n;% while (FOS > 1)% RTN = n;% if RTN>750% break% end% PHA = fseisT(n,LAT,LON,E DAT);% % −−−−−−−% %% SUM1 = 0;% SUM2 = 0;% for i = 1:NUMSL% NUMB1 = (COH R* GE* GEOM(i,17) * GEOM(i,11)) * GEOM(
i,15) * (1 −(Ru * cos(SLP)));% GEOM(i,15) = base length% GEOM(i,11) = hight
% GEOM(i,17) = byuoant density (rho −rho w)
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% SUM1 = SUM1 + NUMB1;% DENB1 = (GE* GEOM(i,17) * GEOM(i,13)) * sin(GEOM(i
,14));% DENB2 = (PHA* GE* GEOM(i,16) * GEOM(i,13)) * (cos(
GEOM(i,14)) − GEOM(i,11)/(2 * RADS));% SUM2 = SUM2 + DENB1 + DENB2;% end% FOS = SUM1/SUM2;% n = n + 10;% end%% phaT=PHA;% rtnT=RTN;%% RTN = 5000;% FOS = 5000;% PHA = 0;
%%Krauses way% calculate pha and therefore get returnperiod!% attention independent variable in curve fitting is g not la mbda
!!!
SUM1 = 0;
woPHA =0;%
without phawPHA = 0;
%with pha
for i = 1:NUMSLNUMB1 = (COH R* GE* GEOM(i,17) * GEOM(i,11)) * GEOM(i,15) * (1 −(
Ru* cos(SLP)));SUM1 = SUM1 + NUMB1;
DENB1 = (GE* GEOM(i,17) * GEOM(i,13)) * sin(GEOM(i,14));DENB2 = 1* (GE* GEOM(i,16) * GEOM(i,13)) * (cos(GEOM(i,14)) −
GEOM(i,11)/(2 * RADS)); %PHA* (...) * (cos...) just PHA=1
wPHA = wPHA+ DENB2;woPHA = woPHA + DENB1;
end
PHA = (SUM1− woPHA) / wPHA;
probExceedance = fseis(PHA,LAT,LON,E DAT);
89
lamda = 1 ./ probExceedance;
%round return period: at least 50, maximum 750, in between st epsof 10
if (lamda <750)
if (lamda < 50)RTN=50;FOS=1;
elselamdaRound=10 * ceil(lamda/10);RTN=lamdaRound;FOS=1;
endelse
%assumed to be stableRTN = 5000;FOS = 5000;PHA = 0;TSUN = [];COHR=0;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
elseRTN = 5000;FOS = 5000;TSUN = [];PHA = 0;COHR=0;
end
STAB3=FOS;
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APPENDIX E
Tsunami Codes and other Supporting Subroutines
Adaptedftimeb.m
%not changed in 2011function [POINTSall] =Adaptedftimeb(POINTS,POINTSall,nmbCP)
for tab = 1:nmbCP
POINTSall(tab,2) = POINTSall(tab,2) + POINTS(tab,2);POINTSall(tab,3) = POINTSall(tab,3) + POINTS(tab,3);POINTSall(tab,4) = POINTSall(tab,4) + POINTS(tab,4);POINTSall(tab,5) = POINTSall(tab,5) + POINTS(tab,5);POINTSall(tab,6) = POINTSall(tab,6) + POINTS(tab,6);POINTSall(tab,7) = POINTSall(tab,7) + POINTS(tab,7);
end
foutput.m
%not changed in 2011function foutput(POINTS,fname1,nmbCP)
% This function stores the travel time data to a text file for t herecords
% This travel time is based on the runups calculated via the MC S% code and not based on the 95% confidence interval runup. The refore
the% time to impact is reduced as the initial tsunami amplitude i s much% greater. However this method yields a conservative magnit ude and
takes% into consideration all failures that yield tsunami waves n ot just
the% maximum runup value.%% By: OLIVER TAYLOR% Date: 01/01/08%
fid = fopen([ 'results' fname1 '/Travel Time Results ' fname1 '.txt' ],'wt+' );
frewind(fid);fprintf(fid, '
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−\n' );fprintf(fid, ' \n' );fprintf(fid, 'Point# T t ab t bo hb xb \n
' );
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fprintf(fid, ' −−−−−− −−−−−− −−−−−−− −−−−−− −−−−−− −−−−−\n' );
for q=1:nmbCPfprintf(fid, '%4.0f %6.4f %6.4f %6.4f %6.4f
%4.1f \n' ,POINTS(q,1),POINTS(q,8),POINTS(q,9),POINTS(q,10),POINTS(q,11),POINTS(q,12));
endfclose(fid);
frunup.m
%not changed in 2011function [RN UP] = frunup(C EXP,SPRD,ETA 0)%% This function simply computes the runup as a function of the
angle and% creates an output file which contains the point numbers, La t and
Lon% values and runup in [m]. The derivation of the equation for t he% variance can be obtained in the paperwork. Basically, thos e
points just% hit ( −10 or +10 degrees at this point) are hit by 5% of the
amplitude% of that point in the propagation line of the tsunami.CALCS = length(C EXP(:,1));VAR = ((SPRDˆ2)/2)/(log(20));%RN UP = zeros(CALCS,4);for i = 1:CALCS
RN UP(i,4) = ETA 0 * exp( −(C EXP(i,6))ˆ2/(2 * VAR)) * C EXP(i,7);end%% Assign Point#, Lat, Lon to RunupsRN UP(:,1:3) = C EXP(:,1:3);RN UP = RNUP(:,1:4);
% DETERMINATION OF RUNUP TIME for predicted tsunamis via the MonteCarlo
% Simulations (V1.2). This program calculates the time requ ired fora
% predicted tsunami, with initial amplitude greater than 5 −m, toreach the
% shoreline.%% By: OLIVER TAYLOR% Date Started: 12/27/07% Date Completed: 5/1/08 − version 1% Re−evaluated: 5/13/08%
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
92
%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
%% Function Name & Input Parameters:
fsaveMatDistr.m
%trick to save a file in a parallel for loop, otherwise saving in aparfor
%loop is not possiblefunction fsaveMat(name, DISTR)save(name, 'DISTR' );
fsaveMatHB.m
%trick to save a file in a parallel for loop, otherwise saving in aparfor
%loop is not possiblefunction fsaveMat(name, Hb)save(name, 'Hb' );
fsedr.m
%not changed in 2011function [SEDR] = fsedr(LAT,LON,SRDAT,MAXSR)%% This function extracts the sediment rate from the related f ile.%%RD LAT = round(LAT * 10)/10;RD LON = round(LON * 10)/10;%for i = 1:MAXSR
if (RD LAT == SRDAT(i,1)) & (RD LON == SRDAT(i,2))SEDR = SRDAT(i,3);
elseSEDR = 0;
endend%% The actual excess pore pressure is depth dependent. That me ans
that it% will be picked for each individual slice in the slope stabil ity% function.
fseis.m
function [probExceedance] = fseis(g,LAT,LON,E DAT)%
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
93
% edited by Krause in April 23 2011% independent variable in curve fitting changed to ground mo tion%% This function extracts the seismicity vector of the closes t
location.%% return period is calculated with polynomial fit of seismic ity
data.% See Excel table (seismicfit.xls).%
−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
RD LAT = LAT;RD LON = LON;%CELL = find((RD LAT == E DAT(:,1)) & (RD LON == E DAT(:,2)));minDist index=length(E DAT)+1;dist=0; %safes distance rfom Transect point to point which has seism ic
information (smallest distance leads to whcih seismic curv e touse)
for (n = 1:length(E DAT)) %1176 anzahl rows in E DAT (length(E DAT) ??)if (n==1)
dist=sqrt((RD LAT−E DAT(n,1))ˆ2 + (RD LON−E DAT(n,2))ˆ2);minDist index=n;
elsedistComp=sqrt((RD LAT−E DAT(n,1))ˆ2 + (RD LON−E DAT(n,2))ˆ2 )
;if (distComp <dist)
dist=distComp;minDist index=n;
end
endend
%if isempty(CELL) == 1if (minDist index==length(E DAT)+1) %not possible because minDist index
=n;disp( 'Error: closest seismicity point could not be found in
fseis.m' );SCURV = 0;
else%SCURV = EDAT(CELL,3:5);SCURV = EDAT(minDist index,3:5);
end
if SCURV == 0
94
probExceedance = 0;else
g=abs(g);
ln x peak=( −SCURV(2)/(2 * SCURV(1)));ln y peak=SCURV(1) * (ln x peak)ˆ2 + SCURV(2) * (ln x peak) + SCURV
(3);x peak=exp(ln x peak);y peak=exp(ln y peak);
if (g <x peak)probExceedance = (2 * y peak) − exp(SCURV(1) * (log(g))ˆ2 +
SCURV(2)* (log(g))+ SCURV(3));else
probExceedance = exp(SCURV(1) * (log(g))ˆ2 + SCURV(2) * (log(g))+SCURV(3));
end
end%%
*************************************************** ********************
fshore.m
%not changed in 2011function [C EXP] = fshore(ZERO,PROP,SPRD,MAXSH,SHORE,TSUN)%% This function uses geometrical relations to compute those points
that% are a) directly exposed to the tsunami source and b) within t he% spreading range of the tsunami but shielded by other points (=
bays).%% Create matrix with angles and distances from tsunami sourc e for
each% coastline point and an index that is set to 1 if angles are
between% PROPL and PROPR.AD PS = zeros(MAXSH,5);%% Create distance vectorDUTMYI = SHORE(:,4) − TSUN(3);DUTMXI = SHORE(:,5) − TSUN(4);AD PS(:,1) = sqrt(DUTMYI(:).ˆ2 + DUTMXI(:).ˆ2);%
95
% Create angle vector; angle between tsunami propagation di rectionand
% line linking tsunami source and coastpoint.% This equation:% ADPS(:,2) = acos((DUTMXI(:). * cos(PROP) + DUTMYI(:). * sin(PROP))./
AD PS(:,1));% only works when zero angle is positive Easting. Calculatin g angle% between defined zero angle and tsunami source/coastpoint and% subtracting propagation direction yields immediate resu lts
anytime.AD PS(:,2) = acos((ZERO(1) * DUTMXI(:) + ZERO(2) * DUTMYI(:))./(sqrt(ZERO
* ZERO') * (AD PS(:,1)))) − PROP;%% Create vector that contains all indices of coastpoints wit hin the% spreading angleCST SE = find(abs(AD PS(:,2)) <= SPRD);AD PS(CST SE,3) = 1;%if numel(CST SE) == 0
C EXP = [];else
% Find first and last coastpoint within this range and add onepoint on
% each side to make creation of segments possibleif CST SE(1) > 1
CST SE(1) = CST SE(1) − 1;endif CST SE(length(CST SE)) < MAXSH
CST SE(length(CST SE)) = CST SE(length(CST SE)) + 1;end%% Calculate number of segments neededINC N = CSTSE(length(CST SE)) − CST SE(1);%% Extract relevant shoreline and relevant calculation matr ix to
decrease% computation timesCST M = SHORE(CSTSE(1):CST SE(length(CST SE)),:);AD PS = ADPS(CST SE(1):CST SE(length(CST SE)),:);%% Create a matrix with coastline segments, defined by every t wo
adjacent% coastal datapoints (ANG I 1, ANG I 2, AVG−DIST)INCS = zeros(INC N,3);for i = 1:INC N
INCS(i,1) = min(AD PS(i,2),AD PS(i+1,2));INCS(i,2) = max(AD PS(i,2),AD PS(i+1,2));INCS(i,3) = (AD PS(i,1) + AD PS(i+1,1))/2;
end%% Now, every point in AD PS is assigned a 0 value if it is
shielded by a
96
% segment (i.e., if it lies in the angle range of a segment andhas a
% higher distance); use elementwise logicals in find comman d(&, not &&)
for i = 1:(INC N+1)DIS I = AD PS(i,1);ANGI = AD PS(i,2);SHDI = find((INCS(:,1) < ANGI) & (INCS(:,2) > ANGI) & (
INCS(:,3) < DIS I));if isempty(SHD I) == 1
AD PS(i,4) = 1;else
AD PS(i,4) = 0;endAD PS(i,5) = AD PS(i,3) * AD PS(i,4);
end%% Every point in the AD PS matrix has now 0 − and/or 1 −values in
those two% columns 3 and 4. If a 0 occurs in the third column, the point
is out of% range and can now be deleted. If a 0 occurs in the fourth
column, the% point is shielded by a segment and cannot be hit.%% Those points at the top and bottom of the matrix that exhibit
at least% one zero value, can be deleted. However, points in the matri x
that% exhibit a zero value but have valid points before and after,
should be% kept, as these denote a bay that could be affected by rising
water% levels as well.BNDT = find(AD PS(:,5), 1, 'first' );BNDB = find(AD PS(:,5), 1, 'last' );CST M = CSTM(BND T:BND B,:);AD PS = ADPS(BND T:BND B,:);CST M(:,6) = AD PS(:,2);CST M(:,7) = AD PS(:,5);C EXP = CSTM;
end%% CEXP contains all points between the leftmost and the rightmo st
point% within the spreading range of the tsunami with direct expos ure to
it.% It also contains the offset angles for each point ( −10 to +10
degs).% Those points that exhibit a zero in the last column will have to
be
97
% assigned interpolated values, or some other technique wil l beused.
fsoil.m
%not changed in 2011function [FIND] = fsoil(S TYP)%% This function returns a failure type, depending on the soil type
of the% point picked for the initial failure depth value. This is ba sed
on the% logic described in the paperwork. Basically, the soil type is an
index% for the slope stability method being used.%% No further explanations required here.%CHIF11 = ceil(rand(1) * 2);CHIF12 = ceil(rand(1) * 3);%% Gravelif S TYP == 2 %
FIND = 1; %>>> Infinite Slope%% Gravel −Sand
elseif S TYP == 3 %FIND = 2; %>>> Infinite Slope%% Sand
elseif S TYP == 4 %FIND = 3; %>>> Infinite Slope%% Clay−Silt/Sand
elseif S TYP == 5 %if CHIF11 == 1 %>>> [Clayey Sand]
FIND = 4; %>>> Infinite Slopeelse %>>> [Silty Sand]
FIND = 5; %>>> Infinite Slopeend %%% Sand−Clay/Silt
elseif S TYP == 6 %if CHIF12 == 1 %>>> [Sandy Silt]
FIND = 6; %>>> Infinte Slopeelseif CHIF12 == 2 %>>> [Silt]
FIND = 7; %>>> Bishopelse %>>> [Clayey Silt]
FIND = 8; %>>> Bishopend %%% Clay
98
elseif S TYP == 7 %FIND = 9; %>>> Bishop%% Sand−Silt/Clay
elseif S TYP == 8 %if CHIF11 == 1 %>>> [Sandy Clay]
FIND = 10; %>>> Bishopelse %>>> [Silty Clay]
FIND = 11; %>>> Bishopend %%% Sand/Silt/Clay
elseif S TYP == 9 %if CHIF12 == 1 %>>> [Sand]
FIND = 12; %>>> Infinite Slopeelseif CHIF12 == 2 %>>> [Silt]
FIND = 13; %>>> Bishopelse %>>> [Clay]
FIND = 14; %>>> Bishopend %
end
ftimeb.m
%not changed in 2011function [POINTS,Hbw] = ftimeb(Tnum, runup, C EXP, PoF, POINTS,SHORE,
nmbCP)
% CEXP = from main code and gives the spread angle from PoF to shor e% runup = Initial Runup matrix (RN UP from main code)% Tnum = Transect #% PoF = point of Faliure (equals IND S from main code)% POINTS = matrix of results based on shoreline points:% point / Sum of Weighted travel time / Sum of runup / Ave Time% {min } / Ave travel Length {m} / Ave Wave Velocity {m/s }%runup(:,5) = C EXP(:,6);runup = runup(:,1:5);Hbw = zeros(1,nmbCP);x = 0;% Constants:g = 9.81; % gravity [m/s2]K = 0.8; % Kappa (from shallow water breaking criteria:
assumed)h min = 65; % Minimum water depth at the end of all transectsm = 1/35; % Slope of the shorefaceN = 100; % Number of segments
% Load transect data:load([ 'datafiles/transect' Tnum]); % corresponds to TS matrix
% Start the determination of runup time for EACH coastal poin t.
99
x = length(runup(:,1));for tab = 1:x
% Determine UTM Coordinates:% SHORELINE POINTYs = SHORE(runup(tab,1),4);Xs = SHORE(runup(tab,1),5);% POINT OF FAILUREYo = TS(PoF,6);Xo = TS(PoF,7);
% Determine TOTAL distance from PoF to Shoreline [Tx]:Tx = (sqrt( ((Xo −Xs)ˆ2) + ((Yo −Ys)ˆ2)));
% Determine the length from failure to end of transect [xt]:xf = TS(PoF,2);
% Determine the distance from end of transect to shore [xl]:xl = Tx − xf;
% Determine the max depth of the nearshore (or shoreface):% assumed to equal the min water depth at the top of all TShs = h min;
% Determine the distance of the shoreface [xs]:xs = hs / m;
% Determine the length of the continental slope [xc]:xc = xl −xs;
% Determine depth to failure [ho]:ho = abs(TS(PoF,3)); % Determined by MC code
% Determine initial tsunami amplitude [Ho]:Ho = runup(tab,4); % Determined by MC code
if Ho>0.02 % Determine travel time for events greater than 0.02m% Determine depth at top of shelf break [hc]:hc = abs(TS(1,3));% Min value at which slope failures can occure (top of shelf
break)
% Determine the slope from end of transect to shoreface [theta] in RADIANS:
theta = atan((hc −hs)/xc);
% Determine the depth for wave breaking point [hb]:hb = (((Ho/K)ˆ4) * ((ho+Ho)/(1+K)))ˆ(1/5);% Equation #25
% Determine the DELTA X intervals [dx]:dx = Tx / N;
100
% Create Vector x(n) from PoF to shore:x = zeros(1,N);for n = 1:N
x(n) = (n) * dx;end
% Create Vector h(n) from PoF to shore:h = zeros(1,N);h(1) = ho;for n = 2:N
if x(n) <= xfh(n) = zone1(TS,xf,x(n));
elseif xf <x(n)&& x(n) <(xf+xc)h(n) = zone2(xf,x(n),theta, hc);
elseh(n) = zone3(xf,xc,x(n),hs,m);
endend
% Determine distance from PoF to breaking [xb]:index = find(h >hb);xin = max(index);if xin == length(h);
lastx = 0; lasth = 0;else
lastx = x(xin+1); lasth = h(xin+1);endy = [h(xin) lasth];z = [x(xin) lastx];xb = interp1(y,z,hb, 'cubic' );dxb1 = xb − lastx;
% Determine wave height [H]H(1) = Ho; % Initial tsunami amlpitudeB = max(find(h(:) > hb));for i = 2:B+1
err =1; pass = 10ˆ −6; Hh = Ho;while err >=pass
H(i) = Ho * (((ho+Ho)/(h(i)+Hh))ˆ(1/4)); % Equation#24
err = abs((H(i) −Hh)/Hh);Hh = H(i);
endenderr = 1; pass = 10ˆ −6;while err >= pass
Hb = Ho * (((ho+Ho) / (hb + Hh))ˆ(1/4));err = abs((Hb −Hh)/Hh);Hh = Hb;
end
101
% Determine the travel time until wave breaking point [t]:t = trapz(dx ./ sqrt(g . * (h(1:B)+H(2:i)) ) ); % Equation
#23t1 = dxb1/sqrt(g * (hb+Hb));t = t + t1;
% Determine the travel time from wave breaking point to shore[tb]:
S = (Tx −xb)/hb;tb = 2 * ((((Tx −xb) * S)/(g * (1+K)))ˆ(1/2)); % Equation #26
% Determine the total travel time [T] in minutes:T = (t + tb)/60; % Equation 27
% Determine weighted time [Tw] and weighted travel distance [Xw]:
Tw = T * Ho;tw = t * Ho / 60;tbw = tb * Ho / 60;Hbw(1,runup(tab,1)) = Hb;Txw = Tx * Ho / 1000;xbw = (Tx −xb) * Ho;
POINTS(runup(tab,1),2) = POINTS(runup(tab,1),2) + Tw;POINTS(runup(tab,1),3) = POINTS(runup(tab,1),3) + Ho;POINTS(runup(tab,1),4) = POINTS(runup(tab,1),4) + tw;POINTS(runup(tab,1),5) = POINTS(runup(tab,1),5) + tbw;POINTS(runup(tab,1),6) = POINTS(runup(tab,1),6) + Txw;POINTS(runup(tab,1),7) = POINTS(runup(tab,1),7) + xbw;
elseend
end
% Determine the average tsunami travel time for each coastal point%for b = 1:nmbCP% if POINTS(b,3)==0% POINTS(b,8) = POINTS(b,8);% POINTS(b,9) = POINTS(b,9);% POINTS(b,10) = POINTS(b,10);% POINTS(b,11) = POINTS(b,11);% POINTS(b,12) = POINTS(b,12);% else% POINTS(b,8) = POINTS(b,2)/POINTS(b,3); % Ave Arrival Tim e
[min]% POINTS(b,9) = POINTS(b,4)/POINTS(b,3); % Ave Time to
Breaker [min]% POINTS(b,10) = POINTS(b,5)/POINTS(b,3); % Ave Time from
breaker to shore [min]% POINTS(b,11) = POINTS(b,6)/POINTS(b,3); % Ave Total
Distance [km]% POINTS(b,12) = POINTS(b,7)/POINTS(b,3); % Ave distance
from Shore to breaker [m]
102
% end%end
%POINTS = POINTS(:,1:12);% End of Subroutine
% Note: The output for this function must be stored into a matr ix of% coastal points affected by the tsunami wave (POINTS) for EA CH% transect BEFORE the main program loops to the next transect . This
must% be done to determine a "weighted" average time (given in min utes)
and a% "weighted" average travel distance.function [h] = zone1(TS,xf,x)index = find(TS(:,2) >(xf −x)); q = min(index);y = [TS(q −1,3) TS(q,3)];y=abs(y);z = [TS(q −1,2) TS(q,2)];h = interp1(z,y,xf −x, 'cubic' );
function [h] = zone2(xf,x,theta, hc)xdif = x −(xf);hdif = xdif * tan(theta);h = hc − hdif;
function [h] = zone3(xf,xc,x,hs,m)xdif = x − (xc+xf);hdif = m * xdif;h = hs − hdif;
103
APPENDIX F
Statistical Analysis
% created by Teresa Krause, May 2011%%this function calculates the joint probabilty of earthqua ke and
slope failure and%does the further statistical analysis
function [] = stat newJoint(nmbTS, nmbCP,nmRunsperts)
N = nmRunsperts ;
numberFailures=0;
MAXMT=1000;T ALL(1)=100;T ALL(2)=500;
for file=1:nmbTSfid = fopen([ 'results500/Data ' num2str(file) '.txt' ], 'r' );RP = textscan(fid, '%f %f %f %f %f %f %f %f %f %f %f %f %f
%f %f %f %f %f' , 'Headerlines' , 0);RP = cell2mat(RP); Q = length(RP); %Rp new variable that contain
textfilefclose(fid);nmbruns=size(RP);
fid2 = fopen([ 'results500/Tsunami ' num2str(file) '.txt' ], 'r' );RP2 = textscan(fid2, '%f %f %f %f %f %f %f %f %f %f %f %f %
f %f %f %f %f %f' , 'Headerlines' , 0);RP2 = cell2mat(RP2); Q = length(RP2); %Rp new variable that
contain textfilefclose(fid2);
TMP=zeros(Q,2);TMP(:,1)=RP(:,13);TMP(:,2)=RP2(:,17);
a=find(TMP(:,1) <=500 & TMP(:,2) >=0.02);
numberFailures=numberFailures+numel(a);
end
% STATISTICAL ANALYSIS CODE
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EQ =500; % input('Enter The earthquake period. \n');psmf=numberFailures/(N * nmbTS) * (1/500);rtn =1/psmf; % input('Enter The SLOPE FAILURE Return Period. \n');
AC = 1/(rtn/100);H1 = zeros(nmbCP,2); H5 = zeros(nmbCP,2); Hm = zeros(nmbCP, 2);eq = int2str(EQ);disp( 'rtn' );disp(rtn);for i = 1:0
MATNUM = N/MAXMT;fname1 = int2str(T ALL(i));start=1;
parfor j = start:nmbCPif (j < 10)
point = [ '000' int2str(j) ];elseif (j > 9) && (j < 100)
point = [ '00' int2str(j) ];elseif (j > 99) && (j < 1000)
point = [ '0' int2str(j) ];else
point = int2str(j);endPROBDIST = zeros(MAXMT,(nmbTS * ceil(MATNUM)));HbDIST = zeros(MAXMT,(nmbTS * ceil(MATNUM)));for k = 1:ceil(MATNUM)
APP = k −1;if (APP < 10)
matnum = [ '000' int2str(APP) ];elseif (APP > 9) && (APP < 100)
matnum = [ '00' int2str(APP) ];elseif (APP > 99) && (APP < 1000)
matnum = [ '0' int2str(APP) ];else
matnum = int2str(APP);endfor index = 1:nmbTS
trnsct = int2str(index);pt = k * index;blu=load([ 'results' fname1 '/temp/' trnsct 'distr'
matnum '.mat' ]);DISTR=blu.DISTR;
bla=load([ 'results' fname1 '/temp/' trnsct 'Hb'matnum '.mat' ]);
Hb=bla.Hb;
PROBDIST(:,pt) = DISTR(:,j);HbDIST(:,pt) = Hb(:,j);
endend
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PROBDIST = sort(nonzeros(PROBDIST(:)), 'descend' );PROBDIST =PROBDIST(PROBDIST>0.02);lp = length(PROBDIST);HbDIST = sort((HbDIST(:)), 'descend' );RP = [];RP = PROBDIST;
%fids = fopen(['results' fname1 '/distributions/point' p oint'.txt'],'wt+');
dist=zeros(lp,2);
for kp = 1:lpRP(kp,1)= PROBDIST(kp);RP(kp,2)= HbDIST(kp);
%fprintf(fids,'%5.2f %9.2f \n',PROBDIST(kp),HbDIST(kp));endname=[ 'results' , fname1, '/distributions/point' , point '.mat'
];fsaveMatHB(name,RP);%fclose(fids);
end
end
parfor i = 1:nmbCPif i < 10
fname = [ '000' int2str(i) ];elseif i > 9 && i < 100
fname = [ '00' int2str(i) ];elseif i > 99 && i < 1000
fname = [ '0' int2str(i) ];else
fname = [ int2str(i) ];end
bla=load([ 'results' fname1 '/distributions/point' fname '.mat' ]);RP=bla.Hb;
if isempty(RP)R1(i) = 0; R5(i) = 0; Rm(i) = 0;
else
Q = length(RP);% fclose(fid);l = find(RP(:,1) >.02); L = max(l); L1 = ceil(.01 * L);rp = RP(1:L,1);if isempty(rp)
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R1(i) = 0; R5(i) = 0; Rm(i) = 0;else
L2 = floor((L1/(AC/0.2))); % 0.2%−annual −chance eventL3 = floor((L1/(AC/1))); % 1%−annual −chance event
if L2>LR1(i) = 0.02; R5(i) = 0.02; Rm(i) = rp(1,1);
elseif (L2 <=L) && (L3 >L)R1(i) = 0.02; R5(i) = rp(L2,1); Rm(i) = rp(1,1);
elseR1(i) = rp(L3);R5(i) = rp(L2); Rm(i) = rp(1);
end% n=n+Q; t=t+L;
endend
end
save([ 'results500/R1.mat' ], 'R1' );save([ 'results500/R5.mat' ], 'R5' );save([ 'results500/Rm.mat' ], 'Rm' );
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APPENDIX G
Evaluation Subroutines
readtxt.m
% created by Teresa Krause, May 2011% place in folder where direction "result500" is saved%%this file reads the saved data files (data 1 to data 91) and draws%diagrams to validate the landslide information by compari ng them
with%observed data%%validated within:%−failure type (rotational, translational)%−volume distribution of failed landslides%−area distribution of failed landslides%−slope angel of failed landslides
close all; clear all;
Ts=91;meanSlopeAngle=zeros(Ts,1);nmbSlopeAngleTooHigh=zeros(Ts,1);meanArea=zeros(Ts,1);meanVolume=zeros(Ts,1);meanThick=zeros(Ts,1);meanWidth=zeros(Ts,1);meanLength =zeros(Ts,1);
nmbRotationalFailures=zeros(Ts,2);nmbTranslationalFailures=zeros(Ts,2);Nr100=0;Nt100=0;Nr500=0;Nt500=0;
failuresWithSLP=zeros(30,4); %okfailuresWithSLPNeu=zeros(30,2);failuresWithArea=zeros(10,2); %okfailuresWithVolume=zeros(10,2); %ok
failuresWithAreaS=zeros(5,2); %okfailuresWithVolumeS=zeros(5,2); %ok
mtokm=1/(1000);m2tokm2=1/(1000 * 1000);
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m3tokm3=1/(1000 * 1000 * 1000);
for file=1:Ts%%%load files
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%fid = fopen([ 'results500/Data ' num2str(file) '.txt' ], 'r' );RP = textscan(fid, '%f %f %f %f %f %f %f %f %f %f %f %f %f
%f %f %f %f %f' , 'Headerlines' , 0);RP = cell2mat(RP); Q = length(RP); %Rp new variable that contain
textfilefclose(fid);nmbruns=size(RP);
index100=find( RP(:,13) <= 100 ); %FOS=RP(:,14)
newRP100=zeros(length(index100),nmbruns(1,2));%length(index100)for o=1:length(index100)
newRP100(o,:)=RP(index100(o,1),:);end
index500=find(RP(:,13) <= 500); %FOS=RP(:,14)%length(index100)newRP500=zeros(length(index500),nmbruns(1,2));for o=1:length(index500)
newRP500(o,:)=RP(index500(o,1),:);end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%number of failurenmbTranslationalFailures(file,1)=length(find(newRP1 00(:,15)==1));
%100nmbRotationalFailures(file,1)=length(find(newRP100( :,15)==2)); %
100
Nr100=Nr100+length(find(newRP100(:,15)==1));Nt100=Nt100+length(find(newRP100(:,15)==2));Nr500=Nr500+length(find(newRP500(:,15)==1));Nt500=Nt500+length(find(newRP500(:,15)==2));
nmbTranslationalFailures(file,2)=length(find(newRP5 00(:,15)==1));%500
nmbRotationalFailures(file,2)=length(find(newRP500( :,15)==2)); %500
%slope angle with failurefor y=1:30
if y==30
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slp1 = find(newRP100(:,7) >=y); %newRP includes just failedslopes
slp2 = find(newRP500(:,7) >=y); %newRP includes just failedslopes
elseslp1 = find(newRP100(:,7)==y); %newRP includes just failed
slopesslp2 = find(newRP500(:,7)==y); %newRP includes just failed
slopesendfailuresWithSLPNeu(y,1)=failuresWithSLPNeu(y,1)+len gth(slp1);failuresWithSLPNeu(y,2)=failuresWithSLPNeu(y,2)+len gth(slp2);
end
%validation area
area100=zeros(length(newRP100(:,4)),1);area100(:,1)=m2tokm2 * times(newRP100(:,4),newRP100(:,3));failuresWithAreaS(1,1) = failuresWithAreaS(1,1) + lengt h(find(
area100 <1));failuresWithAreaS(2,1) = failuresWithAreaS(2,1) + lengt h(find(1 <=
area100 & area100 <10));failuresWithAreaS(3,1) = failuresWithAreaS(3,1) + lengt h(find
(10 <=area100 & area100 <100));failuresWithAreaS(4,1) = failuresWithAreaS(4,1) + lengt h(find
(100 <= area100 & area100 <1000));failuresWithAreaS(5,1) = failuresWithAreaS(5,1) + lengt h(find
(1000 <=area100 ));
area500=zeros(length(newRP500(:,4)),1);area500(:,1)=m2tokm2 * times(newRP500(:,4),newRP500(:,3));failuresWithAreaS(1,2) = failuresWithAreaS(1,2) + lengt h(find(
area500 <1));failuresWithAreaS(2,2) = failuresWithAreaS(2,2) + lengt h(find(1 <=
area500 & area500 <10));failuresWithAreaS(3,2) = failuresWithAreaS(3,2) + lengt h(find
(10 <=area500 & area500 <100));failuresWithAreaS(4,2) = failuresWithAreaS(4,2) + lengt h(find
(100 <= area500 & area500 <1000));failuresWithAreaS(5,2) = failuresWithAreaS(5,2) + lengt h(find
(1000 <=area500 ));%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%area100=zeros(length(newRP100(:,4)),1);area100(:,1)=m2tokm2 * times(newRP100(:,4),newRP100(:,3));failuresWithArea(1,1) = failuresWithArea(1,1) + length( find(
area100 <.1));failuresWithArea(2,1) = failuresWithArea(2,1) + length( find(.1 <=
area100 & area100 <0.5));failuresWithArea(3,1) = failuresWithArea(3,1) + length( find(0.5 <=
area100 & area100 <1));
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failuresWithArea(4,1) = failuresWithArea(4,1) + length( find(1 <=area100 & area100 <5));
failuresWithArea(5,1) = failuresWithArea(5,1) + length( find(5 <=area100 & area100 <10));
failuresWithArea(6,1) = failuresWithArea(6,1) + length( find(10 <=area100 & area100 <50));
failuresWithArea(7,1) = failuresWithArea(7,1) + length( find(50 <=area100 & area100 <100));
failuresWithArea(8,1) = failuresWithArea(8,1) + length( find(100 <=area100 & area100 <500));
failuresWithArea(9,1) = failuresWithArea(9,1) + length( find(500 <=area100 & area100 <1000));
failuresWithArea(10,1) = failuresWithArea(10,1) + lengt h(find(1000 <=area100 ));
area500=zeros(length(newRP500(:,4)),1);area500(:,1)=m2tokm2 * times(newRP500(:,4),newRP500(:,3));failuresWithArea(1,2) = failuresWithArea(1,2) + length( find(
area500 <.1));failuresWithArea(2,2) = failuresWithArea(2,2) + length( find(.1 <=
area500 & area500 <0.5));failuresWithArea(3,2) = failuresWithArea(3,2) + length( find(0.5 <=
area500 & area500 <1));failuresWithArea(4,2) = failuresWithArea(4,2) + length( find(1 <=
area500 & area500 <5));failuresWithArea(5,2) = failuresWithArea(5,2) + length( find(5 <=
area500 & area500 <10));failuresWithArea(6,2) = failuresWithArea(6,2) + length( find(10 <=
area500 & area500 <50));failuresWithArea(7,2) = failuresWithArea(7,2) + length( find(50 <=
area500 & area500 <100));failuresWithArea(8,2) = failuresWithArea(8,2) + length( find(100 <=
area500 & area500 <500));failuresWithArea(9,2) = failuresWithArea(9,2) + length( find(500 <=
area500 & area500 <1000));failuresWithArea(10,2) = failuresWithArea(10,2) + lengt h(find
(1000 <=area500 ));
%validation volumevolume100=zeros(length(nonzeros(newRP100(:,18). * newRP100(:,4)))
,1);volume100(:,1)=m3tokm3 * nonzeros(newRP100(:,18). * newRP100(:,4));failuresWithVolumeS(1,1) = failuresWithVolumeS(1,1) + l ength(find
(volume100 <0.1));failuresWithVolumeS(2,1) = failuresWithVolumeS(2,1) + l ength(find
(0.1 <=volume100 & volume100 <1));failuresWithVolumeS(3,1) = failuresWithVolumeS(3,1) + l ength(find
(1 <=volume100 & volume100 <10));failuresWithVolumeS(4,1) = failuresWithVolumeS(4,1) + l ength(find
(10 <= volume100 & volume100 <100));
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failuresWithVolumeS(5,1) = failuresWithVolumeS(5,1) + l ength(find(100 <=volume100 ));
volume500=zeros(length(nonzeros(newRP500(:,18). * newRP500(:,4))),1);
volume500(:,1)=m3tokm3 * nonzeros(newRP500(:,18). * newRP500(:,4));failuresWithVolumeS(1,2) = failuresWithVolumeS(1,2) + l ength(find
(volume500 <0.1));failuresWithVolumeS(2,2) = failuresWithVolumeS(2,2) + l ength(find
(0.1 <=volume500 & volume500 <1));failuresWithVolumeS(3,2) = failuresWithVolumeS(3,2) + l ength(find
(1 <=volume500 & volume500 <10));failuresWithVolumeS(4,2) = failuresWithVolumeS(4,2) + l ength(find
(10 <= volume500 & volume500 <100));failuresWithVolumeS(5,2) = failuresWithVolumeS(5,2) + l ength(find
(100 <=volume500 ));
end%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%chaytor area and volume observedchaytorS2=zeros(5,2); %SBCT + CTchaytorS2(:,1)=[1 * 100/25 3 * 100/25 8 * 100/25 10 * 100/25 3 * 100/25]; %s 21
a areachaytorS2(:,2)=[4 * 100/24 6 * 100/24 9 * 100/24 2 * 100/24 3 * 100/24]; %s 21 b
volumechaytorS=zeros(5,2); %allchaytorS(:,1)=[1 * 100/107 31 * 100/107 45 * 100/107 27 * 100/107 3 * 100/107];
%s 21 a areachaytorS(:,2)=[19 * 100/104 41 * 100/104 34 * 100/104 7 * 100/104 3 * 100/104];
%s 21 b volume
slopeBooth=zeros(30,1);slopeBooth(:,1)=[8 11 18 19 5 8 7 6 4 3 1 1 2 4 3 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 ];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
total100=sum(nmbTranslationalFailures(:,1))+sum(nmb RotationalFailures(:,1)); %just 500 (100 included in 500)
total500=sum(nmbTranslationalFailures(:,2))+sum(nmb RotationalFailures(:,2)); %just 500 (100 included in 500)
total100Area=sum(failuresWithAreaS(:,1));total500Area=sum(failuresWithAreaS(:,2));
total100Volume=sum(failuresWithVolumeS(:,1));total500Volume=sum(failuresWithVolumeS(:,2));
112
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure (1)Matrix=zeros(30,3);Matrix(:,1)=((failuresWithSLPNeu(:,1))/(sum(failure sWithSLPNeu(:,1)))
) * 100;Matrix(:,2)=((failuresWithSLPNeu(:,2))/(sum(failure sWithSLPNeu(:,2)))
) * 100;Matrix(:,3)=slopeBooth(:,1);bar(Matrix, 'grouped' );legend( 'MCS 100 years ' , 'MCS 500 years' , 'Booth 1993' )xlabel( 'Slope angle [deg.]' )ylabel( 'Failures [%]' )grid onhold on;
figure (2)Matrix=zeros(5,4);Matrix(:,1)=(failuresWithAreaS(:,1)./(total100Area) ) * 100;Matrix(:,2)=(failuresWithAreaS(:,2)./(total500Area) ) * 100;Matrix(:,3)=chaytorS(:,1);bar(Matrix, 'grouped' );legend( 'MCS 100 years ' , 'MCS 500 years' , 'observed' ); %, 'SBCT + CT')set(gca, 'XTickLabel' , {' <1' , '1 −10' , '10 −100' , '100 −1000' , ' >1000' });xlabel( 'A [km2]' )ylabel( 'Failures [%]' )grid onhold on;
figure (3)Matrix=zeros(5,4);Matrix(:,1)=(failuresWithVolumeS(:,1)/(total100Volu me)) * 100;Matrix(:,2)=(failuresWithVolumeS(:,2)/(total500Volu me)) * 100;Matrix(:,3)=chaytorS(:,2);bar(Matrix, 'grouped' );legend( 'MCS 100 years ' , 'MCS 500 years' , 'observed' ); %, 'SBCT + CT')set(gca, 'XTickLabel' , {' <0.1' , '0.1 −0.5' , '0.5 −1' , '1 −5' , '5 −10' , '10 −50' , '
50−100' , '100 −500' , '500 −1000' , ' >1000' });xlabel( 'V [km3]' )ylabel( 'Failures [%]' )grid onhold on;
figure (4)Matrix2=zeros(2,3);Matrix2(1,1)=Nt100/(Nt100+Nr100) * 100%(sum(nmbTranslationalFailures
(:,1)) * 100/total100);%erste zeile is 100 yr, transMatrix2(2,1)=Nr100/(Nr100+Nt100) * 100%(sum(nmbRotationalFailures(:,1))
* 100/total100);%rotMatrix2(1,2)=Nt500/(Nt500+Nr500) * 100%(sum(nmbTranslationalFailures
(:,2)) * 100/total500);%zweite zeile is 500 yr,trans failure
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Matrix2(2,2)=Nr500/(Nt500+Nr500) * 100%(sum(nmbRotationalFailures(:,2))
* 100/total500);%rotMatrix2(1,3)=57 ;Matrix2(2,3)=43 ;bar(Matrix2, 'grouped' ); %bei einer 2x2 matrix plotetd bar()
zeilenweise * (nicht, wie vermutet spaltenweise)legend( 'MCS 100 years ' , 'MCS 500 years' , 'observed' )set(gca, 'XTickLabel' , {'Translational' , 'Rotational' });ylabel( 'Total Failures [%]' )grid onhold on;
% %% %% %%
getVolumeFromRunup.m
% created by Teresa Krause, May 2011% this file reads saved datafiles to find the design landslid e that
caused% the design runup%% transect 72 has not the expected number of runs and cannot% be evaluated in any further, this points to a problem in the c ode!close all; clear all;
load( 'results500/R5.mat' );nmbTS=91;nmbCP=3510;m2km=1/1000;nmbRuns=15000;maxDistr=1000;nmbDistrFiles=nmbRuns/maxDistr;
landslideRot=zeros(nmbCP,8);tsAffectingCPRot=zeros(nmbCP,nmbTS);landslide=zeros(nmbCP,8); %transtsAffectingCP=zeros(nmbCP,nmbTS);
a=0;
for t=1:nmbTSdisp(t);if t˜=72 %problem, see first lines
for distr=0:nmbDistrFiles −1if (distr < 10)
matnum = [ '000' int2str(distr) ];elseif (distr > 9) && (distr < 100)
matnum = [ '00' int2str(distr) ];
114
elseif (distr > 99) && (distr < 1000)matnum = [ '0' int2str(distr) ];
elsematnum = int2str(distr);
end
trnsct = int2str(t);num2str fname1;
load([ 'results500 \temp \' trnsct 'distr' matnum '.mat' ]);
fid = fopen([ 'results500 \Data ' num2str(trnsct) '.txt' ], 'r' );
ts = textscan(fid, '%f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f %f' , 'Headerlines' , 0);
ts = cell2mat(ts); Q = length(ts); %Rp new variable thatcontain textfile
fclose(fid);
if t <45a=1;e=1000;
elsea=900;e=nmbCP;
end
nmbRuns=size(DISTR);
%sum values upfor c=a:e %1:nmbCP%a:e%geht ueber gesamte x der datei
DISTRtsunami=round(R5(1,c) * 100)/100;
whichCP=c;for d=1:nmbRuns(1,1) %dimDistr
if DISTR(d,c)˜=0wavesTs=round(DISTR(d,c) * 100)/100;
if wavesTs==tsunami && R5(1,c)˜=0 && ts((d+(distr) * 1000),14)==1%disp(wavesTs);a=10;if ts(d,15)==2 %rotational
%whichCP=c;tsAffectingCPRot(whichCP,t)=
tsAffectingCPRot(whichCP,t)+1;
115
landslideRot(whichCP,1)=landslideRot(whichCP,1)+(ts((d+(distr) * 1000),3)); %l
landslideRot(whichCP,2)=landslideRot(whichCP,2)+ts((d+(distr) * 1000),4);%w
landslideRot(whichCP,3)=landslideRot(whichCP,3)+ts((d+(distr) * 1000),5);%t
landslideRot(whichCP,4)=landslideRot(whichCP,4)+ts((d+(distr) * 1000),7);%slp
landslideRot(whichCP,5)=landslideRot(whichCP,5)+(ts((d+(distr) * 1000),18). * ts((d+(distr) * 1000),4)); %volume
landslideRot(whichCP,6)=landslideRot(whichCP,6)+ts((d+(distr) * 1000),6);%wd−− water depth
landslideRot(whichCP,7)=landslideRot(whichCP,7)+ts((d+(distr) * 1000),16); %lat
landslideRot(whichCP,8)=landslideRot(whichCP,8)+ts((d+(distr) * 1000),17); %long
else %translationaltsAffectingCP(whichCP,t)=
tsAffectingCP(whichCP,t)+1;landslide(whichCP,1)=landslide(
whichCP,1)+(ts((d+(distr) * 1000),3)); %l
landslide(whichCP,2)=landslide(whichCP,2)+ts((d+(distr) * 1000),4);%w
landslide(whichCP,3)=landslide(whichCP,3)+ts((d+(distr) * 1000),5);%t
landslide(whichCP,4)=landslide(whichCP,4)+ts((d+(distr) * 1000),7);%slp
landslide(whichCP,5)=landslide(whichCP,5)+(ts((d+(distr) * 1000),18). * ts((d+(distr) * 1000),4)); %volume
landslide(whichCP,6)=landslide(whichCP,6)+ts((d+(distr) * 1000),6);%wd−− water depth
landslide(whichCP,7)=landslide(whichCP,7)+ts((d+(distr) * 1000),16); %lat
landslide(whichCP,8)=landslide(whichCP,8)+ts((d+(distr) * 1000),17)
116
; %long
end
end
endend
endend
endend
%take averagefor e=1:nmbCP
notZeroRot=sum(tsAffectingCPRot(e,:));if notZeroRot==0
notZeroRot=1;endlandslideRot(e,1)=landslideRot(e,1) * m2km/notZeroRot; %llandslideRot(e,2)=landslideRot(e,2) * m2km/notZeroRot; %wlandslideRot(e,3)=landslideRot(e,3) * m2km/notZeroRot; %tlandslideRot(e,4)=landslideRot(e,4)/notZeroRot; %slplandslideRot(e,5)=landslideRot(e,5) * m2km* m2km* m2km/notZeroRot; %
volumelandslideRot(e,6)=landslideRot(e,6)/notZeroRot; %wdlandslideRot(e,7)=landslideRot(e,7)/notZeroRot; %latlandslideRot(e,8)=landslideRot(e,8)/notZeroRot; %long
notZero=sum(tsAffectingCP(e,:));if notZero==0
notZero=1;endlandslide(e,1)=landslide(e,1) * m2km/notZero; %llandslide(e,2)=landslide(e,2) * m2km/notZero; %wlandslide(e,3)=landslide(e,3) * m2km/notZero; %tlandslide(e,4)=landslide(e,4)/notZero; %slplandslide(e,5)=landslide(e,5) * m2km* m2km* m2km/notZero; %volumelandslide(e,6)=landslide(e,6)/notZero; %wdlandslide(e,7)=landslide(e,7)/notZero; %latlandslide(e,8)=landslide(e,8)/notZero; %long
end
%delete coastal point 800 to 1100, since these coastal point s havenot tunup and are duplicative
designLandslideRot=zeros((nmbCP −300),8);designLandslideTrans=zeros((nmbCP −300),8);for i=1:nmbCP
if i <800
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designLandslideRot(i,:)=landslideRot(i,:);designLandslideTrans(i,:)=landslide(i,:);
elseif i >1100designLandslideRot((i −300),:)=landslideRot(i,:);designLandslideTrans((i −300),:)=landslide(i,:);
else%between 800 and 1100 − do nothing!
endend
designL(:,1)=designLandslideRot(:,1);designL(:,2)=designLandslideTrans(:,1);save([ 'results500 \designL.mat' ], 'designL' );designW(:,1)=designLandslideRot(:,2);designW(:,2)=designLandslideTrans(:,2);save([ 'results500 \designW.mat' ], 'designW' );designT(:,1)=designLandslideRot(:,3);designT(:,2)=designLandslideTrans(:,3);save([ 'results500 \designT.mat' ], 'designT' );designSLP(:,1)=designLandslideRot(:,4);designSLP(:,2)=designLandslideTrans(:,4);save([ 'results500 \designSLP.mat' ], 'designSLP' );designVolume(:,1)=designLandslideRot(:,5);designVolume(:,2)=designLandslideTrans(:,5);save([ 'results500 \designVolume.mat' ], 'designVolume' );designWD(:,1)=designLandslideRot(:,6);designWD(:,2)=designLandslideTrans(:,6);save([ 'results500 \designWD.mat' ], 'designWD' );%save coordinatesdesignCoordR(:,1)=designLandslideRot(:,7); %latdesignCoordR(:,2)=designLandslideRot(:,8); %longsave([ 'results500 \designCoordRot.mat' ], 'designCoordR' );designCoordT(:,1)=designLandslideTrans(:,7); %latdesignCoordT(:,2)=designLandslideTrans(:,8); %longsave([ 'results500 \designCoordTrans.mat' ], 'designCoordT' );
figure (1)subplot(1,2,1)%Matrix=zeros(nmbCP,1);Matrix(:,1)=designLandslideRot(:,1). * designLandslideRot(:,2);bar(Matrix);xlabel( 'Coastline N −S' )ylabel( 'Area of rotational design landslides [km2]' )grid onhold on;subplot(1,2,2)Matrix(:,1)=designLandslideTrans(:,1). * designLandslideTrans(:,2);bar(Matrix);xlabel( 'Coastline N −S' )ylabel( 'Area of translational design landslides [km2]' )grid on
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hold on;
figure (4)subplot(1,2,1)Matrix(:,1)=designLandslideRot(:,5);bar(Matrix);xlabel( 'Coastline N −S' )ylabel( 'Volume of rotational design landslides [km3]' )grid onhold on;
subplot(1,2,2)Matrix(:,1)=designLandslideTrans(:,5);bar(Matrix);xlabel( 'Coastline N −S' )ylabel( 'Volume of translational design landslides [km3]' )grid onhold on;
figure (3)subplot(1,2,1)Matrix(:,1)=designLandslideRot(:,4);bar(Matrix);xlabel( 'Coastline N −S' )ylabel( 'Slope angle of rotational design landslides [degree]' )grid onhold on;
subplot(1,2,2)Matrix(:,1)=designLandslideTrans(:,4);bar(Matrix);xlabel( 'Coastline N −S' )ylabel( 'Slope angle of translational design landslides [degree]' )grid onhold on;%
cumulativeFrequPrint.m
%august 2001, bby Teresa Krause% this prints the cumulative frequency functions of the inpu t
parameters,% requiremetn: run cumulativeFrequ.m%(cumulativeFrequ.m: combines all depth, density, length information
to one file each)close all;
load( 'results500 \validation \dnstlower.mat' );load( 'results500 \validation \dnstupper.mat' );load( 'results500 \validation \lngth' );load( 'results500 \validation \dpth' );
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load( 'results500 \validation \phi' );load( 'results500 \validation \s' );
% figure(1)% normplot(lngth);% ylabel('P [ −]')% xlabel('length')% view(90, −90)% grid on% hold on;%%%% figure(2)% normplot(dpth);% ylabel('P [ −]')% xlabel('depth')% %view(90, −90)% hold on;%% figure(3)% normplot(dnstupper);% ylabel('P [ −]')% xlabel('density')% view(90, −90)% hold on;%% figure(4)% normplot(dnstlower);% ylabel('P [ −]')% xlabel('density')% view(90, −90)% hold on;% %%%%%%%%%%%%%%%%%%%%% figure(4)% normplot(phi);% ylabel('P [ −]')% xlabel('phi')% view(90, −90)% hold on;%% figure(5)% normplot(s);% ylabel('P [ −]')% xlabel('s')% view(90, −90)
% load(['results500 \distributions \point0700.mat']);% figure% normplot(log(Hb(:,1)));% %normplot((Hb(:,1)));
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% ylabel('P [ −]')% xlabel('runup')% view(90, −90)%% load(['results500 \distributions \point1300.mat']);% figure% normplot(log(Hb(:,1)));% %normplot((Hb(:,1)));% ylabel('P [ −]')% xlabel('runup')% view(90, −90)% load(['results500 \distributions \point1700.mat']);%% figure% normplot(log(Hb(:,1)));% %normplot((Hb(:,1)));% ylabel('P [ −]')% xlabel('runup')% view(90, −90)
% logData=(lngth);%already log% logData=(dpth);%lgnormal% logData=(dnstupper);% logData=(dnstlower);
%% bins=100;% probabilityBin=zeros(bins,1);% binValues=zeros(bins,1);% logData=sort(logData,'ascend');%% maxData=logData(1,length(logData));% minData=logData(1,1);%% width=(maxData −minData)/bins;%% if width˜=0%% for b=1:bins% binValues(b,1)=minData+(width/2)+(b −1) * width;% end
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%% for r=1:length(logData)%% bin=round((logData(r) −minData)/width);% if bin >bins% bin=bins;% elseif bin <1% bin=1;% end%% probabilityBin(bin,1)=probabilityBin(bin,1)+1;% end%% probabilityBin(:,1)=probabilityBin(:,1)./sum(proba bilityBin
(:,1)) /width;%%% [mu,sigma]=normfit(logData);%%% prediction=normpdf(binValues,mu,sigma);%normpdf(lo g−values)
=lognpdf(values)% meanDensity=mean(probabilityBin(:,1));% %%%%%%%%%%%%%%%%%%%%%%%%% % histfit(prediction,50,'normal');%%%% resid = probabilityBin − prediction; %
residuals − measure of mismatch% SSE = sum(resid.ˆ2) ;
% variation NOTaccounted for
%% dev = probabilityBin − meanDensity ;
% deviations − measure of spread% SST = sum(dev.ˆ2);%% RSQ = 1− SSE/SST;
% percent of errorexplained
% RSQ% %coastRunupR2(c,1)=RSQ;% end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%nmbCP=3510;coastRunupR2=zeros(nmbCP,1);coastRunupR2woGap=zeros(nmbCP −300,1);%for c=1700:1700
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for c=1:nmbCP%if c <800 | | c>1200if (c < 10)
matnum = [ '000' int2str(c) ];elseif (c > 9) && (c < 100)
matnum = [ '00' int2str(c) ];elseif (c > 99) && (c < 1000)
matnum = [ '0' int2str(c) ];else
matnum = int2str(c);end
load([ 'results500 \distributions \point' matnum '.mat' ]);
if isempty(Hb)
elselogRunup=log(Hb(:,1));%logRunup=(Hb(:,1));
bins=100;probabilityBin=zeros(bins,1);runupBins=zeros(bins,1);
logRunup=sort(logRunup, 'ascend' );
maxRunup=logRunup(length(logRunup),1);minRunup=logRunup(1,1);
runupWidth=(maxRunup −minRunup)/bins;
if runupWidth˜=0
for b=1:binsrunupBins(b,1)=minRunup+(runupWidth/2)+(b −1) *
runupWidth;end
for r=1:length(logRunup)
bin=round((logRunup(r) −minRunup)/runupWidth);if bin >bins
bin=bins;elseif bin <1
bin=1;end
probabilityBin(bin,1)=probabilityBin(bin,1)+1;
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end
probabilityBin(:,1)=probabilityBin(:,1)./sum(probabilityBin(:,1)) /runupWidth;
[mu,sigma]=normfit(logRunup);
prediction=normpdf(runupBins,mu,sigma);
meanDensity=mean(probabilityBin(:,1));
resid = probabilityBin − prediction ; %residuals − measure of mismatch
SSE = sum(resid.ˆ2) ;% variation
NOT accounted for
dev = probabilityBin − meanDensity ;% deviations − measure of
spreadSST = sum(dev.ˆ2);
RSQ = 1− SSE/SST;% percent
of error explained
coastRunupR2(c,1)=RSQ;
endend
end
% delete gapfor i=1:nmbCP
if i <800coastRunupR2woGap(i,:)=coastRunupR2(i,:);
elseif i >1100coastRunupR2woGap((i −300),:)=coastRunupR2(i,:);
else%between 800 and 1100 − do nothing!
endend
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numel(find(coastRunupR2 <0))coastRunupR2=coastRunupR2(find(coastRunupR2));
mean(coastRunupR2(find(coastRunupR2 >0)))
cumulativeFrequ.m
%august 2001, bby Teresa Krause% combines all depth, density, length information to one fil e each so
that% the cumulative frequency distribution can be printedclose all;close all;clear all;nmbTS=91;nmbCP=3210;runups=zeros(1,15000 * 91);lngth=zeros(1,15000 * 91); %length alls=zeros(1,15000 * 91);phi=zeros(1,15000 * 91);dnstupper=zeros(1,15000 * 91);dnstlower=zeros(1,15000 * 91);dpth=zeros(1,15000 * 91);
%density of ALLfor t=1:nmbTS
if t˜=72 && t˜=2% load(['results500 \temp \' trnsct 'distr' matnum '.mat']);
fid = fopen([ 'results500 \Data ' num2str(t) '.txt' ], 'r' );ts = textscan(fid, '%f %f %f %f %f %f %f %f %f %f %f %f
%f %f %f %f %f %f' , 'Headerlines' , 0);ts = cell2mat(ts); Q = length(ts); %Rp new variable that
contain textfilefclose(fid);
fid = fopen([ 'results500 \Tsunami ' num2str(t) '.txt' ], 'r' );rp = textscan(fid, '%f %f %f %f %f %f %f %f %f %f %f %f
%f %f %f %f %f' , 'Headerlines' , 0);rp = cell2mat(rp); Q = length(rp); %Rp new variable that
contain textfilefclose(fid);
rho=(ts(:,8)); %.* (ts(:,3). * ts(:,4). * ts(:,5))./(1000 * 1000 * 1000));
for i=((ts −1) * 15000)+1:((ts −1) * 15000+15000)s(1,i)=ts(i −((t −1) * 15000),12);phi(1,i)=ts(i −((t −1) * 15000),11);
% dnst(1,i)=rho(i −((t −1) * 15000),1);
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dpth(1,i)=ts(i −((t −1) * 15000),6);lngth(1,i)=ts(i −((t −1) * 15000),3);
end
%densityif t <=45
for i=((ts −1) * 15000)+1:((ts −1) * 15000+15000)dnstupper(1,i)=rho(i −((t −1) * 15000),1);
endelse
for i=((ts −1) * 15000)+1:((ts −1) * 15000+15000)dnstlower(1,i)=rho(i −((t −1) * 15000),1);
endend
endenddnstupper = dnstupper(find(dnstupper));dnstlower = dnstlower(find(dnstlower));
s = s(find(s));phi = phi(find(phi));dpth = log(dpth(find(dpth)));lngth = log(lngth(find(lngth)));
save( 'results500 \validation \dnstlower' , 'dnstlower' );save( 'results500 \validation \dnstupper' , 'dnstupper' );save( 'results500 \validation \s' , 's' );save( 'results500 \validation \phi' , 'phi' );save( 'results500 \validation \dpth' , 'dpth' );save( 'results500 \validation \lngth' , 'lngth' );
126
APPENDIX H
Validation of Input parameters and runup
This chapter shows the validation of input parameters used in the Monte Carlo
model. Fig. H.40 to H.44 show the cumulative frequency distributions of the slide
depth, length, density and runup on one coastal point. All figures also present
a fitted log-normal and/or normal distribution. It is shown that the slide depth,
length, and runup data is log-normally distributed and the density is normally
distributed. Fig. H.45 shows the coefficient of determination R2 for each coastal
point.
5 5.5 6 6.5 7 7.5 8
0.0010.003
0.010.020.050.10
0.25
0.50
0.75
0.900.950.980.99
0.9970.999
depth
P [−
]
Normal Probability Plot
Figure H.40. Cumulative frequency distribution compared to log-normal distribu-tion fit (R2=0.9762) of the randomly generated slide depth input parameter.
127
6.5
7
7.5
8
8.5
9
9.5
10
10.5
0.0010.0030.010.020.050.10 0.25 0.50 0.75 0.900.950.980.990.9970.999
leng
th
P [−]
Normal Probability Plot
Figure H.41. Cumulative frequency distribution compared to log-normal distribu-tion fit (R2=0.6012) of the randomly generated slide length input parameter.
1600
1650
1700
1750
1800
1850
1900
1950
0.0010.0030.010.020.050.10 0.25 0.50 0.75 0.900.950.980.990.9970.999
dens
ity
P [−]
Normal Probability Plot
Figure H.42. Cumulative frequency distribution compared to normal distributionfit (R2=0.9358) of the randomly generated slide density input parameter for thenorthern 45 transect.
128
1350
1400
1450
1500
1550
1600
0.0010.0030.010.020.050.10 0.25 0.50 0.75 0.900.950.980.990.9970.999
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F igure H.44. Cumulative frequency distribution compared to log- nor mal distribu-
tion fit(R2=0.7207)of the calculated runup atcoastal point 700. 129
500 1000 1500 2000 25000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Coastal Points [−]
R2
Figure H.45. Coefficient of determination R2 for a log-normal distribution fitto the cumulative frequency distribution of runup values at each coastal point
(R2
=0.4664).
130
BIBLIOGRAPHY
[1] S. Maretzki, “Numerical Simulation of Tsunami Hazard Maps for the U.S.East Coast,” Master’s thesis, University of Rhode Island, 2006.
[2] O.-D. S. Taylor, “Probabilistic Tsunami Hazard Assessment for the NortheastUnited States,” Master’s thesis, University of Rhode Island, 2008.
[3] S. Grilli, C. Baxter, O. Taylor, and S. Maretzki, “A probabilistic approach fordetermining submarine landslide tsunami hazard along the upper east coastfor the United States,” Marine Geology, vol. 264, 2009.
[4] S. Grilli and P. Watts, Eds., Modeling of tsunami generation by an underwaterlandslide in a 3D-NWT., vol. 3. 11th Offshore and Polar Engng Conf, 2001.
[5] S. Grilli, S. Vogelmann, and P. Watts, “Development of an 3D NumericalWave Tank for modeling tsunami generation by underwater landslides,” eng.Anal. Bound. Elem., vol. 26 (4), pp. 301–313, 2002.
[6] S. Grilli and P. Watts, “Tsunami generation by submarine mass failure. I.modeling, experimental validation, and sensitivity analysis,” J. Waterw. PortCoast, vol. 131 (6), pp. 283–297, 2005.
[7] D. C. Twichell, J. D. Chaytor, U. S. ten Brink, and B. Buczkowski, “Morphol-ogy of late Quaternary submarine landslides along the U.S. Atlantic,” MarineGeology, vol. 264, pp. 4–15, 2009.
[8] J. D. Chaytor, U. S. ten Brink, A. R. Solow, and B. D. Andrews, “Sizedistribution of submarine landslides along the U.S. Atlantic margin,” MarineGeology, vol. 264, pp. 16–27, 2009.
[9] J. Locat, H. Lee, U. S. ten Brink, D. C. Twichell, E. L. Geist, and M. San-soucy, “Geomorphology, stability and mobility of the Currituck slide,” MarineGeology, vol. 264, pp. 28–40, 2009.
[10] H. J. Lee, “Timing of occurrence of large submarine landslides on the AtlanticOcean margin,” Marine Geology, vol. 264, 2009.
[11] CONMAPSG: Continental Margin Mapping (CONMAP) sediments grainsizedistribution for the United States East Coast Continental Margin: Open-FileReport 2005-1001, U.S. Geological Survey Std.
[12] “Transverse Mercator Pojection.” Accessed June 13 2011. [Online]. Available:http://georeference.org/doc/universal transverse mercator utm .htm
131
[13] J. Booth, D. O’Leary, P. Popenoe, and W. Danforth, “U.S. Atlantic continen-tal slope landslides: their distribution, general attibutes, and implications.” inSubmarine Landslides: Selected Studies in the U.S. Exclusive Economic Zone,Schwab, Lee, and Twichell, Eds., no. 2002. U.S. Geological Survey, 1993, pp.14–22.
[14] U. S. ten Brink, H. J. Lee, E. Geist, and D. Twichell, “Assessment of tsunamihazard to the U.S. East Coast using relationships between submarine land-slides and earthquakes,” Marine Geology, vol. 264, pp. 65–73, 2009.
[15] E. L. Geist and T. Parsons, “Assessment of source probabilities for potentialtsunamis affecting the U.S. Atlantic coast,” Marine Geology, vol. 264, pp.98–108, 2009.
[16] E. L. Geist, P. J. Lynett, and J. D. Chaytor, “Hydrodynamic modeling oftsunamis from the Currituck landslide,” Marine Geology, vol. 264, pp. 41–52,2009.
[17] A. S. Nowak and K. R. Collins, Reliability of Structures. McGrawHill, 2000.
[18] “Guidelines and Specifications for Flood Hazard Mapping Partners appendixD: Guidance fro Coastal Flooding Analyses and Mapping,” Federal Emer-gency Management Agency, Tech. Rep., 2003.
[19] “NOAA National Geophysical Data Center, U.S. Coastal Relief Model.”Retrieved January 18 2011. [Online]. Available: http://www.ngdc.noaa.gov/mgg/coastal/crm.html
[20] “U.S. Geological Survey, EGLORIA CNT: US Eastcoast GLO-RIA bathymetry contours.” Accessed January 13 2011. [Online].Available: http://coastalmap.marine.usgs.gov/GISdata/regional/eastcoast/gloria/bathymetry/egloria cnt-faq.htm
[21] M. Somers, R. Carson, J. Revie, R. Edge, B. Barrows, , and A. Andrews,“Gloria II an improved long range sidescan sonar,” Processing of the Instituteof Electrical Engineering on Offshore Instrumentation and Communication,Oceanology International Technical Session J, pp. 16–24, 1978.
[22] “U.S. Geological Survey, Data Earthquake Hazards Program.” Accessed May15 2011. [Online]. Available: http://earthquake.usgs.gov/hazards/products/conterminous/2008/data/
[23] P. Watts, S. Grilli, D. Tappin, and G. Freyer, “Tsunami generation by sub-marine mass failure. II. predictive equations and case studies,” J. Waterw.Port Coast, vol. 131 (6), pp. 298–310, 2005.
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