ArticlePDF Available

Abstract

Breach due to overtopping is the most common failure mode of earthen levees. Historic records and future projections consistently show exacerbating patterns in the frequency and severity of floods in several regions, which can increase the probability of levee overtopping. The main objective of this study is twofold: (1) to present a comprehensive data set of levee overtopping events, and (2) to develop a data-driven model for determining the probability of levee breach due to overtopping that can support risk assessment. For this purpose, we first assessed available performance data to develop a refined data set of 185 riverine levee overtopping events within the portfolio of levee systems maintained by the US Army Corps of Engineers. The data set includes several geometric, geotechnical, and hydraulic variables for each overtopping incident. We then employed the data set along with logistic regression to develop, train and validate a model for calculating the probability of levee breach due to overtopping. Among several variables and functional forms examined, levee construction history, overtopping depth, overtopping duration, embankment erosion resistance, and duration of levee hydraulic loading prior to overtopping were found to be statistically significant, thus were included in the proposed model. The model was validated through k-fold cross validation and tested against a separate performance data set aside for validation purposes. The data set presented in this study can be used for identifying key factors controlling overtopping behavior, validation of model results, and providing new insight into the phenomenon of levee overtopping. The proposed model offers a practical yet robust tool for levee risk analysis that can be readily employed in practice.
Data-Driven Model for Estimating the Probability of
Riverine Levee Breach Due to Overtopping
Stefan Flynn, M.ASCE1; Soroush Zamanian, S.M.ASCE2; Farshid Vahedifard, F.ASCE3;
Abdollah Shafieezadeh, M.ASCE4; and David Schaaf, M.ASCE 5
Abstract: Breach due to overtopping is the most common failure mode of earthen levees. Historic records and future projections consistently
show exacerbating patterns in the frequency and severity of floods in several regions, which can increase the probability of levee overtopping.
The main objective of this study is twofold: (1) to present a comprehensive data set of levee overtopping events, and (2) to develop a data-
driven model for determining the probability of levee breach due to overtopping that can support risk assessment. For this purpose, we first
assessed available performance data to develop a refined data set of 185 riverine levee overtopping eventswithin the portfolio of levee systems
maintained by the US Army Corps of Engineers. The data set includes several geometric, geotechnical, and hydraulic variables for each
overtopping incident. We then employed the data set along with logistic regression to develop, train and validate a model for calculating the
probability of levee breach due to overtopping. Among several variables and functional forms examined, levee construction history, over-
topping depth, overtopping duration, embankment erosion resistance, and duration of levee hydraulic loading prior to overtopping were found
to be statistically significant, thus were included in the proposed model. The model was validated through k-fold cross validation and tested
against a separate performance data set aside for validation purposes. The data set presented in this study can be used for identifying key
factors controlling overtopping behavior, validation of model results, and providing new insight into the phenomenon of levee overtopping.
The proposed model offers a practical yet robust tool for levee risk analysis that can be readily employed in practice. DOI: 10.1061/(ASCE)
GT.1943-5606.0002743.© 2021 American Society of Civil Engineers.
Author keywords: Levees; Levee breach data set; Overtopping; Levee risk analysis; Probabilistic modeling; Logistic regression.
Introduction
Earthen levees are a critical component of flood risk management in
the United States. Over 160,000 km (100,000 mi) of levees protect
the safety and economy of flood-prone areas across the United States
(CRS 2017). The US Army Corps of Engineers (USACE) levee
safety portfolio includes over 24,000 km (15,000 mi) of docu-
mented levee systems as communicated by the National Levee
Database (NLD). More than 14% of USACE levee systems are
classified as having very high, high, or moderate risk (USACE
2021b). Often, high risk levees are associated with high economic
and potential life loss consequences. With over 2,000 systems
contained within the portfolio, the USACE-maintained portion
of the national levee inventory protects a population of nearly
13 million with a property value exceeding $1.3 trillion
(USACE 2021b). According to the American Society of Civil En-
gineers (ASCE) Report Card, identified damages from the recent
2019 flood event in the Midwest exceeded $20 billion with more
than 1,100 km (700 mi) of levee requiring repair (ASCE 2021).
Historic records and projected models consistently show exacer-
bating patterns in the frequency and severity of floods in several
regions (Villarinietal.2011;Mallakpour and Villarini 2015;
Vahedifard et al. 2016,2020;USACE 2018,2021a), which can
increase the probability of levee overtopping and, subsequently,
the risk posed to population and critical economic infrastructure
existing within leveed areas. It is evident that levee performance is
of critical interest to engineers, municipalities, and policy mak-
ers alike.
Levee overtopping is a critical concern for flood risk manage-
ment systems, with breach due to overtopping being the most
common mode of levee failure (Hui et al. 2016;USACE 2018).
In this study, overtopping refers to the static riverine water level
exceeding the elevation of the levee crest. Breach occurs when a
levee gives way, allowing flood water to pass through the barrier
and inundate the leveed area (USACE 2018). In this study breach is
the preferred nomenclature, as opposed to failure, due to the fact
the levee systems are typically not designed to withstand overtop-
ping. Rather, levees are designed to withstand hydraulic loads up to
a specified design height. Failure implies that a levee has failed to
perform as designed, whereas breach implies that a levee failed at
loading beyond its designed capacity.
1Geotechnical Engineer, US Army Corps of Engineers, Rock Island
District, 1500 Rock Island Dr., Rock Island, IL 61201; formerly, Graduate
Student, Richard A. Rula School of Civil and Environmental Engineering,
Mississippi State Univ., Mississippi State, MS 39762. ORCID: https://
orcid.org/0000-0003-1241-3681. Email: Stefan.G.Flynn@usace.army.mil
2Asset Management Analyst, Hazen and Sawyer, 7700 Irvine Center
Dr., Irvine, CA 92615; formerly, Graduate Research Associate, Dept. of
Civil, Environmental, and Geodetic Engineering, Ohio State Univ.,
Columbus, OH 43210. Email: zamanian.2@osu.edu
3CEE Advisory Board Endowed Professor and Professor, Richard A.
Rula School of Civil and Environmental Engineering, Mississippi State
Univ., Mississippi State, MS 39762 (corresponding author). ORCID:
https://orcid.org/0000-0001-8883-4533. Email: farshid@cee.msstate.edu
4Lichtenstein Associate Professor, Dept. of Civil, Environmental, and
Geodetic Engineering, Ohio State Univ., Columbus, OH 43210. Email:
shafieezadeh.1@osu.edu
5Senior Structural Engineer, Risk Management Center, US Army Corps
of Engineers, Lakewood, CO 80228. Email: David.M.Schaaf@usace
.army.mil
Note. This manuscript was submitted on April 14, 2021; approved on
October 22, 2021; published online on December 21, 2021. Discussion per-
iod open until May 21, 2022; separate discussions must be submitted for
individual papers. This paper is part of the Journal of Geotechnical and
Geoenvironmental Engineering, © ASCE, ISSN 1090-0241.
© ASCE 04021193-1 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
When a levee gives way after being overtopped, the flow
through the breach can be substantial, as a river attempts to drain
through the now-available opening. For a levee to breach due to
overtopping, sustained flow over the embankment must occur long
enough to initiate erosion. Once levee erosion has initiated, the con-
tinuation of erosion unravels the embankment, leading to signifi-
cant material loss, resulting in a breach. However, a levee can be
overtopped without breaching. A levee breach may be avoided if
the embankment is resilient enough to substantially resist erosion
caused by overtopping flows. A non-breach overtopping event
occurs when the levee does not experience significant section loss.
Fig. 1shows examples of levee overtopping leading to breach
[Fig. 1(a)] and non-breach [Fig. 1(b)], respectively. When breach
does not occur, the consequences related to life safety and eco-
nomic loss are typically reduced.
Logistic regression models, or logit models, have been widely
used for data analysis in which the outcome variable is binary or
dichotomous and follows a Bernoulli distribution, such as is the
case when considering either breach or non-breach. Several studies
have employed logistic regression to assess a wide array of geo-
technical failure mechanisms, such as soil liquefaction and slope
instability (Das et al. 2010;Gandomi et al. 2013;Zhang and Goh
2013;Vahedifard et al. 2017). Logistic regression has been also
deployed to evaluate the performance of levees (Uno et al. 1987;
Flor et al. 2010;Heyer et al. 2010;Danka and Zhang 2015), includ-
ing considerations of both the rate of breach and overall breach
propagation. A summary of previous levee performance logit mod-
els is well documented by Heyer and Stamm (2013), in an effort
that considers the benefits and limitations of the use of logit models
in assessing levee failure.
As the quantity and quality of levee performance data increase
(e.g. due to advances in remote sensing technologies), so too should
the quantity and quality of models that assist in estimating the risk
of levee breach due to overtopping. Working towards a combined
levee performance data repository is a worthy goal and has been
proposed by many with the intent to increase understanding of
the phenomenon of levee breach due to overtopping. Özer et al.
(2020) provide just one example of such an effort, by introducing
the International Levee Performance Database (ILPD). This work
seeks to create a global data source for levee breach analysis.
Expanding upon the information held within this database and
others like it, such as the NLD, is just one step towards creating
reliable levee performance models both for overtopping breach
and many other failure modes in support of risk assessment.
The primary objective of this study is to develop a data-driven
model using logistic regression for estimating the probability of
levee breach due to overtopping for riverine levees. The proposed
model is best used to evaluate individual cross sections, which is a
discretization of the overall levee system. Additionally, a compre-
hensive data set documenting riverine levee overtopping event per-
formance is presented. Within the data set, and in this study, the
term event refers to any documented case of overtopping such that
the event could result in either breach or non-breach. This study
focuses on riverine levee overtopping events due to the fact that the
physics of dynamic (i.e. coastal) overtopping are materially differ-
ent and should be considered accordingly. The proposed model al-
lows for the calculation of breach probability based on independent
variables. The model is validated using k-fold cross validation and
set aside test data, with the goal of becoming a supplementary tool
for levee risk assessment.
Factors Affecting Levee Breach Due to Overtopping
Understanding and predicting the occurrence of levee breach due to
levee overtopping requires an understanding of geometric, geotech-
nical, and hydraulic parameters. Geometric factors such as levee
height, width, and slope steepness inherently affect the initiation and
progression of embankment erosion when overtopped. Geometric
factors can be influenced by spatial availability, which refers to
Fig. 1. Levee overtopping leading to (a) breach; and (b) non-breach. (Images courtesy of USACE Rock Island District Digital Photo Library.)
© ASCE 04021193-2 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
the area needed to construct a levee. Spatial availability may be
constrained by factors such as floodway impacts, real estate rights,
environmental, and/or cultural impacts. Geotechnical properties in-
cluding, but not limited to, particle size, density, and shear strength,
play critical role in a levees ability to withstand surface erosion.
These properties have been shown to have a significant impact on
the breach potential of an overtopped levee (Briaud et al. 2008).
Hydraulic factors such as overtopping depth, duration, and velocity
are critical in determining forces applied to a levee during overtop-
ping events (Isola et al. 2020).
The selection of geometry is often at least partially dependent
upon geotechnical properties. Factors such as the shear strength of
embankment material impacts slope stability, thus defining the
allowable steepness of slopes. Erosion resistance properties vary
significantly by soil type and are generally considered when estab-
lishing the cross-sectional dimensions of a levee embankment using
modern standards of care. However, many levees in the United
States were built long before the utilization of geotechnical design
standards was standard practice, which is why it is important to
consider levee design and construction history in assessing
performance.
Geometric constraints placed on levee design by hydraulic con-
ditions may have the most significant impacts, as these constraints
typically control the height of the levee. Hydraulic parameters are
also significant in that they are constantly evolving as more data is
collected and statistically updated. Thus, hydraulic impacts must be
continuously updated to assess the ability of levees to withstand the
most up-to-date maximum projected flood.
With a proper knowledge of how these parameters affect levee
performance, in conjunction with known historical design and con-
struction conditions, this information can be used to assist in under-
standing levee overtopping performance. Employing statistical
models can be valuable in predicting the probability of levee breach
as a function of controlling geometric, geotechnical, and hydraulic
parameters. Where used to estimate system reliability, statistical
models have become an integral component in developing risk
assessment frameworks for various structures and infrastructure
systems, due to advances in computational efficiency and robust
predictive capability (Rahimi et al. 2020;Zamanian et al. 2020;
Dehghani et al. 2021). This progress continues to expand the tool-
box of the practicing engineer and improve the professions ability
to perform data-driven analyses that inform decision making when
dealing with large scale performance data.
Levee Risk Assessment
The comprehensive assessment of risk related to levees requires the
consideration of hazard, performance, and consequences as three
components to overall risk formulation (USACE 2018). For levees,
a hazard refers to an environmental load on the levee system, such
as flood or earthquake conditions. Performance refers to the resil-
iency, or reliability, of the levee when a hazard is presented.
Finally, consequences are the potential losses in terms of population
and economic assets that result from hazards affecting levee
performance.
Levee risk assessments are commonly conducted utilizing a
method referred to as semi-quantitative risk assessment (SQRA),
which is a form of risk assessment that utilizes both numerical es-
timates and qualitative descriptions to yield an order of magnitude
risk estimate (USACE 2019). When conducting a levee SQRA, a
primary task is to establish assumed potential failure modes. Each
potential failure mode deemed significant is assessed through the
event tree method, which considers the successive probabilities of
event nodes that must occur sequentially to lead to failure.
The initiating node on the event tree is the hydrologic or seismic
event that presents a hazard to the levee. For hydrologic loading
scenarios, this first node is represented as the annual exceedance
probability (AEP) of the hydraulic load on the levee. The AEP
establishes the anchoring point for the risk associated with a given
failure mode, as it is a quantitatively determined probability of
flood frequency. Subsequent nodes on the event tree, which con-
sider the progression of the failure mode, are then assigned sub-
jective probabilities based on available analysis, circumstantial
evidence, and engineering judgement (OLeary 2018). The prod-
uct of all nodes on an event tree is equal to the estimated annual
probability of failure (APF), which is represented in the SQRA
process as an order of magnitude estimate. Presenting the assessed
risk as an order of magnitude estimate allows for the consideration
of uncertainty in the elicitation of nodal probability values. As
described, the annual probability of failure can be determined
as follows:
APF ¼AEP ×Πn
i¼1PðiÞð1Þ
where PðiÞ= probability of individual node occurring.
When calculating the annual probability of failure of levee
breach due to overtopping, the nodes on the event tree generally
follow the sequence of (1) a hydrologic event occurs which leads
to a given depth of overtopping, (2) erosion of the embankment
initiates, (3) embankment erosion progresses beyond a critical
state, and (4) widespread levee breach occurs. This process, which
considers the levee hazard and performance, is demonstrated in
Fig. 2.
Levee Overtopping Data Set
The data set presented in this study is a subset of the Levee Loading
and Incident Database (LLID), which consists of a collection of
both quantitative and qualitative information that documents past
performance of USACE levees under flood loading (Flynn et al.
2021). The database considers a wide range of flood risk manage-
ment system components, including levees, floodwalls, pump sta-
tions and closure structures. The LLID takes a risk-based approach
to the organization of data, with the data subdivided into categories
based not only on structure type, but also distress mechanisms,
Fig. 2. Levee overtopping breach development.
© ASCE 04021193-3 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
including, but not limited to, overtopping, internal erosion, and sta-
bility. Levee performance data included within the database com-
prises event information ranging from 1948 to 2019.
The compilation of this data was initiated concurrent with the
formalization of the USACE Levee Safety Program in 2006, fol-
lowing the widespread levee breach events that occurred during
the Hurricane Katrina disaster. As a result of both past and on-going
research and data synthesis, the LLID was created by a team of risk
experts using project design, construction, inspection, and flood
response records, with the initial goal of creating a simplified risk
screening tool. Additionally, data compilation and assessment had
the goal of establishing base failure rates from historic perfor-
mance data.
At the time of this study, the LLID contained information on 214
riverine levee overtopping events which occurred across 124 levee
systems. Of the more than 30 variables included to describe the full
range of data in the database, only physically representative data
were used in this study. The levees considered in this study vary
significantly both compositionally and in terms of how they are
loaded hydraulically. Levees range from agricultural dikes that
have been in place for decades to federally authorized and designed
systems protecting large populations at risk. Flood sources, ranging
from minor tributaries to larger rivers, are captured in the data and
represent a wide range of loading, both in terms of magnitude and
duration. Data for overtopping events is a culmination of both
measurement and correlation. Strong emphasis is placed on the fact
that a significant portion of this data is based on human estimation
and recollection, which leads to data being reported in terms of
range, rather than as an exact value in many cases.
The levee overtopping data used in this study include levee sys-
tems over a wide geographical range in the continental United
States, ranging from New York to Washington State, east to west,
and northern Minnesota to Central Texas, north to south. The total
combined length of the levee systems included in this study is ap-
proximately 1,350 km (839 mi), or about 6% of the NLD inventory
in terms of total levee system length (USACE 2021b). The levees
evaluated in this study represent the range of unique factors that
differentiate flood risk management systems in the United States,
reflective of the overall LLID.
Of the 214 levee overtopping events contained within the LLID
overtopping data set, 185 were selected for use in developing a
logistic regression model (see Supplemental Materials for the com-
plete data set used in this study).
Of the 185 selected overtopping events used for the model, 119
events resulted in breach and 66 resulted in non-breach. In the initial
screening of data, event records with significant gaps were excluded
because these data could not be relied upon to provide valuable in-
formation, which led to the use and presentation of only 185 of the
214 known events. Once the final data set for model developmentwas
established, the data were assigned to variables, extrapolated to con-
sider implicit, cumulative effects, and missing data were addressed.
Management of the data is further described in following sections.
Selection of Model Variables
While the LLID considers a wide range of parameters and situa-
tional conditions to describe each overtopping event, only the var-
iables that are intuitively deemed to have a physical impact on the
performance of levee systems were selected for this study. In total,
seven variables were considered for model inclusion based on a
review of database metrics. The variables assessed in this study in-
clude those relating to the physical composition of the levee in
terms of geometry, material type, and consideration of construction
quality. Additionally, external loading on the levee were considered
in the form of hydraulic loading of the levee both prior to and dur-
ing overtopping. In summary, these factors are limited in scope to
geometrical, hydraulic, and geotechnical categorization. The con-
sideration of the number of input variables in this study is driven by
the desire to create a screening level approach that informs risk by
utilizing readily available data that can be categorized to fit a user-
friendly model. In addition to numerical variables, some variables
need to be estimated or ascertained by grouping them into ranges.
These data are considered categorical, which are data whose inputs
are grouped into levels such that the model does not require a pre-
cise numerical value. Categorical variables are also appropriate for
descriptive variables that are non-quantitative, and address the
qualitative information contained within the study data set. A sum-
mary of model variables and the associated categorical levels is pro-
vided in Table 1, with a representation of variables in Fig. 3. See
Supplemental Materials for the complete list of variables for all 185
overtopping events used as a basis for this study.
Table 1. Summary of model variables
Code Variable Type Level code Level description
X1Levee height Numerical m
X2Landside slope geometry Categorical 1 <3H1V
23H1V
X3Levee construction entity Categorical 1 Local
2 Federal
X4Water depth over levee Categorical 1 <0.152 m(<0.5ft)
2 0.1520.305 m (0.51 ft)
3>0.305 m(>1ft)
X5Duration of overtopping flow prior to breach Categorical 1 <6h
2624 h
3>24 h
X6Erosion resistance classification Categorical 1 Low
2 Moderate
3 High
X7Duration of levee loading prior to overtopping Categorical 1 <3days
2314 days
3>14 days
© ASCE 04021193-4 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
Levee Height (X1)
Levee height is a critical component of levee geometry that is often
considered in overtopping analyses and associated risk. Levee
height as a contributing metric has been included by others when
considering levee performance models (Gui et al. 1998;Heyer et al.
2010;Danka and Zhang 2015). Levee height in this study refers to
the average loading height of the overtopped embankment, which is
measured vertically from the riverside toe elevation to the levee
crest elevation. Levee height data is incorporated into analysis
as a continuous numerical variable, using the exact number pre-
sented in the LLID. The loading height for all levees ranges from
0.91 m (3 ft) to 7.32 m (24 ft).
Landside Slope Geometry (X2)
Landside slope geometry refers to the steepness of the landside
levee slope. The landside slope steepness for all levees ranges from
1H:1V to 5H:1V. Slope geometry was considered as a categorical
variable with two levels. Level 1 corresponds to a landside slope
less than 3H:1V, and Level 2 corresponds to a landside slope
greater than or equal to 3H:1V. The delineation between the two
levels of X2was selected as a representation of modernly con-
structed levees being specified to have a minimum slope of
3H:1V to allow for ease of maintenance (USACE 2000). By using
this logic, the authors acknowledge that a partial relationship may
inherently exist between X2and X3(Levee Construction Classifi-
cation), which will be described in the following section.
Levee Construction Classification (X3)
Levee systems are also categorized by quality of construction and
maintenance associated with the levee embankments. This cat-
egorical variable is classified into two levels. Level 1 includes
locally constructed/maintained and re-classified federal levees
and Level 2 includes federally constructed/improved levees.
The differences in these two designations consider construction
authorization, quality of original design and construction, available
data, and observed maintenance actions. A re-classifiedfederal
levee is one which has known design, construction, or historical
maintenance deficiencies. Although levee construction classifica-
tion is easily applied to the data set described within this study
USACE study of portfolio levee systems, the categorization can
also be applied to any levee with a known construction history.
The difference in level of care should be considered when classi-
fying levees from different data sources. Level 1 should be used in
any case where a high level of quality control was not undertaken
during the design and construction process.
Overtopping Depth (X4)
Overtopping depth refers to the height of water over the levee while
being overtopped. This variable may also be referred to as over-
flow depthin related literature, however overtopping is the pre-
ferred nomenclature to align with USACE common terminology.
Additionally, the dynamics of wave loading are not implicitly con-
sidered. The hydraulic load of overtopping depth has been widely
considered in both numerical (Sharp and McAnally 2012) and stat-
istical models for different types of flood loading, including canal
loading (Lendering et al. 2018), riverine loading (Amabile et al.
2016;Isola et al. 2020), and compound riverine and coastal loading
(Jasim et al. 2020). Data for this variable is based on either physical
measurement or nearby stream gauge data to approximate depth at
the location of the breach. Overtopping depth is a categorical var-
iable in this model with three levels. Level 1 includes overtopping
depths less than 0.152 m (0.5 ft), Level 2 represents overtopping
depths between 0.152 m and 0.305 m (0.5 ft and 1.0 ft), and Level 3
denotes overtopping depths greater than 0.305 m (1 ft). These three
levels can be considered as minor,”“moderate,and majorover-
topping, respectively. Assigning categorical levels for this data was
based on an assessment of relative base data distribution.
It was noted during initial review of the data set that a large
percentage of overtopping events, both breach and non-breach,
had associated overtopping depths of less than 0.305 m (1 ft). The
physical relevance of this observation is that hydraulic load leading
to overtopping is often constrained by other systemic factors that
restrict the ability of the river to rise significantly above the crest of
the levee. Some of these factors might be nearby diversion struc-
tures, lower levels of protection across the flood source channel, or
breach at the site of interest. It is critical to note that overtopping
depth in this data set is recorded for both breach and non-breach
events. The depth considered for breach events assumes that the
levee breached in the range represented by the categorical level,
and therefore was not able to increase in height after breach.
Overtopping Duration (X5)
While overtopping duration takes on two distinct meanings within
the data set, it can be treated as a single variable. When overtopping
leads to breach, the overtopping duration is a measure of the du-
ration that the levee crest elevation is exceeded until the breach
occurs. For events where overtopping does not result in breach,
the overtopping duration is simply the measure of time between
the levee crest elevation being exceeded by flood water and the
flood water returning to an elevation below the levee crest. In either
scenario, the duration represents the total load on the levee, so the
variable is treated proportionally for each case. Data for this var-
iable is approximated based on either physical measurement or
the use of stream gauge data. Overtopping duration is a categorical
variable in this model with three levels. Level 1 corresponds to
overtopping that occurred for less than 6 h, Level 2 considers over-
topping that took place for 6 to 24 h, and Level 3 corresponds to
overtopping events that occurred for more than 24 h.
In terms of physical relevance, Level 1 overtopping duration can
be correlated to flashy, or short-term flood events. Level 2 corre-
sponds to moderate term flood events, or those typically experi-
enced on riverine levees. Level 3 is the long-term case in which
a levee is overtopped for more than 1 day prior to breaching or
does not breach at all.
Erosion Resistance Classification (X6)
Each levee embankment used in this study is categorized by ero-
sion resistance, which is determined by the material descriptions
Fig. 3. Representation of model variables.
© ASCE 04021193-5 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
contained within the LLID. Erosion resistance refers to the gen-
eral ability of the levee to resist degradation when subject to over-
topping load. Surface erosion is a field of study of its own with
much work having been done to understand how various material
combinations resist hydraulic stresses. Erosion specific to levees
has been studied by many, who have looked at contributing factors
such as soil type, shear stress from the hydraulic load, and soil
shear strength (Briaud et al. 2008;Kamalzare et al. 2013;Ellithy
et al. 2017;Osouli and Safarian Bahri 2018,Sills et al. 2008).
Additionally, many of the previously referenced levee perfor-
mance logistic regression models considered erosion resistance
as an input variable (Flor et al. 2010;Heyer et al. 2010;Danka
and Zhang 2015).
Erosion resistance classification is a categorical variable in this
model, with Levels 1, 2, and 3 defined as having low,”“moderate,
and highrelative erosion resistance, respectively. Material types
range from clays to sand and gravel mixes, where gravel particle
size is generally assumed to be fine to medium. Erosion resistance
classification in this study does not consider any landside slope ar-
moring or the effects of vegetative cover. The erosion classifica-
tions within the database assumed a general erosion resistance
classification that considers both the general cohesiveness of soil
along with assumed particle size, based on general descriptions.
Erosion resistance classification limitations led to the material de-
scriptions provided in Table 2, which are based on a general review
of surface and embankment erosion literature and data provided to
the authors. The logic used is based on a general trend, and materi-
als encountered within levee embankments that are not listed will
need to be considered accordingly.
Duration of Levee Loading Prior to Overtopping (X7)
Duration of levee loading prior to overtopping refers to the length
of time the embankment was subjected to hydraulic load above the
riverside toe prior to overtopping. This variable is used as a general
representation of the effect of saturation of the levee prior to over-
topping. Physically, when the saturation of the levee increases,
porewater pressures within the levee increase and the overall
strength and stability of the levee decreases. Given how the differ-
ing material types and varying levee geometries included in this
study vary physically, this factor does not behave in a linear manner
from a statistical perspective.
Levee loading duration is a categorical variable in this model,
divided into three levels. Level 1 corresponds to flood water ex-
ceeding the riverside toe 3 days prior to overtopping; Level 2 du-
ration is 3 to 14 days; and Level 3 duration represents a duration
greater than 14 days. The physical relationship between these levels
corresponds to the general hydrograph of a given river during flood
loading. Level 1 can be considered as flashy loading; Level 2 cor-
responds to a moderately rising river; and Level 3 corresponds to a
slow rising river. Like the overtopping duration (X5), the duration
of levee loading data is approximated based on either physical
measurement or using stream gauge data to determine river levels
at the breach area of interest.
Data Cleaning and Processing
Cumulative Effects of Hydraulic Variables
As previously discussed, the data were selected and evaluated
based on a representation of physical processes. Given this consid-
eration, the cumulative effects of each variable also needed to be
incorporated into the model. Most notably, variables related to
hydraulic loading (X4,X
5, and X7) required the consideration of
cumulative effects of intermediate loading given breach or non-
breach results. To account for cumulative effects, the data was man-
ually extrapolated such that if a levee breached at a low level of
loading, it was assumed to fail at the higher levels of loading if
all other variables remain constant. Conversely, if the levee did
not breach at the highest level, it was assumed not to fail at lower
levels if all other variables remain constant. By considering the
implicit loading steps leading up to breach, or non-breach, the
185 events were extrapolated to consider 581 events that were used
for model generation. This is a critical assumption in the model that
leads to a controlled approach in estimating physical factors. All
other variables not directly related to hydraulic loading were con-
sidered independent of cumulative or ordinal effects.
It should be emphasized that data for at least one variable was
not recorded for 104 of the base 185 levee overtopping events.
Variables with missing information include overtopping depth
(X4), overtopping duration (X5), and duration of levee loading
(X7), which are the same variables considered for cumulative ef-
fects. Of the base 185 events, 30.8% of X4, 49.7% of X5, and 5.4%
of X7data was missing. Once data was extrapolated, 10.2% of X4
and 2.4% of X7were missing measurements in the data set. The
variable with the most missing data remained X5(overtopping du-
ration), with 24.1% of the data set missing information on this var-
iable after extrapolation. A summary of the missing data in each
step of the data extrapolation process is summarized in Table 3.
Data extrapolation to account for cumulative hydraulic effects had
a minimal effect on the base breach rate of the entire data set. Prior
to data extrapolation, breach events accounted for 63.8% of all
events. After extrapolation, 59.7% of the data set events resulted
in breach. This is because extrapolation of events was not uniform.
Some events were extrapolated to account for more scenarios than
others, given precedent conditions.
Data Imputation
To account for missing data, the k-nearest neighbor (kNN) impu-
tation algorithm through the VIM package for R version 6.1.1 was
used. The kNN imputation process allows for the replacement of
Table 2. Material description for erosion resistance classification
Material description
Erosion resistance
classification
Sand, silty sand, silty sand with gravel, sand/silt mix, sand/gravel mix, sand/gravel mix with silt, sandy silt, sandy gravel Low
Silt, clayey silt, silt with sand/clay, silt/clay mix with sand, silty loam, silty/clayey loam, sand/silt mix with clay, clayey sand Moderate
Clay, clay/silt mix, clay with sand/silt, zoned embankment with impervious cover, clay enlargement of an existing sand levee High
Table 3. Summary of missing data before and after extrapolation
Level
Portion of missing data
X4X5X7
Before extrapolation 30.8% 49.7% 5.4%
After extrapolation 10.2% 24.1% 2.3%
© ASCE 04021193-6 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
missing data with categorical levels based on comparison of similar
events in the data set using pattern recognition (Beretta and
Santaniello 2016). In this study, an extension of the Gower distance
(Gower 1971) as the most popular distance for mixed-type varia-
bles, which enables the handling of distance for binary, categorical,
ordered, numerical, and semi-numerical variables is used for the
purpose of kNN imputation (Kowarik and Templ 2016;DOrazio
2021).
The kNN is derived for a mix of numerical and categorical var-
iables, and the distance between the ith and jth observations is the
weighted mean of the contributions of each variable. The weight
represents the importance of the variable and is selected based
on the relative importance of the variables (Kowarik and Templ
2016). The distance between the ith and jth observations can be
determined as follows:
di;j¼Pp
m¼1wmδi;j;m
Pp
m¼1wm
ð2Þ
where wmdenotes the weight and δi;j;mrepresents the contribution
of the mth variable. The shortcomings of this method are predomi-
nantly centered on the effects of imputation on data distribution and
representation, where it is recognized that data are being generated
based on statistical interpolation.
A simplified visual representation of k-value selection for im-
putation in this study is shown in Fig. 4. Random data points are
shown based on training data for kNN imputation, with example
kNN groupings. Each data point represents the tendency of the im-
putation process to either assign a missing categorical variable to
Level 1, Level 2, or Level 3. In this scenario, an X1value of ap-
proximately 2.7 is known for an event, but X7data is missing.
When evaluating the scenario with the three nearest neighbors, a
Level 1 response for X7is predicted for the missing data because
the Level 1 data are more prevalent than the Level 2 and Level 3
data. Following the same logic, if the eight nearest neighbors are
used, which includes the previously assessed three nearest neigh-
bors, then the missing categorical variable is imputed as Level 3.
The process of k-value selection is iterative in assessing how
many neighbors need to be considered to minimize the distortion
of the data set while maintaining correlation between observed re-
sults and model prediction. The accuracy metrics considered were
error rates when validating the data using (1) k-fold cross valida-
tion, and (2) test data using a random set of real data that were
excluded from the training set. Both accuracy metrics will be de-
scribed in further detail in subsequent sections. As shown in Fig. 5,
volatility is high for low k-values and attenuates as the k-value
increases.
In addition to assessing the model error convergence, a probabi-
listic distribution of imputed variables needed to be simultaneously
considered, such that the physics of the model relationship re-
mained unchanged, and data were not grossly misrepresented.
As k-values were increased beyond eight within the model, probabi-
listic distribution smoothing to the mean was generally observed,
which led to greater deviation from the original data. Using a
k-value of eight, the imputation of X4(overtopping depth) and X7
(duration of levee loading prior to breach) had maximum probabil-
ity changes of 3.8%, and 2.0%, respectively, with each having an
increased probability of the data being categorized as Level 2.
Imputation had the greatest effect on X5, due to this variable having
the most missing data, with the maximum probability change being
8.5%, as shown in Fig. 6. A summary of changes in probability
distribution is shown in Table 4.
The result of imputation of missing X5data was to force more of
the data to Level 2, given three levels, which in this instance is
Fig. 4. Two-dimensional kNN imputation visualization.
Fig. 5. kNN error rate sensitivity.
Fig. 6. Probability change due to imputation with k¼8for (a) X4; (b) X5; and (c) X7.
© ASCE 04021193-7 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
preferrable due to the fact that many of the missing data were
correlated to larger river events, i.e., the Mississippi and Missouri
Rivers. Level 2 of X5correlates to moderate duration overtopping
(624 h). This result aligns well with the data when comparing to
similar events; therefore it is not considered to be a gross misrep-
resentation of data or trend.
While changes in the probabilistic distribution of the original
data were less when selecting k-values less than eight, the offset in
error rate was not seen to justify the minor improvements in dis-
tribution changes. For these reasons, a k-value of eight was se-
lected for this data set in support of model creation. With these
checks, it is ensured that the applied data imputation does not alter
the key characteristics of the levee data. Finally, Fig. 7presents a
graphical representation of all 581 events, which account for
extrapolation and imputation of the base data, used to create
the proposed model.
Development of the Logistic Regression Model
Logistic regression is a statistical method which allows for the uti-
lization of both numerical and categorical independent input
parameters to predict a categorical outcome, which is often binary
(Kleinbaum 1994;Hilbe 2011). Logistic regression utilizes con-
cepts of linear regression where a logit transformation is applied
to the outcome of a linear regression to calculate a probability. This
probability output is then used to determine a categorical response
based on a set threshold. Because the nature of the studied data
consist of both numerical and categorical independent variables,
and the dependent variables are reported in two levels, binary lo-
gistic regression was used in this study. This method of statistical
analysis for levee overtopping is appropriate given that the phe-
nomenon of levee overtopping is generally well understood in
terms of what factors contribute, and that the result of overtopping
is binary in terms of breach or non-breach. The proposed logit
model serves to assess of the degree of importance of each param-
eter that contributes to overtopping.
The logistic regression model developed for this study attempts
to predict the probability of a levee breach given a set of one
numerical and six categorical variables related to construction, geo-
technical, hydraulic, and geometrical factors. These variables are
denoted as X1through X7. In this study, levee breach is defined
as Y¼1, and non-breach as Y¼0. The probability of breach,
PðY¼1Þ, is defined by the following general form:
Table 4. Change in probability of X4,X
5, and X7after kNN imputation for
k¼8
Level X4(%) X5(%) X7(%)
12.41.91.1
2 3.8 8.5 2.0
31.56.60.9
Fig. 7. Distribution of variables for model creation with extrapolation and imputation.
© ASCE 04021193-8 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
PðY¼1Þ¼ eZ
1þeZð3Þ
where
Z¼β0þX
n
i¼1
βiXið4Þ
and Xiis the observation or predictor, with β0and βibeing the
coefficients estimated by the regression model. When considering
categorical input variables, the output of the proposed model con-
siders each categorical level as a predictor. So, rather than an Xi
input for the categorical variable, a coefficient is calculated for each
level of the categorical input variable relative to the base condition
(categorical Level 1). In the event that a non-base condition is met,
the contribution of the event occurring at that categorical level to
the model is βi×1. In the event that only the base categorical level
is met, the contribution is βi×0. The probability of breach is not
calculated as a binary output, but rather a probability of occurrence
between 0 and 1. Therefore, a threshold is established to determine if
the individual event is likely to result in breach. Breach is assumed to
occur if PðY¼1Þis greater than or equal to 0.5, and non-breach is
assumed to occur if PðY¼1Þis less than 0.5.
The first step in evaluating a logistic regression model is to
assess the statistical significance of each variable, which is accom-
plished in the proposed model using the p-value. It is a long-
established practice in logistic regression analysis that a variable
is significant if its p-value is less than 0.05, which reflects 95%
confidence (Fisher 1925). In this study, p-value computation is
done using a base regression equation, which considers the additive
properties of each variable in succession, and is represented by:
Z¼β0þβ1·X
1þβ2·X
X2¼2þβ3·X
X3¼2þβ4·X
X4¼2
þβ5·X
X4¼3þβ6·X
X5¼2þβ7·X
X5¼3þβ8·X
X6¼2
þβ9·X
X6¼3þβ10 ·X
X7¼2þβ11 ·X
X7¼3ð5Þ
The p-values calculated for each level of the base model are pro-
vided in Table 5. It should be noted that if any level of a categorical
variable was found to be significant, all levels had to be included to
maintain completeness of the model. Significance test results indi-
cate that all variables are significant based on the significance
threshold of 0.05, except for X1(levee height). This result for X1
is intuitive when looking at the distribution of breach and non-
breach data relative to an increasing levee height, as shown in Fig. 7.
Of the variables with greater significance, variable X2(landside
slope geometry) was reviewed by considering the baseline breach
rates to verify its significance, as this value was close to the
threshold. The p-value of 0.037 was found to have a loose relation-
ship with the base events in the overtopping data set, which indi-
cated that X2Level 1 was only 4% more likely to breach than X2
Level 2 when evaluating the pre-imputation data. Note that in
Eq. (5) there is no reference to Level 1. This is because Level 1 is
the base condition for each variable where, if that variable is at
Level 1, then its contribution to base regression equation, or Zin
Eq. (5), is zero. In other words, if all variables are at Level 1, then
the total value of the base regression equation is equal to the inter-
cept value.
Stepwise regression is a commonly used method to determine if
the addition or exclusion of an individual variable, or a combination
of independent variables, can improve accuracy using covariables
(Steyerberg et al. 1999). Stepwise regression was used for the lo-
gistic regression model to determine if covariables in the form of
two-way interactions of variables and quadratic terms could im-
prove the model accuracy while maintaining the simplicity in
the developed model. The stepwise logistic regression model
was evaluated based on an Akaikes information criterion (AIC)
accuracy metric for each combination. When using AIC to compare
model fitting, the model with the lowest AIC value represents the
best performance. AIC scores competing models by reducing the
value if information loss is minimalized and increasing the value if
the model contains unnecessary complexity (Wagenmakers 2007).
For the presented data, the odds ratio represents the relative
change in breach probability for a given categorical level of an indi-
vidual variable. Odds ratios and regression coefficients for each
model term are presented in Table 6. In each case, the odds ratio
is relative to the base case, or Level 1. When the odds ratio is less
than 1, breach is less likely as the categorical level increases. When
the odds ratio is greater than 1, the probability of breach is more
likely as the categorical level increases. This relationship can be
formulated as follows:
Odds Ratio ¼
PðY¼1ÞXi¼n
ð1PðY¼1ÞXi¼nÞ
PðY¼1ÞXi¼1
ð1PðY¼1ÞXi¼1Þ
ð6Þ
Table 6. Variable odds ratio and coefficient
Variable
Coefficient
(β)
Odds
ratio
Intercept β0¼0.93 2.53
Levee construction entity ðX3Þ¼2β3¼1.13 0.32
Water depth over levee ðX4Þ¼2β4¼0.87 2.38
Water depth over levee ðX4Þ¼3β5¼1.27 3.55
Duration of overtopping flow prior to
breach ðX5Þ¼2
β6¼0.08 1.08
Duration of overtopping flow prior to
breach ðX5Þ¼3
β7¼1.85 6.37
Erosion resistance classification ðX6Þ¼2β8¼1.74 0.18
Erosion resistance classification ðX6Þ¼3β9¼3.93 0.02
Duration of levee loading prior to
overtopping ðX7Þ¼2
β10 ¼0.42 0.66
Duration of levee loading prior to
overtopping ðX7Þ¼3
β11 ¼0.17 1.18
X4¼2and X7¼2β12 ¼2.18 8.82
X4¼3and X7¼2β13 ¼2.65 14.08
X4¼2and X7¼3β14 ¼0.60 1.83
X4¼3and X7¼3β15 ¼2.29 9.89
X3¼2and X6¼2β16 ¼1.35 3.84
X3¼2and X6¼3β17 ¼0.51 0.60
Note: β1and β2were not used in the proposed model. Model
AIC ¼479.19.
Table 5. Significance of model variable
Description Variable Level p-valuea
Levee height X1N/A 0.566
Landside slope geometry X22 0.037
Levee construction classification X321.79 ×105
Overtopping depth X424.07 ×105
31.07 ×109
Overtopping duration X52 0.089
31.12 ×107
Erosion resistance classification X624.00 ×104
3<2×1016
Duration of levee loading prior
to overtopping
X72 0.022
3 0.0123
aAll variable significance references to Level 1.
© ASCE 04021193-9 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
where PðY¼1ÞXi¼n= probability of breach given variable Xiat
Level n; and PðY¼1ÞXi¼n= probability of breach given variable
Xiat Level 1.
For example, X6at Level 3 has an odds ratio of 0.02. This im-
plies that breach is 50 (1/0.02) times more likely to occur when
overtopped for a low erosion resistant levee than a high erosion
resistant levee. Conversely, when the X5variable is at level 3, the
odds ratio is 6.37. This implies that overtopping duration greater
than 24 h leads to a breach probability 6.37 times higher than
an overtopping event duration less than 6 h. The difference in these
results is not in the formulation, but rather that as the level of ero-
sion resistance classification (X6) increases, breach is inherently
more likely, whereas the opposite is true for overtopping duration
(X5), where an increased level implies increased loading. Where
two levels are specified for the odds ratio, both cases reference
Level 1 for each variable. To demonstrate, when X3¼2and
X6¼3, the probability of breach is 1.67 (1/0.60) times less likely
compared to the base condition of X3¼1and X6¼1. Conversely,
when X4¼3and X7¼3, breach is 9.89 times more likely than the
base condition of X4¼1and X7¼1.
After the stepwise regression was assessed, X1was removed
due to lack of significance as observed in the base model. X2
was considered in the stepwise model but was not included in
the final model based on the calculated AIC. As previously dis-
cussed, the rejection of this variable in the final model agrees with
the assessment of base data, which shows that landside slope geom-
etry does not have a significant statistical impact on the base rate of
breach.
The proposed logistic regression model for the LLID overtop-
ping data set is presented as follows:
Z¼β0þβ3·X
X3¼2þβ4·X
X4¼2þβ5·X
X4¼3þβ6·X
X5¼2
þβ7·X
X5¼3þβ8·X
X6¼2þβ9·X
X6¼3þβ10 ·X
X7¼2
þβ11 ·X
X7¼3þβ12 ·X
X4¼2;X7¼2þβ13 ·X
X4¼3;X7¼2
þβ14 ·X
X4¼2;X7¼3þβ15 ·X
X4¼3;X7¼3þβ16 ·X
X3¼2;X6¼2
þβ17 ·X
X3¼2;X6¼3ð7Þ
The proposed model considers the base interactions of X3,X
4,
X5,X
6, and X7and two-way interactions of X4with X7and X3
with X6.
Model Validation
The proposed model was validated using cross validation as well as
a test data set where a portion of the base data was set aside to be
used to evaluate the proposed model. Cross validation was con-
ducted using the k-fold cross validation method. In this method,
the data set is divided into kevenly distributed groups and sub-
sequently compared against the selected logistic regression model
to determine the model accuracy (Valavi et al. 2019). Each time the
data is redistributed to validate, a fold is created. For this study, a
k-value of 5 was selected to test 20% of the data set against the
remainder of the data set in each fold. Note that k-value here rep-
resents a different value than the k in kNN imputation. In this pro-
cess, each event for validation is selected randomly in each fold.
Cohens kappa value, which ranges between 1and þ1, assesses
relative model agreement for multiclass data with an unbalanced
response (Delgado and Tibau 2019). Results of cross validation in-
dicated model accuracy of 80.7% with a standard deviation of 3.4%
and a Cohens kappa value of 0.592. While there is no standardized
scale for kappa score, a value between 0.41 and 0.60 has been
considered as moderate agreement, with values of 0.610.80 as
being substantial agreement (Landis and Koch 1977).
Set aside data for validation purposes included 37 of 185 events
that were not used in model development. Test data were randomly
chosen, with the condition that each event must not have any miss-
ing variable data. These data were then extrapolated to consider
intermediate, implicit events that had to occur leading up to breach
using the same extrapolation process that was applied to model
data, which yielded 116 test data. As indicated in Table 7, the ac-
curacy of the fitted model based on the randomly selected test data
set was 73.3%, with the model predictions from 85 of 116 events in
agreement with the observed results. Accurate predictions are high-
lighted in Table 7as either a true positive (TP) or true nega-
tive (TN).
Validation using the set aside test data set indicates that there is a
slight tendency of the model to predict a false positive (FP), as op-
posed to a false negative (FN). The probability of false positive and
false negative predictions when using the test data are 14.7% and
12.1%, respectively. Fig. 8presents the calculated breach probabil-
ity of all real base events used to create the proposed model with
respect to the incident number, as identified in the presented
data set.
Application of Logit Model in Levee Risk
Assessment
Remember that for assessing the hazard and performance compo-
nents of risk related to levee breach due to overtopping, the nodes
on the event tree typically follow the sequence of (1) hydraulic
load of interest occurring, (2) initiation of embankment erosion,
(3) propagation of embankment erosion progressing beyond a criti-
cal state, and (4) breach. Because overtopping is assumed to be
occurring, the breach probability calculated by the proposed model
represents steps (2) through (4) of this process. The calculated
probability of breach, PðY¼1Þ, should be treated as a factor
which, when multiplied by the annual exceedance probability
(AEP), yields an annual probability of failure. This relationship
can be shown as:
APF ¼AEP ×PðY¼1ÞLogit ð8Þ
where PðY¼1ÞLogit represents the probability of breach as deter-
mined by the logit model.
This process can be demonstrated through the example event set
forth in Table 8. This scenario considers a non-federally con-
structed clay levee. The levee is assumed to be overtopped by
0.22 m for three hours, with loading above the riverside toe begin-
ning six days prior to overtopping. Given these conditions, the logit
model estimates a probability of breach, PðY¼1Þ, of 0.293, where
breach is not considered likely. If we assume the AEP of the over-
topping depth considered in the example has an annual probability
of occurrence equal to 0.1%, then the APF for this scenario can be
Table 7. Accuracy of model predictions versus observations
Observation
Model prediction
Non-breach (Y¼0) Breach (Y¼1)Σ
Non-breach (Y¼0)26 (TN) 17 (FP) 43
Breach (Y¼1) 14 (FN) 59 (TP) 73
Σ40 76 116
Note: Bold values signify correct predictions by the model. TN = true
negative; FN = false negative; FP = false positive; and TP = true positive.
© ASCE 04021193-10 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
calculated using Eq. (8)as2.93 ×104, or 0.0293%. This value
would then be combined with either economic or life loss conse-
quences of breach to form the full representation of risk.
Discussion
The LLID overtopping data set can be used for many other pur-
poses that support both USACE and other parties interested in levee
performance. For instance, the information in the overtopping data
set can be used to highlight areas of typical poor performance of
past overtopping locations for various systems. The LLID overtop-
ping data set can also provide valuable information for researchers
looking to develop models related to overtopping reliability or sim-
ilar topics, such as breach propagation. Additionally, the presented
model can be modified such that only specific variables of interest,
such as hydraulic loading or erosion resistance, are considered rel-
ative to each system, to inform more specific research or program-
matic interests. Using the overtopping data, studies could be
considered set that focus on regional performance specific to water-
shed, river, or other specific geographical locations.
While the assessment of levee reliability analysis contributing to
risk assessment is generally thought to require a complex set of
hydrological and geotechnical parameters, one valuable trait of the
proposed model is that the input parameters are relatively easy to
ascertain or estimate. Variables such as levee construction classi-
fication can be categorized based on the known history of the struc-
ture. Erosion resistance classification can be determined by visual
inspection or with minimal sampling. Often, if engineering records
exist for a levee, this information is located within design documen-
tation. The hydraulic variables related to overtopping depth, over-
topping duration, and duration of levee loading prior to breach can
generally be estimated using known river gauge information for
levees within the United States. Furthermore, visual inspection
prior to, or during, the event can often provide enough insight into
the event that the magnitude of these variables can be estimated.
Geometric factors such as levee height and slope steepness were
found to be minimally impactful to the overall model, which was
not an expected result. Given the lack of inclusion of X1(levee
height) and X2(landside slope geometry), levees are differentiated
largely on composition and hydraulic loading. Thus, geometric fac-
tors are not considered to be highly critical in the evaluation of
cross sections using this method.
A key benefit of the presented model is that a relatively small
number of variables are required. This reduces the complexity of
interactions within the model and eliminates some potential factors
that may have highly variable effects. However, further studies are
suggested to examine whether the inclusion of additional variables
could be beneficial in potential future model updating where the
variables are reasonably easily obtained and do not lead to unnec-
essary model complexity. For example, the proposed model does
not explicitly consider the effect of slope vegetation, overtopping
velocities, cracking, or the initiation point of erosion (i.e. landside
slope or crest), which have been shown to affect the process of soil
erosion and levee overtopping breach. With additional investigation
and testing, erosion resistance properties could be better defined to
align more closely with documented studies. Additionally, flood
fighting and emergency response have likely varied across events
but were not considered in model creation. Considering such var-
iables, if available and applied in a direct manner, can potentially
improve the model accuracy but would need to be accurately as-
sessed in future studies.
Conclusions
Flood risk within the United States poses an existing and increasing
threat due to the increased frequency of extreme weather events and
expanding development within floodplains. It is imperative that
risks related to levee systems are thoroughly evaluated and regu-
larly assessed. Utilizing available tools and evolving methods,
levee data collection should be prioritized such that levee perfor-
mance can be better understood through both statistical and deter-
ministic means.
A comprehensive data set is presented within this study that
documents the performance of known overtopping events within
the United States. The data set, along with any future data addi-
tions, has the potential to allow for further refinement or expansion
of numerical values and categorical levels. The proposed model
uses known ranges of performance information in an effort to help
calibrate the minds of individuals involved with the technical as-
pects of levee risk assessment. One significant advantage of the
proposed model is that it can be updated as additional data is col-
lected and refined. The proposed model can be used by many with a
basic understanding of the limited range of required input variables.
The current study yields promising results when utilizing the
proposed model as a screening measure, given then extensive work
Fig. 8. Calculated probability of breach for 185 overtopping incidents included in the data set.
Table 8. Example overtopping scenario
Value/Level
Logit model inputs
PðY¼1ÞLogita
X3X4X5X6X7
Value Local 0.22 m 3 h Clay 6 days 0.293
Level 1 2 1 3 2
aProbability of breach as determined by logit model.
© ASCE 04021193-11 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
that has gone into data collection. An accuracy range of 73.3% to
80.7% indicates quality model fitting of data for a process that is
inherently variable. Application of the proposed logit model is most
appropriate for assessing individual levee system cross sections.
When analyzing a full levee system, discretization should be con-
sidered where there are significant changes in conditions across the
system. The proposed model offers a viable alternative to the sub-
jective, judgment-based components typically relied upon in levee
risk assessment.
Efforts to refine the existing database will only help to improve
the models reliability. In the logit models current state, machine
learning is relied upon to fill in gaps where data has not been dis-
covered. This leads to an acknowledged level of uncertainty where
significant portions of data are generated rather than measured. As
such, continued research that attempts to fill these gaps should be
considered. Future data collection efforts should also consider as-
pects which further the understanding of breach due to overtopping
in a way that not only can predict its occurrence but also its mag-
nitude. Data related to vegetation, flow velocity, emergency re-
sponse, and other considerations not covered in this model may
have the potential to improve the models accuracy.
Lastly, it is highly recommended that unified data collection ef-
forts be considered that document levee performance not only of
USACE levees but also of those within the United States and
abroad which are maintained by other entities. In doing so, models
such as the one presented in this study can gain efficiency. An in-
creased understanding of levee performance during flood events
serves to benefit those who maintain, design, and create policy
for flood risk management projects.
Data Availability Statement
Some or all data, models, or code that support the findings of this
study are available from the corresponding author upon reasonable
request. Data includes that which was used in the Levee Loading
and Incident Database. Model and/or code includes text of code
used to create the logit model.
Acknowledgments
The authors thank the US Army Corps of Engineers (USACE) for
support related to this research.
Disclaimer
The opinions expressed in this paper are those of the authors and do
not necessarily reflect those of the US Army Corps of Engineers.
Supplemental Materials
The levee overtopping data set is available online in the ASCE
Library (www.ascelibrary.org).
References
Amabile, A., M. Cordão-Neto, F. De Polo, and A. Taratino. 2016.
Reliability analysis of flood embankments taking into account a sto-
chastic distribution of hydraulic loading.In Proc., 3rd European
Conf. on Unsaturated Soils. Les Ulis, France: EDP Sciences.
https://doi.org/10.1051/e3sconf/20160919005.
ASCE. 2021. A Comprehensive Assessment of Americas Infrastructure.
Accessed March 9, 2021. https://infrastructurereportcard.org/wp
-content/uploads/2020/12/National_IRC_2021-report-2.pdf.
Beretta, L., and A. Santaniello. 2016. Nearest neighbor imputation algo-
rithms: A critical evaluation.Supplement, BMC Med. Inf. Decis.
Making 16 (S3): 197208. https://doi.org/10.1186/s12911-016-0318-z.
Briaud, J.-L., H.-C. Chen, A. V. Govindasamy, and R. Storesund. 2008.
Levee erosion by overtopping in New Orleans during the Katrina
Hurricane.J. Geotech. Geoenviron. Eng. 134 (5): 618632. https://doi
.org/10.1061/(ASCE)1090-0241(2008)134:5(618).
CRS (Congressional Research Service). 2017. Levee safety and risk: Status
and Considerations. Version 3. Washington, DC: CRS.
Danka, J., and L. M. Zhang. 2015. Dike failure mechanisms and breaching
parameters.J. Geotech. Geoenviron. Eng. 141 (9): 04015039. https://
doi.org/10.1061/(ASCE)GT.1943-5606.0001335.
Das, I., S. Sahoo, C. van Westen, A. Stein, and R. Hack. 2010. Landslide
susceptibility assessment using logistic regression and its comparison
with a rock mass classification system, along a road section in the
northern Himalayas (India).Geomorphology 114 (4): 627637. https://
doi.org/10.1016/j.geomorph.2009.09.023.
Dehghani, N. L., A. B. Jeddi, and A. Shafieezadeh. 2021. Intelligent hur-
ricane resilience enhancement of power distribution systems via deep
reinforcement learning.Appl. Energy 285 (Mar): 116355. https://doi
.org/10.1016/j.apenergy.2020.116355.
Delgado, R., and X.-A. Tibau. 2019. Why CohensKappa should be
avoided as performance measure in classification.PLoS One 14 (9):
e0222916. https://doi.org/10.1371/journal.pone.0222916.
DOrazio, M. 2021. Distances with mixed type variables some modified
Gowers coefficients.Preprint, submitted January 7, 2021. http://arxiv
.org/abs/2101.02481.
Ellithy, S., G. Savant, and J. L. Wibowo. 2017. Effect of soil mix on over-
topping erosion.In Proc., World Environmental and Water Resources
Congress 2017,3449. Reston, VA: ASCE. https://doi.org/10.1061
/9780784480625.005.
Fisher, R. A. 1925. Statistical methods for research workers. Edinburgh,
Scotland: Oliver and Boyd.
Flor, A., N. Pinter, and J. W. F. Remo. 2010. Evaluating levee failure sus-
ceptibility on the Mississippi River using logistic regression analysis.
Eng. Geol. 116 (12): 139148. https://doi.org/10.1016/j.enggeo.2010
.08.003.
Flynn, S. G., F. Vahedifard, and D. M. Schaaf. 2021. A dataset of levee
overtopping incidents.In Proc., Geo-Extreme 2021: Infrastructure
Resilience, Big Data, and Risk,99108. Reston, VA: ASCE. https://doi
.org/10.1061/9780784483701.010.
Gandomi, A., M. Fridline, and D. Roke. 2013. Decision tree approach for
soil liquefaction assessment.Sci. World J. 2013: 346285. https://doi
.org/10.1155/2013/346285.
Gower, J. C. 1971. A general coefficient of similarity and some of itsprop-
erties.Biometrics 27 (4): 857871. https://doi.org/10.2307/2528823.
Gui, S., R. Zhang, and X. Xue. 1998. Overtopping reliability models for
river levee.J. Hydraul. Eng. 124 (12): 12271234. https://doi.org/10
.1061/(ASCE)0733-9429(1998)124:12(1227).
Heyer, T., H.-B. Horlacher, and J. Stamm. 2010. Multicriteria stability
analysis of river embankments based on past experience.In Proc.,
1st European IAHR Congress. Madrid, Spain: International Association
for Hydro-environment Engineering and Research.
Heyer, T., and J. Stamm. 2013. Levee reliability analysis using logistic
regression modelsAbilities, limitations and practical considerations.
Georisk 7 (2): 7787. https://doi.org/10.1080/17499518.2013.790734.
Hilbe, J. 2011. Logistic regression.In International encyclopedia of stat-
istical science,1532. New York: Springer.
Hui, R., E. Jachens, and J. Lund. 2016. Risk-based planning analysis for a
single levee.Water Resour. Res. 52 (4): 25132528. https://doi.org/10
.1002/2014WR016478.
Isola, M., E. Caporali, and L. Garrote. 2020. River levee overtopping: A
bivariate methodology for hydrological characterization of overtopping
failure.J. Hydrol. Eng. 25 (6): 04020026. https://doi.org/10.1061
/(ASCE)HE.1943-5584.0001929.
Jasim, F. H., F. Vahedifard, A. Alborzi, H. Moftakhari, and A. Aghakouchak.
2020. Effect of compound flooding on performance of earthen levees.
© ASCE 04021193-12 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
In Geo-Congress 2020: Engineering, Monitoring, and Management of
Geotechnical Infrastructure,707716. Reston, VA: ASCE.
Kamalzare, M., T. S. Han, M. McMullan, C. Stuetzle, T. F. Zimmie,
B. Cutler, and W. R. Franklin. 2013. Computer simulation of levee
erosion and overtopping.In Geo-Congress 2013: Stability and Perfor-
mance of Slopes and Embankments III, 18511860. Reston, VA: ASCE.
Kleinbaum, D. G. 1994. Logistic regression: A self-learning text.NewYork:
Springer.
Kowarik, A., and M. Templ. 2016. Imputation with the R package VIM.
J. Stat. Software 74 (7): 116. https://doi.org/10.18637/jss.v074.i07.
Landis, J. R., and G. G. Koch. 1977. The measurement of observer agree-
ment for categorical data.Biometrics 33 (1): 159174. https://doi.org
/10.2307/2529310.
Lendering, K., T. Schweckendiek, and M. Kok. 2018. Quantifying the fail-
ure probability of a canal levee.Georisk 12 (3): 203217. https://doi
.org/10.1080/17499518.2018.1426865.
Mallakpour, I., and G. Villarini. 2015. The changing nature of flooding
across the central United States.Nat. Clim. Change 5 (3): 250254.
https://doi.org/10.1038/nclimate2516.
OLeary, T. 2018. SQRA calculation methodology. RMC-TN-2018-01.
Lakewood, CO: USACE.
Osouli, A., and P. Safarian Bahri. 2018. Erosion rate prediction model
for levee-floodwall overtopping applications in fine-grained soils.
Geotech. Geol. Eng. 36 (4): 28232838. https://doi.org/10.1007/s10706
-018-0505-z.
Özer, I. E., M. van Damme, and N. Jonkman. 2020. Towards an
international levee performance database (ILPD) and its use for macro-
scale analysis of levee breaches and failures.Water 12 (1): 119.
Rahimi, M., Z. Wang, A. Shafieezadeh, D. Wood, and E. J. Kubatko. 2020.
Exploring passive and active metamodeling-based reliability analysis
methods for soil slopes: A new approach to active training.Int. J. Geo-
mech. 20 (3): 04020009. https://doi.org/10.1061/(ASCE)GM.1943
-5622.0001613.
Sharp, J. A., and W. H. McAnally. 2012. Numerical modeling of surge
overtopping of a levee.Appl. Math. Modell. 36 (4): 13591370.
https://doi.org/10.1016/j.apm.2011.08.039.
Sills, G. L., N. D. Vroman, R. E. Wahl, and N. T. Schwanz. 2008. Over-
view of New Orleans leveefailures: Lessons learned and their impact on
national levee design and assessment.J. Geotech. Geoenviron. Eng.
134 (5): 556565. https://doi.org/10.1061/(ASCE)1090-0241(2008)
134:5(556).
Steyerberg, E. W., M. J. C. Eijkemans, and J. D. F. Habbema. 1999. Step-
wise selection in small data sets: A simulation study of bias in logistic
regression analysis.J. Clin. Epidemiol. 52 (10): 935942. https://doi
.org/10.1016/S0895-4356(99)00103-1.
Uno, T., H. Morisugi, T. Sugii, and K. Ohashi. 1987. Application of a logit
model to stability evaluation of river levees.J. Nat. Disaster Sci.
9 (1): 6177.
USACE. 2000. Design and construction of levees. Engineer Manual, EM
1110-2-1913. Washington, DC: USACE.
USACE. 2018. Levee portfolio report. Washington, DC: USACE.
USACE. 2019. Interim approach for risk-informed designs for dam and
levee projects. ECB No. 2019-15. Washington, DC: USACE.
USACE. 2021a. Climate hydrology assessment tool v1.0. Washington, DC:
USACE.
USACE. 2021b. National levee database. Washington, DC: USACE.
Vahedifard, F., A. AghaKouchak, and N. H. Jafari. 2016. Compound haz-
ards yield Louisiana flood.Science 353 (6306): 1374. https://doi.org
/10.1126/science.aai8579.
Vahedifard, F., F. H. Jasim, F. T. Tracy, M. Abdollahi, A. Alborzi, and
A. AghaKouchak. 2020. Levee fragility behavior under projected future
flooding in a warming climate.J. Geotech. Geoenviron. Eng. 146 (12):
04020139. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002399.
Vahedifard, F., S. Sehat, and J. Aanstoos. 2017. Effects of rainfall,
geomorphological and geometrical variables on vulnerability of the
lower Mississippi River levee system to slump slides.GeoRisk 11 (3):
257271. https://doi.org/10.1080/17499518.2017.1293272.
Valavi, R., J. Elith, J. J. Lahoz-Monfort, and G. Guillera-Arroita. 2019.
blockCV: An R package for generating spatially or environmentally
separated folds for k-fold cross-validation of species distribution mod-
els.Methods Ecol. Evol. 10 (2): 225232. https://doi.org/10.1111/2041
-210X.13107.
Villarini, G., J. A. Smith, M. L. Baeck, and W. F. Krajewski. 2011.
Examining flood frequency distributions in the Midwest U.S.J. Am.
Water Resour. Assoc. 47 (3): 447463. https://doi.org/10.1111/j.1752
-1688.2011.00540.x.
Wagenmakers, E.-J. 2007. A practical solution to the pervasive problems
of pvalues.Psychonomic Bull. Rev. 14 (5): 779804. https://doi.org
/10.3758/BF03194105.
Zamanian, S., J. Hur, and A. Shafieezadeh. 2020. Significant variables for
leakage and collapse of buried concrete sewer pipes: A global sensitiv-
ity analysis via Bayesian additive regression trees and Sobolindices.
Struct. Infrastruct. Eng. 17 (5); 113. https://doi.org/10.1080/15732479
.2020.1762674.
Zhang, W. G., and A. T. C. Goh. 2013. Multivariate adaptive regression
splines for analysis of geotechnical engineering systems.Comput.
Geotech. 48: 8295. https://doi.org/10.1016/j.compgeo.2012.09.016.
© ASCE 04021193-13 J. Geotech. Geoenviron. Eng.
J. Geotech. Geoenviron. Eng., 2022, 148(3): 04021193
Downloaded from ascelibrary.org by Mississippi State Univ Lib on 12/22/21. Copyright ASCE. For personal use only; all rights reserved.
... A logistic regression model, referred to henceforth as the "logit model", was recently developed by Flynn et al. (2021) with the purpose of estimating the probability of levee breach due overtopping based on a performance dataset of 185 historical riverine levee overtopping events. For completeness, the key features of the logit model proposed by Flynn et al. (2021) are encapsulated in this section. ...
... A logistic regression model, referred to henceforth as the "logit model", was recently developed by Flynn et al. (2021) with the purpose of estimating the probability of levee breach due overtopping based on a performance dataset of 185 historical riverine levee overtopping events. For completeness, the key features of the logit model proposed by Flynn et al. (2021) are encapsulated in this section. ...
... Based on these thresholds, the predictive accuracy of the logit model was found to be 81.8%, with the computed results of the 11 new data points matching the observed result in 9 cases. This result is comparable to previous model validation efforts (Flynn et al. 2021), and exceeds the previously documented test data accuracy of 73.3%. Previous validation efforts evaluated the predictive capability of the model with an initial subset of 116 overtopping events using the same criteria. ...
Conference Paper
Full-text available
Breach due to overtopping is the most prevalent failure mode of levees; therefore, special consideration should be given to this mechanism when conducting levee risk assessments. The main objective of this study is to apply a recently developed logistic regression model, which estimates the probability of breach due to overtopping, to levee risk assessment. The model is first introduced, and then employed for risk assessment purposes by comparing probabilistic model estimates to the results of eight semi-quantitative risk assessments based on expert elicitation of subjective probability. The model is then validated by testing model accuracy using data from 11 new levee overtopping events. Findings suggest that the proposed logit model can support risk assessment by offering a viable alternative for estimating the system response probability of levees when overtopped.
Conference Paper
Full-text available
The most common mode of levee failure, breach due to overtopping, is generally considered as a function of a complex set of hydraulic and geotechnical factors. The US Army Corps of Engineers (USACE) actively tracks and compiles data related to such events across the United States within their portfolio of levee systems. Recent experience suggests that frequency of flood events is increasing, leading to both increased stress on levees, as well as the probability of overtopping. As such, data related to this failure mode is constantly evolving. This paper presents and discusses a dataset of more than 200 overtopping events of USACE levee systems throughout the nation. The dataset is employed to examine the effects of various factors and to establish correlations among parameters using both breach and nonbreach events. Generating a discussion based on empirical evidence, this research is aimed at furthering the profession’s collective understanding of levee behavior when overtopping occurs. The dataset can provide a valuable basis for planning, design, and risk assessment of levees systems.
Article
Full-text available
Adaptation to climate change requires careful evaluation of infrastructure performance under future climatic extremes. This study demonstrates how multidisciplinary approach integrating geotechnical engineering, hydrology and climate science can be employed to quantify site-specific impacts of climate change on geotechnical infrastructure. Specifically, this paper quantifies effects of changes in future streamflow on the performance of an earthen levee in Sacramento, California, considering multiple modes of failure. Streamflow for historical (1950-2000) and projected (2049-2099) scenarios with different recurrence intervals were derived from routed hydrological simulations driven by bias-corrected global climate models. The historical and future flood levels were then applied in a set of transient coupled finite element seepage and limit equilibrium slope stability analyses to simulate the levee subjected to extreme streamflow. Variability in hydraulic and mechanical properties of soils was addressed using a Monte Carlo sampling method to evaluate and compare the probability of failure of the levee under different historical and future climate scenarios. Three individual modes (under seepage, uplift, and slope stability) along with lower and upper bounds for the combined mode of failure were examined. Results showed that incorporating future floods into levee failure analysis led to considerable reductions in the mean factor of safety and increases in the levee’s probability of failure, suggesting that risk assessment based on historical records can significantly underestimate the levee’s failure probability in a warming climate. Despite inherent uncertainties in future projections and substantial variability across climate models, evaluating infrastructure against projected extremes offers insights into their likely performance for the future.
Conference Paper
Full-text available
Earthen levees protecting coastal regions can be exposed to compound flooding induced by multiple drivers such as coastal water level, river discharge, and precipitation. However, the majority of flood hazard analyses consider only one flood driver at a time. This study numerically investigates the performance of an earthen levee in Sherman Island, Sacramento, CA, under compound flooding induced by fluvial and pluvial flooding. A finite element model is built for fully coupled 3D stress-flow simulations of the levee. The finite element model is then used to simulate the hydro-mechanical response of the levee under different flood scenarios. Fluvial flood hydrographs for different scenarios are obtained using a bivariate extreme analysis of peak river discharge and peak ocean level while accounting for the significance of correlation between these two variables. Pluvial flooding is characterized using intensity-duration-frequency (IDF) curves of extreme precipitations for the study area. The fluvial and pluvial flood patterns for different recurrence intervals are used in the finite element model to simulate the hydro-mechanical response of the levee. Results show that considering compound flooding leads to 8.7% and 18.6% reduction in the factor of safety for 2 and 50-year recurrence intervals, respectively.
Article
Full-text available
Understanding levee failures can be significantly improved by analysing historical failures, experiments and performance observations. Individual efforts have been undertaken to document flood defence failures but no systematically gathered large scale, open access dataset is currently available for thorough scientific research. Here, we introduce an efficiently structured, global database, called International Levee Performance Database (ILPD), which aims to become a valuable knowledge platform in the field of levee safety. It comprises information on levee characteristics, failure mechanisms, geotechnical investigations and breach processes for more than 1500 cases (October 2019). We provide a macro-scale analysis of the available data, aiming to provide insights on levee behaviour based on historical records. We outline common failure mechanisms of which external erosion is identified as the most frequent for levees. As an example, we investigate flood events occurred in Germany (2002, 2013) and examine breach characteristics of hundreds of failures. It is found that initial failure mechanisms have an influence on breach characteristics and that failures due to instability and internal erosion are less frequent but lead to larger breaches. Moreover, a relation between the return period and the expected breach density during a flood event is identified. These insights could complement flood risk assessments.
Article
Full-text available
We show that Cohen's Kappa and Matthews Correlation Coefficient (MCC), both extended and contrasted measures of performance in multi-class classification, are correlated in most situations, albeit can differ in others. Indeed, although in the symmetric case both match, we consider different unbalanced situations in which Kappa exhibits an undesired behavior (i.e. a worse classifier gets higher Kappa score), differing qualitatively from that of MCC. The debate about the incoherence in the behavior of Kappa revolves around the convenience, or not, of using a relative metric, which makes the interpretation of its values difficult. We extend these concerns by showing that its pitfalls can go even further. Through experimentation, we present a novel approach to this topic. We carry on a comprehensive study that identifies a scenario in which the contradictory behavior among MCC and Kappa emerges. Specifically, we find out that when there is a decrease to zero of the entropy of the elements out of the diagonal of the confusion matrix associated to a classifier, the discrepancy between Kappa and MCC rises, pointing to an anomalous performance of the former. We believe that this finding disables Kappa to be used in general as a performance measure to compare classifiers.
Article
Power distribution systems are continually challenged by extreme climatic events. The reliance of the energy sector on overhead infrastructures for electricity distribution has necessitated a paradigm shift in grid management toward resilience enhancement. Grid hardening strategies are among effective methods for improving resilience. Limited budget and resources, however, demand for optimal planning for hardening strategies. This paper develops a planning framework based on Deep Reinforcement Learning (DRL) to enhance the long-term resilience of distribution systems using hardening strategies. The resilience maximization problem is formulated as a Markov decision process and solved via integration of a novel ranking strategy, neural networks, and reinforcement learning. As opposed to targeting resilience against a single future hazard – a common approach in existing methods – the proposed framework quantifies life-cycle resilience considering the possibility of multiple stochastic events over a system’s life. This development is facilitated by a temporal reliability model that captures the compounding effects of gradual deterioration and hazard effects for stochastic hurricane occurrences. The framework is applied to a large-scale power distribution system with over 7000 poles. Results are compared to an optimal strategy by a mixed-integer nonlinear programming model solved using Branch and Bound (BB), as well as the strength-based strategy by U.S. National Electric Safety Code (NESC). Results indicate that the proposed framework significantly enhances the long-term resilience of the system compared to the NESC strategy by over 30% for a 100-year planning horizon. Furthermore, the DRL-based approach yields optimal solutions for problems that are computationally intractable for the BB algorithm.
Article
Identifying key variables that influence crack formation in buried concrete sewer pipes and impact their structural integrity is crucial for evaluating the leakage and collapse vulnerability of these underground structures. The present study performs a comprehensive global sensitivity analysis for these critical pipe responses considering various uncertainties associated with material properties and loading. A high-fidelity three-dimensional nonlinear Finite Element (FE) model of a typical pipe is developed and used to capture pipe behavior. Considering the significantly high computational demand of the generated FE model, a surrogate model using Bayesian Additive Regression Trees (BART) is developed to accurately approximate input-output relationships in this high-dimensional problem. Significant variables are subsequently determined via a global sensitivity analysis based on Sobol’s theorem through the application of Markov Chain Monte Carlo simulation to the trained BART model. Results indicate that concrete and backfill soil properties and variables associated with truckloads contribute significantly to the variation of key pipe responses, thereby affecting the likelihood of leakage and collapse. Findings of this study can benefit the design and management of sewer pipes in large wastewater networks and significantly reduce the complexity of assessing the reliability of sewer pipes.
Article
For geotechnical systems involving complex behaviors and significant uncertainties, metamodeling-based reliability methods based on fixed designs of experiment (passive metamodeling methods) are frequently applied. However, because of the passive nature of these methods, they do not guarantee accurate probability estimates. This issue also persists in estimates obtained from active metamodeling methods (metamodeling methods that update the design of experiment iteratively) if a global stopping criterion or a nonoptimal learning function is used for the type of problem. This study highlights the importance of addressing these issues by investigating an example of failure analysis of soil slopes and concludes that the stopping criteria for development and refinement of metamodels need to be objective and locally defined with respect to the limit state function (LSF) and with a direct link to the accuracy of the reliability estimates. To address these challenges, this study established an effective sampling region that optimally ignores candidate design samples with weak probability densities. This enabled the development of an effective learning function that facilitates the active learning process. Moreover, an analytical upper bound for the error in failure probability estimation, proposed by the authors, was adopted here to arrive at a local and objective stopping criterion. This method was applied on two soil slopes, the stability of which was evaluated by the strength reduction method (SRM) in FLAC3D. The results highlight that passive and active methods with global stopping criteria cannot guarantee an accurate estimate of the failure probability. Furthermore, the developed method can considerably reduce the computational demands while achieving accurate estimates of failure probabilities of soil slopes.