This document describes a comparative slope stability analysis of a levee in New Orleans using four different methods: the Method of Planes (MOP), limit equilibrium analysis, elastic finite element analysis, and elastoplastic finite element analysis using strength reduction. The analyses were performed on a levee section with known soil properties from site investigations. Results showing minimum factors of safety using each method are presented.

1. - 325 -
A Comparative Slope Stability Analysis
of New Orleans Levee Subjected to
Hurricane Loading
Yingzi Xu
Professor
College of Civil & Architectural Engineering, Guangxi University, P.R. China
e-mail: xuyingzi@gxu.edu.cn
Jaideep Chatterjee
Adjunct Assistant Professor
Department of Civil & Environmental Engineering, Jackson State University
e-mail: jaideep.chatterjee@jsums.edu
Farshad Amini
Professor and Chair
Department of Civil & Environmental Engineering, Jackson State University
e-mail: famini@jsums.edu
ABSTRACT
During Hurricane Katrina, New Orleans, Louisiana area and its vicinity suffered
significant damage to its Hurricane Protection System. Levees are one of the major
components of protection systems. Due to the unsatisfactory performance of some of the
protection measures during Hurricane Katrina, questions were raised regarding the choice
of the modeling and stability analysis methodology of the protection systems. Levees are
one of the major components of the hurricane protection systems. In the past, the New
Orleans District of the U.S Army Corps of Engineers had mostly relied upon the a
simplified slope stability analysis for design of levees in the New Orleans area. Thus,
there is a significant need to compare the stability analysis results of hurricane levees
using rigorous simulation and invoking numerical procedures so that the desired
confidence level can be established. In this paper, the slope stability analysis of New
Orleans levees is presented via rigorous modeling and simulation using simplified Corps
Method, limit equilibrium as well as Finite Element Method incorporating strength
reduction technique. To the best of author’s knowledge, such an extensive simulation of
slope stability analysis of hurricane protection levees does not exist in published
literature.
KEYWORDS: Slope Stability, Hurricane Protection, Levee, New Orleans
INTRODUCTION
Prior to Hurricane Katrina, the New Orleans District of the U.S. Army Corps of Engineers
(USACE) had relied on the method of planes (MOP) slope stability analysis for design of
hurricane protection measures (HPS) in the New Orleans area and vicinity. MOP slope stability
analysis is a simplified procedure in which the limit equilibriums of two wedges and a block,

2. Vol. 16 [2011], Bund. C 326
namely, the active wedge, the neutral block and the passive wedge are considered and the
minimum factor of safety for sliding along a horizontal plane is determined by summing the
horizontal forces. However, this method satisfies only horizontal force equilibrium and, therefore,
is not a total equilibrium method of slope stability analysis. On the other hand, many other slope
stability analysis procedures based on limit equilibrium methods utilizing slice discretiaztion
(Morgenstern and Price, 1965; Spencer, 1967) satisfy both force and moment equilibrium.
In the aftermath of Hurricane Katrina, due to the unsatisfactory performance of some of the
protection measures, including the I-wall levee system (Brandon et. al., 2008; Duncan et. al.,
2008) and regular mainline levees (Sills et al., 2008; Briaud et al., 2008) questions were raised
regarding the suitability of the MOP in analyzing the various components of the HPS. Levees are
the primary component of the HPS in the New Orleans area and its vicinity along the Mississippi
River and various outfall canals within the city limits. As a result, the interest in comparing the
simplified slope stability analysis results of levees with rigorous numerical analysis techniques
has intensified. Sills et al. (2008) discusses in detail about the lessons learned in levee failure in
New Orleans and their impact on the national levee design. A recent effort in this direction
addressing the stability of I-wall in New Orleans with gap condition invoking the limit
equilibrium method can be found in Brandon et al. (2008) and Chatterjee et al. (2009) However,
their efforts were mostly focused on the investigation of the effect of gap formation on stability of
I-wall.
Limit equilibrium based methods of slope stability analysis using slice discretiaztion
(Morgenstern and Price, 1965; Spencer, 1967; Janbu, 1964) is being widely used in the
geotechnical engineering practice. The method requires the soil mass to be divided into slices.
The limit equilibrium method of slices is purely based on the principle of statics in which the
force and/or moment equilibrium have to be satisfied. A rigorous review of equilibrium method
of slope stability can be found in Duncan (1996). Various commercial computer programs
(Slope/W, 2007) are available to perform rigorous slope stability analysis of soil slopes.
However, limit equilibrium method is not considered the primary design method in analyzing
levee stability because of the requirement of significant amount of modeling effort involved in the
process. MOP is considered as the primary design tool within the USACE districts because of its
simplicity and because it permits rapid re-calculation of factor of safety with minor changes in
design soil strength. As a consequence, prior to Katrina, the reliability of MOP in analyzing
levees with multiple soil layers and spatially varying strengths were not adequately addressed by
comparing with other rigorous numerical analysis techniques.
In the recent past, elastoplastic Finite Element Method (FEM) based on Strength Reduction
Technique (Griffiths and Lane, 1999; Dawson et al., 1999) has been proposed to analyze soil
slopes. Although this method is supposed to be most robust and free from any prior assumption of
the shape of the possible failure surface, most of the previous efforts in this direction involving
the Strength Reduction Method were restricted to verify simple slopes involving one or a few soil
layers without any spatial variation of soil strength within a layer. Extensive Finite Element
simulation of slope stability of real life problem involving multiple soil layers with spatial
variation of strength are very rare in published literature. In many cases, an elastic FEM analysis
is adequate to obtain a reasonable stress distribution within the slope, from which factor of safety
can be computed using regular slice discretization. Nonlinear constitutive models (Chen, 1982)
are often essential when the primary concern is the deformation. In the later case, excessive
movement of the slope governs the design compared to shear failure. However, the criteria of

3. Vol. 16 [2011], Bund. C 327
limiting slope movement have not been well established and the factor of safety is considered as
the popular choice in assuring its stability.
From the above discussion, it becomes evident that there are many uncertainties involved
with accurate prediction of stability of levees in New Orleans where the levees rest of multiple
layers of soft clay alluvial deposits with spatially varying shear strengths. The degree of
complexity involved with the levee modeling and stability analysis in this area makes it quite
challenging in the accurate prediction of the levee stability. There is a significant need to compare
the stability analysis results of hurricane protection levees using rigorous simulation and invoking
numerical procedures so that the desired confidence level can be established. In this paper, the
slope stability analysis of New Orleans levees is presented via rigorous modeling and simulation
using simplified method routinely used by the USACE, limit equilibrium, elastic FEM and
elastoplastic FEM based on Strength Reduction Technique using an explicit FEM program
ANSYS. A subroutine to perform the iterative Strength Reduction procedure has been developed
and implemented in ANSYS. To the best of author’s knowledge, such an extensive and
comprehensive simulation of slope stability analysis of the practical problem of New Orleans
hurricane protection levees does not exist in published literature.
MATERIALS AND METHODS
An overview of the numerical simulation procedures adopted in this comparative slope
stability work on New Orleans levee is presented as follows.
Method of Planes
The Method of Planes (MOP) slope stability analysis was developed by the Department of
Army, Lower Mississippi Valley Division, in Vicksburg, Mississippi in the 1950’s. It was later
implemented in a simple script based computer program “Stability with Uplift” (2002) which is
primarily used in the design of levees within the Mississippi Valley Division of the USACE.
MOP is a simplified procedure in which only the horizontal force equilibrium of two wedges and
a block, namely, the active wedge, a central or neutral block and a passive wedge, are considered.
The driving forces and the resisting forces in each block are obtained from the equilibrium of
these blocks by constructing the force diagrams. The buoyant force of water for the submerged
soil used in the shear strength calculation is incorporated in the formulation as an uplift force
acting normal to the sliding plane. A factor of safety against sliding is computed. Assuming the
slope movement occurs from left to right, the various forces acting on each block are shown in
Fig. 1. The following notations are used to denote the forces acting on the blocks and wedges in
MOP analysis:
W = Weight of water and soil in wedge
U = Total uplift force acting normal to sliding plane
H = Height of the block
N = Normal reaction on sliding plane
c = Cohesion of soil along the length of the sliding plane L
φ = Angle of internal friction of soil
AP and BP are active and passive forces, respectively

4. Vol. 16 [2011], Bund. C 328
Individual Forces Acting on the Blocks
Active Wedge Neutral Block Passive Wedge
Active Wedge Neutral Block Passive Wedge
Net Driving and Resisting Forces on the Blocks
Figure 1: Wedges and forces used in Method of Planes
For each of the active, passive and neutral blocks, let us identify D as the driving force and R
as the resisting force. For each of these blocks, D and R can be obtained by constructing the force
polygon which consists of the weight of the block W , the normal force N on the slide plane, and
the shear strength of soil being mobilized along the sliding plane. The uplift force U can also be
considered in the polygon of forces when the effective strength parameters are used for freely
draining material. However for purely cohesive material with undrained shear strength, the
consideration of uplift force is not necessary in the estimation of its shear strength.
The factor of safety with respect to the shear strength of soil can then be expressed as
Factor of safety (F.S) =
R
D


=
A B p
A p
R R R
D D
+ +
−
(1)
The subscripts A and P used in Eqn. (1) denote active and passive wedges, respectively, and
the subscript B denotes the central block. The above terms can be derived by drawing the force
polygons and by considering the equilibrium of the three wedges which can be used in lieu of
drawing force polygons when the active and passive failure planes are assumed inclined at angles
of ( )45 2φ+
and ( )45 2φ−
, respectively, with respect to the horizontal.
Limit Equilibrium
There are many different solution procedures using limit equilibrium using discretization of
slices (Morgenstern and Price, 1965; Spencer, 1967) which have been developed over the years.
AP
tanN φ
cL
U
N
o
45 + 2φ
W W
tanN φcL
N U
pP
45 2φ−
tanN φ
N
U
cL
H H
W
DA
RA
RB DP
RP

5. Vol. 16 [2011], Bund. C 329
Fundamentally, they are similar in nature. The differences among the various methods lie in the
fact that different equations of statics (moment, force) are being satisfied, different interslice
forces are considered, and different relationships between interslice forces are assumed. For
example, Janbu (1954) method only considers force equilibrium, which is similar to the
equilibrium equation used in MOP, whereas, Morgenstern and Price (1965) and Spencer (1967)
methods satisfy both force and moment equilibriums. These procedures have been extensively
documented in various literatures and are now standard routines in many commercial computer
programs. The details of limit equilibrium equations pertaining to slope stability are not presented
in this paper. Also, the limit equilibrium method requires continuous surfaces pass through the
soil mass along which the soil is considered to fail. Various shapes of these failure surfaces are
normally assumed which include circular, non-circular, wedge-shaped or surfaces with
combination of different shapes. All of these slip surfaces are essential in calculating the
minimum factor of safety against sliding, shear or rotational failure.
Finite Element and Strength Reduction
As mentioned earlier, FEM can be invoked to analyze the slope stability in two different
ways. In the first procedure, the finite element stresses obtained from a simple elastic analysis can
be incorporated in a conventional limit equilibrium analysis. Once the stresses, obtained using a
simple plane strain analysis of the slope are known within each element, the normal and
mobilized shear stresses at the base midpoint of each slice can be evaluated. Consequently, the
conventional factor of safety can be computed using regular slice discretization. This type of
elastic FEM analysis is incorporated in SLOPE/W (2007). It is important to note that this
approach based on elastic FEM stresses still requires an assumed shape of the failure surface.
Thus, this method does not completely eliminate the uncertainties associated with the prediction
of factor of safety.
The most accurate and mathematically sound methodology available to date is the
elastoplastic FEM based on Strength Reduction Technique (Griffiths and Lane, 1999; Dawson et
al., 1999). This method has many advantages over the conventional limit equilibrium methods.
No prior assumption of the failure surface is needed. Elastoplastic behavior of soil can be
modeled using any suitable nonlinear constitutive model such as elastic-perfectly plastic Mohr-
Coulomb and Drucker-Prager (Chen, 1982) models, which can be implemented in the FEM
formulation. This obviously represents more realistic soil behavior. The factor of safety of the
slope is defined as the factor or margin by which the original shear strength parameters are
reduced to bring the slope to the point of incipient failure. The failure is normally indicated by the
non-convergence of the FEM equations. The details of the Strength Reduction Technique can be
found in published literature and are not presented here. Unfortunately, due to the modeling
complexity, prediction of soil stiffness parameters and significant computational burden, most of
the work reported to date was restricted to comparison of simple slopes with published solutions.
As a result, the desired degree of confidence in using this method to analyze real life problems
has not been adequately established.
RESULTS
In this work, a New Orleans levee section located in the Orleans parish, Louisiana has been
chosen as shown in Fig. 2. The existing levee was enlarged to a higher elevation to provide
future level of hurricane protection. The geometry of the enlarged levee section and the ground

6. Vol. 16 [2011], Bund. C 330
surface elevations on the flood side and protected side of the levee were determined during a
recent survey conducted by the USACE. The elevations shown in Fig. 2 are based on the North
American Vertical Datum of 1988 (NAVD88). As shown in Fig. 2, the elevation of the top of
levee was at El. +7.9 m. The water elevation on the flood side of the levee due to hurricane
loading was assumed at the top of levee.
Figure 2: Carrollton Levee, soil layer number and failure surfaces for MOP analysis
The soil stratification, as shown and numbered in Fig. 2, is based on post Katrina undisturbed
test borings and cone penetration tests performed as part of the hurricane protection improvement
plan undertaken by the USACE. The design undrained shear strengths and wet densities were
obtained from the undisturbed borings and cone penetration tests conducted at the centerline,
protected side and flood side toes of the levee. The design shear strength and wet density
parameters used in the analyses are listed in Table 1. It should be noted that the Verticals 1, 2 and
3 denote, respectively, the flood side toe, centerline of the levee and the protected side toe.
Whenever there was a variation in the shear strengths and wet densities between the flood and
protected side toes and the centerline, a linear variation was assumed between the toe and the
centerline. Beyond the toe, the shear strengths and wet densities were assumed to remain
constant. In addition, shear strengths varied linearly with depth in some soil strata. Within these
strata, average strengths at the center and strengths at the bottom of each soil stratum are
presented in Table 1. The slope stability of this levee was evaluated via four distinct simulation
techniques which are described below.

7. Vol. 16 [2011], Bund. C 331
Table 1: Soil layer design strength and wet densities
The slope stability analysis was first conducted using MOP. In the MOP analysis, the water
on the flood side of the levee was modeled as a region having material unit weight of 9.81 kPa.
Based on the practice followed by the New Orleans District of the U.S. Army Corps of Engineers,
the width of the neutral blocks along the failure planes were not allowed to be shorter than 0.7 H ,
where H is the height of the active wedge. In MOP, failure surfaces were analyzed at the bottom
of each soil stratum and the minimum factors of safety at the bottom of each soil stratum are
reported. The results of the MOP slope stability analysis are presented in Table 2 where the
minimum factors of safeties of various failure surfaces (shown in Figure 2) at different elevations
are presented along with the corresponding driving and resisting forces. The minimum factor of
safety of 1.51 was obtained at El. -3.7 m using the MOP analysis.
Table 2: Summary of MOP analysis
Next, the levee was analyzed using conventional limit equilibrium methods based on slice
discretization using three procedures namely, Janbu (1954), Morgenstern and Price (1965) and
Spencer (1967) methods. In order to compare the MOP results, block type failure surfaces of
similar shape are analyzed at the bottom of each soil layers. The critical failure surface elevation
for all of these methods was at El. -3.7 m. The minimum factors of safety using the above three
methods were 1.53, 1.72 and 1.66, respectively for Janbu (1954), Morgenstern and Price (1965)
and Spencer (1967) methods.
Next, using the elastic stress based FEM approach, the levee was first analyzed for stress-
deformation using the computer program SIGMA/W (2007). The undrained shear strengths of
each soil layers were averaged and the elastic modulus was computed using the correlation
suggested by Duncan and Buchignani (1976) as 200 times the undrained shear strength of
respective soil layers. The undrained Poisson ratio was set to 0.49 to avoid any computational
difficulty with the use of exact value of 0.5. The elastic ground stresses were first established by
simple gravity turn on technique available in SIGMA/W (2007). Then, the water loading was
Vertical 1 Vertical 2 Vertical 3
Soil Layer Description Friction Unit Cohesion (Kpa) Unit Cohesion (Kpa) Unit Cohesion (Kpa)
Number Angle Weight Weight Weight
(degrees) (KN/M
3
) Center Bottom (KN/M
3
) Center Bottom (KN/M
3
) Center Bottom
1 WATER 0 9.81 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2 CLAY 0 17.3 20.0 20.0 17.3 20.0 20.0 17.3 20.0 20.0
3 CLAY 0 18.4 17.5 17.5 18.4 25.0 25.0 18.4 17.5 17.5
4 CLAY 0 18.4 17.5 17.5 18.4 26.7 28.4 18.4 17.5 17.5
5 CLAY 0 16.3 19.5 21.5 16.3 30.0 31.7 16.3 17.5 17.5
6 CLAY 0 17.3 35.5 49.5 17.3 43.4 55.0 17.3 31.8 46.0
Elastic
Modulus Es
Factor of
Safety
Plastic
Strain εp1
Plastic
Strain εpxy
Displacement
usum
Displacement
uxmin
Displacement
uxmax
150Cu 1.87 0.522 -1.045 0.828 -0.642 0.034
200Cu 1.87 0.401 -0.802 0.6296 -0.489 0.026
400Cu 1.87 0.196 -0.393 0.312 -0.241 0.013
1000Cu 1.88 0.907 -1.83 0.838 -0.835 0.0077
2000Cu 1.88 0.458 -0.916 0.424 -0.4224 0.0039
5000Cu 1.88 0.1929 -0.386 0.179 -0.179 0.0016

8. Vol. 16 [2011], Bund. C 332
applied on the flood side of the levee as uniform loading on ground surface and the resultant
elastic stresses were superimposed on the previously calculated in-situ ground stresses. Then, the
resultant stress field was used in a conventional limit equilibrium analysis in SLOPE/W (2007)
based on slice discretization. SLOPE/W (2007) can handle spatial variation of soil strength. For
comparison, similar failure surface shapes were also assumed for analysis based on finite element
elastic stresses. The critical failure surface elevation was again at El. -3.7 and the corresponding
minimum factor of safety was 1.58.
Finally, in order to assess the reliability of the above predictions and to get a clear picture of
the degree of conservativeness of each of the simulation results, the levee was analyzed using
elastoplastic FEM invoking the Strength Reduction Technique using the FEM code ANSYS.
Here, it should be pointed out that the elastic stress based FEM simulation does not predict the
realistic soil stresses as the real behavior of soil is elastoplastic rather than purely elastic. Also, it
that FEM simulation, a shape of the failure surface was assumed in the traditional limit
equilibrium method, which might not reflect the shape of the actual failure surface. Using the
elastoplastic FEM, it was possible to simulate the realistic stress field within the levee
embankment. Also, no assumption was necessary regarding the shape of the failure surface as
ANSYS automatically detects the critical surface. In the ANSYS simulation, the levee was
modeled as a plane strain problem. Four nodded PLANE82 element was found to be adequate in
capturing the stresses in soil. Elastic-perfectly plastic Drucker Prager model (Chen, 1982) was
used to simulate the elastoplastic soil behavior. The far field boundary conditions were modeled
appropriately and the model was fixed at the base. The hurricane loading on the flood side of the
levee was simulated using externally applied hydrostatic pressure on the model. The Poisson ratio
of the soil was selected as 0.49 which is very close to the exact value of 0.5 to simulate undrained
soil behavior. The value of 0.49 was chosen to avoid numerical error in convergence of the
ANSYS simulation. As with the elastic FEM simulation, the spatially varying undrained shear
strengths of each soil layers were averaged and the elastic modulus was computed using the
correlation suggested by Duncan and Buchignani (1976) as 200 times the undrained shear
strength of respective soil layers. The finite element mesh used in the ANSYS simulation is
shown in Fig. 3.
Figure 3: ANSYS simulation, Finite Element Mesh

9. Vol. 16 [2011], Bund. C 333
In the ANSYS model, the flood side is located on the right hand side of the model and the
slope movement was from right to left which is opposite to what was used in other simulations.
The Strength Reduction Scheme was externally programmed and fed into ANSYS. The critical
failure surface in the ANSYS simulation was located at about El. -4.0 m which is almost similar
to the elevation of the critical failure surface obtained using the previous simulations. In order to
investigate the effect of elastic modulus values of soil layers on the final factor of safety, the
ANSYS model was analyzed for different ratios of the elastic modulus of each soil layers to their
respective shear strengths. The changes in elastic modulus do not appear to influence the factor of
safety. However, the slope displacements were obviously different in each of the ANSYS
simulations. Since there is no specific guidance available on the limiting slope movement for the
New Orleans levee, it was difficult to determine the failure based on the slope movement rather
than allowing ANSYS to continue solution until no convergence based on conventional shear
failure criteria. However, ANSYS provides the user the freedom to choose a limiting value based
on movement and decide the failure whenever the displacement is unreasonably large. The results
of ANSYS simulation is summarized in Table 3. As mentioned before, analyzing failure surface
at each elevation does not apply to ANSYS simulation as the program automatically detects the
shape and location of the critical surface as collapse occurs. The displacements and plastic strains
for each simulation are indicated in Table 3. In this table, uC denotes the undrained shear
strength of soil. The critical failure surface at collapse using ANSYS simulation is presented in
Fig. 4.
Figure 4: ANSYS simulation, results at collapse (FOS = 1.87)

10. Vol. 16 [2011], Bund. C 334
Table 3: Summary of ANSYS simulations
DISCUSSION
The comparative slope stability analysis is summarized in Table 4. The results obtained using
Janbu (1954) method appears to be almost identical with those of MOP. This is expected since
both of these methods satisfy only horizontal force equilibrium. The factors of safety obtained
using Spencer (1967) and Morgenstern and Price (1965) methods appears to be slightly higher
than the MOP factors of safety. However, very close agreement can be observed, as expected
between these two limit equilibrium methods since both satisfy force as well as moment
equilibriums. Interestingly, the finite element stress based limit equilibrium method appears to
produce factors of safety values which are not very different from other results. They are more
close to Janbu (1954) and MOP factors of safety. MOP results appear to be most conservative.
The most robust and comprehensive analysis using ANSYS produced a factor of safety of 1.87 at
El. -3.7 m which appears to be slightly higher than all of the other simulation results. Thus, in
terms of factor of safety, ANSYS simulation appears to suggest that all of the other simulations
are conservative compared to ANSYS simulation. A comparison based on slope movement
cannot be performed because none of the simulations other than ANSYS simulation could predict
the slope movement.
CONCLUSIONS
For the first time, a comprehensive study of slope stability and rigorous description of
available analysis procedures has been presented in the context of hurricane protection levees in
New Orleans resting on soft marsh deposits. Previous design efforts of New Orleans levees were
restricted to the use of simple MOP analyses and a comparative picture of using all possible
methods of analysis was never investigated. For a typical New Orleans levee adopted in this
FAILURE
SURFACE
SUMMATION OF FORCES
IN KN/M
RESISTING DRIVING
FACTOR OF
SAFETY
600.5 260.3 2.29
671.7 311.8 2.15
718.7 325.7 2.19
840.5 32.92 1.75
924.5 480.6 1.73
1012.4 575.1 1.76
1084.8 712.8 1.52
1130.0 746.1 1.51
1175.3 772.5 1.52
3577.3 2088.1 1.71
A 1
A 2
A 3
B 1
B 2
B 3
C 1
C 2
C 3
D 1

11. Vol. 16 [2011], Bund. C 335
work, it was found that the MOP analysis produces conservative factors of safety as compared to
other available methods. The most comprehensive and accurate simulation using ANSYS based
on Strength Reduction Technique appears to suggest that all of the other methods are
conservative. However, ANSYS simulation provides an opportunity of establishing a criterion
based on limiting slope movement which is not well established for analysis of New Orleans
levees. For relatively simple levees, the use of at least limit equilibrium method in conjunction
with MOP is suggested to verify the results and adopt the appropriate factor of safety based on
experience. However, for more complex levee geometry, loading and soil stratification, the
verification of results by invoking elastoplastic FEM using Strength Reduction Technique is
highly recommended. The authors believe that the findings of this comparative study will
advance the design and analysis of New Orleans Hurricane Protection levees in future assessment
of stability of this important hurricane protection measure in New Orleans area.
ACKNOWLEDGEMENTS
The authors would like to express their sincere thanks to the Engineer, Research and
Development Center (ERDC) of U.S. Army Corps of Engineers, Vicksburg, Mississippi for
making available the computer program “Stability with Uplift (2002)” based on Method of Planes
for slope stability analysis. The computing resources provided by Jackson State University are
gratefully acknowledged. This enabled us to invoke various sophisticated slope stability programs
into this simulation work. This support by the Department of Homeland Security (DHS) through
the Department of Energy Oak Ridge National Laboratory is also gratefully acknowledged. The
conclusions in this paper are solely those of the authors and do not necessarily reflect the opinions
or policies of DHS. Endorsement by DHS is not implied and should not be assumed.
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