SimEx: A tool for the rapid evaluation of the effects of
Juan Sánchez-Monreal †, Alberto Cuadra , César Huete and Marcos Vera*
Citation: Sánchez-Monreal, J.;
Cuadra, A.; Huete, C; Vera, M.
SimEx: A tool for the rapid
evaluation of the effects of
explosions. Appl. Sci. 2022,1, 0.
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Copyright: © 2022 by the authors.
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Departamento de Ingeniería Térmica y de Fluidos, Escuela Politécnica Superior,
Universidad Carlos III de Madrid, 28911 Leganés, Spain
*Correspondence: firstname.lastname@example.org; Tel.: +34 91 624 99 87
† Current address: Institute of Engineering Thermodynamics, German Aerospace Center (DLR),
Pfaffenwaldring 38–40, 70569 Stuttgart, Germany
The dynamic response of structural elements subjected to blast loading is a problem
of growing interest in the ﬁeld of defense and security. In this work, a novel computational tool
for the rapid evaluation of the effects of explosions, hereafter referred to as SimEx, is presented
and discussed. The classical correlations for the reference chemical (1 kg of TNT) and nuclear
kg of TNT) explosions, both spherical and hemispherical, are used together with the blast
wave scaling laws and the International Standard Atmosphere (ISA) to compute the dynamic
response of Single-Degree-of-Freedom (SDOF) systems subject to blast loading. The underlying
simpliﬁcations in the analysis of the structural response follow the directives established by UFC
3-340-02 and the Protective Design Center Technical Reports of the US Army Corps of Engineers.
This offers useful estimates with a low computational cost that enable in particular the computation
of damage diagrams in the Charge Weight-Standoff distance (CW-S) space for the rapid screening
of component (or building) damage levels. SimEx is a computer application based on Matlab and
developed by the Fluid Mechanics Research Group at University Carlos III of Madrid (UC3M).
It has been successfully used for both teaching and research purposes in the Degree in Security
Engineering, taught to the future Guardia Civil ofﬁcers at the Spanish University Center of the
Civil Guard (CUGC). This dual use has allowed the development of the application well beyond
its initial objective, testing on one hand the implemented capacities by undergraduate cadets with
end-user proﬁle, and implementing new functionalities and utilities by Masters and PhD students.
With this experience, the application has been continuously growing since its initial inception in
2014 both at a visual and a functional level, including new effects in the propagation of the blast
waves, such as clearing and conﬁnement, and incorporating new calculation assistants, such as
those for the thermochemical analysis of explosive mixtures; crater formation; fragment mass
distributions, ejection speeds and ballistic trajectories; and the statistical evaluation of damage to
people due to overpressure, body projection, and fragment injuries.
Effects of Explosions; Blast loading; SDOF systems; Thermochemistry of Explosives;
Fragments; Crater formation; Damage to people
Unlike the slow energy release exhibited by deﬂagrations, the instantaneous energy
deposition associated with the detonation of a high explosive produces an extremely
rapid increase in temperature and pressure due to the sudden release of heat, light and
]. The gases produced by the explosion, initially at extremely high temperatures
and pressures, expand abruptly against the surrounding atmosphere, vigorously pushing
away any other object that may be found in their path. This gives rise to the two most
notable effects of explosions: the aerial, or blast, wave [
], and the projection of shell
fragments or other items (i.e., secondary fragments) located in the surroundings of the
]. If the explosive device is located at ground level, a fraction of its energy is
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Version September 5, 2022 submitted to Appl. Sci. 2 of 23
effectively coupled to the ground, generating seismic waves and a well distinguished
surface crater that results from the ejection of the shattered ground materials in direct
contact with the charge [
]. Quantifying these phenomena and assessing their effect
on the environment, including structural elements, vehicles, objects, or people located
around the blast site, is a highly complex task that requires a thorough knowledge of the
physical-chemistry of explosions [
] and their dynamic interactions with nearby
structures  or the human body .
As a result of the growing terrorist threat experienced in the last decades [
estimating the effects of explosions has become a critical issue in the design, protection
and restoration of buildings and infrastructures, both civil and military [
this task is far from trivial, in that it involves transient compressible ﬂows, non-linear
structural response, and highly dynamic ﬂuid-structure interactions. These phenomena
can be described with some accuracy using multiphysics computational tools, also
known as hydrocodes [
], such as Ansys Autodyn, LS-Dyna, or Abaqus, based on the
explicit ﬁnite element method [
]. In the simulations, all the critical components are
modeled, including the detonation of the explosive charge, the resulting blast wave,
the induced dynamic loads, and the non-linear structural response. However, the
enormous computational effort required to complete detailed computational analyses,
which includes not only the calculation time itself, but also complex pre- and post-
processing stages, remains a critical issue. For instance, simulating the effect of an
explosive charge on a full-scale bridge may require more than 10 million ﬁnite elements
]. For this reason, most engineering analyses still make use of simpliﬁed models
for determining the explosive loads and estimating the resulting dynamic structural
response in a timely manner. This enables the fast computation of damage diagrams in
the Charge Weight-Standoff distance (CW-S) space, of utility to determine the level of
protection provided by an input structural component loaded by blast from an input
equivalent TNT charge weight and standoff .
In this regard, the American Uniﬁed Facilities Criteria UFC 3-340-02 [
supersedes former ARMY TM 5-1300, establishes the requirements imposed by the US
Department of Defense in the tasks of planning, design, construction, maintenance,
restoration and modernization of those facilities that must be protected against explosive
threats. In the absence of similar regulations in other countries, UFC 3-340-02 [
widely used by engineers and contractors outside the US, as it provides a valuable
guide for calculating the effects of blast-induced dynamic loads, including step-by-step
procedures for the analysis and design of buildings to resist the effects of explosions.
To facilitate the application of the procedures set forth in the UFC 3-340-02 [
as well as other analyses established in classic references of explosives engineering
], fast evaluation software tools have been developed that incorporate
the vast amount of data available as tables or graphs in the literature [
]. For instance,
the United States Army Corps of Engineers (USACE) has developed and provides
support for a series of software packages related to the design of explosion-resistant
]. Those tools were developed with public funding, and therefore there
are regulations that restrict distributing those products outside of the United States. In
addition, given the critical nature of this knowledge, access to these packages is severely
limited to US government agencies and their contractors, with use only authorized to
The inability to access these software packages motivated the authors to develop
their own computational toolbox for the rapid evaluation of the effects of explosions.
The result was the SimEx platform to be presented in this work. Conceived initially
for educational purposes, the main goal was to develop a virtual software platform
with an easy and intuitive Graphical User Interface (GUI) to be used in the computer
lab sessions of the Explosion Dynamics course of the Degree in Security Engineering,
taught at the University Center of the Civil Guard (CUGC) in Aranjuez, Spain. The Civil
Guard is the oldest and biggest law enforcement agency in Spain. Of military nature, its
Version September 5, 2022 submitted to Appl. Sci. 3 of 23
competencies include delinquency prevention, crime investigation, counter-terrorism
operations, coastline and border security, dignitary and infrastructure protection, as
well as trafﬁc, environment or weapons and explosives control using the latest research
techniques. The paradigm of the Civil Guard’s capacity is its outstanding role in the
defeat of the terrorist group ETA, the longest-running terrorist group in Europe and
the best technically prepared. In this context, the main target of the Degree in Security
Engineering is the training of Guardia Civil cadets (i.e., the Guardia Civil’s future ofﬁcer
leadership) in the development, integration and management of last generation civil
The purpose of SimEx was initially limited to the blast damage assessment on
simple structural elements [
], such as beams, columns, pillars, or walls, following the
Single-Degree-of-Freedom (SDOF) system analysis established by UFC 3-340-02 [
tool has been successfully used since its initial inception in 2014 in both the computer lab
sessions of the Explosion Dynamics course, and as a research tool for the development
of a number of Bachelor and Master’s thesis on explosion dynamics and blast effects.
This double use as end-users and software developers by the Civil Guard cadets and
students from other UC3M degrees has enabled the development of the application well
beyond the initially planned objectives [
]. As a result, the current version of SimEx
incorporates advanced topics in blast wave propagation, such as the prediction of cleared
blast pressure loads due to the generation of rarefaction waves, as well as conﬁned blast
loading in vented structures [
]. It also includes several other calculation assistants for
the thermochemical analysis of explosive mixtures [
]; crater formation [
fragment mass distributions, ejection speeds and ballistic trajectories [
the statistical evaluation of damage to people due to overpressure, body projection and
fragment injuries [24,51,58].
2. SimEx capabilities
This section presents the current capabilities of SimEx, starting with the main
interface used for computing the dynamic response of SDOF systems subjected to blast
loading, and following with the description of the remaining calculation assistants.
2.1. Single-Degree-of-Freedom system analysis
In many situations of practical interest, the response of structural elements to blast
loading can be reduced, in ﬁrst approximation, to that of an equivalent spring-mass
SDOF system. As sketched in Figure 1, this system is made up by a concentrated
mass subject to external forcing and a non-linear weightless spring representing the
resistance of the structure against deformation [
]. The mass of the equivalent system is
based on the component mass, the dynamic load is imposed by the blast wave, and the
spring stiffness and yield strain on the component structural stiffness and load capacity.
Generally, a small viscous damping is also included to account for all energy dissipated
during the dynamic response that is not accounted by the spring-mass system, such
as slip and friction at joints and supports, material cracking, or concrete reinforcement
bond slip .
If the system properties are properly deﬁned, the deﬂection of the spring-mass
, will reproduce the deﬂection of a characteristic point on the actual system
(e.g., the maximum deﬂection). The system properties required for the determination of
the maximum deﬂection are the effective mass of the equivalent SDOF system,
effective viscous damping,
, the effective resistance function,
, and the effective
load history acting on the system,
. To systematize the calculations, the effective
properties are obtained using dimensionless transformation factors that multiply the
actual properties of the blast-loaded component, respectively,
These factors are obtained from energy conservation arguments in order to guarantee
that the equivalent SDOF system has the same work, kinetic, and strain energies as the
Version September 5, 2022 submitted to Appl. Sci. 4 of 23
real component for the same deﬂection when it responds in a given, assumed mode
shape, typically the fundamental vibrational mode of the system .
In the analysis of blast-loaded SDOF systems it is therefore of prime importance to
identify the fundamental vibrational mode of the structural element. This procedure is
not trivial, since obtaining the fundamental mode can entail certain difﬁculties, in which
case its shape must be approximated in some way [
]. To determine the equivalent
properties of the SDOF system it is also necessary to determine the type of structure
(beam, pillar, frame, etc.) and how the load is applied (typically, a uniform load is
assumed). The elastic behavior of the material is often modeled as perfect elasto-plastic,
probably the simplest of all nonlinear material models. This assumes that the initial
response follows a linear elastic behaviour described by an apparent elastic constant K,
but once the yield strain is reached,
, the material behaves as plastic, ﬂowing at a
constant stress with an ultimate resistance Ru=Kxu, i.e.,
R(x) = (Kx for |x|<xu
Rufor |x| ≥ xu(1)
Although more complex models could be used, they are not considered here due to the
heavy simpliﬁcations introduced in the formulation of the problem.
The mass transformation factor,
, is deﬁned as the ratio between the equivalent
and the real mass
of the blast-loaded component; the load transformation
is deﬁned as the ratio between the equivalent load
and the actual load
, and usually coincides with the resistance and damping transformation factors; and
ﬁnally the load-mass factor
is deﬁned as the ratio between the mass factor and the
Although all these factors are easy to obtain, even through analytical expressions in
some cases, most of them can be found tabulated in the UFC-3-340-02 .
The linear momentum equation for the equivalent SDOF system then takes the
x+R(x) = F(t)(3)
where, as previously discussed,
represents the viscous damping constant of the blast-
loaded component. This constant is often speciﬁed as a small percentage,
, of the
critical viscous damping,
, with a damping coefﬁcient
2 being a
good value when not otherwise known (for further details see [
]). Note, however, that
damping has very little effect on the maximum displacement, which typically occurs
during the ﬁrst cycle of oscillation, so the actual value of
is not of major relevance. The
, appearing on the right hand side of Equation
the dynamic load associated with the blast wave, to be discussed in Section 2.1.1 below.
SimEx provides an easy and intuitive GUI environment for the study of the dynamic
response to blast loadings of a variety of structural elements that can be modeled as
SDOF systems. Figure 2shows the main SimEx interface, divided into three calculation
assistants for the three basic elements that make up the SDOF system: a module for
calculating the properties of the blast wave (forcing term,
), a module for calculating
the equivalent mechanical properties (resistance term,
), and a module for the
numerical integration of the problem, which includes the post-processing of the results
and their graphic representation in the form of displacements, forces and deformation
diagrams (see the bottom plots of Figure 2) and of CW-S damage charts, to be discussed
in Section 3.3.
As a ﬁnal remark, it is important to note that, following standard practice, the SDOF
analysis carried out by SimEx uses the load deﬁned in terms of pressure,
F(t) = p0(t)
(Pa), so that both the mass
), the damping coefﬁcient
) and the
Version September 5, 2022 submitted to Appl. Sci. 5 of 23
Sketch of the equivalent SDOF system showing the different terms involved in its
mathematical description. Left: forcing term; right: resistance term; center: equivalent spring-
mass SDOF system and its associated differential equation.
(Pa) must all be introduced as distributed values per unit surface
(p.u.s.) in the different calculation assistants.
2.1.1. Forcing term
As previously discussed, the blast wave overpressure deﬁned in Equation (4) below
can be used directly in Equation (3) as forcing term,
F(t) = p0(t)
, as long as the analysis
is formulated per unit surface and uses distributed masses and forces. In order to
determine the blast parameters (arrival time, peak overpressure, positive phase duration,
impulse per unit area, waveform parameter, etc.), classical correlations [
] in terms of scaled distance are used together with the scaling laws for spherical
or hemispherical blast waves [
], which allow their evaluation for arbitrary
CW-S pairs. It is interesting to note that the standoff distance is deﬁned as the minimum
distance from the charge to the structural element under study (e.g., a wall). However,
the actual distance to a given point of that element, e.g., the centroid (or geometric
center), which may be considered the most representative point of the structure, may by
slightly different due to the incidence angle being larger than 0 at that point.
The local atmospheric pressure,
, and temperature,
, are determined using
the International Civil Aviation Organization (ICAO) Standard Atmosphere (ISA) [
with a temperature offset (ISA
). The user must specify the geopotential height,
in meters, and the non-standard offset temperature
, although arbitrary ambient
temperature and pressure can also be introduced directly [
]. TNT is used as reference
explosive, although the results can be extrapolated to other compositions using either the
equivalence tables included in SimEx for selected explosives [
], or the thermochemical
calculation assistant, to be presented in section 2.2.1, for less conventional formulations
or explosive mixtures.
To estimate the dynamic load exerted by the blast wave, the angle of incidence of
the incoming shock wave must be considered, the worst-case conditions being usually
those of normal incidence. UFC 3-340-02 [
] contains scaled magnitude data for both
spherical and hemispherical blast waves. It also provides methods to calculate the
properties of the blast wave with different incidence angles, including both ordinary and
Mach reﬂections for oblique shocks. The time evolution of the blast wave overpressure
at a ﬁxed distance,
, sufﬁciently far from the charge (at least, larger than the
ﬁreball scaled distance) is approximated using the modiﬁed Friedlander’s equation,
which captures also the negative overpressure phase [8,21,35]
p0(t0) = p(t0)−p1=p◦1−t0
represents the peak overpressure measured from the undisturbed
denoting the peak post-shock pressure,
Version September 5, 2022 submitted to Appl. Sci. 6 of 23
Charge weigth (kg)
Incident angle (deg)
Atmosphere (ISA +/- DT)
DT (ISA +/- DT)
Altura (m - ISA)
UFC 3-340-02 Hemi Friendlander
I/A (kPa ms)
i_g (kPa ms)
Damage analysis. CW-S diagram
Standoff distance interval (m)
Charge weight interval (kg)
Number of points
z (% C_cr)
C_cr (kg/(m² s))
Equivalent mechanical properties
Main interface of SimEx showing the “Blast wave”, “Resistance” and “Integration” assistants for the computation
of the structural response of perfect elasto-plastic SDOF systems under blast loading. The access buttons to the other
calculation assistants are seen under the top toolbar. The bottom plots shows the post-processing pop-up window that
displays the results of the numerical integration in terms of displacements, forces and deformation diagrams (for a detailed
discussion of these diagrams see Section 2.1.4).
is time measured from the blast arrival time,
is the positive phase duration, and
is the waveform parameter, closely related to the impulse per unit area of the positive
(area under the positive phase of the overpressure-time curve)
. SimEx performs by default the complete
integration of the Friedlander waveform, but the equivalent triangular pressure pulse
can also be used without signiﬁcant errors [
]. This simpliﬁed waveform has the same
maximum peak overpressure,
, but a ﬁctitious positive duration computed in terms of
the total positive impulse and the peak over pressure, td=2(I/A)/p◦.
The “Blast wave” calculation assistant allows the activation of the effects of clearing
and conﬁned explosions, which increases the computational capabilities to more realistic
situations. The clearing effect takes into account the time required for reﬂected pressures
to clear a solid wall that has received the impact of a blast wave as a result of the
propagation of rarefaction waves from the edges of the wall. In the case of conﬁned
Version September 5, 2022 submitted to Appl. Sci. 7 of 23
explosions, SimEx implements the procedure outlined in UFC 3-340-02 [
] to estimate
the gas phase peak overpressure and duration of the equivalent triangular pressure
pulse in terms of the chamber’s total vent area and free volume. These effects can be
activated on the lower part of the “Blast wave” calculation assistant.
2.1.2. Resistance term
The “Resistance” calculation assistant provides a means to deﬁne the equivalent
mechanical properties (i.e., structural mass, damping coefﬁcient, and structural strength)
of the SDOF system under study modeled as a perfectly elasto-plastic system with elastic
until the yield strain, as given in Equation
. The characteristic length,
, of the structural element must also be provided, as it is required to determine the
maximum rotation angle at its boundaries, often referred to as support rotation,
the equivalent SDOF system, the assistant computes the fundamental natural period,
, the critical damping,
, and the deﬂection at which
plastic deformation initiates in the system,
. Direct access to calculation assistants that
compute the equivalent properties (
) required for the calculations are also
provided for various types of systems. Currently, standard European wide ﬂange “metal
] and reinforced “concrete beams” are included (see Section 3.2), although it
could be possible to incorporate additional assistants for other elements, such as metal
panels/plates, open-web steel joists, reinforced concrete slabs, reinforced/unreinforced
masonry, or wood panels/beams. The metal beams assistant also provides the possibility
of studying custom (i.e., non-normalized) proﬁles and materials in order to widen the
2.1.3. Numerical integration
Once the characteristics of the equivalent SDOF system have been deﬁned, the
resulting ordinary differential equation that models the transient non-linear response
of the equivalent structural system
must be integrated numerically. The integration
module implements the two numerical methods recommended by UFC-3-340-02 [
namely the “Acceleration-Impulse-Extrapolation Method” and the “Average Accelera-
tion Method” [
], which can be selected from a drop-down menu. Text boxes are also
included to set the initial conditions (displacement and initial speed, which are zero by
default) as well as the ﬁnal integration time. Since both numerical methods use constant
time steps, a sufﬁciently short time increment, typically of the order of a few percentage
of the natural period or the positive phase duration (usually, fractions of a millisecond),
should be used in order to ensure the numerical convergence of the integration.
After integration, three plots appear in a pop-up window and a summary table
is provided at the bottom left corner of the main window. The left plot shows the
instantaneous displacement (solid line) and the permanent displacement, or deformation
(dashed line). The central plot shows the temporal variation of the forcing term (i.e.,
the blast pressure wave, solid line) together with the resistance strength of the SDOF
system (dashed line). The right plot shows the displacement-resistance graph, in which
it is possible to determine more clearly whether permanent deformations occur or not.
Finally, the table of results shows the maximum displacement obtained,
, along with
two damage indicators: the ductility ratio,
, deﬁned as the ratio of the peak
deﬂection to the ultimate elastic deﬂection, and the maximum support rotation,
calculation depends on the type of structure under study.
By integrating different combinations of charge weights and standoff distances
for the same structural element, damage level diagrams can be rapidly obtained in
the CW-S distance space. SimEx has a function for it located in the central part of the
integrator module. One can select the range of charge weights and standoff distances,
the number of intermediate values and the type of damage in terms of the quantitative
Version September 5, 2022 submitted to Appl. Sci. 8 of 23
]. From the two quantitative indicators, the structural damage level
can be classiﬁed qualitatively into: superﬁcial, moderate, heavy, hazardous failure, and
blowout, with response limit boundaries between these levels denoted respectively by B1
(superﬁcial to moderate), B2 (moderate to heavy), B3 (heavy to hazardous failure), and
B4 (hazardous failure to blowout). Convenient limits for the boundaries of component
damage levels for common structural components in terms of
are provided in
]. An example of a damage level diagram for the façade of a conventional building
subject to blast loading computed with SimEx will be presented in Section 3.3 .
2.2. Other calculation assistants
The main SimEx interface gives access to several other calculation assistants. These
include: a module for the calculation of the theoretical (i.e., thermochemical) properties
of explosives and explosive mixtures; a module for estimating the initial velocity, mass
distribution and ballistic trajectories of primary fragments; a crater formation calculator;
and a module for estimating damage to people, including both primary and tertiary
injuries. The fragment assistant also provides estimations of the secondary injuries due
to the impact of primary fragments on people. In this section we shall brieﬂy present
and discuss the above-mentioned assistants.
2.2.1. Assistant for the calculation of the thermodynamic properties of explosives
For the calculation of the theoretical thermodynamic properties of explosives and
explosive mixtures, SimEx includes an extensive database of pure CHNO propellants
and explosives extracted from Kinney & Graham [
], updated with data from Meyer
] and Akhavan [
] for more recent explosives. From the properties of pure explosives,
the thermochemical assistant estimates the properties of explosive mixtures formed by
two or more components by specifying the mass fractions and the density of the mixture.
First, it computes the apparent chemical formula of the explosive mixture along
with its molecular weight and maximum density. For the calculation of the decom-
position reaction in nominal products, which provides the heat of explosion and the
volume of gases generated, one can choose different calculation hypotheses: Kamlet-
Jacobs (KJ), Kistiakowsky-Wilson (KW), Modiﬁed Kistiakowsky-Wilson (modiﬁed KW),
Springall-Roberts (SR), or chemical equilibrium [
]. In the latter case, SimEx determines
the composition of the product mixture following the chemical equilibrium approach
considering a constant-volume explosion transformation that uses the ideal gas Equation
Entropy [kJ/(kg K)]
gamma = cp/cv [-]
Volume gases [m3/kg]
Internal energy [kJ/kg]
Sound speed [m/s]
Mean Molecular Weight [g/mol]
cp [kJ/(kg K)]
Heat release [kJ/kg]
Detonation speed [m/s]
Gurney constant [m/s]
Explosive force [kJ/kg]
Oxygen Balance [%]
Charge weight [kg]
C 7.1885 CA 0.0999 H 43.9106 MG 0.0791
N 20.7720 O 35.6249 SI 0.1055
Equation of State
Interface of the assistant for the calculation of the theoretical thermodynamic properties
of explosives and explosive mixtures.
Version September 5, 2022 submitted to Appl. Sci. 9 of 23
Composition [mass %], density, and oxygen balance of different explosive mixtures tested.
Component ANFO ANFO-Al Emulsion Dinamite I Dinamite II
Aluminium — 5 — — —
Ammonium nitrate 94 91 80 — 49
Cellulose — — — — 3
2,4-Dinitrotoluene — — — — 4
Nitrocellulose 12% — — 10 — 4
Nitroglycerin — — — 45 20
Nitroglycol — — — 45 20
Fuel oil 6 4 7 — —
Sodium nitrate — — 5 — —
Water — — 8 — —
Density [kg/m3]850 850 1300 1500 1500
Oxygen balance [%] −1.7 0.08 −5.57 −2.26 0.84
Comparison of the calculated temperature at constant volume,
, detonation pressure,
, detonation velocity,
, heat release at constant volume,
, and explosive force,
, with the
results provided by the European Standard EN 13631-15 [
] and by the thermochemical code
W-DETCOM  for different explosive mixtures using the BKW-S EoS.
Explosive Source T[K] pCJ [GPa] vCJ [m/s] Qv[kJ/kg] Fe[kJ/kg]
CT 2592 7.14 5353 3845 943
EN 13631-15 2586 — — 3820 945
W-DETCOM12919 6.62 5326 3849 —
CT 3026 7.38 5442 4666 1009
EN 13631-15 3060 — — 4642 1020
W-DETCOM13370 6.55 5215 4655 —
CT 2112 15.3 6549 3263 766
EN 13631-15 2099 — — 3236 771
W-DETCOM12438 13.9 6758 3214 —
Dinamite I CT 4173 25.03 7960 6452 1147
EN 13631-15 4130 — — 6338 1138
Dinamite II CT 3165 23.58 7729 5049 987
EN 13631-15 3151 — — 4989 984
1Calculation performed assuming Chapman-Jouguet detonation.
of State (EoS) for the products according to the norm UNE 31-002-94 , as illustrated
in Figure 3.
More complex computations based on the European Standard EN 13631-15 [
which use the semi-empirical Becker-Kistiakowsky-Wilson (BKW) EoS [
] or the
Heuzé (H9) EoS [
] for the products, are also supported in the last version of SimEx. As
sample results of these computations, Table 2shows the detonation properties obtained
by SimEx for different explosive mixtures (see Table 1for its composition) compared
with the results reported in the European Standard EN 13631-15 [
], and obtained with
the W-DETCOM code [36,55], which computes directly the Chapman-Jouguet state.
Version September 5, 2022 submitted to Appl. Sci. 10 of 23
The equilibrium calculations are carried out using Combustion Toolbox (CT), an in-
house thermochemical equilibrium package developed at UC3M [
]. CT determines
the equilibrium composition of the product mixture through the Gibbs free energy
minimization method by using Lagrange multipliers combined with a multidimensional
Newton-Raphson method. The thermodynamic properties (speciﬁc heat, enthalpy, and
entropy) are computed as a function of temperature derived from NASA’s 9-coefﬁcient
polynomial ﬁts for combustion of ideal and non-ideal gases and condensed phases.
From the resulting composition of the product mixture at equilibrium, the assistant
computes the volume of gases generated, the heat of explosion, the Gurney constant, the
detonation pressure, the detonation velocity, and the explosive force (or power index).
To estimate the detonation pressure and velocity, the approximate expressions of Kamlet
& Jacobs [
] are used, whereas the explosive force is estimated using the well-known
Berthelot approximation [
]. These data are subsequently used to calculate the TNT
equivalent of the explosive composition under study.
SimEx also has an assistant for the direct and inverse calculation of craters based on
the classical correlations for craters reviewed by Cooper [
] (see also Refs. [
] and [
whose interface is shown in Figure 4. With this assistant, one can calculate the radius
of the crater generated by the detonation of a certain amount of a given explosive at a
certain height above the ground, considering different types of soil. It is also possible to
calculate the explosive charge required to produce a crater of a certain size, which may
be useful for the forensic analysis of explosions [
]. Buried craters are not yet included in
the assistant, but could be incorporated in future versions following the work of Westine
, as reviewed by Baker et al. .
Interface of the assistant for the calculation of craters. HOB denotes the height of burst.
2.2.3. Primary fragments
SimEx incorporates assistants for calculating the mass distribution, ejection velocity
and ballistic trajectory of primary fragments. The corresponding interfaces are shown
in Figures 5–7. The fragment size distribution is estimated using Mott’s statistical
theory for fragmentation of steel cylindrical shells [
], as suggested by UFC-
]. As shown in Figure 5, this model determines the average number of
fragments and their average weight. It also provides the size of the largest fragment
corresponding to a given Conﬁdence Level (CL). SimEx also includes a ballistic trajectory
assistant for primary fragments that, in addition to the ﬂight path, provides the ﬂight
time, velocity and maximum distance, as illustrated in Figure 6. The initial velocity of
primary fragments is computed using Gurney’s analysis [
] for cylindrical, spherical,
and symmetrical/asymmetrical sandwich charges. Although this analysis assumes that
Version September 5, 2022 submitted to Appl. Sci. 11 of 23
all fragments have the same the initial velocity, given the different fragment sizes both
their initial kinetic energy and their subsequent aerodynamic deceleration are different.
The assistant thus includes an initial aerodynamic deceleration chart, shown in Figure 7,
that provides the fraction of the initial velocity achieved at a certain distance, given the
fragment mass and material, and the local air density, speciﬁed through the ISA
model. The aerodynamic assistants assume spherical fragments with a variable drag
coefﬁcient for all Mach numbers [
], although the model could be extended to account
for more realistic (i.e., irregular) fragment shapes in future versions [
]. The results of
these models are also used to estimate the lethality risk by impact of primary fragment
in the event of a strike on a person, which is found to depend on the speed and the mass
of the fragment, as illustrated by Figure 5.
Charge weight (kg)
Shell weight (kg)
Maximum distance (m)
TNT eq (kg)
Cte Gurney (m/s)
Fragments statistics and secondary injuries
Confidence level (%)
Average weight (g)
CL weight (g)
Average fragment (m)
CL fragment (m)
Velocity vs distance
Number of fragments
Figure 5. Interface of the primary fragment mass distribution and lethality assistant.
Height (ISA) (m)
Initial velocity (m/s)
DT (ISA +/- DT)
min alpha (deg)
max alpha (deg)
step alpha (deg)
Ballistic fragment trajectories
Initial deceleration chart
Interface of the primary fragment calculation assistant showing the ballistic fragment
trajectory, ﬂight time, velocity and maximum distance charts. Fragments are assumed spherical.
Version September 5, 2022 submitted to Appl. Sci. 12 of 23
Height (ISA) (m)
Initial velocity (m/s)
DT (ISA +/- DT)
min alpha (deg)
max alpha (deg)
step alpha (deg)
Ballistic fragment trajectories
Initial deceleration chart
Interface of the primary fragment calculation assistant showing the initial deceleration
chart, which provides the fraction of the initial velocity,
, achieved at a certain distance
(contour lines), given the fragment mass,
, and material (e.g., lead), and the atmospheric
conditions (e.g., ISA mean sea level). Fragments are assumed spherical.
Non-tabulated explosives or explosive mixtures can also be considered, with the
Gurney constant being computed by the thermochemical assistant presented in Section
2.2.1. In this case, the user must select a “custom” explosive, and the thermochemical
assistant will open to specify the desired explosive composition. Once the wizard is
closed, the Gurney constant is automatically exported to the fragment wizard.
2.2.4. Damage to people
SimEx includes an assistant for estimating damage to people using the widely
accepted probit (probability unit) functions [
] provided by the TNO’s Green Book [
and summarized in Table 3. For each type of injury or cause of death (eardrum rupture,
lung injury, etc.), a probit function is deﬁned that depends on the blast parameters: side-
on, dynamic or reﬂected peak overpressure (depending on the body position), impulse
per unit area, etc. For primary injuries, lethality due to lung damage is evaluated together
with the probability of eardrum rupture. For tertiary injuries, lethality is evaluated for
shock-induced body displacement and subsequent direct impact, either with the head or
the whole body .
The appearance of the interface is shown in Figure 8. All necessary parameters
can be selected on the left: size, type and geometry of the explosive charge, as well as
the body position relative to the incoming pressure wave, which determines whether
side-on, dynamic or reﬂected pressure is used to compute the peak overpressure and
impulse. The rest of the window presents the results both numerically and graphically,
using overpressure-impulse diagrams on the left and CW-S diagrams on the right,
with primary injuries shown above and tertiary injuries below. Overpressure-impulse
diagrams display the characteristic overpressure–impulse–distance curve for the selected
charge weight to facilitate the interpretation of results [
], while CW-S diagrams include
a diagonal dashed line indicating the approximated position of the ﬁreball radius,
corresponding roughly to an scaled distance
1 m. Above this line
the Freidlander waveform is not valid and the blast wave parameters are increasingly
Version September 5, 2022 submitted to Appl. Sci. 13 of 23
Interface of the assistant for estimating blast-induced damage to people. The CW-S and atmospheric data,
along withe the body position relative to the incoming pressure wave, are introduced on the top-left corner, the blast
wave parameters and the statistical damage indicators for the chosen CW-S combination appear on the bottom left corner.
The right plots represent graphically the statistical damage indicators in the form of overpressure-impulse and CW-S
diagrams. Both show the conditions corresponding to the speciﬁed CW-S combination with a solid red dot, while the CW-S
diagrams include also a diagonal dashed line indicating the approximated position of the ﬁreball radius. Above this line the
Freidlander waveform is not valid and the blast wave parameters are increasingly imprecise .
3. Example of application: façade of a building under blast loading
To illustrate the capabilities of SimEx, this section presents a preliminary study
to asses the ability of a conventional three-story steel frame building, such as the one
shown in Figure 9, to resist three different combinations of charge weight,
, preserving a similar scaled distance,
. The three CW-S
combinations are summarized in Table 4. For simplicity, we assume mean sea level ISA
conditions for all the calculatons. For illustrative purposes, the ﬁgures quoted below
show results corresponding to the ﬁrst ﬂoor of the building (hereafter referred to as
Level 1) and Case 2 conditions. That is, we shall consider as reference conditions a
ground explosion of 150 kg of TNT at 20 m standoff distance from the front façade of the
building, as depicted in Figure 9a.
3.1. Incident load
As previously discussed, SimEx allows the user to enter directly the desired CW-S
combination to deﬁne the incident blast load. Figure 2shows the results corresponding
to the reference conditions (Level 1, Case 2). For a more detailed analysis of the load
induced by the blast wave, the “Blast Wave” calculation assistant shown in Figure 10
allows a fast evaluation of all blast parameters as a function of the standoff distance. To
Version September 5, 2022 submitted to Appl. Sci. 14 of 23
Probit functions used to estimate the probability of different types of primary and tertiary
injuries. Pr is the probit value,
[Pa] the peak overpressure,
[Pa] the maximum effective
overpressure, depending on the relative orientation of the person with respect to the shock wave,
[Pa] the atmospheric pressure,
s] the impulse per unit area and
[kg] the weight of
the person .
Effect Probit function
Eardrum rupture Pr =−12.6 +1.52 ln p◦
Death due to lung
damage Pr =5−5.74 ln 4.2
Death due to displacement
and whole-body impact Pr =5−2.44 ln7380
Death due to displacement
and skull impact Pr =5−8.49 ln2430
, explosive charge,
, and scaled distance,
, of the different case
studies. The reference case is shown in blue.
Variables Case 1 Case 2 Case 3
d(m) 12 20 25
W(kg) 30 150 300
Z(m/kg1/3)3.86 3.76 3.73
this end, the user must provide the following input data: the ground distance from the
explosion to the point of calculation,
, the elevation of the explosive charge,
, and the
elevation of the calculation point, h0, both measured from the ground.
0, an hemispherical surface burst computed from Kingery & Bulmash
parameters for TNT [
] is considered, although other correlations for hemispherical
] could also be selected. For
0, hemispherical or spherical blasts are
both available, letting the user decide what is the best option based on the height of
burst. The code does not include correlations for more complex conﬁgurations, such as
air bursts producing regions of regular and Mach reﬂections that eventually modify the
incident shock wave. The user must also introduce the angle formed by the normal to
the structural element at the point of calculation with the horizontal projection of the
line joining the center of the explosion with that point,
, which is identically zero in
our case studies if we assume a symmetric conﬁguration with a pillar in the center of
the front façade. These distances and angles are employed for simplicity in obtaining
With these data, the wizard is able to compute the real distance and incidence
angle, thereby providing the peak overpressure,
, the impulse per unit area,
the duration of the positive phase,
, the blast arrival time,
, the average speed
of the pressure front,
, the positive phase length,
, and the waveform
. The results are presented in a table for several standoff distances,
gives also the real distances,
, and angles of incidence,
. The maximum and
minimum distances that appear in the table can be easily modiﬁed by the user, who
can select any intermediate value using a slider bar to compute the blast parameters
at a ﬁxed speciﬁed distance. A button has also been included to graphically represent
the variation of any of the blast parameters as a function of the distance to the center of
Version September 5, 2022 submitted to Appl. Sci. 15 of 23
Schematic diagram of the three-story building under study, composed of equally spaced pillars and an outer
enclosure wall, including: (a) the distances and angles used for the different ﬂoor levels (
0, 1, and 2), including the
, the real distance to the midpoint of the different levels,
, and the corresponding angles of incidence,
; (b) schematic of the façade constructive details and dimensions; and (c) diagram of the equivalent façade element
used in the SDOF analysis. L
denotes the height of Level
, representing the length of the pillars, and
is the spacing
between pillars, representing the tributary loaded width.
the explosion. The results are also exportable as a "comma-separated-value" format for
For more qualitative information, two exportable graphs are presented in the lower
part. The graph on the left displays the time evolution of the overpressure at a ﬁxed
horizontal distance. The user can change this distance easily with the slider bar. All
the characteristics of the blast wave are shown for the particular distance chosen by the
user. The graph on the right represents the maximum overpressure and the impulse per
unit area as a function of the horizontal distance. As previously indicated, the range of
distances is also adjustable by the user. Using the "Export and exit" button, the module
is closed and the weight and type of explosive, the distance to the charge, and the real
angle of incidence to be used in the integration of the SDOF system are exported to the
main SimEx module. Figure 10 shows the calculation of the blast parameters for an
explosive charge of 150 kg of TNT on a point at a height of 5.5 m above the horizontal,
i.e., the geometric center of the façade of the ﬁrst ﬂoor, corresponding to the reference
case (Level 1, Case 2). Other distances are also included in the top table, showing how
the angle of incidence tends to become normal as the charge moves away from the target.
3.2. Estimation of the equivalent SDOF system response
To study the structural response to an explosive charge it is necessary to know in
detail the type of construction. However, when using a simpliﬁed SDOF model, the
study can be simpliﬁed and generalized for many different cases. In the present example
we will analyze a façade structure like the one in Figure 9b, composed of equally spaced
pillars and an outer enclosure wall.
The ﬁrst element that receives the blast wave is the enclosure of the façade. This,
in turn, transmits the load to the rest of the structure. In most constructions the façade
is only an enclosure without structural function (glass façades, brick, etc.). In ﬁrst
approximation, it can be considered that the exterior enclosure transmits the full load
received directly to the pillars. The pillars are structural elements whose integrity is
considered critical. It will therefore be the ﬁrst element to be studied since the protection
of the supporting structure is pivotal to avoid the potential collapse of the building. The
enclosure can be considered as a secondary element in most constructions and therefore
a signiﬁcantly higher level of damage than in primary elements can be allowed.
Version September 5, 2022 submitted to Appl. Sci. 16 of 23
Charge weight (kg)
W TNT eq Dp (kg)
W TNT eq i (kg)
DT (ISA +/- DT)
Height (m - ISA)
Blast wave type
UFC 3-340-02 Hemispheric
Export and exit
Standoff d (m)
4 0543 03
d min (m)
d max (m)
I/A (kPa ms)
Interface of the Blast Wave calculation assistant for a charge weight of 150 kg of TNT at ISA mean sea level,
showing the variation of the blast parameters with the standoff distance from the front façade (top table). The lower part of
the assistant shows the blast parameters calculated at a point located at
20 m standoff distance and
5.5 m above
Figure 9c shows the simplest element in which the façade is to be divided. Each
pillar receives loads from a part of the façade corresponding to the distance between
pillars and the height between ﬂoors. The load generated by the explosion is applied to
the pillars crosswise, so they behave in ﬁrst approximation as bending elements. For
the calculation of the equivalent properties, the beam assistants available in SimEx are
employed. Either for metal or concrete beams, the length corresponds to the height
between ﬂoors, while the span is the spacing between pillars. In the case of pillars, the
boundary condition between ﬂoors is that of embedment on both sides, whereas a free
conditions is preferred at the roof. As a result, we use ﬁxed-ﬁxed conditions for Levels
0 and 1 and cantilever (or ﬁxed-free) for Level 2. The presence of a roof diaphragm
element may require additional considerations regarding the boundary condition at the
roof top, but we prefer to use a ﬁxed-free boundary condition for the second ﬂoor both
for simplicity and for illustrating the effect of considering different boundary conditions
on different ﬂoors.
In the case of metal beams, it is only necessary to indicate the standard shape of the
proﬁle and the size. SimEx uses European cross-section proﬁles HEB, IPE, and IPN in
accordance with Euronorm 53–62 (DIN 1025) [
]. Figure 11 shows the result for a HEB
340 proﬁle with a length of 3 m and a separation between pillars of 5 m. The assistant
uses standardized proﬁles, so if a non-existent measure is introduced, it corrects down
to the nearest lower normalized proﬁle. However, it is also possible to select custom
proﬁles and materials. In this case, the area, ﬁrst moment of area about the bending axis,
moment of inertia about the bending axis, density, Young’s modulus, and resistance
must be provided by the user. Once the structural properties have been introduced,
closing the assistant incorporates the computed data into the main SimEx interface.
Figure 2shows the result for the case under study. It should be noted that the additional
enclosure mass supported by the pillar when ﬂexed must also be included in the mass
of the equivalent SDOF system in the main interface.
If a rectangular reinforced concrete pillar is considered, SimEx requires that the
(perpendicular and parallel to the direction of application
Version September 5, 2022 submitted to Appl. Sci. 17 of 23
Tipo de perfil
1st moment of area (cm3)
Moment of inertia (cm4)
Young's modulus (kPa)
Resistance f_y (kPa)
Type of edge
Total mass (kg)
Mass p.u.s. (kg/m2)
Metal beam calculation assistant showing results for a HEB 340 pillar with a length of 3
m and a spacing between pillars of 5 m. Note that even though a HEB 350 is requested, which is
not included in the norm, the assistant corrects down to the nearest normalized value, HEB 340.
Reinforced concrete beam calculation assistant showing results for a pillar of 45 x 45
with a length of 3 m and a spacing between pillars of 5 m. The pillar is reinforced using 5 A36
steel reinforcement bars of 22.5 mm of diameter per side spaced apart 37 cm.
of the load, respectively) be introduced. In addition, the properties of the reinforcement
should be indicated in a simpliﬁed manner, that is, interior spacing,
, and reinforcement
represents the number of steel reinforced bars per side.
Figure 12 shows results for a pillar of 45 x 45 cm
with 5 A36 steel reinforcement bars
of # 7 (approximately 22.5 mm in diameter) per side, for a length of 3 m and a spacing
between pillars of 5 m. The distance
must be estimated according to the constructive
detail. In this particular case, it is assumed that the reinforcement centers are located at
4 cm from the edge, resulting in an interior reinforcement spacing of dc=37 cm.
It is worth noting that neglecting axial load can be considered a conservative
approach, particularly in the case of columns or pillars. These elements are initially
subjected to a signiﬁcant compression load due to the weight of the supported structure,
which reduces the tensile stresses caused by bending. This simpliﬁcation constitutes a
ﬁrst approximation in the study of the structural response. For a more detailed analysis,
the wall should be the next element to be analyze in order to assure that it is able to fully
transmit the blast load to the load-bearing element. If the wall was made of concrete, this
could be done using the concrete beam assistant with
. In this case, the mass of the
Version September 5, 2022 submitted to Appl. Sci. 18 of 23
element under study would be the total mass of the equivalent SDOF system. However,
in the case considered here of load-bearing elements (beams or columns/pillars) the
total mass can be signiﬁcantly larger than the mass of the element.
3.3. SDOF system integration and CW-S damage diagrams
Once the user sets the explosive charge and the properties of the equivalent SDOF
system, SimEx is ready to integrate the resulting mathematical problem. Figure 2shows
the results for the case of a HEB 340 proﬁle with a 5 m span between pillars. The
main results are the maximum deﬂection,
, the ductility ratio,
, and the maximum
. The two latter parameters are used as indicators to quantify the
component damage levels [
]. Assuming that the Level of Protection (LOP) required is
very low, in case of a hot rolled compact steel shape for the columns, according to [
the allowable component damage is heavy (response between B2-B3).
For ﬁxed values of the structural parameters, a parametric sweep can be carried
out in CW-S space to obtain damage diagrams such as the ones shown in Figure 13. To
this end, it is enough to indicate in the assistant the charge weight and standoff distance
ranges to be analyzed and the number of intervals to be used for each parameter. In
addition, the desired damage level criteria must be indicated to separate the zones.
Figure 2shows characteristic values of
for metallic elements, although other
values could be selected from [
] for other structural elements and materials. Note that
CW-S damage diagrams are presented both in linear and log-log scales.
As can be seen, the CW-S damage diagrams shown in Figure 13 include three points
corresponding to the three cases considered in Table 4. As the three scaled distances are
almost equal then the damage levels are also very similar, although differences in real
distances an incidence angles make them grow from superﬁcial-moderate (B1) to (almost)
moderate-heavy (B2) for increasing charge weights and standoff distances. According
to the PDC-TR 06-08 [
], a superﬁcial damage level implies “no visible permanent
damage”, whereas a moderate damage level implies “some permanent deﬂection” that
generally can be repaired. By way of contrast, a heavy damage is associated with
“signiﬁcant permanent deﬂections” that cause the component to be unrepairable.
To summarize the results obtained in the different case studies, Table 5reports the
incident blast load parameters and the corresponding component damage indicators
per ﬂoor for Cases 1, 2, and 3. The reference case (Level 1, Case 2) and the worst-case
scenario (Level 2, Case 3) are both highlighted for clarity. As can be seen, damage levels
are signiﬁcantly higher in the upper ﬂoor (Level 2) as a result of the lowest rigidity
imposed by the cantilever boundary condition at the roof top, resulting in heavy damage
levels for cases 2 and 3.
CW-S linear (left) and log-log (right) damage diagrams for reﬂected blast load on the
façade of the ﬁrst ﬂoor (Level 1): Case 1 (), Case 2 (♦), Case 3 (4).
Version September 5, 2022 submitted to Appl. Sci. 19 of 23
Incident load parameters and component damage indicators per ﬂoor. According to the
], the response limits for hot rolled structural steel can be deﬁned in terms of the
, and support rotation angle,
, as follows: B1 - superﬁcial
; B2 -
; B3 - heavy
; B4 - hazardous
reference case and worst-case scenario are indicated in blue and gray, respectively.
Level Type Variables Case 1 Case 2 Case 3
Incident load parameters
∆p(kPa) 168.30 182.50 186.80
I/A(kPa ·ms) 406.70 724.40 922.20
dreal (m) 12.17 20.10 25.08
δreal (deg) 9.46 5.71 4.57
Damage level indicators µ(-) 1.60 3.26 4.40
θ(deg) 0.19 0.39 0.53
Incident load parameters
∆p(kPa) 139.40 169.50 178.00
I/A(kPa ·ms) 349.90 688.10 893.00
dreal (m) 13.20 20.74 25.60
δreal (deg) 24.62 15.38 12.41
Damage level indicators µ(-) 0.90 1.64 2.10
θ(deg) 0.08 0.15 0.19
Incident load parameters
∆p(kPa) 110.20 152.00 165.40
I/A(kPa ·ms) 293.00 630.50 845.50
dreal (m) 14.71 21.73 26.41
δreal (deg) 35.31 23.03 18.78
Damage level indicators µ(-) 1.67 5.85 9.26
θ(deg) 0.87 3.05 4.83
3.4. Crater, fragments and damage to people
Figure 4presents an estimation of the crater generated in the reference case on a
sandstone soil, with an approximated radius of 1.6 m. For surface bursts, HOB
m, as the one considered here, the equivalent charge radius is irrelevant, as it is only
used to determine the dimensionless height of burst which is identically zero in our
example. The ﬁgure also shows that for above-surface bursts, HOB
0 m, the crater
radius is signiﬁcantly smaller for the same amount of explosive due to the air cushion
that exists between the load and the ground, which reduces to a great extent the pressure
that reaches the ground surface .
Figure 5shows the interface of the fragment assistant using the input data of the
reference case. For the application of Mott’s statistical theory for fragmentation of
steel cylindrical shells [
], the explosive charge is approximated to a cylinder of
approximately 50 cm diameter surrounded by a steel fragmentation shell with a mass of
the order of about 13% of the charge and a thickness of 2 mm.
Finally, Figure 8shows the calculating assistant for estimating damage to people in
the reference case. As an illustrative example, the ﬁgure presents the results of lethality
due to different types of injuries at a distance of 20 m from the origin of the explosion,
assuming the worst-case scenario of an average person located close to the façade of the
building being attacked. In the pressure-impulse graphs, representative distances are
indicated using red dots plotted along the characteristic overpressure–impulse–distance
]. As can be seen, at 20 m standoff distance lethality due to lung damage or
whole-body projection is negligible, but large primary fragments (e.g., CL 99%) may still
produce secondary injuries with fatal results, as indicated by Figure 5.
Version September 5, 2022 submitted to Appl. Sci. 20 of 23
SimEx is a computational tool that allows a rapid and easy estimation of the effects
of explosions on structural elements and their damage to people. It has been developed
in accordance with the speciﬁcations of American standard UFC-3-340-02 and other
widely accepted directives published in the open literature. It provides assistants for the
calculation of the blast-wave load; SDOF dynamic response, including the calculation
of the equivalent structural properties of standardized metal and reinforzed concrete
beams; thermodynamic properties of explosive mixtures; crater formation; projection of
primary fragments; and damage to people.
After presenting the main calculating assistants, a preliminary study has been
presented to illustrate the full capabilities of SimEx in the assessment of the ability of a
building to resist a given explosive charge. The analysis enables the determination of
component damage levels for the main structural components, and a further study of
the reference case has led to the computation of CW-S damage diagrams for a pillar of
the ﬁrst ﬂoor. These diagrams are very useful to provide design guidelines for those
facilities that must be protected against explosive threats.
Although still under development, SimEx is being successfully used for research
and teaching activities at the Spanish University Center of the Civil Guard. Due to its
advanced stage of maturation, it could also be used in other areas within the Army and
Law enforcement Agencies involved in the ﬁght against terrorism and the design of
blast resistant buildings and structures.
SimEx License & Distribution:
SimEx is a closed-source proprietary software that may be licensed
by the copyright holders, UC3M & Guardia Civil, under speciﬁc conditions. Please contact the
corresponding author for further information.
Conceptualization, J.S.-M. and M.V.; methodology, J.S.-M. and M.V.; soft-
ware, J.S.-M. and A.C.; validation, all authors; formal analysis, J.S.-M. and M.V.; investigation,
all authors; resources, C.H. and M.V.; data curation, J.S.-M. and A.C.; writing—original draft
preparation, J.S.-M., A.C. and M.V; writing—review and editing, C.H and M.V.; visualization,
J.S.-M and A.C.; supervision, C.H. and M.V.; project administration, M.V.; funding acquisition,
C.H. and M.V. All authors have read and agreed to the published version of the manuscript.
This research was partially funded by UE (H2020-SEC-2016-2017-1) grant number # SEC-
08/11/12-FCT-2016 and by proyect H2SAFE-CM-UC3M awarded by the Spanish Comunidad de
Madrid. The authors would like to thank Dr. Henar Miguelez from University Carlos III of Madrid
and Col. Fernando Moure from the University Center of the Civil Guard for their continuous
support, as well as Com. Miguel Ángel Albeniz from the SEDEX-NRBQ (EOD-CBRN) service of
the Civil Guard for many enlightening discussions. Fruitful discussions with Dr. Lina López from
the School of Mines at Technical University of Madrid are also gratefully acknowledged.
Institutional Review Board Statement: Not applicable
Informed Consent Statement: Not applicable
Conﬂicts of Interest:
The authors declare no conﬂict of interest. The funders had no role in the
design of the study; in the collection, analyses, or interpretation of data; in the writing of the
manuscript, or in the decision to publish the results.
The following abbreviations are used in this manuscript:
BKW Becker-Kistiakowsky-Wilson EoS
CL Conﬁdence Level
CT Combustion Toolbox
CUGC Centro Universitario de la Guardia Civil
CW-S Charge Weight-Standoff
EoS Equation of State
GUI Graphical User Interface
Version September 5, 2022 submitted to Appl. Sci. 21 of 23
H9 Heuzé EoS
HOB Height of Burst
IED Improvised Explosive Device
ISA International Standard Atmosphere
LOP Level of Protection
PDC Protective Design Center
SDOF Single Degree of Freedom
SEDEX-NRBQ Explosive Ordnance Disposal (EOD) and CBRN Defense Service
UC3M University Carlos III of Madrid
UFC Uniﬁed Facilities Criteria
US United States
USACE United States Army Corps of Engineers
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