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Impact response of UHPC and UHPFRC: experimental study and numerical simulation


Abstract and Figures

When a projectile hits a concrete target, several specific mechanisms are activated. Craters forms on front and rear faces of the target mainly due to shear and tensile damage. In the vicinity of the projectile nose, the concrete material is subjected to intense pressures (several hundreds of MPa), increasing its apparent ductility. Ultra-high performance concrete (UHPC) and ultra-high performance fiber reinforced concrete (UHPFRC) represent new opportunities to design protective structures. The compressive strength of these materials is commonly five times the one of standard concrete. Compared to usual concrete, the tensile behaviour of UHPC is also different: the composition is optimized to reduce the porosity and fibers can be included in the formulation (UHPFRC). To study the impact response of this kind of materials, penetration tests are conducted in Gramat on Ductal ® FM targets using a steel projectile. Perforation experiments allowed investigating the influence of steel fibers on the impact craters and exit velocities. To simulate impact event on UHPFRC, the Pontiroli-Rouquand-Mazars (PRM) model developed in CEA-Gramat is modified based on characterization tests performed on material specimens. Hydrostatic loading, triaxial tests and shock experiments are done to study the compressive response of UHPC under high confining pressures. Quasi-static bending tests and spalling experiments are useful to investigate the tensile response and the influence of fibers on the fracture energy. This modified version of the PRM model is used to simulate the impact response of UHPC and UHPFRC.
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10th International Conference on Fracture Mechanics of Concrete and Concrete Structures
G. Pijaudier-Cabot, P. Grassl and C. La Borderie (Eds)
F-46500 Gramat, FRANCE
Key words: Ballistic impact, Fiber Reinforced Concrete, Modeling, Simulation
Abstract: When a projectile hits a concrete target, several specific mechanisms are activated.
Craters forms on front and rear faces of the target mainly due to shear and tensile damage. In the
vicinity of the projectile nose, the concrete material is subjected to intense pressures (several
hundreds of MPa), increasing its apparent ductility. Ultra-high performance concrete (UHPC) and
ultra-high performance fiber reinforced concrete (UHPFRC) represent new opportunities to design
protective structures. The compressive strength of these materials is commonly five times the one of
standard concrete. Compared to usual concrete, the tensile behaviour of UHPC is also different: the
composition is optimized to reduce the porosity and fibers can be included in the formulation
(UHPFRC). To study the impact response of this kind of materials, penetration tests are conducted
in Gramat on Ductal®FM targets using a steel projectile. Perforation experiments allowed
investigating the influence of steel fibers on the impact craters and exit velocities. To simulate
impact event on UHPFRC, the Pontiroli-Rouquand-Mazars (PRM) model developed in CEA-
Gramat is modified based on characterization tests performed on material specimens. Hydrostatic
loading, triaxial tests and shock experiments are done to study the compressive response of UHPC
under high confining pressures. Quasi-static bending tests and spalling experiments are useful to
investigate the tensile response and the influence of fibers on the fracture energy. This modified
version of the PRM model is used to simulate the impact response of UHPC and UHPFRC.
In the last decades, the possibilities offered
by ultra-high performance concrete (UHPC)
have been exploited by engineers and
architects to design structural elements with
unusual thin shapes. These families of material
constitute interesting candidates for protective
structures or structural elements. Indeed, the
high compressive strength and the high-energy
dissipation capacity due to the presence of
steel fibers (UHPFRC) allow designing
effective protection towards blast and ballistic
Penetration tests carried out in the past 20
years have showed that increasing concrete
compressive strength resulted in decreasing
penetration depths or residual velocities of the
projectile after perforating concrete slabs [0-
0]. It was found also that adding steel fibers
was the most effective method in reducing
spalling and scabbing crater dimensions of
both impacted and rear faces of the targets [0-
0]. Twelve years ago, CEG-DGA has
conducted penetration tests on standard and
ultra-high strength concrete (Ductal-FM®)
targets using a steel penetrator [0]. For impact
velocities ranging from 250 to 450 m/s, the
penetration depths have been found to be 1.4
times less for a UHPFRC with a compressive
C. Pontiroli and B. Erzar
strength of 200 MPa than in a standard
concrete (fc = 40 MPa). Blast experiments and
ballistic impact experiments with small-calibre
bullet and fragment simulating projectile have
been carried out on Ductal® targets by Cavill
[0]. The ability of such concrete material to be
used as protective elements has been
Nowadays, the CEA Gramat makes
constant efforts to develop and to validate
models describing accurately the dynamic
behaviour of concrete under extreme
conditions. The numerical simulation
represents a versatile tool to assess the damage
and the residual load capacity of a structure
subjected to blast loading or projectile impact.
However, the ability of a simulation to be
predictive is closely linked to the consistency
of the material model. The modeling approach
should to take into account the main physical
phenomena activated in dynamic conditions
and it must be identified with reliable
experimental data. This is of primary
importance in the case of high amplitude
loading under high strain rates, a specific
loading regime associated to high velocity
impact or contact detonation. Unfortunately
only few experimental data under high
pressure and high strain rates are available
today in the literature for UHPC.
In this work, the modeling approach
developed in CEA Gramat for standard
concrete is first described. Then, several
characterization experiments at the material
scale are presented as well as corresponding
calibration of PRM model for UHPC. Then,
experimental results of ballistic impacts on
Ductal are reported and compared to similar
tests carried out on a standard concrete.
Finally, numerical simulations of perforation
tests have been conducted and confronted to
experimental data.
2.1 Damage model
The PRM model has been developed to
simulate the behaviour of concrete under
severe loading [0]. This macroscopic model,
based on the Mazars damage model proposed
in 1984 [0], includes two scalar damage
variables Dt and Dc that give respectively the
loss of stiffness under pure tensile loading and
pure compressive loading. In this generalized
version of the damage model, t evolves
between 0 and 1 (see Equation 1):
D =
t Dt + (1-
t) Dc
The general 3D constitutive relations
relating stress and strain tensors are given by
Equation 2, where 0 and 0 are the Lamé
constants defining the initial elastic stiffness of
the material.
= (1-D)0 tr I+ 2 0 )
A problem of mesh size dependency is
often observed for damage models. In order to
limit this effect, the Hillerborg regularization
model has been included [12]. In this method,
the energy consumed by a crack to propagate
through a band of finite elements is no more
dependent of the mesh size thanks to a fixed
characteristic length Lc. In fact, the method
consists in modifying the softening part of the
stress-strain relation in order to get the same
fracture energy whatever the mesh size. To do
so, a new variable is introduced:
 if ε ε (3)
 
󰇛󰇜 if ε ε (4)
where p = t pt + (1-t) pc with pt and pc
respectively the peak strain in tension and
compression. a(Rt) is a corrective function
dependent of the dynamic increase factor Rt.
This variable is included into the damage
formula (Eq. 5) to adapt the damage kinetic,
taking into account the characteristic length Lc
of the material and the finite element
characteristic length Le:
 ω󰇡ω ε󰇢 (5)
In the precedent relations, 0t, 0c, At, Ac, Bt
and Bc are material parameters and the
equivalent strain is defined by Eq. 6. In this
relation, Xi corresponds to the positive
principal strain components.
ε ²
(6) ( (6)
First A. Author, Second B. Author and Third C. Coauthor
As proposed by Hillerborg [12], the
characteristic length Lc is assumed to be
directly linked to the fracture energy Gf and
the static tensile strength ft of the considered
For compressive loading at high strain-
rates, no dynamic increase factor has been
considered because the apparent increase of
compressive strength is certainly due to
inertial auto-confinement or non-homogeneous
lateral deformation of concrete specimens
during dynamic compressive tests [0], [0], [0].
2.2 Strain-rate sensitivity of tensile strength
For dynamic regime, one has to take into
account the strain-rate sensitivity of concrete.
Indeed, the ultimate tensile stress reached by
concrete at 100 s-1 is usually 4 to 5 times
higher than its quasi-static strength [18].
Authors are agreed to consider this effect like
an intrinsic material phenomena. This aspect
of the behaviour is accounted for by replacing
the parameter d0t (initial deformation for
damage in tension) by its dynamic equivalent
d0t computed thanks to the dynamic increase
factor Rt :
d0t / 0t = 1 + at 󰇛󰇗󰇜
This power model has already been
identified for standard concrete using quasi-
static direct tension experiments and spalling
tests conducted with a Hopkinson bar device
[18], and with ultra-high strain-rate uniaxial
deformation tests carried out with a pulsed
power generator named GEPI [19]. The strain-
rate sensitivity of UHPC and UHPFRC has
been investigated with the same devices.
Experimental results are showed on Figure 1.
No differences are observed between concrete
with or without fibers. Tensile strength
depends essentially on cement paste
behaviour. The main difference lies in the
post-peak tensile behaviour. The comparison
of the velocity profiles during spalling tests for
UHPC and UHPFRC (with 2% steel fibers
volume) allows to identify clearly the
influence of fibers: the presence of fibers
induces additional residual strength and the
residual velocity for this specimen is below the
signal measured for a UHPC specimen which
appears more brittle (see Figure 2).
Figure 1: Strain rate effects on the dynamic tensile
strength obtained on dried concrete and mortar, and
on UHPC with and without fibers
Figure 2 : Typical signals of spalling tests conducted
on a UHPC and a UHPFRC specimens
2.3 Fibers influence on tensile behaviour
Besides the compressive strength, the main
difference between standard concrete and
UHPFRC lies in the post-peak tensile behavior
(see Figure 2). Indeed, the presence of fibers
offers a pronounced ductility to UHPFRC.
Disseminated in the microstructure, steel fibers
play a major role during the fracture process,
bridging the cracks and retaining fragments.
To model their influence, the fracture energy
due to fibers has been introduced directly in
the evolution of the tensile damage variable
Dt, depending on Lf the fiber length and on the
volume fraction of fibers Vf actually
participating into the resistance to crack
1.E-07 1.E-05 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05
Tensile strength (MPa)
Strain rate (1/s)
Dry concrete (R30A7)
Dry mortar (MR30A7)
3.E-06 4.E-06 5.E-06 6.E-06 7.E-06 8.E-06 9.E-06 1.E-05
Velocity (m/s)
Time (s)
UHPC (no fibre)
C. Pontiroli and B. Erzar
opening. We can rewrite equations (3) and (4)
 if ε ε (9)
 󰇧
if ε ε (10)
where a(Rt, Vf) and b(Vf) are functions
dependent of the dynamic increase factor Rt
and of the volume fraction of fibers Vf.
2.4 Plasticity and compaction modelling
The PRM damage model is efficient to
simulate the dynamic response of concrete
under very low confinement. However, an
elastic-plastic model is more appropriate for
simulating the impact of a steel projectile in a
concrete slab at about 300 m/s. Indeed, in this
case, pressure level of several hundreds of
MPa can be observed in the vicinity of the
projectile nose. Specific phenomena such as
pore collapse or increase of shear strength
have to be considered to model accurately the
dynamic response of concrete.
To do so, the PRM damage model has been
coupled with a simple plasticity model
proposed by Krieg, Swenson and Taylor [20],
On the one hand, in this elastic-plastic
model, a parabolic relation describes the
pressure-dependency of the yield stress q:
 (11)
where p is the pressure and a0, a1 and a2 are
material parameters. q is the yield stress in the
sense of Von Mises plasticity:
  (12)
 being the deviatoric stress tensor defined as
 . The increase of q with pressure can
be limited by a saturation value qmax. This is
particularly important for standard concrete
which presents a saturation value linked to its
water saturation level [22], [23].
On the other hand, the pore-collapse
phenomenon occurring at high pressure is
described by a piecewise-linear compaction
curve. The elastic behaviour becomes more
and more non-linear up to the full
consolidation of concrete: at this point, the
pore collapse phenomenon is achieved and the
material is considered fully compacted.
To identified PRM material parameters,
two kinds of experiments have been carried
out on the UHPC with the load cell of CEA
Gramat (Figure 3a). The first test is dedicated
to the determination of the compaction curve:
a hydrostatic experiment is conducted by
increasing the fluid pressure pf in the load cell
(Figure 3b). This test has been used to identify
the response of UHPC (pressure vs volumetric
strain) up to nearly 1 GPa (Figure 4a). It
should be noted that at 900 MPa, only 6% of
volumetric strain is observed. This value, very
low in comparison to a standard concrete, is
the consequence of the optimization of the
composition to fill the pores at every scale.
The second type of experiment is the
triaxial test. It begins with a hydrostatic
loading due to fluid pressure. Then, an axial
loading is applied to increase the deviatoric
stress in the concrete specimen. Four tests with
increasing fluid pressure of pf = 200, 300, 400
and 600 MPa have been conducted. The Figure
4b presents the results through q-p plot where
the stress difference q and the average stress p
are defined by:
fz pp 2
where z is the axial compression stress
amplitude, counted as positive. It can be
pointed out that q corresponds to the
equivalent stress defined by Von Mises and
Tresca in this particular case.
First A. Author, Second B. Author and Third C. Coauthor
Figure 3. (a) High capacity load cell in CEA Gramat
and (b) experiments in confined compression conducted
on UHPC specimens.
Figure 4. Compaction curve of UHPC (without steel
fibers) obtained through a purely hydrostatic test (a),
and shear failure from different triaxial tests (b)
Even if the data gathered in the quasi-static
experimental configuration are necessary to
assess the pressure dependency of the
deviatoric strength, the characterization is
limited to pressures lower than 1 GPa.
However, the stress level reached locally in a
concrete target near an explosive charge or in
front of a penetrating fragment may be notably
higher. Consequently, the dataset has been
completed in the shock regime response up to
6 GPa by means of plate impact experiments
These plasticity and compaction models are
complementary to the PRM damage model.
The fully coupled PRM model includes all
these mechanisms with a perfect continuity
between the compressive damage definition
and the plasticity model. It has been
implemented in a classical finite elements code
(Abaqus/Explicit [25]) through a VUMAT
subroutine. This choice allows conducting
numerical simulations from the material scale
up to the structural response.
To translate the experimental results from
the material scale to the structure scale,
perforation tests have been performed at CEA-
Gramat on UHPC and UHPRFC concrete
(Ductal®FM with a compressive strength of
180-200 MPa). A 98 mm caliber gas gun has
been used for impact tests (Figure 5).
Figure 5. Gas launcher
The conical nose projectile has a total
length of 240 mm and 40 mm in diameter. The
total mass is 1.6 kg. The body is made of high
strength steel 35NCD16. The targets were 150
cm squared slabs of concrete. The thickness
was either 10 and 30 cm. As concrete is a
highly fibered material (2% steel fiber volume
ratio), no additional rebar was needed, only
single rebar were added closest to the target
C. Pontiroli and B. Erzar
boundaries. The experiments considered
different impact velocities and angles of
obliquity 0°, 15 and 30°. Yaw and pitch angles
have been verified to be negligible.
Figure 6 shows projectile and experiment
configuration for impact tests.
Table 1Table 2 give perforation results in
terms of exit velocity function on impact
velocity, obliquity angle and concrete
thickness. Fibers affect exit velocities
especially for thick slabs. Figure 7 allows
comparing crater dimensions on the front face
with or without fiber. Brittle fracture mode can
be observed on concrete without fiber while
with fiber cratering is driven by ductile
Figure 6. Projectile and experiment configuration
Table 1 : Experimental results for 10 cm in thickness
Table 2 : Experimental results for 30 cm thickness
Figure 7 : Cratering with or without fiber
The capabilities of the PRM model have
been analyzed with ABAQUS/explicit code
(v2018) by the restitution of experiments
conducted on projectile perforation in concrete
We have used 3D solid finite elements and
the projectile has been assumed to behave as a
rigid body (no deformation has been observed
on projectile after experimental tests and we
neglect slight erosion induced on the projectile
nose). For concrete without fiber, PRM model
has been used. For UHPFRC two modeling
approaches have been tested:
a macroscopic approach using PRM
model by considering an homogenized
a mesoscopic approach with a separate
discrete modeling for cement paste and
fiber. 3D solid finite elements are used
for mortar and steel fibers are
introduced in volumic model using
embedded two-node beam finite
Some technical problems and limitations
with Abaqus/Explicit have obligated to used
mesoscopic approach only for perforation
target with 10 cm in thickness. Furthermore, to
reduce finite element model size only the
projectile penetration zone is modeling with
this approach (a cylindrical zone with 30 cm in
diameter and 10 cm in thickness). From the
fiber content Vf and the geometrical properties
of both the steel fiber Lf and concrete
specimen, a cloud of fibers is generated using
uniform random distribution. Single segments
are sufficient for generating straight fibers.
Due to the cast and target thickness, fiber
orientation is not random but has a bias
First A. Author, Second B. Author and Third C. Coauthor
towards a preferential direction parallel to the
target surface. For target with 10 cm in
thickness, algorithm code has generated about
1.8 millions beam elements for modeling steel
fibers. About 7 millions 3D finite elements are
used to discretize concrete material.
PRM model is chosen for plain concrete
and a one-dimensional elastoplastic
constitutive model is using for steel fiber.
Using embedded method for steel fiber, a
perfect adherence is assumed with concrete 3D
finite element.
Figure 8 : FE model of UHPFRC target under impact
Perforation simulations have been
performed with Abaqus/Explicit code.
Comparisons between experimental and
numerical results are presented in Table 3
andTable 4 in terms of exit velocities obtained
for 10 and 30 cm thickness targets. As said
previously, mesoscopic approach could be
only applied for thin wall.
For concrete with 10 cm in thickness, a
good correlation has been obtained between
experimental tests and the two numerical
approaches proposed in this study. Figure 9
shows numerical damage on front and rear
UHPC target faces during projectile
perforation simulation.
The most significant difference between
numerical and experimental result is observed
for the incident impact on thick UHPFRC slab.
Further investigations and mesoscopic
simulations had to be performed to understand
this gap.
Table 3 : Experimental/numerical comparisons for 10
cm in thickness
Table 4 : Experimental/numerical comparisons for 30
cm thickness
(a) (b)
Figure 9 : Front (a) and rear (b) UHPC target faces
during penetration obtained by numerical simulation
Damage patterns can be also assessed and
C. Pontiroli and B. Erzar
compared with experimental results. Figure 10
and Figure 11 compare experimental cracks
zones and numerical damage patterns for
normal incidence perforation and with an
obliquity angle of 30° for impact on UHPC
target. Crater dimensions due to scabbing
spalling phenomena on front and rear faces of
concrete slabs are similar between
experimental and numerical results. PRM
model is able to reproduce correctly the brittle
behaviour of plain concrete.
Figure 10 : Comparison of damage pattern on front (a)
and rear (b) faces for UHPC normal perforation with
320 m/s impact velocity
Figure 11 : Comparison of damage pattern on front (a)
and rear (b) faces for UHPC perforation with AOI = 30°
and 331.2 m/s impact velocity
Figure 12 shows comparisons between
experimental and, macroscopic and
mesoscopic numerical approaches for
UHPFRC normal incidence perforation.
Numerical simulations using PRM model with
homogenized behaviour (concrete + steel
fibers) or using separate discretization of steel
fibers and cement paste give together similar
damage pattern compare to experimental
facies. Numerical model can reproduce
correctly the ductility behaviour of UHPFRC
due to steel fibers presence.
(a) (b)
(c) (d)
(e) (f)
Figure 12 : Comparison of damage pattern on front (a),
(c), (e) and rear (b), (d), (f) faces for UHPFRC normal
perforation with 331.5 m/s impact velocity using
macroscopic approach (c), (d) and mesocospic approach
(e), (f)
Figure 13 give comparison between
experiment and simulation of bridge effect due
to fibers. Fibers prevent the crack opening on
cement paste. Erosion method is used on
numerical simulations to remove 3D finite
elements with large deformations which could
be slowed down or sometimes stopped
First A. Author, Second B. Author and Third C. Coauthor
(a) (b)
Figure 13 : Experimental (a) and numerical (b)
comparison of fiber effect to bridge cracks
The design of new protective structures
exposed to blast loads or high velocity impact
using UHPFRC can be undertaken through
numerical simulations. However, the
constitutive and damage models have to be
accurate and validated with reliable data. Thus,
considering the relatively recent knowledge
concerning mechanical response of this class
of materials, extensive mechanical
characterization is still necessary.
In this work, quasi-static and dynamic
mechanical tests have been conducted on
UHPC and UHPFRC to identify the main
characteristics of the UHPFRC response in
tension and in confined compression. Then, a
new material parameters dataset has been
calibrated for fully coupled PRM model. This
sophisticated concrete model consists in a
phenomenological modeling approach
including the main mechanisms activated
under high strain rate and high confining
pressure, coupling damage to plasticity and
compaction. The influence of steel fibers
disseminated in the concrete has been included
in the model: the damage kinetic has been
modified to improve the description of the
fiber influence on the dynamic tensile fracture
The modeling approach has been validated
step by step using characterization data. The
final evaluation of the PRM model consists in
simulating perforation problems in UHPC and
UHPFRC targets. Two numerical approaches
for modeling cement paste and steel fibers
have been proposed, one using the
macroscopic and homogenized PRM model,
the other using a discrete representation of
fibers independently of cement paste material.
Projectile residual velocities and damage
patterns in the concrete block allowed
comparing qualitatively the numerical
predictions with experimental results. First
perforation simulations show the capacities of
the two numerical methods to reproduce the
UHPC brittle and the UHPFRC ductile
behaviours. Further works and others
numerical comparisons with experimental
tests, as closest detonation near UHPFRC
slabs, had to be continued to validate and
improve PRM model.
This work was supported by DGA (French
General Delegation for Armament, Ministry of
Defence). The authors are also grateful to P.
Forquin (3SR Laboratory, Grenoble Alpes
University, France) for his technical
contribution to this project.
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[25] Abaqus Manual. 2018, Dassault Systèmes.
... However, the related studies are insufficient, especially for the systematic fundamental test data on mechanical properties of the matrix are limited. Besides, most of the existing mesoscale analysis studies were performed [22][23][24][25] based on an assumption that the behavior between fibers and matrix is perfect, i.e., neglecting the bond-slip and bridging effect of fibers, which may lead to an overestimation of the member resistance. ...
Ultra-High Performance Concrete (UHPC), which mainly consists of the cementitious matrix and incorporated fibers, has superior impact-resistance compared with the normal strength concrete. Concerning the impact-resistant evaluation and performance-based design of UHPC structure under lateral low-velocity impact, a mesoscale modeling analysis approach considering the bond-slip behavior between random distributed fibers and cementitious matrix of UHPC is proposed. Firstly, the Continuous Surface Cap (CSC) model parameters for the matrix of UHPC were calibrated, and validated through a series of fundamental mechanical tests and low-velocity impact test. Secondly, by conducting a single steel fiber pull-out test, the fiber-matrix interaction was examined, and an appropriate interaction algorithm considering bond-slip effect was employed in the commercial program LS-DYNA. Then, the mesoscale model of UHPC was established through a self-coding program in MATLAB. The reliability of the mesoscale model and analysis approach were systematically verified at both material level (uniaxial compression, uniaxial tension, three- and four-point bending tests) and member level (total 15 low-velocity impact scenarios considering various member types, sectional shapes, sectional dimensions, and compressive strength). Finally, the influence of fiber volume fraction on the dynamic behavior of UHPC member was examined. It derives that the incorporated fibers can help reduce the lateral deflections and avoid the brittle punching-shear failure mode of UHPC members, and the optimal fiber volume fraction of 1.5% for the impact-resistant design is recommended. The present work provides a new way to accurately and conveniently evaluate the low-velocity impact-resistance and predict the dynamic behavior of the arbitrary configured UHPC structure.
... However, in such plasticity model the tensile response remains roughly described. On the other hand, a continuum model based on an isotropic damage description may be used to account for the loss of stiffness and mode I fracturing under tensile dynamic loading as in [19], for conventional concrete, and in [20], for UHPFRC. Finally, a coupled plasticity-damage model seems to provide the most efficient tools in order to simulate the penetration process and induced damage mechanisms in concrete targets under impact of rigid projectile [12]. ...
This paper proposes an experimental identification of the parameters of a coupled plasticity-damage model to be used for numerically simulate the mechanical behaviour of an Ultra-High Performance Fibre-Reinforced Concrete (UHPFRC) under impact. In the DFHcoh-KST model, a parabolic relation describes the pressure dependency of yield stresses (in the sense of Von Mises plasticity), and an anisotropic damage model (accounting for strain rate effect and crack bridging of fibre) is used to describe the tensile failure of concrete. This model is implemented in the Finite Element (FE) code Abaqus to simulate the ballistic impact of an AP (Armour-Piercing) projectile. The model parameters are identified under different loading conditions based on quasi-oedometric compression tests, bending tests and spalling tests. Tunnelling and erosion criterion are used in the numerical simulation to overcome the strong element distortions in the FE simulation in the tunnel region. The influence of friction at the projectile-target interface is also discussed. This study shows that yield strength and tensile damage are fundamental to predict the penetration depth of an almost rigid projectile into a UHPFRC target and that the crack bridging of fibre needs to be taken into account to correctly predict the final damage pattern. In contrast, the modelling of the UHPFRC material compaction is found to be negligible due to its low porosity. Finally, numerical results are compared to classical post-mortem observation and a 3D X-ray Computed Tomography (X-ray CT) reconstruction.
Concrete material is widely used in military facilities to resist the deliberate attacks by earth penetration weapon (EPW). The charge of EPW is more nearly cylindrical than spherical in geometry, and its explosion usually occurs in a certain depth of burial (DoB). To quantify the influences of charge shape and DoB on blast waves in concrete, experimental and numerical investigation on the attenuation of blast waves in concrete induced by cylindrical charge explosion is carried out in the present study. Firstly, a set of blast wave test in concrete with cylindrical charges is conducted to provide fundamental data including the stress-time histories and failure in concrete with the considerations of aspect ratio and DoB. Then based on the concrete material model by Kong and Fang and LS-DYNA's multi-material ALE algorithm, the attenuation of free-field blast waves in concrete generated from spherical charges and cylindrical charges with different aspect ratios is numerically investigated in detail. Finally, the influence of DoB on the peak stress directly below cylindrical charges is discussed and a coupling factor for peak stress is proposed. Several empirical formulas are presented based on dimensional analysis and curve-fitting the numerical data, including the critical distance beyond which the charge shape effect could be neglected, coupling factor for peak stress and peak stress from cylindrical charges with varied aspect ratio under different DoBs, all of which are useful for blast-resistant design.
This paper presents a new 3D mesoscopic model of ultra-high performance cement-based composite (UHPCC) to investigate its dynamic tensile behavior. In this model, the UHPCC is regarded as a two-phase material composed of cementitious matrix and randomly distributed fibers. The model is established using the commercial software LS-DYNA and involves generating the randomly distributed fiber elements with considerations of diameter, length, orientation and volume fraction, and then fully constraining them with the matrix. In particular, to capture the slipping effect between fibers and matrix that has a strong influence on the dynamic tensile behavior, the fibers are modelled by a fictitious material represented by the load-slip relation. The strain-rate effect of slipping force neglected in most of previous studies is considered by calibrating constitutive parameters of the fictitious material under different strain-rates based on the single fiber pullout tests. Finally, the 3D mesoscopic model is validated against three sets of tension-dominated experiments covered a wide range of loading intensity. Numerical predictions demonstrate that strain-rate effect of slipping force must be considered, and the neglect of it may lead to a great underestimation of the dynamic tensile strength of UHPCC material and would unavoidably underestimate the blast resistance of UHPCC components.
Ultra-high performance cement based composite (UHPCC) is a prospective material for protective structures subjected to intensive loadings such as impact and blast due to its prominent dynamic mechanical properties. With the aid of an accurate material model, numerical simulation plays an increasingly important role in prediction of dynamic responses of UHPCC structures. It is known that existing concrete material models are developed for traditional concrete and cannot be applied to UHPCC material directly. In the present study, a new constitutive model of UHPCC material under impact and blast loadings is developed, which involves proposing a new tensile damage model for UHPCC which is then incorporated into the Kong-Fang material model recently developed (Int J Impact Eng 2018, 120: 60-78), and calibrating parameters of this modified material model based on existing test data. The modified material model for UHPCC is implemented into the finite element code LS-DYNA through user defined material model. Single element tests including unconfined uniaxial compression and tension and triaxial compression are firstly conducted to demonstrate the improved performances of the modified material model for UHPCC material. Then three selected experiments on UHPCC structures subjected to impact and blast loadings are numerically simulated and compared with corresponding experimental data. Numerical predictions by the modified material model are well consistent with experimental data in terms of impact force, deflection and failure.
Ultra-high performance cement based composite (UHPCC) is a relatively new cement based composite with both prominent static and dynamic mechanical properties, such as the ultra-high compressive strength, high elastic modulus and good durability. Particularly, the incorporation of fibers can effectively hinder the propagation of microcracks and significantly improve its toughness, ductility and energy absorption capacity.
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Nowadays, the design of protective structures may imply ultra-high performance concretes. These materials present a compressive strength 5 times higher than standard concretes. However, few reliable data on the shock response of such materials are available in the literature. Thus, a characterization of an ultra-high strength concrete has been conducted by means of hydrostatic and triaxial tests in the quasi-static regime, and plate impact experiments for shock response. Data have been gathered up to 6 GPa and a simple modelling approach has been applied to get a reliable representation of the shock compression of this concrete.
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This paper describes the potential suitability of a new family of concrete mixtures for use in protective structures. Two very-high-strength concrete mixtures are discussed and experimental results of penetration studies on one of these are presented. The results are compared to penetration-study results of other, more conventional concrete mixtures, and the advantages of the very-high-strength mixtures are described.
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During the lifetime of a structure, concrete and mortar may be exposed to highly dynamic loadings, such as impact or explosion. The dynamic fracture at high loading rates needs to be well understood to allow an accurate modeling of this kind of event. In this work, a pulsed-power generator has been employed to conduct spalling tests on mortar samples at strain-rates ranging from 2 × 104 to 4 × 104 s-1. The ramp loading allowed identifying the strain-rate anytime during the test. A power law has been proposed to fit properly the rate-sensitivity of tensile strength of this cementitious material over a wide range of strain-rate. Moreover, a specimen has been recovered damaged but unbroken. Micro-computed tomography has been employed to study the characteristics of the damage pattern provoked by the dynamic tensile loading.
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This paper presents the main results obtained during a long and intensive research period on the modelling of the main physical mechanisms related to damage and fracture of concrete. The starting point has been the Mazars one scalar damage model (Mazars, 1984, 1986). On this base Pontiroli & Rouquand have proposed in 1995 a two scalar damage model (PRM model) which takes into account the crack closure mechanism, irreversible strains, strain rate effects and internal friction stresses. This model has been recently completed in order to take into account pore collapse phenomena, plastic shear deformations and the water content effect on the behaviour of concrete for confined loading. All these mechanisms allow the simulation of a large range of loadings from static to high velocity impacts. After a presentation of the most important features of the “PRM coupled model” several applications are given related to quasi static loading, blast or impact effects on concrete structures.
Rear face damage assessment of scabbed, punched, or perforated concrete barriers due to hard projectile impact was evaluated according to the spalling volume and size by using existing, classica,l and more modern penetration formulas. The damage level calculations are done for various velocity ranges, below and above the perforation limit. An experimental work included a comparison between the response of normal strength concrete (NSC) and high-strength concrete (HSC) barriers to hard projectile impact. The experiments were done with a gas gun that accelerated 165 g (including the sabot), hard steel projectiles, whose impact velocities ranged between 100 and 250 m/sec, and were measured by an electro-optical system. Craters at the rear face of the plate specimens were examined and showed that the NSC and HSC volumes were similar at similar velocity levels (i.e., relative to the perforation velocity). The NSC experimental results showed an increased damage level at velocities that were near or less than the perforation limit velocity. This trend is similar to that of a theoretical model prediction.
The ultra-high performance cement based composites (UHPCC) with the additions of steel fibers and basalt coarse aggregates was prepared under ambient temperature and pressure. In order to apply the UHPCC in the constructions of anti-strike protective structures, the impact resistance of UHPCC was investigated experimentally by conducting the high-speed projectile penetration tests with the broad striking velocities from 510 m/s to 1320 m/s. The rigid and mass abrasive penetration regimes are observed when the projectile striking velocity was lower than 1 km/s and increased up to 1–1.5 km/s, respectively. The experiments validated that UHPCC material has excellent projectile impact resistance, such as reducing the depth of penetration (DOP) and the crater dimensions of the rigid projectile, as well as defeating the structure and deviating the terminal ballistic trajectory of the abrasive projectile. The previously proposed models for rigid penetration depth on fiber reinforced high strength concrete as well as the limit striking velocity causing the structural destruction of mass abrasive projectile are both well validated.
When concrete impact and penetration simulations are discussed, the question of increased strength due to high strain rates arises. Many concrete material modelers cite and use the seminal work of Bischoff and Perry (1991), or the widely accepted standard reference for concrete Comite Euro-International du Beton (1993) or CEB for short. Bischoff and Perry amassed a large amount of concrete laboratory data addressing strain-rate induced Dynamic Increase Factors (DIF) or the ratio of the measured dynamic to quasi-static strength. Figure 2 is taken from Bischoff and Perry (1991) and shows the large amount of data they collected, along with the strain-rate equations recommended in the CEB for two concrete strengths. The data shows a large amount of scatter in reported strength increases. The depicted CEB equations approximately bound the data.
Some particularities of the microstructure of concrete are first presented: they lead us to conclude that damage by microcracking is the main phenomenon in the mechanical behavior of the material. An isotropic elastic damage model is then proposed by using the coupling of two damage variables, (tensile effects) and (compressive effects). The model is built according to the framework of thermodynamics, and then we show that it is possible to describe the birth and growth of cracks, using a combination linear elastic damage mechanics and linear elastic fracture mechanics. Some results attest the interest in that kind of approach.
The relatively recent technology, which enables the production of high strength concrete (HSC), makes HSC a prospective material for the construction of impact-resisting barriers. However, current penetration formulae are based on test data of normal strength concrete (NSC) and their extrapolation to higher concrete strengths is unsafe. The response of 80×80cm high performance concrete (HPC) plate specimens to an impact of non-deforming steel projectiles was examined in an experimental study. The tests were planned with an aim to observe the influence of the concrete mix ingredients and amount and type of reinforcement on the performance of HSC under this type of loading. The variants that were examined were the aggregates (different types and maximum size), addition of micro-silica (MS) and steel fibers, and reinforcement details. The main findings show that design of HPC barriers to withstand impact loads involves several aspects. These are aimed at achieving enhanced properties of the structural element, where only one of which is the concrete's compressive strength.
A constitutive model is described for the prediction of dynamic crack formation in geological media. The model includes a simple tensile failure criterion for crack formation and a soil plasticity model for both deviatoric and volumetric plasticity. Numerical results are presented which show that the model reproduces the observed dependence of fracture formation on loding rate for dynamic pressure loading of boreholes. The use of the model as a numerical tool for design is demonstrated through two example parameter studies.