Meso-Scale Modeling of Irradiated Concrete
in Test Reactor – Response to Reviewers’
comments
A. Giorla, M. Vaitová, Y. Le Pape and P. Štemberk
Replies to the reviewers comments should be provided in blue in this documents. Same
drill with any change made in the manuscript per editorial rules. Thanks.
Tasks in pink. Now, if anyone thinks he/she has a killing argument or a point to make,
don’t hesitate!
1 Reviewer #1
The author present an interesting manuscript which performs the numerical simulation of
irradiated concrete at the meso-scale level.
Whereas strictly speaking there is no new contribution to either the physics of the problem or the numerical tool (both previously published), the strength of this paper is the clear
explanation of the transition from a physical model (as understood by nuclear scientists
and material scientists) to an engineering one (as understood by structural analysts). As
such it could serve as a future template for similar studies as to the best of this reviewer’s
knowledge no similar work has been published.
Having said, there is a minor/major flaw in the mode: the non inclusion of the Interface
Transition Zone (ITZ) which surrounds the aggregate and which could play a major role
in the context of this simulation. There are also a few minor points which require further
clarifications: selection of rnl which can greatly affect the results, reference for the fracture
model, and last but not least a paragraph or two about the numerical model should have
been presented (along with figures of the meshes and details of the computation).
About the ITZ (Yann’s task) 1. not enough data (plain/irradiated aluminous cement/serpentine.
2. mesoscale modeling/cohesive model 3. no envisioned impact on damage extent/expansion
but damage mechanism propagation.
Mesoscale modeling of ITZ requires an interface element like a cohesive crack approach
for which obtaining mechanical parameters like bond strength and elastic stiffness remain
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problematic, even for non irradiated ordinary concrete. A fortiori, interface properties
between an hydrated, and thermally cured, aluminous cement and serpentine aggregate
were not documented in Elleuch et al,’s article, and literature on the subject could not be
found.
It is acknowledged though that the introduction of an interface model could modify the
development of the crack pattern by favoring interface damage before propagating through
the paste. However, the authors strongly think that including interface properties will not
impact the final macroscopic expansion or the extent of paste damage.
About rnl (Alain’s task) 1. calibration to avoid numerical instability. 2. add two lines
of discussion on possible impact.
The choice of rnl is discussed in section 4.2, paragraph Damage properties. When rnl
becomes too large (approximately larger than the size of the smallest particle in the mesh),
it becomes easier for damage to bridge between several particles and create a macro-crack.
In the experiments simulated, the initial thermal treatment phase had caused some damage
to the material, but the concrete still retained a relatively high stiffness and strength,
indicating that no macro-crack had propagated through the sample at this phase. This
observation provides an upper limit for rnl . The text has been clarified with that respect.
Ref. on fracture model (Alain’s task). cite recently published paper with Dunant.
The model uses continuum damage mechanics with the hypothesis of isotropic damage.
A reference to general continuum damage mechanics have been added the first time the
damage variable d is introduced in the text (section 3.1, paragraph Elastic deformations).
The description of the damage algorithm (section 3.1, paragraph Strength and StressStrain behaviour) has also been expanded, and references have been added as suggested.
Furthermore, to avoid confusion, the term "fracture" has been replaced with "damage"
wherever necessary.
About the mesh (Alain’s task). modify Fig. 1 to show mesh.
Fig 1. has been modified to show better the details of the mesh as requested by the
reviewer.
About adding details on the computation (Yann’s task). Ask directly the reviewer.
2 Reviewer #2
The target of this research is important for long-term operation of nuclear power plant,
however, obtained results and path to the results are week and do not have originality
and importance in the related field. Actually, the obtained results can be reached through
the expanded method by Le Pape 2015 in which fracture energy of past is not considered
explicitly, there is no reason to use AMIE and develop meso-scale model. And obtained
results are commonly recognized by the concrete researcher and easily estimated from open
literature. The results are still not proven or newly persuaded by this paper.
Creep and shrinkage impacts are considered as equivalent force or drift of original point
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with regards stress-strain relationship during the numerical analysis, this can be easily applied. Fracture energy is related to the definition of damage and rate of crack propagation,
but it can be included in the softening process of paste for damage analysis.
Softening of aggregate is obviously minor because it value is quite higher than that of
paste and tensile strength of paste is quite low which means that stress in aggregate is
limited due to easy cracking in paste. Expansion of aggregate is comparably larger than
the thermal deformation and the shrinkage of paste, therefore, impact of creep is limited,
especially in case of low tensile strength of paste.
As a conclusion, this paper is not worth being published as it is, and needs substantial
revision.
Common task to Alain (about the benefits of meso-scale simulation against micromechanics), Petr (shooting stand!) and Yann (about the interest of mesoscale modeling for
future works).
The reviewer states that the obtained results can be reached using the analytic method
proposed in an earlier paper. This is not true, as the two methods serve different purposes
and require different information. While both method provide tools to characterize the
damage in the cement paste, they do it with different approaches. In the analytic method
proposed by Le Pape et al. (2015), the damage in the cement paste is back-calculated
from the loss of stiffness of the concrete samples, which is generally unknown in actual
structures. The damage description is highly simplistic, as it is restricted to a set of
homogeneously spread micro-cracks. In the current paper, the damage of the cement paste
is calculated without a-priori knowledge of the concrete loss of stiffness, and therefore
depends only on the mechanical properties of each phase and the irradiation conditions.
The finite element representation of the microstructure provides insight on the damage
process inside the material, by showing different stages of the damage pattern: debonding
of large aggregates, bridging between aggregates, and debonding of small aggregates. This
information is highly valuable in order to understand the damage process in irradiated
concrete.
Another benefit of the proposed meso-scale modeling resides in its future capabilities
to evaluate the actual damage development in Light Water Reactors, i.e., in structurally
restrained conditions, under different exposure and subjected to varied rate effects. Hence,
the need for an assessment of the model capabilities against experimental data, as detailed
in the submitted manuscript.
There are two reasons for this paper to be written and published:
• 1/ extension of service life of NPPs is imminent and by the law it requires careful
assessment of health of the key structural parts, such as the cavity walls which serve
as biological shielding and also as the support of the reactor vessel;
• 2/ such assessment requires reliable knowledge represented by relevant experimental
data, which are insufficient;
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Then, the proposed material model, which is calibrated on a 2D representation of concrete,
provides a numerical tool for description of the rather complex combined effect of neutrons,
temperature and humidity on concrete while it can be calibrated with acceptable precision
using the scarce experimental data; and most importantly, this approach can be implemented in FE numerical codes used for structural analyses of civil engineering structures,
which are greatly enhanced when the meso-scale aspects of concrete behaviour are also
considered.
The purpose of this paper is clearly stated on page 7 by a sentence starting at line 9 as
“The approach adopted . . . ”. The proposed material model after implementation in civil
engineering structural analysis numerical codes can serve with the important assessment
of volumetric changes of the supporting structures which besides the reduction of the loadbearing capacity will lead to geometrical changes of the reactor vessel supports which may
affect the safe operation of the reactor.
3 Reviewer #3
The authors present a numerical study of the degradation induced by the expansion of
aggregates under the influence of heat and radiation. In particular, this work accounts for
the coupling between creep and damage. The manuscript is good but could be slightly
improved.
• the authors present a number of factors which may be relevant, and neglect a number
of them. It would be valuable to have them collected in a table and the magnitude
of the expected effect should be stated for each.
• it would be nice to have an idea of the time required for the calculations provided.
• the authors say the results match these obtained by Le Pape using analytical tools.
A more direct comparison might be appropriate.
• The damage algorithm is described as being close to that of Rots, but:
– the authors do not damage a single element at the time
– the authors compute the time at which the damage occurs
– the authors do not over/under damage to keep the energy constant
– the author’s method is non-local
It seems that this is not the same algorithm!
All in all the paper is interesting and insightful.
(Alain’s tasks). 1. answer about Rots vs. actual algorithm. 2. add citation. 3. add
sentence of the computation time.
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While the reviewer is right about the points raised concerning the damage algorithm, it
still shares a certain number of similarities with the saw-tooth algorithm proposed by Rots
and co-worker, notably since both compute the sequence in which elements are damaged.
In fact, the algorithm used can be understood as an extension of the saw-tooth algorithm
to a) non-local damage and b) time-dependent materials. The description of the algorithm
in section 3.1, paragraph Strength and Stress-Strain behaviour has been slightly expanded,
and appropriate references have been added.
Computation time has been indicated in the first paragraph of section 2.
(Michaela’s task). make a list of neglected parameters including ITZ too. Neglected
parameters:
• polyphasic character of aggregate-it is assumed as homogeneous (p.10,31)
• aggregate particles smaller than size of mesh-however the elastic properties of the
sample correspond to the measured by Elleuch (p.10)
• transport processes-the fields such as temperature, neutron fluence and relative humidity are assumed as uniform which is acceptable assuming the small size of the
sample (p.12)
• coefficient of the thermal expansion for a cemetitious material changes with the relative humidity-ignored because of the lack of the proper data (p.13)
• effect of gamma radiation and its potential intrinsic effect on the moisture loss and
the creep-lack of data of gamma radiation effect (p.14)
• Pickett effect (creep)-there is no gradient of the relative humidity in the sample (p.17)
• effect of a strain rate of the loading on the strength of the material-lack of data in
literature (p.20)
• effect of a radiation on the strength of the material-high temperature and the loss of
water primarily affect the strength (Kelly et al., 1969)(p.20)
• effect of temperature and relative humidity on the strength of material-lot of unknown
parameters for the aluminious cement to evaluate this effect (p.20)
• damage properties of aggregate-the damage occurs purely in the cement paste (p.21)
• ITZ-not enough data, especially for irradiated concrete
(Yann’s task). about damage comparison micromechanics vs. continuum damage,
2D/3D . . .
About the comparison between the mesoscale numerical approach and micromechanics,
the authors wrote “The comparison between the two approaches is to be made cautiously”
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because a 2D-average damage based on continuum mechanics cannot be compared, strictly
speaking, to a 3D-crack density, i.e. random distribution of ellipsoid-shaped cracks, index.
Qualitatively, similar trends are observed.
4 Reviewer #4
This paper presented one numerical model to study the irradiated concrete damage subjected to aggregate expansion and cement paste shrinkage due to moisture loss as well as
thermal expansion. This paper was well written with computation modeling and experimental comparison.
Several comments need be addressed:
1. The concrete microstructure model is very idealized as two-dimensional circle aggregateswhich has limitation to represent the real materials
2. The pore structures or pores are ignored in the modeling. However, the moisture loss
from pores will directly lead to cement paste shrinkage
3. The model parameters from cement paste modeling (including elastic, viscoelastic
creep and shrinkage/expansion) need be better calibrated from experimental data
About the 2D/shape of aggregate (Alain’s task). find and cite relevant papers
The reviewer is right, and the shape of the particles (notably their angularity) has an
influence on the brittleness of the overall behavior of the sample. This effect is neglected
in the present approach due to lack of experimental data. Comments with appropriate
references have been added as suggested by the reviewer.
About the pore (Petr’s task). about the size of pore. how moisture is actually accounted
for. The presented meso-scale representation of concrete does not account for moisture
transport and so the information on pore distribution and their size distribution is not
necessary. The effect of moisture is considered simply as given “at a material point”
and is adopted from the experiments when available or estimated when not available. The
actual effect of moisture on the mechanical response of the model is expressed by the drying
shrinkage, which is governed by the rate of drying defined by the prescribed actual moisture
content. This simplification in definition of moisture content and its changes was possible
as the specimens were small. For larger specimens or entire structures, the proposed
mechanical approach should be coupled with a heat and moisture analysis, however, this
will not affect the performance of the proposed model as it only requires the resulting
moisture and temperature as the input parameters. This coupling, which is beyond the
scope of this paper will also help reduce the uncertainty described on page 5, paragraph
starting with “(2) Moisture content: . . . ”
About the calibration (Petr’s task). re-read text and check for potential confusion.
The calibration of the model parameters for the cement paste were carried out using a
three-step strategy:
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1. The parameter was given by Elleuch et al, in which case we used it directly. This is
for example the case of the tensile strength of the Young’s modulus.
2. The parameter could be found in the literature (at least for a similar material). This
is for example the case for the creep properties.
3. The parameter could be obtained from backward analysis of Elleuch et al experiments.
This would be the properties of the damage model.
The introduction paragraph of section 4.2 has been updated to better explain this strategy.
Additionally, Table 2 contains all necessary references for the different properties of the
cement paste and the aggregates.
5 Reviewer #5
The authors present a very interesting meso-scale model for simulating the effects of
radiation-induced aggregate swelling on the overall damage of a piece of concrete. The
work is extensively described, well documented, and in principle, of considerable interest for the readership of Nuclear Engineering and Design. However, before its potential
publication, a few rather fundamental issues should be please more carefully and comprehensively discussed:
• The question arises on how realistic the simple damage model of Eq.(1) might really
be. Micromechanical considerations, as shortly alluded to in the paper as well, might
actually propose mathematical relationships quite deviating from Eq.(1). In this context, the authors are particularly reminded of the following published results: Comparison of micromechanical homogenization schemes (self-consistent, Mori-Tanaka,
differential, etc.) with full microstructural computations reveals that the MoriTanaka method is (by far) the most appropriate scheme for damage quantification
by means of homogenization over randomly oriented cracks, see Appl Mech Rev 45,
304-335, 1992; as also discussed in Int J Anal Num Meth Geomech 31, 111-132,
2007. However, except for very small values for the crack density parameter, MoriTanaka-based stiffness reductions are not linearly related to the latter, see e.g. Int
J Anal Num Meth Geomech 31, 111-132, 2007. (Yann’s task) The reviewer points
out that the stiffness tensor of elastic mediums containing a distribution of randomly
distributed cracks does not remain necessarily isotropic as suggested by Eq. (1):
isotropic damage variable, d. This theoretical point is fully acknowledged. However,
it must be emphasized (1) that experimental data supporting these results are scarse
for ordinary Portland cement paste, and unavailable for aluminous cement paste.
(2) because of the quasi-brittle behavior of the paste and the stress distribution in
the mesoscale model, damage develop rapidly in the finite elements to a close-tofull-damage situation, as supported by the damage patterns presented in Fig. 10-12
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for example. Intermediate damage in the cement paste states do not seem predominant for the macroscopic behavior of concrete Hence, as a first-order parameter,
Eq. (1) is considered by the authors as reasonable and computationally acceptable
approximation to describe the cement paste behavior for the proposed application.
• Page 15, creep formulation: Logarithmic creep at the nanoscale, as reported in PNAS
106, 10552-10557, 2009 relates to creep durations of several seconds; this is obviously
not the time scale referred to when talking about long-term creep! Hence, reformulation of some text seems to be due. In this context, some reference to the probable
origin of creep in form of sliding nanolayers of glassy water might be appropriate, see
e.g. J Mech Phys Sol 60, 1350-1362, 2012. In particular, microstress-induced spreading of such viscous interfaces (similar to damage propagation in the sense of crack
radius growth, as modelled in Int J Anal Num Meth Geomech 31, 111-132, 2007) has
been recently discussed as a possible mechanism for non-linear (logarithmic) creep
occurring both under very short time spans (but high stresses), and under very long
time spans, see Eur J Mech 45A, 41-58, 2014. This is also consistent with the repeated discussion on coupling between creep and damage, as reported in Engineering
Structures 27, 239-250, 2005. (Alain’s task) add more ref. on logarithmic creep at
the macroscale. The reviewer raises excellent points concerning the origin of creep
in cementitious materials. Additional references showing the long-term logarithmic
creep of concrete have been inserted to emphasize the fact that the current model
focuses on long-term effects rather than short-term. A sentence has been added to
provide a possible link between micro-mechanics of the cement paste and the longterm logarithmic creep.
• Eq.(4) implies identical Poisson’s ratios for elasticity and creep. Given isochoric
creep at the hydrate level in combination with clearly compressible creep-inert clinker
particles and aggregate inclusions, the aforementioned identity does not hold (strictly
speaking), see e.g. J Eng Mech 135, 307-323, 2009 for a detailed micromechanical
analysis. The question arises how large the error induced by the assumption of
one Poisson’s ratio for both creep and elasticity might be? (Petr’s task) point fully
acknowledged theoretically BUT no data, no foreseen effects. Poisson’s ratio depends
on the stress level and load duration while in both cases in has an increasing trend.
Regarding the presented meso-scale model, there is no relevant experimental data for
the concrete considered therefore the load duration on the change of Poisson’s ratio
was not included.
• Page 17: the authors give a large range of values for the activation energy – how would
such different values affect the simulation results reported later on? (Michaela’s task)
note absence of reference given by reviewer. add line in discussion about creep. Given
the fact that creep did not seem to have a significant impact on the results in this
specific case (with a material that creeps at a very slow rate), we did not evaluate
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the effect of activation energy. A sentence was added in that sense in the discussion.
• Page 27: The authors introduce dynamic versus static elastic moduli. While this is of
course customary in the context of engineering standards, the question could also be
tackled from a more fundamentally scientific viewpoint: elasticity per se is a physical
quantity which is independent of the applied strain rate! – as given in any thermodynamically motivated mechanics textbook, such as Handbook of Continuum Mechanics, Springer, 2001. Accordingly, the question arises whether the “static elastic
modulus” might not actually be a dissipation-related elasto-(visco-)plastic hardening
modulus; as has been recently discussed for another hydrated nano-ceramic, bone,
see J Mech Beh Biomed Mat doi:10.1016/j.jmbbm.2015.03.001, 2015. As the authors
appreciate clear physical foundations of their work, this might well deserve some comments/discussion. (Petr’s task) I didn’t take very good notes of what we said. Sorry.
But I remember you had a strong point to make! Stiffness of concrete, commonly
expressed with the modulus of elasticity, depends on the loading rate, which ranges
from an instantaneous impact to the infinitesimally slow loading and as such it can be
studied with the focus on the dynamic effects, physical changes in the microstructure
or chemistry, and others. However, the focus of this paper is to provide a material
model which can be calibrated with the scarce but available data and which can be
then implemented in the standard structural analysis software. Therefore, a simple
method upon which the static and dynamic moduli of elasticity could be correlated
was proposed. The proposed method is based on the commonly accepted definition
of the static and the dynamic modulus of elasticity. This is because these values are
obtained using the standardized testing procedures, which were established in order
to set agreement about the effect of the loading rate on the measured values. The
authors acknowledge the research advances in the description of stiffness, but they
understand this comment is out of the scope of the paper.
The authors would like to express their appreciation to Reviewer #5 for providing such
a detailed, constructive and informative review.
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