Post on 16-Apr-2018
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Mechanical behaviour assessement of reinforced concrete
with steel wool
Nuno Alexandre Matos Ferreira
Extend Abstract
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Abstract
This work main objective is to contribute to deepening the knowledge of cement matrix composites
reinforced with steel wool. The use of these composites in the construction industry has assumed
greater importance over time since, without losing the characteristics attributed to conventional
concrete, some of the weakest aspects are improved, such as flexural strength and crack control.
To strengthen the cement matrix it was utilized a commercial steel wool used to prepare wood
surfaces and Portland cement of high initial strength and low setting time.
The formulation, production methods and techniques that enabled the analysis of the properties of the
composite are described.
Production of the composite was based on the concept SIMCON, Slurry infiltrated Mat Concrete, the
main objective being the evaluation of the influence of the percentage of steel wool in mechanical
performance of the composite. 5% to 10% by weight of the quantity of cement were the steel wool
percentages used. The effect of different doses and types of superplasticizers additives in rheological
properties of the cement matrix in fresh state were also studied, in means to determine the best
conditions for infiltration of wool. The influence of different dosages and types of superplasticizers
additives in the composite performance in hardened state was measured.
The slurry used in this work is composed of cement, water (30% of the amount by mass of cement)
and adjuvants. For its characterization the following properties were studied: Spreading by its own
weight and the density in fresh state. In the characterization of the composite in the hardened state,
density, the dynamic modulus of elasticity, tensile strength in bending, resistance to compression, the
open porosity and water absorption by capillary action were studied.
For the evaluation of the increase in flexural strength as a result of the introduction of commercial wool
as a reinforcement material, it was possible to assess that the increased percentage of fiber had a
significant impact, occurring increases of 100% in relation with the reference mixes with the
introduction of 10% fibers, these being the studied compositions that were more interesting.
Key-words: SIMCON, Steel wool, Flexural Strength
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Concrete reinforced with steel fibers
The concrete reinforced with steel fibers (SFRC) is a cementitious matrix composite to which is added
certain percentage of fibers. The use of composites in the construction industry has been rising
continuously. As conventional concretes, the SFRC remains a lower cost material to the potential
competitors in the construction industry. The fragility that characterizes conventional concrete is
decreased by means of share of fibers as a reinforcement element (ACI, 2002).
The fibers when crossing the micro cracks, which exist in the cementitious matrix, offer additional
resistance to degeneration in macro cracks, since it’s necessary to expend additional energy for
sliding the fibers relative to the surrounding matrix. Thus, since the composition and mixing techniques
and application of SFRC are suitable, it is found that the energy absorption capability, fatigue and
impact resistance increases with the percentage of fibers in the mixture (Balaguru and Shah, 1992)
(ACI, 2002) (Bentur and Mindess, 2007). It is also verified improvement in crack control (Barros, 1995)
and resistance under static loads (ACI, 2002) (Balaguru and Shah, 1992).
Applications that mobilize the ability of the material to absorb energy are the most appropriate to be
carried out with SFRC. Moreover, if the fibers replace conventional armor, it may be possible to obtain
a considerable saving in the solution to be adopted. Thus, the ground floors of industrial buildings
(ACI, 2002) and the tunnel walls (Bekaert, 2015) are examples of the proper use of SFRC. The partial
replacement of conventional equipment, particularly the shear strength, is also an example of
application of SFRC (Casanova, 1996). The nodes of gateways are chronic areas of damage due to
intense seismic actions (ACI, 2002). The resistance of such zones, and particularly its ductility can be
significantly enhanced if a suitable percentage of steel fibers are applied. If in areas such as these, it
is usual occur congestion shear strength reinforcement, the fibers effectively replace at least some
percentage of such reinforcement, the concrete conditions can improve, thus enhancing the quality of
the applied concrete in these areas.
In the recent years have seen the reinforcement of concrete of high strength steel fiber, since the
decrease in ductility occurs with increased concrete strength can be overcome by ductility introduced
by the fiber reinforcement (Rossi et al. 1996).
The SFRC technology has become a mature industry in recent decades, but the constant need to
optimize the use of fiber for demanding applications led to the emergence of new technologies. One of
the technologies that came up with this need for improvement was the Slurry infiltrated Fiber Concrete
(SIFCON).
The nature of the cementitious matrix, which initially consists of discrete particles makes it difficult to
incorporate a large amount of fibers, or fibers with an aspect ratio (ratio of length to diameter) greater
than 100. In the mix based production technologies, maximum fiber content which may be
incorporated is less than 2% by volume, and when using special techniques, such as the Hatschek
process or spray, this limit can be exceeded to between 5% and 12% using short fibers. These are the
limitations to consider when trying to maximize the potential of reinforcing fibers.
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To produce a reinforced concrete with high volume content of discrete fibers it was developed by
Lankard (Bentur and Mindess, 2007), a method based on pre placing a steel fiber bed which is
infiltrated with a cement slurry. In this system, called SIFCON, the placement of the fibers may be
performed manually or fiber distribution units. The pre placed in fiber is controlled by the length of the
fiber and its aspect ratio, a higher percentage of fibers can be obtained with the aid of vibration of the
mold during filling. Fiber volumes can be achieved in the order of 20% (Bentur and Mindess, 2007).
With these high fiber contents, it is possible to increase by more than an order of magnitude of the
flexural strength and toughness as compared to the unreinforced matrix, or a reinforced matrix with
low volume of discrete fibers, as shown in figure 1.
In the preparation of the composite is necessary to prevent non-uniform distribution of fibers.
However, as result of the nature of the preparation of the fiber bed, exist a tendency for the preferred
orientation which depends on the relationship between the size of the mold, the fiber length and
placement method. The effect of orientation can have a considerable influence on the properties. The
type and size of steel fibers can also affect the properties of the composite (Bentur and Mindess,
2007).
Naaman and Homrich (Bentur and Mindess, 2007) studied the mechanisms to strengthen the SIFCON
and found that the failure occurs by yielding of the fiber / adhesive rupture and not by rupture of the
fiber. The cementitious matrix of the blend composition is particularly important to ensure an efficient
leakage during production, and to control the properties of the hardened concrete.
The cementitious matrix may consist of a slurry or mortar with fine aggregate. Generally
superplasticizers are necessary to enhance their rheological properties so that it can be applied in
SIFCON.
In SIFCON technology, the fibers are pre-placed in the mold to prepare the reinforcing bed. This
operation is time consuming. Thus are continually sought new alternative methods to overcome the
limitations of SIFCON. One of these methods consists in producing a fiber mat, which can then be
easily transported as rolls, easily placed and impregnated with the slurry. With these mats or steel
wool is possible to use higher aspect ratio fibers and have a better control of the orientation, thus
Figure 1 - Comparison of stress-strain curves of SIFCON, SFRC and without any concrete
reinforcement element 3 with bending points (Naaman 1992)
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enabling reduction of the amount of fiber. This mesh of interconnected fibers prevents the free
retraction of the array producing lower values of linear retraction, this advantage comes with the easy
handling and better quality control in the production of such compounds and its local application. This
composite is called SIMCON, Slurry Infiltrated Mat Concrete (Bentur and Mindess, 2007).
In this type of composite, an increase in the fiber volume above a value such that it is impossible to
occur infiltration by cement paste can result in a reduction of mechanical properties due to difficulties
in compression. This critical value, depends on the production process, and can be increased by using
more fluid suspension techniques and more intensive compression.
The high flexural strength obtained with a low percentage of fibers reflects the high efficiency of high
aspect ratio fibers used in such composites.
SIMCON properties such as tensile strength, have been reported by A.M. Krstulovic-Opara and Malak
(Bentur and Mindess, 2007), and showed that SIMCON efficiency is higher than SIFCON. With fiber
content in the range of 3-5%, the obtained tensile strength was 10-16 MPa (figure 2). For the same
values in SIFCON, the use of 14% fibers is required.
Both in SIFCON as in SIMCOM fibers are responsible for increased energy absorption capacity
during pull-out, which results in increased strength compared with normal concrete. As result,
these composites have been applied in rehabilitating structures earthquake-resistant
components, explosion resistant structures and fine pre-molded product (Bentur and Mindess,
2007).
Materials and compositions studied
Cement
In this work is used a Portland cement, high early strength, the Supremo Cimento CP V-ARI, provided
by SECIL to the Brazilian market. It is a gray Portland cement, with initial resistance to compression
greater than 34 MPa at 7 days of age and low setting time (less than 60 minutes) that complies with
Figure 2 - Relationship between the fiber and the mechanical properties of SIMCON (Bentur and
Mindess, 2007).
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the technical recommendations of the Brazilian Norm - NBR 5733/1991. It is used in situations that
require a quick undercut (Supremo Cimento, 2015)
Steel wool
Is used a commercial steel wool (Figure 3) in order to reduce the production cost of the composite.
The wool is distributed by Productos PROMADE S.A., according to the manufacturer's product
intended for the preparation of wooden surfaces for the subsequent application of products such as
varnishes. Can be seen in the steel wool roll that fibers are not uniform, either in terms of length,
straight section and tensile strength even when requested by human force.
Plasticizer
Two types of superplasticizers of MC-Bauchemie were used. MC-TechniFlow 91 (hereinafter
superplasticizer 1 - SP1) is a concrete superplasticizer adjuvant that reduces surface tension of water
even with small dosages. It facilitates the dispersion of cement particles and thereby obtains a higher
concrete workability with a reduced need for compression. Depending on the type of cement,
temperature and weather may be a slight retarding effect of prey.
The other product was used Muraplast FK 98 (superplasticizer 2 - SP2) which is a dispersing agent for
cement particles avoiding their agglomeration and reducing the surface tension of water from the
mixture as a consequence of the better distribution of the cement particles and the aggregate is
obtained an improvement in cohesion and workability of the concrete.
Studied compositions
This study investigated the effect on the fluidity of the mortars in the fresh state of two different
plasticizers and the percentage of infiltrated fiber. To determine the dosages to use that offering better
workability was tested what dosage that offered more fluidity to the mix without it appeared
segregation or exudation. With initial reference the recommended dosage by the manufacturer tests
were made until, for each plasticizers would arise not the phenomena mentioned above. For a fixed
amount of cement and water, water represents 30% of the amount by weight of cement, were made
varying the fiber percentages and superplasticizer according to the cement mass. The following table
(Table 1) shows the dosages used for each plasticizer.
Figure 3 - Steel wool in the form provided by the manufacturer.
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Table 1 – Dosage of plasticizer applied
SP1 SP2
Amount of plasticizer
(g/ Kg of cement) 6; 7 e 9 3; 3,5 e 4
After performing exploratory mixtures, were studied the mixtures presented in Tables 1 and 2. Was
varied percentage of fiber and superplasticizer, for each type of this material.
The test pieces will be designated by the following criteria: "SP1" and "SP2" as used plasticizer, "-X",
which is the dosage of the superplasticizer and finally said "Y%" represents the percentage of fiber.
For example, "SP1-6 5%" represents the superplasticizer 1 with a dosage of 6% and 5% of fibers.
Table 2 - Composition studied with SP1
Designation Percentage of fibre(%) Percentage of SP(%)
SP1-6 0 6
SP1-7 0 7
SP1-9 0 9
SP1-6 5% 5 6
SP1-6 10% 10 6
SP1-7 5% 5 7
SP1-7 10% 10 7
SP1-9 5% 5 9
SP1-9 10% 10 9
Table 1 – Composition studied with SP2
Designation Percentage of fibre(%) Percentage of SP(%)
SP2-3 0 3
SP2-3,5 0 3,5
SP2-4 0 4
SP2-3 5% 5 3
SP2-3 10% 10 3
SP2-3,5 5% 5 3,5
SP2-3,5 10% 10 3,5
SP2-4 5% 5 4
SP2-4 10% 10 4
Results
This section presents the results is considered as the most relevant, open porosity, Young's modulus,
compressive strength, flexural strength and SEM micrographs.
Open porosity
For SP1, as shown below (figure 5), it is common to all the dosages SP that the lower porosity value is
obtained for the reference mixtures, increasing to 5% fiber and lowering for 10%
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.
Figure 1 – Open porosity referring to SP1, steel wool evaluation
For SP2, the dosages of 3% and 4%, promote the increase of the porosity with the percentage of
introduced fiber. With 3,5% the porosity increased for 5% of the fiber but decreases to 10%.
Figure 2 – Open porosity related to SP2, steel wool evaluation
Dynamic module of elasticity (ultrasound)
The module of elasticity was only evaluated for superplasticizer 2.
Evaluating the effect of introducing fibers, figure 7, it can be seen that for dosage 3% of SP the
module of elasticity increases with the increasing of the percentage of embedded fiber. For all other
dosages, the module of elasticity decreases with increased amount of incorporated fiber, although the
lowest value is presented by the intermediate dosage of 5%.
Figure 3 – Module of elasticity for SP2, evaluation of steel fibers
12,2 14,5 13,9
25,1 28,0
25,5
20,4 20,7 21,5
0
5
10
15
20
25
30
SP1-6 SP1-7 SP1-9
Op
en
po
ros
ity S
P1 (
%)
SP1 - 0% SP1 - 5%
SP1 - 10%
15,3
22,2 20,2 24,7
28,0 23,8 25,2 24,8 25,1
0
5
10
15
20
25
30
SP2-3 SP2-3,5 SP2-4
Op
en
po
ros
ity S
P2 (
%)
SP2 - 0% SP2 - 5%
SP2 - 10%
51,3 58,7 60,1
53,5 53,4 54,0 55,2 56,0 56,8
0
10
20
30
40
50
60
70
SP2-3 SP2-3,5 SP2-4
Dyn
am
ic m
od
ule
of
ela
sti
cit
y S
P2 [
MP
a]
SP2 - 0% SP2 - 5%
SP2 - 10%
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Determination of compressive strength
The structural elements of cementitious composites are not only exposed to tensile stresses, these
elements are also exposed to the compression, one property whose results are presented below.
When evaluating the effect of the percentage of fiber, is common to all dosages of SP that a lower
value corresponding to mixtures with 5% fiber and a higher value corresponding to 10% fiber. The
reference mixtures have an intermediate value.
Figure 4 - Resistance to compression referring to SP1, steel wool evaluation
For mixtures of SP2 the dosage of 3 and 3,5% it was observed that the compressive strength
increases with the proportion of fiber. For the dosage of 4% the lowest value corresponds to 5% fiber.
For the reference mixture and the mixture with 10% the compressive strength of the fiber increases
with the percentage of fiber.
Figure 5 - Resistance SP2 related to compression, steel wool evaluation
Determination of tensile strength in bending
The tensile strength in bending is an important property to airframe design and it becomes vital to
evaluate the behavior of the cementitious matrix composites with fiber. In this type of composite steel
fiber function is to increase the flexural strength making the material more ductile.
In the case of mixtures prepared with SP1 is common to all dosages of SP that the composition which
has the highest resistance to bending is one that contains 10% fiber, in these cases the values
83,5 81,0 80,6 76,9 74,5 77,6 84,7 84,0 84,0
0
10
20
30
40
50
60
70
80
90
SP1-6 SP1-7 SP1-9
Co
mp
ressiv
e s
tren
gth
SP
1
[MP
a]
SP1 - 0% SP1 - 5%
SP1 - 10%
75,0 69,6 86,2 81,0 79,4 84,5 83,2 87,6 87,5
0
20
40
60
80
SP2-3 SP2-3,5 SP2-4
Co
mp
ressiv
e s
tren
gth
SP
2
[MP
a]
SP2 - 0% SP2 - 5% SP2 - 10%
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increase in the order of 50% against the reference mixtures. For the incorporation of 5% of fiber we
didn’t observe significant increases.
Figure 6 - Flexural strength of SP1, steel wool evaluation
For SP2 mixtures the highest values of flexural strength are also provided by the compositions with
10% of fibers. With the exception of mixtures with 3,5% SP values of bending strength increase with
increasing of the percentage of the embedded fiber. For compositions containing 3,5% of SP in the
case of no fiber incorporation, was obtained a higher value than for the 5% fiber, contrary to other
cases.
Figure 7 - Flexural strength for SP1, steel wool evaluation
Scanning electron microscopy
In order to try to understand the mechanisms leading to increased mechanical strength as a
consequence of steel wool incorporation were performed microscopy to fracture surfaces after
bending test of some of the mixtures. Samples for analysis were prepared according to the procedure
described in Guedes et al., 2013, consisting in impregnating the sample under vacuum in a low
viscosity resin which is followed mechanical polishing and subsequent wear. The polishing was
performed using fine abrasives to 1mm. The equipment used was a Scanning Electronic Microscope
FEG-SEM JSM-7001F, JEOL, Tokyo, Japan. Which is coupled EDS Microanalysis Inca PentaFETx3,
Oxford Instruments, Abingdon, Oxfordshire, UK. The choice fell on the SP1 9% blends with 5% and
10% incorporated steel wool.
8,7 7,8 6,6 8,8 8,9 9,2
16,0 17,0 17,1
0
4
8
12
16
20
24
SP1-6 SP1-7 SP1-9
Fle
xu
ral str
en
gth
SP
1 [
MP
a]
SP1 - 0% SP1 - 5% SP1 - 10%
6,3
14,3
7,6 8,9 9,5 8,9
17,5
22,7 20,0
0
4
8
12
16
20
24
SP2-3 SP2-3,5 SP2-4
Resis
tan
ce t
o b
en
din
g
SP
2[M
Pa]
SP2 - 0% SP2 - 5% SP2 - 10%
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Figure 8. Microscopy: mixture SP1-9% with 5% steel wool (Left) and 10% steel wool (right)
Figure 13. Microscopy: mixture SP1-9% with 5% steel wool after polishing
Discussion of Results
For the module of elasticity, property which was only performed for SP2 in case of 3% dosage SP2,
we observed that this property increases with steel wool embodiment. In other cases the module of
elasticity decreases with wool incorporation and it had more incidence in mixtures with 5% fiber. The
results obtained in this property induce in different conclusions, i.e. we cannot find a link between
other properties already discussed. It’s not possible to conclude what is the effect of the addition of
steel wool in the Module of Young. This may be due to the presence of closed porosity which would
lower the Module of Young.
In relation to compressive strength this we can, in the case of SP1, found that the introduction of steel
wool has a slight effect on the compressive strength. With the exception of mixtures containing 5%,
wherein the compressive strength decreases (which are also the mixtures show the highest porosity)
there is an increase in this property to 10% fiber even with increased porosity. In SP2 case we also
seen compressive strength increases with the introduction of wool, as a result of better control of
cracking caused by fibers. The only exception was in the case of dosage 4% of SP to 5% fiber,
however the reference mixture has a higher standard deviations, which may indicate that the value
could even be lower and thus kept to compressive strength increasing trend with increasing
percentage of incorporated wool.
Regarding the flexural strength of the blends prepared with SP1 it was concluded that the
incorporation of steel wool has a significant impact on the flexural strength of the composites. The
incorporation of 5% of steel wool does not result in a significant improvement of this property, however
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with the addition of 10% wool in relation to the reference mixtures the improvement was of the order of
100%.
In the case of blends prepared with SP2 where the dosage is 3% and 4% SP, the results obtained
were in line with those obtained in the case of SP1. Slight increases occur for the incorporation of 5%
fiber; with 10% fiber the flexural strength increases for more than doubled. It was also found that, for
both SP, are generally mixtures with a 5% steel wool which have higher values of porosity. For
mixtures with 3,5% the trend is not similar, the mixture of reference without fiber added showed a
mechanical resistance higher than the other mixtures without fiber or with 5% fiber.
As previously stated, in order to try to understand the mechanisms leading to the increase of
mechanical strength as a result of the steel wool incorporation were realized some microscopy to
fracture surfaces after the test of bending of some mixtures.
For mixtures of SP1 it was possible to observe that pull-out occurred, as shown in figures 40 and 41.
And it was proved that it was the steel wool present in the composite that resisted to bending stress. It
was observed that the filaments of steel wool which suffered pull-out, i.e. they suffered tearing as a
result of bending stress in the case of the composite with 10% wool rushes incorporated into the same
kind of phenomenon.
Another mechanism mentioned was the better control of cracking introduced by the fiber in the steel
wool. The presence of steel wool filament stopped the propagation of a crack thus proving the
improvement introduced by the steel wool in mechanical performance of composites made with steel
wool.
Conclusion and Future Work
The experimental campaign followed in this work enabled us to understand several important aspects
for the BRFA behavior.
Regarding steel wool embodiment, it was concluded that:
That could cause a very significant increase in tensile strength by bending;
In general, causes an increase in compressive strength;
Increase the amount of pores in the cementitious matrix composite;
Lead to increased capillary coefficients relative to the mixtures without steel wool ;
Although the steel wool has a high variety of types of fibers and that the influence of this variability
have not been considered in the behavior of the produced composite, it was considered that producing
a concrete reinforced with steel wool as a variant of low-cost SIMCON composite.
This work identified that with the introduction of 5% fiber slight gains are obtained in increasing the
flexural strength of the composite. However with the introduction of 10% fiber are significant gains may
submit increments greater than 100% as in the case of mixtures produced with SP2.
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As future work it could be developed the BRFA production technique, which can be improved the wool
infiltration conditions and controlled parameters such as vibration time that this work has not been
quantified and has considerable influence on the final properties of the composite.
It is also important to study the durability of the composite, as well as the steel wool resistance to
corrosion processes.
References
ACI (2002) American Concrete Institute – State of the art – Report on Fiber Reinforced Concrete. Reported by ACI Committee 544. 66p.
Balaguru, P.N.; Shah, S.P. (1992) Fiber Reinforced Cement Composites. McGraw-Hill International Editions. Civil Engineering Series. 531p.
Barros, J. A. O. (1995) - Comportamento do Betão Reforçado com Fibras, Análise Experimental e Simulação Numérica. Tese de Doutoramento, Dep. Engª Civil, FEUP.
Bekaert (2015) – Products and applications: Construction. Disponível em: www.bekaert.com. Acesso: 25.09.2015.
Bentur A.; Mindess, S. (2007) – Fibre Reinforced Cementitious Composites. 2ª Edição. Taylor & Francis. USA. – Ramakrishnan, V.; Coyle, W.V.; Dahl, L.F.; Shrader, E.K., “A Comparative Evaluation of Fiber Shotecrete”, Concrete International: Design and Construction, Vol. 3, Nº 1,1981, pág. 56-59.
BOTAS, S. (2009) – Avaliação do comportamento de argamassas em climas frios. Dissertação para obtenção do grau de Mestre em Engenharia Civil. Caparica,. FCT/UNL.
Casanova, P. (1996) - Bétons Renforcés de Fibres Métalliques, du Matériau à la Structure. Laboratoire Central des Ponts et Chaussées. Février.
Coutinho, A.M. (2006) Fabrico e Propriedades do Betão. Edições LNEC. 646p.
CRAST (2015) Centro Ricerche Archeologiche e Scavi di Torino – Activities of the Institute of Archaeological Sciences and of the Centre for the Restoration of Monuments in Baghdad. Disponível em http://www.centroscavitorino.it/ (Acesso em 03 de Abril de 2015).
Engineer Statistics Handbook (2014) – Estatísticas. Disponível em: http://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm. Acesso em: 25.09.2015.
Guedes, M.; Evangelista, L.; Brito. J.; Ferro, A. F. (2013) – Microstructural Characterization of Concrete Prepared with Recycle Aggregates. Microscopy and Microanalysis. Pág: 1-9.
LNEC E 393. 1993. Absorção de água por capilaridade. Portugal: Laboratório Nacional de Engenharia Civil.
MARTINS, A. I. (2010) - A influência das condições de cura em argamassas de cais aéreas com e sem adição de metacaulino. Dissertação apresentada para: cumprimento dos requisitos necessários à obtenção do grau de Mestre em Construção Civil. Escola Superior de Tecnologia do Barreiro do Instituto Politécnico de Setúbal.
Naaman, A. E. (1992) - SIFCON: Tailored Properties for Structural Performance, HighPerformance Fiber Reinforced Cement Composites. E & FN Spon. London, UK: 18-38.
Odelson, J.B.; Kerr, E.A.; Vichit-Vadakan, W. (2007) – Young’s modulus of cement paste at elevated temperatures. Cement and Concrete Research, 37: 258-263.
14
Rossi, P.; Renwez, S.; Guerrier, F. (1996) Les bétons fibrés à ultra-hautes performances. L'expérience actuelle du LCPC. Bulletin des Laboratoires des Ponts et Chaussées Nº 204. 87-95.
Simões, A.; Diogo, A. C.; Costa, C. M.; Montemor, F.; Margarido, F.; Flores-Colen, I.; Custódio, J. E.; Correira, J. R.; Fernandes, J. S.; Almeira, J V.; Fernandes, J. C.; Brito, J. M.; Neves, J.; Nunes, L.; Gil, L.; Rosa, L. G.; Vieira, M.; Gonçalves, M. C.; Amaral, P. M.; Pontifice, P.; Colaço, R.; Pires, V. C. (2012) – Ciência e Engenharia de Materiais de Construção. IST Press. 1ªEdição. 1057p.
Vilardell, J.; Aguado, A.; Agullo, L.; Gettu, R. (1998) - Estimation of the modulus of elasticity for dam concrete. Cement and Concrete Research, 28: 93- 101.