Investigation of shrinkage of concrete mixtures used for bridge construction in Lithuania/ Tiltu statybai Lietuvoje naudojamu betono misiniu susitraukimo deformaciju tyrimas/ Rukuma izpete Lietuvas tiltu buvnieciba lietotajiem betona maisijumiem/ Leedu sillaehituses kasutatud betoonisegude mahukahanemise uurimine.
Gribniak, Viktor ; Kaklauskas, Gintaris ; Bacinskas, Darius 等
1. Introduction
Advanced civil engineering structures, especially bridges, are
exclusively recognised in every society as a measure of culture,
economical and social development. This development leads to steady
increasing traffic. Therefore, in the modern societies, the civil
engineers should secure the performance and durability of the
transportation infrastructure. Naturally that the bridges, as a part of
this infrastructure, are requested being reliable, efficient, and safe.
The demerits in the concrete structures can arise from the mechanical
and environment loading coupled with deleterious reactions. Moreover,
concrete shrinks as it dries under ambient conditions.
The researches performed by the authors indicated that the
shrinkage may reduce significantly the serviceability of the concrete
structures (Gribniak et al. 2007, 2008, 2010; Kaklauskas et al. 2009a).
It was found that the restrained shrinkage is one of the major causes of
defects in the bridges all over the world. The shrinkage is among the
most uncertain mechanical properties of concrete. Therefore, it is
important for structural designers to know accuracy of shrinkage
prediction models.
In last decades, steel fibre reinforcement is widely used in many
countries as additive for concrete and cement mortar mixture for
production of the concrete structures. Application of fibre
reinforcement in Lithuania is often restricted to production of concrete
floor for different purposes. Whereas, in other countries (USA, Japan,
Germany, Australia, etc) application area of fibre reinforcement is much
wider, for example: bridge decks, thin-walled structures (tunnels,
reservoirs, etc), pavements, pipelines, pile foundations. Thus
application of the fibre reinforcement is considered as one of the most
important branches of engineering science.
This paper investigates shrinking of the concrete mixture which is
often used for casting bridges in Lithuania. The following objectives of
the study have been followed: 1) to investigate accuracy of the
shrinkage prediction models; 2) to explore whether steel fibre
reinforcement has influence on the shrinkage magnitude.
2. Consequences of restrained shrinkage cracking
The term free shrinkage is commonly used to describe the
contraction of hardened concrete exposed to relative humidity less than
100%. Magnitude of the shrinkage depends on the concrete mixture
proportions and material properties, method of curing, ambient
temperature and humidity conditions, geometry of the element. It
develops gradually with time; the word free refers to the case of a
member that can shorten without restraint, thus producing no stresses.
Fig. 1 illustrates how volumetric changes of the hardened concrete can
result cracking. It compares development of the cracking resistance
(time-dependent tensile strength) with the restrained shrinkage-induced
stresses. The specimen will crack when the two lines representing the
tensile strength and the shrinkage-induced stress, will intersect.
Analogously, if the strength is always greater than the stress, no
cracking occurs.
The restrained shrinkage-induced stress might be difficult to
quantify. It is not equal to the 'elastic' stress, defined by
multiplying the free shrinkage strain by the elastic modulus due to the
creep effect (Gribniak et al. 2007). Moreover, the shrinkage strain
increases with time. The authors proposed the simple procedure for
defining the stress taking an accompanying creep effect into
consideration (Kaklauskas et al. 2009a).
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
Effects of shrinkage and accompanying creep of concrete, along with
cracking, provide a major concern to the structural designer because of
the inaccuracies and unknowns that surround them. These effects led to
much deterioration in newly constructed or repaired reinforced concrete
bridges all across Europe. Daly (1999) reported that restrained
shrinkage-induced cracks cause 12% and 10-14% of deteriorations in the
bridges in France and in Germany, respectively; in UK and Norway the
shrinkage cracking is one of the major causes of such defects.
The fibre reinforcement is commonly used for mitigating cracking in
newly constructed or repaired concrete bridge elements. The presented
experimental investigations were performed avoiding the uncertainties
that may arise during construction due to the influence of early-age
concrete properties on the total stress state while focusing an
attention on the influence of steel fibres on magnitude of shrinkage.
3. Shrinkage tests
This Section presents the results of the experimental
investigations on the concrete shrinkage. The research projects were
performed at the Vilnius Gediminas Technical University from 2005 to
2009 under financial support provided by the Lithuanian State Fund of
Research and Studies (Kaklauskas et al. 2005, 2008, 2009b).
3.1. Material properties
Present study has been dedicated to investigation of shrinkage of
concrete (grade C35/45 S3) which is commonly used in newly constructed
bridges in Lithuania. In recent years, the concrete for bridge
construction sites in Vilnius area is most frequently supplied by the
industrial plant "Betono Centras". For this reason, the
concrete produced at the "Betono Centras" plant was selected
for the investigation. The tests cover a four-year period when a large
number of different engineering structures (overpasses, high-rise
buildings and so on) were constructed.
The present investigation is based on the test measurements given
in the three research projects performed by the authors in 2005, 2008,
and 2009. The database contains measurements of 72 specimens from 13
batches. The mix proportion was taken to be uniform for all the batches
and is given in Table 1. The ordinary Portland cement and crushed
granite aggregate (16 mm max nominal size) were used. Water/cement and
aggregate/cement ratio by weight were taken as 0.42 and 2.97,
respectively. Some of the specimens were cast using the steel fibres
reinforced concrete. Two different types of fibres were used:
Krampe-Harex KP 35/1.95 and Duoloc 55/1 (Fig. 2). In Table 2 the
fibre-concrete mixtures are noted as F1 and F2, respectively.
In order to determine material properties of concrete, 12 of [empty
set] 15 x 300 mm cylinders, 12 of 150 mm cubes, 15 of 100 x 100 x 400 mm
and 17 of 300 x 280 x 350 mm prisms were cast. The cylinders and prisms
were used for shrinkage measurements. The compressive strength was
measured at the test finish day and at three time intervals during the
tests, approximately 1, 2 and 4 weeks after casting. 3 cylinders, 3 of
150 mm cubes and 3 of 100 x 100 x 400 mm prisms were tested at each age
for each mixture determining the compressive strength and the stress and
strain relationship. Variation of the compressive strength in time is
given in Table 2, where [f.sub.cm] and [f.sub.cm,cube] are the mean
values of concrete compressive strength obtained from [empty set] 150 x
300 mm cylinders and 150 mm cubes, respectively.
The results given in Table 2 indicate that all the mixtures at
early age reached the design value of compressive strength (C35/45). The
strengths of most mixtures (shown in the gray-filled cells) were found
to be greater than the nominal strength. Due to the fact that the
compressive strength is traditionally assumed as the quality indicator
of the technological process and is continually controlled at the plant,
the obtained results can be considered quite natural. However, shrinkage
(another important characteristic of structural concrete) often is not
controlled. Therefore, this study deals with shrinking properties of
concrete.
3.2. Free shrinkage measurements
In the first project (2005), the mechanical strain gauges were used
for the shrinkage measurements, whereas, in other two projects (2008 and
2009), the Demec-200 strain gauge (Fig. 3) was applied. The measurements
started 2-5 days after casting and were performed daily on 100 x 100 x
400 mm and 280 x 300 x 350 mm prisms and [empty set] 150 x 300 mm
cylinders. After start of drying, ends of the cylinders and 280 x 300 x
350 mm prisms were isolated with a polyester film. The experimental
set-up is presented in Fig. 4.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
4. Analysis of the test results
The reference database contains 4299 test points. The structure of
the test data is given in Table 3. In this table, [n.sub.m] and n are
the numbers of the specimens and the observation points, respectively;
RH is the relative humidity in %; [V.sub.f] is the amount of the fibres
in mixture in % by volume; [t.sub.0] and [t.sub.max] are the
member's ages at start of drying and at finish of test in days,
respectively; Sh is the shape of the member (2 and 3 represent the
infinite cylinder and the square prism, respectively); V/S is the
relationship between the volume of element and its surface subjected to
drying in mm.
As it was reported previously (Gribniak et al. 2007), the drying
shrinkage effect on the cracking behaviour of reinforced concrete
structures is limited to relatively short period (about 2-3 months after
casting). When this period is finalised, the shrinkage effect becomes
un-significant. Due to this the shrinkage measurements performed at time
period of 90 days were accepted for the analysis. This reduces number of
the reference test points to 3293 measurements under consideration.
The study was performed in two steps. 1st--the accuracy of the most
popular shrinkage prediction techniques was analysed and 2nd--the
influence of the fibre reinforcement on the shrinkage was investigated.
These steps are presented below.
4.1. Accuracy of the shrinkage predictions
The comparative study was based on the predictions made by EN
1992-1-1:2004 Eurocode 2: Design of Concrete Structures--Part 1: General
Rules and Rules for Buildings and by ACI 209.2R-08 Guide for Modeling
and Calculating Shrinkage and Creep in Hardened Concrete; B3 model
(Bazant, Baweja 1995a; 1995b); and GL 2000 model (Gardner, Lockman
2001). Accuracy of the methods was analysed in term of a relative
prediction:
[DELTA] = [[epsilon].sub.cs,calc]/[[epsilon].sub.cs,obs], (1)
where [[epsilon].sub.cs, calc] and [[epsilon].sub.cs, obs] are the
calculated and the measured free shrinkage strains of concrete,
respectively. The relative prediction is considered as a random
variable. Therefore, statistical methods can be used for assessment of
the accuracy. Central tendency and variability statistics were used for
this purpose. The central tendency can be regarded as the precision
parameter of a calculation method. The postulate of min variance was
used to evaluate consistency of a model.
The experimental data was divided into 2 groups separating the
measurements of ordinary and fibre reinforced concretes. Fig. 5 shows
the relative prediction of the shrinkage of ordinary concrete.
[FIGURE 5 OMITTED]
It should be noted that Fig. 5 gives the relative predictions in
logarithmic scale. The logarithmic transformation was performed securing
equal contribution of underestimated and overestimated predictions to
the accuracy estimation. As can be observed, all the methods
underestimate the shrinkage effect, whereas the EN 1992-1-1:2004
demonstrates the best accuracy: after 28 days EN 1992-1-1:2004, ACI
209.2R08, B3 and GL 2000 methods underestimated the shrinkage at average
of 14.6, 43.6, 128.1 and 16.2%, respectively. The EN 1992-1-1:2004
method, as the normative document accepted in the EU, was chosen for the
further analysis.
4.2. The effect of fibres on the shrinkage
It is important that the statistical evaluation should be performed
only for data, which is nominally identical, with variation due to
random effects. However, it was found that the drying period has a
systematic effect on the accuracy of the shrinkage prediction methods
(Bacinskas et al. 2009). Therefore, the analysed data was separated into
groups according to the specimen's age. A normality test was used
to include data point in the group. For this purpose, a statistical
procedure has been developed (Gribniak 2009). Results were divided into
2 groups. The 1st group (I) contains the measurements, performed on the
specimens which age do not exceeded 21 days. The 2nd group (II)
represents the data obtained after 21 day.
As was mentioned, [DELTA] does not allow objective interpretation
of the accuracy due to the uneven contribution of underestimated and
overestimated predictions. Therefore, the logarithmic scale of [DELTA]
was introduced in Figs 5 and 6. The following analysis is based on the
arithmetical error:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)
Fig. 6 presents the shrinkage predictions for ordinary and
fibre-reinforced concretes. This Fig also gives the 95% confidence
intervals of the expectation of the EN 1992-1-1:2004 predictions
(considered as estimator of the central tendency). The confidence
intervals have become narrower for the concrete reaching 21 days of age.
The upper and lower bounds of the obtained intervals are presented in
Table 4. This Table gives the main statistics of the EN 1992-1-1:2004
predictions in terms of the arithmetical error. In this Table,
[n.sub.obs] is the number of the measurements in the age interval.
[FIGURE 6 OMITTED]
The calculation method is assumed to be precise (with 95%
probability), if the confidence interval covers unity. It can be
observed that in both cases the EN 1992-1-1:2004 underestimates the
shrinkage (Fig. 6), whereas the deformations of the fibre-concrete seem
to be more accurate. This statement can be supported statistically using
the hypothesis test procedure. This procedure can be used for deciding
between two hypotheses. In each age interval, two hypotheses were
formulated. The null hypothesis states that the accuracy of the EN
1992-11:2004 in both cases is equal:
[H.sub.0] : [m.sub.1] = [m.sub.2], (3)
where [m.sub.1] and [m.sub.2] are the sample means of the shrinkage
predictions of ordinary and fibre-concrete, respectively. The
alternative hypothesis identifies that the shrinkage of the
fibre-concrete was predicted more accurate. Due to the fact that the
shrinkage was underestimated in both cases; the alternative hypothesis
can be formulated as
[H.sub.1] : [m.sub.1] < [m.sub.2]. (4)
The two-step one tailed test procedure was used for the analysis.
The procedure was linked to the modified Fisher's ANOVA (analysis
of the variance) test (Mardia, Zemroch 1978) and Satterthwaite's
criteria for the mean comparison (Satterthwaite 1946). The hypothesis
test was considered being significant (at the 5% level). This leads to
the decision rejecting [H.sub.0] to the benefit of [H.sub.1]. In other
words, the shrinkage prediction for the fibre-concrete was admitted more
accurate than for the ordinary one. The accepted hypothesis [H.sub.1]
stands the following inequality:
[m.sub.1] < [m.sub.2] < 1. (5)
This indicates that the sample mean of fibre-concrete is closer to
unity than the mean of ordinary concrete. Taking into account the Eq
(1), it allows to state that the shrinkage of fibre-concrete was less
significant (in a statistical sense) than the ordinary one. This finding
supports the results obtained by Swamy and Stavrides (1979) who found
that the shrinkage was reduced by about 15-20% due to the presence of 1%
of steel fibres. Barr et al. (2003) reported that the fibres effect
reducing the shrinkage rises gradually with the increase of the concrete
strength.
However, free shrinkage is not really a useful needle of the
effectiveness of the fibres in reducing the shrinkage problems. It is
not the free shrinkage strains which should be reduced, but the cracking
associated with the restrained shrinkage (Zanuy 2010; Lampropoulosa,
Dritsos 2011; Kaklauskas, Gribniak 2011). Shah et al. (1994) reported
that 0.5% (by volume) of steel fibres reduced the average crack width by
90%. The authors obtained analogous results (Kaklauskas et al. 2009b).
4.3. Discussion on the findings
Table 4 indicates that the EN 1992-1-1:2004 method (the most
accurate among the analysed ones) for ordinary concrete has
underestimated shrinkage almost by 20%. The authors recommend
introducing the correction factor 1.2 for the calculated value of
shrinkage of industrial concrete mixture C35/45 S3. The analysis
demonstrates that the application of the steel fibres as an admixture
was capable of reducing the shrinkage deformation of concrete. It can be
observed that fibre-reinforced concrete with given amounts of fibres has
shrunk almost 10% less than the ordinary one.
5. Concluding remarks
Present paper investigates drying shrinkage strain of the concrete
mixture which is usually used for casting the newly constructed bridges
in Lithuania. As the shrinkage effect on the cracking behaviour of such
structures is limited to relatively short period (about 2-3 months), the
time period of 90 days was accepted for the investigation.
Accuracy of the well-known shrinkage prediction techniques was
analysed. It was obtained that all the methods employed in the analysis
(i.e. EN 1992-1-1:2004, ACI 209.2R-08, B3 and GL 2000) have
underestimated the shrinkage strain. Among these four techniques, the EN
1992-1-1:2004 have demonstrated the best accuracy giving 14.6% error of
the mean value of shrinkage of concrete C35/45 at the age of 28 days.
The analysis has resulted in 43.6, 128.1 and 16.2% errors for the ACI
209.2R-08, B3 and GL 2000 methods.
The authors have also studied the influence of steel fibres on the
shrinkage deformations. It was statistically proved that the application
of fibre in concrete resulted in the reduction of shrinkage strain. The
study indicates that the application of the steel fibres as an admixture
is an effective way of decreasing shrinkage of concrete.
doi: 10.3846/bjrbe.2011.10
Acknowledgements
The authors wish to express their sincere gratitude for the
financial support provided by the Research Council of Lithuania (grant
No. MIP-126/2010). Dr. Viktor Gribniak also wishes to acknowledge the
support by the Research Council of Lithuania for the Postdoctoral
Fellowship granted within the framework of the EU Structural Funds
(project "Postdoctoral Fellowship Implementation in
Lithuania").
Received 13 September 2010; accepted 1 April 2011
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Viktor Gribniak (1), Gintaris Kaklauskas (2), Darius Bacinskas (3),
Wen-Pei Sung (4), Aleksandr Sokolov (5), Darius Ulbinas (6)
(1, 2, 3, 5, 6) Dept of Bridges and Special Structures, Vilnius
Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius,
Lithuania
(4) Dept of Landscape Architecture, National Chin-Yi University of
Technology, Chung-Shan Road 35, Lane 215, Sec. 1, Taiping City, Taichung
County, 41111 Taiwan
E-mails: (1) Viktor.Gribniak@vgtu.lt; (2)
Gintaris.Kaklauskas@vgtu.lt; (3) Darius.Bacinskas@vgtu.lt; (4)
wps@ncut.edu.tw; (5) Aleksandr.Sokolov@vgtu.lt; (6)
Darius.Ulbinas@vgtu.lt
Table 1. Mix proportion of the concrete, kg/[m.sup.3]
Material Amount
Sand 0/4 mm 905 [+ or -] 2%
Crushed granite aggregate 5/8 mm 388 [+ or -] 1%
Crushed granite aggregate 11/16 mm 548 [+ or -] 1%
Cement CEM I 42.5 (Class N) 400 [+ or -] 0.5%
Water 123.8 [+ or -] 5%
Plasticiser Muraplast FK 63.30 2 [+ or -] 2%
Table 2. The compressive strength of concrete, MPa
Producing
Mixture data Parameter Measurements
I 2005-09-30 [f.sub.cm,cube] -- 36.9
Age, days -- 7
II 2005-10-07 [f.sub.cm,cube] -- 34.4
Age, days -- 5
III 2005-10-14 [f.sub.cm,cube] -- 32.4
Age, days -- 6
IV 2005-10-24 [f.sub.cm,cube] -- 45.4
Age, days -- 7
V 2008-09-19 [f.sub.cm] -- --
[f.sub.cm,cube] -- 44.2
Age, days -- 7
VI 2008-09-26 [f.sub.cm] -- --
[f.sub.cm,cube] 43.4 50.8
Age, days 3 7
VII 2008-10-03 [f.sub.cm] -- --
[f.sub.cm,cube] -- 50.7
Age, days -- 5
VIII(F1) 2008-10-03 [f.sub.cm] -- --
[f.sub.cm,cube] -- 45.4
Age, days -- 5
IX 2008-10-16 [f.sub.cm] -- --
[f.sub.cm,cube] 40.3 --
Age, days 4 --
X(F1) 2008-10-16 [f.sub.cm] -- --
[f.sub.cm,cube] 39.8 --
Age, days 4 --
XI(F2) 2009-05-26 [f.sub.cm] -- --
[f.sub.cm,cube] 37.4 --
Age, days 2 --
XII(F2) 2009-05-29 [f.sub.cm] -- --
[f.sub.cm,cube] 36.2 --
Age, days 3 --
XIII(F2) 2009-06-03 [f.sub.cm] -- --
[f.sub.cm,cube] 36.8 --
Age, days 2 --
Producing
Mixture data Parameter Measurements
I 2005-09-30 [f.sub.cm,cube] 40.9 -- 47.3
Age, days 14 -- 47
II 2005-10-07 [f.sub.cm,cube] 39.9 48.7 48.2
Age, days 11 28 29
III 2005-10-14 [f.sub.cm,cube] 37.7 41.2 41.6
Age, days 15 31 32
IV 2005-10-24 [f.sub.cm,cube] 47.7 55.5 52.9
Age, days 14 31 35
V 2008-09-19 [f.sub.cm] -- 42.5 48.3
[f.sub.cm,cube] 50.4 48.7 56.3
Age, days 14 28 69
VI 2008-09-26 [f.sub.cm] -- 45.5 49.7
[f.sub.cm,cube] 54.6 52.9 64.7
Age, days 14 28 76
VII 2008-10-03 [f.sub.cm] -- 49.5 52.8
[f.sub.cm,cube] 59.7 66.3 68.0
Age, days 14 28 77
VIII(F1) 2008-10-03 [f.sub.cm] -- 49.5 50.5
[f.sub.cm,cube] 54.4 58.4 72.3
Age, days 14 28 77
IX 2008-10-16 [f.sub.cm] -- 43.7 44.6
[f.sub.cm,cube] 48.6 55.4 61.5
Age, days 14 28 50
X(F1) 2008-10-16 [f.sub.cm] -- 43.8 46.5
[f.sub.cm,cube] 51.4 55.7 60.9
Age, days 14 28 50
XI(F2) 2009-05-26 [f.sub.cm] -- 46.2 54.8
[f.sub.cm,cube] -- 50.5 65.7
Age, days -- 28 176
XII(F2) 2009-05-29 [f.sub.cm] -- 42.0 48.1
[f.sub.cm,cube] -- 47.4 55.6
Age, days -- 28 173
XIII(F2) 2009-06-03 [f.sub.cm] -- 46.9 52.6
[f.sub.cm,cube] -- 51.1 61.7
Age, days -- 28 168
Table 3. Structure of the test data
Projects' [n.sub.m] n RH [V.sub.f] [t.sub.0]
year
members pts % % (by volume)
2005 11 336 65 0 1-4
2008 43 2031 76 0, 0.3, 0.6 1-4
2009 18 1932 73 0.5, 1.0, 1.5 3
Projects' [t.sub.max] Sh V/S
year
days -- mm
2005 31-55 3 25.0-72.4
2008 49-89 2/3 25.0-72.4
2009 161-172 2/3 25.0-72.4
Table 4. The arithmetical errors of the EN 1992-1-1:2004
predictions
Age group, [n.sub.obs],
Concrete days pts
Ordinary I ([less than or equal to] 21) 580
II (22-90) 1148
Fibre- I ([less than or equal to] 21) 342
reinforced II (22-90) 1223
Arithmetical errors
[epsilon].sub.[DELTA]], %
The 95% confidence
bounds
Age group,
Concrete days Mean lower upper
Ordinary I ([less than or equal to] 21) -14.5 -18.0 -7.8
II (22-90) -23.1 -24.3 -20.6
Fibre- I ([less than or equal to] 21) -8.3 -12.0 -1.5
reinforced II (22-90) -9.9 -10.9 -8.0
