Cite this article
Research Article
Vijaya Bhaskara GS, Balaji Rao K and Anoop MB (2018)
Model for compressive strength development of OPC concrete and fly ash concrete with time
Magazine of Concrete Research 70(11): 541–557,
https://doi.org/10.1680/jmacr.17.00203
Paper 1700203
Received 26/04/2017; Revised 01/08/2017;
Accepted 11/09/2017;
Published online 18/12/2017
Keywords: compressive strength/
modelling/plain concrete
ICE Publishing: All rights reserved
Magazine of Concrete Research
Model for compressive strength development
of OPC concrete and fly ash concrete
with time
Gollapalli S. Vijaya Bhaskara
Madambikkattil B. Anoop
Scientist, Risk and Reliability of Structures, CSIR-Structural Engineering
Research Centre, Chennai, India (corresponding author:
vbhaskara@serc.res.in)
Principal Scientist, Risk and Reliability of Structures, CSIR-Structural
Engineering Research Centre, Chennai, India
Kanchi Balaji Rao
Advisor and Chief Scientist, Risk and Reliability of Structures,
CSIR-Structural Engineering Research Centre, Chennai, India
Towards promoting the use of higher percentage levels of fly ash in concrete in order to reduce its carbon dioxide
footprint, rational models for estimating the mechanical properties of fly ash concrete (FAC) are required. A simple
model for predicting the mean compressive strength development with age of both FAC and ordinary Portland
cement concrete (OPCC) is proposed. The model is applicable to concrete containing 0–75% class F fly ash, type I
cement and normal-weight aggregates and having a 28 d average compressive strength up to 65 MPa. The model
was developed based on two-stage regression analyses of the experimental data of 512 concrete mixtures
collected from the literature. The predictions made using the model were found to be in good agreement with the
results of experimental investigations carried out at CSIR-Structural Engineering Research Centre and additional
experimental data collected from the literature. From a comparison with a reaction-kinetics-based strength
development model available in the literature, it was noted that the proposed model is able to reflect the reaction
kinetic processes involved in strength development in both OPCC and FAC. The proposed model should help
in developing specifications related to strength development for FAC similar to that given in fib Model Code 2010
for OPCC.
Notation
A
B
Bce
BF
C
Cce
CF
Cw-free
CF0
CH
CSH(t)
CSH28
De
De0
De0F
E0
F
fcm(t)
fcm,u
fcm,28
empirical constant
binder/cementitious material (cement and fly ash)
ratio
coefficient depending on the rate of initial
shell formation
coefficient
cement content
coefficient depending on the rate of initial shell decay
coefficient
amount of water at exterior of calcium silicate
hydrate (CSH) gel
mass of free calcium oxide content in fly ash
amount of calcium hydroxide
average CSH content at age t d
average CSH content at age 28 d
effective diffusion coefficient of water through
CSH gel
initial value of effective diffusion coefficient
initial diffusion coefficient for fly ash reaction
initial apparent activation energy
fly ash content
mean cylinder compressive strength in MPa at age t d
limiting cylinder compressive strength in MPa
mean cylinder compressive strength in MPa at age 28 d
fi,c, fi,p
f1cm(t)
k
kd
kdF
kr
krF
m
P
p
R
RCHC
RCWF
RPWF
Ru
ˉ
weight fractions of constituent i (i = C, CF, S, A, F, S)
in cement and fly ash other than free calcium
oxide, respectively
conservative mean compressive strength at age t d
(with 95% confidence limit)
coefficient of reaction rate of free calcium oxide
reaction coefficient in induction period
reaction rate coefficient of fly ash in dormant period
coefficient of reaction rate of cement
reaction rate coefficient of the phase boundary
reaction process
parameter depending mainly on water content,
aggregate content and type and other compositional
parameters of concrete
amount of fly ash phases other than free
calcium oxide
percentage of fly ash content
gas constant (= 8·3144 J/K mol)
amount of calcium hydroxide produced from
1 g of cement
mass of chemically bound water from 1 g of reacted
fly ash
mass of physically bound water from 1 g of reacted
fly ash
limiting relative compressive strength (= fcm,u/fcm,28)
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541
Magazine of Concrete Research
Volume 70 Issue 11
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
r0
r0F
Sw
Although experimental investigations on the compressive
strength of FAC carried out by various researchers are available in the literature, there is still a need to develop models for
the mechanical properties of FAC through comprehensive analyses of existing experimental results (Dragaš et al., 2016).
Some models to predict compressive strength development in
FAC have been developed (Han et al., 2003; Yoon et al.,
2014), but they are based on limited experimental data (less
than 30 concrete mixes) and have a small range of applicability. For instance, the model proposed by Yoon et al. (2014)
is only applicable to concretes with fly ash contents of 50% or
60% and the model of Han et al. (2003) is valid only for concretes with less than 30% fly ash. There is thus a need to
develop models for predicting compressive strength development in FAC that have a large range of applicability.
S0
s
T
t
t0
v
W
Wcap
wg
α
αC
αCF
αF
αF−total
βcc(t)
βCSH(t)
γactive
γS, γA
νF
ρc
ρF
ρw
radius of unhydrated cement particles
radius of fly ash particles
effective surface area of cement particles in contact
with water
total surface area if surface area is unconstrained
strength development coefficient
curing temperature
age of concrete
age when strength development is assumed to begin
stoichiometric ratio by mass of water to cement
(= 0·25)
water content
mass of capillary water
physically bound water in the CSH gel (= 0·15)
constant
degree of cement hydration
reaction degree of free calcium oxide
reaction degree of the active part in fly ash
reaction degree of total fly ash other than free
calcium oxide
function to describe mean strength development with
age ( fcm(t)/fcm,28)
normalised value of CSH content age t d with respect
to 28 d CSH content
weight fraction of active part of fly ash other than
free calcium oxide
weight fraction of active parts of S and A in fly ash
stoichiometry ratio by mass of CH to P
density of cement
density of fly ash
density of water
Introduction
Cement manufacturing is responsible for 5–7% of global
carbon dioxide emissions, and reducing the cement content of
concrete is a major step towards realising a sustainable habitat
(Barcelo et al., 2014). The amount of cement used in concrete
can be reduced through the use of supplementary cementitious
materials such as fly ash, silica fume and ground granulated
blast-furnace slag (Soutsos et al., 2017), and the use of fly ash
in concrete is increasing rapidly in infrastructure construction
(Yoon et al., 2014). To predict time-dependent properties such
as creep and shrinkage of fly ash concrete (FAC) mixtures and
to predict the concrete strength at the time of transfer of prestress in prestressed concrete structures (generally at 7 d),
strength development models are required. A rational estimation of compressive strength provides the opportunity to
optimise the time of formwork removal. However, the compressive strength development models available in fib Model
Code 2010 (fib MC 2010) (fib, 2013a), IRC 112-2011 (IRC,
2011) and ACI 209 (ACI, 1992) are for normal-hardening concrete and thus they may not be applicable to FAC since the
hydration process of FAC is different from that of ordinary
Portland cement concrete (OPCC).
542
Strength development depends on the types of cement, fly ash
and aggregate used (Hanif et al., 2017; Soutsos et al., 2017).
Type I cement and class F fly ash (as per ASTM recommendations) are widely used in concrete production due to their
range of applicability and availability. Experimental data concerning concrete containing other types of cement and fly ash
are limited, so strength development in concrete mixtures containing type I cement and class F fly ash was considered in the
study presented in this paper. With the aim of developing a
strength development model for FAC, relevant data for 512
concrete mixtures (with 1343 results for average compression
strength) were collected from the literature. Based on two-stage
regression analyses of average compressive strength data of
concretes with various percentages of fly ash, a model for predicting mean compressive strength development was developed. The proposed model is applicable for concrete mixtures
with 28 d average compressive strength up to 65 MPa containing 0–75% class F fly ash, type I cement and normal-weight
aggregate. The proposed model has the form of the compressive strength development model (for OPCC) given in fib MC
2010. The results of the model were compared with the results
of experimental investigations carried out at CSIR-Structural
Engineering Research Centre (CSIR-SERC) and the results of
a reaction-kinetics-based model, and were found to be in satisfactory agreement. An equation was also developed for predicting conservative values of the mean compressive strength
of FAC at different ages with a 95% confidence limit.
Compressive strength development with age
It is known that concrete gains strength with age. fib MC 2010
(fib, 2013a), IRC 112-2011 (IRC, 2011) and ACI 209 (ACI,
1992) specify a strength development model to predict the
mean compressive strength at age t (in days) of normal concrete ( fcm(t)), based on its 28 d average compressive strength
( fcm). The model is given by
1:
fcm ðtÞ ¼ βcc ðtÞfcm;28
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Magazine of Concrete Research
Volume 70 Issue 11
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
According to fib MC 2010 and IRC 112-2011, βcc(t) is
given by
28
t
05 ##
whereas ACI 209 defines βcc(t) as
3:
t
βcc ðtÞ ¼
α þ γt
For ordinary concrete with 28 d average compressive strength
less than 60 MPa and for normal Portland and rapidhardening cement, the value of s given in MC 2010 and IRC
112-2011 is 0·20 and 0·25, respectively. For moist-cured
samples and type I cement, the values of α and γ as per ACI
209 are 4 and 0·85, respectively.
Concrete containing fly ash, depending on the amount of
fly ash present, gains strength over longer periods of time
than concrete without fly ash under the same curing
regime. The applicability of Equations 1–3 to FAC was studied
using test data available in the literature, and typical results
of the comparison are presented in Figure 1. The figure
shows that predictions made using the strength development
models of fib MC 2010, IRC 112-2011 and ACI 209 are closer
to average experimental values for OPCC, as expected, and
underpredict the mean compressive strength of FACs after
28 d. In FAC, glass phase silica (SiO2) and alumina (Al2O3)
progressively react with calcium hydroxide (Ca(OH)2) formed
by cement hydration, forming hydrates of calcium silicate
and aluminate. There is thus a reduction in calcium hydroxide
content and an increase in calcium silicate hydrate (CSH)
gel. The hydration of cement forms the hardened structure
and the pozzolanic reaction of fly ash improves the structure.
Thus, FAC exhibits higher strength development than
OPCC at later ages, depending upon the percentage of
fly ash, as has been observed by various researchers. The
attempts made by researchers to develop compressive
strength development models for FAC can be broadly classified
into regression-based models and reaction-kinetics-based
models.
80
Compressive strength: MPa
IRC 112-2011
fib MC 2010
ACI 209
Concrete without fly ash
60
40
20
0
1
10
100
60
Concrete with 50% fly ash
Compressive strength: MPa
βcc ðtÞ ¼ exp s 1 45
30
15
0
1
10
100
60
Concrete with 60% fly ash
Compressive strength: MPa
" "
2:
Experiment (Yoon et al., 2014)
45
30
15
0
1
10
100
Age of concrete: d
Regression-based strength development models
Yoon et al. (2014) and Han et al. (2003) developed strength
development models for FAC. The model proposed by Yoon
et al. (2014) is a linearised form of the fib model (Equations 1
and 2)
4:
rffiffiffiffiffi
28
lnð fcm ðtÞÞ ¼ s
þ ðln fcm;28 þ sÞ
t
Figure 1. Comparison of predictions of compressive strength
development models with corresponding experimental data of
Yoon et al. (2014)
Using experimental data of 27 concrete mixes, Yoon et al.
(2014) estimated the values of the empirical coefficient s to be
0·57 ± 0·08 and 0·89 ± 0·05 for concrete having 50% and 60%
fly ash, respectively.
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543
Magazine of Concrete Research
Volume 70 Issue 11
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
For concrete with ≤30% fly ash, Han et al. (2003) proposed a
prediction model using the apparent activation energy (E0),
given by
(
)
fcm
1
5:
¼ Ru 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
αt
fcm;28
1 þ A½eðE0 =RTÞeαt þ eðE0 =RTÞe 0 ðt t0 Þ
Prediction of compressive strength development in
FAC using reaction kinetics (Fan et al., 2015)
The compressive strength of FAC can be related to CSH
content (Papadakis et al., 2002)
Using experimental data of 21 concrete mixes with ≤30% fly
ash, Han et al. (2003) estimated the model parameters to be
where the parameter m depends on the water content, aggregate content and type and other compositional parameters of
the concrete.
&
&
&
&
&
t0 = 0, A = 107 and α = 0·000615
Ru = 1·66 + 0·008p for a water/binder (w/b) ratio of ≤ 0·40
Ru = 1·313 + 0·013p for w/b > 0·40
E0 = 39 720 + 119p for w/b ≤ 0·40
E0 = 42 920 + 90p for w/b > 0·40.
Reaction-kinetics-based strength development models
The compressive strength development of concrete can be correlated to the reaction kinetics in concrete (Jiang et al., 2015).
A review of the relevant literature revealed that several reaction-kinetics-based strength development models for OPCC
are available (Maekawa et al., 1999). These models are based
on the total porosity or the gel/space ratio (the ratio of the
volume of hydration products to the volume of both hydration
products and capillary pores) or CSH content. However,
these models cannot be used to predict strength development
in FAC because of the different reaction kinetics in FAC
and OPCC (Maekawa et al., 1999). Based on reaction stoichiometry, Papadakis (1999) proposed models for predicting the
final calcium hydroxide and CSH contents in FAC. However,
Papadakis (1999) did not consider the kinetics of the reactions
of silica with calcium hydroxide and free calcium oxide with
water. Wang (2014) combined Papadakis’ model with the
reaction kinetics of cement and fly ash to model the evolution
of calcium hydroxide and CSH contents over time. Fan et al.
(2015) improved the model by considering the production
of calcium hydroxide from the reaction of free calcium oxide
with water in fly ash and the proposed CSH-based model for
predicting the evolution of compressive strength in FAC.
The model developed by Fan et al. (2015) is a reactionstoichiometry-based model for predicting the evolution of
calcium hydroxide content, CSH content and mean compressive strength development with time in FAC. The model
takes into account the chemical compositions of cement
and fly ash. The model also considers the kinetic reaction
mechanisms involved in cement hydration and fly ash reactions, and the effect of cement hydration on fly ash reactions
is considered through the calcium hydroxide content and the
capillary water content. The model proposed by Fan et al.
(2015) was adopted in this study for predicting CSH content
and mean compressive strength development in FAC using
reaction kinetics. The salient details of the model are now
presented.
544
6:
fcm ðtÞ ¼ mCSHðtÞ
By normalising the mean compressive strength with the 28 d
compressive strength, normalised strength development can be
represented through the development of CSH content using
Equation 4. The normalised average compressive strength
(βcc(t)) is same as the normalised CSH content (βCSH(t)), that is
7:
βcc ðtÞ ¼
fcm
CSHðtÞ
¼
¼ βCSH ðtÞ
CSH28
fcm;28
Development of CSH with time in FAC
CSH is formed during the hydration of cement according to
the following reactions (Hewlett, 2003).
I:
2C3 S þ 6H ! C3 S2 H3 þ 3CH
II:
2C2 S þ 4H ! C3 S2 H3 þ CH
The formation of CSH from the pozzolanic reaction of the reactive silica of fly ash is given by Reaction III (Papadakis, 1999).
III:
2S þ 3CH ! C3 S2 H3
Papadakis (1999) proposed simple equations for determining
the final volumes of the reaction products (i.e. after complete
reaction of the cement and fly ash) by considering the stoichiometry of chemical reactions and the weight fractions of oxides
in cement and fly ash as well as the molar weights of reactants
and products. However, the change in calcium hydroxide
content and CSH content with time cannot be obtained using
the Papadakis model. By analysing experimental results, Wang
(2014) noted that amount of calcium hydroxide available at any
time is directly proportional to the degree of hydration of
cement. The evolution of calcium hydroxide content in a
cement–fly ash blend can be evaluated as (Fan et al., 2015)
8:
CHðtÞ ¼ CRCHC αC þ 1321CF0 αCF ðtÞ vF αF P
9:
vF ¼ ð1851γS fS;p þ 2182γA fA;p Þ 1321ð fC;p 07fS;p
ˉ Þ
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Magazine of Concrete Research
Volume 70 Issue 11
where RCHC is the calcium hydroxide produced from 1 g of
hydrated cement. The term CRCHCαC represents the calcium
hydroxide produced from cement hydration. The term
1·321CF0αCF(t) is calcium hydroxide production from the reaction of free calcium oxide in the fly ash. The term − vFαFP
considers calcium hydroxide consumption by the reaction of
fly ash phases other than free calcium oxide. Similarly, the
evolution of CSH content can be determined as
10:
CSHðtÞ ¼ 285ð fS;c αC C þ γS fS;p αF PÞ
where 2·85fS,cαCC is the amount of CSH production from
the cement hydration and 2·85γS,pαFP is the amount of CSH
production from the reaction of fly ash.
The reaction kinetics such as cement hydration, the reaction of
free calcium oxide in the fly ash and the pozzolanic reactions
of fly ash phases other than free calcium oxide in cement–fly
ash blends is as follows.
(a) Kinetic model for cement hydration. From experimental
investigations on the isothermal heat evolution rate of
Portland cement paste, Tomosawa (1997) found that
cement hydration generally consists of three processes: an
initial dormant process, a phase boundary reaction
process and a diffusion process. In the current work, the
hydration model originally proposed by Tomosawa (1997)
and developed by Park et al. (2008) was used to simulate
cement hydration. The model assumes a spherical shape
for the cement particles. It has been used by several
researchers (Fan et al., 2015; Park et al., 2008; Tomosawa,
1997) to determine the heat evolution rate, chemically
bound water and compressive strength of hardening
concrete, who found good correlation between predicted
and experimental results. The formation and destruction
of an initial impermeable layer is also considered in the
model. Furthermore, the initial resistance to mass
transport from the surface layer is the rate-controlling
process that gradually turns to a diffusion-controlled
process. The rate of penetration of a reaction front into a
cement particle is modelled based on diffusion of
moisture across the product layer. Park et al. (2008)
modified the model of Tomosawa (1997) to include the
effect of capillary water content on the rate of cement
hydration as
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
13:
De ¼ De0 ln
14:
Cwfree ¼
1
α
W 04αC
W
Arrhenius’ law (Park et al., 2008) is used to consider
the effect of curing temperature on the reaction coefficients Bce, Cce, De0 and kr.
(b) Simulation of reaction of free calcium oxide in fly ash.
Calcium hydroxide will be produced from the reaction of
free calcium oxide of the fly ash with water, while other
active phases in fly ash react with calcium hydroxide to
produce CSH. The hydration of free calcium oxide to form
calcium hydroxide is given by Reaction IV
IV:
C þ H ! CH
From investigations of the hydration kinetics of free
calcium oxide, Chen and Chen (2000) proposed a formula
for the reaction degree of free calcium oxide as
15:
αCF ðtÞ ¼ 1 1
ekt
The reaction rate coefficient k is 0·09/h at 20°C and the
dependence of k on the curing temperature is described
using Arrhenius’ law. However, it may be noted that the
dependence of k on the availability of water for the reaction of free calcium oxide is not considered.
(c) Simulation of pozzolanic reactions of fly ash phases
other than free calcium oxide. Wang (2014) revised the
cement hydration model for determining the reaction
degree of fly ash by considering similarities in the kinetic
mechanisms and differences in the reactions between
cement hydration and the pozzolanic reaction of fly ash.
The similarities between cement hydration and pozzolanic
reaction of fly ash are as follows.
(i) Cement hydration at later ages and pozzolanic
activity are diffusion-controlled processes.
(ii) Similar to cement hydration products adhering to the
surface of cement particles, pozzolanic products also
adhere to fly ash particles.
11:
dα 3ðSw =S0 Þρw Cwfree
1
¼
dt
ðv þ wg Þr0 ρc ½ð1=kd Þ ðr0 =De Þ þ ðr0 =De Þð1 αÞ1=3 þ ð1=kr Þð1 αÞ2=3
12:
kd ¼
Bce
þ Cce α3
α15
(ii) Fly ash exhibits a longer initial dormant period
because fly ash reaction activation depends on
breaking of its glassy phase in a similar way to large
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545
Magazine of Concrete Research
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cement particles showing a longer initial dormant
period than smaller particles.
Due to these similarities, the form of the fly ash reaction is
considered to be similar to that of cement hydration.
The major difference between the reactions of cement and fly
ash is that cement hydration produces calcium hydroxide while
pozzolanic activity consumes it. The rate of the fly ash reaction
depends on the calcium hydroxide content available in concrete
(McCarthy et al., 2017), which is taken into account in the fly
ash reaction as
16:
17:
18:
kdF
BF
¼ 15 þ CF α3F
αF
DeF
1
¼ De0F ln
αF
Wcap ¼ W 04Cα RCWF αF P 0321CF0 αCF ðtÞ
RPWF αF P
Considering both the inert part and active part of the fly ash,
the reaction degree of fly ash other than calcium oxide is
20:
αFtotal ¼ γactive αF
By using concrete mix proportions and chemical compositions
of cement and fly ash as input in the model of Fan et al.
(2015), the properties of hardening fly ash blended concrete,
such as the reaction degrees of cement and fly ash, the calcium
hydroxide content, CSH content and compressive strength, can
be determined. The model proposed by Fan et al. (2015) also
considers the influence of the particle sizes of cement and
fly ash and curing conditions on the reaction. The model is
applicable to low-calcium and high-calcium fly ash because it
considers calcium hydroxide production from the reaction
of free calcium oxide in fly ash. The reaction-kinetics-based
model proposed by Fan et al. (2015) was thus used for comparison in this study for predicting CSH content and mean
compressive strength development in FAC.
546
From the above discussion it is clear that the reaction-kineticsbased strength development model requires the concrete mix
proportions and the chemical compositions of the cement and
fly ash as inputs for predicting strength development. However,
this information may not be readily available for engineers at
the design stage. The models available in the codes of practice
use the 28 d average compressive strength for predicting the
mean compressive strength development and are simple to use
by design engineers. However, at present, the strength development models in the existing codes are not applicable for FAC.
Since microstructure development in FAC significantly differs
dαF CH ðtÞ Wcap 3ρw
1
¼
P
dt
W vF r0F ρF ½ð1=kdF Þ ðr0F =DeF Þ þ ðr0F =DeF Þð1 αF Þ1=3 þ ð1=krF Þð1 αF Þ2=3
The mass of capillary water (Wcap) depends on the cement
hydration, the reaction of free calcium oxide in the fly ash and
the reaction of fly ash phases other than free calcium oxide. It
can be determined as
19:
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
from that in OPCC, there is a need to develop such models for
FAC, using the large amount of experimental data available in
the literature (Dragaš et al., 2016).
Proposed model for strength development
of FAC
The compressive strength development of concrete containing
fly ash differs from that of concrete without fly ash (Lu et al.,
2017). Although different models (e.g. artificial neural network
models) have been proposed for the prediction of mean
compressive strength development (Topcu and Sarıdemir,
2008), models that are simple to use and hence could be
readily included in codes of practice are more useful. With the
aim of developing strength development relations for FAC, relevant data of 512 concrete mixtures (with a total of 1343
average compressive strength results) in which only fly ash was
used along with cement as the binder were collected from
the literature (Aggarwal et al., 2012; Arunachalam and
Gopalakrishnan, 2004; Bharatkumar et al., 2005; Bouzoubaa
et al., 2001; Burden, 2006; Duran-Herrera et al., 2011;
Elshekh et al., 2013; Faseyemi, 2012; Haranki, 2009; Harison
et al., 2014; Huang et al., 2013; Jatale et al., 2013; Jayesh
et al., 2013; Kate and Murnal, 2013; Krishnapal et al., 2013;
Lam et al., 1998; Lee, 2003; Mathur et al., 2005; Mittal et al.,
2005; Mohamed, 2011; Naik and Ramme, 1989; Naik et al.,
1991, 1997, 2003; Narendra, 2013; Oner et al., 2005; Patel and
Jayeshkumar, 2013; Patel et al., 2011; Patil et al., 2012;
Pattanaik and Sabat, 2010; Peter et al., 1999; Poon et al.,
2000; Rao and Andal, 2014; Sarika et al., 2013; Sasatanil
et al., 1995; Seshasayi et al., 2001; Shrivastava and Bajaj,
2012; Siddique, 2004; Soman and Sobha, 2014; Soni and
Saini, 2014; Tia et al., 2005; Turk and Karatas, 2011; Vamshi
and Krishna, 2011; Yazici and Arel, 2012; Yoon et al., 2014).
The data collected featured fly ash contents of 0, 10, 20, 30,
35, 40, 50, 60 and 75, w/b ratios in the range 0·19–0·60, ratios
of coarse to fine aggregate (by weight) in the range 1·18–1·85,
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Magazine of Concrete Research
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Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
binder contents of 300–593 kg/m3 and 28 d average compressive strengths in the range 9·8–65 MPa. Concrete mixtures containing type I cement, class F fly ash and normal-weight
aggregate were considered. The data also included average compressive strengths of both cubic and cylindrical specimens at
different ages (7, 14, 21, 28, 56, 90, 180 and 365 d). The cylindrical specimens were 150 mm in diameter and 300 mm high and
the cubic specimens were of side 100 mm or 150 mm.
regression analyses such as the number of data points considered, coefficient of determination (R 2) and the standard
error in the estimation of s values are also given in Table 1.
Assuming a normal distribution for s, the upper and lower
95% confidence limits of s were determined using the values of
standard error, and these are also listed in Table 1 for each fly
ash percentage.
fib MC 2010 (fib, 2013a) gives a simple form of strength development model for OPCC (Equations 1 and 2) and this model
provided a better fit to the experimental data than the other
models (fib, 2013b). By normalising the average compressive
strength at different ages by the 28 d average compressive
strength, strength development can be expressed by βcc(t)
(Equations 1 and 2). The fib model implicitly considers the
strength dependency on several parameters, such as w/b ratio,
aggregate type and content, through the 28 d average compressive strength as the input parameter. The compressive strength
development process influenced by reaction kinetics is considered implicitly through the parameter s. Values of βcc(t) were
determined for the experimental data for various percentages of
fly ash according to
21:
βcc ðtÞ ¼
fcm;t;Cylinder
γðtÞfcm;t;Cube
¼
fcm;28;Cylinder γð28Þfcm;28;Cube
where γ(t) and γ(28) are shape factors for converting concrete
cube compressive strength to cylinder compressive strength at
concrete ages t and 28 d, respectively. Due to a lack of experimental data on the variation of shape factors with age, the
shape factor dependency on time for a given concrete mix was
not considered in this study (i.e. γ(t) = γ(28)) (although this
approximation was used in this study, there is a need to carry
out independent experimental investigations to validate this
assumption). Hence, the values of βcc(t) computed from either
concrete cylinder strengths or cube strengths were the same
and no separate treatment was required for cylinder and cube
compressive strengths.
The variations of βcc(t) with concrete age are shown in
Figure 2 for concretes with different percentages of fly ash.
The figure shows that the trend of mean compressive strength
development in FAC is different for different percentages of fly
ash. Therefore, separate s values need to be determined for
concretes with various percentages of fly ash. To describe FAC
strength development with age, two-stage regression analyses
of compression strength data of concretes with different percentages of fly ash were carried out.
In stage 1, exponential curves having the form of Equation 2
were fitted to the experimental βcc(t) values using an iterative
least-squares estimation, and values of s were determined for
concretes with different percentages of fly ash. The results of
the analyses are presented in Table 1. Details of the non-linear
It can be noted from Table 1 that the R 2 values for most cases
were more than 0·8. Considering that concrete is a heterogeneous material and concrete mixes from different investigations were considered in this study, the coefficient of
variation (CoV) of concrete compressive strengths could be
high. Bearing this in mind, the R 2 values in Table 1 are reasonable. The values of s given in Table 1 can thus be used for predicting the mean compressive strength development of FAC at
different ages. Table 1 also shows s increases with the percentage of fly ash. This indicates that the mean compressive
strength development after 28 d is higher for concrete with a
higher percentage of fly ash, which can be attributed to the
increase in pozzolanic reactions at greater ages with an
increased amount of fly ash in the concrete.
In the second stage of the regression analysis, an exponential
curve having the form aebp (where a and b are coefficients to
be determined) was fitted to the s values presented in Table 1
(see Figure 3). The equations proposed for predicting the mean
value of s and its 95% confidence limit (i.e. the lower 5% significance level of s) for obtaining a conservative estimation of
mean compressive strength ( f1cm) are
22:
smean ¼ 0298e00134p
(
23:
95% limitof s for
1
fcm
¼
0268e00132p
t , 28 d
00135p
t 28 d
0315e
where
24:
p¼
F
100
CþF
Equation 22, along with Equations 1 and 2, is useful for predicting mean compressive strength development of concretes
with different percentages of fly ash (up to 75%). The 95%
confidence limits of s value can be used for conservative predictions of mean compressive strength development in FAC, by
considering Equation 23 along with Equations 1 and 2.
The predictions made using the proposed model were
compared with (a) the models given in existing codes,
(b) regression-based models of FAC, (c) the reaction-kineticsbased model and (d) additional experimental results based on
experimental investigations undertaken at CSIR-SERC and
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547
Magazine of Concrete Research
Volume 70 Issue 11
1·5
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
1·5
0% fly ash
1·0
βcc(t)
1·0
10% fly ash
s = 0·289
Experiment
0·5
0
100
1·5
s = 0·335
Experiment
0·5
101
102
0
100
20% fly ash
101
102
30% fly ash
1·5
βcc(t)
1·0
s = 0·39
Experiment
0·5
0
100
1·0
s = 0·421
Experiment
0·5
101
102
0
100
2·0
40% fly ash
101
102
50% fly ash
1·5
βcc(t)
1·5
1·0
1·0
s = 0·505
Experiment
0·5
0
100
101
102
2·0
βcc(t)
0
100
2·0
60% fly ash
1·5
1·5
1·0
1·0
s = 0·651
Experiment
0·5
0
100
101
102
Age: d
s = 0·552
Experiment
0·5
101
102
75% fly ash
s = 0·801
Experiment
0·5
0
100
101
102
Age: d
Figure 2. Variation of βcc(t) with age for concretes containing various percentages of fly ash (0–75%); s is the parameter in Equation 2
from the literature. Details of the experimental investigations
carried out at CSIR-SERC are now presented.
(F40). Concrete cubes of size 150 mm were cast and tested for
compressive strength at ages of 7, 14, 21, 28, 56, 90 and 180 d.
Experimental investigations at CSIR-SERC
Characterisation of materials
To compare the proposed model predictions with experimental
data that were not used in regression analyses, experimental
investigations were carried out on OPCC, concrete with a fly ash
content of 30% (F30) and concrete with a fly ash content of 40%
OPC of grade 53, conforming to IS 12269 (BIS, 2004) was
used in the experimental study. The soundness and specific
gravity of the cement were 0·2% and 3·145, respectively. The
chemical composition of the cement is given in Table 2.
548
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Magazine of Concrete Research
Volume 70 Issue 11
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
Table 1. Results of regression analyses of strength development coefficient (s)
Fly ash: %
0
10
20
30
35
40
50
60
75
Number of data points
Mean s
Standard error
R2
Upper 95% confidence limit
Lower 95% confidence limit
218
138
211
155
83
163
209
130
38
0·289
0·335
0·391
0·421
0·481
0·505
0·552
0·651
0·801
0·01146
0·02301
0·01138
0·01600
0·02495
0·01467
0·01700
0·02554
0·05533
0·77
0·64
0·87
0·84
0·85
0·87
0·83
0·80
0·81
0·31
0·38
0·41
0·45
0·53
0·53
0·58
0·70
0·91
0·27
0·29
0·37
0·39
0·43
0·48
0·52
0·60
0·69
0·9
0·8
y = 0·3152e0·0135x
R2 = 0·9852
Mean s value
Upper 95% limit
Lower 95% limit
Expon. (mean s)
Expon. (upper 95% limit)
Expon. (lower 95% limit)
y = 0·2919e0·0134x
R2 = 0·9948
0·7
y = 0·2684e0·0132x
R2 = 0·9864
s
0·6
0·5
0·4
0·3
0·2
0
20
40
Fly ash percentage, p
60
80
Figure 3. Variation of mean and bounds of s with percentage of fly ash ( p)
Fly ash from Ennore thermal power plant near Chennai,
India, was used. The chemical composition of the fly ash
was tested as per IS 1727 (BIS, 1967) and is given in Table 2.
Based on its composition, the fly ash conformed to ASTM
requirements for class F fly ash (ASTM, 2005). The soundness
and specific gravity of the fly ash were 0·05% and 2·056,
respectively.
Natural river sand was used as fine aggregate. Sieve analysis
was carried out using a mechanical sieve shaker. The fine
aggregate used conformed to zone II aggregate according to
IS 383 (BIS, 1970). The coarse aggregate was crushed granite
of nominal size 10 mm and 20 mm, combined in the ratio of
40:60 by weight, such that the grading of the combined aggregate conformed to IS 383 (BIS, 1970). The physical properties
of the aggregates are presented in Table 3.
Concrete mix proportioning, casting and testing
The concrete mix proportions were designed to achieve a specified 28 d mean compressive strength of 48 MPa and a slump
of 75–100 mm, using the method proposed by the UK
Table 2. Chemical composition of cement and fly ash used in
experimental investigations at CSIR-SERC
Cement
Silicon dioxide (SiO2 or S in cement
chemistry notation)
Aluminium oxide (Al2O3 or A)
Ferric oxide (Fe2O3 or F)
Calcium oxide (CaO or C)
Sulfur trioxide (SO3 or S̄)
Magnesium oxide (MgO): %
Sodium oxide (Na2O): %
Potassium oxide (K2O): %
Fly ash
16·16
61·53
3·67
4·76
70·46
2·70
0·73
0·10
0·67
27·64
7·92
0·50 (0·36 free)
0·05
0·97
0
0·03
Department of Environment (Teychenné et al., 1997). The
cementing efficiency factors of fly ash for the F30 and F40
concretes were taken from the literature (Babu and Rao, 1993)
for an initial trial mix and then adjusted, by trial and error,
to achieve a 28 d mean compressive strength of 48 MPa.
The cementing efficiency factors of fly ash for the F30 and
F40 concrete were determined to be 0·65 and 0·44, respectively.
The mix proportioning details are given in Table 4. The slump
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549
Magazine of Concrete Research
Volume 70 Issue 11
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
Table 3. Characteristics of aggregates used in experimental investigations at CSIR-SERC
experimental average compressive strength to the predicted
mean compressive strength, was considered for the purposes of
comparison. Values of the mean and CoV of the modelling
error and R 2 values were used as a measure of the predictive
capability of the model.
Coarse aggregate
Fine aggregate
10 mm
20 mm
Zone II
—
—
2·67
0·8
3·81
36·18
—
2·8
0·8
4·6
—
1508
2·85
0·2
5·46
—
1517
Grading zone conforming
to IS 383 (BIS, 1970)
Specific gravity
Water absorption: %
Fineness modulus
600 μm passing: %
Dry rodded density: kg/m3
Table 4. Details of concrete mix proportions used in experimental
investigations at CSIR-SERC
Fly ash: %
Free w/b ratio
Cement content: kg/m3
Fly ash content: kg/m3
Superplasticiser
(Master Rheo Build 1125): %
Water content: kg/m3
Fine aggregate content: kg/m3
Coarse aggregate content: kg/m3
OPCC
F30
F40
0
0·49
367·3
0
1
30
0·43
293·2
125·7
1
40
0·37
289·9
193·3
1
180
871·6
1065
180
828·8
1013
180
791
967
of the fresh concrete batches was measured before casting;
the average slump values for OPCC, F30 and F40 were 89, 84
and 85 mm, respectively.
Concrete cubes (150 mm 150 mm 150 mm) of OPCC, F30
and F40 were cast. The specimens were demoulded 24 h after
casting and then moist-cured for 28 d, after which they were
stored in air. Compressive strength tests were carried out at the
ages of 7, 14, 28, 56, 90 and 180 d as per IS 516 (BIS, 1959).
The average compressive strengths obtained at different ages
are given in Table 5.
Results and discussion
To examine the predictive capability of the proposed model,
the model-predicted strengths were compared with strengths
predicted using other models available in the literature and
with experimental results that were not used for model development. The modelling error, defined as the ratio of the
Comparison with strength development models
available in the literature
Comparison with models in codes of practice
The predicted mean compressive strengths using the proposed
model, fib MC 2010 (fib, 2013a), IRC 112-2011 (IRC, 2011)
and ACI 209 (ACI, 1992) are compared with the corresponding experimental values in Figure 4 for OPCC and Figure 5
for FAC. Figure 4 shows that (based on R 2) all the compressive strength development models considered satisfactorily
predict the mean compressive strength for OPCC. As shown in
Figure 5, the R 2 value for the proposed model was higher than
the R 2 values of the other models considered; this indicates
that the proposed model better predicts mean compressive
strength development in FAC.
The modelling errors of the strength development models
specified in fib MC 2010, IRC 112-2011 and ACI 209 and the
proposed model were computed for all 1343 data points.
Values of the mean and CoV of the modelling error for concrete aged under 28 d and more than 28 d were determined
separately for both OPCC and FAC and the results are given
in Table 6. For OPCC, the mean of the modelling error was
close to 1 for all the models considered, irrespective of concrete
age, but the mean of the modelling error of the proposed
model was slightly better than that of the other models. For
FAC, the means of the modelling error of the models specified
in fib MC 2010, IRC 112-2011 and ACI 209 were less than
one (0·82, 0·86 and 0·95, respectively) for concrete aged less
than 28 d and more than one (1·18, 1·15 and 1·26, respectively) for concrete more than 28 d old. This indicates that, as
expected, the code-specified models (which were developed for
OPCC) overestimate the mean compressive strength for FAC at
early ages (less than 28 d) and underestimate the mean compressive strength after the age of 28 d. The predictions of the
proposed model were better than those of the other models in
terms of the mean and CoV of the modelling error. The proposed model can thus be used for predicting mean compressive
strength development of both OPCC and FAC. Statistical
properties of the modelling error are useful in probabilistic
Table 5. Compressive strength of concrete mixtures tested at CSIR-SERC
Average compressive strength of three cubes: MPa
Mix
w/b
7d
14 d
28 d
56 d
90 d
180 d
OPCC
F30
F40
0·49
0·43
0·37
39·56
30·44
31·05
43·28
38·23
39·16
48·52
48·03
48·63
49·97
56·19
56·32
54·82
58·11
60·16
57·25
60·03
67·23
550
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Magazine of Concrete Research
Volume 70 Issue 11
ACI 209
80
Predicted mean compressive strength: MPa
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
fib MC 2010
80
R2 = 0·9383
R2 = 0·9139
60
60
40
40
20
20
0
0
20
40
60
80
0
0
IRC 112-2011
40
60
80
Proposed model
80
Predicted mean compressive strength: MPa
20
80
R2 = 0·9377
R2 = 0·9445
60
60
40
40
20
20
0
0
20
40
60
Experimental average compressive strength: MPa
80
0
0
20
40
60
Experimental average compressive strength: MPa
80
Figure 4. Comparison of predicted mean compressive strengths with corresponding experimentally measured values for OPCC
analysis, where the modelling error is treated as a random variable. For studies involving probabilistic analysis, mean values
of 1·10 and 1·02 and CoVs of 20% and 15% of the modelling
error of the proposed model are suggested for concrete of age
less than 28 d and more than 28 d, respectively.
Comparison with regression models
Mean compressive strengths predicted by the models proposed
by Yoon et al. (2014) (Equation 4) and Han et al. (2003)
(Equation 5) and the model proposed in this study (Equation
22 with Equations 1 and 2) were compared with the corresponding experimental values. As shown in Table 7, the value
of R 2 of the proposed model was higher than the R 2 value
obtained by the models of Yoon et al. (2014) and Han et al.
(2003). In addition, it is worth noting that the model of Yoon
et al. is applicable only for concretes with 50% or 60% fly ash
and the model of Han et al. is only applicable for concrete
with less than 30% fly ash, whereas the model proposed in this
study is applicable for concrete with 0–75% fly ash.
Comparison with reaction-kinetics-based model
An attempt was made to compare the predictions of the proposed model with the predictions of the reaction-kinetics-based
model for the OPCC and F30 and F40 concretes in order to
examine whether the proposed regression model is able to
capture the kinetics of the chemical process involved in strength
development. The chemical compositions of the cement and fly
ash and the concrete mix proportions used in this study are
given in Tables 2 and 4, respectively. The mean particle diameters of the cement and fly ash used were 3·31 μm and 5·17 μm,
respectively. The average curing temperatures were 31·2, 31·3
and 30·6°C for OPCC, F30 and F40, respectively. The cement
hydration parameters were taken from the work of Park et al.
(2008). The parameters of the equations for the reaction of fly
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551
Magazine of Concrete Research
Volume 70 Issue 11
ACI 209
80
Predicted mean compressive strength: MPa
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
fib MC 2010
80
R2 = 0·8754
R2 = 0·8217
60
60
40
40
20
20
0
0
20
40
60
80
0
0
20
IRC 112-2011
Predicted mean compressive strength: MPa
60
80
Proposed model
80
80
R2 = 0·8581
R2 = 0·9173
60
60
40
40
20
20
0
40
0
20
40
60
Experimental average compressive strength: MPa
80
0
0
20
40
60
Experimental average compressive strength: MPa
80
Figure 5. Comparison of predicted mean compressive strengths with corresponding experimentally measured values for FAC
Table 6. Statistical properties of modelling errors
OPCC
FAC
t < 28 d
Compressive strength development model
Proposed model
fib MC 2010 (fib, 2013a)
IRC 112-2011 (IRC, 2011)
ACI 209 (ACI, 1992)
t < 28 d
t > 28 d
Mean
CoV: %
Mean
CoV: %
Mean
CoV: %
Mean
CoV: %
0·99
0·90
0·94
1·04
15·02
15·02
15·02
15·02
1·00
1·04
1·02
1·02
8·52
8·67
8·57
8·78
1·10
0·82
0·86
0·95
20·11
19·01
19·01
19·01
1·02
1·18
1·15
1·16
14·30
16·26
16·07
16·43
ash in concrete are dependent on the physical and chemical
characteristics of the fly ash (Fan et al., 2015; Sadique and
Coakley, 2016). In the present study, the values of these parameters for class F fly ash were determined by a predictor–corrector algorithm using the results of experimental investigations
carried out by Papadakis (1999) on cement–fly ash paste (see
Table 8). The normalised mean compressive strength
552
t > 28 d
Table 7. R 2 values of FAC strength development models
Compressive strength
development model
Fly
ash: %
Number of
data points
R2
Yoon et al. (2014)
Han et al. (2003)
Proposed model
50–60
0–30
0–75
339
722
1343
0·86
0·82
0·92
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Magazine of Concrete Research
Volume 70 Issue 11
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
Table 8. Parameters of fly ash reaction degree model (Equation
16) for class F fly ash
De0F: cm2/h
0·07
5·45 10−7
1·6 10−8
development was calculated using Equation 7 from the predicted CSH content using the model of Fan et al. (2015)
(Equation 10). The results are compared with the predictions of
the proposed simple regression model (Equation 22 with
Equation 2) and the experimental results in Figure 6.
Figure 6 shows that the trends of mean compressive strength
development obtained using the reaction-kinetics-based model
were in satisfactory agreement with the experimental results
for both OPCC and FAC. This may be due to use of the
chemical compositions of cement and fly ash and the concrete
mix proportions (used in the present experimental study) as
inputs to the reaction-kinetics-based strength development
model. Sensitivity analysis revealed that, in the reactionkinetics-based strength development model, the compressive
strength was significantly influenced by the w/b ratio at early
ages (≤ 28 d) and the fly ash/binder ratio at later ages (> 28 d).
It was also noted that the trend predicted by the proposed
model was in good agreement with that of the reactionkinetics-based model at both early and later ages. This suggests
that the proposed regression model is able to consider the
reaction kinetic processes involved in strength development
implicitly through the parameter s as a function of the fly
ash/binder ratio. The reaction-kinetics-based strength development model requires the concrete mix proportions and the
chemical composition of the cement and fly ash as inputs for
predicting strength development, but this information may not
be readily available to engineers at the design stage. The proposed model requires only the 28 d average compressive
strength and the percentage of fly ash for predicting the mean
compressive strength development, and hence is simple to use.
Comparison with results of experimental
investigations at CSIR-SERC
The average compressive strength results at different ages given
in Table 5 show that, as expected, compared with OPCC, concrete containing fly ash shows less strength at an early age and
higher strength after 28 d. This is due to the pozzolanic reaction of fly ash with the surplus lime produced during cement
hydration. The mean compressive strengths predicted using the
code-specified models and the proposed model are compared
with the average compressive strengths of three cubes obtained
from the experimental investigations in Figure 7.
It can be noted from Figure 7 that the predictions of the codespecified models are close to the average experimental values for
OPCC but underestimate mean compressive strength after the
age of 28 d for FAC. By contrast, the predictions of mean
Experiment
Proposed model (R2 = 0·966)
1·2
βcc(t)
krF: cm/h
Reaction-kinetics based model (R2 = 0·961)
0·8
0·4
0
0·01
0·1
1
10
100
Concrete with 30% fly ash
1·6
Experiment
1·2
Proposed model (R2 = 0·985)
Reaction-kinetics based model (R2 = 0·964)
βcc(t)
3·22 10−9
CF: cm/h
0·8
0·4
0
0·01
0·1
1
10
100
Concrete with 40% fly ash
1·6
Experiment
1·2
βcc(t)
BF: cm/h
Concrete without fly ash
1·6
Proposed model (R2 = 0·996)
Reaction-kinetics based model (R2 = 0·989)
0·8
0·4
0
0·01
0·1
1
10
100
Age: d
Figure 6. Comparison of proposed model predictions of mean
compressive strength development with that of reaction-kineticsbased model
compressive strength using the proposed model were in good
agreement with the experimental data for both OPCC and FAC.
Comparison with other experimental results from
the literature
To examine the predictive capability of a model, it is desirable
to consider experimental data that were not used for model
development (i.e. data not used in the regression analysis in this
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553
Magazine of Concrete Research
Volume 70 Issue 11
80
Concrete without fly ash
60
40
Experiment
fib MC 2010 (R2 = 0·940)
IRC 112-2011
20
ACI 209
(R2
(R2
= 0·958)
= 0·822)
Proposed model (R2 = 0·899)
0
1
10
100
Predicted mean compressive strength: MPa
Compressive strength: MPa
80
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
Dragaš et al. (2016)
Hedegaard and Hansen (1992)
Yamato and Sugita (1983)
Carette et al. (1993)
Thomas et al. (1989)
Langley et al. (1989)
Eren (2002)
60
Proposed model
40
R2 = 0·931
20
80
Compressive strength: MPa
Concrete with 30% fly ash
0
20
40
60
80
Experimental average compressive strength: MPa
60
Figure 8. Comparison of proposed model predictions with
experimental results that were not considered in development of
the model
40
Experiment
fib MC 2010 (R2 = 0·709)
20
IRC 112-2011 (R2 = 0·816)
ACI 209 (R2 = 0·877)
Proposed model (R2 = 0·980)
0
1
10
100
80
A model for predicting mean compressive strength development in both OPCC and FAC has been proposed in this paper.
The model was developed based on two-stage regression analyses of average compressive strengths of a large number (512)
of concrete mixtures collected from the literature. The model is
given by
60
40
Experiment
fib MC 2010 (R2 = 0·636)
20
IRC 112-2011 (R2 = 0·746)
ACI 209 (R2 = 0·780)
0
Proposed model (R2 = 0·994)
1
10
strengths estimated by the proposed model are compared with
these experimental data in Figure 8. The figure shows that
proposed model estimates were in good agreement with the
experimental results, with R 2 = 0·931. This provides further confirmation that the proposed model can be used for predicting
the compressive strength development of both OPCC and FAC.
Summary and conclusions
Concrete with 40% fly ash
Compressive strength: MPa
0
100
fcm ðtÞ ¼ βcc ðtÞfcm;28
where
" "
05 ##
28
βcc ðtÞ ¼ exp s 1 t
Age: d
Figure 7. Comparison of predicted mean compressive strength
with results of experimental investigations carried out at CSIR-SERC
work). To this end, the experimental results of average compressive strengths of 101 FAC mixes were collected from the literature (Carette et al., 1993; Dragaš et al., 2016; Eren, 2002;
Hedegaard and Hansen, 1992; Langley et al., 1989; Thomas
et al., 1989; Yamato and Sugita, 1983). The compressive
554
in which the mean value of s for different proportions of fly
ash (up to 75% fly ash content) is given by smean = 0·298e0·0134p
and the equations for 95% confidence limits of s (i.e. lower 5%
significance level of s) for obtaining conservative estimations of
mean compressive strength development are
(
95% limit of s for
l
fcm
¼
Downloaded by [ Structural Engineering Research Centre SERC] on [31/08/18]. Copyright © ICE Publishing, all rights reserved.
0268e00132p
t , 28 d
0315 e00135p
t 28 d
Magazine of Concrete Research
Volume 70 Issue 11
Model for compressive strength
development of OPC concrete and fly ash
concrete with time
Vijaya Bhaskara, Balaji Rao and Anoop
The model is applicable to concrete mixtures containing
0–75% class F fly ash, type I cement and normal-weight
aggregate with 0·19 ≤ w/b ≤ 0·6, 9·8 MPa ≤ fcm,28 ≤ 65 MPa,
300 kg/m3 ≤ B ≤ 593 kg/m3 and 3 d ≤ t ≤ 365 d.
Burden D (2006) The Durability of Concrete Containing High Levels of
The mean compressive strength development predicted by the
proposed model was found to be in good agreement with data
from experimental investigations (which were not considered
in the regression analyses) for both OPCC and FAC. From a
comparative study using a reaction-kinetics-based model, it
was found that the proposed model is able to implicitly reflect
the reaction kinetics involved in the strength development
of FAC. The proposed strength development model is useful
for predicting concrete strength at the time of the transfer of
prestress in prestressed concrete structures (generally at 7 d)
and for optimising the formwork removal time.
Acknowledgements
This paper is published with kind permission of the Director
of CSIR-SERC, Chennai, India. The authors thank Shatabdi
Mallick (CSIR-SERC) for her help during the experimental
investigations.
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