INTRODUCTION
Concrete is a versatile construction material owing to the benefits it provides
in term of strength, durability, availability, adoptability and economy. Great
efforts have been made to improve the quality of concrete by various means in
order to raise and maximize its level of performance. Using same ingredients
with little adjustments in the microstructure (and probably adding specific
materials), it is possible to obtain high performance concrete. The development
of HPC has brought forth the need for admixtures, both mineral and chemical,
to improve the performance of concrete (Zain et al.,
2000).
There is no shortage of information on the properties of Hardened High Performance
Concrete (HPC). Numerous publications are available showing that the range of
outstanding properties of hardened HPC can be obtained not only in the laboratory
but also in real construction. Compared to ordinary concrete, HPC has extraordinary
rheological properties, especially its superworkability and flowability that
make it superior to other concrete mixes (Zain et al.,
1999).
What is highperformance concrete? According to a recent study by Aitkin (Mehta,
2004), what was known as highstrength concrete in the late 1970s is now
referred to as High Performance Concrete (HPC) because it has been found to
be much more than simply stronger. ACI defines HPC as a specially engineered
concrete, one or more specific characteristics of which have been enhanced through
the selection of component materials and mix proportions. Note that this definition
does not cover a single product but a family of hightech concrete products
whose properties have been tailored to meet specific engineering needs, such
as high workability, veryhigh early strength (e.g., 3040 MPa compressive strength
in 24 h), high toughness and high durability to exposure conditions.
In construction industry, strength is a primary criterion in selecting
a concrete for a particular application. Concrete used for construction
gains strength over a long period of time after pouring the characteristic
strength of concrete is defined as the compressive strength of a sample
that has been aged for 28 days.
Neither waiting 28 days from such a test would serve the rapidity of construction,
nor neglecting, it would serve the quality control process on concrete in large
construction sites. Therefore, rapid and reliable prediction for the strength
of concrete would be of great significance. For example, it provide a chance
to do the necessary adjustment on the mix proportion used to avoid situation
where concrete does not reach the required design strength or by avoiding concrete
that is unnecessarily strong and also, for more economic use of raw materials
and fewer construction failures, hence reducing construction cost (Kheder
et al., 2003).
Prediction of concrete strength, therefore, has been an active area of
research and a Considerable number of studies have been carried out.
Many attempts have been made to obtain a suitable mathematical model
which is capable of predicting strength of concrete at various ages with
acceptable (high) accuracy.
MATERIALS AND METHODS
Prediction methods for strength of concrete: Under the currently
quicker pace of construction, there was a great need for more production
of concrete with persisting on the conformability of the quality of the
produced concrete with the standards and specifications. The compliance
of any produced concrete with these specifications consider to be significant
evidence for good concrete. The specifications, generally, include a statement
of physical and chemical requirements. Among all, strength tests are prescribed
by all specifications, because compressive strength of concrete in the
hardened condition is very important and perhaps it is the most obviously
required for structural use.
Specifications usually specify test method as well as age of test. Strength
of concrete, as specified by all the standards, is very important (from 1 to
28 days), because the early development of strength (early gain in strength)
is very important. But, as early strength of concrete is important, strength
at later ages is more important, because after all, it is this property which
is relied upon in structural design of concrete as a construction material.
The traditional 28 days standard test has been found to give general index of
the overall quality (used in quality control process) and acceptance of concrete
and has served well for so many years. Neither waiting for the result of such
a test would serve the rapidity of construction, nor, neglecting it would serve
the quality control process of the concrete. Moreover, rapid and reliable prediction
of the results of 28 days strength test as early as possible would be of satisfaction
for all parties instead of waiting for the traditional 28 days results (Kheder
et al., 2003).
A number of improved prediction techniques have been proposed by including
empirical or computational modeling, statistical techniques and artificial
intelligence approaches.
Computational modeling: Many attempts have been made for modeling
this process through the used of computational techniques such as finite
element analysis. These techniques often based on the complex thermodynamic
equations that underpin the aging of concrete in addition the computational
complexity of the models is prohibiting in many cases, requiring nonproprietary
mathematical tools.
Statistical techniques: A number of research efforts have concentrated
on using multivariable regression models to improve the accuracy of predictions.
Statistical models have the attraction that once fitted they can be used
to perform predictions much more quickly than other modeling techniques
and are correspondingly simpler to implement in software.
Popovics augments Abrams model, a widely accepted equation relating the water
cement ratio w/c of concrete to its strength with additional variables such
as slump and uses least square regression to determine equation coefficients
(Popovics and Ujhelyi, 2008). Apart of its speed, statistical
modeling has the advantage over other techniques that it is mathematically rigorous
and can be used to define confidence interval for the predictions. This is especially
true when comparing statistical modeling with artificial intelligence techniques.
Statistical analysis can also provide insight into the key factors influencing
28 days compressive strength through correlation analysis. For these reasons
statistical analysis was chosen to be technique for strength prediction of this
study.
Artificial neural networks: Because strengthening of concrete
is a complex nonlinear process dependent on many variables, it is a problem
well suited to the artificial intelligence concept known as Artificial
Neural Networks (ANNs). Much of the current research into concrete strength
prediction recognizes that neural nets are appropriate for the problem.
In the last years, Artificial Neural Networks (ANN) technology, a subfield
of artificial intelligence, are being used to solve a wide variety of problems
in civil engineering applications (Bai et al., 2003;
Topcu et al., 2008a, b,
2007; Pala et al., 2007; Adhikary
et al., 2006). The most important property of ANN in civil engineering
problems are their capability of learning directly from examples.
Modeling the prediction of compressive strength of concrete: The
most popular regression equation used in the prediction of compressive
strength is:
Where:
f 
= 
Compressive strength of concrete 
w/c 
= 
Water/cement ratio 
b_{0}, b_{1} 
= 
Coefficients 
The earlier equation is the linear regression equation. The origin of this
equation is Abram’s Law (Popovics and Ujhelyi, 2008)
which relate compressive strength of concrete to the w/c ratio of the mix and
according to this law, increasing w/c ratio will definitely lead to decrease
in concrete strength. The original formula for Abram is:
Where:
f 
= 
Compressive strength of concrete 
A, B 
= 
Empirical constants 
Lyse (Jee et al., 2004) made a formula similar
to Abram but he relate compressive strength to cement /water ratio and not water
/cement ratio. According to Lyse strength of concrete increase linearly with
increasing c/w ratio .the general form of this popular model was:
Where:
f 
= 
Compressive strength of concrete 
c/w 
= 
Cement /water ratio 
A, B 
= 
Empirical constants 
The quantities of cement, fine aggregate and coarse aggregate were not included
in the model and not accounted for the prediction of concrete strength. So,
for various concrete mixes were their w/c ratio is constant, the strength will
be the same and this is not true. Therefore, efforts should be concentrating
on models taken into account the influence of mix constituents on the concrete
strength in order to have more reliable and accurate results for the prediction
of concrete strength.
For this reason, Eq. 1 which referred to Abrams Law was extended to include
other variables in the form of multiple linear regression equation and
used widely to predict the compressive strength of various types of concrete
as below:
Eq. 1 linear least square regression (referred to Abram) and Eq. 4 is
multiple linear regression:
Where:
f 
= 
Compressive strength of concrete 
w/c 
= 
Water/cement ratio 
C 
= 
Quantity of cement in the mix 
CA 
= 
Quantity of coarse aggregate in the mix 
FA 
= 
Quantity of fine aggregate in the mix 
According to Eq. 4 all the variables related to the compressive strength
in a linear fashion, but this is not always true because the variables
involved in a concrete mix and affecting its compressive strength are
interrelated with each other and the additive action is not always true.
Here, it appears that there is a need to another type of mathematical
model can reliably predicts strength of concrete with acceptable high
accuracy. So, if we took the general form of the multiple linear regressions
as below:
For situations where the multiple dependencies are curvilinear (nonlinear),
the logarithmic transformation can be applied to this type of regression:
This equation could be transformed back to a form that predicts the dependent
variable (Y) by taking the antilogarithm to yield an equation of the type:
This equation called the multivariable power equation and in engineering, variables
are often dependent on several independent variables, this functional dependency
is best characterized by the equation mentioned earlier and is said to give
results that are more realistic too. This equation has been used successfully
to predict the compressive strength for ordinary Portland cement also (Kheder
et al., 2003).
In this study, the multivariable power equation was found to be very
suitable for prediction strength of high performance concrete (as a dependent
variable). Factors affecting this strength were the elements of the concrete
mix itself.
EXPERIMENTAL WORK
This study has been conducted at UKM UniversityMalaysia 2008. The main
characteristics of materials and procedures used for the purpose of this
research are as explained below:
Materials: Locally available crushed stone granite aggregate,
mining sand and type I normal Portland cement were used in this study.
Table 1: 
Physical properties of the materials 

Table 2: 
Mix proportions 

Class F Malaysian fly ash and Elkem silica fume have been used as mineral
admixtures. Sulfonated naphthalene condensatebased Super Plasticizer (SP)
and Darex Air Entraining Admixture (AEA) were also used as liquid chemical
admixtures. Normal tap water (pH = 6.9) was used as mixing water. The physical
properties of the materials are shown in Table 1.
Mix proportions: Four types of high performance concrete with
two water / binder ratios were designed including the control mix. These
are Normal Portland Cement (NPC), Silica Fume (SF), Fly Ash (FA) and Silica
FumeFly Ash (SFFA) concrete. The proportions of the constituent materials
obtained from mix design were based on saturated surface dry condition.
Thus, necessary corrections were made to get the weight of materials in
air dry basis. The details of various mix proportions are given in Table
2.
Curing: Three types of curing were adopted. These are dry air
(after demoulding, the specimens were marked weight and stored in an air
conditioned room, maintaining temperature at 20°C), wrapped (after
demoulding, the specimens were marked wrapped and stored inside an air
conditioned room, keeping temperature at 20°C) and water curing (after
demoulding, the specimens were marked weight and stored inside the water
tank suited in an air conditioned room, maintaining temperature at 20°C).
Table 3: 
Slump and unit weight of concrete mixes 

RESULTS AND DISCUSSION
The properties of freshly mixed high performance concrete were determined
with respect to slump and unit weight for each type of concrete (Table
3).
The compressive strength test specimens were determined at 3, 7, 14,
28 and 91 days after casting under the curing temperature of 20 °C
for different types of concrete and for different types of curing. The
results for compressive strength test are given in (Table
4).
Rapid determination or prediction of the strength of concrete could be
attained by Suitable mathematical model (with variables affecting strength
development of concrete) capable of predicting strength of concrete at
different ages . The final form of the regression model proposed in this
study was:
The variables used in the mathematical model in this study are:
Table 4: 
Compressive strength of concrete at different ages and different
curing conditions 

• 
Mix proportions elements, i.e., cement, fly ash, silica
fume, water and coarse aggregate 
• 
Slump test results 
• 
Density of concrete 
The basic concept of this model is that, it produces a reliable relationship
between strength of concrete and its own characteristics (the proposed model
uses the mix proportions which believed to have significant effect on the
characteristics of the produced concrete and one of the most important indications
on the properties of the freshly mixed concrete which is slump test results).
Also, the unit weight of the concrete was used as variable in this model
for its important role in the explanation of strength development process
of concrete. These factors were considered to be independent variables in
the equation .The multivariable power equation was used to relate all these
variables with the strength of concrete at the specified ages until getting
the final and best form of the
mathematical model.
Table 5 shows the relationship between the compressive
strength of high performance concrete at different ages (3, 7, 14, 28
and 91 days) with the selected variables that are going to be used in
the proposed model for the type of water curing. This relationship is
represented by the correlation coefficient between each variable and each
strength. Also, from this table, it can be seen that some variables have
significant correlation with the predicted strength at the specified age.
The highest significant correlations were with cement content, water content,
fine aggregate and coarse aggregate. These significant correlations were
for compressive strength at all ages.

Fig. 1: 
Relation ship between observed and predicted compressive strength
of high performance concrete at 28 days 
Depending on the above mentioned variables, the form of the proposed
model will be:
where, f_{age} is the compressive strength of concrete at specific
age, for example f_{28} is the compressive strength of high performance
concrete at the age of 28 days. The coefficient of correlation for the
28 days compressive strength prediction was 99.99%. Figure
1 shows the relationship between the predicted and observed 28 days
compressive strength for high performance concrete and the high correlation
between the two set of data is very clear. Using the same model to predict
the compressive strength of high performance concrete at different ages,
i.e., 3, 14 and 91 days give coefficient of correlation of 99.99% for
each strength. Also, the proposed model proved its validity to be use
for predicting the compressive strength of high performance concrete for
different types of curing yielding high coefficient of correlation for
each type of curing and strength at specified age.
CONCLUSION
Earlier and accurate estimation of concrete strength are valuable to
the construction industry. The presence of such model would possibly obtain
the hard balance and equality between controlling the quality (quality
control process) and economics (saving time and expense, i.e., this model
could be used in construction to make the necessary adjustments on mix
proportion used, to avoid situations where,concrete does not reach the
required design strength or by avoiding concrete that is unnecessarily
strong.
This methodology allows a fast and accurate prediction of values for
compressive strength on site. Common methods for estimation of in place
strength requires extensive use of curing of mortar cubes at constant
temperatures or the use of databases containing a large number of compressive
strength values made at many ages and cured at different temperatures.
These databases have to be fed with a statistical relevant number of data
before a reliable estimation of the strength can be made. Furthermore
all of these methods requires many hours of lab and field time for testing,
collecting and analyzing data.
Furthermore, the existing variables in the model yielded good reasonable
results. Also, it is not preferred to load the prediction model with large
number of variables, because it is preferred to use a model with lesser
number of variables with most higher possible accuracy to assure the rapid
and easy use of the model.