Strength Prediction Model for Accelerated Cured Fly-Ash Based Concrete

The most important property of concrete is its compressive strength, which is carried out after 28-days proper curing of concrete. This test is affected by other factors like the condition of curing, water to cement ratio, method of transportation, handling of the concrete, extent of vibrations and quality of the ingredients of mix proportion. This research study is an attempt to develop a simple Mathematical equation also known as mathematical model, by using linear regression analysis to estimate the 28-day f c ’ (Compressive Strength) of concrete from the test results carried out atearly age. This simple linear equation develops a relationship of 28.5 hours accelerated cured compressive strength with normal cured compressive strength after 28-days. These results show that most of the predicted values of compressive strength, calculated via equations, lies within permissible range difference for compressive strength achieved by experimental method, which is clear indication of credibility of the equations obtained for compressive strength at different age of concrete. The results showed that compressive strength of concrete increases with the increase in content of FA (Fly Ash) upto 30% replacement, and the compressive strength of the concrete starts decreasing beyond 30% FA substitution. This argument is totally in line with all the literature carried out for this research.

large structures might get completed even before the 28days strength. By depending on the test results in order to be sure that proper strength and quality of concrete is satisfied, there is a chance that noticeable quantity of inferior concrete might have been placed before the detection. After the test results, it might not be possible to substitute the inferior quality of concrete without damaging the acceptable quality of concrete in the structure. The cost increase due to this misshape is a consequence of this practice. The 7-days strength of cylinder is not the solution due to unreliable result for the 28-days strength prediction. Besides, even 7-day wait for the test results is a large amount of time to waste in the modern fast construction era. This fact is evident that the compressive strength of concrete is important in today's concrete construction industry [1][2]. The need to be able to predict the 28-days strength of concrete at early age is influenced by the following factors: (1) The rush and tight schedule of construction in the modern fast and machined world.
(2) Quality control issue is to be observed strictly via testing.
To be able to know that the quality of concrete for the said project is suitable even before 28 days testing.

MATERIALS AND METHODOLOGY
Material used in this research is listed as follow:

Natural Coarse Aggregate (Margalla Crush)
Maximum aggregate size used is 19mm. The Fineness Modulus was calculated to be 7.32. Specific Gravity was calculated to be 2.5, and the water absorption of coarse aggregate was found to be 1.1%.

Fine Aggregate (Lawrencepur Sand)
Lawrencepur sand is known for its superior quality and higher strength. The fineness modulus of fine aggregate was calculated to be 2.55. the bulk specific gravity of fine aggregate was calculated to 2.78. and the water absorption for fine aggregate was to found to be 1.2%.

Portable Water (Free from Impurities)
Ordinary tap water of PH from 6-8, colorless, odorless and free from impurities is used.

Ordinary Portland Cement (Maple Leaf Cement)
Maple Leaf cement is the best available cement in the market which gives the highest compressive strength. It is slightly expensive than the other brands of cement.

Fly Ash
The FA used in this research was of Class-F as per the specification of ASTM C-618. This class is produced from older and harder coal and it contains more iron.

Methodology
Casting of concrete specimens. 6  Hence, 90 cylinders are casted and tested in this phase.
Detail is shown in Table 1 and Fig. 1.

RESULTS AND DISCUSSION
The average of each day's compressive strength is mentioned in Table 2.  Table 2 were compared with the control sample's test for each day. And the percentage variation is listed in  variable and X is the explanatory variable, "m" denotes the gradient of the line and "c" is the y-intercept when the value of "x" is zero.

R-Squared
It is the measure of how close the regression equation is to the data observed. Statistically it is also known as coefficient of determination. This value varies between 0-100%. The closer this value to 100% the most accurate will be the results obtained by putting the data into it. It can simply be stated that higher value of R-squared means that model fits the data more accurately. Usually any value more than 80% is acceptable in a research. It means that there is an 80% chance/probability, that the model would give nearly 80% accurate value to the data.

Linear Regression Analysis
Regression analysis carried out for the data observed from the compressive strength values shown in Table 2 has been done via developing graphs (scatter plots). The

Linear Regression Equations
The mathematical equations obtained after carrying out regression analysis are listed in Table 4.

Difference between Actual and Predicted Values
The mathematical models obtained after carrying the    Furthermore, the regression models have been further verified through graphs and tables for each day strength, and it is found that all the variation in the predicted values is in permissible zone. The authenticity of these equations has been clearly explained by the R 2 values for each equation. Which, in each case, is more than 80%.
It is to be clearly noted that each regression model is valid for a certain percentage of FA. These equations cannot be used as generalized equations for any type of concrete or any percentage of FA. The equation can be used as such that the user only needs to put any number of day as value of "x" and will get the result of the equation as "y", which is the compressive strength for that day. In general, now any user would be able to predict the strength of concrete with a specific amount of FA substitution in just a few minutes due to the availability of these regression models. Which means that the chance of predicted value to be different from actual value is only 2%. In both these extreme condition cases, the regression models fits the data by minimum of 83% and maximum of 98%.

RECOMMENDATIONS
Stated below are some of the recommendations to be carried out in further studies by the researchers.