Prediction of the curing time to achieve maturity of the nano-cement based concrete using the Weibull distribution model: A complementary data set

This data article provides a comparison data for nano-cement based concrete (NCC) and ordinary Portland cement based concrete (OPCC). Concrete samples (OPCC) were fabricated using ten different mix design and their characterization data is provided here. Optimization of curing time using the Weibull distribution model was done by analyzing the rate of change of compressive strength of the OPCC. Initially, the compressive strength of the OPCC samples was measured after completion of four desired curing times. Thereafter, the required curing time to achieve a particular rate of change of the compressive strength has been predicted utilizing the equation derived from the variation of the rate of change of compressive strength with the curing time, prior to the optimization of the curing time (at the 99.99% confidence level) using the Weibull distribution model. This data article complements the research article entitled “Prediction of the curing time to achieve maturity of the nano-cement based concrete using the Weibull distribution model” [1].


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This data article provides a comparison data for nano-cement based concrete (NCC) and ordinary Portland cement based concrete (OPCC). Concrete samples (OPCC) were fabricated using ten different mix design and their characterization data is provided here. Optimization of curing time using the Weibull distribution model was done by analyzing the rate of change of compressive strength of the OPCC. Initially, the compressive strength of the OPCC samples was measured after completion of four desired curing times. Thereafter, the required curing time to achieve a particular rate of change of the compressive strength has been predicted utilizing the equation derived from the variation of the rate of change of compressive strength with the curing time, prior to the optimization of the curing time (at the 99.99% confidence level) using the Weibull distribution model. This data article complements the research article entitled "Prediction of the curing time to achieve maturity of the nano-cement based concrete using the Weibull distribution model" [1]. & 2015 Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Optimization of the curing time to achieve a particular rate of change of compressive strength of OPCC using the Weibull distribution model.

Specifications table
Weibull distribution analysis of the curing time to achieve maturity of the OPCC.

Data, experimental design, materials and methods
Strength data presented here are from ten different concrete samples (OPCC) fabricated to compare nano-cement based concrete (NCC) with ordinary Portland cement based concrete (OPCC).

Sample preparation method
In this investigation, concrete samples were fabricated using ordinary Portland cement, variable amounts fine and coarse aggregate and water (Table 1). Initially, required amount of cement was mixed with the required amount of fine and coarse aggregate, followed by mixing with quantified amount of water. Thereafter, the concrete samples were cast immediately into the mold of the dimension 10 cm Â 20 cm. After complete setting, the samples were removed from the mold and allowed to cure for four different curing times such as 3, 7, 14 and 28 days.

Characterization and data analysis
The prime focus of this investigation was to optimize the curing time using Weibull distribution model. Initially, the compressive strength of concrete (OPCC) was measured using a universal testing machine with a loading rate 0.06 MPa/min in accordance with the Korean standard KS F 2405 [2]. The compressive strengths of ten different mix design of the ordinary Portland cement based concrete (OPCC) are presented in Table 2. The plot of compressive strength vs curing time as well as the plot of the rate of change of compressive strength (df c /dt) vs curing time of the ten different mix design of OPCC is presented in Fig. 1. A trend line for the variation of compressive strength with curing time was predicted. Thereafter, a first order derivative of the data points of trend line w.r.t. curing time was calculated to obtain a rate of change of compressive strength. Additionally, a best fitted equation of the plot of the rate of change of compressive strength (df c /dt) vs curing time of each type of concrete was estimated. The values of the various parameters of the best fitted equation are tabulated in Table 3. From this best fitted equation of the each type of concrete mix design, the times (t r1 , t r2 , t r3 , and t r4 ) required to achieve a different rate of change of compressive strength ((df c /dt)¼(df c /dt) max Â 10 À 2 , (df c /dt) max Â 10 À 3 , (df c /dt) max Â 10 À 4 , and (df c /dt) max ¼0) were estimated (Table 4). Analyzing the results, a range of the curing time is observed to achieve a particular rate of change of compressive strength of the ordinary Portland cement based concrete fabricated using ten different mix design. Therefore, to normalize this range of the data, a widely used statistical model (Weibull distribution) has been selected. Using this two parameter Weibull distribution model, we are trying to normalize the data at 99.99% probability.
The probability function of two-parameter semi-empirical distribution (Weibull distribution) is given by Barsoum [3]. Hence, to analyze the curing time such as t r1 , t r2 , t r3 , and t r4 of the OPCC using the Weibull distribution model, initially survival probability (S) was calculated. Determination of the survival probability (S) for each set of the data, such as t r1 , t r2 , t r3 , and t r4 leads to predict the m and σ 0   value. From this m and σ 0 , the design value (σ) of the curing time was calculated. Where m is a shape factor usually referred as Weibull modulus [3], σ is the design value of the curing time (at the survival probability equal to 99.99%) to achieve a particular rate of change of the compressive strength and σ 0 is a normalizing parameter (at the survival probability equals to 1/e, i.e. 37%). In this study, σ refers to a minimum value of the t r1, t r2 , t r3 , and t r4 at the 99.99% confidence level. It means that a minimum value of t r1, t r2 , t r3 , and t r4 , which will be achieved in 99.99% case, if it is predicted for 100 times. Accordingly, σ 0 refers to a minimum value of the t r1, t r2 , t r3 , and t r4 at the 37% confidence level. It indicates that a minimum value of t r1, t r2 , t r3 , and t r4 , which will be achieved in 37% case, if it is predicted for 100 times. Table 5 represents the values of S j and Ln(t r1 ) of the OPCC. Likewise t r1 , the values of Ln(t r2 ), Ln(t r3 ) and Ln(t r4 ) were calculated. The plot of -LnLn(1/S j ) vs Ln(t r1 ), -LnLn(1/S j ) vs Ln(t r2 ), -LnLn(1/S j ) vs Ln(t r3 ) and -LnLn(1/S j ) vs Ln(t r4 ) of OPCC are shown in Fig. 2. From this plot, σ 0 is calculated using the slope (m) and intercept values for the OPCC. The values of the Weibull modulus m, σ 0 (predicted curing time at survival probability ¼ 37%) and σ (predicted curing time at survival probability ¼99.99%) for Table 3 The values of the different parameters of the exponential equation for different concrete samples obtained by fitting of the rate of change of the compressive strength (df c /dt) vs time (t) plot.  Table 4 The estimated time to reach a different value of the (df c /dt) for each concrete mix design using the equation represented in Table 3. ordinary Portland cement based concrete (OPCC) are represented in Table 6. From the analysis, the values of t r1 , t r2 , t r3 , and t r4 at the 99.99% confidence level of ordinary Portland cement based concrete are estimated to be 37.3, 51.7, 56.8 and 57.7 days, respectively. Nonetheless, the values of the nanocement based concrete were calculated to be 19.57, 20.91, 21.05 and 21.07 days, respectively [1]. Therefore, it is assessed that ordinary Portland cement requires more time (58 days) to be cured  completely as compared to that of the nano-cement based concrete (21 days). Although, it was reported by ACI Committee 308 [4] that different types of cement take different times to cure completely. Additionally, ACI 214R-02 [5] reported that usually 28 days are required to yield adequate curing of the Portland cement based concrete.  Fig. 2. c σ 0 is the value of the component like t r1, t r2, t r3 and t r0 at 37% confidence level. d σ is the value of the component like t r1, t r2, t r3 and t r04 at 99.99% confidence level.