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Value of the data
Data, experimental design, materials and methods
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 Senexin B immediately into the mold of the dimension 10cm×20cm. 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 0.06MPa/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/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/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, t, t, and t) required to achieve a different rate of change of compressive strength ((df/dt)=(df/dt)max×10−2, (df/dt)max×10−3, (df/dt)max×10−4, and (df/dt)max=0) 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, t, t, and t 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, t, t, and t leads to predict the m and σ0 value. From this m and σ0, 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 σ0 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 tt, t, and t at the 99.99% confidence level. It means that a minimum value of tt, t, and t, which will be achieved in 99.99% case, if stomach is predicted for 100 times. Accordingly, σ0 refers to a minimum value of the tt, t, and t at the 37% confidence level. It indicates that a minimum value of tt, t, and t, which will be achieved in 37% case, if it is predicted for 100 times. Table 5 represents the values of S and Ln(t) of the OPCC. Likewise t, the values of Ln(t), Ln(t) and Ln(t) were calculated. The plot of –LnLn(1/S) vs Ln(t), –LnLn(1/S) vs Ln(t), –LnLn(1/S) vs Ln(t) and –LnLn(1/S) vs Ln(t) of OPCC are shown in Fig. 2. From this plot, σ0 is calculated using the slope (m) and intercept values for the OPCC. The values of the Weibull modulus m, σ0 (predicted curing time at survival probability=37%) and σ (predicted curing time at survival probability=99.99%) for ordinary Portland cement based concrete (OPCC) are represented in Table 6. From the analysis, the values of t, t, t, and t 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 nano-cement 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.