Two Statistical Scrutinize of Impact Strength and

KSCE Journal of Civil Engineering (0000) 00(0):1-13 Copyright ⓒ2017 Korean Society of Civil Engineers DOI 10.1007/s12205-017-1554-1

Structural Engineering

pISSN 1226-7988, eISSN 1976-3808 www.springer.com/12205

TECHNICAL NOTE

Two Statistical Scrutinize of Impact Strength and Strength Reliability of Steel Fibre-Reinforced Concrete G. Murali*, R. Gayathri**, V. R. Ramkumar***, and K. Karthikeyan**** Received September 8, 2016/Revised November 24, 2016/Accepted January 11, 2017/Published Online April 6, 2017

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Abstract The variations in impact strength of steel Fibre Reinforced Concrete (FRC) were statistically, commanded in this research. For this purpose, the experimental impact test results of earlier researchers were investigated using two statistical approaches. Firstly, normality test was carried out on first crack strength (N1) and failure strength (N2) using distribution plot and its accuracy was verified with Kolmogorov-Smirnov, Shapiro-Wilk and Chen-Shapiro test. Secondly, strength reliability analysis was carried out using two parameter Weibull distribution and their Weibull parameters were determined using three methods viz., Empherical Method of Justus (EMJ), Method of Moments (MOM) and Empherical Method of Lysen (EML). Results suggested that, if three samples are used to determine the N1 value for researchers’ data, at 95% levels of confidence, then the error in the measured value is about 50%. The 0.1 reliability level of the impact strength values of EMJ, EML and MOM were 153, 120 and 153 respectively in case of N1 and were 198, 156, and 198 respectively in case of N2 based on earlier researcher’s data. Keywords: statistical analysis, steel fibre, impact strength, normality test, weibull distribution ··································································································································································································································

1. Introduction Recently, there is a growing trend to enhance the impact resistance of civil and military infrastructure owing to the increasing number of missile or airplane attacks and bombings (Sun et al., 2015). One of the promising solutions for enhancing the impact resistance of such structures is adding small amounts of different types of fibres into concrete which can significantly reduce the damage due to impact load by arresting crack development and bridging of cracks (Mohammadi et al., 2008; Nili and Afroughsabet, 2010; Faiz, 2013; Shahid et al., 2015). The tensile force (which occurs at cracking load) after first cracking, becomes lower than the cracking load for the concrete incorporating lesser amount of steel fibres, owing to increase in elongation. During this stage, strain-softening occurs in the presence of a single crack leading to the brittle failure of concrete. On the other hand, subsequent to first crack growth the tensile force increases after the softening stage and reaches the ultimate load value for the concrete incorporating higher amount of steel fibres (Barros et al., 2012; Taheri et al., 2012; Murali et al., 2016). Thus, it shows the ductile response of specimens which undergoes strain-hardening behaviour and multiple cracking. On the transition from brittle to ductile response, when ultimate

load value equals the cracking load, the corresponding critical value of fibre volume can be considered as the minimum amount of fibres that ensures the strain-hardening behaviour of the fibre reinforced concrete (Fantilli et al., 2016). Also, the use of steel fibres was found to be effective for shear-critical beams since it enhances the strength, stiffness and cracking characteristics, decreases deflections and, under specific conditions, it alters failure modes from brittle and dangerous shear failures into more ductile flexural failures (Lim and Oh, 1999; Cucchiara et al., 2004; Adhikary and Mutsuyoshi, 2006; Juarez et al., 2007; Chalioris, 2013). The impact strength of concrete can be assessed via, explosive test, drop-weight test, and projectile impact test (Song et al., 2005-b). Among them, drop-weight test is the simplest, popular and attractive method to determine the impact strength of FRC as suggested by the ACI Committee 544. Cylindrical disc specimens of 150 mm in diameter and 64 mm in height were placed on the base plate of testing machine and it was struck with repeated number of blows. The number of impacts (blows) required to cause the first visible crack (N1) and failure (N2) were recorded. Banthia et al. (1996) reported that by adding 0.5% dosage of hooked end steel fibers displayed an increase in failure energy by 2.4 times when compared to non-fibrous concrete. Yan et al.

*Assistant Professor-III, School of Civil Engineering, SASTRA University, Thanjavur, Tamil Nadu, India (Corresponding Author, E-mail: [email protected]) **M. Tech Student, School of Civil Engineering, SASTRA University, Thanjavur, Tamil Nadu, India (E-mail: [email protected]) ***Research Scholar, Division of Structural Engineering, Anna University, Chennai, India (E-mail: [email protected]) ****Assistant Professor (Senior), SMBS, VIT University, Chennai, Tamil Nadu, India (E-mail: [email protected]) −1−

G. Murali, R. Gayathri, V. R. Ramkumar, and K. Karthikeyan

(1999) reported that the addition of steel fibers and partial replacement of cement by silica fume in concrete effectively diminishes the number and size of cracks, and improves the impact resistance of high strength concrete. Using a drop weight device, Marar et al. (2001) presented that for FRCs containing hooked-end steel fibers of 0.5%, 1%, 1.5% and 2% dosage with an aspect ratios of 60, 75 and 83, the specimens with a higher fiber dosage had a higher impact strength; likewise, for specimens containing 2% fiber dosage and an aspect ratios of 60, 75 and 83, the energy absorption is improved by 38, 55 and 74 times, respectively with reference to non-fibrous concrete. Nataraja et al. (1999) statistically investigated the impact strength variations of steel FRC and Plain Concrete (PC) measured from a drop weight test. The goodness- of-fit test indicated poor fitness of the impact strength test results in the normal distribution plot, at 95% level of confidence for both steel FRC and plain concrete. Results suggested that based on the observed level of variations, a minimum of 143 specimens per concrete mix was required to assure an error below 5%. Song et al. (2005-a) investigated the strength reliability of steel–polypropylene hybrid FRC and steel FRC subjected to drop weight test statistically. The normality and reliability tests were carried out using Kolmogorov-Smirnov test and Kaplan–Meier analysis respectively. The KolmogorovSmirnov test indicated that the strength of two FRCs hardly followed the normal distributions and the Kaplan-Meier analysis indicated that the increase in impact strength reliability of hybrid FRC was slightly higher than the steel FRC. Rahmani et al. (2012) carried out the extensive statistical analysis to assess the variations in cellulose, polypropylene, and steel FRC subjected to drop weight test. The result showed that the first crack and failure strengths of steel FRC were hardly distributed normally which is supported by the p-value of 0.036. Kruskal-Wallis test indicated that the addition of cellulose fibres improved the first crack and failure strength than polypropylene fibres. Several impact tests have been carried out to determine the relative brittleness and impact resistance of FRC (Mohammadi et al., 2008; Nili and Afroughsabet, 2010; Alavi Nia et al., 2012; Kim et al., 2016; Richardson et al., 2016). The experimental impact test results obtained from the ACI Committee 544 recommended drop weight test could be noticeably scattered as reported in the previous studies (Nataraja et al., 1999; Song et al., 2005-a; Song et al., 2005-b; Atef et al., 2006; Chen et al., 2011; Rahmani et al., 2012; Mastali and Dalvand, 2016). The sources of large scatter in drop weight test results may be attributed to the following reasons: (i) the test results are interpreted based on the recognition of first crack and failure by visual means and this crack may occur in any direction. (ii) It is intricate to control the height of fall of drop hammer exactly, as it is being done manually (iii) the impact strength of concrete is determined by the impact occurring at a single point, which may be either, on a tough coarse aggregate or fibre or matrix. (iv) any variation occurring in concrete mix design would result in change of its impact strength (v) the drop weight test is influenced by handmade work and hence the test results would also be greatly influenced

by man made errors. In the view of features of impact test results, the statistical analysis is the best choice for resolving the variations in impact test results and determining the significance of steel fibre in concrete (Chen et al., 2011). Two such analyses namely the normality test and Weibull distribution are recently been used widely for the determination of static and dynamic mechanical properties of FRC structures (Goel et al., 2012; Dias et al., 2015; Arora and Singh, 2016; Mastali and Dalvand, 2016).

2. Research Significance To the authors' best knowledge; though there are few studies available for assessing the variations in impact test results statistically (Nataraja et al., 1999; Song et al., 2005-a; Song et al., 2005-b; Atef et al., 2006; Chen et al., 2011; Rahmani et al., 2012; Mastali and Dalvand, 2016), there is only one study reporting (Murali et al., 2014) impact strength in terms of reliability by graphical method of Weibull distribution. In this study two statistical analyses were employed; firstly, statistical analysis was carried out to determine the normal distribution of test results and it reported the number of specimens required to retain the error below a specified limit at 90% and 95% of confidence level. Secondly, a two parameter Weibull distribution analysis was employed on same (Nataraja et al., 1999; Song et al., 2005-a; Song et al., 2005-b; Rahmani et al., 2012) experimental results using three different methods to determine Weibull parameters and it presented the impact strength in terms of required reliability level. The three methods used in this study namely Empherical Method of Justus (EMJ), Method of Moments (MOM) and Empherical Method of Lysen (EML), to determine the impact strength of steel FRC in terms of reliability (by two parameter Weibull distribution) has not been performed by any of the earlier researchers.

3. Statistical Analysis The probability distribution of FRC specimens are discussed in this section. Since 2015, only one study has discussed (Mastali and Dalvand, 2016) the statistical distribution of the impact strength of self-compacting concrete reinforced with recycled CFRP pieces. This indicates that application of statistical analysis is a new approach and would be a suitable method to further study and develop an understanding of impact strength properties of FRC. Execution of statistical analysis provides a better understanding of the impact resistance of FRC and this requires a collection of large number of experimental data that acts as a reliable database. It is essential to describe the significant effect of fibre type and fibre dosage on statistical parameters and distribution of impact strength. 3.1 Probability Distribution In order to represent the material property distribution, Normal and lognormal distributions are generally identified to be the suitable statistical distribution models (Lin et al., 2014). The

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KSCE Journal of Civil Engineering

Two Statistical Scrutinize of Impact Strength and Strength Reliability of Steel Fibre-Reinforced Concrete

Table 1. Impact Strengths of Results of Earlier Researchers Specimen No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Nataraja et al. (1999) N1 N2 196 270 98 140 72 95 46 80 46 86 153 181 144 189 160 210 39 60 35 70 81 128 130 153 84 131 160 222 34 68 98 139 54 64 -

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Song et al. (2005-a) N1 N2 1450 1650 1510 1590 2012 2088 2890 3590 1306 1525 1104 1238 1250 1336 2504 2718 1274 1385 2750 2832 1367 1424 1683 1780 1991 2074 1463 1617 1396 1490 1429 1478 1450 1580 1147 1224 1255 1316 1335 1449 2895 2967 1872 2108 1287 1386 1750 1871 1085 1407 1783 1897 1802 1987 2112 2433 1262 1501 1258 1292 3739 3900 5408 5609 1038 1223 2346 2535 1624 1763 1514 1600 1650 1874 1155 1370 1676 2150 1306 1429 1700 1900 1285 1456 1141 1274 1521 1775 1647 1741 1444 1561 1894 1993 1476 1606

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Song et al. (2005-b) N1 N2 160 290 292 400 158 220 226 320 200 301 600 711 190 261 172 244 114 228 163 467 166 210 535 727 200 308 280 360 200 276 307 446 214 410 234 350 315 409 256 384 191 256 246 427 252 385 296 399 580 700 753 846 267 319 245 300 392 452 317 390 269 333 216 256 113 207 160 358 130 200 126 198 236 300 184 336 300 525 212 250 252 270 52 124 155 208 259 356 153 331 253 437 190 320 90 295

Rahmani et al. (2012) N1 N2 268 390 129 157 38 168 42 281 276 383 71 346 181 391 166 192 70 251 97 308 210 365 63 176 60 135 49 166 168 198 36 124 77 240 118 135 95 111 128 154 84 102 141 170 209 251 179 307 255 361 161 192 148 177 83 302 43 139 122 173 95 214 77 252 -


previously used statistical model to represent the concrete material property is the normal distribution which is a bellshaped curve that is symmetrical about the mean of the population (MacGregor et al., 1983; Nataraja et al., 1999; Song et al., 2005-a; Song et al., 2005-b; Rahmani et al., 2012). The normal distributions are also well suitable for describing the strength variability of most ductile phases such as FRC (Azeko Salifu et al., 2015). The lognormal distribution is usually tilted towards one end of the distribution instead of being symmetrical about the mean. Steel material property distributions are often represented by Lognormal distributions such as in the study conducted by Galambos et al. (1982). The tensile tests conducted on 829 concrete specimens by Rusch (1975) showed that 93% of these specimens were distributed normally. The statistical analysis and probability distribution of the impact strength of FRC were executed using SPSS software. Furthermore, herein this study, the Kolmogorov-Smirnov, ShapiroWilk and Chen-Shapiro methods were used to test normality of the data. The Kolmogorov-Smirnov test is based on the maximum deviation of the observed cumulative histogram from the hypothesized cumulative distribution function. The ShapiroWilk test is a test of normality in frequentist statistics. ChenShapiro normality test that compares the spacings among order

statistics with the spacings between their expected values under normality (Chen and Shapiro, 1995). For the most alternative study of normality test Chen-Shapiro is used and it is easy to compute and has to be as powerful as or superior to the ShapiroWilk test. These tests examine, whether if the observations could reasonably have come from a normal distribution. In three test cases, the obtained p-value is less than 0.05 which means the null hypothesis (i.e. normal distribution) is rejected (Mastali and Dalvand, 2016). The p-values which quantifies strength indicates against the null hypothesis. 3.2 Normality Test of Nataraja et al. (1999) Data The data for this statistical approach, obtained from the earlier researchers is presented in Table 1. From the Nataraja et al. (1999) data, the N1and N2 for the 17 specimens ranged from 32 to 196 blows and 60 to 270 blows, respectively. Table 2 shows the statistical parameters for N1 including the mean, standard deviation, and the coefficient of variation are 96 blows, 52 blows, and 52%, respectively and for N2 it is 134 blows, 63 blows, and 43%, respectively. The 95% confidence interval on the mean for the N1 was 69-122 blows; for N2 was 102-166 blows, which suggests that in 95% of the results, these intervals contain the estimated mean.

Table 2. Statistical Evaluation of Impact Strength Test Results 95% Confidence interval (blows) p-Value of p-Value of p-Value of K-S test S-W test C-S test Upper Lower bound bound N1 34 196 96 52 52 13 122 69 0.200 0.117 0.055 Nataraja et al. (1999) N2 60 270 134 63 43 15 166 102 0.200 0.195 0.055 N1 1038 5408 1734 769 44 111 1957 1510 0.000 0.000 0.030 Song et al. (2005-a) N2 1223 5609 1896 801 42 116 2128 1662 0.000 0.000 0.030 N1 52 753 247 133 54 19 285 208 0.000 0.000 0.030 Song et al. (2005-b) N2 124 846 356 146 41 21 398 313 0.010 0.000 0.030 N1 36 276 123 68 56 12 147 98 0.071 0.029 0.039 Rahmani et al. (2012) N2 102 391 228 89 39 16 260 196 0.028 0.016 0.039 SD: Standard deviation, COV: Coefficient of variation, SEM: Standard error of mean, N1: Number of blows required to cause first crack and N2: Number of blows required to cause failure. Author

N1 & N2

Min

Max

Mean (blows)

SD (blows)

COV (%)

SEM (blows)

Fig. 1. Distribution Plot of Nataraja et al. (1999) Results: (a) N1, (b) N2 −4−



The frequency histograms with fitted normal curves of the first crack strength (N1) and failure strength (N2) of Nataraja et al. (1999) specimens are illustrated in Fig. 1(a) and (b). The figure displays that the N1 and N2 distribution is barely normally distributed. The histogram in Fig. 1(a) and (b) re-emerges as the normal probability plot in Fig. 5(a) and (b), which suggests that the most of data points falls on fitted line that indicating normality distribution of the N1 and N2 is normal. This conclusion can also be stated based on p-values that are listed in Table 2. For more accuracy, the N1 and N2 distribution was verified with Kolmogorov–Smirnov and Shapiro-Wilk test at a significance level α = 0.05. The obtained p-values for the N1 and N2 were 0.200 and 0.200 respectively in Kolmogorov-Smirnov test, and were 0.117 and 0.195 respectively in case of Shapiro-Wilk test and were 0.055 and 0.055 respectively in case of Chen-Shapiro test which lies above the significance level 0.05; this confirms the null hypothesis at 0.05 significant levels that follows the normal distribution. 3.3 Normality Test of Song et al. (2005-a) Data From the Song et al. 2005 data, the N1 for the 48 specimens ranged from 1038 to 5408 blows and their N2 ranged from 1223 to 5609 blows. The mean, standard deviation, and the coefficient

of variation are 1734 blows, 769 blows, and 44%, respectively for N1, and 1896 blows, 801 blows, and 42% for N2. The 95% confidence interval on the mean for the N1 was 1510-1957 blows; for N2 was 1662-2128 blows, which suggests that in 95% of the results, these intervals contain the estimated mean as shown in Table 2. The frequency histograms presented in Fig. 2 (a) and (b), displays that the N1 and N2 distribution fails to follows a normal distribution and shows poor fitting normal curves (bell-shaped curve). In addition, the data points are severe departure from straight line as shown in Fig. 6(a) and (b). From the Kolmogorov-Smirnov, Shapiro-Wilk tests and Chen-Shapiro tests the p-values less than 0.05 that confirms the non-normality (i.e. normal distribution) is rejected. 3.4 Normality test of Song et al. (2005-b) Data The N1 and N2 ranged from 52 to 753 blows and 124 to 846 blows, respectively. The mean, standard deviation, and the coefficient of variation are 247 blows, 133 blows and 54%, respectively for N1, and 356 blows, 146 blows and 41% respectively for N2. The 95% confidence interval on the mean for the N1 was 208-285 blows; for N2 was 313-398 blows, which suggests that in 95% of the results, these intervals contain the estimated mean as shown in Table 2. The frequency histograms presented in Fig.

Fig. 2. Distribution Plot of Song et al. (2005-a) Results: (a) N1, (b) N2

Fig. 3. Distribution Plot of Song et al. (2005-b) Results: (a) N1, (b) N2 Vol. 00, No. 0 / 000 0000

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Fig. 4. Distribution Plot of Rahmani et al. (2012) Results: (a) N1, (b) N2

Fig. 5. Normal Probability Plots of Nataraja et al. (1999) Results for: (a) N1, (b) N2

Fig. 6. Normal Probability Plots of Song et al. (2005-a) Results for: (a) N1, (b) N2

3(a) and (b), displays that the N1 and N2 distribution fails to follow a normal distribution and shows poor fitting normal curves. In addition, the data points are extremely falling off the straight line as shown in Fig. 7(a) and (b). From the KolmogorovSmirnov, Shapiro-Wilk and Chen-Shapiro tests, the p-values were less than 0.05 that confirms the non-normality of N1 and N2. 3.5 Normality Test of Rahmani et al. (2012) Data

The N1 ranged from 36 to 276 blows and their N2 ranged from 102 to 391 blows. Table 2 shows the mean, standard deviation, and the coefficient of variation are 123 blows, 68 blows, and 56%, respectively for N1, and 228 blows, 89 blows, and 39% respectively for N2. The 95% confidence interval on the mean for the N1 was 98-147 blows; for N2 was 196-260 blows, which suggests that in 95% of the results, these intervals contain the estimated mean. The frequency histograms presented in Fig. 4 (a) and (b), displays that the N1 and N2 distribution fails to

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Fig. 7. Normal Probability Plots of Song et al. (2005-b) Results for: (a) N1, (b) N2

Fig. 8. Normal Probability Plots of Rahmani et al. (2012) Results for: (a) N1, (b) N2 Table 3. Number of Sample as a Function of Percent Error in Average Level of confidence

90

95

Error