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K. Hover (1995)
Graphical Approach to Mixture Proportioning by ACI 211.1-91Concrete international, 17
S. Popovics, J. Popovics (1995)
Computerization of the strength versus w/c relationshipConcrete international, 17
V. Malhotra (1981)
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Concrete Standard Specification
S. Popovics, J. Popovics (1996)
Novel Aspects in Computerization of Concrete ProportioningConcrete international, 18
T. Nagaraj, S. Shashiprakash (1991)
Analysis of Concrete Strength Versus Water-Cement Ratio Relationship
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Japanese Architectural Standard Specification (JASS 5 Reinforced Concrete Work)
Standard Specification for Ready Mixed Concrete
S. Popovics (1990)
ANALYSIS OF THE CONCRETE STRENGTH VERSUS WATER CEMENT RATIO RELATIONSHIPAci Materials Journal, 87
This paper presents the regression equation for predicting compressive strength of in-situ concrete. For this purpose, this study used the data of mixture proportions of ready-mixed concrete and test results of compressive strength at construction sites. This study used 1442 compressive strength test results obtained from the specimens having 59 different kinds of mixtures with specified compressive strength of 18~27MPa, water-cement ratio of 0.39~0.62, maximum aggregate size of 25mm, and slump of 12~15cm. Principal factors that influence compressive strength of concrete are selected by a correlation analysis, and then the multiple linear regression analysis is carried out for predicting compressive strength according to water-cement ratio or cement-water ratio, cement contents and cement-aggregate ratio. Keywords: mix proportions; correlation analysis; multiple linear regression analysis; prediction of compressive strength 1. Introduction This study aims to make the regression equation and review applicability of prediction equation as a means 1.1 Background and Significance of strength control of concrete, which enables to predict Ready-mixed concrete (RMC) was first produced compressive strength by a multiple linear regression through RMC plant constructed by J. H. Magen in analysis with respect to mixture proportions from RMC Germany in 1903, but was not settled at that time because plants and corresponding field test results of compressive of segregation on carrying. Together with development strength. of agitator equipments in 1926, RMC had grown steadily. In case of RMC industry in Korea, since 1965, 1.2 Procedure and Scope production capacity and consumption of RMC have Data, mixture proportions of RMC plants and quality reached 355million cubic meter and 137million cubic test results of fresh concrete and hardened concrete at meter in 2002, respectively. However, several quality the construction sites, were attained from 8-apartment problems of RMC remained. construction sites located in the district of In-cheon and Only a few tests have been done to ensure concrete Kyeong-gi between April 1999 and July 2001 for this quality before placing; the slump test for workability, study. Mixtures using a binder except normal portland tests of air contents and chloride contents for durability. cement were excluded. Data of this study are 1442 The compressive strength that is the one of influential compressive strength test results based on 59 different factors on concrete quality has been tested at 7 and 28 kinds of mixtures with specified compressive strength days. Several methods for early estimation of concrete of 18~27MPa, water-cement ratio of 0.39~0.62, strength have been introduced for concrete quality maximum aggregate size of 25mm, and slump of control, but they are expensive and time-consuming, and 12~15cm. need experienced skill as well. Sampling concrete was carried out just before placing Therefore, these strength tests are not practical to in structures. Compressive strength test specimens were predict. In addition, available documents offered from cast and cured according to KS F 2403, that is, stored in RMC plants were not applied to strength control of water at the laboratory of construction site until the concrete at construction sites. moment of strength test in accordance with KS F 2405. Table1 represents physical characteristics of concrete *Contact Author: Jee, Namyong, Assistant Professor, Department constituents. of Architectural Engineering, Hanyang University, Haengdang1- The flow diagram for predicting compressive strength Dong Seongdong-Gu, Seoul, Korea of in-situ concrete is shown in Fig.1. Tel: +82-02-2290-0302 Fax: +82-02-2293-3119 Commercial software(SPSS) is used for statistical E-mail: nyjee@hanyang.ac.kr analysis. (Received November 12, 2003 ; accepted April 6, 2004 ) Journal of Asian Architecture and Building Engineering/May 2004/16 9 Fig.1. Flow diagram for predicting concrete strength 2. Variability of concrete strength Variation in concrete strength of the test specimens depends on how well the materials, concrete manufacture, and testing is controlled. Especially construction practices may cause variation in strength of in-situ concrete due to inadequate mixing, poor compaction, delay, and improper curing. Table 2 shows mixture proportions on 59 kinds of in- situ concretes and corresponding compressive strength. Water-cement ratio for specified compressive strength of 18, 24, and 27MPa are 0.57~0.62 (average: 0.60), 0.44~0.52 (average: 0.47), and 0.39~0.48 (average: 0.43), and cement contents are 289~315kg/m (average : 305), 328~401kg/m (average : 374), and 390~420kg/ m (average: 420), respectively. Table 1. Physical characteristics of constituents of concrete 10 JAABE vol.3 no.1 May. 2004 Jee, Namyong Table 2. Mixture proportions of in-situ concrete and comcrete and compressive strength JAABE vol.3 no.1 May. 2004 Jee, Namyong 11 Table 3. Compressive strength and standard deviation of RMC 1997) is “Excellent”. Standard deviation is bellow plants by strength(MPa)-slump(cm) at 28 days 2.8MPa as shown in Fig. 2 and Fig. 3. However, compressive strength of specimens cured in water on construction site is over 14~29% as compared with specified compressive strength. It is estimated that mixture proportions are not economical in case of some RMC plants. Standard deviations of compressive strength at 7 days are bigger than those of compressive strength at 28 days, which means that the magnitude of variation in strength is big at early ages. It can be seen that the frequency distribution of strength test results by specified compressive strength follows normal distribution curve as shown in Fig. 4. Fig.2. Standard deviation by specified compressive strength on RMC plants at 28 days Fig.3. Standard deviation by specified compressive strength on construction sites at 28 days. The class of strength control for in-situ concrete can be evaluated by standard deviation. Mean and standard deviation of compressive strength(MPa) at the RMC plants are given on Table 3. Based on the analysis of standard deviation of strength obtained by RMC plants and construction sites, the class Fig.4. Frequency distribution of strength data and of strength control given in ACI 214-77 (Reapproved corresponding normal distribution curve 12 JAABE vol.3 no.1 May. 2004 Jee, Namyong 3. Prediction of compressive strength of concrete long as their w/c and c/w remain the same regardless of the details of the compositions. The quantity of the According to the formula by Abrams, an increase in cement or aggregate was not accounted for predicting the water-cement ratio decreases the concrete strength, concrete strength. whereas a decrease in the water-cement ratio increases However quite a few investigators have reported that the strength. the higher the cement contents, the lower the strength of The formula of Abrams is; concrete in identical water-cement ratio. Therefore, effort should be made to analyze the role of constituents of concrete. ..................................................... Eq. (1) It is worthwhile to analyze effects of cement, water, and aggregate contents including water-cement ratio as Eq. (1) can be rewritten in the following form; well as those of water-cement ratio for the increase of reliability on the concrete strength prediction. Log f = logA - w/c logB = b + b w/c ............. Eq.(2) 0 1 3.1 Analysis of influential factors on compressive strength where, f : compressive strength of concrete Table 4 shows correlation coefficients between w/c : water-cement ratio compositions of mixture based on documented data from A, B : empirical constants RMC plants and field test results of compressive b , b : correlation coefficient strength. 0 1 Correlation coefficients between compressive strength Another model for the strength versus concrete and factors for mixture such as water-cement ratio, constituents relationship is based on the cement-water cement-water ratio, cement contents, and cement- ratio, that is, the reciprocal value of w/c. Lyse made the aggregate ratio are above 0.6. These are considered as formula, wherein concrete strength and cement-water the principal influential factors that determine ratio are linearly related. This formula becomes very compressive strength of concrete. popular because of its arithmetic simplicity. The strength of concrete increases with increasing The general form of linear c/w model is shown as cement-water ratio, cement contents, coarse aggregate following; contents, and cement-aggregate ratio, and with decreasing water-cement ratio, water contents, fine f = A + B c/w .........................................Eq.(3) aggregate contents, total aggregate contents and fine aggregate-total aggregate ratio. where, f = compressive strength Thus compressive strength of in-situ concrete is found c/w = cement-water ratio to be closer correlation with cement contents than water A, B = empirical constants contents. In case of aggregates, it was analyzed that correlation of fine aggregate with strength is higher than By the numerical form of the Abrams and Lyse, that of coarse aggregate with compressive strength of strength values are identical with various concretes as in-situ concrete. Table 4. Correlation coefficients between compositions of mixture on the basis of documented data and compressive strength JAABE vol.3 no.1 May. 2004 Jee, Namyong 13 3.2 Prediction of compressive strength Table 8. Best-fit coefficient for various augmentations of the Lyse formula. f = b + b (c/w) + b c + b (c/(s+g)) – at 28 days Influential factors that determine compressive strength p 0 1 2 3 of concrete are analyzed by correlation analysis. Then, a multiple linear regression analysis is carried out with respect to compressive strength and principal influencing factors of mixture such as water-cement ratio, cement- water ratio, cement contents, and cement-aggregate ratio. Prediction equations are augmented on the basis of Eq.(1) and Eq.(3). Table 5 represents variables of multiple regression analysis and compressive strength prediction model. Table 5. A variable of multiple linear regression analysis and compressive strength prediction model Table 9. Best-fit coefficient for various augmentations of the Abrams formula. log f = b + b (w/c) + b c + b (c/(s+g))–at 28 days p 0 1 2 3 Tables 6~9 show best-fit coefficient for various augmentations of the Abrams and Lyse at 7 and 28 days. Table 6. Best-fit coefficient for various augmentations of the Lyse formula. f = b + b (c/w) + b c + b (c/(s+g)) – at 7 days p 0 1 2 3 Prediction equations of No. 14 in Table 7 and 9 have best-fit coefficient among various augmentations of equations. Therefore, prediction equations of concrete strength at 7 and 28 days are expressed as Eq.(4) and (5). These are augmented from Abrams formula with cement contents and cement-aggregate ratio. To predict the compressive strength at 7 days the following equation is obtained. The standard prediction error of Eq.(4) is 1.1MPa. f = exp[2.393 - 1.217(w/c) - 0.0048c + 6.16{c/(s + g)}] ...................... Eq.(4) Table 7. Best-fit coefficient for various augmentations of the Abrams formula. log f = b + b (w/c) + b c + b (c/(s+g))– at 7 days p 0 1 2 3 To predict the compressive strength at 28 days the following equation is obtained. The standard prediction error of Eq.(5) is 1.1MPa. f = exp[2.98 - 1.588(w/c) - 0.00642c +7.6888{c/(s + g)}] ...................... Eq.(5) where, f : prediction compressive strength, MPa w/c : water-cement ratio c : cement contents, kg/m w : water contents, kg/m c/(s+g) : cement-aggregate ratio In Fig. 5, the experimental strength are compared to corresponding values calculated by Eq.(4), whereas in Fig. 6 the experimental values are compared to the 14 JAABE vol.3 no.1 May. 2004 Jee, Namyong Table10. Experimental compressive strength and corresponding values calculated by Eq.(4) & (5) Fig.5. Comparison of experimental compressive strength with corresponding values calculated by Eq.(4) at 7 days Fig.6. Comparison of experimental compressive strength with corresponding values calculated by Eq.(5) at 28 days calculated values of Eq. (5). Table 10 shows experimental compressive strength, calculated compressive strength by Eq.(4) and (5), and prediction error with respect to each mixture. In case of mix No. 8 and 15 of Table 10, the prediction error of compressive strength at 28 days is above 3MPa, due to the high standard deviation of compressive strength on RMC plant of K. When standard deviation is high at the RMC plants, it can be recognized that prediction error is high. Therefore, superior quality management is demanded at the RMC plants in order to be more applicable prediction by mixture proportions. Fig. 7 shows the relation of experimental compressive strength at 7 and 28 days. JAABE vol.3 no.1 May. 2004 Jee, Namyong 15 formula of Abrams with respect to cement contents and cement-aggregate ratio. Standard prediction error of prediction equation is 1.1MPa. To predict the compressive strength at 7 days the following equation is obtained. f = exp[2.393 - 1.217(w/c) - 0.0048c + 6.16{c/(s + g)}] To predict the compressive strength at 28 days the following equation is obtained. f = exp[2.98 - 1.588(w/c) - 0.00642c +7.6888{c/(s + g)}] Fig.7. Relationship between in-situ compressive strength at 7 where, f : prediction compressive strength, MPa days and In-situ compressive strength at 28 days w/c : water-cement ratio c : cement contents, kg/m 4. Conclusions w : water contents, kg/m c/(s+g) : cement-aggregate ratio From this study the following conclusions are deduced. References 1) Architectural Institute of Korea, “Korean Architectural Standard 1) In this study, standard deviation of compressive Specification”, 1999 2) Korea Concrete Institute,“Concrete Standard Specification”, 2003 strength of in-situ concrete is almost ‘Excellent’ level 3) ACI Committee 214 (Reapproved 1997), “Recommended Practice according to ACI 214. However, compressive strength for Evaluation of Strength Test Results of Concrete” of specimens cured in water at the laboratory 4) ACI Committee 211.1-91, “Standard practice for selecting construction sites is over 14~29% as compared with proportion for Normal, Heavyweight, and Mass concrete” specified compressive strength. 5) ASTM C94-96,“Standard Specification for Ready Mixed Concrete” 6) Snador Popovics, “Analysis of Concrete Strength versus Water- Cement Ratio Relationship”, ACI Material Journal, V.87, No.5, 2) Based on the results of correlation analysis September-October 1990, pp.517 529 influential factors are water-cement ratio, cement-water 7) Sandor Popovics and John S. Popovics, “Computerization of the ratio, cement contents, cement-aggregate ratio in order. Strength Versus w/c relationship”, Concrete International, April 1995, pp.37-40 The w/c is most influential. 8) Sandor Popovics and John S. Popovics,“Novel Aspects in It is efficient to consider the effects of these influential Computerization of Concrete Proportioning”, Concrete factors for reliability of prediction of compressive International, December 1996, pp.54-58 strength. 9) Ken Hover,“Graphical Approach to Mixture Proportioning by ACI 211.1-91”, Concrete International, September 1995, pp.49-53 10) Architectural Institute of Japan, “Japanese Architectural Standard 3) Compressive strength prediction equations were Specification (JASS 5 Reinforced Concrete Work)”, 1997, pp.200- provided for in-situ concrete with water-cement ratio of 0.39~0.62 and specified compressive strength of 18~27MPa at 7 and 28 days, which are modified from 16 JAABE vol.3 no.1 May. 2004 Jee, Namyong
Journal of Asian Architecture and Building Engineering – Taylor & Francis
Published: May 1, 2004
Keywords: mix proportions; correlation analysis; multiple linear regression analysis; prediction of compressive strength
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