Prediction of Strength and Slump of Rice Husk Ash Incorporated High-Performance Concrete

Abstract This paper describes the development of statistical models to predict strength and slump of rice husk ash (RHA) incorporated high-performance concrete (HPC). Sixty samples of RHA incorporated HPC mixes having compressive strength range of 42–92 MPa and slump range of 170–245 mm were prepared and tested in the laboratory. These experimental data of sixty RHA incorporated HPC mixes were used to develop two models. Six variables namely water-to-binder ratio, cement content, RHA content, fine aggregate content, coarse aggregate content and superplasticizer content were selected to develop the models and ultimately to predict strength and slump of RHA incorporated HPC. The models were developed by regression analysis. Additional five HPC mixes were prepared with the same ingredients and tested under the same testing conditions to verify the ability of the proposed models to predict the responses. The results of the prediction of the models showed good agreement with the experimental data. Thus the dev...


Introduction
High-performance concrete (HPC) is defined as concrete, which meets special performance and uniformity requirements that cannot always be achieved routinely by using conventional materials and normal mixing, placing and curing practices (Zia et al. 1991). The requirements may involve enhancements of characteristics such as placement and compaction without segregation, longterm mechanical properties, early-age strength, volume stability or service live in severe environments. HPC is a relatively new product and its characteristics differ from that of normal concrete (Zain et al. 2002).
HPC mixtures are usually more expensive than conventional concrete mixtures because they usually contain more cement, several chemical admixtures at higher dosage rates than for conventional concrete, and one or more supplementary cementitious materials (Simon 2003). As the cost of materials increases, optimizing concrete mixture proportions becomes more desirable. Furthermore, as the number of constituent materials increases, the problem of identifying optimal mixtures becomes increasingly complex. Not only are there more materials to consider, but there also are more potential interactions among materials. Combined with several performance criteria, the number of trial batches required to find optimal proportions using traditional methods could become prohibitive. HPC is a highly complex material and modeling its beha-vior is a difficult task (Yeh 1998). Therefore, there is a need to find new methods for prediction of HPC properties. Although several models were developed for prediction and optimization of concrete properties (Zain et al. 2002;Simon 2003;Yeh 1998;Saridemir 2009a, b;Bai et al. 2003;Tanyildizi 2009;Bilim et al. 2009;Özcan et al. 2009;Guang, Zong 2000;Kasperkiewics et al. 1995;Lai, Serra 1997;Lee 2003;Lim et al. 2004;Patel 2003;Jaśniok, Zybura 2009;Kamaitis 2008;Bai, Gailius 2009), none of these models includes rice husk ash (RHA) as a supplementary cementitious material in making HPC. Rice husk, an agricultural waste, constitutes about one fifth of the 500 million metric tons of rice produced annually in the world (Mehta 1989). Due to the growing environmental concern, and the need to conserve energy and resources for sustainable development, efforts have been made to burn the husks at controlled temperature and atmosphere, and to utilize the ash so produced as a building material (Columna 1974;Mehta 1977Mehta , 1989Ismail, Waliuddin 1996;Zhang, Malhotra 1996;Jauberthie et al. 2000;Bui 2001;Nehdi et al. 2003;Agarwal 2006;de Sensale 2006;Chindaprasirt et al. 2007;Gastaldini et al. 2007;Giaccio et al. 2007;Saraswathy, Song 2007;Sata et al. 2007;Ganesan et al. 2008;Nair et al. 2008;de Sensale et al. 2008;Zain et al. 2011). The main concern of this study was to develop statistical models for predicting strength and slump of RHA incorporated HPC.

Material properties
Ordinary Portland cement (Type I) was used that meets the ASTM C150 (2011) specifications. RHA used was produced in the laboratory. The chemical and physical properties of the cement and RHA are shown in Table 1. Natural river sand and crushed limestone were used as aggregates. The gradation of both fine and coarse aggregates met the ASTM C33 (2011) specification. The details of physical properties of both aggregates are shown in Table 2. Glenium 100 M superplasticizer complying with the requirements of ASTM C494 (2011) and ASTM C1017 (2007) was used (solid content = 25.25% and specific gravity = 1.28). Normal tap water (pH = 6.9) was used as mixing water and for curing. 3. Concrete mixes, specimen preparation and testing Sixty samples of RHA incorporated HPC mixes were prepared in the laboratory. Table 3 shows water-to-binder ratio (W/B), cement (C), rice husk ash (RHA), water (W), fine aggregate (FA), coarse aggregate (CA) and superplasticizer (SP) contents of these mixes. A rotating pan-type mixer of 0.05 m 3 capacity was used to mix concrete. Each batch included sufficient concrete for three slump tests and four 100×200 mm cylinders for compressive strength test. The cylinders were fabricated in accordance with ASTM C192 (2007). To obtain adequate consolidation, the cylinders were rodded. The cylinders were covered with plastic and left in the molds for 24 hours, after which they were stripped and placed in limewater-filled curing tanks for moist curing at 23±2 °C. Slump test of fresh concrete was carried out as per ASTM C143 (2010). Compressive strength tests (ASTM C39 2010) were conducted on the cylinders at the age of 28 days. In most cases, three cylinders were tested. A fourth test was performed in some cases if one result was significantly lower or higher than the others. Before testing, the cylinder ends were ground parallel to meet the ASTM C39 (2010) requirements using an end-grinding machine designed for this purpose. The average strength of three cylinders was reported as result of the test. Results of slump test (range: 170 mm to 245 mm) and compressive strength test (range: 42.47 MPa to 92.21 MPa) are also shown in Table 3.

Model development
Six variables were selected to derive statistical models and ultimately to predict the properties of RHA incorporated HPC. The limits of the variables were decided by conducting some preliminary tests and from past experience. The notations used and limits of the variables are as follows: The MINITAB statistical software (Minitab Inc. 2004) was used to derive two models by the least square approach. The general structure of the statistical model is as follows: where: y is the response; x i are the independent variables; β o is the independent term; β i , β ii and β ij are the coefficients of independent variables and interactions, representing their contribution to the response; ε is the random residual error term representing the effects of variables or higher order terms not considered in the model (Kutner et al. 2004).
The interaction between the six variables (x i x j ) and quadratic effect ( ) 2 i x of variables were also considered in the proposed models as shown in Eq. (1). By trial and error, the best-fit models were identified from different probability distribution functions. The 't' test was carried out to decide the statistical significance of variables. The null hypothesis was the presupposition that the true value of coefficient is zero. In other words, the variable or variables associated with that coefficient are statistically not significant and it has no influence on the response y. If the probability greater than 't statistic' is less than 0.05 (5%), the null hypothesis (the coefficient value is zero) can be rejected and established that the variable or variables with the estimated coefficient has significant influence on the response. If the probability greater than 't statistic' is more than 0.05 (5%), the null hypothesis can be accepted and it can be established that the variable or variables with estimated coefficient has no influence on the response and hence that variable or variables cannot be included in the model. In the proposed models, the probability greater than 't statistic' was found less than 0.05. This signifies that there is less than 5% probability that the contribution of a given variable with the respective coefficient to the tested response exceeds the value of the specified estimated coefficient. A possible higher value of determination coefficient (R 2 ) was considered while selecting the proposed models. After many trials with MINITAB software, best-fit two models were found out for HPC properties e.g., compressive strength and slump as described in the following sections.

Model 1: 28-day compressive strength
In design and quality control of concrete, 28-day compressive strength is normally specified. The 28-day compressive strength of concrete determined by a standard uniaxial compression test is universally accepted as a greater index of concrete strength (Patel 2003 The statistical details of the model are presented in Table 4. The model is fit in normal (Gaussian) probability distribution function. All the six variables such as waterbinder ratio (x 1 ), cement (x 2 ), RHA (x 3 ), fine aggregate (x 4 ), coarse aggregate (x 5 ) and superplasticizer (x 6 ) have direct influence on the response (28-day compressive strength, y 1 ). Some variables are interacting with each other. Some of them have positive influence and some of them have negative influence on the response. The R 2 value is 85.3% which is an indication of reasonably good fitness. From the results of ANOVA analysis, it appears that the probability greater than "F statistic" (Fisher statistic) is less than 0.0005 (Table 4). The model is highly statistically significant with confidence level more than 99.95%. All the variables were also tested individually for 't statistic'. The probability greater than 't statistic' for intercept, all variables, and their interaction are indicated in Table 5. The probability greater than 't statistic' for all variables is found to be less than 0.006 (confidence level more than 99.4%). Therefore, all the variables indicated in the model are statistically significant and have influence on the 28-day compressive strength.  x 1 x 6 -38.60 10.58 -3.65 0.001 x 2 x 6 -0.04838 0.01502 -3.22 0.002 x 3 x 6 -0.04965 0.01719 -2.89 0.006 x 4 x 6 -0.07433 0.02018 -3.68 0.001 Fig. 1 shows the residual plot of the compressive strength model. The figure shows that the errors are independent. The residuals in the plot appear to be randomly scattered about zero. The other assumptions of regression analysis are also satisfied. The adjusted correlation coefficient is 81.6% (Table 4), which indicates a very good fit. The root mean square error is 4.96, which is also an indication of accuracy of the model fit. The model is significant as can be seen from the significance value that is very close to zero.

Model 2: slump
The slump is one of the most important properties of HPC. If the slump of fresh concrete is between 180 and 220 mm without any segregation, the concrete can be qualified for HPC. Of course, other fresh concrete tests are also important to evaluate thoroughly the fresh HPC properties. However, one can take decision from slump test, if other test set-ups are not available. The proposed slump model is: The statistical details of this model are also presented in Table 4. The model was fit in normal (Gaussian) probability distribution function. Some of the variables have positive influence and some have negative influence on the response (slump, y 2 ). The R 2 value is 84.1%, which indicates reasonably good fitness. From the results of ANOVA analysis (Table 4), it appears that the probability greater than 'F statistic' (Fisher statistic) is less than 0.0005. The model is highly statistically significant with a confidence level more than 99.95%. All the variables were also tested individually for 't statistic' (Table 6). It can be observed from Table 6 that the 'probability greater than t' for RHA (x 3 ) is greater than 0.05. It is still included in the model to maintain the hierarchy of the model terms. Hierarchical terms are linear terms that may be insignificant by themselves but are part of significant higher order terms.    on 2003). All the variables in the model are statistically significant and have influence on the slump. Fig. 2 shows the residual plot of the slump model. The figure shows that the errors are independent. The residuals appear to be randomly scattered about zero. The other assumptions of regression analysis are also satisfied. The adjusted correlation coefficient is 78.7% (Table 4), which indicates a good fit. The root mean square error is 7.21, which is also an indication of a good fit of the model. The model is significant as can be seen from the significance value that is very close to zero.

Model validation
Five additional mixtures were prepared and tested with the same ingredients to verify the ability of the proposed models to predict the responses. Table 7 shows the quantities of the ingredients, 28-day strength and slump of these five concrete mixes. The slump and the 28-day compressive strength were measured in the laboratory and compared with those of the prediction by the respective models. The experimental and model predicted values of slump and 28-day compressive strength are shown in Table 8. The tests were carried out with the same materials and under the same testing conditions. Table 8 shows that the variations among model predicted and experimental values for slump and strength were not significant, which is an indication that the models predict 28-day strength and slump with reasonable accuracy.

Limitations of the models
The proposed statistical models for prediction of strength and slump of RHA incorporated HPC were derived from sixty HPC mixes with ordinary portland cement (ASTM Type I), rice husk ash (specific gravity = 2.0, specific surface area = 183.3 m 2 /kg), natural river sand (specific gravity = 2.6, absorption = 1.47%, fineness modulus = 3.04), crushed lime stone (specific gravity = 2.61, absorption = 0.82%, fineness modulus = 6.68, maximum size = 19 mm), and Glenium 100 M superplasticizer complying with the requirements of ASTM C494 (2011) and ASTM C1072 (2011) (solid content = 25.25% and specific gravity = 1.28). The models predict strength and slump with acceptable accuracy for ranges of mix proportions as shown in Table 3  It was found from the ANOVA analysis that all the six selected variables i.e., water-binder ratio (W/B), cement (C) content, rice husk ash (RHA) content, fine aggregate (FA) content, coarse aggregate (CA) content, and superplasticizer (SP) content are statistically significant and have direct influence on strength of RHA incorporated HPC. On the other hand, water-binder ratio, cement content, fine aggregate content and coarse aggregate content have significant influence on slump of RHA incorporated HPC.
The proposed models can be used to predict strength and slump of RHA incorporated HPC. Developed models were evaluated and the results of prediction were reasonably accurate. Similar to other statistical prediction models, the proposed models are depended on material properties and mix proportions. The absolute value of the predicted strength and slump may not be the same if different sets of materials are used. However, the models can still be useful for prediction of strength and slump when presented with different sets of materials and mix proportions. RHA incorporated HPC reduces use of cement in concrete, consumes waste, and increases durability of concrete. Thus, these models can be useful as tools for sustainable development because they can substantially reduce time, effort, and cost associated with selection of trial batches of HPC.