Research Article A Statistical Approach to Optimizing Concrete Mixture Design Shamsad Ahmad and Saeid A. Alghamdi Civil and Environmental Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia Correspondence should be addressed to Shamsad Ahmad; shamsad@kfupm.edu.sa Received 19 November 2013; Accepted 24 December 2013; Published 9 February 2014 Academic Editors: H. Cui, ˙ I. B. Topc ¸u, and H. Wang Copyright © 2014 S. Ahmad and S. A. Alghamdi. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A step-by-step statistical approach is proposed to obtain optimum proportioning of concrete mixtures using the data obtained through a statistically planned experimental program. he utility of the proposed approach for optimizing the design of concrete mixture is illustrated considering a typical case in which trial mixtures were considered according to a full factorial experiment design involving three factors and their three levels (3 3 ). A total of 27 concrete mixtures with three replicates (81 specimens) were considered by varying the levels of key factors afecting compressive strength of concrete, namely, water/cementitious materials ratio (0.38, 0.43, and 0.48), cementitious materials content (350, 375, and 400 kg/m 3 ), and ine/total aggregate ratio (0.35, 0.40, and 0.45). he experimental data were utilized to carry out analysis of variance (ANOVA) and to develop a polynomial regression model for compressive strength in terms of the three design factors considered in this study. he developed statistical model was used to show how optimization of concrete mixtures can be carried out with diferent possible options. 1. Introduction Optimization of the concrete mixture design is a process of search for a mixture for which the sum of the costs of the ingredients is lowest, yet satisfying the required performance of concrete, such as workability strength and durability. he basic ingredients of concrete can be classiied into two groups: cement paste and aggregates. Although the quality of cement paste is governed mainly by the water/cement ratio, the quantity of cement paste required to achieve a targeted quality of concrete depends on the characteristics of aggregates. hese characteristics mainly include surface area and voids in aggregates. While surface area is governed by the shape and maximum size of aggregates, the void content is afected mainly by the particle size distribution of aggregates. he requirement of the paste can be reduced by reducing the void content of aggregates through proper packing of the aggregates [1–5] and also by increasing the aggregate/cement ratio [6]. Goltermann et al. [1] have suggested a packing model for the aggregate selection and combination to obtain aggregate mixes having the lowest void contents with maxi- mum packing degree (the ratio between bulk density and the aggregate grain density). hus, the packing degree according to them is a characteristic of the speciic aggregate type or mix and it indicates the void volume and the amount of cement paste necessary in the concrete. his indicates that a concrete mixture design can be optimized by adjusting the levels of the key mixture factors such as water to cementitious materials ratio, coarse aggregate to total aggregate ratio, and cementitious material content or aggregate to cementitious materials ratio as reported by various researchers [7–12]. Attempts have been made in the past to optimize the concrete mixture design using either the fully experimental methods or fully analytical methods or semiexperimen- tal (half-analytical) methods or statistical methods. Fully experimental methods involve an extensive series of tests, sometimes conducted on a trial-and-error basis, and the optimization results are oten applicable only to a narrow range of local materials [13, 14]. In order to reduce the number of trial mixtures required to obtain an optimal mixture, eforts have been made towards developing analyti- cal methods rationalizing the initial mixture proportioning into a more logical and systematic process [15]. Analytical methods help in searching for an optimum concrete mixture based on detailed knowledge of speciic weights of mixture components and on certain basic formulas, which result from Hindawi Publishing Corporation e Scientific World Journal Volume 2014, Article ID 561539, 7 pages http://dx.doi.org/10.1155/2014/561539