Mix Proportioning of High Performance Self-Compacting Concrete using Response Surface Methodology

High performance self compacting concrete (HPSCC) is typically proportioned with mineral and chemical admixtures leading to relatively high material cost. Such cost can be tolerated in high value added applications specially when cost savings can be realized using HPSCC in terms of reduction in size of reinforced concrete members. Efforts are still needed to reduce material cost of HPSCC to gain wider acceptance in variety of applications. Proper material selection and sound mixture proportioning can achieve this [1]. The derived statistical Response Surface Methodology (RSM) is targeted to develop cost effective HPSCC mixtures [2]. RSM can be used effectively in analyzing the cause and effect of the process parameters on response. This paper presents an experimental program in which RSM are employed to optimize a four-component concrete containing fly-ash subjected to six performances criteria. The four key mixture constituents used in the models included cement, fly-ash, and high range water reducer and water binder ratio. The modeled response that included were the compaction factor, compressive strength, split tensile strength and flexural strength at 28 days. The anticipated responses are not expected to vary in linear manner with selected variables; a central composite plan was selected to enable the model of any response in a quadratic manner. Therefore each of the four selected mixture constituents is studied in five distinct levels corresponding to codified value-2,-1,0,1,2.A total of 31 mixture combinations were used in the experimental design which consisted initially of a matrix 2 4 (=16) factorial design plus seven central points and eight star points. The derived models are valid for a wide range of mixtures with ranges of water binder ratio of 0.28-0.44, cement content of 400 to 600 kg/m 3 , fly-ash 0 to 10% (by weight of mass cement and HRWR dosage of 1 to 3% (by weight of mass cement). INTRODUCTION The proportioning of concrete mixture is a process by which one arrives at the right combination of cement, aggregates, water and admixtures for making concrete according to the given specifications. The purpose of mix proportioning is to obtain a product that will perform according to certain predetermined requirements [3], the most essential requirements being the workability of fresh concrete and the strength and durability of the hardened concrete. Another purpose of mix proportioning is to obtain a concrete mixture satisfying the performance requirements at the lowest possible cost by selecting available materials. The partial replacement of binder by fly-ash results in the reduction of heat of hydration without any reduction in strength [4]. The aim of mix proportioning exercise is to achieve a set of critical properties at optimum cost and to enhance the performance of concrete for non-critical properties [5]. Mix proportioning is not unique, because all parameters are not practically measurable and are not amendable to mathematical manipulation. *Address correspondence to this author at the Kongu Nadu College of Engineering and Technology, No 19/33, GVK Building, 10 Avenue, Ashok Nagar, Chennai -600083, Tamilnadu, India; Tel: 044-24719792; Mobile: +919600033717; Tel/Fax: 044-2471843; E-mails: [email protected],[email protected] Mixture proportion selection for HPSCC is often best handled by using systematic optimization processes and methods of experimental design [3]. An attempt has been made in this experimental investigation to formulate a procedure for mix proportioning of HPSCC using a statistical method called RSM [6]. RSM is a set of techniques that encompasses: • Designing of a set of experiments for adequate and reliable measurement of the true mean response. • Determining the mathematical model with best fit. • Finding the optimum set of experimental factors that produces maximum and minimum value of the response. • Representing the direct and interactive effect of the process parameters. RESEARCH OBJECTIVES AND SCOPE This paper presents and examines the mix proportioning of HPSCC using RSM technique. • To optimize the HPSCC mixture proportions. • Development of mathematical model for desired properties of concrete strength like compressive, tensile, flexural and workability in terms of process control parameters. • To study the influence of process parameters on responses. 94 The Open Civil Engineering Journal, 2009, Volume 3 Murali and Kandasamy • Total percentage of deviations between the observed values and the values computed from the models. • Relation between the process control parameters and responses. EXPERIMENTAL DESIGN Materials Ordinary Portland cement of 53 grade as per IS 12269, obtained from a local cement-manufacturing factory having a specific gravity of 3.15 was used. Locally available river sand confined to IS 383-1970 having fineness modulus of 2.6 and specific gravity of 2.68 and locally available blue granite as per IS 383-1970 passing through 16mm sieve with a specific gravity 2.6 and fineness modulus of 5.65 was used. Flay-ash contains extremely fine amorphous particles of SiO2.The specific gravity and bulk density of fly-ash used is 2.2 and 280kg/m 3 . The superplasticizer used in this study is CONPLAST -SP337 (SNF) of specific gravity 1.2. Identification of Process Control Parameter Process control parameters listed in Table 1 Variables 1. Binder (Kg/m 3 ) B 2. Water -Binder ration (No Unit) W/B 3. Fly Ash (percentage) F 4. Superplasticizer (percentage) S Constants 1. Fine Aggregates -660-720 Kg/m 3 2. Coarse Aggregates -1100Kg/m 3 Finding the Limits of the Process Control Variables The working range was decided based upon the strength aspects of HPSCC. The coded forms of process control parameters were found by fixing the values for central parameter (0), maximum (+2) and minimum (-2) value of the variable. The coded values being calculated from the following relationships. Xi = 2[2X (Xmax + Xmin)] / (Xmax Xmin) Where, Xi = Required coded value of a variable X X = Any value of the variable form Xmin to Xmax The conversions between coded and absolute values can be calculated as follows Coded B = AbsoulteB 500 45 Coded W/B = AbsoulteW / B 0.36 0.04 Coded F = AbsoulteF 5.0 2.5 Coded S = AbsoulteS 2 0.5 Developing the Design Matrix The design matrix was developed using the software called SYSTAT 10.2. This software increases analytical power with more statistics by delivering extensive list of algorithms. It also visualizes the data provided with more graphing capabilities. SYSTAT 10.2 offers a large variety of scientific and technical graphs for a desktop statistics package. The selected design matrix shown in Table 2 is a central composite rotatable factorial design consisting of 31 set of coded values. It comprises of a full replication of 2 4 (=16) factorial design plus seen center points and eight star points. All the variables at the intermediate level (0) constitute the highest (+2) level with other three variables at the intermediate levels constitutes the star points. Thus the 31 experimental run allowed the estimation of the linear, quadratic and two-way interactive effect of the process parameters. Recording of Responses The ingredients for the various mixtures were weighed and mixing was carried out using pan type concrete mixer. Precautions were taken to ensure uniform mixing of ingredients. The specimen were cast in steel moulds and compacted on a table vibrator. 100 mm cube specimens were cast for the determination of compressive strength at 28 days. 100x100x500 mm beam specimens and 100mm diameter x 200mm long cylinder specimens were cast for the determination of flexural and split tensile strength at 28 days respectively. Curing of specimen was started as soon as the top surface of the concrete in the mould was stiff (hard) enough. Spreading wet gunny bag over the moulds carried out for the initial curing. 24 hours after the casting the specimen were demoulded and placed immediately in water tank for further Table 1. Process Control Parameters under Limits Limits Parameters Units Notations -2 -1 0 1 2 Binder Kg/m B 400 450 500 550 600 Water Binder ratio No unit W/B 0.28 0.32 0.36 0.40 0.44 Fly-Ash % F 0 2.50 5.002. 7.50 10.0 Super Plasticizer % S 1.00 1.50 00 2.50 3.00 Mix Proportioning of High Performance Self-Compacting Concrete The Open Civil Engineering Journal, 2009, Volume 3 95 curing. Compaction factor test were carried out as per the IS specification to find the workability of concrete. Development of Mathematical Model The response function representing any of the recorded responses of HPSCC can be expressed Y = f (B, W/B, F, S) The relationship selected being a second-degree response surface expressed as follows Y = b0+b1B+b2 F/B +b3F+b4 S+b11 B2 +b22 W/B. W/B +b33 F.F +b44 S.S+b12 B. W/B +b13 B.F +b14 B.S +b23 W/B.F +b24 W/B.S +b34 F.S Table 2. Design Matrix in Coded Form and Observed Values of the Responses Mix Design Matrix in Coded Form Measured Responses No. B W/B F S C T F X 1 -1 -1 -1 -1 69.91 4.750 7.84 0.89 2 1 -1 -1 -1 77.63 6.465 8.77 0.86 3 -1 1 -1 -1 65.20 4.756 7.68 0.92 4 1 1 -1 -1 72.51 5.980 7.75 0.89 5 -1 -1 1 -1 80.92 6.570 8.452 0.86 6 1 -1 1 -1 87.24 6.820 8.46 0.83 7 -1 1 1 -1 74.14 6.350 8.618 0.89 8 1 1 1 -1 75.42 6.370 8.194 0.86 9 -1 -1 -1 1 71.73 6.250 7.940 0.92 10 1 1 -1 1 80.14 8.530 8.50 0.89 11 -1 1 -1 1 70.81 4.720 7.69 0.94 12 1 1 -1 1 73.84 6.300 7.90 0.92 13 -1 -1 1 1 81.32 6.620 8.83 0.89 14 1 -1 1 1 94.14 7.020 8.92 0.86 15 -1 1 1 1 75.93 5.480 8.22 0.92 16 1 1 1 1 79.20 6.530 9.34 0.89 17 -2 0 0 0 65.30 4.280 6.33 0.90 18 2 0 0 0 73.71 7.240 8.93 0.83 19 0 -2 0 0 72.40 6.300 8.05 0.83 20 0 2 0 0 67.26 5.120 7.26 0.92 21 0 0 -2 0 63.55 4.310 7.86 0.86 22 0 0 2 0 74.63 5.400 8.01 0.84 23 0 0 0 -2 72.52 4.400 8.46 0.83 24 0 0 0 2 71.70 4.880 7.8 0.88 25 0 0 0 0 69.00 4.460 7.53 0.867 26 0 0 0 0 68.20 5.680 6.98 0.85 27 0 0 0 0 69.10 5.640 7.90 0.87 28 0 0 0 0 68.90 5.060 7.63 0.86 29 0 0 0 0 68.15 5.720 7.00 0.79 30 0 0 0 0 68.84 5.930 7.24 0.86 31 0 0 0 0 68.32 5.710 7.72 0.79 CCompressive Strength in N/mm T= Tensile strength in N/mm F Flexural Strength in N/mm W= Workability (CF). 96 The Open Civil Engineering Journal, 2009, Volume 3 Murali and Kandasamy The values of the coefficients were calculated by regression analysis using SYSTAT 10.2 software. Final Mathematical Model The values of the regression coefficient give an idea as to what extent the control variables affect the responses quantitatively. In significance coefficient using student t-test can be dropped along with responses to which they are associated without affecting much of the accuracy of the model. As per this test, when the calculated value of t corresponding to a coefficient exceeds the standard tabulated value for the desired level of confidence (say 95%) the coefficient becomes significant. The significant regression coefficient tabulated in Table 3 was recalculated and the final models were developed using only these significant coefficients are given below. The final models for the various responses as determined by the above analysis are represented below. C = 68.630+2.791B-2.761W/B+3.696F+1.343B.B+1.424W/ B.W/B+1.239 F.F +1.994 S.S 1.274B.W/B 1.367 W/B.F T = 5.431+0.6.2 B 0.371 W/B +0.258 F + 0.181 S + 0.242 B.B + 0.229 W/B.W/B 0.317 B.F 0.265 W/B.S 0.269 F.S F = 7.429 + 0.323B 0.162 W/B + 0.220F +0.131 B.B + 0.137B.B +0.137 W/B.W/B + 0.206 F.F + 0.256 S.S W = 0.841-0.015B+0.017 W/B 0.011 D + 0.014 S + 0.011 B.B + 0.013 W/B.W/B + 0.007 F.F +0.008 S.S The validity of the above equation can be judged from the coefficient of determination Table 3 between the experimental values and calculated values obtained from the response surface equation. The mathematical model furnished above can be used to predict the proportions of HPSCC mix constituents by substituting the value in coded form, of the respective factors. RESULTS AND DISCUSSIONS Effect of Fly-Ash on the Fresh Properties of Concrete The water demand of concrete containing fly-ash increases with increasing amount of fly-ash. The increase is primarily due to the high surface area of the fly-ash. Fresh concrete containing fly-ash is more cohesive and less prone to segregation. As the fly-ash content increased, the concrete may appear to become sticky. Concrete containing fly-ash normally does not segregate appreciably because of the fineness of the fly-ash and the use of HRWRA. Concrete containing fly-ash shows significantly reduced bleeding. This effect is primarily by the high surface area of the fly-ash to be wetted; there is very little water left in the mixture for bleeding. The colors of the fresh and hardened concretes containing fly-ash are generally darker than the conventional concrete. From Table 2 it was found that the optimum replacement of fly-ash for getting strength of 90Mpa is 7.5%. As the compressive strength increases, the tensile and flexural strength of the concrete also increases but at a gradually decreasing rate. Table 3. Estimated Values of Coefficients of the Models Coefficient Compressive Strength in 28 days N/mm 2 R 2 =0.75 Tensile Strength in 28 days N/mm 2 R 2 =0.60 Flexural Strength in 28 days N/mm 2 R 2 =0.60 Workability C.F R 2 =0.70 b0 Mean 68.630 5.431 7.429 0.841 b1 B 2.791 0.602 0.323 -0.015 b3 W/B -2.761 -0.371 -0.162 0.017 b4 F 3.696 0.258 0.220 -0.011