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Materials and Manufacturing Processes, 22: 333 336, 2007 Copyright Taylor & Francis Group, LLC ISSN: 1042-6914 print/1532-2475 online DOI: 10.1080/10426910701190352 Prediction of Portland Cement Strength Using Statistical Methods P. E. García-Casillas 1, C. A. Martinez 1, H. Camacho Montes 1, and A. García-Luna 2 1 Instituto de Ingeniería y Tecnología, Universidad Autónoma de Cd. Juárez, Juárez Chih, México 2 Departamento de Investigación y Desarrollo, Cd. Chihuaha Chih, México The Portland cement strength is the most important mechanical property that should be tested for quality control. Because 28 days represents a very long period for the cement industry, a faster determination of the cement strength represents a favorable research objective of the recent research in the cement industry. In the present work, a mathematical model for the prediction of cement strength is developed based on a standard specifications for Portland cement: chemical-mineralogical synthesis of the cement (%C 3 S, %C 2 S, %C 3 A, %C 4 AF), fineness by air permeability apparatus, lime saturation factor (LSF), particle size distribution, position parameter, and uniform factor. The strength values predicted were validated with consistently high accuracy, based on a linear regression of selected physical and chemical characteristics routinely obtained in the cement laboratory. The maximum errors were 4.54%, 2.66%, and 4.86% at 3, 7, and 28 days, respectively. The proposed model provides the opportunity to predict the compressive strength in a very short time and this will save cost and make a competitive advantage in the Portland Cement production market. Keywords Alite; ASTMC109; Belite; Cement industry; Chemical-mineralogical synthesis; Clinker; Compressive strength; Dicalcium silicate; Mathematical model; Portland cement; Quantitative X-ray diffraction analyses; Statistical methods; Tetracalcium aluminoferrite; Tricalcium aluminate; Tricalcium silicate. 1. Introduction Vital interest to the cement chemistry are the factors that affect the cement s strength performance in concrete. In general, these include: 1) Changes in phase chemistry; 2) Changes in clinker burning condition; 3) Changes in clinker cooling condition; 4) Cement fineness and particle size distribution; 5) Alkali levels and weather alkali salts are water soluble; 6) Skill of laboratory personnel. Although this list is not complete, many of the factors are considered in the tests made in the modern cement plant laboratory under ASTM C114 to meet the requirements of ASTM C150. The methods for establishing the test values can vary widely, phase chemistry can be calculated from an oxide analysis, or measured directly by quantitative X-ray diffraction analyses. The results are often somewhat different, raising the question of which method yields the most accurate response. There are two methods for the faster determination of cement strength: the accelerated strength test methods [1] and the use of suitable mathematical models [2 5]. A fundamental question is how to predict the strength performance of these cementations systems based on data from the cement manufacturing process. Answering this question is the objective of the investigation reported here in. Received January 16, 2006; Accepted September 11, 2006 Address correspondence to P. E. García Casillas, Instituto de Ingeniería y Tecnología, Universidad Autónoma de Cd. Juárez, Ave. del Charro # 610, C.P. 32250, Cd. Juárez Chih., México; E-mail: pegarcia@uacj.mx and perlaelviagarcia@yahoo.com 333 Generally, it is known in the cement industry which cement characteristics (such as C3S and Blaine fineness) affect the strength, but may not know how these characteristics change with cement type or manufacturer. A value can be assigned to the Compositional changes in the chemistry of cement. If a quantitative choice can be made of the most economic set of characteristics required to make a change in strength performance, more cost effective cements can be produced. The advantages in competitive market situation are obvious and may well favor one process over another. Accordingly to current state of the art literature physical and chemical data about cement has been produced in a massive amount, but the chemistry must wait until the mortar cube strengths are obtained in period of 28 days in accordance with ASTM C109(1). 2. Experimental A lineal regression model was chosen to explain the fundamental relationship between strength performances and cement characteristics. The cement used was ordinary Portland cement, having a 28-day compressive strength of 40 MPa. The data used for the development of the strength model and the standard test method are given in Tables 1 and 2, respectively, which present the chemical-mineralogical data and the data concerning the fineness of the cement, respectively. 3. Result and discussion The following series of variables have been tested in order to certify their effect on the cement strength: A) Chemical-mineralogical variables: Percentage content of C 3 S, C 2 S, C 3 A, C 4 AF, Na 2 O, SO 3 fcao, values of C 3 A/C 4 AF, C 3 S/C 2 S, lime saturation factor (LSF) (%), alumina ratio;

334 P. E. GARCÍA-CASILLAS ET AL. Table 1. Variables of the 10 samples of Portland cement. Sample C 3 S/C 2 S C 3 A/C 4 AF LSF (%) S b (cm 2 /g) P p µm P 80 µm <3 µm 3 32 µm 3 16 µm 16 24 µm 1 7.96 0.77 111.9 4060 15.44 24.69 28.28 59.80 38.41 12.45 2 7.51 0.75 112.3 4075 15.57 25.62 27.21 59.02 38.09 12.81 3 6.35 0.79 113.7 4296 15.57 24.99 28.65 58.80 37.24 12.87 4 6.00 0.79 114.4 4186 15.59 25.50 28.42 58.63 37.61 12.12 5 6.23 0.79 113.9 4163 15.78 25.83 28.20 57.84 37.02 12.65 6 5.93 0.76 114.4 4163 15.52 25.24 27.60 59.36 38.19 12.70 7 6.35 0.76 113.7 4058 15.65 25.50 28.21 58.45 37.43 12.56 8 5.95 0.79 114.5 4097 15.94 25.87 29.05 56.95 36.62 12.19 9 6.56 0.79 113.3 4128 15.99 25.79 29.16 56.76 36.61 12.21 10 7.22 0.75 112.6 4098 15.54 26.12 27.06 58.87 37.30 13.10 B) Particle size distribution variables: Specific surface S b position parameter P p 80% passing size P 80, uniformity factor n; C) Size fractions variables: Percentage content in <3 µm, 3 32 µm, 31 µm, 3 16 µm, and 16 24 µm. The selection of the variables that contribute to the prediction of the cement strength is based on stepwise regression analysis. In Fig. 1, the variables that are inserted in mathematical models by this statistical procedure are illustrated. It must be noticed that, in case of strongly correlated parameters, the effect of each one on the development of cement strength cannot be drawn from this figure. The stepwise regression analysis of the data presented in Table 1 leads to Eq. (1): A = B C (1) where Strength at 3 days S 3 A = Strength at 7 days S 7 Strength at 28 days S 28 C3S/C2S C3A/C4AF LSF % S b cm 2 /g C = P p µm P 80 µm <3µm 3 32 µm 3 16 µm 16 24 µm Figure 1. Selected variables by stepwise regression analysis for the prediction of cement strength (dark blocks are variables that contribute to the cement strength). 0 00 0 00 0 00 X 4 0 00 X 6 0 00 X 8 X 9 X 10 B = Y 1 0 00 Y 3 0 00 Y 5 Y 6 Y 7 0 00 0 00 0 00 Z 1 Z 2 Z 3 0 00 Z 5 Z 6 Z 7 Z 8 0 00 Z 10 Eq. (1) result in: S 3 = 0 0826S b 127P 80 + 30 377 %3 32 µm 49 91 %3 16 µm + 27 509 %16 24 µm (2) S 7 = 0 3 C 3S C 2 S 9 04LSF + 123 04pp 32 59P 80 6 85 % < 3µm (3) Table 2. Test method for Portland cement. Variable Test method Description Tricalcium silicate (C3S) ASTM-C150 Standard specification for Portland cement Dicalcium silicate (C2S) Tricalcium aluminate (C3A) Tetracalcium alulminoferrite (C4AF) LSF(%) ASTM-C114 Standard test methods for chemical analysis of hydraulic cement S b (cm 2 /g) ASTM-C204 Standard test method for fineness of hydraulic cement by air permeability apparatus <3µ 3 32 µ 3 16 µ 16 24 µm Laser diffraction Distribution particle size

PREDICTION OF PORTLAND CEMENT STRENGTH 335 Figure 2. Predicted vs. measured strength of Portland cement. S 28 = 164 2 C 3S C 2 S + 1054 7 C 3A 132 9LSF + 444 3pp C 4 AF + 67 87P 80 + 1 69 % < 3µm + 128 07 %3 32 µm 34 68 %16 24 µm (4) The measured and predicted strength values are presented in Fig. 2. The average difference between measured and predicted strength are 4.53%, 3.65%, and 4.86% or more specifically, 11.69, 12.28, and 19.87 k/cm 2 for the models 2, 3, and 4, respectively. In order to investigate the fitting quality of the multiple regression models 2, 3, and 4 in the data set, the statistic Figure 3. Compressive cement strength vs. predicted cement strength at 3, 7, and 28 days. multiple coefficient of determination R 2 (R square) was determined. The R 2 is 0.9989, 0.9975, and 0.9979 for the models 2, 3, and 4, respectively. This R 2 values mean that 99.8% of the derivation squares sum in the measured strength values about their mean is attributable to the leastsquares prediction equations indicating which that S 3 model best fit the data. In Fig. 3, the values of cement strength after 3, 7, and 28 days vs. predicted values are presented. Therefore the simulation of the strength development is very satisfactory. From the relations 2, 3, and 4, it is obvious that the fineness of the cement is the significant factor for the strength after 3 days. More specifically, the particle fractions (3, 3 16, and 16 24 µm have a positive effect on the strength while the fraction 24 32 µm has a negative one. In addition, the increase of the specific surface and P 80 of the cement leads to higher strength values. The cement strength after 7 days is affected by the ratios C3S/C2S and the LSF value as well as by the characteristics of the particle size distribution P p and P 80. The fraction with size less than 3 µm lowers the strength value as it was expected. The 28 day strength is affected by the LSF value and the ratios C3S/C2S and C3A/C4AF. Besides it is observed that the fraction 16 24 µm has a positive effect while the fractions 3, 3 16 and 24 32 µm have a negative one. It must be noticed that it is not possible to extract conclusions concerning the individual contribution of the C3S/C2S, C3A/C4AF, and LSF values on the strength as these variables are strongly correlated.

336 P. E. GARCÍA-CASILLAS ET AL. The models described by Eqs. (2) (4) have been tested for the prediction of the strength of cements produced by the Mexican companies and the results were very satisfactory. 4. Conclusion The following conclusions can be drawn from the present study: 1. A mathematical model for the prediction of the 3, 7, and 28 day compressive strength of the cement is developed based on stepwise regression analysis; 2. The proposed model predicts the cement strength with a satisfactory accuracy. At early ages the strength is affected mainly by the fineness parameters; 3. At later ages, the chemical-mineralogical synthesis of the cement influences the strength growth; 4. The 28 days strength is strongly affected by the distribution of the cement particles in the size fractions <3 µm, 3 16 µm, 16 24 µm, and 24 32 µm. Specifically the 16 24 µm fraction is the only one which has a positive effect on the strength development. References 1. Akkurth, S.; Tayful, G.; Can, S. Fuzzy logic model for the prediciton of cement compressive strength. Cem. Concr. Ress. 2004, 34, 1429 1433. 2. Barnett, S.J.; Soutsos, M.M.; Millard, S.G.; Bungey, J.H. Strength development of mortars containin ground granulated blast furance slag. Cem. Concr. Ress. 2006, 36, 434 440. 3. American Standards Test Methods Book, Cement and Gypsum, Section 4, 2004. 4. Bhanja, S.; Sengupta, B. Investigation on the compressive strength of silica fume concrete using statistical methods, Cem. Concr. Ress. 2002, 32, 1391 1394. 5. Zelic, J.; Rusic, D.; Krstulovic, R. A mathematical model for prediction of compresive strength in cement silica fume blends. Cem. Concr. Ress. 2004, 34, 2319 2328. 6. Baykasoglu, A.; Dereli, T.; Tanis, S. Prediciton of cement strength using soft computing techniques 2004, 32, 2083 2090. 7. Akkurt, S.; Ozdemir, S.; Tayfur, G.; Akyol, B. The use of GA-ANNs in the modelling of compressive strength of cement mortar. Cem. Concr. Ress. 2003, 33, 973 979.