Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 196 A STATITICAL MODEL FOR PREDICTIN AUTO-CLAVE EXPANSION OF PORTLAND CEMENT Dr. Mahdi S. Essa Al-Saegh Asst. Prof./Department of Civil Eng. College of Engineering/University of Babylon Abstract: The present study aims aimed to investigate factors affecting the soundness of Portland cement (in terms of autoclave expansion test). These factors are C3S, C2S, C3A, C4AF, fineness (in terms of specific surface measured by Blaine method), the minor oxides MgO, free CaO, SO3, and the variables obtained from the chemical analysis of cement like silica modulus (SM), alumina ratio (AR), loss on ignition (LOI), insoluble residue (IR), and lime saturation factor (LSF). The autoclave expansion prediction models were built by using multiple linear regression analysis and based on (40) different cement samples taken from (7) different Iraqi cement factories, Indian cement, and Kuwaiti cement. (29) of the samples were ordinary Portland cement while the other (11) samples were sulphate resisting Portland cement. It was found that the multiple linear regression is very suitable for predicting the autoclave expansion of Portland cement. It was also found that the increase of fineness of cement, LSF, and LOI decreases the autoclave expansion, while the increase in the other factors increases the autoclave expansion. The correlation coefficients of the proposed models were (0.71002 and 0.98338) for the first model, (0.84366 and 0.98789) for the second model, and (0.85593 and 0.98872) for the third model, with and without intercept respectively. Key words: soundness of cement, autoclave test, Portland cement, expansion, oxides of cement. التمدد في فحص المحمم البخاري للسمنت البورتالندي موديل إحصائي للتنبؤ بمقدار :خالصةال للسمنت )بخاريمعبرَا عنه بطريقة المحمم ال(فحص الثبات ي تؤثر على الدراسة الحالية تهدف إلى تحري العوامل الت بطريقةبالمساحة السطحية النوعية المقاسة معبرًا عنها (النعومة ، (C3S, C2S, C3A, C4AF) هي العوامل هذه. البورتالندي (Blaine االآاسيد الثانوية ،MgO الجير الحر،free CaO ،SO3 عليها من التحليل الكيميائي للسمنت لحصوليتم ا، والمتغيرات التي ، ومعامل اإلشباع الجيري (IR) المخلفات غير الذائبة ،(LOI)الفقدان أثناء اإليقاد ،(AR)، نسبة االلومينا (SM)مثل معامل السليكا (LSF).من عينات السمنت ) 40 ( علىمستند و الخطي المتعدد باستخدام تحليل االنحدارت بني التمدد بطريقة المحممذج تخمينا إن نم من العينات آانت سمنت بورتالندي ) 29. (سمنت هندي، و سمنت آويتي معامل سمنت عراقية مختلفة،) 7(المختلفة مأخوذة من مين لقد وجد ان االنحدار الخطي المتعدد مالئم جدًا لتخ. آانت سمنت بورتالندي مقاوم للكبريتاتاألخرىعينة ) 11(اعتيادي بينما الـ الفقدان أثناء ، (LSF)ومعامل اإلشباع الجيري آذلك وجد ان الزيادة في نعومة السمنت،. تمدد السمنت البورتالندي بطريقة المحمم معامل االرتباط للنماذج . تقلل التمدد بطريقة المحمم، بينما الزيادة في العوامل االخرى تزيد التمدد بطريقة المحممLOI)(اإليقاد ) 0.98872 و 0.85593(للنموذج الثاني، و) 0,98789 و0,84366 (للنموذج االول،) 0,98338 و 0,71002(ن المقترحة آا .ثابت التناسب على الترتيب بوجود وعدم وجود للنموذج الثالث، Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 197 Introduction: It is essential that cement paste does not undergo a large change in volume. In particular, there must be no appreciable expansion which, under conditions of restraint, could result in a disruption of the hardened cement paste. Such expansion may take place due to the delayed or slow hydration, or other reaction of some compounds present in the hardened cement, namely free lime , magnesia, and calcium sulfate (Neville 1995 p.51). The testing of the soundness of cements, so as to ensure that no material showing such a subsequent expansion shall be used, has always therefore been considered of prime importance (Lea 1976 p.366). Research Significance: It is developing a statistical model for predicting the Autoclave Expansion that comprises most chemical factors and fineness of cement which affect this property. Such model help to assess the degree of Soundness of cement which a very substantial aspect of durability if the elaborate Autoclave test is unavailable. Literature Review: The autoclave expansion test described by ASTM C151 is used to detect soundness of neat cement paste. In this test a bar of 25 mm (1 in) square in cross section and with 250 mm (10 in) gauge length, is cured in humid air for 24 hours. The bar is then subjected to accelerated conditions (a steam pressure of about 2±0.07 MPa. (295 psi) and a temperature of 216˚C (240˚F)) for 3 hours. The expansion of the bar due to autoclaving must not exceed 0.8 per cent. The high steam pressure accelerates the hydration of both magnesia and lime (Neville 1995 p.53). MgO and free lime are the effective components in cement that can cause delayed expansion. This expansion is due to the formation of Ca(OH)2 and Mg(OH)2 upon hydration of free CaO and MgO respectively. Unsoundness due to the presence of free lime may arise from an over-limed mix, inadequate burning, or insufficiently fine grinding and mixing of the raw materials fed to the kiln (Lea 1976 p.368). On the other hand, lime added to cement does not produce unsoundness because it hydrates rapidly before the past has set (Neville 1995 p.51). The reactivity of MgO depends on rate of cooling of clinker. Neville (1995 p.52) stated that only periclase is deleteriously reactive, and MgO present in glass is harmless. Up to about 2% of periclase (by mass of cement) combines with the main cement compounds, but excess periclase generally causes expansion and leads to slow disruption. Lea (1976 p.369-370) reported that clinkers that are cooled rapidly can carry more magnesia safely than slowly cooled clinkers. Cements with as much as 5 per cent magnesia will pass the autoclave test if quickly cooled, and the free lime is low. In slowly cooled clinkers, failure to pass the autoclave test may occur with magnesia content of 3 per cent. The quicker the clinker is cooled the smaller will be the periclase crystallization of the liquid. In addition, MgO content can be made up of magnesia held in solid solution in other clinker compounds or as small crystallization of the clinker liquid. The extent to which the periclase crystals may themselves have impurities in solid solution also appears to influence their speed of hydration. The correlation between autoclave expansion and the (MgO + free CaO) content in cement is not strong enough to attribute such expansion entirely to the amount of MgO and free lime in cement. This means that there are other factors that affect autoclave expansion (Abdul-Latif 2001). The third compound liable to cause expansion is calcium sulfate. This expansion is attributed to the formation of calcium sulphoaluminate. This is harmless when formed in small amounts during the setting of cement, but if large amount of gypsum are present, such that formation of the sulphoaluminate salt continues Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 198 after setting and hardening, expansion occurs. The maximum amount of gypsum that can safely be added is thus related to the ability of the cement to combine with it during the setting, or very early hardening period (Lea 1976 p.370). A study by Abdul-Latif (2001) showed that the autoclave expansion at first decreased as the SO3 content increased, while at higher SO3 contents there was an increase in expansion. He attributed the reduction in autoclave expansion to the formation of monosulfate phase. When SO3 is insufficient to allow C3A and C4AF to react completely to form ettringite, the hydration product of these components (i.e. C4AH13) reacts with ettringite under the autoclave test conditions. He suggested that such reaction leads to a decrease, rather than an increase, in solid volume. However, the results obtained by Al-Jabiri (2002) contradict this interpretation, she stated that an increase in SO3 content at low percentage of MgO (originally in cement) does not lead to a significant expansion in the autoclave test for cement paste when either O.P.C. or S.R.P.C. are used. In contrast, there is a tendency for a decrease of expansion with increasing SO3 content in cement even at high percentages of SO3. She, also, reported that Lawrence (1995) in his study on the effect of cement composition on the delayed ettringite formation observed that MgO content has a significant effect on expansion including that due to ettringite formation. He suggested that the expansive hydration of MgO during the elevated temperature hydration or during room temperature water storage may increase the sensitivity of cement to heat curing by acting as an initiator for subsequent ettringite recrystallizion pressure generation and expansion. This interpretation can also be applicable to the results of the autoclave test at high MgO percentages. The C-S-H gel may play a role in the expansion process. The condition of the autoclave test may generate the adsorption of SO4-2 ions by C-S-H gel, which causes the decrease or no more expansion in cement pastes, Mg(OH)2 may increase the alkalinity of the solution which leads to an expansion in the rate of hydration. More etringite can be formed and more SO4-2 can be adsorbed in C-S-H gel that affects its structure and results in poor strength and then high expansion. A further factor that influences the expansion in the autoclave test, though it does not lead to long term expansion in practice, is the content of C3A. Lea (1976 p.370) showed that even when the magnesia and free lime are low, the autoclave expansion increases as the calculated content rises about 8 per cent in well crystallized clinker and may exceed the permitted limit at about 14-16 per cent. The iron compound , C4AF, has little effect. It is well known that the formation of ettringite as a result of the chemical reaction of gypsum and alumina phase associated with expansion. However, there is still some uncertainty as to precise mechanism. It has been suggested for example, that the solid stage conversion of C3A.13H to C4AS.12H is responsible for sulfate expansion, but the evidence points to the presence of 19H, and not 13H hydrate of C3A in set cement. The conversion of 19H hydrate would lead to a decrease, not an increase in solid volume. There is, also, little correlation between the amount of ettringite formed and the degree of expansion observed (Lea 1976 p.347-348). From this discussion, it is clear that it is difficult to ascribe expansions directly to increased volume of solid. Fineness of cement containing free CaO and MgO is the most interesting factor affecting the soundness of cement. As reported by Al-Jabiri (2002), Czenin in 1980 stated that little, but large, free lime particles in hardened paste will cause cracking and spalling, whereas, with increasing fine division of free lime the expansion will become less and more regular. He proved that by taking a neat cement prism with a high content of free lime 13 per cent and finely ground cement. The expansion which occurred was 20 per cent in length but without causing disintegration of the test specimen. The extremely fine distribution of the free lime prevent destruction of the prism. According to Lea (1976 p.369), Keil (1957) found that a content of 4 per cent periclase crystals below 5µ in size produced only about the same autoclave expansion as 1 per cent of crystals of 30µ-60 µ size. It will be apparent that expansion in the autoclave test is the integrated effect of a number of separated factors. The test gives, therefore, no more a broad indication of the risk of long-term Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 199 expansion in practice, it is not an exact guide and various anomalies are apparent in the available data (Neville 1995 p.53 and Lea 1976 p.370). Abdul-Latif (2001) proposed a statistical model for predicting autoclave expansion from MgO content, free lime content, C3A content, and fineness in terms of Blaine specific surface. This model was as follows: Auto. = 0.06811*Free CaO% + 0.04394*MgO% - 0.0000577*Blaine (cm2/gm) + 0.01943*C3A% .….eq.(1) This model is based on 35 observations. The correlation coefficient, standard error, and Fvalue are 0.812, 0.1023, and 14.965 respectively. Experimental Work: In this study, (40) different cement samples were tested, (29) of them were ordinary Portland cement while the other (11) samples were sulphate resisting Portland cement. Table (1) shows the cement sources and the type of their production with the number of samples taken from each factory. Tables (2) shows the chemical analysis and physical properties of the cements used in this study. And Tables (3) shows the chemical analysis and physical properties limits of the cements used in this study. The autoclave test was used to determine the unsoundness of the cement samples used throughout the present study. The results of this test were obtained from Consultant Engineering Bureau of University of Babylon, and it was accomplished according to the Iraqi standard specification (IQS No.5 : 1984). Model Development: The multiple linear regression analysis was used to build the present models. The general purpose of regression analysis is to learn more about the relationship between one or several independent or predictor variables and a dependent or criterion variable. The regression equation or the best-fitting line is determined by minimizing the sum of squares of the residuals between the actual and predicted values of the dependent variables (stat soft 2003). The various elements of the multiple linear regression equation can be illustrated from the general form of the following equation: Y = a0 + a1x1 + a2x2 +….+anxn Where: Y: the predicted value of the dependent variable. x1, x2,…, xn: the independent variables (predictors). a0: the intercept coefficient (constant). a1, a2,…, an: the partial regression coefficients of the independent variables. n: the number of independent variables included in regression equation. The statistical analysis was done with the aid of computer software STATISTICA version 6-2001. Three methods of regression were applied. They are: 1. Backward elimination. 2. Forward regression. 3. Standard method or all variables regression. To evaluate the proposed models, the following statistical factors are used: Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 200 Multiple R: The coefficient of multiple correlation is the positive square root of R-square (the coefficient of multiple determination). This statistical factor is useful in multivariate regression (i.e. multiple independent variables) when it is wanted to describe the relationship between the variables. R-square: This coefficient of multiple determination measures the reduction in the total variation of the dependent variable due to the (multiple) independent variables. R2 = 1 - [Residual SS/Total SS] Where: Residual SS: is the error sums of square. Total SS: is the total sums of square. The R-square value is an indicator of how well the model fits the data, R-square close to 1.0 indicates that it has accounted for almost all of the variability with the variables specified in the model. Adjusted R-square: The R-square is adjusted by dividing the error sum of squares and total sums of square by their respective degrees of freedom. adjusted R2 = 1 - [(Residual SS/dfr)/(Total SS/dft)] Std. Error of estimate: This statistic coefficient measures the dispersion of the observed values about the regression line. F-value: The F-value is used as a test of the relationship between the dependent variable and the set of independent variables. F = Regression Mean Square/Residual Mean Square. The range of difference (df) between the actual and predicted Autoclave expansion values was calculated for each model within confidence interval of 0.95. This means that there is a probability of 95% of difference between the actual and the predicted values falls within a range of ±df, thus, the actual values equals to predicted values ± df Independent Variables: The following variables are selected to be as the independent variables: 1. The four main compounds of Portland cement (i.e. C3S, C2S, C3A, and C4AF) which were calculated using Bogue`s equations. 2. The fineness of cement (in terms of Blaine specific surface). 3. Chemical analysis parameters (i.e. MgO, Free CaO, SO3, LOI, IR, and LSF). 4. Silica modulus and alumina ratio. Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 201 The Proposed Models: The following statistical models are obtained: 1. Model (1): In this model, backward stepwise method was applied. The final form of this model is as follows: With intercept: Auto. exp. = 0.09929 + 0.076702*MgO% ….eq.(2) R = 0.71002 R2 = 0.50412 adjusted R2 = 0.49107 S.E.= 0.064467 Fvalue = 38.63166 Without intercept: Auto. exp. = 0.061130*MgO% + 0.061591*SO3% ….eq.(3) R = 0.98338 R2 = 0.96704 adjusted R2 = 0.96530 S.E.= 0.06201 Fvalue = 557.4398 2. Model (2): Forward stepwise method was used in developing this model. The final form of this model is as follows: With intercept: Auto. exp. = 2.91305 + 0.06627*MgO% + 0.07888*IR% + 0.113195*SO3% - 2.96120*LSF% -0.02958*LOI% - 0.10252*SM - 0.00925*C2S% ..…eq.(4) R = 0.84366 R2 = 0.71176 adjusted R2 = 0.64871 S.E.= 0.05356 Fvalue = 11.28843 Without intercept: Auto. exp. = 0.05756*MgO% + 0.06185*IR% + 0.15899*SO3% - 1.38250*LSF% -0.01368*LOI% + 0.01482*C3S% + 0.09823*AR + 0.00700*C2S% ..…eq.(5) R = 0.98789 R2 = 0.97594 adjusted R2 = 0.96993 S.E.= 0.05774 Fvalue = 162.2572 3. Model (3): Standard method in which all possible factors are included in this model: With intercept: Auto. exp. = 3.07983 + 0.05393*MgO% + 0.12288*SO3% - 0.01306*FreeCaO% - 0.03444*LOI% + 0.07678*IR% - 3.28013*LSF% - 0.13571*SM + 0.00301* AR + 0.00757*C3S% - 0.00472* C2S% - 0.00272*C3A% - 0.01667* C4AF% - 0.00013*Blaine(m2/kg) ….eq.(6) R = 0.85593 R2 = 0.73261 adjusted R2 = 0.59892 S.E.= 0.05723 Fvalue = 5.47972 Without intercept: Auto. exp. = 0.06236*MgO% + 0.15717*SO3% + 0.04806*Free CaO% - 0.01037*LOI% + 0.04256*IR% - 1.84275*LSF% + 0.10076*SM + 0.07660* AR + 0.01478*C3S% + 0.00510* C2S%+ 0.01761*C3A% + 0.01648* C4AF% - 0.00038*Blaine(m2/kg) ….eq.(7) R = 0.98872 R2 = 0.97756 adjusted R2 = 0.96675 S.E.= 0.06071 Fvalue = 90.4699 Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 202 Comparison Between Models With and Without Intercept: As mentioned earlier, two models were developed for each method of regression (i.e. Backward stepwise (model (1)), Forward stepwise(model (2)), and standard method or all variables in model (model (3))) using the same data and the same independent variables, to prove that regression through the origin is more suitable for the data. The first model passes through the origin and the other had an intercept (a0) of 0.09929, 2.91305, and 3.07983 for the three method of regression respectively. Table (4) shows R, R2, adjusted R2, Fvalue, S.E., and df for the models with and without intercept. It is obvious that R, R2, adjusted R2, Fvalue, S.E., and df for models with intercept are less than that of models without intercept. It is decided that the models which pass through the origin (without intercept) are more suitable and recommended. Models Examination: Model examination was done for the models which pass through the origin (without intercept), which were found to be more suitable. The distribution of residuals is shown in Figure (1). From this figure it is clear that the residuals are almost normally distributed. It is also clear that the residuals gathered around zero. This indicates that there are no evidences that the models are inadequate, or there is an error in analysis. In Figure (2) the observed values of the autoclave expansion test are plotted against the predicted values. It is clear that the points roughly follow a straight line. This indicates that the models are appropriate for the data, and they are correctly specified. To check the validity of the proposed models to predict the autoclave expansion of cement, Two samples of Portland cement were tested. One of them is sulphate resisting Portland cement while the other is ordinary Portland cement. The details of these cements are given in Table (5). Table (6) gives the observed and predicted values of the autoclave expansion. From this table it is clear that the maximum difference between the observed and predicted values is about +0.07. Thus, it may be concluded that the present model is appropriate to predict the autoclave expansion with a good accuracy. Discussion: As mentioned earlier, the models which pass through the origin (without intercept) are more suitable and recommended. From these models the following points have been recorded: 1. It is obvious that the correlation coefficients, Fvalue, and the standard error of the three models are very close. 2. As explained earlier, fineness of cement is the most interesting factor affecting the soundness of cement. From the third model, it is clear that the autoclave expansion decreases with the increase in cement fineness. This result is in agreement with the results obtained by (Czenin 1980). 3. From the three models, it can be deduced that the increase in MgO and SO3 contents increase the autoclave expansion. The free CaO has the same effect but at a lesser degree. This result seems acceptable as they play a role in cement paste volume change as mentioned earlier. 4. As expected C3A and C4AF increase the autoclave expansion, this is obvious from the correlation coefficient in third model. This may be attributed to the fact that these two compounds cause expansion of cement paste as discussed earlier. This is online with what was demonstrated by Lea (1976 p.370). Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 203 5. On the basis of the present models, it is proven statistically that the autoclave expansion increases when the contents of C3S and C2S are increased. This behavior may be explained in the light of the fact that the hydration of silicates is associated with a volume increase. 6. Depending on the present models, The autoclave expansion increases with the increase in IR (Insoluble Residual) content. IR is defined the amount of amorphuse silica present in the clay minerals of the raw materials used in cement manufacture (since this silica is not soluble in hydrochloric acid unlike most of cement constituents). In addition, IR gives an indication on the efficiency of the burning process. On the basis of this discussion the effect of IR seems reasonable. 7. It is clear that LOI negatively affects the autoclave expansion. This behavior seems acceptable as LOI refers to the extent of carbonation and hydration of free magnesia due to the exposure of cement to the atmosphere (Neville 1995 p.11). 8. The appearance of AR and SM as positive factors to autoclave expansion in the present models may be explained as alumina and iron oxides are the main fluxes in cement burning process. When the content of them are low the amount of liquid formed at clinkering temperature becomes insufficient to permit sufficiently rapid combination of the remaining CaO (Lea 1976 p.135). 9. Lime saturation factor LSF appears as a negative factor in the second and the third models. This seems reasonable as lime saturation factor represents the factors obtained by equation (8). The increase in (Al2O3 and Fe2O3) results in a decrease in LSF and subsequently in an increase in the autoclave expansion. ( ) )8.....( 0.65Fe2O3) 1.2Al2O3 (2.8SiO2 0.7SO3 CaO LSF ++ − = Conclusion: 1. The multiple linear regression is found to be very suitable for predicting the autoclave expansion of Portland cement. 2. It is found that the models which pass through the origin (without intercept) are more suitable and recommended. 3. The increase in MgO and SO3 contents increases the autoclave expansion. The free CaO has the same effect but at a lesser degree. 4. The increase in fineness of cement, LSF, and LOI decreases the autoclave expansion, while the increase in the other factors increases the autoclave expansion. 5. The correlation coefficients of the proposed models were (0.71002 and 0.98338) for the first model, (0.84366 and 0.98789) for the second model, and (0.85593 and 0.98872) for the third model, with and without intercept respectively. REFERENCES: Abdul-Latif, A.M., 2001 “Optimum Gypsum Content in Concrete and Cement Mortar”, Ph.D. Thesis, University of Baghdad. College of Engineering. Al-Jabiri, T.M., 2002 “Concrete Strength Development Related to MgO and SO3 Contents in Cement”, M.Sc Thesis, University of Baghdad. College of Engineering. ASTM C151-84 “Standard Test Method for Autoclave Expansion of Portland Cement” Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 204 Annual Book of ASTM Standards 1989, section 4, volume 04.01, pp. 120-122. ASTM C204-84 “Standard Test Method for Fineness of Portland Cement by Air Permeability Apparatus” Annual Book of ASTM Standards 1989, section 4, volume 04.01. Czernin, W., 1980 “Cement Chemistry and Physics of Civil Engineering” English Edition, George Godwin LTD., London, 196 pp. (Cited by Al-Jabiri 2002). Iraqi Organization of Standards IQS No.5, 1984 “Iraqi Standard Specification for Portland Cements, ICOSQC”, Baghdad, Iraq. Keil, F., (1957) Revue Mater, Constr. Trav. Publ. 503/504,262. (Cited by Lea 1976). Lawrence, C.D., 1995 “Mortar Expansions Due to Delayed Ettringite Formation: Efect of Curing Period and Tempreature”, CCR, Vol.25, No.4, pp.903-914. (Cited by Al- Jabiri 2002). Lea, F.M., 1976 “The Chemistry of Cement and Concrete”, 3rd Edition, Edward Arnold, London 727 pp. Neville, A.M., 1995 “Properties of Concrete”, 4th and final Edition, Pitman publishing, London. 844 pp. Stat Soft 2003, “Multiple Regreesion”, Electronic Text Book. http://www.statsoft.com/textbook/stnonlin.html#general Table (1): Sources of the cement samples used in the analysis No. Factory Type of cement No. of samples 1 Al-Najaf Al- Ashraf cement plant O.P.C. 5 2 New cement plant of Kufa O.P.C. 5 3 Al- Sada cement plant O.P.C. 7 4 South cement plant O.P.C. 6 5 Um-Qaser grinding station O.P.C. 4 6 Lion cement -India O.P.C. 2 7 Al-Muthana cement plant S.R.P.C. 5 8 Kerbala cement plant S.R.P.C. 5 9 Kuwait cement plant S.R.P.C. 1 Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 205 Auto. Exp. .4 0 .3 6 .4 5 .3 4 .4 3 .4 9 .4 2 .4 4 .2 3 .3 3 .3 2 .3 3 .3 7 .4 0 .2 2 .2 4 .4 0 .3 3 .3 0 .3 4 Blaine (m2/kg) 31 4. 4 28 8. 0 30 2. 7 29 6. 6 29 8. 1 32 3. 0 31 4. 8 30 6. 1 29 0. 9 32 7. 3 38 6. 2 32 8. 4 34 9. 6 33 9. 6 39 8. 4 29 1. 5 39 1. 0 29 7. 0 28 4. 7 30 5. 7 FST (min) 2 25 24 0 22 5 20 0 21 5 24 5 26 5 23 5 21 0 23 0 19 0 24 5 23 0 22 0 17 0 19 0 15 5 23 0 26 0 23 0 Ph ys ic al P ro pe rti es IST (min) 1 25 14 0 14 5 11 0 12 5 14 5 17 0 16 0 12 0 16 0 10 0 14 0 12 0 12 0 10 0 10 0 95 10 0 15 0 14 0 L.S.F.% 0. 85 0. 90 0. 86 0. 87 0. 88 0. 93 0. 88 0. 85 0. 9 0. 9 0. 89 0. 86 0. 86 0. 85 0. 89 0. 87 0. 86 0. 89 0. 89 0. 88 IR% 0. 53 0. 92 1. 04 0. 73 1. 30 0. 78 0. 81 1. 35 0. 58 0. 65 1. 22 1. 40 1. 15 1. 30 0. 55 0. 63 0. 80 1. 15 1. 40 0. 86 L.O.I.% 1. 57 1. 23 1. 32 1. 13 1. 35 1. 61 1. 55 1. 61 0. 92 .9 4 3. 30 3. 53 2. 61 1. 93 1. 24 1. 19 2. 22 1. 77 2. 31 1. 39 Free lime% 1. 27 1. 29 1. 40 0. 95 1. 17 1. 19 1. 35 1. 60 0. 88 1. 17 1. 34 1. 29 1. 46 1. 77 1. 42 0. 9 2. 02 1. 22 1. 23 1. 40 SO3% 2. 43 2. 48 2. 41 2. 32 2. 60 2. 47 2. 63 2. 57 2. 75 2. 33 2. 77 2. 40 2. 40 2. 61 2. 54 2. 44 2. 61 2. 38 2. 18 2. 39 MgO% 3. 35 2. 55 3. 55 3. 82 3. 51 3. 87 2. 93 3. 11 4. 43 4. 41 3. 28 2. 71 3. 15 3. 45 3. 20 4. 19 3. 41 2. 73 2. 56 2. 37 Fe2O3% 3. 20 3. 80 3. 80 3. 96 3. 76 3. 44 3. 30 3. 28 3. 24 3. 20 3. 08 3. 60 3. 60 3. 00 3. 08 3. 24 3. 80 4. 32 4. 16 4. 68 Al2O3% 5. 44 5. 08 4. 66 4. 62 4. 72 4. 94 6. 06 5. 94 5. 82 5. 98 4. 44 4. 76 4. 76 5. 30 6. 14 5. 38 4. 48 4. 30 4. 28 3. 58 SiO2% 21 .6 5 21 .2 0 21 .5 0 21 .6 6 21 .2 0 20 .1 0 20 .6 4 20 .9 4 20 .0 6 20 .6 8 20 .8 4 21 .1 8 21 .3 8 21 .6 4 21 .0 6 21 .3 8 21 .1 2 21 .1 4 21 .2 4 21 .7 2 Ch em ic al A na ly si s CaO% 61 .8 63 .0 3 62 .2 3 61 .5 62 .2 3 62 .7 8 62 .6 4 62 .2 3 62 .0 6 61 .8 7 61 .4 3 61 .1 0 61 .3 8 61 .6 9 63 .3 5 61 .2 3 61 .6 9 62 .7 8 62 .9 1 63 .3 2 TY PE O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . FA CT OR Y Al -N aj af AL -A sh ra f Al -N aj af AL -A sh ra f Al -N aj af AL -A sh ra f Al -N aj af AL -A sh ra f Al -N aj af AL -A sh ra f Ne w Ku fa Ne w Ku fa Ne w Ku fa Ne w Ku fa Ne w Ku fa Al -S ad a Al -S ad a Al -S ad a Al -S ad a Al -S ad a Al -S ad a Al -S ad a So ut h So ut h So ut h No . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 206 Auto. Exp. .3 3 .3 2 .2 8 .4 3 .3 9 .3 1 .4 0 .2 3 .2 4 .2 3 .2 4 .2 2 .2 3 .2 2 .2 3 .2 3 .2 2 .2 2 .2 4 .3 0 Blaine (m2/kg) 30 0. 2 29 0. 9 29 2. 5 34 1. 8 34 7. 0 30 5. 7 34 2. 2 28 1. 6 29 3. 8 28 1. 6 26 5. 0 30 3. 0 29 1. 0 30 9. 0 29 0. 0 28 1. 0 30 0. 4 31 6. 3 28 4. 7 28 4. 0 FST (min) 2 10 21 0 24 0 24 0 23 5 23 5 20 5 22 5 25 0 22 5 28 0 26 0 23 0 21 5 27 0 27 5 24 0 18 0 22 5 26 0 Ph ys ic al P ro pe rti es IST (min) 1 20 11 0 12 5 13 5 14 5 15 0 10 5 14 5 15 0 14 5 17 5 14 5 17 0 13 5 16 5 15 0 13 0 80 14 0 14 5 L.S.F.% 0. 88 0. 89 0. 87 0. 87 0. 87 0. 89 0. 90 0. 88 0. 90 0. 88 0. 89 0. 88 0. 90 0. 86 0. 88 0. 90 0. 88 0. 88 0. 90 0. 87 IR% 0. 92 0. 51 0. 32 0. 95 0. 83 1. 00 1. 09 0. 79 0. 90 0. 79 0. 73 1. 35 1. 05 1. 30 0. 92 1. 30 1. 17 0. 54 0. 42 0. 70 L.O.I.% 1. 62 1. 30 1. 04 3. 00 2. 55 3. 56 1. 98 1. 90 2. 50 1. 90 2. 10 2. 33 1. 41 2. 50 1. 80 1. 21 1. 16 0. 81 1. 23 1. 20 Free lime% 1. 04 0. 95 0. 78 1. 40 1. 23 1. 20 1. 68 1. 35 1. 10 1. 35 1. 29 1. 35 1. 47 0. 61 1. 51 1. 52 1. 57 0. 81 1. 23 1. 20 SO3% 2. 23 2. 67 2. 73 2. 75 2. 23 2. 66 2. 21 2. 49 2. 41 2. 49 1. 89 2. 03 1. 85 2. 03 1. 92 2. 15 1. 90 2. 05 1. 90 2. 16 MgO% 2. 66 3. 75 2. 76 3. 85 3. 31 3. 55 4. 28 1. 85 1. 90 1. 85 2. 00 1. 95 2. 14 3. 20 1. 40 1. 87 1. 71 2. 00 1. 72 1. 40 Fe2O3% 4. 80 3. 72 4. 39 3. 32 3. 40 3. 60 3. 60 4. 16 4. 20 4. 16 5. 40 5. 80 5. 68 3. 16 5. 20 5. 90 5. 32 5. 60 5. 44 5. 50 Al2O3% 4. 50 4. 88 4. 52 5. 10 5. 78 4. 20 4. 84 5. 34 5. 55 5. 34 3. 55 3. 72 3. 06 4. 36 3. 94 3. 04 3. 68 3. 22 3. 58 3. 60 SiO2% 21 .2 8 21 .0 21 .8 20 .5 2 20 .8 0 20 .9 6 20 .4 2 21 .0 0 20 .3 0 21 .0 0 21 .5 3 21 .2 0 21 .6 0 22 .0 0 21 .6 0 21 .4 2 21 .7 2 21 .9 0 21 .5 6 22 .1 0 Ch em ic al A na ly si s CaO% 62 .5 9 61 .9 6 62 .4 5 60 .7 9 61 .3 8 61 .1 0 62 .2 3 62 .7 1 62 .5 0 62 .7 1 62 .9 8 62 .5 0 64 .0 3 61 .1 8 63 .4 7 63 .7 5 63 .7 5 62 .4 2 64 .4 0 63 .5 0 TY PE O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . S. R. P. C. S. R. P. C. S. R. P. C. S. R. P. C. S. R. P. C. S. R. P. C. S. R. P. C. S. R. P. C. S. R. P. C. S. R. P. C. S. R. P. C. FA CT O RY So ut h So ut h So ut h Um -Q as er Um -Q as er Um -Q as er Um -Q as er Li on c em en t -In di a Li on c em en t -In di a Al -M ut ha na Al -M ut ha na Al -M ut ha na Al -M ut ha na Al -M ut ha na Ke rb al a Ke rb al a Ke rb al a Ke rb al a Ke rb al a Ku wa it ce m en t p la nt No . 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 207 Auto. Exp. .3 4- .4 5 .2 3- .4 9 .2 2- .4 .2 8. 34 .3 1- .4 3 .2 3- .2 4 .2 2- .2 4 .2 2- .2 4 .3 0 Blaine (m2/kg) 28 8- 31 4. 4 29 0. 9- 32 7. 3 29 1. 5- 39 8. 4 28 4. 7- 30 5. 7 30 5. 7- 34 7. 0 28 1. 6- 29 3. 8 26 5. 0- 30 9. 0 28 1. 0- 31 6. 3 28 4. 0 FST (min) 20 0- 24 0 21 0- 23 0 15 5- 24 5 21 0- 26 0 20 5- 24 0 22 5- 25 0 21 5- 28 0 18 0- 27 5 26 0 Ph ys ic al P ro pe rti es IST (min) 11 0- 14 5 12 0- 17 0 95 - 14 0 10 0- 15 0 10 5- 15 0 14 5- 15 0 13 5- 17 5 80 - 16 5 14 5 L.S.F.% 0. 85 - 0. 90 0. 85 - 0. 93 0. 86 - 0. 89 0. 87 - 0. 89 0. 87 - 0. 90 0. 88 - 0. 90 0. 86 - 0. 90 0. 88 - 0. 90 0. 87 IR% 0. 53 - 1. 30 0. 58 - 0. 81 0. 55 - 1. 40 0. 32 - 1. 40 0. 83 - 1. 09 0. 79 - 0. 90 0. 73 - 1. 35 0. 42 - 1. 30 0. 70 L.O.I.% 1. 13 - 1. 57 0. 92 - 1. 61 1. 19 - 3. 53 1. 04 - 2. 31 1. 98 - 3. 56 1. 90 - 2. 50 1. 41 - 2. 50 0. 81 - 1. 80 1. 20 Free lime% 0. 95 - 1. 29 0. 88 - 1. 60 0. 9- 2. 02 0. 78 - 1. 4 1. 20 - 1. 68 1. 10 - 1. 35 0. 61 - 1. 47 0. 81 - 1. 57 1. 20 SO3% 2. 32 - 2. 60 2. 33 - 2. 75 2. 4- 2. 77 2. 18 - 2. 73 2. 21 - 2. 75 2. 41 - 2. 49 1. 85 - 2. 49 1. 9- 2. 15 2. 16 MgO% 2. 55 - 3. 82 2. 93 - 4. 41 2. 71 - 4. 19 2. 37 - 3. 75 3. 31 - 4. 28 1. 85 - 1. 90 1. 85 - 3. 20 1. 40 - 2. 00 1. 40 Fe2O3% 3. 20 - 3. 96 3. 2- 3. 44 3. 0- 3. 80 3. 27 - 4. 80 3. 40 - 3. 60 4. 16 - 4. 20 3. 16 - 5. 80 5. 20 - 5. 90 5. 50 Al2O3% 4. 62 - 5. 44 4. 94 - 6. 06 4. 44 - 5. 38 3. 58 - 4. 88 4. 20 - 5. 78 5. 34 - 5. 55 3. 06 - 5. 34 3. 04 - 3. 94 3. 60 SiO2% 21 .6 6- 21 .2 0 20 .0 6- 20 .9 4 20 .8 4- 21 .6 4 21 .0 - 21 .8 20 .4 2- 20 .9 6 21 .0 - 20 .3 21 .0 - 22 .0 21 .4 2- 21 .9 22 .1 0 Ch em ic al A na ly si s CaO% 61 .0 5- 63 .0 3 61 .8 7- 62 .7 8 61 .1 0- 63 .3 5 61 .9 6- 63 .3 2 60 .7 9- 62 .2 3 62 .5 0- 62 .7 1 61 .1 8- 64 .0 3 62 .4 2- 63 .7 5 63 .5 0 TY PE O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . O .P .C . S. R. P. C S. R. P. C S. R. P. C FA CT O RY Al -N aj af AL -A sh ra f Ne w Ku fa Al -S ad a So ut h Um -Q as er Li on ce m en t - In di a Al - M ut ha na Ke rb al a Ku wa it ce m en t pl an t No . 1 2 3 4 5 6 7 8 9 Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 208 Table (4): R, R2, adjusted R2, Fvalue, and S.E. for the models with and without intercept. Model R R2 Adjusted R2 Fvalue S.E. df with intercept 0.71002 0.50412 0.49107 38.63166 0.06446 ±0.080 1 without intercept 0.98338 0.96704 0.96530 557.4398 0.06201 ±0.075 with intercept 0.84366 0.71176 0.64871 11.28843 0.05356 ±0.073 2 without intercept 0.98789 0.97594 0.96993 162.2572 0.05774 ±0.068 with intercept 0.85593 0.73261 0.59892 5.47972 0.05723 ±0.072 3 without intercept 0.98872 0.97756 0.96675 90.4699 0.06071 ±0.070 Table (5) Property of cement used for checking the proposed models. Chemical Analysis Physical Properties No. Factory Type CaO% SiO 2 % Al2 O 3 % Fe 2 O 3 % M gO % SO 3 % Free lim e% L.O .I% IR% L.S.F.% Blaine (m 2/kg) Auto. Exp. 1 Al-Sada O.P.C. 61.48 20.96 5.92 3.0 3.55 2.41 1.23 2.17 1.18 0.86 348.5 0.36 2 Kerbala S.R.P.C. 64.5 2.2 3.67 5.54 1.5 2.06 1.68 0.5 1.13 0.91 320 0.25 Table (6) Observed and predicted autoclave expansion. Predicted Auto. Exp. Model(1) Model(2) Model(3) No. Factory Observed Auto. Exp. With intercept W ithout intercept W ith intercept W ithout intercept W ith intercept W ith intercept 1 Al-Sada 0.36 0.371 0.365 0.351 0.390 0.32 0.38 2 Kerbala 0.25 0.214 0.218 0.181 0.20 0.180 1.181 Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 209 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 Residual Values of The Autoclave Expansion Obtained by The First Model. (a) 0 2 4 6 8 10 12 14 16 18 N o of o bs er va ti on s -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 Residual Values of The Autoclave Expansion Obtained by The Second Model. (b) 0 2 4 6 8 10 12 14 16 18 20 N o. o f O bs er va ti on s -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 Residual Values of The Autocalve Expansion Obtained by The Third Model. (c) 0 2 4 6 8 10 12 14 16 18 20 N o. o f O bs er va ti on s Fig. (1) The Residuals Distribution of The Autoclave Expansion Obtained by The Present Models. Al-Qadisiya Journal For Engineering Sciences Vol. 1 No. 2 Year 2008 210 0.18 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 Predicted Values of Autoclave Expansion by The First Model (a) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 O bs er ve d V al ue s of A ut oc la ve E xp an si on T es t R es ul ts 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Predicted Values of Autoclave Expansion by The Second Model (b) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 O bs er ve d V al ue s of A ut oc la ve E xp an si on T es t R es ul ts 0. 14 0. 16 0. 18 0. 20 0. 22 0. 24 0. 26 0. 28 0. 30 0. 32 0. 34 0. 36 0. 38 0. 40 0. 42 0. 44 0. 46 Predicted Values of Autoclave Expansion by The Third Model (c) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 O bs er ve d V al ue s of A ut oc la ve E xp an si on T es t R es ul ts Fig. (2) The Predicted Values of The Autoclave Expansion Against the Predicted Values Obtained by The Present Models.