Development of the implementation of response surface methodology in concrete technology

The response surface methodology (RSM) is used for providing the customer with a product of adequate quality level. In concrete industry, it is important to produce concretes having workability and strength each within corresponding appropriate range of standard deviation. To this end, simultaneously controllable variables significantly affecting workability and strength were determined from among the many parameters in the ready-mixed concrete production (S/Ç (water/cement ratio by mass), Dosage (cement content), fcc (cement standard strength), kk (fineness modulus of aggregate), İA (fine aggregate percentage of the aggregate mix by absolute volume), KM (plasticizer content), and AT (aggregate stone origin)).The ranges of controllable variables differ with the maximum aggregate size. Therefore, separate designs were performed for the most widely used maximum particle sizes of 11.2 mm and 22.4 mm. The term ?simultaneously controllable? in the context of this work is used in the sense that the properties of concrete mixes were determined using constituents with known properties, as opposed to that in ready-mixed concrete industry where there are considerable time lags between the tests on each of the constituents and the concretes produced.The application of response surface methodology incorporates series of sequentialoperations. These operations are named as ?screening experiments (phase 0)?, ?phase1? and ?phase 2?. In the screening experiments 27-3fractional factorial design was used, and D-Optimal designs were used in ?phase one? and ?phase two?.The feasible zone or ?operability region? was determined by performing 27-3, 26-2 and 2 6-1fractional factorial designs on the cone slump values of concrete mixes. The results of 27-3fractional factorial design showed that the ?aggregate mix fineness modulus? in xxthe Dmax = 11.2 mm concretes, and the ?fine aggregate content (İA)? in the Dmax = 22.4 mm concretes did not have significant effects on the response variables, namely, cone slump and compressive strength. Hence, the numbers of controllable effect variables were reduced to 6 for both of the Dmax designs, and the D-Optimal designs obtained by augmenting (forward selecting) the 27-3fractional factorial designs were used. Response models were set up for the designs 1, 2 and 3, selecting model terms from sets of data (with vertex and central) points obtained from the D-Optimal design. Response models (Design 4) were set up also with the effect variable ç/(ç+s+h)in use in concrete technology instead of the effect variable S/Ç. Transformation was applied on the slump response variable to improve the model adequacy for the Dmax = 11.2 mm Designs 1 (Square root), 2 (Square root), 3 (Square root), and Dmax = 22.4 mm Designs 1 (Power), 2 (Power), 4 (Power). As for the compressive strength response variable, transformations were appplied for Dmax = 22.4 mm Designs 1 (Natural log), 2 (Natural log), 3 (Inverse square root) and 4(Inverse square root), and for Dmax = 11.2 mm Design 1 (Square root) only, not in Designs 2, 3 or 4.It can be seen that the compressive strength and cone slump models are significant (p(Model) < 0.0001) in the Designs 1, 2, 3 and 4. However, the significance of the ?lack of fit? varies with designs. The significance of lack of fit of the cone slump response variable for the Dmax = 11.2 mm Designs 1, 2, 3 are not significant (in other words, the models obtained are adequate within the determined operable region), significant in the Design 4 (in other words, the models obtained are inadequate within the determined operable region). The lack of fit for the compressive strength for Dmax = 11.2 mm is insignificant for the Designs 1, 3, but significant for the Designs 2, 4. The lack of fit for the cone slump for Dmax = 22.4 mm came out to be significant in the Designs 1, 2, 3, insignificant in the Design 4, and, as for the compressive strength, the lack of fit was found to be insignificant in the Designs 1, 2, 4, significant in the Design 3.In the cone slump models, for Dmax = 11.2 mm, the minimum values of the R2, the adjusted R2 and the predicted R2(0.8154, 0.7758 and 0.6920, respectively) were obtained in the Design 4, and the maximum values (0.9305, 0.9045 and 0.8665, respectively) were obtained in the Design 3. As for the Dmax = 22.4 mm, the minima (0.8794, 0.8552 and 0.7942, respectively) were obtained in the Design 4, and the maxima (0.9713, 0.9475 and -(Undefined)) were obtained in the Design 3.In the compressive strength models, for Dmax = 11.2 mm, the minimum values of the R2 , the adjusted R2 and the predicted R2(0.9540, 0.9479 and 0.9341, respectively) were obtained in the Design 4, and the maximum values (0.9798, 0.9730 and 0.9618, respectively) were obtained in the Design 1. As for the Dmax = 22.4 mm, the minimum R2(0.9765, 0.9765 and 0.9770, respectively) were obtained in the Designs 1, 2, 4, and the maximum R2(0.9838) was obtained in the Design 3, the minimum adjusted R2(0.9693) was obtaned in the Design 4, the maximum (0.9748) was obtained in the Design 3, the minimum predicted R2(0.9301) was obtained in the Design 3, and the maximum (0.9651) was obtained in the Designs 1 and 2.In the diagnostic case statistics, the number of runs exceeding the limiting values for the Designs 1, 2, 3 and 4 were obtained as 14, 4, 23 and 6, respectively. The maximum xxitotal number of runs exceeding the limits, being 35, was in the leverage values, the maximum (16) taking place in the Design 3.The run points of the Designs 1, 2 and 3 were chosen as the corners (lower and upper limits) and the central points of the corresponding effect variables. The run points of the Design 4 made by substituting ç/(ç+s+h) instead of S/Ç ratio do not correspond to the corner or central points of the effect variables (especially the categoric variables). Therefore, the comparison of the designs should be made separately, taking into consideration the corresponding different sets of effect variables.It is possible to explain on physical bases the levels of significance of the effect variables in the first, second, the third and higher order interaction terms on the response variables. Nevertheless, increasing R2value (approximately > 0.90) by addition of terms (in forward selection), that is, the model?s yielding almost exactly the recorded data value (with residuals ? 0), will be accompanied by the incorporation ofthe effects of errors in the related measurements and amplify the effects of uncontrollable variations. Therefore, a straight, simple statistical significance based on hypotheses testing (that is, p(Model) < 0.0001 (<< level of significance = 0.0100)) and R2being close to unity is not sufficient for the model to qualify as physically significant. The diagnostic case statistics (leverage, Cook?s distance, etc.), the response surfaces, and the response values? ranges as compared to the functional or feasible ranges should also be taken into account for an accurate assessment of the model.The level of significance (?) adopted in statistical analyses influences the number of terms included in the model. In general, an increase in the number of terms causes an increase in R2 towards unity, but also amplifies the effects of experimental and measurement errors. Therefore, an investigation incorporating models for various levels of significance is required for determining an optimal model.It is appropriate to determine feasible regions for sets of categoric effect variables (such as aggregate stone type for limestone and basalt separately) for a properdetermination of statistical significance levels of the effect variables. The categoric properties such as stone type (geological origin), particle shape and surface propertiesof the aggregate can be included in a unified model if they can be made controllable,and reliable numerical values can be assigned.In the optimization operations of concrete mix designs, the types of effect variables should be chosen according to the desirability levels of the response variables; the level of quality control, starting with the sampling frequencies, should be adopted to achieve sufficient level of concurrency so as to minimize losses.Key words: Concrete, slump, compressive strength, response surface methodology, fractional factorial design, D Optimal design, desirability