STATISTIC MODELING OF RESULTS IN CIVIL ENGINEERING Częstochowa, 2004

MATHEMATICAL DESIGN OF EXPERIMENTS Basing on the available date it was assumed that the unknown mathematical characteristic of the object of studies can be approximated with a sufficient accuracy by a second-order non-linear function in the form: Basing on the available date it was assumed that the unknown mathematical characteristic of the object of studies can be approximated with a sufficient accuracy by a second-order non-linear function in the form:

The function was calculated by the method of regression analysis, using IBM PC computer and Statistica 5.01 PL for Windows. The analysis included: The function was calculated by the method of regression analysis, using IBM PC computer and Statistica 5.01 PL for Windows. The analysis included: - the calculation of regression coefficients, - the calculation of regression coefficients, - the estimation of the significance of regression coefficients and regression function, - the estimation of the significance of regression coefficients and regression function, - the estimation of the adequacy of regression function to the object studies. - the estimation of the adequacy of regression function to the object studies.

The significance of regression coefficients and function was estimated on the basis of Fisher’s test, using the method of rejection. Each regression coefficients was tested by comparing the test value F with the critical value F cr =F 0,05; 1;N-K

Results. The first stage of investigation involved the determination of the dependence of the phase composition and the physics-mechanical properties of burnt bodies upon the batch components and firing temperature. The first stage of investigation involved the determination of the dependence of the phase composition and the physics-mechanical properties of burnt bodies upon the batch components and firing temperature. The computer programme was written on the basis of second-order plan. It was assumed that the input factors vary over the range The computer programme was written on the basis of second-order plan. It was assumed that the input factors vary over the range

X 1 – ash content in the batch - 0÷30% wt., X 1 – ash content in the batch - 0÷30% wt., X 2 – phonolite content in the batch - 0÷40% wt. X 2 – phonolite content in the batch - 0÷40% wt. X 3 – firing temperature – 1180 ÷ 1300 o C. X 3 – firing temperature – 1180 ÷ 1300 o C.

Nr Input factorsOutput factors*) CodedActualGfcN X1X1 X2X2 X3X3 X1X1 X2X2 X3X3 Mg/m 3 MPa% ,34 2,09 2,08 1,96 2,01 1,79 1,95 2,10 2,25 2,00 2,03 2,04 2,05 1,89 2,08 2,02 2,03 2,06 2,07 63,9 84,0 37,2 51,3 46,3 17,7 37,5 70,7 79,4 45,9 32,5 51,9 59,3 24,8 41,4 35,0 39,9 35,1 54,6 0,75 1,10 0,55 4,55 10,04 0,68 0,69 1,44 0,79 4,04 0,85 4,75 3,58 0,69 1,98 1,53 1,95 1,70 1,45 Table 1. Computer programme and apparent density, water absorption and compressive strength of modified clays after burning

Table 2. Regression analysis of the dependence of apparent density, water absorption and compressive strength of clays on modifying additives and firing temperature Number of regression coefficient Significant regression coefficients Apparent density Compressive strength Porosity b0 b1 b2 b3 b12 b13 b23 b11 b22 b33 2, , ,0643 0, , , , ,373 -3,0413 4, ,6893 3, , , , ,0273 1,973 1,6893 1, ,5983 0,723 -1,483 -0, ,

Fig. 1. Plot of apparent density (G) of clay samples modified with flay-ash (P) vs. firing temperature (T)

Fig. 2. Plot of apparent density (G) of clay samples fired at 1180 o C vs. amount of additives: flay-ash (P) and phonolite (F)

Fig.3. Plot of water absorption (N) of clay samples modified pfonolite (F) vs. firing temperature (T)

Fig.4. Plot of water absorption (N) samples fired vs. flay-ash (P) and phonolite (F) content in the batch

Fig. 5. Plot of compressive strength (fc) of clay samples modified with flay-ash (P) vs. firing temperature (T)

Fig. 6. Plot of compressive strength (fc) samples fired vs. flay-ash (P) and phonolite (F) content in the batch

CONCLUSIONS To summarize, it appears from result presented in this paper that the regression analysis is a useful tool for planning of ceramic properties and other. In view of differences in the mineralogical and chemical compositions of clays, their essential ceramic properties should be checked for each variety separately and the optimum parameters should be determined by way of the design of experiments To summarize, it appears from result presented in this paper that the regression analysis is a useful tool for planning of ceramic properties and other. In view of differences in the mineralogical and chemical compositions of clays, their essential ceramic properties should be checked for each variety separately and the optimum parameters should be determined by way of the design of experiments

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