THREE-PARAMETRIC MODEL FOR ASSESSMENT

 OF THE 1-DAY STRENGTH OF A SILICATE COMPOSITE

Violeta J. Petkova

Central Laboratory of Physico-Chemical Mechanics,

Bulgarian Academy of Sciences, Acad. G. Bonchev St., Bl. 1, 1113 Sofia,

E-mail: malahit@bgcict.acad.bg

Received: 20.07.01; Cited: 9.10.01

 Abstract

Polynomial models describing the mechanical properties of composite mortars, including a new combined admixture in their formulation, have been developed on the basis of three-factor planned experiment. The obtained mathematical relationships are presented in graphic form. They represent the influence of the proportions between the admixture ingredients and the water/cement ratio on the changes in the 1-day compressive strength of the composite in the broad range of the factor space with high values of the investigated parameter. The obtained results can be used for the solution of a number of technological and technical problems connected with the application of the new composite elements.

Key words: silicate composite, combined admixture, compressive strength, planned experiment.

The application of different admixtures provides an alternative possibility of extending the production methods of silicate composite elements. The combined admixtures are suitable in the cases where accelerated hardening and high mechanical parameters are necessary. Different industrial sub-products (by-products or wastes) can be used as fillers of the cement matrix. Their rational utilization leads to improved ecology of the environment. The compressive strength is considered to be the main factor in such cases according to the technological and construction requirements in connection with the application in building practice, while the 1-day strength is considered as a criterion for comparative assessments related with the investigation and choice of optimal solutions concerning the development of new high-strength and economical non-metallic composites.

The possibility of obtaining a new composite material (CM) based on cement [1, 2] is proved using the above mentioned parameters. The formulation includes a new combined admixture (CA). Its components – alkaline (A) and pozzolanic (P) one, are cheap and available waste raw materials. The admixture is in conformity with the requirements of the Bulgarian State Standards (BDS EN 196-5 and BDS EN 196-6) [1] with respect to its dispersity, chemical composition and activity. It can be added both to pure clinker cements and to lower-quality plant cements with restricted alite content.

The experimental results from the preliminary investigations of CM show the substantial advantages of the admixture. It accelerates the hydration and structure formation of the slag-cement stone and contributes to considerable increase of the mechanical strength. The assessment of the influence of some important parameters is made by means of suitable cybernetic method in order to predict the compressive strength kinetics for one-year period of hardening [2]. The obtained regression models show that quantitative relationships exist between the formulation components (combined admixture, Portland cement) and the water/cement ratio. At the same time, high values of the investigated characteristics have been reached.

The present report considers the data reflecting the three-factor influence of the main parameters – the ingredients A and P composing of the combined admixture and the water/cement ratio, on the changes of the 1-day strength. The possibility for effective choice of suitable optimal solutions is shown with the variation of the quantitative participation of the accepted factors, as well as their contribution to the development of a silicate composite with high early strength. 

Materials and methodology of research

Multiple regression analysis has been applied in the presented investigations for the assessments of the 1-day compressive strength. The method does not ignore the complex physico-chemical processes taking place during the hydration and hardening of the composite material. Portland cement PC35 D20 has been used for the purpose, its mineral composition being С₃S=50 %, С₂S=28 %, С₃А= 8 % and С₄АF=10 %, the dispersity of grinding being 11.1 %. The cement meets the requirements of BDS EN 196-1.

The experiments were carried out with composite mortars with work composition 1:3. The used CA has a definite grain-size composition and activity [1]. Its two components are mixed and homogenized with the Portland cement in dry state. The test series were performed using a medium-grained artificial sand. The latter represented well-designed mixture of granulated acidic slag and flotation sterile material. In this way, the basic aim of the author was reached to effectively utilize more secondary by-products from metallurgy in combination with ionized in a constant electric field mixing water with рН = 10-11 [1].

The choice of the single factors - Х₁ (W/C), Х₂ (A), Х₃ (P) and their variation levels in natural and coded coordinates are shown in Table 1. The alkaline and pozzolanic ingredients of the combined admixture are expressed in percent from the total mass of the samples. The selected proportions allow the real and exact prediction of the complex relationship between both formulation parameters, the water/cement ratio and the 1-day strength of the new composite.

 Table 1.

The plan of the experiment was developed with 27 test points, Table 2. Three tests of the 1-day compressive strength were made for each point. The calculations were performed using the EXEL electronic sheets and the LINEST multiple linear regression function. The chosen three factors varied within the limits of -1 to +1.

The unknown target function Rc =f (X₁, X₂, X₃) describes the relationship between the compressive strength at the age of 1 day, the quantities of the components A and P and the value of the corresponding water/cement ratio. It is determined as a second order polynomial:

Rc = b_o + S b_iХ_i + S b_iiХ_i² + S b_ijХ_iХ_j                                                                           (1)

Table 2

The mathematical model of the investigated output in MPa for the age of 24 hours is developed on the basis of the experimental data, Table 2 and the methodology in [3]:

Rc = 28,44-52,91 Х₁+1,12 Х₂+1,13 Х₃ - 0,13 Х₂² - 0,051 Х₃² + 0,062 Х₂.Х₃                       (2)

The model satisfies the Fisher adequacy criterion for confidence interval 0.95. The assessment of the accuracy of the used method is made by comparing the experimental data for the 1-day strength of all compositions with the respective calculated values. The obtained errors are in the admissible limits, which proves good coincidence between the results, Table 2. The regression coefficients in equation (2) determine the direction and degree of influence of the factors on the investigated parameter. The factor Х₁ (water/cement ratio) exerts the greatest impact on the strength. The coefficient b₁ in front of it has the highest absolute value. The sign “-“ reflects the negative influence of the water/cement ratio when increased on the strength. The 1-day strength has a maximum value in point Х₁ = -1 (W/C = 0,40) and is 15.8 МРа. The influence of the two formulation factors Х₂ and Х₃ (the amount of the components A and P) is significantly lower and almost equal. Their coefficients b₂ and b₃ have low and almost the same values. The sign “+” shows that their increase within the shown range lead also to the increase of the 1-day strength. The presence of square-effects with a minus sign in front of them, which have significantly lower absolute values, proves that there is an extremum (minimum) within the studied limits.

The relative effect of each of the factors and the mutual relations between them as – W/C and the quantity of the component A or the amounts of the pozzolanic and alkaline components in the CA, describe concrete relationships and the existence of different effects on the studied parameter. They are best explained by the plotted quasi one-factor models. The quasi one-factor dependence of Rc on W/C when the quantity of the component A is varied is shown in Fig. 1. The quasi one-factor model for Rc and the amount of P when component A varies is shown in Fig. 2. The relationship in Fig. 1 is determined for the maximal value of P and in Fig. 2 – for the minimal value of W/C.

It is seen in Fig. 1 that the 1-day strength decreases within the mentioned limits of variation of the component A from -1 to +1 with the increase of the water/cement ratio. The function of this relation has a hyperbolic character (curves 1, 2 and 3). The test compositions 1 and 2, containing lower amounts of the alkaline component, show lower compressive strengths.

Fig. 1. Quasi one-factor dependence of Rc on W/C for changes of the component A, P = 7.0 %

The relationship between the 1-day strength and the pozzolanic component P when A varies within the accepted limits is shown in Fig. 2. The dependence has an expressed extremum (minimum) of the strength. It changes in a parabola-like manner, reaching its minimum in points where the amount of the pozzolanic component P is 3.53 %, 3.55 % and 3.57 % (samples 1, 2 and 3), and the amounts of the alkaline component A are respectively А= 0, 1.5, and 3.0 %. The 1-day strength increases from 7.8 МРа for А=0 % to 15.8 МРа for А=3.0 %. Obviously the influence of the component P and its contribution to the 1-day strength is positive, compared to the technological factor of the water/cement ratio.

  Fig. 2. Quasi-factor dependence of Rc on the component P for varying A, W/C=0.40

Two-factor graphs are plotted in figures 3-5 using the isolines, taking under consideration the influence of the two components A and P composing the new combined admixture on the one-day strength for three single levels of the water/cement ratio. The graphs provide the possibility of making an assessment of the mutual interaction between the factors, as well as of determining their optimal quantitative participation for the choice of preliminary determined compressive strength of the silicate composite.

It is seen in Fig. 3 that that the maximal value of the compressive strength of CM for the age of 24 hours can be obtained by different combinations of the two components: А = 2.4 % and P = 13.0 % or А = 3.0 %, P = 7.9 % and W/C = 0.40. This strength is 15.8 МРа. The comparison with the reference sample (Rc=7.8 МРа) proves that the contribution of the components is 8 МРа.

For W/C=0.43 the greatest effect of the combined use of the alkaline and the pozzolanic components in the formulation is obtained for economically chosen amount of the components - А = 3 % and P = 4.9 %. The 1-day strength increases from 5.7 МРа (reference sample) to 13.7 МРа for CM, i.e. the increase is 8 МРа, Fig. 4.

It is seen from the isolines in Fig. 5 that for W/C=0.46 the composite reaches its maximal compressive strength, equal to 14 МРа. The amount of the two components is respectively А=3 % and P=7.0 %, or the effect is also high. The strength increases with 7.8 МРа.

The retrospection of the obtained results during the analysis of the changes in the compressive strength at the age of 24 hours proves the positive effect of the participation of the components A and P in the accepted variation range. Their use leads to acceleration of the hydration and structure formation processes, as well as to quick formation of strong crystalline framework in the slag-cement stone. This contributes to the considerable growth of the 1-day strength. The recorded relative increase is of the order of 254 %, 202 % and 161 % for W/C values 0.40, 0.43 and 0.46 respectively.

Fig. 3. Isolines of the changes of Rc depending on the quantity of the components A and P, W/C=0.40

Fig. 4. Isolines of the changes of Rc depending on the quantity of the components A and P, W/C=0.43

So, the achieved results confirm the good effectiveness of the CA. It ensures high strength, including high 1-day compressive strength. In this way the aim of the author to develop a new high-strength composite material with dominating role of the components A and P on the mechanical properties has been successfully achieved.

Fig. 5. Isolines of the changes of Rc depending on the quantity of the components A and P, W/C=0.46

Conclusions

1. The high 1-day compressive strength of the new class of silicate composites is achieved mainly by adequately selected quantitative proportion of the two components of the composing the combined admixture.

2.   A three-factor mathematical model has been developed for the influence of the three main factors on the value of the 1-day strength. The presented regression coefficients for the degree and direction of the influence confirm the expected results that the compositions with certain amount of the components A and P and respective water/cement ratio possess high compressive strength.

3. It is seen from the considered two quasi one-factor models that for other equal conditions the dependence of the 1-day compressive strength preserves a hyperbolic character with the increase of the water/cement ratio and the variation of the component A, and that a certain amount of the A and P components minimizes the target function.

4.   The plotted two-factor graphs by means of the isolines of the 1-day strength illustrate the influence of the chosen factors in the accepted variation range. They can be successfully used for the development of different variant solutions in order to reach any designed 1-day compressive strength. Other practical problems concerning the relationship between the formulation components and the mechanical properties of the construction composite elements can also be solved using the isolines.

References

1.   Petkova V. Pozzolanic activity of a combined admixture for a new silicate composite, Х Jubilee Symposium “Ecology 2001”, 07-09.06.2001, Bourgas, 353-358.

2.   Petkova V., R. Krastev. On the strength changes of a new class of silicate composites, Х Jubilee Symposium “Ecology 2001”, 07-09.06.2001, Bourgas, 346-352.

3.   Iberla K. Factor analysis. Statistika, Moscow, 1980.