Effect of Water and Admixture on Foam Concrete Properties

The paper presents mathematical modeling of additives and water’s effect on foam concrete’s compressive and flexural strength at 28 days of normal hardening. The requirements of GOST 10180-2012 determined the compressive and flexural strength of foam concrete. The initial composition of the foam concrete mix was calculated using the absolute volume method. Results received first-order regression equations. The compressive strength and flexural strength of foam concrete depended on the relations from x1(WOPC+BFS)tox3(SF90OPC) and the image surface expression and objective function for the regression equations. The optimal value obtained: compressive strength = 8.075 MPa and flexural strength 1.087 MPa.


Introduction
Foam concrete is a lightweight concrete with a porous structure obtained by curing solutions, including binders, fine aggregates of various origins, water, additives and a foaming agent. Besides, foam concrete is an economical, environmentally friendly, lightweight construction material that provides heat and sound insulation, as well as fire resistance [1][2][3][4][5].
Foam concrete has the following advantages [1,4,16]: + Thermal and moisture resistance. + Soundproofing. + Possibility of producing bricks or blocks of different geometrical shapes with high accuracy of adherence to dimensions and accuracy of edges, and, consequently, during construction, optimally smooth walls are obtained, which leads to a decrease in the cost of finishing work. + Elements made of foam concrete are convenient for transportation. + Significantly simplify the construction of buildings and their commissioning. + Save money, time and effort. In addition, in scientific research, numerical simulation methods are often used to predict special properties' effects on the research object. In addition, in concrete technology, experimental planning methods are often used to find the optimal components for technological processes. According to IOP Publishing doi: 10.1088/1757-899X/1030/1/012003 2 studies [7,8], it is necessary to collect information about previous studies' input variables when planning an experiment.
When using the experimental planning method, the following should be taken into account.
-Study some major factors affecting the properties of the materials to plan the experiment.
-Assume that some factors do not change.
-Note to minimize the number of experiments. On the other hand, according to Vietnamese standard TCVN 1451: 1998 [9], clay bricks have a density =1600 kg/m³ and compressive strength = 7.5MPa. Therefore, foam concrete density with a density lower than 1000 kg/m³ instead of clay bricks can reduce the load to the building [1,5,10].
According to the research [3,4], foam concrete with a density < 1000 kg/m 3 has a compressive strength of 4÷6 MPa. Besides, according to studies [11,12], the water content in foam concrete has a significant effect on concrete's compressive strength. The addition of silica fume to the concrete mixture increases the strength of concrete.
Therefore, this study aims to use mathematical modeling about the influence of input factors on the concrete strength foam at 28 age days with a density of 900 kg/m 3 .
In this study, superplasticizers (SR5000) were used to improve the performance of concrete mixtures with  = 1.1 g/m 3 at a temperature of 25 ± 5°C.
The physical and chemical properties of cement (OPC), silica fume (SF90) and blast furnace slag (BFS) are shown in Table 1.  3 . For this study, the EABASSOC foaming agent is mixed with water at a rate of 2.5%.

Procedure for the preparation of foam concrete
The fresh foam concrete comes from a process of continuously mixing foam and paste until an even mixture is obtained. The foam concrete preparation process is illustrated in Figure. 1. Cement, silica IOP Publishing doi:10.1088/1757-899X/1030/1/012003 3 fume and blast furnace slag are first mixed at a lower speed of about 40÷50 rpm for a short while, followed by the addition of water and superplasticizer to mix for 2 minutes during the mixing process to obtain a wet binder mixture. Then, the foaming agent is added to the mixture and continue to mix. The mixture is then put into a mold and put it in a static state for 24 hours. These foam concrete samples were then tested after 28 days of age [14,15].

Research Methods
The absolute volume method was used to determine the composition of the foam concrete mixture [16,17].
The mechanical properties of foam concrete at the age of 28 days are determined according to Russian standard GOST 10180-2012 [18] (Figures 2 and 3). Using the method of Box-Wilson central composite designs to find the optimal amount of additive silica fume (SF90), superplasticizer (SR5000) and the water-cement ratio [8,19].
The coefficient b j is considered significant if: t bj  t  (f). in which: t  (f) -critical value for student's t distribution at a significance level  = 0.025 and degrees of freedom f = (k -1)×N = (3 -1)×8 =16.
According to [21] on the table 3.2  t  (f) = 2.1199. The formula determined regression equations: The formula determined the variance estimates of the regression coefficients of the S ve equation:   Table 8.
(c) Verification of equations (9) and (11) The testing of the model's full hypothesis is based on calculations of the full variance S 2 av (12) and the Fisher F fc (13) criterion: The values F расс was compared with the value F tab (f 1 . f 2 ) from the table 3.5 [21]. determined by the number of degrees of freedom f 1 = N = 8 and f 2 = Nm = 8 -3 = 5. Therefore F tab (8. 5) = 3.69.
With regression equation (8) Therefore. equations 9 and 11 satisfy the condition F fc < F tab Using the Matlab computer program. We can obtain the response surfaces for the regression equations (9) and (11)   increases: the compressive strength and flexural strength of foam concrete increase. The increase in foam concrete's power can be explained by the fact that SF90 contained 90.78% of amorphous silica. It is shown that silica fume densifies compressed products' structure due to the binding of free calcium hydroxide with calcium hydro-silicate. Besides, according to research [4][3] also shows that the concrete strength increases when the water-cement ratio increases.

Conclusions
Based on the test results, the following conclusions are drawn on tested foam concrete samples: Foam concrete containing a modifier of organic minerals, including blast furnace slag, silica fume, superplastic additive SR5000, the purpose of which is to plan a first-order experiment: compressive  (9) and (11).
From the regression equations (9), (11), we see that a decrease in the ratio (x 1 ) simultaneously an increase in the rate (x 3 ) leads to an increase in the compressive strength and flexural strength of the concrete sample under test. The influence of the ratio (x 2 ) in the range of the considered value is insignificant, and therefore it can be neglected.
Compressive strength of foam concrete = 8.075 MPa and density <1000kg/m 3 can replace clay bricks to help reduce building load.
Soon the authors continue to study the effects of rates x 1 ( W OPC BFS  ) and x 3 ( 90 SF OPC ) to the mechanical properties of foam concrete by the method of central composite design for two input factors.