Response surface design of solid waste based geopolymer

Abstract

Solid waste (slag and fly ash) based geopolymer (SWG-SF) was developed on the basis of response surface methodology (RSM), using the fly ash to slag ratio (FSR), alkali content (AC), makeup of alkali activator (n) and binder to water ratio (BWR) as design parameters. Flexural strength (f_f-3d) and compressive strength (f_c-3d) after 3 days of standard curing were tested, the early strength systems were established, the prediction of strength system was validated by comparison, and the effects of design parameters on f_f-3d were studied. The test result shows that the reliability and accuracy of the early strength system of SWG-SF by adopting RSM can be verified in terms of mathematics and application, and the early strength system can be used for theoretical study and practice guidelines; according to analysis on the strength system, f_f-3d increases linearly with BWR, and the increasing rate is closely related to FSR; f_f-3d increases linearly with n, and the increasing rate is closely related to AC; f_f-3d decreases continuously with FSR, but the decreasing rate gets slower and slower, and BWR has certain influence on the change rate of strength; and f_f-3d increases at the beginning and then decreases with AC, which suggests that AC has an optimum value (0.146–0.055n). Thus it can be seen that RSM can be widely used in the preparation of new solid waste based geopolymer and has promising applications in the utilization of solid waste.

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1 Introduction

In China, industrial development has left behind a large amount of solid waste. At present, instead of decreasing, solid waste is only increasing and there is no comprehensive management of it. As a result, solid waste has become one of the most serious environmental problems. It is important to work out a new way to increase utilization of solid waste. Cement plays an important role in national economic development. However, it also brings about problems such as high resource and energy consumption and serious waste emission. So, it is urgent to develop new cementitious materials to better allocate resource and to better protect the environment.

To solve the current problems, turning waste into wealth should be set as the guiding concept. It will have great influence. It reduces the negative environmental and social effects brought by the solid waste, as well as cutting the financial and manual cost to dispose of the waste. Furthermore, the waste becomes the raw material for manufacturing other products, which saves costs in both ways. So, the recycling of industrial solid waste deserves comprehensive study to realize this double win. The key issue is the recycling technology.

Combined with the latest construction development,^1–4 the most effective method is to use alkali activation technology^5,6 to turn industrial waste into new cementitious materials – geopolymer,^7–9 which is a kind of alkali-activated polyaluminosilicate material. Slag and fly ash are the main industrial waste products, and the potential activity of slag and fly ash is of great concern. Based on the ideas above, solid waste (slag-fly ash) based geopolymer (SWG-SF)¹⁰ has drawn the attention of researchers. At present, research on SWG-SF mainly concentrates on the preparation: a Luxembourg patent disclosed a method for manufacturing the binding material with fly ash and slag; Shi and Day¹¹ studied the influence of two types of fly ash and lime on an alkali-activated fly ash-slag system; Ma¹² developed a solid alkali-activated slag-high calcium fly ash cementing material, and cement-like products of strength grade 325#-525# (according to Chinese standard GB177 85) have been prepared. These studies have the following characteristics: a “single factor variation method” is used in the preparation, which leads to the lack of systematic researches, and the interaction and the influence of quadratic term are ignored, which reduces the model precision.

Response surface methodology (RSM) is a kind of advanced new experimental design method. The application of RSM can improve the preparation concept of a new composite cementitious material, as it overcomes the constraints of a one-dimensional linear model. The interaction and the influence of quadratic term are introduced to the model, so the test accuracy is improved, which ensures the scientific nature of the research. Moreover, a multi-factor dynamic analysis method is used in the analysis of each component's influence on strength. Compared with the traditional “single factor variation method”, a model based on RSM can reveal the essence of the phenomenon at the extreme.

Taking the improvement of deficiency as the research target, the preparation of SWG-SF was conducted by using response surface methodology (RSM). Slag and fly ash were used as the main raw materials, and the solid NaOH (NH) and Na₂CO₃ (NC) were used as activator. In order to effectively eliminate the influence factors of sand and gravel to better explore the SWG-SF preparation technology, a paste specimen was used as the research object. First of all, the test plan was made on the basis of a response surface orthogonal rotational combination design method, and the design parameters were as follows: fly ash to slag ratio (FSR = m_Flyash/m_Slag), alkali content (AC = m_(NH+NC)/m_{(Flyash+Slag)}), makeup of alkali activator (n = m_NH/m_NC), and binder to water ratio (BWR = m_{(Flyash+Slag)}/m_water). Then, the flexural and compressive strength of specimens after 3 days of standard curing was tested, the response surface between compressive strength and design parameters was obtained, the effect of the design parameters on the compressive strength was analyzed, and prediction and verification of the compressive strength were conducted.

2 Experiments

2.1 The raw materials

Powder material: slag, specific surface area of 491.6 m² kg⁻¹, 28 days activity index ≥95%; fly ash, grade I by Chinese national standard, and chemical composition as shown in Table 1.

Table 1 The chemical constituents of slag and fly ash (mass %)

Oxide	SiO2	Al2O3	Fe2O3	CaO	Na2O	TiO2	MgO	K2O	P2O5	SO3	Other	Loss on ignition
Slag	29.2	19.4	5.8	38.6	0.2	0.6	2.8	0.1	—	2.6	0.4	0.3
Fly ash	45.8	21.4	12.6	13.7	1.1	0.2	1.3	1.8	0.1	1.9	—	0.1

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Raw materials of activator: NH: analytical reagents, flake, content ≥99.0%; NC: analytical reagents, powdery, content ≥99.8%;

Admixture: sodium tripolyphosphate, with content percentage of 0.4%.

2.2 Specimen preparation and test method

Numerous experimental studies have shown that the temperature of the activator has a strong influence on the early strength of the specimens. In the preparation of activator, the reaction of solid NH encountering water produces a lot of heat, and the temperature of the solution will rise rapidly, and generally can reach 80 °C. To ensure comparability, the activator should be cooled down to room temperature. Through constant temperature tests by using a thermometer, when the temperature has dropped to 40 °C, the preparation starts.

First, mix NH, NC and water for 60 s; second, mix slag and fly ash for 60 s; and when the temperature of the activator has dropped to 40 °C, mix alkali-activator and composite material obtained through the two steps above for 120 s. The mixtures can act as a paste, and the paste specimen should be cured in standard conditions of 20 °C and >95% relative humidity for 3 days.

After 3 days of standard curing, the flexural strength test and compressive strength test were implemented according to GB/T 17671-1999, “Method of Testing Cements – Determination of Strength”.

3 Response surface tests

3.1 Basic introduction

RSM^13,14 is an approach to conducting testing, modeling, data analysis, optimizing and predictive parsing on the research objects by the method of combining mathematics and statistics. The aim is to obtain the functional relationship between response y and element ζ₁, ζ₂, …, ζ_K, as shown in eqn (1).

y = f(ζ₁, ζ₂, …, ζ_K) + ε (1)

where ε represents system error, which cannot be explained by f; f(ζ₁, ζ₂, …, ζ_K) is the true response of the function.

Central composite circumscribed (CCC)¹⁵ is a specific design method of RSM. In CCC, the scope of factor levels would be wide and forecasting accuracy can be guaranteed. Furthermore, by means of adjusting the parameters, the experimental design can be apt to reach some properties, such as orthogonality and rotatability, and these characteristics provide a more expansive stage for the application of materials research. CCC is usually used in biotechnology, and is rarely used in building materials research and development.

The basic process of RSM is as follows: firstly, the model of the response surface equation in line with practice should be chosen based on the expertise related to the subject of response surface tests; secondly, according to the least squares method, estimate the corresponding coefficient of the model, and the initial response surface equation can be obtained make a significance analysis of the regression equation and regression coefficients, and reject the variable whose coefficient is the least significant based on the significance test, then establish the response surface equation after this rejection, and then retest until all of the coefficients are significant, so the modified response surface equation can be obtained.

In the process of experimental design, adjusting the concrete parameters of CCC can make the design achieve the requirement of orthogonality and rotatability. The design rotatability could reach the level of consistency of predicted variance, improving the accuracy. Design orthogonality could fit the objective of reasonable design and work with data more easily. This experiment has adopted the above-mentioned methods, to be called “orthogonal rotation combination design of RSM (RSM-ORCD)”.

Based upon the RSM-ORCD, flexural strength and compressive strength after 3 days of standard curing were tested, and the relationship between compressive strength and design parameters was established.

3.2 Test methods and results

In CCC, there are five design levels for each factor: ±r, 0, ±1. The tests generally consist of three kinds of test points. If the number of design factors is K, the total tests number (identified as M) can be calculated as eqn (2).

M = m_K + m_r + m₀ (2)

where m_K = 2^K, the test points when all factors get two levels; m_r = 2K, coordinate points, and r is the distance between pivot point and central point; and m₀ is the central point when all factors are at zero level.

In order to satisfy the consistency of variance, design r = 2 to make the CCC have rotatability, on the premise of guaranteeing the accuracy. To achieve a reasonable design and data processing, when r = 2, design m₀ = 12 to satisfy the requirement of orthogonality. Therefore, when r = 2, m₀ = 12, N = 36, the experimental design meets the rotatability and orthogonality, which can be called a response surface orthogonal rotational combination design method.

Based on a coding transform principle, the corresponding table of factor and coding is established, as is shown in Table 2.

Table 2 The corresponding table of factor and coding

Coding	Factor
	BWR	FSR	AC	n
−2	2.2	0.2	4.00%	0.4
−1	2.6	0.6	6.00%	0.7
0	3.0	1.0	8.00%	1.0
1	3.4	1.4	10.00%	1.3
2	3.8	1.8	12.00%	1.6

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The experimental scheme and results are shown in Table 3, where the coding of BWR is x₁, the coding of FSR is x₂, the coding of AC is x₃, the coding of n is x₄, the 3 days flexural strength is f_f-3d, and the 3 days compressive strength is f_c-3d.

Table 3 Experimental scheme and results

Serial number	x1	x2	x3	x4	ff-3d	fc-3d	Serial number	x1	x2	x3	x4	ff-3d	fc-3d
1	1	1	1	1	2.91	14.58	19	0	2	0	0	1.43	12.54
2	1	1	1	−1	1.87	10.54	20	0	−2	0	0	4.87	32.54
3	1	1	−1	1	3.32	16.11	21	0	0	2	0	1.94	8.09
4	1	1	−1	−1	0.87	5.21	22	0	0	−2	0	1.42	8.39
5	1	−1	1	1	5.70	24.13	23	0	0	0	2	3.84	13.35
6	1	−1	1	−1	4.02	24.01	24	0	0	0	−2	0.38	1.23
7	1	−1	−1	1	5.54	28.36	25	0	0	0	0	2.76	13.17
8	1	−1	−1	−1	2.99	19.17	26	0	0	0	0	2.32	14.22
9	−1	1	1	1	2.08	10.17	27	0	0	0	0	2.83	14.72
10	−1	1	1	−1	0.94	4.29	28	0	0	0	0	2.64	12.35
11	−1	1	−1	1	2.83	12.37	29	0	0	0	0	2.30	11.68
12	−1	1	−1	−1	0.00	0.00	30	0	0	0	0	2.72	13.90
13	−1	−1	1	1	3.58	16.60	31	0	0	0	0	2.62	13.23
14	−1	−1	1	−1	1.58	9.68	32	0	0	0	0	2.77	12.11
15	−1	−1	−1	1	3.14	17.58	33	0	0	0	0	2.41	14.78
16	−1	−1	−1	−1	0.35	1.90	34	0	0	0	0	2.33	13.41
17	2	0	0	0	3.69	23.23	35	0	0	0	0	2.76	12.48
18	−2	0	0	0	1.03	4.47	36	0	0	0	0	2.64	15.12

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According to the comparison between the response data, the proportions of no. 7 and no. 20 demonstrate excellent mechanical strength. From analysis based on the choosing principle “high volume fly ash, low volume alkali”, the no. 7 proportion has the advantage of strength with 37.5% of fly ash and 6.0% of alkali. Moreover, from observations in the course of the experiments, this proportion possesses excellent workability. Thus it can be seen that this proportion can give full play to the synergies with each component, and achieve the purpose of stimulating potential activation greatly.

In the view of chemistry, for slag and fly ash, SiO₂, CaO, Al₂O₃, Fe₂O₃ are the main chemical components, and play a significant role in the alkali-activated reaction. Under the same alkali activator (AC = 6.0%, n = 1.3), the optimum ratio (in mass) of SiO₂, CaO, Al₂O₃ and Fe₂O₃ is 4.24 : 3.50 : 2.41 : 1.00; in terms of chemical elements, the optimum ratio (in mass) of Si, Ca, Al and Fe is 2.12 : 1.75 : 2.41 : 1.00.

The process of making geopolymer is a series of chemical reactions. Under the optimal composition, raw materials have been fully used. That is an ideal condition in the preparation of material.

3.3 Establishment of the response surface

Taking response f_f-3d as an example, make an analysis of the relation between f_f-3d and components based on the theory of RSM. After successive rejecting and testing, the information about the final testing is as follows:

Adaptability test: F_Lf = 2.64142 < F_α(f_Lf, f_e) = F_0.05(16, 11), and “p value >F” is 0.0556 > 0.05, so the model is adaptable.

Significance test of equation: , moreover approaches 1, so the significance of the equation can be judged by the two points above.

Significance test of regression coefficients: “p value >F” of the final regression coefficients <0.05, which suggests that each regression coefficient is significant.

The modified response surface equation can be expressed as eqn (3).

f_f-3d = ζ^TA_f-3dζ (3)

where ζ = (1, ζ₁, ζ₂, ζ₃, ζ₄)^T = (1, BWR, FSR, AC, n)^T;

With the same method, the relation between f_c-3d and components can also be expressed as eqn (4).

f_c-3d = ζ^TA_c-3dζ (4)

where.

Based on RSM related theory, through repeated testing and correction, the relationship between f_f-3d and f_c-3d with design parameters has been obtained, and from the point of mathematical analysis, the early strength system based on RSM-ORCD was reliable.

4 The prediction and validation of response surface

It is necessary to implement prediction and validation of the early strength system. Establish the experimental scheme of strength prediction, predict f_f-3d and f_c-3d in the light of the early strength system, and at the same time, test the strength after 3 days of standard curing, aiming at making a comparative analysis. The experimental scheme and the results are shown in Table 4.

Table 4 Experimental scheme of prediction and validation

Serial number	BWR	FSR	AC	n	ff-3d prediction intervals		ff-3d measured value	fc-3d prediction intervals		fc-3d measured value
YC-1	3.2	0.6	6.00%	1.3	4.605	5.369	5.01	25.654	27.398	26.25
YC-2	3.2	0.4	6.00%	1.3	5.361	6.072	5.43	30.124	33.444	32.1
YC-3	3.2	0.6	7.00%	1.3	4.837	5.306	4.98	24.783	27.199	26.54
YC-4	3.2	0.6	6.00%	1.8	6.576	7.640	7.27	23.458	29.959	25.36
YC-5	2.8	0.6	6.00%	1.3	3.549	4.113	3.97	19.751	22.081	20.56
YC-6	2.8	0.4	6.00%	1.3	4.002	4.713	4.51	23.032	27.182	24.36
YC-7	2.8	0.6	7.00%	1.3	3.680	4.150	3.84	20.113	21.887	20.68
YC-8	2.8	0.6	6.00%	1.8	5.419	6.484	6.05	17.437	26.373	21.39
YC-9	2.4	0.6	6.00%	1.3	2.292	3.056	2.66	12.744	17.538	15.67
YC-10	2.4	0.4	6.00%	1.3	2.505	3.492	2.85	14.903	21.822	18.75
YC-11	2.4	0.6	7.00%	1.3	2.409	3.107	3.04	14.326	17.395	15.64
YC-12	2.4	0.6	6.00%	1.8	4.203	5.386	4.83	17.702	23.72	19.81

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According to Table 4, all the measured strengths are within the prediction interval, which indicates that, from the viewpoint of application, the early strength system can endure the examination of practice, and be feasible in practice. The response surface can also be used as the principle of proportion design to prepare composite materials of different strength grade.

5 Theoretical application of response surface

The analysis above shows that, from the perspective of either mathematics or application, the SWG-SF response surface equation is reliable, so it can be used to conduct a theoretical analysis of the effect of each component on f_f-3d.

When the research focuses on the effect of some design parameter on f_f-3d, the rest of the design parameters should be seen as constant; ζ₁, ζ₂, ζ₃, ζ₄ are respectively replaced by letter a, b, c, d; the range of various factors are respectively [2.6, 3.4], [0.6, 1.4], [0.06, 0.10], [0.7, 1.3]; accordingly, constant terms are represented by K₁, K₂, K₃, K₄.

5.1 The effect of BWR on f_f-3d

In order to facilitate the analysis, BWR is seen as an independent variable, and the remaining factors are replaced by letters, then according to eqn (3), the relationship between BWR and f_f-3d can be expressed as eqn (5).

Fig. 1 gives the schematic drawing of the quadratic function above.

Fig. 1 The effect of BWR on f_f-3d.

From the analysis of the figure, the slope of the straight line can be expressed as k = 4.41 − 2.53b. According to the value ranges of b, it can be seen that k > 0, so f_f-3d will increase linearly with increasing BWR, within certain ranges. Moreover, the increasing rate is closely related to FSR, which can be concluded from analyzing the straight slope in eqn (5).

With a decrease of BWR, the reaction is more complete, but the pore volume gets bigger accordingly. Then the structure of the hardened paste (including the interfacial transition zone between paste and aggregate) is looser, the bond strengths of the paste and the paste-aggregate interface are weaker, and the strength of the geopolymer is also lower.

5.2 The effect of FSR on f_f-3d

FSR is seen as an independent variable, and the rest of the factors are replaced by letters. According to eqn (3), the relationship between FSR and f_f-3d can be expressed as in eqn (6).

f_f-3d = 1.17ζ₂² + (3.29 − 2.53a)ζ₂ + K₂ (6)

Fig. 2 gives the schematic drawing of the quadratic function above.

Fig. 2 The effect of FSR on f_f-3d.

According to the function above, the symmetry axis of the quadratic function can be expressed as . According to the value range of a, ζ_{2 peak(min)} = 1.41 can be worked out. Based on the properties of quadratic functions, f_f-3d will decrease continuously with FSR, but the decreasing rate will get slower and slower, and the BWR will have a certain influence on the change rate of strength.

Puertas et al.¹⁶ pointed out that when slag and fly ash are activated to produce cementitious materials, slag is almost completely activated, but fly ash is only partly activated. Therefore, more slag, more strength. So the increase of FSR means an increase of fly ash and a decrease of slag, which will lead to a decrease of strength.

5.3 The effect of AC on f_f-3d

AC is seen as an independent variable, and the rest of the factors are replaced by letters. According to eqn (3), the relationship between AC and f_f-3d can be expressed as in eqn (7).

f_f-3d = −452.08ζ₃² + (131.67 − 49.58d)ζ₃ + K₃ (7)

Fig. 3 gives the schematic drawing of the quadratic function above.

Fig. 3 The effect of AC on f_f-3d.

From the function above, the symmetry axis of the quadratic function can be expressed as . According to the value range of d, ζ_{3 peak(min)} = 7.43%, ζ_{3 peak(max)} = 10.72% can be worked out, and at the same time, ζ₃ ∈ [0.06, 0.10]. Based on the properties of quadratic functions, the effects of AC on f_f-3d correspond to the shaded part of Fig. 3. As AC increases, f_f-3d will increase during the initial stage and then decrease, which indicates that there is a best AC value.

Fig. 4 The effect of the factor n on f_f-3d.

5.4 The effect of n on f_f-3d

‘n’ is seen as an independent variable, and the rest of the factors are replaced by letters. According to eqn (3), the relationship between n and f_f-3d can be expressed as in eqn (8).

f_f-3d = (7.22 − 49.58c)ζ₄ + K₄ (8)

Fig. 4 gives the schematic drawing of the quadratic function above.

From the figure, the slope of the straight line can be expressed as k = 7.22 − 49.58c. According to the value ranges of c, k > 0 can be worked out. So, within a certain range, f_f-3d increases linearly with n, and the increasing rate is closely related to AC.

There is a complex chemical reaction process: slag and fly ash are activated by NH and NC to produce geopolymer. The vitreous structure in the slag and fly ash is dissolved in the composite alkali environment, and Si–O– and Al–O– bonds are broken, then Si and Al oligomers are formed under the effect of Na⁺, OH⁻ et al. Then the polycondensation reaction occurs among these oligomers. In the process of the polycondensation reaction, with oligomers as the bonding agent, an inorganic polymer with a three-dimensional network structure was formed.

According to the “alkali activation theory”⁵ and the analysis above, alkali plays an important role in the chemical reaction. However, the excess alkali that corresponds to the greater AC will have unexpected damage on the reaction. This reflects that there is a suitable dosage for alkali. NH can stimulate the potential activity of slag and fly ash better than NC, which can be concluded by the effect of n on the early strength. These features can be adopted in the application of the new alkali-activated material.

6 Application prospects

The experimental scheme was established by using the response surface orthogonal rotational combination design method, and the early strength system of SWG-SF was built; the reliability of the strength system was confirmed through mathematical analysis, so the system has a definite guiding function and can be used for theoretical research, such as studies on the effect of each component on early strength, or studies on the synergy of each component; the predicting ability of this strength system has been tested through practice, indicating that this system can be taken as the basis for the proportion design used for the preparation of composite materials with different strength grades or in other application fields.

Thus it can be seen that, as a kind of advanced new experimental design method, RSM can be widely used in the establishment of the strength system of composite cementitious material, and the reliability and practice test can be guaranteed. Moreover, the model based on RSM can also extend to theoretical research and has promising application prospects.

7 Conclusions

Based on a response surface orthogonal rotational combination design method, a testing program has been made, the response surface research on the preparation of SWG-SF has been carried out, and the application prospects of RSM in strength systems of new materials have also been analyzed. The main conclusions are as follows:

(1) When FSR = 0.6, AC = 6.0% and n = 1.3, it can give full play to the synergies of the components, and can well inspire the potential activity of slag and fly ash.

(2) The early strength system of a solid waste (slag-fly ash) based geopolymer system can be established on the basis of RSM. From the viewpoint of mathematical analysis, it is reliable, and can be used in the theoretical analysis of the effect of various factors on the early strength.

(3) For this new composite material, f_f-3d increases linearly with BWR and n; as FSR increases, f_f-3d decreases continuously, with the relationship corresponding to the concave descent stage of the quadratic function; the relationship between f_f-3d and AC corresponds to the maximum area of the quadratic function, and this shows that there is a best dosage for AC.

(4) The predicting ability of the early strength of a solid waste (slag and fly ash) based geopolymer has been verified. From the application perspective, it is feasible, so it can play a role in the practice of proportioning design.

(5) RSM is an advanced experiment design method, and it can be widely used in the preparation of new solid waste based geopolymers and has promising application prospects in the utilization of solid waste.

Acknowledgements

Foundation item, Foundation item: Projects of National Natural Science Foundation of China (51208507, 51378497); Industrial Public Relation Project for science and technology development in Shaanxi province of China (2014K10–15); Open Foundation for State Key Laboratory of explosion shock, disaster prevention and reduction (DPMEIKF201406); Projects of youth technology new star of Shaanxi province in China (2013KJXX-81); Doctorate Fellowship Foundation of Air Force Engineering University (kgd082314005).

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