The paper investigates the secondorder interactions of parameters in an alkaliactivated mixture of paper production waste (PPW) and blast furnace slag (BFS) in Taguchi method. The PPW including lime mud (LM) and paper sludge (PS). This paper provides the experimental models to assess the compressive and flexural strength of them at 7day and 28day. The results have shown that the secondorder interactions between PPW and alkaliactivated activator exists in each experimental model, and the significant interactions affect the selection of optimal compositions. Compared with the interactions between the PPW themselves, the interactions between PPW and alkaliactivated parameters are the main significant factors affecting its physical properties. In each experimental model, the maximum compressive strength was 47.41 MPa in 7day and 65.64 MPa in 28day. Compared with the confirmatory experiments, the deviation of prediction calculated by experimental models was 3.08% and 0.56%, respectively. The maximum flexural strength was 5.74 MPa in 7day and 5.96 MPa in 28day; compared with the confirmatory experiments, the deviation of prediction calculated by experimental models was 5.40% and 0.17%. Considering the influence of circular materials, 30% of PPW should be a suitable ratio to replace BFS as the raw material of alkaliactivated slag (AAS).
As the globalization accelerates, sources exhaustion, environmental pollution, and climate warming have become challenges to all countries and industries, which has to be faced and tackled together. As far as the paper industry is concerned, the volume of worldwide paper production in 2018 was nearly 420 million tons [
In current studies, utilizing PPW as a substitute for Portland cement is one of the ways to translate translating wastes into building materials. Yan et al. [
Although recently there are some studies on utilizing PPW as a raw material of cement or alkaliactivated cementitious binder, there are still many problems to be resolved. One of the problems is the applicability of the research. Considering the diversity of waste sources on qualities and compositions, the universality of the single study result is undermined. Meanwhile, most studies focus on a single kind of PPW, but there are few reports on the systematic integration of different PPW and translating them into building materials, which means that the previous studies cannot systematically assess the possibility of translating wastes into building material in the paper industry. Therefore, it is necessary to find a way for the rapid screening of specific batches of PPW.
Taguchi method is a fractional factorial design method that can investigate a large number of parameters with a small number of experiments [
This study uses Taguchi methods and analysis of variance (ANOVA) to analyze the effect of the significant interaction of parameters in an alkaliactivated mixture of PPW and BFS. The experimental models are established by significant factors to investigate different mechanical properties (compressive and flexural strengths of 7day and 28day). The optimal composition of each experimental model is given and verification experiments have been conducted. It is hoped that researchers using the Taguchi method to conduct similar research may ensure the accuracy of the optimization design through the proposed analysis of the interaction effects.
The materials used in this study were blast furnace slag (BFS), lime mud (LM) and primary sludge (PS). According to Taiwan Standard CNS12549 [
Parameters  Composition (%)  

BFS  Lime Mud  Paper sludge  
SiO_{2}  33.46  –  1.42 
Al_{2}O_{3}  13.70  –  – 
CaO  42.69  78.00  19.9 
SO_{3}  1.48  18.40  2.41 
Fe_{2}O_{3}  0.42  1.75  0.72 
K_{2}O  0.35  –  0.08 
MnO  0.39  0.08  0.01 
Cl  –  –  0.13 
TiO_{2}  0.46  0.01  0.01 
LOI  0.42  1.44  75.3 
To simplify the manufacture and for convenient storage of raw materials, solid powder was used to prepare the activator solution. The sodium hydroxide pellet composition was 99.45% NaOH and 0.27% Na_{2}CO_{3}. The composition of sodium silicate powder was 46.07% SiO_{2}, and 51.35% Na_{2}O. Its silicate modulus (SiO_{2}/Na_{2}O) was 0.93. To vary the silicate modulus activator, the NaOH pellets content would be raised to change the Na_{2}O ratio. The alkali equivalent of activator could be calculated by the weight ratio of Na_{2}O to binder.
According to ASTMC141 [
The study chose the
Note: T: Time; AE: Alkali equivalent; Ms: Silicate modulus; LM: Lime mud; PS: Primary sludge.
Given the huge number of factors, the generalized linear model, which was built with experimental values directly, might not accurately evaluate the effects every factor. It is because the higherorder items possibly existed in the experimental model [
The parameter
The twoway interaction of parameters means that the effect of one of the parameters differs depending on the other level of parameter. Similar calculation applies to the effect of parameters; the level +1 of interactions can be defined as two parameters having the same level (the product of parameter level is +1), and the level −1 of interactions are the parameters that have the different level (the product of parameter level is −1). The calculation formula on the twoway interaction of A × B was [
The parameter
The
Whether parameter or factor, the interaction of D is not the significant factor, so D is not in the calculation formula. The
According to the results of previous experiments [
Parameters  Level 1  Level 2 

Time (T/min)  10  20 
Alkali equivalent (AE%)  5%  10% 
Silicate modulus (Ms)  0.5  0.9 
Lime mud (LM)  5%  15% 
Paper sludge (PS)  5%  15% 
Experiment series  Activator  BFS (kg/m^{3})  Lime mud (kg/m^{3})  Paper sludge (kg/m^{3})  Sand (kg/m^{3})  Water/Binder (wt./wt.)  Mixing time (min)  

AE (wt.%)  Ms  Sodium silicate powder (kg/m^{3})  Sodium hydroxide powder (kg/m^{3})  
TM1  5  0.5  23.7  13.3  405  22.5  22.5  1237.5  0.55  10 
TM2  5  0.5  23.7  13.3  315  67.5  67.5  10  
TM3  5  0.9  42.6  0.8  360  22.5  67.5  10  
TM4  5  0.9  42.6  0.8  360  67.5  22.5  10  
TM5  10  0.5  47.3  26.7  360  67.5  22.5  10  
TM6  10  0.5  47.3  26.7  360  67.5  22.5  10  
TM7  10  0.9  85.3  1.6  405  22.5  22.5  10  
TM8  10  0.9  85.3  1.6  315  67.5  67.5  10  
TM9  5  0.5  23.7  13.3  360  22.5  67.5  20  
TM10  5  0.5  23.7  13.3  360  67.5  22.5  20  
TM11  5  0.9  42.6  0.8  405  22.5  22.5  20  
TM12  5  0.9  42.6  0.8  315  67.5  67.5  20  
TM13  10  0.5  47.3  26.7  405  22.5  22.5  20  
TM14  10  0.5  47.3  26.7  315  67.5  67.5  20  
TM15  10  0.9  85.3  1.6  360  22.5  67.5  20  
TM16  10  0.9  85.3  1.6  360  67.5  22.5  20 
The repeated orthogonal experimental design was adopted in this experiment. Compressive and flexural strength of mortar were examined at 7 and 28day. In advance, sodium hydroxide pellet and sodium silicate powder were dissolved in water as the activator and cooled down to room temperature. The solid materials were mixed for 2 mins and added in activator solution to prepare mortar according to ASTM C305 [
Experiment series  Compressive strength  Flexural strength  

7day  28day  7day  28day  
Value (MPa)  Standard deviation  Value (MPa)  Standard deviation  Value (MPa)  Standard deviation  Value (MPa)  Standard deviation  
TM1  21.93  1.65  29.66  2.86  3.42  0.12  5.18  0.45 
TM2  23.78  1.19  37.61  0.99  3.74  0.16  5.65  0.34 
TM3  29.57  1.13  38.01  2.30  4.87  0.38  5.40  0.27 
TM4  30.69  1.81  51.05  2.24  4.05  0.17  5.96  0.37 
TM5  27.85  1.34  45.92  1.17  4.18  0.36  5.32  0.40 
TM6  26.29  1.21  40.40  0.97  4.27  0.22  4.60  0.52 
TM7  33.68  0.95  65.64  3.24  5.08  0.50  5.22  0.63 
TM8  26.58  1.52  48.52  2.14  5.25  0.40  4.44  0.46 
TM9  19.16  0.63  43.60  1.69  2.90  0.30  5.39  0.32 
TM10  18.28  0.86  37.66  1.08  3.49  0.31  5.19  0.33 
TM11  33.93  1.93  47.68  2.76  3.93  0.34  5.65  0.42 
TM12  19.43  1.40  52.52  1.78  4.36  0.28  5.38  0.60 
TM13  24.50  1.86  34.19  1.33  4.24  0.35  4.42  0.49 
TM14  22.68  0.73  29.45  0.98  3.36  0.21  4.01  0.24 
TM15  47.41  1.34  42.82  2.40  4.86  0.71  3.35  0.40 
TM16  40.10  3.19  42.82  2.23  3.60  0.64  4.08  0.65 

27.87    42.97    4.10    4.95   

1.4294    1.6238    0.6057    0.6884   
In this experiment, a multivariate analysis of variance (ANOVA) was used to test the significance of each factor. For the experimental models with excess significant factors (>7), ‘onehalf criterion’ [
From
Factors  7day  28day  

Contribution (%)  Contribution (%)  
T  −0.0066  0.008  0.33  −0.0141  0.000  2.44 
AE  0.0501  0.000  19.04  0.0056  0.010  0.38 
T × AE  −0.0323  0.000  7.94  0.0491  0.000  29.62 
Ms  0.0710  0.000  38.28  0.0574  0.000  40.32 
T × Ms  −0.0300  0.000  6.83  0.00205  0.340  0.05 
AE × Ms  −0.0067  0.007  0.34  −0.00435  0.044  0.23 
LM × PS  0.0259  0.000  5.09  0.00525  0.016  0.34 
LM  −0.0279  0.000  5.90  −0.00245  0.252  0.07 
T × LM  0.0183  0.000  2.54  0.00825  0.000  0.83 
AE × LM  0.0015  0.547  0.02  0.0290  0.000  10.28 
Ms × PS  0.0210  0.000  3.34  0.0235  0.000  6.80 
Ms × LM  0.0226  0.000  3.87  −0.00745  0.001  0.68 
AE × PS  −0.0103  0.000  0.80  0.0139  0.000  2.37 
T × PS  0.0077  0.002  0.44  −0.0088  0.000  0.95 
PS  −0.0149  0.000  1.68  −0.00365  0.092  0.16 
Error      3.55      4.47 
From
Factors  7day  28day  

Contribution (%)  Contribution (%)  
T  −0.02835  0.000  12.94  −0.026  0.000  11.54 
AE  0.0266  0.000  11.39  −0.0485  0.000  40.15 
T × AE  0.00765  0.063  0.94  0.0204  0.000  7.10 
Ms  0.04195  0.000  28.34  −0.0041  0.341  0.29 
T × Ms  0.00305  0.456  0.15  0.0063  0.143  0.68 
AE × Ms  0.0102  0.014  1.68  0.0137  0.002  3.20 
LM × PS  −0.00845  0.041  1.15  −0.0054  0.211  0.50 
LM  −0.00765  0.063  0.94  −0.0031  0.475  0.16 
T × LM  0.0057  0.164  0.52  −0.0036  0.405  0.22 
AE × LM  0.0183  0.000  5.39  0.0082  0.059  1.15 
Ms × PS  −0.0265  0.000  11.31  0.01865  0.000  5.94 
Ms × LM  0.0112  0.007  2.02  −0.0074  0.089  0.93 
AE × PS  0.0029  0.480  0.14  0.00745  0.085  0.95 
T × PS  0.008  0.053  1.03  0.0076  0.078  0.99 
PS  0.0076  0.065  0.93  −0.0088  0.043  1.32 
Error      21.13      24.89 
The stepwise regression analysis was used to check the statistical accuracy of experimental models and evaluate the goodness of fit of experimental models. In the investigation, the confidence interval of ANOVA was 99%.
Experimental model  

Standard deviation  0.043  0.025  0.044  0.045 
83.72  161.31  36.97  38.04  
<0.001  <0.001  <0.001  <0.001  
0.932  0.963  0.845  0.824 
The significant interactions were mainly related to lime mud (LM) in 7day compressive strength, and its coefficient accounted for 18.6% of the total significant factors in the experimental model. The significant interactions are shown in
With the ratio of LM increased in binder, the compressive strength showed different trends on the Ms and Ps at different levels. The compressive strength exhibited a small fluctuation with the low Ms concentration (0.5). And an increase in the ratio of LM from 5% to 15% with the high Ms concentration (0.9) resulted in a 19.2% reduction in the 7day compressive strength (
In experimental models of 28day compressive strength, the significant interactions related to waste were AE × LM, AE × PS, AE × PS, AE × PS, and the coefficient accounted for 38.4% of the total significant factors in the experimental model. The significant interactions existed in AE and PPW, PS and alkaliactivated parameters. The interactions of those factors are shown in
From
From
In addition to PPW, alkaliactivated conditions also had an important impact on compressive strength. In the experimental mode of compressive strength, the contribution of the Ms accounted for 38.28% and 40.32% of the total parameters in the 7day and 28day compressive strength respectively. In terms of the increase in Ms from 0.5 to 0.9, the 7day and 28day compressive strength increased by 9.62 and 11.32 MPa, respectively. The trend of compressive strength was the same as alkaliactivated slag (AAS) [
The high concentration of AE was conducive to the 7day compressive strength. With the increase in AE from 5% to 10%, the 7day compressive strength was enhanced by 6.54 MPa. It was attributed to the high concentration of Na^{+} and OH^{−} that accelerated the dissolution of raw material and the formation of hydrates [
In experimental models of 7day flexural strength, the significant interactions related to waste were Ms × PS, AE × LM, Ms × LM, and the coefficient accounted for 36.6% of the total significant factors. In experimental models of 28day flexural strength, the significant interactions related to waste were Ms × PS, and the coefficient accounted for 14.7% of the total significant factors. The interactions of those factors are shown in
From
In the interactions of Ms × PS, the 7day and 28day flexural strength were completely opposite. At the low Ms concentration (0.5) (
In the experimental models of 7day flexural strength, the contribution of the Ms accounted for 28.34% of the total parameters. Combined with the effect of Ms increasing, the 7day flexural strength increased by 0.8 MPa. It was not the same as AAS [
As the purpose of Taguchi Method is to find an optimal composition of alkaliactivated binder, it is necessary to investigate the different ratios of PPW substituted for BFS in the mixture. The strengths of different ratios in binder are shown in
As seen in
From the experimental models of 7day compressive strengths, the equation has the optimal value in following conditions:
Therefore with
The optimal composition of 7day compressive strength is:
From the experimental models of 28day compressive strengths, the equation has the optimal value in following conditions:
Therefore with
The optimal composition of 28day compressive strength is:
From the experimental models of 7day flexural strengths, the equation has the optimal value in the following conditions:
Therefore with
The optimal composition of 7day flexural strength is:
From the experimental models of 28day flexural strengths, the equation has the optimal value in following conditions:
Therefore with
The optimal composition of 28day flexural strength is:
In previous literatures [
Because of the effect of parameters without interactions, there is only a 50% chance to have the real optimal compositions (28day compressive strength and 7day flexural strength) and other optimal compositions are proved to be wrong. Among them, the optimal composition of 7day compressive strength obtained by the effect of parameters without interactions is 33.68 MPa, which is significantly smaller than the actual optimal ratio 47.41 MPa. The optimal composition of 28day flexural strength obtained by the effect of parameters without interactions is 5.18 MPa, which is significantly smaller than the actual optimal ratio 5.96 MPa. Therefore, from the perspective of chosen optimal compositions, it is necessary to consider the significant interaction of parameters while the waste, which has inseparable impurities is used as the substitution for BFS.
This paper has investigated the secondorder interactions of parameters in an alkaliactivated mixture of PPW and BFS. Based on the test results, the following conclusions can be drawn:
In selecting the optimal composition, interactions of parameters should firstly be investigated because interactions of parameters will affect the optimal composition selection. If not considering the effects of parameters interactions, it may lead to the wrong selection of the optimal composition. Compared with the interactions between the PPW themselves, the interactions between PPW and alkaliactivated parameters are the main significant factors to the physical properties.
The experimental models of compressive and flexural strengths, which alkaliactivated the PPW as a substitution for BFS, have been given in this investigation. The maximum of 7day and 28day compressive strengths are 47.41 and 65.64 MPa, respectively; the prediction errors of 7day and 28day compressive strengths are 3.08% and 0.56%, respectively; the maximum of 7day and 28day flexural strengths are 47.41 and 65.64 MPa, respectively; the prediction errors of 7day and 28day flexural strengths are 3.08% and 0.56%, respectively.
Although the compressive and flexural strengths will decrease with the increase of the PPW ratio, this decrease is limited. When the PPW increased from 10% to 30%, the reduction of strength is 5%. Therefore, considering the coefficient of utilization in translating PPW into building materials, 30% of PPW should be a suitable ratio in replacing BFS as the raw material of AAS under the consideration of circular materials.