Effect of different soluble salt ions on deformation of desulfurization gypsum in high humidity environment: a statistically designed experimental analysis method

In response to the green energy-saving goal of carbon neutralization and carbon peak, the research and development of green building materials have become a key research direction. Desulfurization gypsum is widely used in building materials because of its good energy saving, but it cannot be used in high humidity areas because of its highly soluble salt. Based on this reason, this paper uses statistically designed experiments (SDE) to design the experiments on the influence of four common soluble salt ions Na+,Mg2+,Cl− and K+ on the sagging deformation of desulfurization gypsum, and studies the significance of their influence by SDE experimental analysis method. The results show that: (1) in the environment of a single salt solution, K+ ion, Mg2+ ion, Na+ ion, and Cl− ion will cause sagging deformation of desulfurization gypsum, and their values are 0.432 mm, 1.933 mm, 0.942 mm, and 0.940 mm respectively. It can be seen that the effect of the Mg2+ ion is the most significant. (2) In the environment of composite salt solution, K+ ions will inhibit the sagging deformation of desulfurization gypsum. Specifically, in the compound salt solution environment of K++Mg2+ and K++Na+, the deformation values are 0.605 mm and 0.596 mm respectively.


Introduction
As a by-product of thermal power plants, the output of desulfurization gypsum is increasing rapidly with the large-scale application of flue gas desulfurization devices in China (Li and Wang 2018). According to statistics, the annual output of desulfurization gypsum in 2014 was about 75.5 million tons. China's 13th five-year plan puts forward that it is necessary to speed up the recycling of waste resources (Hao et al 2016, Ding et al 2021, Ding et al 2023a, 2023b. Thereforethe desulfurization gypsum has excellent utilization prospects. Currently, the desulfurization gypsum is mainly used in building materials (Li et al 2019). However, due to the particularity of the production process of desulfurization gypsum, it contains a high content of soluble salt, so the soluble salt content in its products is also correspondingly high, which may affect the service performance of desulfurization gypsum (Zhong et al 2017. In the rainy season in the Southeast coastal areas of China, there are often reports of large sagging deformation of ceiling gypsum (Han et al 2016). The preliminary investigation Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
shows that desulfurization gypsum is used in gypsum, and the high content of soluble salt in it leads to deformation due to moisture absorption under high air humidity (Guan et al 2017, Graves et al 2017. At present, the soluble salts in domestic desulfurization gypsum are mainly soluble salts composed of sulfate or chloride of sodium, potassium, and magnesium (Lefers et al 1987, Wang et al 2013. For example, Zhao et al (2018) evaluated the long-term effects of flue gas desulfurization gypsum application on soil salinity and sodicity, crop production, and heavy metals in soils and crops. Song et al (2015) developed a process for the precipitation of pure CaCO 3 by exploiting the induction period of one-step mineral carbonation of flue gas desulfurization gypsum. Therefore, it is necessary to profoundly and comprehensively explore the influencing factors and significance of moisture absorption and sagging of desulfurization gypsum in a high-humidity environment.
Nowadays, the most reliable tool to study the significance of influencing factors is the SDE analysis method (Chen et al 2020, Llewelyn et al 2020. It is a frontier discipline based on mathematical modeling, statistical theory, computer-aided modeling, and model optimization (Badizi et al 2020, Jeong et al 2020. Applying it to the experiment of building materials can effectively improve the experimental quality and simplify the number of experiments (Chong et al 2021). At the same time, it can avoid the intuitive misjudgment of analysts to improve the reliability of analysis results in the analysis of experimental results. For example, Atiq et al (2017) presented a study on the DOE approach to optimize the electrophoretic deposition process parameters for PEEK base coatings. Shen et al (2008) used DOE to systematically compare several microstructural features' effects on the mechanical responses via 2D and 3D finite element simulations. Petrone et al (2016) selected a set of five plasterboard typologies, and the tests were performed in two different load directions: parallel or transversal to the direction of production. Kamara et al (2021) used a statistical mixture design program to design the experiment.
This paper conducted an experimental analysis of the excessive hygroscopic sagging deflection of desulfurization gypsum, exploring the influence of different kinds, different contents, and different combinations of soluble salts on the excessive hygroscopic sagging deflection of desulfurization gypsum, and analyzed the significance of its influencing factors with SDE.

Raw materials
The desulfurization gypsum produced by a Shanghai power plant is high-quality with few impurities. which are analytical pure chemical reagents provided by the Sinopharm group.

Specimen preparation and testing
Firstly, the desulfurization gypsum board is prepared according to the standard of Building Gypsum (GB/T 9766), and different soluble salts are added according to the experimental settings during the preparation process. Secondly, the desulfurization gypsum board is 320 mm × 40 mm × 10 mm size cutting, each group of 4 shall be placed parallel in the test box. Then, we place the saturated solution prepared in the water tank inside the test box to ensure the internal temperature is 20°C and humidity is 90%. Finally, we place a 500 g load in the middle of the desulfurization gypsum board and install a laser displacement meter.
During the experiment, the humidity and temperature inside the experimental box are detected in real-time to distinguish and deal with abnormal data after the experiment. Install the complete experimental device, as shown in figure 1.

Experimental design
According to the actual situation, this experiment adopts the full-factor experimental design. Strictly implement the three basic principles of experimental design: complete repetition of experiment, randomization, and can be obtained. At the same time, considering the actual production, the + Mg 2 content in desulfurization gypsum is high, so the + Mg 2 ion content in the experiment is set to be twice that of other factors. The experimental plan is formulated by using the full-factor experimental design in Minitab software, and the phase experimental grouping, experimental sequence, and experimental results are obtained, as shown in table 2. Especially, the Y1 through Y4 are experimental run replicates. In addition, some missing data in the Y3 and Y4 is caused by invalid samples during the experiment, and we ignore the impact of missing data on the results.

Visual analysis
The experimental results are shown in table 2. It can be seen that compared with the control group, the presence of + Na , + Mg 2 and -Cl ions will significantly increase the sagging deflection of desulfurization gypsum board after moisture absorption in a high salt environment. The effect of + Mg 2 ion is the most significant, and the final sag deflection is 5 times that of the control group, because the existence of + Mg 2 ion will slow down the growth rate of gypsum crystal, change its crystal morphology, and lead to the formation of acicular gypsum crystal (Gao et al 2008, Sahibin et al 2018. Further analysis from the mechanical point of view shows that acicular gypsum crystals are prone to dislocation and deformation, especially when gypsum is hygroscopic, there will be water  The mean sagging deflection of desulfurization gypsum board in the + Na and -Cl ion addition groups were 0.942 mm and 0.940 mm respectively. This is because a large number of + Na and -Cl ions will form sodium sulfate crystals and calcium chloride crystals respectively, which makes the surface of desulfurization gypsum board prone to frost return, increases the water absorption of the board, and then improves the sag deflection (Guan and Zhang 2020, An et al 2019, Saez et al 2019).
Compared with the control group, it can be seen that the existence of + K ion does not promote the sagging of desulfurization gypsum board after moisture absorption, and even inhibits the sagging deflection of desulfurization gypsum board after moisture absorption to a certain extent. From the combination of + + + K Mg , 2 we can more clearly see the inhibition effect of the + K ion on the sagging of desulfurization gypsum board. Compared with the sagging deflection of + Mg , 2 the sagging deflection of + K + + Mg 2 decreased from 1.933 mm to 0.605 mm, and the inhibition degree was 69.4%. This is because + K as a strong electrolyte ion can effectively promote the growth of whiskers along the c-axis, so that the aspect ratio increases, and the whiskers crystallize well (Miyi et al 2015, Wettstein et al 2021. This whisker with a large aspect ratio is interspersed between gypsum crystals, which can increase the lap point between crystals, improve the energy required for the ring-breaking process, and then reduce the sagging deflection of desulfurization gypsum board. This effect is similar to that in cement-based materials, that is, the unhydrated whiskers are tightly inserted into the cement stone, and the toughness of the cement stone is improved through crack bridging (Lucksanasombool et al 2002, Rahman et al 2020, Wakeel et al 2020.
On the other hand, this phenomenon can also be explained from the perspective of solubility. The solubility of K SO 2 4 at 20°C is 110 g l −1 , while the solubility of MgSO 4 at the same temperature is 255 g l −1 , the existence of + K ions will reduce the solubility of desulfurization gypsum, reducing the entry of water molecules, and finally reduce the sag and deflection of desulfurization gypsum board (Schneider et al 2020, Ji et al 2021. Furthermore, in the comparison of + + Na Mg , 2 and -Cl combination with + + -Na Mg Cl , , 2 and + K combination, this inhibition effect is more obvious. The corresponding sag deflection decreases from 2.924 mm before + K addition to 0.796 mm after + K addition, and the inhibition degree reaches 72.9%. However, in the application of desulfurization gypsum, it is also found that + K and double salt, which will affect the combination of paper's core (Alghamdi et al 2021, Han and Kim 2021, Moorthy et al 2021. Therefore, it is necessary to find an additive that can control the hygroscopic sag deflection of desulfurization gypsum board in a high-humidity environment without affecting other properties of gypsum, which is the next experimental research direction.

Analysis and evaluation of significant effects
In analyzing a complete factor experiment, it is necessary to consider the influence of the interaction between the combinations of factors. Using the SDE method can scientifically and effectively analyze the significant factors in the experiment.
(1)Fourth-order interaction: The fourth-order interactive Normal Plot of the Effects can be obtained by Minitab software, as can be seen in figure 2. The intermediate effect point group fits the oblique line in the figure, that is, the effect of the blue circular point group is not significant, and follows the normal distribution, and the points are on or near the straight line. Therefore, according to the normalized effect normal diagram of fourth-order interaction, the following conclusions can be obtained: (a) The factors that significantly affect the sagging of desulfurization gypsum board after moisture absorption are + K and Mg 2 ion is the promotion effect, and + K and Excluding the third-order and fourth-order interaction composed of multiple ions in the presence of + K , the effect is not significant, that is, there is no interaction. The sag deflection increasing effect caused by multiple ion combinations is only a superposition effect. (c) There is a significant interaction between + K and + Mg 2 ions. The existence of + K significantly changes the promoting effect of + Mg 2 ions on the sagging of desulfurization gypsum board after moisture absorption. There is a similar interaction between + K and + Na ions, but the effect is not significant when considering the fourth-order interaction.
(2)Second-order interaction: From the above analysis, it can be seen that the third-order and fourth-order interaction has no significant effect on the sagging of desulfurization sulfur, which is only the superposition effect between ions. Therefore, the influence of second-order interaction is further accurately analyzed. Minitab software can obtain the second-order interactive standard plot of the effects. It can be seen from figure 3 that due to the deepening of analysis accuracy, the combination of + Na ions and + K + + Na ions has a significant effect in the second-order interaction analysis. It is further proved that there is an interaction effect between + K and + Na ions, but the effect is less than that of + K and + Mg 2 ions.

Model residual analysis
The validity of the analysis model determines the accuracy of the SDE experimental analysis conclusion. The p-value comparison method is used to test the effectiveness of the model. That is, the main effect (deflection) p-value is >0.10 (90% guarantee rate) in the analysis model, which shows that the analysis model cannot reject the original hypothesis, and the model can be determined to be invalid (Habiger et al 2014, Moscovich et al 2015. Using the Minitab software ANOVA table, it can be found that the main effect p-value of the analysis model established in this experiment is 0.021, as can be seen in table 3, which proves that the regression effect of the analysis is noticeable, and the model is effective (Gudo et al 2020, Lee et al 2020. In addition, we share the data and processing process, that is, the Minitab file, in https://pan.baidu.com/s/ 1mGzoji4CEodIPodzgB3bEQ (Password: 1029).

Conclusions
In this paper, we obtain the ANOVA table through the SDE on the common soluble salts in desulfurization gypsum. From the ANOVA table, the significant factors affecting the moisture and deformation of desulfurization gypsum board are found, and the following conclusions are drawn: (1) + K ions, + Mg 2 ions and, + Na ions will affect the hygroscopic sag deflection of desulfurization gypsum board. Among them, + K ions and + Mg 2 ions have the most significant effects.
(2)Under a high humidity environment, + Mg 2 ions and + Na ions will increase the sagging deflection of desulfurization gypsum board. When + Mg 2 and + Na ions coexist, the sagging deflection of desulfurization  gypsum board will be significantly increased, but this increase is only a superposition effect and there is no interaction.
(3)The experimental results of different combinations of + K ions with + + Na Mg , 2 show that + K ions interact with the above two ions to varying degrees. This interaction has an obvious inhibitory effect on the sagging deformation of salt containing desulfurization gypsum, which is reflected in that + K ions significantly reduce the sagging deformation of desulfurization gypsum board caused by the addition of + + Na Mg , 2 ions.