Performance Study and Multi-Index Synergistic Effect Analysis of Phosphogypsum-Based Composite Cementitious Material

Abstract

The application of phosphogypsum in building materials can consume waste phosphogypsum and reduce ecological pressure. In this study, building phosphogypsum was used as the base material, and fly ash, lime, cement, and other materials were added to explore the performance of phosphogypsum-based cementitious composite building materials via orthogonal experimental method. Variance analysis and multiple regression analysis were used to summarize the performance variation of these phosphogypsum-based composite cementitious materials. This work demonstrates that the building phosphogypsum content and the water-cement mass ratio are significant factors affecting the thermal conductivity and mechanical properties of these materials scanning electron microscopy (SEM) analysis showed that the mechanical properties and thermal insulation properties of the prepared phosphogypsum-based composite cementitious materials were good in the C-S-H gel system and ettringite formation uniform specimens. Regression analysis showed a significant relationship between the building phosphogypsum content, fly ash content in the supplementary cementitious material, lime content, water-cement mass ratio, compressive strength, and thermal conductivity. The compressive strength and the thermal conductivity were analyzed by the index membership degree. The comprehensive performance of the phosphogypsum-based composite cementitious materials was evaluated, and basic theoretical research into the use of the phosphogypsum-based composite cementitious materials in a building non-load-bearing wall was carried out.

1. Introduction

The major production method for preparing wet-process phosphoric acid uses sulfuric acid, as shown in Formula (1) [1,2].

Due to the stable operation of the dihydrate method and the strong adaptability to bore [3], 80% of phosphoric acid production in China uses the wet dihydrate phosphoric acid method [4]. Formula (1) shows that phosphogypsum is the main by-product of this production method [5]. The accumulated phosphogypsum contains a large amount of acidic substances (such as HF, H₃PO₄, etc.) that cause serious damage to the atmospheric environment. Moreover, due to rainwater erosion, some mineral acids can enter groundwater systems and cause harm to freshwater ecological environments and human health [6]. The industrial production of 1 ton of phosphoric acid also leads to the production of 5 tons of phosphogypsum [7]. In China, 70 million tons of phosphogypsum are annually generated [8], while the annual global production of phosphogypsum is 280 million tons [9]. However, only approximately 15% of discharged phosphogypsum is recycled [10]. This phosphogypsum is mainly accumulated on arable land, leading to a reduction in available human living space. Therefore, the comprehensive and large-scale resource utilization of phosphogypsum is an important strategy for the healthy and sustainable development of the force-feeding industry. At the same time, the utilization of phosphogypsum is also important for reducing the amount of phosphogypsum stored today and alleviating environmental pressure.

$${\mathrm{Ca}}_5{\mathrm{F}(\mathrm{PO}}_4{)}_3{+5\mathrm{H}}_2{\mathrm{SO}}_4{+10\mathrm{H}}_2{\mathrm{O}=5\mathrm{CaSO}}_4{·2\mathrm{H}}_2{\mathrm{O}+3\mathrm{H}}_3{\mathrm{PO}}_4+\mathrm{HF}$$

(1)

One important strategy for using phosphogypsum is as a building material. The large-scale usage of phosphogypsum in building applications is highly significant for achieving sustainable development [11]. Shuhua Liu et al. [12] added phosphogypsum neutralized by lime to persulfate cement, which accelerated the hydration process of the persulfate cement, shortened the time required for setting, and improved the cement strength. Kang Gu [13] used cement, phosphogypsum, fly ash, and lime to prepare self-compacting rammed earth in loess. Their results show that the addition of cement and other admixtures enhances the compressive strength and softening coefficient of self-compacting rammed earth. Xibing Li [14] used phosphogypsum to prepare a polyethylene glycol-based cemented paste filling body to fill a mine. Their results show that the filling body strength is significantly improved by the addition of phosphogypsum, and the precipitation of harmful metals in the filling body is inhibited. Mustapha Amrani et al. [15] studied a mixture of clay, fly ash, lime, calcareous material, and phosphogypsum as a road pavement material. Their results show that this mixed material has excellent performance in terms of particle size distribution, bearing capacity, immersion resistance, and compaction characteristics after adding a large amount of phosphogypsum. This research shows that phosphogypsum has obvious advantages as a new green building material. Therefore, phosphogypsum can be used to replace natural gypsum in the construction industry, reducing the exploitation of natural gypsum resources. Mohamed Ouakarrouchi et al. [16] used a mixture of gypsum and chicken feathers as a surface decorative coating for walls. Their results show that, by mixing the two materials, the thermal conductivity is reduced by 36%, the thermal diffusivity is reduced by 13%, the heat leakage rate is reduced by 23%, and the volume heat capacity is reduced by 16%. Linchun Zhang [17] directly studied the effect of dehydration time and aging time on the flexural strength and compressive strength of phosphogypsum slurry, as well as the influence of silica fume, blast furnace slag, and Portland cement on the compressive strength of phosphogypsum. Their results show that cement and slag enhance the phosphogypsum mechanical strength. With 40% cement content (relative to the mass of cementitious materials), the 28 d compressive strength of the phosphogypsum is enhanced by 97.8%.

These studies demonstrate that the current research on phosphogypsum-based composite cementitious materials has mainly focused on single mechanical properties or thermal insulation properties. Therefore, the synergistic effect of thermal insulation and mechanical properties related to the structural applicability and economic practicability of these materials needs to be further studied. In this study, the relationship between the compressive strength and the thermal conductivity of phosphogypsum-based composite cementitious materials as building envelopes was explored, and the performance indicators of these materials were synergistically analyzed. The mechanism of these materials was analyzed by multi-index collaborative analysis, providing a theoretical basis for utilizing phosphogypsum-based cementitious materials as building insulation wall materials in practical applications.

2. Experiment

2.1. Material

Guizhou Kailai Green Building Materials Co., Ltd. (Guiyang, China) provided the phosphogypsum used in this study. The bleeding phenomenon of the original phosphogypsum was serious and the cementation of performance was weak. Shuhua Liu et al. [18] calcined phosphogypsum at 150 °C, 350 °C, 600 °C, and 800 °C, reporting that the calcined building phosphogypsum had better performance. Combined with the work of Lang Xie et al. [19], a building phosphogypsum method was proposed. Therefore, the building phosphogypsum in this work was prepared by drying at 160 °C for 2 h. The X-ray fluorescence (XRF) composition of this building phosphogypsum is shown in

Table 1. Composition of building phosphogypsum used in this work determined by XRF (w/%).

Project	SO3	CaO	SiO2	P2O5	Al2O3	Fe2O3	K2O	TiO2	Na2O	SrO	Cl	Y2O3	MgO
Building Phosphogypsum	54.94	41.04	1.80	1.30	0.38	0.27	0.12	0.07	0.05	0.02	0.01	-	-
Fly ash	1.24	5.22	49.10	0.40	36.87	3.13	0.98	1.83	0.34	0.03	0.05	0.13	0.68

and the SEM is displayed in Figure 1.

Table 1 shows that the building phosphogypsum contains P₂O₅ and Cl in addition to the major components such as CaO and SO₃. Soluble P₂O₅ and Cl will affect the hydration effect of phosphogypsum-based composite cementitious materials. Therefore, in this work, lime was added to the prepared phosphogypsum-based composite cementitious materials to absorb acidic impurities. The reaction formulas are as follows [20]:

$${\mathrm{CaSO}}_4\cdot 0{.5\mathrm{H}}_2\mathrm{O}+1{.5\mathrm{H}}_2\mathrm{O}\to {\mathrm{CaSO}}_4\cdot {2\mathrm{H}}_2\mathrm{O}+\mathrm{Q}$$

(2)

$${\mathrm{P}}_2{\mathrm{O}}_5{+3\mathrm{H}}_2\mathrm{O}\to {2\mathrm{H}}_3{\mathrm{PO}}_4$$

(3)

$${2\mathrm{H}}_3{\mathrm{PO}}_4{+3\mathrm{CaO}+3\mathrm{H}}_2\mathrm{O}\to {\mathrm{Ca}}_3{{(\mathrm{PO}}_4)}_2\downarrow {+6\mathrm{H}}_2\mathrm{O}$$

(4)

$${2\mathrm{F}}^{-}{+\mathrm{CaO}+\mathrm{H}}_2\mathrm{O}\to \mathrm{CaF}\downarrow {+2\mathrm{OH}}^{-}$$

(5)

$${2\mathrm{Cl}}^{-}{+\mathrm{CaO}+\mathrm{H}}_2\mathrm{O}\to \mathrm{CaCl}\downarrow {+2\mathrm{OH}}^{-}$$

(6)

Hebei Jianshi Mineral Powder Factory (Jianshi, China) provided the fly ash used in this work. The composition of the fly ash was determined by XRF, as shown in Table 1. Commercially available conch ordinary Portland cement (PO 42.5) was used in this work. Sichuan Yibin Sichuan Ash Biotechnology Co., Ltd., Yibin, China, provided the lime used in this study, and the CaO content was higher than 98%. The water reducer used in this study was polycarboxylate superplasticizer, and the gypsum retarder was obtained from Shanghai Chenqi Chemical Technology Co., Ltd., Chenqi, China.

2.2. Experimental Design

An orthogonal test method was designed to explore the impact of building phosphogypsum content, fly ash content in supplementary cementitious materials, quicklime content, and water-cement mass ratio on the performance of the phosphogypsum-based composite cementitious materials. An L16 (4⁵) orthogonal test table was used, and the selected factor level table is displayed in

Table 2. Factor level table.

Level	Factor
	A (Building Phosphogypsum/%)	B (Fly Ash/%)	C (Quicklime/%)	D (Water-Cement Mass Ratio)
1	30	30	5	0.250
2	40	40	6	0.275
3	50	50	7	0.300
4	60	60	8	0.325

[21]. The test design is displayed in

Table 3. Orthogonal test results.

Sample Number	A (Building Phosphogypsum/%)	B (Fly Ash/%)	C (Quicklime/%)	D (Water-Cement Mass Ratio)
1	30	30	5	0.250
2	30	40	6	0.275
3	30	50	7	0.300
4	30	60	8	0.325
5	40	30	6	0.325
6	40	40	5	0.300
7	40	50	8	0.275
8	40	60	7	0.250
9	50	30	7	0.275
10	50	40	8	0.250
11	50	50	5	0.325
12	50	60	6	0.300
13	60	30	8	0.300
14	60	40	7	0.325
15	60	50	6	0.250
16	60	60	5	0.275

[21].

2.3. Test Piece Production Method

The fabrication process of the specimens used in this study is shown in Figure 2. First, the phosphorus building gypsum, fly ash, cement, quicklime, water reducing agent, and retarder were weighed according to the mix ratio, followed by mixing and stirring in an electric mixing instrument for 2 min to acquire a uniform powder mixture. Second, the required mass of water to achieve the specified water-cement mass ratio was mixed with the powders prepared in the first step. To prepare a uniform and well-mixed slurry, the water and powders were slowly stirred for 30 s and then rapidly stirred for 90 s in electric mixing equipment. Third, the slurry was poured into 40 mm × 40 mm × 160 mm and 300 mm × 300 mm × 30 mm triple molds, and bubbles were eliminated by vibration for leveling. This was followed by curing. The curing process of the specimens was maintained according to the requirements of Chinese standard GB/T17669.3-1999 “Determination of Mechanical Properties of Building Gypsum” [22] until the test age was reached.

2.4. Test Method

2.4.1. Sample Phase

The experimental materials were subjected to phase analysis (XRD) using a Rigaku Smartlab X-ray diffractometer (XRD, Rigaku Corporation, Tokyo, Japan). The experimental materials were tested by composition detection (XRF). The instrument used was a Zetium X-ray fluorescence spectrometer produced by Pana company in Gorinchem, Netherlands.

2.4.2. Unconfined Compressive Strength

The Chinese standard GB/T 17669.3-1999 “Determination of Mechanical Properties of Building Gypsum” [22] was used to determine the compressive strength of specimens aged for 7 d and 28 d. The calculation method is shown in Formula (7). In this study, a YA-300 electro-hydraulic servo pressure testing machine controlled by a microcomputer was supplied by China Changchun Kexin Testing Instrument Company (Changchun, China) for compressive strength testing.

$$f=\frac{F}{A}$$

(7)

In Formula (7): f is the compressive strength; A is the compression area; F is the carrying capacity.

2.4.3. Thermal Conductivity

The Chinese standard GB/T 10294-2008 “Thermal Insulation-Determination of Steady-State Thermal Resistance and Related Properties-Guarded Hot Plate Apparatus” [23] was used to determine thermal conductivities after 28 d; the calculation is shown in Formula (8). A CD-DR3030 thermal conductivity testing instrument was supplied by Shenyang Ziweiheng Testing Equipment Co., Ltd. (Shenyang, China) for thermal conductivity testing. During the test, the cold plate temperature was set to 15 °C and the hot plate temperature was set to 35 °C.

$$\mathsf{\lambda }=\frac{\mathrm{Q}\times \mathrm{d}}{2·{\mathrm{A}(\mathrm{T}}_1-{\mathrm{T}}_2)}$$

(8)

In Formula (8): λ is the thermal conductivity; d is the plate thickness; Q is the heat flow; A is the plate area through which the heat flow passes; T₁ and T₂ are the hot plate and cold plate temperatures, respectively.

2.4.4. Micromorphology of Specimens

Scanning electron microscopy (SEM) was employed to investigate the microstructures of the specimens after aging for 28 d. A Sigma 300 field emission SEM produced by Zeiss, Germany, was used with a magnification of 400 times.

3. Results and Discussion

In this work, the performance optimization and comprehensive performance index evaluation of phosphogypsum-based composite cementitious materials are studied. In our previous study [21], the performance of phosphogypsum composite cementitious material was analyzed by range analysis and intuitive analysis. This paper mainly studies the mechanism of multi-index synergy and the establishment of evaluation equation of multi-index synergy analysis based on variance analysis of orthogonal test.

3.1. Compressive Strength Test Analysis

The compressive strengths of each specimen group in the orthogonal test are shown in Figure 3. Sample 4 shows the lowest 7 d and 28 d compressive strengths. Table 3 shows that the composition of this sample is 30% building phosphogypsum, 60% fly ash, 8% quicklime, and a 0.325 water-cement mass ratio. Sample 15 exhibits the highest 7 d and 28 d compressive strengths. The composition of this sample is 60% building phosphogypsum, 50% fly ash, 6% lime, and a 0.250 water-cement mass ratio.

The variance analysis of the 7-d compressive strengths from the orthogonal test is displayed in

Table 4. 7-d compressive strength variance analysis.

Source of Difference	SS	DF	MS	F	F0.01, F0.05, F0.1
A	958.90	3	319.63	335.08	F0.01 = 29.46 F0.05 = 9.28 F0.1 = 5.39
B	13.13	3	4.38	4.59
C	18.02	3	6.01	6.30
D	415.85	3	138.62	145.31
e△	2.86	3	0.95	-	-

. The variance analysis of the 28-d compressive strength values obtained from the orthogonal test is displayed in

Table 5. 28-d compressive strength variance analysis.

Source of Difference	SS	DF	MS	F	F0.01, F0.05, F0.1
A	1250.79	3	416.93	280.70	F0.01 = 29.46 F0.05 = 9.28 F0.1 = 5.39
B	33.46	3	11.15	7.51
C	7.46	3	2.49	1.67
D	718.87	3	239.62	161.32
e△	8.91	6	1.49	-	-

. As indicated by Table 4, the water-cement mass ratio of the building phosphogypsum content and lime content is a significant influencing factor in the initial stage of hydration. Table 5 shows that the content of building phosphogypsum, the content of fly ash, and the water-cement mass ratio are significant influencing factors in the later stage of hydration. The building phosphogypsum acts as the building skeleton during this hydration process. Moreover, the building phosphogypsum has a faster hydration speed after mixing with water, and the strength achieved during the early stage is remarkably enhanced. The fly ash is excited by alkaline materials in this cementitious system, generating C-S-H and C-A-S-H gels. These gels fill and connect the phosphogypsum-based cementitious system, and this process mainly occurs in the later stages of hydration.

In the early hydration stage, the influencing factors that restrict the compressive strengths of the specimens are the same factors that affect the hydration rate of building phosphogypsum. Some mineral acids affect the hydration of building phosphogypsum. Quicklime can adsorb these mineral acids, increasing the hydration rate of building phosphogypsum.

In the later stages of hydration, fly ash is hydrated in an alkaline environment, which is mainly because OH⁻-containing substances destroy the tetrahedral structure of SiO44 in fly ash. This leads to Si-O and Al-O bond breakage followed by recombination to form hydrated calcium aluminosilicate (C-A-S-H) and hydrated calcium silicate (C-S-H) [24,25]. This phenomenon explains the enhanced cementitious material strength after the addition of fly ash. However, an excessively high concentration of lime in these materials leads to a high OH⁻ concentration that causes the polymerization of fly ash to rapidly occur. The resulting gel attaches to the surface of some unreacted admixtures, hindering the hydration of other admixtures and reducing the hydration degree of these materials [26,27]. At the same time, during the curing process, the pores left by the evaporation of water make the sample have a bad effect on the mechanical properties test [28].

3.2. Thermal Conductivity Test Analysis

Figure 4 shows the thermal conductivity test results of each group in the orthogonal test. Sample 9 has the highest thermal conductivity value of 0.4500 W/(m·K). This sample has 50% building phosphogypsum content, 30% supplementary cementitious material fly ash content, 7% quicklime content, and a 0.275 water-cement mass ratio. Sample 13 has the lowest thermal conductivity of 0.3383 W/(m·K). This sample has 60% building phosphogypsum content, 30% supplementary cementitious material fly ash content, 8% quicklime content, and a 0.300 water-cement mass ratio.

The thermal conductivity variance analysis of the prepared specimens is shown in

Table 6. Thermal conductivity coefficient variance analysis.

Source of Difference	SS	DF	MS	F	F0.01, F0.05, F0.1
A	0.006948825	3	0.002316275	4.387456907	F0.01 = 6.99 F0.05 = 3.86 F0.1 = 2.81
B	0.001014805	3	0.000338268	0.640743321
C	0.001285165	3	0.000428388	0.811447411
D	0.006023855	3	0.002007952	3.803435002
e△	0.00475138	9	0.000527931	0.00475138	-

. The amount of building phosphogypsum and the water-cement mass ratio are significant factors that influence the thermal conductivity of these materials, which is consistent with the range analysis results [21]. Porosity is typically an important evaluation index for evaluating the suitability of building materials as thermal insulation [29]. In the phosphogypsum-based composite cementitious materials prepared in this work, the main source of pores is the water that provides the hydration environment. The pores remaining after evaporation during the later curing process and the skeleton of the building phosphogypsum constructed during the hydration process are completely filled.

3.3. Multi-Index Collaborative Analysis

3.3.1. Index Membership Calculation

Other studies have reported that compressive strength and thermal conductivity have a certain correlation in phosphogypsum-based composite cementitious materials [30]. To obtain good thermal insulation building materials, key indicators were selected for evaluation to obtain building materials in line with actual engineering applications. In this study, compressive strength and thermal conductivity were selected as the main evaluation indexes. The index membership degree was used as the conversion tool to comprehensively evaluate the experimental results of compressive strength and thermal conductivity obtained by orthogonal test to determine the optimal combination of mechanical and thermal conductivity. The index membership degree was calculated with Formula (9) [21,31]:

$$\theta =\frac{c-d}{e-d}$$

(9)

In Formula (9), θ is the reverse index membership degree. Variables c, d, and e are the experimental value, the minimum value of the test, and the maximum value of the test, respectively. When calculating the index membership degree, the maximum and minimum values of the experiment are constant, and the index membership degree changes with changing experimental values. In a group of experiments, when the experimental value is substituted into the maximum value of the experiment for calculation, the highest index membership degree of 1 is obtained. When the minimum value of the experiment is calculated, the lowest index membership degree of 0 is obtained. In this study, a higher membership degree of the thermal conductivity index indicates worse thermal insulation performance. Meanwhile, a greater membership degree of the compressive strength index indicates better mechanical properties. Therefore, to facilitate the weighted calculation of the index membership degree of compressive strength and thermal conductivity, the concept of reverse index membership degree is proposed, as calculated by Formula (10):

$$\psi =\frac{e-c}{e-d}$$

(10)

In Formula (10), ψ is the reverse index membership degree. Variables c, d, and e are the experimental value, the minimum value of the test, and the maximum value of the test, respectively. The calculation results of the index membership of compressive strength and the reverse index membership of thermal conductivity are displayed in

Table 7. Calculation table of the degree of compressive strength membership and the degree of thermal conductivity reverse membership.

Specimen Number	Degree of Membership of Compressive Strength Index	Degree of Membership in the Reverse Index of Thermal Conductivity	Overall Rating
1	0.4652	0.2516	0.3584
2	0.3453	0.2704	0.3079
3	0.1185	0.8013	0.4599
4	0.0000	0.6965	0.3483
5	0.3117	0.5246	0.4182
6	0.3201	0.2739	0.2970
7	0.6091	0.0322	0.3207
8	0.6489	0.1826	0.4157
9	0.8452	0.0000	0.4226
10	0.8562	0.5936	0.7249
11	0.4309	0.5783	0.5046
12	0.5375	0.0591	0.2983
13	0.7996	1.0000	0.8998
14	0.5877	0.7950	0.6913
15	1.0000	0.7081	0.8541
16	0.8622	0.4091	0.6356

.

The membership degrees in Table 5 are weighted by using Formula (11).

$$\eta =\mathrm{aU}+\mathrm{bV}$$

(11)

In Formula (11), η is the comprehensive score, a and b are important evaluation coefficients of the index, V is the reverse index membership degree of the thermal conductivity, and U is the index membership degree of the compressive strength. In this study, a and b are both 0.5. The calculated comprehensive scores of this study are shown in Table 7.

3.3.2. Synergistic Effect of Thermal Conductivity and Compressive Strength

A multiple linear regression model for the compressive strengths of the phosphogypsum-based composite cementitious materials was established to explore the synergistic relationship between compressive strength and thermal conductivity. The multiple linear regression formula of compressive strength (M) with building phosphogypsum content (A), fly ash content (B) in the supplementary cementitious materials, lime content (C), and water-binder ratio (D) is shown in Formula (12):

$$\mathrm{M}=7.86\mathrm{A}-1.09\mathrm{B}+0.57\mathrm{C}-5.896\mathrm{D}+30.90$$

(12)

The variance analysis results of this model are shown in

Table 8. Analysis of variance for the regression formula.

Parameter	R	R2min	R2	F Value	F0.01, F0.05	Significance
Compressive strength	0.987	0.752	0.974	107.00	F0.01 = 5.670 F0.05 = 3.360	**
Thermal Conductivity	0.998	0.752	0.996	83.02	F0.01 = 27.05 F0.05 = 8.74	**
Overall rating	0.999	0.712	0.999	37,923.65	F0.01 = 6.700 F0.05 = 3.810	**

Note: “**” means F_0.01 < F.

. The correlation coefficient (R) of the multiple regression analysis of each admixture and compressive strength is 0.987, which is greater than the critical value (R_min) of 0.752. The F value of the variance test in the regression analysis is 107.00. This shows that there is a significant linear relationship between the building phosphogypsum content, supplementary cementitious material fly ash content, lime content, water-binder ratio, and compressive strength. By substituting the content of each factor in Table 3 into Formula (12), the actual 28-d compressive strength values in Figure 3 and the obtained model compressive strength values of the phosphogypsum-based composite cementitious materials can be plotted, as shown in Figure 5a.

In this study, a thermal conductivity multivariate nonlinear regression model was established for the phosphogypsum-based composite cementitious materials, as displayed in Formula (13). This model was used to analyze the multiple regression relationship between the building phosphogypsum content (A), fly ash content (B) in the supplementary cementitious materials, lime content (C), water-binder ratio (D), and thermal conductivity (N).

$$\begin{array}{l}\mathrm{N}=-0{.008\mathrm{A}}^3+0{.043\mathrm{A}}^2-0.063\mathrm{A}+0.012\mathrm{A}\cdot \mathrm{C}+0{.0007\mathrm{B}}^3+0{.001\mathrm{B}}^2-0.061\mathrm{B}+0.021\mathrm{B}\cdot \mathrm{C}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}-0{.0007\mathrm{C}}^3+0{.002\mathrm{C}}^2-0.086\mathrm{C}+0{.024\mathrm{D}}^3-0{.197\mathrm{D}}^2+0.492+0.241\end{array}$$

(13)

Table 8 shows that the correlation coefficient (R) of the regression analysis of each admixture and thermal conductivity is 0.998, which is greater than the critical value (R_min) of 0.752. The F value of the variance test of the regression analysis is 27.31. This shows that there is a significant multiple regression relationship between the building phosphogypsum content, fly ash content in the supplementary cementitious materials, lime content, water-binder ratio, and thermal conductivity. By substituting the content of each factor in Table 3 into Formula (13), the obtained model thermal conductivity values of the phosphogypsum-based composite cementitious materials and the actual thermal conductivity values in Figure 4 can be plotted, as shown in Figure 5b.

In this study, thermal conductivity and compressive strength were weighted and integrated based on index membership calculations. At the same time, a multivariate linear evaluation model was established with the compressive strength (M) and thermal conductivity (N) as independent variables and the comprehensive score (η) as the dependent variable, as shown in Formula (14):

$$\eta =0.0122\mathrm{M}-4.45\mathrm{N}+1.855$$

(14)

Table 8 shows that the correlation coefficient (R) of the thermal conductivity, compressive strength, and comprehensive score regression analysis is 0.999, which is higher than the critical value of the multiple correlation coefficient (R_min) of 0.712. The F value of the variance test in regression analysis is 37,923.65. This shows that there is a significant multiple regression relationship between the thermal conductivity, compressive strength, and comprehensive score. The thermal conductivity and compressive strength values of each group in Table 3 can be substituted into Formula (14), and the obtained comprehensive score model value of the phosphogypsum-based composite cementitious materials and the actual comprehensive score values in Table 7 can be plotted, as shown in Figure 5c.

Formula (12) is the fitted relationship between building phosphogypsum and other admixtures with the compressive strength of the specimens. Formula (13) is the fitted relationship between the building phosphogypsum and other admixtures with the thermal conductivity of these materials. Formula (14) combines the two indexes of compressive strength and thermal conductivity to obtain a method for intuitively describing the comprehensive influence of building phosphogypsum content and other factors on the performance of phosphogypsum-based composite cementitious materials.

3.4. Analysis of Influence Mechanism of the Comprehensive Performance of Phosphogypsum-Based Composite Cementitious Materials and the Synergistic Effect

The influence mechanism of the phosphogypsum-based composite cementitious material and their synergistic effect were explored, and the unity of the compressive strength and thermal conductivity of these materials was analyzed. SEM micrographs of the samples with the maximum and minimum compressive strength and thermal conductivity values obtained in the orthogonal experiment are displayed in Figure 6. SEM micrographs of the samples with the highest and lowest comprehensive scores are shown in Figure 7.

Figure 6a displays an SEM image of sample 4, which exhibits the minimum 28 d compressive strength. This sample contains many unreacted fly ash particles. Large pores are ob-servable between the substances in this system, and a dense whole is not formed. During the unconfined compression test, stress concentration easily occurs, leading to low macroscopic compressive strength. Figure 6b shows an SEM image of sample 15, which has the maximum 28-d compressive strength. Only a small number of fly ash particles that did not react could be observed in this sample. Moreover, the reactants in this cementitious system are closely connected, and no large pores are visible. This in-dicates that the stress concentration of sample 15 is lower than that of sample 4 during the unconfined compressive test, leading to high compressive strength.

Figure 6c shows an SEM image of sample 9, which has the maximum thermal conductivity. A small number of unreacted fly ash particles are present in this system, and the reac-tants are uniformly formed into a dense whole without high porosity. The small num-ber of pores means that the resistance to heat transfer is low, resulting in high thermal conductivity. Figure 6d shows an SEM image of sample 13, which has the minimum thermal conductivity. No large amount of unreacted substances are visible in this system and the pores are evenly distributed. This leads to high heat transfer resistance and low thermal conductivity.

Figure 7a shows an SEM image of sample 6, which has the lowest comprehensive score in the synergistic analysis of the prepared phosphogypsum-based composite cementitious materials. This sample contains some unreacted fly ash particles; the bonding between each product is not dense, and there are a large number of pores. The pore sizes in this cementitious system are not uniform, and some of the pores are connected. This leads to significant stress concentration when subjected to an unconfined compression test as well as low heat transfer resistance. Figure 7b shows an SEM image of sample 13, which has the highest comprehensive score in the synergistic analysis of these materials. The components in this system are thoroughly reacted, and the pore distribution and pore size are uniform. Therefore, this sample exhibits high compressive strength as well as good heat transfer resistance.The contradiction between the mechanical properties and thermal insulation properties of phosphogypsum-based composite cementitious materials as retaining structures is an important factor affecting their practical application as wall materials. By selecting compressive strength and thermal conductivity for evaluation, this contradiction can be reconciled. This provides a theoretical basis for utilizing phosphogypsum-based composite cementitious materials in thermal insulation applications, thereby improving the self-insulation capacity of buildings and reducing their energy consumption.

Comparing Figure 6 and Figure 7 shows that the reaction in the material with the highest comprehensive score is complete and the product is tightly bonded, leading to good compressive strength. This phosphogypsum-based composite cementitious material has a uniform pore size distribution, leading to good thermal insulation properties. The decline in compressive strength caused by the pores can be mitigated by controlling the pore structure and pore distribution, leading to good comprehensive performance.

4. Conclusions

(1)

From the coefficient of the numerical fitting equation of the phosphogypsum-based composite cementitious material, it can be seen that the content of building phosphogypsum has the greatest influence on the compressive strength and is a positive influence. The influence of water cement mass ratio and fly ash content on compressive strength ranks second and third, both of which are negative. The above fitting results are consistent with the actual performance analysis results.

(2)

From the numerical fitting equation of the thermal conductivity of phosphogyp-sum-based composite cementitious materials, it can be seen that the water-cement mass ratio has the greatest influence on the thermal conductivity, which is mainly due to the hindering effect of the pores left by water evaporation on heat transfer. At the same time, the combined effect of building phosphogypsum content and lime content and the combined effect of fly ash and lime also have an effect on the change of thermal conductivity.

(3)

The comprehensive evaluation equation of mechanical and thermal insulation properties of phosphogypsum-based composite cementitious materials was ob-tained by synthesis. The comprehensive performance of phosphogypsum-based composite cementitious materials can be predicted by substituting the content of each component into the evaluation equation. This method provides an evaluation equation for the comprehensive performance evaluation of phosphogypsum-based composite cementitious materials.