A Study on the Preparation and Performance Optimization of Alkali-Activated Fly Ash-Based Aerogel-Modified Foam Concrete

1. Introduction

The global environmental crisis is intensifying, and projections indicate that the building sector in China will account for over 40% of total societal energy consumption by 2050[1]. The development of energy-efficient materials, such as FC, is therefore crucial for the sustainable development of the construction industry. FC offer advantages such as thermal insulation, fire resistance, and low cost. However, a significant paradox exists: conventional FC relies on Ordinary Portland Cement (OPC), a binder with a highly energy-intensive production process that contributes to approximately 8% of the global carbon emissions [2]. In contrast, Alkali-Activated Materials (AAMs), which can reduce associated carbon emissions by over 80% [3], present a sustainable alternative and are widely recognized as "green cement."

The properties of AAFC are significantly influenced by the raw material composition, activator parameters, and production methods. Waste utilization strategies significantly enhance specific properties: FA with clinoptilolite improves thermal and frost resistance [4,5], pinecone powder increases the 91-day strength by 256.6% [6], recycled brick powder with Na₂O reduces thermal conductivity to 0.1067–0.1121 W/(m·K) [7,8], and waste glass enhances mechanical and corrosion resistance[9]. Process optimization through red mud addition and mechanical activation improves the pore structure and strength [10,11], while advanced composites containing hollow glass beads, rice husk, silica fume, and FA demonstrate synergistic thermal-mechanical performance enhancement [12,13,14,15].

Lightweight design strategies are implemented through the incorporation of Expanded Polystyrene (EPS) beads[16], waste polyurethane (PUR) [17], and lightweight aggregates [18], with densities of ≤800 kg/m³ and thermal conductivity as low as 0.07 W/(m·K) being achieved. Foaming techniques, including chemical (H₂O₂ and zinc/aluminum metal powders) and physical methods (Sodium Dodecyl Sulfate(SDS)), allow tailored pore structures. The H₂O₂/SDS combination enables the production of materials with either ultra-low thermal conductivity (0.072W/(m·K)) or high compressive strength (19.6MPa)[19,20,21], demonstrating flexibility in property design through processing optimization.

The pore characteristics critically govern the thermal and mechanical properties of AAFC. Jaya et al.[22]identified that the activator composition primarily controls the compressive strength (0.4–6MPa), whereas the precursor/activator ratio dictates the thermal conductivity (0.11–0.30 W/(m·K)). The synergistic use of H₂O₂ and Tween 80 enabled porosity control within 36–86%. A more than two-fold increase in the 28-day strength was achieved by Su et al.[23] by optimizing the activator modulus (SiO₂/Na₂O=1.2–1.8) under high-humidity curing conditions (RH≥90%). A key research challenge is to balance low thermal conductivity with high strength. Huan et al.[24]developed a hierarchically porous material with 93.8% porosity and 0.040 W/(m·K) thermal conductivity, albeit at low strength (0.27 MPa). In contrast, Berkouche et al.[25]balanced both properties (0.13 W/(m·K), 4.26 MPa) using rice husk ash (RHA) and glass powder (GP). RHA enhanced the strength through geopolymerization, whereas GP refined the pore structure as an inert filler. The microstructural analysis confirmed that the performance stems from the synergy between the gel phases (C-A-S-H/N-A-S-H) and pore distribution.

Nanomaterials provide a superior approach for tailoring material properties. Rong et al.[26]demonstrated that combining 12% aerogel with 75% foam reduces thermal conductivity to 0.18 W/(m·K), while adding 1% polypropylene fibers increases compressive strength to 23.7 MPa. Similarly, Pan et al.[27]found that silica aerogel decreases the thermal conductivity by 24% (to 0.0886 W/(m·K)) through multi-scale porosity, and Ji et al.[28] reported that 0.4% CMC enhances the pore structure, improving the strength by 44.7% and pore sphericity.

While existing research often prioritizes the extreme optimization of one or a few properties, such as achieving ultralow thermal conductivity, a more holistic approach was adopted in this study. Using FA-based AAFC as the matrix, this work is designed around the multi-performance requirements of envelope materials for ultra-low energy consumption buildings. A comprehensive set of seven key indicators was established, including thermal conductivity, mechanical strength, fire resistance, and freeze-thaw durability. Notably, a critical focus is placed on enhancing waterproofing performance, effectively addressing the long-standing issue of high water absorption in FC. Specifically, SiO₂ aerogel, a super thermal insulation material, was incorporated to enhance the thermal performance of AAFC. Resolve the conflict between the mechanical and thermal properties of conventional FC. Ultimately, all parameters met the requirements of the performance index system. A synergistic enhancement in the range of key material properties was achieved.

2. Construction of Target Performance Index System for AAFC

2.1. Determination of Target Performance Indicators and Parameters

To address the energy efficiency requirements of ultra-low energy consumption buildings in hot-summer and cold-winter regions, a high-performance AAFC has been developed with the objective of achieving self-insulation through 300 mm-thick exterior walls, satisfying mechanical standards for non-load-bearing walls, demonstrating excellent water resistance, and conforming to specifications for dry density, fire resistance, and frost resistance.

(1)

Dry Density and Mechanical Properties

The dry density was optimized by balancing the sound insulation and the mechanical requirements. For non-load-bearing exterior walls, mechanical targets–compressive strength, flexural strength, and drying shrinkage–were defined according to relevant standards[29,30,31].

(2)

Thermal Performance

The thermal performance was characterized by two key parameters: wall thermal transmittance and thermal conductivity of the AAFC. To fulfill the self-insulation criteria for ultra-low energy buildings in hot-summer and cold-winter regions, the thermal transmittance was limited to ≤0.4 W/(m²·K) [32,33,34]. The exterior wall thickness is set to 300 mm. The thermal conductivity of the AAFC was then calculated in compliance with the relevant design codes, as follows[35]:

$$\mathrm{K} =1/\left({\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${\mathrm{h}}_1$}\right.}+{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${\mathrm{h}}_2$}\right.}+{\displaystyle \raisebox{1ex}{$\mathsf{\delta }$}\!\left/ \!\raisebox{-1ex}{$\mathsf{\lambda }$}\right.}\right)$$

(1)

In the equation, K(0.4 W/(m²·K)) is the wall thermal transmittance; h₁ and h₂ are the interior and exterior surface heat transfer coefficients, taken as 8.7 and 23 W/(m²·K) respectively, with the latter representing the most severe condition; δ is the wall thickness (0.3 m); λ is the thermal conductivity of the AAFC(W/(m·K)); and a thermal conductivity correction factor (α) of 1.05 was incorporated. Thus, the corresponding thermal conductivity of AAFC should not exceed 0.1216 W/(m·K).

(3)

Fire Resistance and Water Resistance

The AAFC material exhibits Class A fire resistance as an inorganic noncombustible material,thus meeting these requirements.

To address the inherent drawback of high water absorption in FC, mass water absorption was adopted as a key performance indicator. The influence of moisture content (varied from 0% to 55% at 5% intervals) on thermal conductivity was investigated using the weight method. A well-fitted correlation (R²=0.97669) was established between the thermal conductivity and water absorption, demonstrating a significant dependence of thermal performance on moisture content.

$$\mathsf{\lambda }=0.2016+0.00853\mathrm{x}-0.0001{\mathrm{x}}^2$$

(2)

where λ is the thermal conductivity of the AAFC(W/(m·K)), x is the mass water absorption (%); the results are shown in the figure below:

The thermal conductivity exhibited a significant dependence on mass water absorption, increasing by 105.31% from 0.1975 W/(m·K) in the dry state to 0.4055 W/(m·K) at 55% moisture content (Figure 1). A near-linear rapid rise occurred within 0–10% absorption, where the conductivity exceeded the target value by 37.35%. Given that the existing standards are inadequate for practical requirements [29], the mass water absorption is targeted at ≤5% based on a comprehensive analysis.

(5)

Frost Resistance

According to national standards, the frost resistance for the hot summer and cold winter ( non-central-heating) region is set as F25 [36], with the strength and mass loss rates serving as the secondary indicators.

2.2. Target Performance Indexes of AAFC

According to the requirements in Section 2.1, the target performance indices established in this study and the corresponding values are presented in the Table 1 below.

3. Mix Proportion Design Method for AAFC

3.1. Basic Principles

A mix proportion design method for AAFC was developed based on the volume method, which operates on the principle that the volume of the fresh slurry equals the sum of the volumes of all solid components and the entrapped air. In this approach, the target performance values are first established, followed by theoretical calculations of raw material dosages and experimental refinement. The dry density was selected as the primary design target because of its ease of control.

3.2. Design Steps and Calculation Methods for Mix Proportion

Based on the above principles, the mix proportion design steps for the AAFC are as follows:

(1)

The mass of each precursor component and other curable materials was determined according to the target dry density of the AAFC.

(2)

Determine the water-to-binder ratio, activator dosage, and additional water amount, based on the precursor dosage.

(3)

The volume of each constituent material in the slurry was calculated to determine the foam volume.

(4)

The foam mass was determined using the calculated foam volume and foam density.

(5)

The required foaming agent mass was calculated based on its dilution ratio and foam mass.

The mix proportion design relationship for the precursor (including silico-aluminate raw materials)–activator–physical foaming system is:

$${\rho }_{d }=\left(m_{\mathit{pre}}+m_{\mathit{act}}+\sum _{i=1}^n{m}_i\right)\text{×}{S}_a$$

(3)

where ρ_d denotes the design dry density of AAFC (kg/m³); m_pre represents the mass of precursor materials in 1 m³ of AAFC (kg); m_act is the mass of the curable portion of the alkali activator in 1 m³ of AAFC (kg); m_i denotes the mass of each additional curable raw material in 1 m³ of AAFC (kg); S_a is the mass coefficient determined by the total dry material mass of each component and the total non-evaporable matter in the finished product after curing of AAFC, with a range of 1.0 to 1.3, determined experimentally.

In the preparation of 1 m³ AAFC slurry, the sum of the volumes of silico-aluminate-containing precursor materials, activator, water required except for diluting the foaming agent, and other curable raw materials is denoted as V₁, which is calculated using Eq.4; The portion where the slurry volume is less than 1 m³ is considered to be filled by foam, and the foam volume V₂ can be calculated using Eq.5.

$${\mathrm{V}}_1={\displaystyle \frac{m_{\mathit{pre}}}{{\rho }_{\mathit{pre}}}}+{\displaystyle \frac{m_{\mathit{act}}}{{\rho }_{\mathit{act}}}}+{\displaystyle \frac{m_w}{{\rho }_w}}+\sum _{i=1}^n{m}_i/\sum _{i=1}^n{\rho }_i$$

(4)

where V₁ denotes the sum of the volumes of precursor materials, activator, water required except for diluting the foaming agent, and other curable raw materials (m³); m_w represents the mass of water required except for diluting the foaming agent (kg); ρ_pre is the density of the precursor materials (kg/m³); ρ_act is the density of the prepared activator (kg/m³); ρ_w is the density of water (kg/m³), with a value of 1000 kg/m³; ρ_i denotes the respective densities of other curable raw materials in the AAFC (kg/m³).

$${\mathrm{V}}_{2 }=k \left(1-{\mathrm{V}}_1\right)$$

(5)

where V₂ denotes the foam content in 1 m³ of AAFC (m³/m³); k is the surplus coefficient, which should be determined according to the type and quality of the foaming agent, foam preparation time, etc., for foaming agents with good stability; the value range is 1.1 to 1.4; and the specific value is determined through experimental and theoretical analysis.

The dosage of the foaming agent m_f in 1 m³ of AAFC can be calculated using Eq.6 and 7:

$$m_p={ \mathrm{V}}_2 \text{×} {\rho }_{\mathit{foam}}$$

(6)

where m_p denotes the mass of foam in 1 m³ of AAFC (kg) and ρ_foam denotes the mass of foam in 1 m³ of FC (kg).

$$m_f=m_p \text{÷} \left(\beta +1\right)$$

(7)

where m_f denotes the dosage of foaming agent in 1 m³ of AAFC (kg) and β represents the dilution multiple of the foaming agent, which can be determined through experiments.

3.3. Test Raw Materials and

(1)

FA and activators

FA from Xuzhou China Resources Power Co., Ltd., was used as the primary raw material. A binary composite activator was prepared by mixing water glass (modulus=3.3, Baume degree =38.5°Be′) from Yourui Refractory Materials Co., Ltd. with sodium hydroxide (NaOH, ≥99% purity, IS-I grade) supplied by Shandong Binzhou Chemical Group Co., Ltd.

(2)

Foaming Agents

The HTQ-1 composite polymer foaming agent was supplied by Henan Huatai New Material Technology Co. Ltd. Its performance was tested in accordance with the national standards [37] under a foaming pressure of 0.5 MPa. The foaming performance parameters are listed in Table 2.

(3)

Lightweight Aggregate—Vitrified Microspheres

Lightweight aggregates can reduce density while enhancing mechanical properties. Vitrified microspheres (Figure 2(a)) from Hebei Yixin Energy Conservation and Thermal Insulation Building Materials Co., Ltd., were used, and their properties are listed in Table 3.

(4)

Basalt Fiber

The fibers enhanced the tensile strength of FC. Basalt fibers (Figure 2(b)) from Changsha Ningxiang Building Materials Co., Ltd. were used, and their properties are listed in Table 4.

(5)

Foam stabilizers.

Hydroxypropyl methylcellulose ether (HPMC) was used as the foam stabilizer. A white powder (Figure 2(c)) with a molecular weight of 86,000 and a viscosity of 200,000 effectively thickens the foam film and reduces defoaming or bubble merging.

(6)

Calcium Hydroxide

Low-calcium ash was used as the FA. Calcium hydroxide was added to enhance the mechanical properties of the AAFC. Calcium hydroxide powder (Figure 2(d)) was supplied by Nanjing Baore Chemical Co. Ltd.

(7)

Waterproofing agents.

The internally admixed waterproofing agent sodium methyl silicate solution, as shown in Figure 2(e), was produced by Shanxi Jing Chen Building Materials Co., Ltd.

(8)

SiO₂ Aerogel

The SiO₂ aerogel was supplied by Shenzhen Zhongning Technology Co., Ltd., and its performance parameters are summarized in Table 5 below.

The SiO₂ aerogel appears as a white powder (Figure 3a) with an irregular particle morphology and a broad size distribution ranging from 3.78 to 37.1 μm (D90=37.1 μm), as shown in Figure 3(b–c). Its high specific surface area (707.8 m²/kg) and nanoscale surface roughness (amplitude ≈ 80 nm, Figure 3d) contribute to its effective thermal insulation, which stems from its nanoporous structure that markedly suppresses both solid conduction and gas convection [26,27].

3.4. Experimental Verification of Mix Proportion Design Method and Preliminary Mix Design

A preliminary mix design was conducted using the proposed method based on the upper dry density limit (650kg/m³). For 1 m³ AAFC, raw material dosages were calculated: foam from 40 times diluted foaming agent, alkali equivalent 0.1, empirical water-to-binder ratio 0.4, activator modulus 1.5, and curing at 55°C for seven days. The calculation results are listed in Table 6 below.

3.5. Testing and Results Analysis

The specimens were prepared according to the mix proportion and preparation process, and their relevant properties were tested. The test results are listed in Table 7.

Figure 4. Test results of mechanical properties of preliminary mix ratio samples and deviation rates from the target values.

Figure 4. Test results of mechanical properties of preliminary mix ratio samples and deviation rates from the target values.

Figure 5. Test results of frost resistance and thermal conductivity of the preliminary mix ratio samples and deviation rates from the target values.

Figure 5. Test results of frost resistance and thermal conductivity of the preliminary mix ratio samples and deviation rates from the target values.

The preliminary mix specimens exhibited deficiencies in several key properties. The compressive strength (3.86 MPa), flexural strength (0.83 MPa), and drying shrinkage (1.432 mm/m) fell short of their target values by 24.8% and 17.7%, respectively, and exceeded their target values by 43.2%. The thermal conductivity reached 0.1975 W/(m·K), exceeding the limit by 62.4%, while the mass water absorption (57.1%) was 11.42 times the target value. Poor water resistance also led to excessive frost-induced damage, with the strength and mass loss rates surpassing their thresholds by 122.7% and 247.2%, respectively. Consequently, among all the properties evaluated, the feasibility of the design method was validated, but only the dry density met the target requirements, indicating the necessity for comprehensive formulation optimization.

4. Performance Optimization of AAFC Based on Orthogonal Experimental Design

4.1. Performance Optimization Methods and Schemes

Based on the Preliminary Mix, an L₃₂ (4⁸) orthogonal experiment was designed for comprehensive performance optimization. Eight variables were set at four levels. Considering foam loss, the foam volume dosage was 3.0–4.5times the theoretical value. A foam stabilizer was added at 1–3.5% of the foaming-agent mass. The SiO₂ aerogel was specifically used to enhance the thermal properties and as an internal waterproofing agent to optimize the water resistance. The aerogel dosage was in the range of 2–8 kg/m³. The calcium hydroxide and waterproofing agent dosages were based on the mass of FA. The vitrified microspheres, basalt fiber, and curing process used fixed parameters of 5% and 1% of FA mass for vitrified microspheres and basalt fiber, respectively.

Table 8. Levels of factors.

Level	Factors
	Alkali Equivalent (A)	Activator Modulus (B)	Water-to-Binder Ratio (C)	Foam Dosage (D)	Foam Stabilizer Dosage (E)	Aerogel Dosage (F)	Calcium Hydroxide Dosage (G)	Waterproofing Agent Dosage (H)
1	0.08	0.9	0.40	3.0	1%	2	5%	1.5%
2	0.09	1.1	0.45	3.5	1.5%	4	10%	3%
3	0.10	1.3	0.55	4.0	2.5%	6	15%	4.5%
4	0.11	1.5	0.60	4.5	3.5%	8	20%	5.5%

Table 8. Levels of factors.

Level	Factors
	Alkali Equivalent (A)	Activator Modulus (B)	Water-to-Binder Ratio (C)	Foam Dosage (D)	Foam Stabilizer Dosage (E)	Aerogel Dosage (F)	Calcium Hydroxide Dosage (G)	Waterproofing Agent Dosage (H)
1	0.08	0.9	0.40	3.0	1%	2	5%	1.5%
2	0.09	1.1	0.45	3.5	1.5%	4	10%	3%
3	0.10	1.3	0.55	4.0	2.5%	6	15%	4.5%
4	0.11	1.5	0.60	4.5	3.5%	8	20%	5.5%

4.2. Orthogonal Experimental Design

An orthogonal experimental design was constructed using the eight variables mentioned above, each at four levels. The factor-level table and orthogonal array are provided below:

Table 9. Orthogonal experimental design table for L₃₂ (4⁸).

NO.	Factors
	Alkali Equivalent (A)	Activator Modulus (B)	Water-to-Binder Ratio (C)	Foam Dosage (D)	Foam Stabilizer Dosage (E)	Aerogel Dosage (F)	Calcium Hydroxide Dosage (G)	Waterproofing Agent Dosage (H)	Empty Column (J)
1	1 (0.08)	1 (0.9)	1 (0.40)	1 (3.0)	1 (1%)	1 (2)	1 (5%)	1 (1.5%)	1
2	1	1	2 (0.45)	2 (3.5)	4 (3.5%)	4 (8)	3 (15%)	3 (4.5%)	2
3	1	2 (1.1)	3 (0.55)	4 (4.5)	1	2 (4)	3	4 (5.5%)	3
4	1	2	4 (0.60)	3 (4.0)	4	3 (6)	1	2 (3%)	4
5	1	3 (1.3)	1	3	2 (1.5%)	4	2 (10%)	4	4
6	1	3	2	4	3 (2.5%)	1	4 (20%)	2	3
7	1	4 (1.5)	3	2	2	3	4	1	2
8	1	4	4	1	3	2	2	3	1
9	2 (0.09)	1	3	4	3	4	2	1	4
10	2	1	4	3	2	1	4	3	3
11	2	2	1	1	3	3	4	4	2
12	2	2	2	2	2	2	2	2	1
13	2	3	3	2	4	1	1	4	1
14	2	3	4	1	1	4	3	2	2
15	2	4	1	3	4	2	3	1	3
16	2	4	2	4	1	3	1	3	4
17	3 (0.10)	1	3	1	4	2	4	2	3
18	3	1	4	2	1	3	2	4	4
19	3	2	1	4	4	1	2	3	1
20	3	2	2	3	1	4	4	1	2
21	3	3	3	3	3	3	3	3	2
22	3	3	4	4	2	2	1	1	1
23	3	4	1	2	3	4	1	2	4
24	3	4	2	1	2	1	3	4	3
25	4 (0.11)	1	1	4	2	3	3	2	2
26	4	1	2	3	3	2	1	4	1
27	4	2	3	1	2	4	1	3	4
28	4	2	4	2	3	1	3	1	3
29	4	3	1	2	1	2	4	3	3
30	4	3	2	1	4	3	2	1	4
31	4	4	3	3	1	1	2	2	1
32	4	4	4	4	4	4	4	4	2

Table 9. Orthogonal experimental design table for L₃₂ (4⁸).

NO.	Factors
	Alkali Equivalent (A)	Activator Modulus (B)	Water-to-Binder Ratio (C)	Foam Dosage (D)	Foam Stabilizer Dosage (E)	Aerogel Dosage (F)	Calcium Hydroxide Dosage (G)	Waterproofing Agent Dosage (H)	Empty Column (J)
1	1 (0.08)	1 (0.9)	1 (0.40)	1 (3.0)	1 (1%)	1 (2)	1 (5%)	1 (1.5%)	1
2	1	1	2 (0.45)	2 (3.5)	4 (3.5%)	4 (8)	3 (15%)	3 (4.5%)	2
3	1	2 (1.1)	3 (0.55)	4 (4.5)	1	2 (4)	3	4 (5.5%)	3
4	1	2	4 (0.60)	3 (4.0)	4	3 (6)	1	2 (3%)	4
5	1	3 (1.3)	1	3	2 (1.5%)	4	2 (10%)	4	4
6	1	3	2	4	3 (2.5%)	1	4 (20%)	2	3
7	1	4 (1.5)	3	2	2	3	4	1	2
8	1	4	4	1	3	2	2	3	1
9	2 (0.09)	1	3	4	3	4	2	1	4
10	2	1	4	3	2	1	4	3	3
11	2	2	1	1	3	3	4	4	2
12	2	2	2	2	2	2	2	2	1
13	2	3	3	2	4	1	1	4	1
14	2	3	4	1	1	4	3	2	2
15	2	4	1	3	4	2	3	1	3
16	2	4	2	4	1	3	1	3	4
17	3 (0.10)	1	3	1	4	2	4	2	3
18	3	1	4	2	1	3	2	4	4
19	3	2	1	4	4	1	2	3	1
20	3	2	2	3	1	4	4	1	2
21	3	3	3	3	3	3	3	3	2
22	3	3	4	4	2	2	1	1	1
23	3	4	1	2	3	4	1	2	4
24	3	4	2	1	2	1	3	4	3
25	4 (0.11)	1	1	4	2	3	3	2	2
26	4	1	2	3	3	2	1	4	1
27	4	2	3	1	2	4	1	3	4
28	4	2	4	2	3	1	3	1	3
29	4	3	1	2	1	2	4	3	3
30	4	3	2	1	4	3	2	1	4
31	4	4	3	3	1	1	2	2	1
32	4	4	4	4	4	4	4	4	2

Specimens were prepared according to the mix proportions listed in Table 9. The preparation and testing processes are shown in the figure below, and the performance test results for the specimens are listed in Table 10.

Figure 6. Samples preparation and testing, (a) samples preparation,(b) curing,(c) thermal conductivity measurement,(d) samples drying,(e) water absorption test, (f) frost resistance test.

Figure 6. Samples preparation and testing, (a) samples preparation,(b) curing,(c) thermal conductivity measurement,(d) samples drying,(e) water absorption test, (f) frost resistance test.

As shown in the table, the 32 mix proportion samples exhibited dry densities of 556.83–655.77 kg/m³, with only two slightly exceeding the target. The thermal conductivity ranged from a minimum of 0.0929 W/(m·K) (sample 32) to a maximum of 0.1377 W/(m·K) (sample 1); only samples 1, 13, and 31 marginally exceeded the target. The mechanical properties and freeze-thaw resistance (F25) met these requirements. The lowest mass of water absorption was 4.12% (below the target), although 13 samples exceeded the target. Further analysis is required to identify the optimal mix for achieving the best comprehensive performance.

4.3. Analysis of Influences of Different Factors on Performance

4.3.1. Range Analysis of Test Results

(1)

Range Analysis of Dry Density

The range (R) values reveal that the foam content and water-binder ratio are the primary factors influencing dry density, with curves showing the steepest slopes. In contrast, the aerogel content and calcium hydroxide content are secondary factors, while the remaining factors have minimal impacts.

Table 11. Results of dry density range analysis.

Index		Factors
		A	B	C	D	E	F	G	H	Empty Column
Dry Density (kg/m³)	K11	4774.53	4798.98	4927.13	4968.90	4766.83	4831.29	4796.23	4746.49	4790.03
	K12	4778.42	4766.03	4836.45	4931.66	4754.90	4774.60	4735.01	4789.31	4789.73
	K13	4777.99	4769.53	4728.79	4635.85	4781.93	4749.58	4749.11	4773.36	4795.16
	K14	4772.68	4769.08	4611.25	4567.21	4799.96	4748.15	4823.27	4794.46	4789.77
	k11	596.82	599.87	615.89	621.11	595.85	603.91	599.53	593.31	598.75
	k12	597.30	595.75	604.56	616.46	594.36	596.83	591.88	598.66	598.72
	k13	597.25	596.19	591.10	579.48	597.74	593.70	593.64	596.67	599.40
	k14	596.59	596.14	576.41	570.90	600.00	593.52	602.91	599.31	598.72
R		0.72	4.12	39.49	50.21	5.63	10.39	11.03	6.00	0.68
Optimal Level		2	1	1	1	4	1	4	4

Note: K_ij represents the sum of test results corresponding to level j in any factor column under the performance index i. k_ij denotes the average value of test results for level number j in any factor column.

Table 11. Results of dry density range analysis.

Index		Factors
		A	B	C	D	E	F	G	H	Empty Column
Dry Density (kg/m³)	K11	4774.53	4798.98	4927.13	4968.90	4766.83	4831.29	4796.23	4746.49	4790.03
	K12	4778.42	4766.03	4836.45	4931.66	4754.90	4774.60	4735.01	4789.31	4789.73
	K13	4777.99	4769.53	4728.79	4635.85	4781.93	4749.58	4749.11	4773.36	4795.16
	K14	4772.68	4769.08	4611.25	4567.21	4799.96	4748.15	4823.27	4794.46	4789.77
	k11	596.82	599.87	615.89	621.11	595.85	603.91	599.53	593.31	598.75
	k12	597.30	595.75	604.56	616.46	594.36	596.83	591.88	598.66	598.72
	k13	597.25	596.19	591.10	579.48	597.74	593.70	593.64	596.67	599.40
	k14	596.59	596.14	576.41	570.90	600.00	593.52	602.91	599.31	598.72
R		0.72	4.12	39.49	50.21	5.63	10.39	11.03	6.00	0.68
Optimal Level		2	1	1	1	4	1	4	4

Note: K_ij represents the sum of test results corresponding to level j in any factor column under the performance index i. k_ij denotes the average value of test results for level number j in any factor column.

Figure 7. Dry density of AAFC varies with the levels of various factors.

Figure 7. Dry density of AAFC varies with the levels of various factors.

(2)

Range Analysis of Thermal Conductivity

The thermal conductivity decreased with increasing foam and aerogel content. The curve slope for aerogel content was the steepest, indicating the greatest influence magnitude, significantly exceeding the other factors. This demonstrates that aerogel, as a super-insulating material, can remarkably reduce the thermal conductivity of FC. Foam content is the next most influential factor, and is well documented[38,39,40]. Other factors exerted minimal effects.

Table 12. Results of thermal conductivity range analysis.

Index		Factors
		A	B	C	D	E	F	G	H	Empty Column
Thermal Conductivity (W/(m·K))	K21	0.8484	0.8486	0.8510	0.8645	0.8564	0.9671	0.8610	0.8478	0.8035
	K22	0.8388	0.8169	0.8421	0.8422	0.8426	0.8113	0.8310	0.8358	0.7887
	K23	0.8430	0.8447	0.8484	0.8319	0.8236	0.8010	0.8371	0.8233	0.8049
	K24	0.8254	0.8454	0.8141	0.8170	0.8330	0.7761	0.8265	0.8486	0.7885
	k21	0.1060	0.1061	0.1064	0.1081	0.1071	0.1209	0.1076	0.1060	0.1004
	k22	0.1049	0.1021	0.1053	0.1053	0.1053	0.1014	0.1039	0.1045	0.0986
	k23	0.1054	0.1056	0.1060	0.1040	0.1029	0.1001	0.1046	0.1029	0.1006
	k24	0.1032	0.1057	0.1018	0.1021	0.1041	0.0970	0.1033	0.1061	0.0986
R		0.0029	0.0040	0.0046	0.0059	0.0041	0.0239	0.0043	0.0032	0.0021 0.0021
Optimal Level		4	2	4	4	3	4	4	3

Table 12. Results of thermal conductivity range analysis.

Index		Factors
		A	B	C	D	E	F	G	H	Empty Column
Thermal Conductivity (W/(m·K))	K21	0.8484	0.8486	0.8510	0.8645	0.8564	0.9671	0.8610	0.8478	0.8035
	K22	0.8388	0.8169	0.8421	0.8422	0.8426	0.8113	0.8310	0.8358	0.7887
	K23	0.8430	0.8447	0.8484	0.8319	0.8236	0.8010	0.8371	0.8233	0.8049
	K24	0.8254	0.8454	0.8141	0.8170	0.8330	0.7761	0.8265	0.8486	0.7885
	k21	0.1060	0.1061	0.1064	0.1081	0.1071	0.1209	0.1076	0.1060	0.1004
	k22	0.1049	0.1021	0.1053	0.1053	0.1053	0.1014	0.1039	0.1045	0.0986
	k23	0.1054	0.1056	0.1060	0.1040	0.1029	0.1001	0.1046	0.1029	0.1006
	k24	0.1032	0.1057	0.1018	0.1021	0.1041	0.0970	0.1033	0.1061	0.0986
R		0.0029	0.0040	0.0046	0.0059	0.0041	0.0239	0.0043	0.0032	0.0021 0.0021
Optimal Level		4	2	4	4	3	4	4	3

Figure 8. Thermal conductivity of AAFC varies with the levels of various factors.

Figure 8. Thermal conductivity of AAFC varies with the levels of various factors.

(3)

Mass Water Absorption Rate

Analysis of the range values (R) and curves in Figure 9 shows that the waterproofing agent dosage was the most significant factor affecting the mass water absorption rate, which decreased significantly with increasing dosage. Compared with previous studies, the waterproofing performance has been effectively improved[9]. Foam content was the next most influential factor, although the range value (R) of the former was approximately 2.7 times that of the latter. Factors such as activator modulus, water-binder ratio, and calcium hydroxide content showed negligible effects.

Table 13. Results of mass water absorption rate range analysis.

Index		Factors
		A	B	C	D	E	F	G	H	Empty Column
Mass Water Absorption Rate(%)	K31	107.210	107.416	106.121	98.576	102.751	107.851	106.806	127.835	108.301
	K32	109.207	101.146	96.030	105.642	109.775	106.910	103.246	109.090	103.271
	K33	102.181	103.661	109.311	102.950	106.476	103.552	107.170	92.385	106.46
	K34	101.185	107.560	108.321	112.615	100.781	101.470	102.561	90.473	101.751
	k31	13.401	13.427	13.265	12.322	12.844	13.481	13.351	15.979	13.538
	k32	13.651	12.643	12.004	13.205	13.722	13.364	12.906	13.636	12.909
	k33	12.773	12.958	13.664	12.869	13.310	12.944	13.396	11.548	13.308
	k34	12.648	13.445	13.540	14.077	12.598	12.684	12.820	11.309	12.719
R		1.003	0.802	1.660	1.755	1.124	0.798	0.576	4.670	0.819
Optimal Level		4	2	2	1	4	4	4	4

Table 13. Results of mass water absorption rate range analysis.

Index		Factors
		A	B	C	D	E	F	G	H	Empty Column
Mass Water Absorption Rate(%)	K31	107.210	107.416	106.121	98.576	102.751	107.851	106.806	127.835	108.301
	K32	109.207	101.146	96.030	105.642	109.775	106.910	103.246	109.090	103.271
	K33	102.181	103.661	109.311	102.950	106.476	103.552	107.170	92.385	106.46
	K34	101.185	107.560	108.321	112.615	100.781	101.470	102.561	90.473	101.751
	k31	13.401	13.427	13.265	12.322	12.844	13.481	13.351	15.979	13.538
	k32	13.651	12.643	12.004	13.205	13.722	13.364	12.906	13.636	12.909
	k33	12.773	12.958	13.664	12.869	13.310	12.944	13.396	11.548	13.308
	k34	12.648	13.445	13.540	14.077	12.598	12.684	12.820	11.309	12.719
R		1.003	0.802	1.660	1.755	1.124	0.798	0.576	4.670	0.819
Optimal Level		4	2	2	1	4	4	4	4

(4)

Mechanical Properties

Analysis of the range values (R) for compressive and flexural strengths (Table 14, Table 15 and Table 16) reveals that aerogel content, foam content, and water-binder ratio are the three most influential factors. The foam stabilizer dosage had the least significant effect on the compressive strength, while calcium hydroxide content had a relatively minor influence on the flexural strength. As shown in the curves in Figure 9, both the compressive and flexural strengths decrease significantly with increasing foam content, aerogel content, and water-binder ratio. A higher foam content introduces more air bubbles into the solid matrix, which increases the porosity and degrades the mechanical properties. The hydration products (C(N)-A-S-H) are critical for the strength development of AAFC[41,42]. Appropriate addition of calcium hydroxide can increase the proportion of C-A-S-H in the hydration products[43], thereby improving the mechanical properties. The effect of foam stabilizer dosage on the mechanical properties follows a pattern of first decreased and then increased. As a surfactant, an appropriate amount of stabilizer improves the stability of bubble membranes, prolongs their rupture half-life, and controls the bubble uniformity, size, and quantity in the slurry to enhance the mechanical properties[44].

Figure 10. Mechanical properties of AAFC varies with the levels of various factors.

Figure 10. Mechanical properties of AAFC varies with the levels of various factors.

Range analysis indicated that foam content was the most dominant factor influencing drying shrinkage, followed by the water–binder ratio, with other factors having negligible effects. As shown in Figure 11, the drying shrinkage decreases nearly linearly with increasing foam content, which is attributable to the increased porosity, which reduces the solid phase fraction and thus the autogenous shrinkage of the AA matrix. In contrast, drying shrinkage increases with the water–binder ratio; higher ratios improve workability but also increase macroporosity and connectivity, accelerating moisture loss and capillary evaporation. The resulting capillary pressure difference further intensifies the shrinkage stress.

(5)

Frost Resistance

The range calculation and analysis results of the strength loss rate and mass loss rate are listed in Table 17 and Table 18:

By comparing the range values (R), it can be seen that the three most influential factors on the freezing resistance of the AAFC are, in order: waterproofing agent dosage, foam content, and water-binder ratio. The other factors had relatively minor effects.

The dosage of the waterproofing agent demonstrated the most significant effect on frost resistance, with both the strength and mass loss rates decreasing approximately linearly as its content increased. This improvement was attributed to the reduction in water absorption, which mitigated the 9% volumetric expansion of water upon freezing and the resultant frost-heave pressure within the pores. In contrast, increased foam content reduces frost resistance by increasing porosity, coarsening pore structures, and thinning pore walls, thereby elevating water absorption and exacerbating frost-induced damage. Similarly, a higher water–binder ratio diminishes frost resistance by promoting slurry fluidity and altering pore characteristics, leading to internal stress differences between saturated and unsaturated zones during freeze–thaw cycles.

Figure 12. Frost resistance of AAFC varies with the levels of various factors.

Figure 12. Frost resistance of AAFC varies with the levels of various factors.

4.3.2. Analysis of Variance (ANOVA) of Test Results

Range analysis of orthogonal test results can effectively determine the primary and secondary orders of influencing factors, but it cannot distinguish data fluctuations caused by changes in test conditions and errors, nor evaluate the significance level of the influencing factors. Therefore, ANOVA was conducted. The significance of the influence of each factor can be determined by constructing an F-statistic for the F-test.

The range and variance analysis results in Table 19 show good consistency. A comprehensive analysis of both methods led to the following conclusions.

(1) Foam content significantly affects all properties, reducing density and thermal conductivity, but increasing water absorption and shrinkage while compromising mechanical and frost resistance, requiring careful optimization.

(2) The aerogel content exhibited an extremely significant effect on thermal performance. Combining the increased aerogel content with moderately reduced foam content simultaneously enhanced the thermal and mechanical properties.

(3) The water-binder ratio significantly influences the mechanical properties and density, with significant effects on water absorption and frost resistance. Its complex effects necessitate careful optimization.

(4) Calcium hydroxide moderately improved the mechanical properties through an initial-decrease-then-increase pattern, while showing negligible effects on other parameters.

(5) The waterproofing agent significantly enhances the water resistance and frost durability, slightly improves the mechanical properties, and minimally affects the thermal and density characteristics.

4.3.3. Microscopic Analysis

(1)

SEM

The variations in the mix proportions resulted in significant changes in the micro-morphologies of the specimens (Figure 13). Among the six groups of specimens, both pore size and porosity generally showed an increasing trend: Specimen S3 had the largest pore size, along with the smallest thermal conductivity and dry density, whereas the opposite was true for Specimen S1.This trend shows a strong correlation with the pore size and characteristics[45,46]. This indicated that the foam content and water-to-binder ratio exerted a significant influence on the pore structure. Although Specimens S5 and S11 differ in water-to-binder ratio and foam content, their low thermal conductivity, attributed to the high aerogel content, confirms that the aerogel is a key influencing factor. SEM images reveal that Specimen S3 features high porosity and thin pore walls, whereas Specimen S11, with a higher dosage of foam stabilizer, exhibited fewer interconnected pores and more uniform pore sizes[47]. The random dispersion of basalt fibers is conducive to enhancing the mechanical properties, and the absence of independent FA particles is consistent with the reaction mechanism of alkali-activated FA.

(2)

FTIR

The analysis indicates that the wavenumber range of 1000–1040 cm < B-> ¹ corresponds to the asymmetric stretching vibration peak of Si-O-X (Na/Al), which is the most prominent characteristic absorption peak of alkali-activated FA cementitious materials[48]. The absorption peak intensities vary among the six groups of specimens: a stronger and sharper peak suggests a higher content of hydrated sodium (calcium) aluminosilicate (C,N-A-S-H) in the reaction products, which is beneficial for enhancing the mechanical properties of FC[49,50]. Additionally, compared with the infrared spectrum of FA, the characteristic peak of Si-O-X (Na/Al) in the products shifted to a lower wavenumber, a feature that reflects the gradual increase in C,N-A-S-H gel products[29,31]. Moreover, due to differences in alkali concentration among systems with various mix proportions, there are certain variations in the extent of the peak shift. The peak at 1430 cm < st > ¹ corresponds to the asymmetric stretching vibration of carbonate, with the peak of S11 being the strongest. Because S11 had the highest alkali equivalent among the six mix proportions, the system of this mix proportion exhibited strong alkalinity, indicating the maximum formation of carbonate. Furthermore, there are two characteristic peaks at 3433 cm⁻¹ and 1630 cm⁻¹, which correspond to the bending vibration peak of H-O-H bonds, among which the peak at 1630 cm⁻¹ is the characteristic peak of bound water in cementitious materials[51].

Figure 14. FTIR diagram of samples with different mix ratios.

Figure 14. FTIR diagram of samples with different mix ratios.

4.4. Determination of Optimal Mix Proportion for AAFC

4.4.1. Mix Proportion Optimization Method

Both range and variance analyses are single-factor analysis methods that cannot determine the optimal mix proportion under multi-factor conditions in orthogonal experiments. The matrix analysis method can objectively conduct a comprehensive analysis of multifactor and multiindex systems and calculate the weights of each factor level. Therefore, matrix analysis was used to determine the optimal mix proportion for the AAFC.

Based on the orthogonal experimental scheme and the performance index system of the AAFC, a three-layer hierarchical structure model was constructed, including the index, factor, and level layers. The model consists of eight factors with four levels each, and eight performance indicators were investigated. The constructed structural model is presented in the following table:

Table 20. Orthogonal test of AAFC data structure model.

Index Layer

Performance Indicators

Factor Layer

Factor A

Factor B

⋅⋅⋅

Factor H

Level Layer

A1

A2

⋅⋅⋅

A4

B1

B2

⋅⋅⋅

B4

⋅⋅⋅

H1

H2

⋅⋅⋅

H4

Table 20. Orthogonal test of AAFC data structure model.

Index Layer

Performance Indicators

Factor Layer

Factor A

Factor B

⋅⋅⋅

Factor H

Level Layer

A1

A2

⋅⋅⋅

A4

B1

B2

⋅⋅⋅

B4

⋅⋅⋅

H1

H2

⋅⋅⋅

H4

Index Layer Matrix: The average value of the test index for factor X_i at the j level is defined as m_ij. For indicators in which larger values indicate better performance, M_ij=m_ij; for indicators in which smaller values are preferable, M_ij=1/m_ij. The established index matrix is expressed by Eq.8:

$$M=\left[\begin{array}{ccccc}{M}_{11}& 0& 0& \cdots & 0\\ M_{12}& 0& 0& \cdots & 0\\ \cdots & \cdots & \cdots & \cdots & \cdots \\ M_{1m}& 0& 0& \cdots & 0\\ 0& M_{21}& 0& \cdots & 0\\ 0& M_{22}& 0& \cdots & 0\\ \cdots & \cdots & \cdots & \cdots & \cdots \\ 0& M_{2m}& 0& \cdots & 0\\ 0& 0& 0& \cdots & 0\\ 0& 0& 0& \cdots & M_{l1}\\ 0& 0& 0& \cdots & M_{l1}\\ \cdots & \cdots & \cdots & \cdots & \cdots \\ 0& 0& 0& \cdots & M_{lm}\end{array}\right]$$

(8)

Factor Layer Matrix: Let $T_i={\displaystyle \frac{1}{{\displaystyle \sum _{j=1}^m{M}_{ij}}}}$, the factor matrix is established as shown in Eq.9:

$$T=\left[\begin{array}{cccc}{T}_1& 0& \cdots & 0\\ 0& T_2& \cdots & 0\\ \cdots & \cdots & \cdots & \cdots \\ 0& 0& \cdots & T_l\end{array}\right]$$

(9)

Level Layer Matrix: Calculate the range S_i of factor A_i, Let $S_i={\displaystyle \frac{s_i}{{\displaystyle \sum _{i=1}^l{s}_i}}}$, the factor matrix is established as shown in Eq.10:

$$S=\left[\begin{array}{c}{S}_1\\ S_2\\ \cdots \\ S_l\end{array}\right]$$

(10)

Weight Matrix: For the weight matrix of the factors influencing the test indices ${\omega }_i=M_i{T}_i{S}_i$, ${\omega }_i^T$can be expressed as follows:

$${\omega }_i^T=[{\omega }_1,{\omega }_2,\mathrm{L},{\omega }_{\mathrm{m}}]$$

(11)

The total weight matrix was obtained by averaging the sum of the weight matrices for each factor ω_i, as shown in Eq.12:

$${\omega }^{\mathrm{T}}=({\omega }_1^{\mathrm{T}}+{\omega }_2^{\mathrm{T}}+\mathrm{L}+{\omega }_x^{\mathrm{T}})/l$$

(12)

4.4.2. Analysis and Determination of Optimal Mix Proportion

The weight matrix for eight performance indicators, including dry density, was calculated based on the established three-layer hierarchical structure model. For five indicators (thermal conductivity, mass water absorption rate, drying shrinkage, strength loss rate, and mass loss rate), smaller values were preferable; therefore, M_ij=1/m_ij was adopted. For dry density, compressive strength, and flexural strength (where larger values are preferable), M_ij=1/m_ij was used. The calculation results based on this method are listed in the following table:

Table 21. Results of matrix analysis.

Factors	ρ	λ	Wr	f	Rf	ε	Fc	Mm	Total Weight Weight
A1	0.001406	0.001355	0.019789	0.015929	0.021806	0.007451	0.005086	0.011342	0.010521
A2	0.001405	0.001371	0.019427	0.016174	0.023565	0.007413	0.005119	0.011370	0.010731
A3	0.001405	0.001364	0.020763	0.016044	0.023033	0.007567	0.005116	0.011436	0.010841
A4	0.001407	0.001393	0.020967	0.016004	0.023050	0.007459	0.005084	0.011093	0.010807
B1	0.008032	0.001869	0.015798	0.020380	0.018552	0.015159	0.012301	0.007790	0.012485
B2	0.008087	0.001941	0.016777	0.020430	0.019814	0.015119	0.012222	0.007748	0.012767
B3	0.008081	0.001878	0.016370	0.020780	0.019673	0.014684	0.012131	0.007629	0.012653
B4	0.008082	0.001876	0.015777	0.020485	0.019428	0.015297	0.012332	0.007776	0.012632
C1	0.074948	0.002170	0.033044	0.042511	0.059972	0.058656	0.033702	0.031382	0.042048
C2	0.076354	0.002193	0.036516	0.041752	0.056736	0.053662	0.033227	0.030637	0.041385
C3	0.078092	0.002177	0.032080	0.041865	0.052582	0.052590	0.032492	0.029458	0.040167
C4	0.080083	0.002269	0.032373	0.040853	0.049872	0.050538	0.032240	0.028928	0.039645
D1	0.094436	0.002759	0.037616	0.053465	0.058186	0.114342	0.043226	0.037643	0.055209
D2	0.095149	0.002832	0.035100	0.053067	0.058202	0.128440	0.041975	0.036368	0.056392
D3	0.101221	0.002867	0.036018	0.051078	0.048713	0.150061	0.041536	0.035001	0.058312
D4	0.102742	0.002919	0.032927	0.050880	0.048599	0.167893	0.040850	0.034166	0.060122
E1	0.011058	0.001923	0.023148	0.010166	0.020177	0.012008	0.012556	0.012551	0.012948
E2	0.011085	0.001954	0.021667	0.010100	0.020630	0.012173	0.012558	0.012643	0.012851
E3	0.011023	0.001999	0.022339	0.010102	0.019567	0.012415	0.012772	0.012991	0.012901
E4	0.010981	0.001977	0.023601	0.010198	0.019295	0.012184	0.012728	0.012774	0.012967
F1	0.001905	0.011869	0.016304	0.064976	0.052377	0.008781	0.012750	0.005270	0.021779
F2	0.001895	0.011718	0.015792	0.065705	0.059349	0.008681	0.012808	0.005282	0.022654
F3	0.001873	0.009831	0.015654	0.069156	0.063528	0.008829	0.012591	0.005207	0.023334
F4	0.001906	0.012250	0.016638	0.065258	0.055032	0.008621	0.012657	0.005279	0.022205
G1	0.001637	0.002063	0.011381	0.024228	0.008808	0.008058	0.008951	0.007552	0.009085
G2	0.001642	0.002078	0.011814	0.023845	0.008684	0.008135	0.008845	0.007438	0.009060
G3	0.001621	0.002006	0.011420	0.024352	0.008646	0.008129	0.008861	0.007547	0.009073
G4	0.001612	0.002090	0.011893	0.023801	0.008555	0.007959	0.008854	0.007590	0.009044
H1	0.001672	0.001500	0.075879	0.019184	0.013437	0.004420	0.113216	0.114664	0.042996
H2	0.001657	0.001521	0.088917	0.018940	0.013747	0.004415	0.119851	0.128726	0.047222
H3	0.001662	0.001545	0.104995	0.019004	0.013241	0.004457	0.127713	0.147112	0.052466
H4	0.001655	0.001498	0.107214	0.019287	0.013144	0.004403	0.133648	0.167607	0.056057

Table 21. Results of matrix analysis.

Factors	ρ	λ	Wr	f	Rf	ε	Fc	Mm	Total Weight Weight
A1	0.001406	0.001355	0.019789	0.015929	0.021806	0.007451	0.005086	0.011342	0.010521
A2	0.001405	0.001371	0.019427	0.016174	0.023565	0.007413	0.005119	0.011370	0.010731
A3	0.001405	0.001364	0.020763	0.016044	0.023033	0.007567	0.005116	0.011436	0.010841
A4	0.001407	0.001393	0.020967	0.016004	0.023050	0.007459	0.005084	0.011093	0.010807
B1	0.008032	0.001869	0.015798	0.020380	0.018552	0.015159	0.012301	0.007790	0.012485
B2	0.008087	0.001941	0.016777	0.020430	0.019814	0.015119	0.012222	0.007748	0.012767
B3	0.008081	0.001878	0.016370	0.020780	0.019673	0.014684	0.012131	0.007629	0.012653
B4	0.008082	0.001876	0.015777	0.020485	0.019428	0.015297	0.012332	0.007776	0.012632
C1	0.074948	0.002170	0.033044	0.042511	0.059972	0.058656	0.033702	0.031382	0.042048
C2	0.076354	0.002193	0.036516	0.041752	0.056736	0.053662	0.033227	0.030637	0.041385
C3	0.078092	0.002177	0.032080	0.041865	0.052582	0.052590	0.032492	0.029458	0.040167
C4	0.080083	0.002269	0.032373	0.040853	0.049872	0.050538	0.032240	0.028928	0.039645
D1	0.094436	0.002759	0.037616	0.053465	0.058186	0.114342	0.043226	0.037643	0.055209
D2	0.095149	0.002832	0.035100	0.053067	0.058202	0.128440	0.041975	0.036368	0.056392
D3	0.101221	0.002867	0.036018	0.051078	0.048713	0.150061	0.041536	0.035001	0.058312
D4	0.102742	0.002919	0.032927	0.050880	0.048599	0.167893	0.040850	0.034166	0.060122
E1	0.011058	0.001923	0.023148	0.010166	0.020177	0.012008	0.012556	0.012551	0.012948
E2	0.011085	0.001954	0.021667	0.010100	0.020630	0.012173	0.012558	0.012643	0.012851
E3	0.011023	0.001999	0.022339	0.010102	0.019567	0.012415	0.012772	0.012991	0.012901
E4	0.010981	0.001977	0.023601	0.010198	0.019295	0.012184	0.012728	0.012774	0.012967
F1	0.001905	0.011869	0.016304	0.064976	0.052377	0.008781	0.012750	0.005270	0.021779
F2	0.001895	0.011718	0.015792	0.065705	0.059349	0.008681	0.012808	0.005282	0.022654
F3	0.001873	0.009831	0.015654	0.069156	0.063528	0.008829	0.012591	0.005207	0.023334
F4	0.001906	0.012250	0.016638	0.065258	0.055032	0.008621	0.012657	0.005279	0.022205
G1	0.001637	0.002063	0.011381	0.024228	0.008808	0.008058	0.008951	0.007552	0.009085
G2	0.001642	0.002078	0.011814	0.023845	0.008684	0.008135	0.008845	0.007438	0.009060
G3	0.001621	0.002006	0.011420	0.024352	0.008646	0.008129	0.008861	0.007547	0.009073
G4	0.001612	0.002090	0.011893	0.023801	0.008555	0.007959	0.008854	0.007590	0.009044
H1	0.001672	0.001500	0.075879	0.019184	0.013437	0.004420	0.113216	0.114664	0.042996
H2	0.001657	0.001521	0.088917	0.018940	0.013747	0.004415	0.119851	0.128726	0.047222
H3	0.001662	0.001545	0.104995	0.019004	0.013241	0.004457	0.127713	0.147112	0.052466
H4	0.001655	0.001498	0.107214	0.019287	0.013144	0.004403	0.133648	0.167607	0.056057

Based on the above results, the optimal mix proportion of AAFC was determined to be A₃B₂C₁D₄E₄F₃G₁H₄, with the following factor levels: alkali equivalent of 0.1, activator modulus of 1.1, water-to-binder ratio of 0.4, foam dosage of 4.5 (multiple of theoretical value), foam stabilizer dosage of 3.5% (by mass of foaming agent), aerogel dosage of 6 kg/m³, calcium hydroxide dosage of 5% (by mass of FA), and waterproofing agent dosage of 5.5% (by mass of FA). The specimens were prepared and cured again according to the above mix proportion, and the performance parameters of the optimal mix AAFC were measured as follows: dry density of 576.34 kg/m³, thermal conductivity of 0.1107 W/(m·K), mass water absorption rate of 3.87%, compressive strength of 5.83 MPa, flexural strength of 1.41 MPa, drying shrinkage of 0.614 mm/m, strength loss rate of 10.433%, and mass loss rate of 1.764%. This indicates that all the indicators of the AAFC with the optimal mix proportion meet the target requirements.

5. Conclusions

(1) A target performance system was established for ultralow energy buildings in hot-summer and cold-winter regions, comprising six primary and ten secondary indicators, with particular emphasis on water resistance.

(2) A volume-based mix design method was proposed for the AAFC. Preliminary mixes only met dry density targets, with mass water absorption reaching 57.1% (11.42 times the target), indicating the need for comprehensive optimization.

(3) An 8-factor, 4-level orthogonal experiment was designed. The SiO₂ aerogel (6 kg/m³) effectively reduced the thermal conductivity without compromising its mechanical properties. The waterproofing agent (5.5% FA mass) achieved optimal water resistance and frost durability.

(4) The optimal mix proportion of AAFC was determined to be A₃B₂C₁D₄E₄F₃G₁H₄ by matrix analysis. The performance indicators were as follows: dry density 576.34 kg/m³; thermal conductivity, 0.1107 W/(m·K); water absorption, 3.87%; compressive strength 5.83 MPa, flexural strength 1.41 MPa, drying shrinkage, 0.614 mm/m; frost resistance (10.433% strength loss and 1.764% mass loss). All parameters satisfied the target requirements.