Study on Multi-Scale Strength Formation Mechanism of Fly Ash-Based Geopolymer Concrete Based on Statistical Damage Theory

Abstract

Uniaxial compression tests were conducted on fly ash-based geopolymer concrete (FAG) with varying alkali-binder ratios (0.25, 0.35, 0.45, 0.55, 0.65) and curing ages (7 d, 28 d) to ascertain its mechanical performance parameters and stress–strain relationship curves. The formation mechanism of FAG multiscale strength is revealed through a systematic process that integrates statistical damage theory with microscopic testing techniques. This process involves the progression of microstructural state and the evolution of mesoscopic damage, providing a comprehensive understanding of the multiscale strength formation process. The results indicate that as the alkali-binder ratio increased, there was an initial rise and subsequent decline in microstructure density. At an alkali-binder ratio of 0.45, the alkaline activator can fully stimulate the fly ash to undergo depolymerization and polycondensation reactions. The result of this process is the formation of a continuous and dense cementitious matrix, thereby achieving the optimal improvement in macroscopic initial mechanical properties. Concurrent microstructural alterations further modify the morphology and path of microcrack initiation and propagation during uniaxial compression, as well as the effective force skeleton adjustment process. The characteristic parameters that are indicative of the evolution of microfracture and yield damage demonstrate regular changes in accordance with the alkali-binder ratio. The joint effect of these two factors determines the evolution characteristics of the macroscopic nonlinear stress–strain behavior of FAG, ultimately resulting in an increasing and then decreasing trend of FAG strength with the increase of alkali-binder ratio, while ductility shows a trend of decreasing first and then increasing. At an equivalent alkali-binder ratio, the porosity of the 7 d sample exhibited a decrease of 1.13% to 17.13%. Conversely, the strength of the 7 d sample increased by 39% to 312%. However, the deformation capacity of the 7 d sample decreased, with a peak strain reduction of 21% to 52% at 28 d. This research achievement has the potential to provide significant theoretical support for the practical engineering promotion and application of FAG.

1. Introduction

In the context of accelerating urbanization, Ordinary Portland cement (OPC) has emerged as a predominant building material. The production of this cement involves the substantial consumption of natural resources and the emission of significant quantities of carbon dioxide. As demonstrated in studies [1,2,3], it is evident that the global cement industry is responsible for 8% of carbon dioxide emissions on a global scale. It has been determined that cement is responsible for the highest contribution to the carbon footprint of concrete production [4]. In order to coordinate the development of buildings with carbon-reducing measures, it is necessary to substitute OPC with eco-efficient cementitious materials [5]. Geopolymer binders are a typical example of this type of material [6], offering mechanical properties comparable to cement while exhibiting significantly lower carbon emissions. It can thus be concluded that they possess significant potential to serve as an ideal substitute for OPC [5,7]. Geopolymer binders are defined as inorganic polymers formed through a three-dimensional network structure, achieved by catalyzing the polymerization reaction of silica-alumina tetrahedral structural units in raw materials that are rich in silica and aluminum using alkaline activators [8,9]. Fly ash (FA), slag, and kaolin are the predominant industrial solid waste materials that constitute aluminosilicate raw materials [10,11,12]. At present, the global annual production of FA is estimated to be approximately 2.8 billion metric tons. China is the leading producer, with an annual output of 1.569 billion metric tons. Despite the substantial production of FA, its global average utilization rate remains at only 53% [13]. Furthermore, according to Diaz-Loya et al. [6], fly ash-based geopolymer concrete (FAG) and traditional OPC concrete can exhibit equivalent mechanical properties. It is evident that FAG has the capacity to utilize industrial solid waste as a substitute for traditional cement in the production of low-carbon building materials. This approach facilitates the effective utilization of resources [14,15].

The formation of N-A-S-H gel has been demonstrated to result in superior performance characteristics in FAG, including corrosion resistance, high temperature resistance, and environmental protection [16,17,18,19]. The calcium aluminosilicate gel formed in alkali-activated high-calcium systems (e.g., certain blast furnace slag systems) exhibits a relatively compact structure, while the sodium aluminosilicate gel generated from the reaction of FAG possesses a unique microstructure with low porosity. The reaction process is primarily concentrated in two stages: depolymerization and polycondensation [20,21,22]. The mechanical properties and durability of FAG are contingent on the alkali-binder ratio (AL/B), which directly affects the phase density and microstructural integrity of gel by affecting the depolymerization–polycondensation reaction of the precursor [23,24]. Rao and Kumar et al. [25] investigated the compressive strength of geopolymer concrete (GPC) at AL/B of 0.30, 0.35, and 0.40, and the results showed that the compressive strength reached its peak at AL/B of 0.40. This indicates that a moderate AL/B can fully activate the cementitious materials and promote gel phase formation. In their study on replacing fine aggregates with iron ore tailings, Sharath et al. [26] found that the compressive strength was optimal at AL/B of 0.6. Thakur and Bawa et al. [27] have indicated that the addition of slag has the potential to enhance the compressive strength of FAG. However, it is crucial to note that this enhancement is only attainable when combined with AL/B optimization, thereby ensuring a balanced workability. As posited by Ali-Abdo et al. [28], an increase in the ratio of alkaline solution to FA has been demonstrated to enhance the mechanical properties of FAG. Evidently, the AL/B exerts a substantial influence on the mechanical properties of FAG. However, the optimal AL/B remains a subject of debate in extant research, as evidenced by the absence of a consensus on this matter. Consequently, it is imperative to conduct FAG-related tests to ascertain the optimal AL/B, with a view to enhancing the mechanical properties of materials.

Curing age is a pivotal factor affecting the mechanical properties of FAG, which is primarily attributed to the continuous evolution of alkali-activated polymerization reaction inside the matrix with curing age. In the initial curing stage, the dissolution of FA particles is facilitated by the action of alkaline activators, resulting in the release of active silicon and aluminum components. This process initiates the formation of low-polymerization-degree N-A-S-H gels. At this stage, the internal pore structure is well-developed, and the matrix is relatively compact. As the curing age increases, the FA particles that have not yet undergone complete reaction continue to participate in the alkali-activated polycondensation reaction. This results in the steady generation of N-A-S-H gel products. The products under consideration are capable of filling the capillary pores and microcracks present within the matrix. This process leads to the progressive optimization of the interfacial transition zone, thereby rendering the overall structure denser and more stable. Consequently, the mechanical properties of the material, such as compressive strength, tensile strength, and elastic modulus, are continuously enhanced. As Rangan [29] noted in his report, the strength development of geopolymer concrete deviates from that of conventional cement concrete. The initial strength of the substance is primarily contingent upon the curing temperature and duration, as opposed to extended ageing processes. Nath and Sarker [30] conducted a study on the mechanical properties of FAG under conditions of room-temperature curing. The findings indicate that the elastic modulus of 28-day cured FAG is lower than that of ordinary Portland concrete with equivalent compressive strength grade under identical curing conditions. In their study, Memon et al. [31] investigated the impact of curing age and silica fume content (0 wt%, 5 wt%, 10 wt%, 15 wt%) on the mechanical properties of fly ash-based self-compacting geopolymer concrete. It has been established that, under equivalent silica fume replacement ratios, the 28 d compressive strength, splitting tensile strength, and flexural strength of the concrete are evidently higher than those at 7 d. In their study, Hashmi et al. [32] examined the impact of Class F FA on the age-dependent performance of concrete. Their findings revealed that fly ash concrete demonstrated a more substantial increase in strength from 28 d to 180 d in comparison to conventional concrete.

The mechanical properties of FAG depend not only on curing age, but also exhibit an obvious coupling effect with alkali-binder ratio. The majority of current research has been conducted through single-variable experiments, primarily concerned with the macroscopic strength evolution and qualitative microscopic morphological characterization under individual factors. Nevertheless, there is still a notable lack of systematic studies on the mechanical behavior, full stress–strain response, and mesoscopic damage evolution of FAG under the coupled influence of AL/B and curing age. Concrete is a typical quasi-brittle material. The deformation and failure of concrete is essentially a continuous damage evolution process. Initial internal defects, such as micro-pores and microcracks, undergo a series of processes. These processes include nucleation, initiation, propagation and final coalescence. Its failure behavior involves cross-scale interactions among disordered and inhomogeneous structures at macroscopic, mesoscopic, and microscopic scales [33]. The macroscopic non-linear stress–strain behavior of materials is determined by the inhomogeneity of micro-structure and nonlinear damage evolution at the micro level. It is therefore vital to explore the mechanical properties and mesoscopic damage mechanism of FAG under the combined influence of AL/B and curing age, in order to reveal the intrinsic physical mechanism of its damage and failure.

Derived from continuum damage mechanics, statistical damage mechanics has emerged as a popular research direction, offering an effective way to explore the mesoscopic damage mechanism of quasi-brittle materials like concrete. Since Krajcinovic et al. [34] proposed the parallel bar system (PBS) model for the uniaxial tensile process of concrete, statistical damage theory is extensively adopted in damage mechanics studies on concrete, rock, and other materials. This type of model abstracts concrete as a complex system composed of mesoscopic elements. By assuming that the characteristic parameters of the mesoscopic units follow a probability distribution such as the Weibull distribution, the heterogeneity of the material is captured while the complex physical details of the damage process are neglected. In this way, an organic connection is established between the damage mechanism and the macroscopic constitutive behavior. Bai et al. [35,36,37,38,39] assumed that there exist two mesoscopic damage modes, namely fracture and yield damage, established uniaxial and multiaxial statistical damage models for concrete, and put forward the theory of intrinsic mechanical property exertion mechanism. They also discussed the nonlinear stress–strain behavior and mesoscopic damage mechanism of concrete under complex service environments.

The objective of this study is to elucidate the coupling mechanism of AL/B and curing age on the macroscopic mechanical performance, pore structure, and microscopic morphology of FAG. In addition, the study seeks to clarify the multi-scale strength formation and failure mechanism of FAG. In this study, five groups of FAG with AL/B of 0.25, 0.35, 0.45, 0.55, and 0.65 are prepared. After standard curing for 7 d and 28 d, uniaxial compression tests are carried out using a microcomputer-controlled electro-hydraulic servo pressure testing machine. The full stress–strain curves are obtained to analyze the coupling effects of AL/B and curing age on the mechanical properties as well as deformation and failure characteristics of FAG. Microscopic testing methods including nuclear magnetic resonance (NMR), scanning electron microscopy (SEM), and X-ray diffraction (XRD) are adopted to analyze the internal pore structure variation and microscopic morphology characteristics of FAG. On this basis, combined with the mesoscopic statistical damage model, the influence laws of AL/B and curing age on the mesoscopic damage mechanism of FAG during uniaxial compression are investigated, and the internal correlation between mesoscopic damage mechanism and macroscopic nonlinear constitutive behavior under such coupling conditions are further discussed.

2. Materials and Methods

2.1. Experimental Materials

2.1.1. FA

This experiment selects Grade 1 FA produced by Henan Bairun Casting Materials Co., Ltd., Zhengzhou, China. Figure 1a illustrated that FA is a fine powder presenting a light gray appearance. Its bulk density is 1.12 g/cm³, and its density is 2.55 g/cm³. Figure 1b clearly displays numerous spherical FA particles with sleek exterior morphology.

2.1.2. Alkali Activator

An alkaline solution made up of sodium hydroxide (NaOH) solution and water glass (Na₂SiO₃) solution is the alkali activator that is utilized. Industrial-grade solid NaOH is dissolved in tap water to create the NaOH solution. The NaOH solid appears as pure white flakes supplied by Inner Mongolia Junzheng Chemical Co., Ltd., Wuhai, China (net content ≥ 98%). The water glass solution is colorless and transparent, purchased from Henan Bairun Casting Materials Co., Ltd., Zhengzhou, China with physicochemical properties as shown in

Table 1. Physical and chemical properties of water glass.

SiO2/%	Na2O/%	Modulus	Density/(g/cm3)	Baume/°Bé	Transparence/%
29.5	8.88	3.43	1.41	42	88

. Experiments are conducted with city tap water.

Considerable heat is liberated during NaOH dissolution; the alkali activator solution is normally prepared 24 h before the manufacture of GPC [40]. The alkali activator preparation process in this study is as follows: first, solid NaOH is dissolved in water to form a 14 mol/L NaOH solution (density: 1.3275 g/cm³); subsequently, the NaOH solution is added to water glass and stirred thoroughly to modify the modulus of water glass (SiO₂/Na₂O molar ratio, MS), ultimately achieving a modulus of 1.3 [41]. At this point, the alkali activator preparation is sufficient. The solid NaOH, water glass, and prepared alkali activator solution are shown in Figure 2.

2.1.3. Aggregates

This experiment took natural river sand as fine aggregate, possessing a fineness modulus of 2.73. The coarse aggregate is selected from 5–20 mm natural crushed stone with good grading. The specific morphology of the aggregates is shown in Figure 3. Relevant properties of the aggregates are tested according to the “Test Procedures for Hydraulic Concrete” (SL352-2020) [42], with results presented in

Table 2. Related properties of aggregates.

Aggregate	Apparent Density/(kg/m3)	Tap Density/(kg/m3)	Bulk Density/(kg/m3)	Water Content/%	Water Absorption/%	Crushing Index /%
River sand	2580	1750	1500	0.3	0.3	-
Coarse aggregate	2810	1720	1500	1.0	0.1	10.6

. The particle gradation curve is shown in Figure 4, which complies with the requirements of the “Building Aggregates—Crushed Stone and Gravel” (GB/T14685-2022) standard [43].

2.1.4. Water-Reducing Agent

According to Reference [44], the preferred water-reducing agent for FAG is polycarboxylic acid superplasticizer. However, a dosage exceeding 2% may lead to strength deterioration. Therefore, the water-reducing agent used in this study for preparing FAG is polycarboxylate acid superplasticizer, which is a white powder with a dosage of 2% (by mass) of FA. Its primary performance indicators are shown in

Table 3. Main performance indexes of polycarboxylate superplasticizer.

Test Item	Chloride Ion Content/%	Total Alkali Content/%	Solid Content/%	Water Reduction Rate/%	Bleeding Rate/%	Air Content/%
Result	0.044	0.35	98	30	58	4.0

.

Table 4. Mixing proportions of FAG under the influence of AL/B (kg/m³).

Mix Proportion Number	Alkali- Binder Ratio	Fly Ash	River Sand	Coarse Aggregate	Alkali Activator		Effective Water Content of the Alkaline Solution	Wate Reducing Agent	Additional Water
					NaOH	Na2SiO3
FAG25	0.25	400.00	668.97	1242.37	30.78	69.22	60.45	8.00	49.44
FAG35	0.35	400.00	660.68	1226.98	43.09	96.91	84.62	8.00	29.22
FAG45	0.45	400.00	652.39	1211.59	55.40	124.60	108.80	8.00	9.00
FAG55	0.55	400.00	633.40	1176.32	67.71	152.29	124.00	8.00	0.00
FAG65	0.65	400.00	605.83	1125.11	80.02	179.98	132.00	8.00	0.00

Negative calculated values of additional water mass are set to zero uniformly.

lists the precise mix proportions utilized in the trials. The content of FA is 400 kg/m³ [28], and the sand ratio is set at 35% [45]. Previous studies have demonstrated that the compressive strength of geopolymer concrete declines with the increase in the water-to-geopolymer solid ratio within the range of 0.24–0.32 [45]. A preliminary experimental investigation further indicated that a water-to-geopolymer solid ratio of 0.25 can deliver favorable mechanical performance for geopolymer concrete. Considering the trade-off between mechanical strength and fresh-state workability comprehensively, the water-to-solid ratio is fixed at 0.25 for all test groups in this work. An appropriate amount of polycarboxylic acid superplasticizer is added simultaneously. Five FAGs with AL/B of 0.25, 0.35, 0.45, 0.55, and 0.65 are prepared using the absolute volume method [14]. It should be noted that the alkali activator must be prepared one day prior to the experiment and then left to stand at room temperature for 24 h. Let, S_NaOH and ${\mathrm{S}}_{{\mathrm{N}\mathrm{a}}_2{\mathrm{s}\mathrm{i}\mathrm{o}}_3}$ be the percentage of solids in NaOH and Na₂SiO₃, respectively, then the water content is determined as follows:

Mass of water in NaOH = M_NaOH − (S_NaOH × M_NaOH)

$$\mathrm{Mass}\mathrm{of}\mathrm{water}\mathrm{in}{\mathrm{Na}}_2{\mathrm{SiO}}_3={\mathrm{M}}_{{\mathrm{N}\mathrm{a}}_2{\mathrm{s}\mathrm{i}\mathrm{o}}_3}-({\mathrm{S}}_{{\mathrm{N}\mathrm{a}}_2{\mathrm{s}\mathrm{i}\mathrm{o}}_3}\times {\mathrm{M}}_{{\mathrm{N}\mathrm{a}}_2{\mathrm{s}\mathrm{i}\mathrm{o}}_3})$$

2.1.5. Sample Preparation and Test Procedure

Based on the amounts shown in Table 4, each part of the blend is weighed. Sample preparation is carried out as follows: first, prepare a dry mixture of FA and river sand; then, the coarse aggregate is placed inside the concrete mixer and stirred for 2 min. Once materials are thoroughly dry-mixed, add formulated alkali activator and stir for another 2 min. Subsequently, incorporate the water-reducing agent and water, and mix thoroughly for 3 min. Slump tests are then performed, revealing that slump rises progressively as AL/B increases within the range of 45–75 mm, which complies with GB/T 50080-2016 [46]. Pour fresh FAG into 100 mm × 100 mm × 100 mm mold cavities in three separate pours, compacting the fresh FAG with a tamper during each pour. Each mold cavity is filled with fresh FAG, and the molds are vibrated. After 24 h, all test blocks are removed from the molds and cured under standard conditions (20 ± 2 °C, relative humidity ≥ 95%). Figure 5 presents the procedure for preparing the samples.

2.2. Experimental Methods

2.2.1. Uniaxial Compression Test

FAG samples serve to carry out uniaxial compression tests using the YAW-5000 microcomputer-controlled electro-hydraulic servo compression testing machine. The testing procedure strictly adheres to the “Standard Test Methods for Physical and Mechanical Properties of Concrete” (GB/T 50081-2019) [47]. During testing, the loading is applied at a quasi-static strain rate. During specific implementation, the actual loading rate is controlled at 0.18 mm/min. A high-precision displacement sensor placed between the pressure plates of the testing equipment records the deformation data of the sample in real time. To reduce the impact of end friction and related shear stresses on test results, paraffin wax is uniformly applied to the contact surfaces between the samples and the pressure plates before testing. Preloading and calibration are carried out at the initial loading stage until all gaps at the contact surfaces are fully eliminated and the load reaches the threshold of 5 kN. Afterwards, formal loading is performed at the standard rate until the completion of the test, so as to obtain the true stress–strain curve of each specimen. Tension is defined as positive and compression as negative in this paper.

2.2.2. NMR Test

NMR technology is widely applied in non-destructive testing of concrete [48], using water or hydrogen atoms as probes to perform heterogeneous evaluations of microscopic pores in saturated samples, including pore size distribution and pore proportion. This study applies the MacroMR12-150H-I geotechnical pore structure imaging analyzer manufactured by Suzhou Nuomai Analytical Instruments Co., Ltd. The specimens are fully saturated via vacuum soaking for 1 d, then taken out, wiped to a saturated surface-dry state, and immediately placed inside the magnetic coil for testing. The CPMG (Carr–Purcell–Meiboom–Gill) pulse sequence is adopted for measurement, with key test parameters set as follows: recycle delay of 3000 ms, echo number of 5000, and scanning accumulations of 16. After all samples are loaded, the test is initiated. Upon completion, the specimens are removed, the raw data exported, and the porosity calculated accordingly. All samples tested were standard-cured FAG samples.

2.2.3. SEM Test

SEM is employed to observe the microstructure of FAG fragment sections in order to analyze the morphological characteristics of geopolymerization reaction products and perform detailed observation of crack and pore distribution. Test samples for SEM analysis consist of FAG fragments approximately 1 cm in size. Before the test, vacuum and spray gold on the sample to ensure better observation. The sample is placed into the SEM instrument, a vacuum is applied to the sample to reach a vacuum level of 2.79 × 10⁻⁵ mbar, then a photograph is taken. Gold is sprayed for 45 s using an Oxford Quorum SC7620 sputter coater with a current of 10 mA. Subsequently, the sample morphology is observed under a Zeiss sigma 300 field emission environment, the typical parts are selected according to the apparent morphology, and the accelerating voltage is 3 kV when shooting. The characteristic micro-zone morphology is photographed, and SEM images are obtained with corresponding magnification according to the demand.

2.2.4. XRD Test

To clarify the phase composition of FAG, this study employs XRD testing and analysis. First, sample fragments are finely ground into powder and dehydrated for 24 h in a 105 °C constant-temperature drying oven to eliminate moisture interference with diffraction signals. Subsequently, testing is conducted using a Japanese Rigaku SmartLab SE high-resolution X-ray diffractometer. Cu-Kα radiation is adopted as the X-ray source. Full-spectrum scanning is conducted at a tube voltage of 40 kV and tube current of 40 mA, with a scanning rate of 2° per minute and a step size of 0.02°. To balance the accuracy of feature peak recognition and testing efficiency, the scan range is set from 5° to 90° (2θ).

3. Test Results Analysis

3.1. Uniaxial Compression Test Analysis

3.1.1. Elastic Modulus

The E is a pivotal factor in evaluating the deformation capacity of concrete under stress and is of considerable importance in the field of concrete mechanical property research [30,38]. As illustrated in Figure 6a, there is a corresponding relationship between E and the AL/B, where E denotes the mean value of three samples. In a manner analogous to the trend of σ_p, E of FAG attains its maximum at the AL/B of 0.45. The data presented here indicates that, based on the E at AL/B of 0.25, when AL/B increased to 0.35, 0.45, 0.55, and 0.65, the growth rates of E at 7 d were 84%, 170%, 50%, and −4%, respectively; at 28 d, the E growth rates were 219.72%, 935.21%, 609.87%, and 430.96%, respectively. The E growth rate at 28 d is significantly higher than that at 7 d, with an initial increase followed by a subsequent decrease as AL/B rises. This indicates that the development of mechanical properties in geopolymer concrete is highly dependent on the synergistic effect of curing age and AL/B [49]. At 7 d, due to the shorter curing age, the depolymerization–polycondensation reaction of FA has not yet been fully completed, and the gel network is in its initial formation stage. At this stage, there is a possibility that unreacted active particles or pores may still be present within the material, resulting in limited enhancement of E. However, it has been demonstrated that long-term curing at 28 d leads to a more thorough interaction between the alkali activator and the FA particles, forming a denser N-A-S-H gel network that enhances the E value of FAG [50]. The E of FAG reaches its maximum value at an AL/B ratio of 0.45, and gradually decreases when the ratio exceeds this value. This is due to the fact that the presence of excessive alkali solution has the potential to disrupt the continuity of the gel phase, thereby resulting in the accumulation of unreacted alkaline substances at the interface. Furthermore, an increase in the moisture content of the alkali solution has been shown to impede the polymerization process by lowering the alkali concentration. Concurrently, porosity has been observed to increase due to water evaporation from the pores, thereby decreasing compressive strength [25,27]. For 7 d and 28 d, the standard deviation of E ranges from 2.17% to13.33% and from 2.81% to 17.82%, respectively.

3.1.2. Peak Stress

Figure 6b shows the variation trends of peak stress (σ_p) at 7 d and 28 d at various AL/B, where σ_p denotes the mean value of three samples. It is evident that various AL/B notably influence the σ_p of FAG. Within the AL/B of 0.25–0.65, the σ_p of FAG at 7 d and 28 d exhibited a pattern of rising at first and then declining, with the maximum value obtained at AL/B = 0.45. This variation law fully conforms to the optimal depolymerization–polycondensation mechanism clarified in Section 3.1.1. As AL/B increased within the range of 0.25–0.45, the σ_p of sample at 28 d significantly increased from −4.39 MPa to −20.44 MPa, with an increase of 365.60%. However, as the AL/B continued to increase to 0.55 and 0.65, the σ_p of sample at 28 d decreased to −18.36 MPa and −14.97 MPa, respectively, showing reductions of 10.18% and 26.76% compared to FAG45. For 7 d and 28 d, the standard deviation of peak stress ranges from 5.00% to 20.11% and from 2.50% to 12.15%, respectively.

3.1.3. Peak Strain

Peak strain (ε_p) refers to the strain value corresponding to the σ_p on the stress–strain curve. The specific trend of ε_p variation is shown in Figure 6c, where ε_p denotes the mean value of three samples. As AL/B varies, ε_p exhibits a negative correlation with σ_p and E, displaying a tendency to decrease initially and then rise, reaching the minimum at AL/B = 0.45. This phenomenon can be reasonably explained by the dense gel skeleton formed under the optimal matching ratio elaborated in Section 3.1.1. Based on the ε_p at AL/B of 0.25, when AL/B increased to 0.35, 0.45, 0.55, and 0.65, the ε_p growth rates at 7 d were −9.91%, −15.37%, −11.40%, and 25.77%, respectively; at 28 d, the ε_p growth rates were −38.64%, −59.20%, −44.37%, and −48.05%, respectively. For 7 d and 28 d, and the standard deviation of peak strain ranges from 8.25% to 17.60% and from 3.50% to 23.28%, respectively.

3.1.4. Stress–Strain Curves

The stress–strain curves of FAG demonstrate a parabolic characteristic, akin to that of traditional concrete [39]. It is noteworthy that the stress–strain curves obtained at varying curing ages (7 d and 28 d) demonstrate a similar evolutionary trend, thereby signifying the age stability of the mechanical properties of FAG as shown in Figure 7. In particular, samples with an AL/B ratio of 0.45 demonstrated optimal mechanical properties under identical ageing conditions. These samples exhibited the steepest ascent slope and the highest σ_p value. It has been hypothesized that this is attributable to more thorough depolymerization–polycondensation reactions at this AL/B, forming a denser silicoaluminate network structure. As the AL/B ratio increases from 0.25 to 0.65, there is a marked shift in the transition characteristics from the elastic stage to the failure stage. When the AL/B ratio is less than 0.45, the turning point of the curve becomes steeper, indicating an increase in brittleness. Conversely, when the AL/B ratio is more than 0.45, the turning point of the curve tends to flatten, and the FAG exhibits ductile failure characteristics. The presence of nonlinear behavior suggests the existence of an optimal AL/B ratio of 0.45, beyond which alkaline solutions have been shown to reduce the mechanical strength of FAG.

3.1.5. Damage Characteristics

As illustrated in Figure 8, the failure characteristics of samples with various AL/B at 7 d and 28 d are demonstrated. As the failure laws of samples manifest equivalent failure mechanisms at both 7 d and 28 d, samples that were cured for 28 d were selected for analysis in this study. As demonstrated in Figure 8, the sample of 28 d-0.45 (Figure 8e) exhibited a reduced surface crack density, fewer irregular cracks, and a significantly diminished exposed area of internal aggregates on the sample surface when compared to the 28 d-0.25 (Figure 8d) sample. As the AL/B increases, the sample of 28 d-0.65 (Figure 8f) exhibits an increase in both the number and width of surface fissures, as well as an increase in the presence of uneven mortar pieces in the spalling debris.

The analysis of failure characteristics indicates that in instances where AL/B is less than 0.45, there is inadequate supply of alkali activator. This, in turn, results in insufficient depolymerization–polycondensation reaction of silicon aluminum oxide in FA, leading to a gel with a loose structure and weak strength. This gel is unable to effectively inhibit the expansion of cracks, resulting in a significant number of cracks when the sample is damaged. It has been demonstrated that when the AL/B is 0.45, the reaction matching between the alkali activator and FA is optimal. This has been shown to be able to fully stimulate FA activity, promote the formation of a dense gel structure, significantly enhance the load-bearing capacity and crack resistance of FAG, and result in fewer cracks at failure. In instances where the AL/B ratio exceeds 0.45, the presence of excessive alkali activator has been shown to impede the depolymerization–polycondensation reaction of the sample. This inhibition can lead to the formation of microcracks, which, under further stress, may progress to larger fissures during the failure process.

3.2. NMR Testing Analysis

Figure 9 shows the variation laws of porosity at 7 d and 28 d under various AL/B, with the porosity values representing the mean of three samples. The figure reveals consistent variation laws between 7 d and 28 d: as the AL/B increases, porosity declines initially and subsequently rises, attaining lowest values of 8.01% and 7.63% at AL/B = 0.45. The minimum porosity at AL/B = 0.45 is a direct microscopic reflection of the sufficient geopolymerization reaction described in Section 3.1.1. This result corroborates the research outcomes of Garcia [51]. Furthermore, porosity presents a trend of decreasing first and then increasing as AL/B increases, which reveals a negative correlation between peak stress and porosity. During the AL/B of 0.25 to 0.45, porosity exhibited a decreasing trend. This is because the increase in the amount of alkali will lead to an increase in the degree of alkali activation, therefore increasing the density of the pore structure and the number of N-A-S-H gel formed. This finding fits with what other researchers have found [52,53]. When the AL/B is between 0.45–0.65, excess alkali impedes depolymerization–polycondensation, deteriorating the microstructure and lifting porosity.

Figure 10 illustrates the pore size distribution at 7 d and 28 d under varying AL/B. A similar mountain-shaped distribution is observed in the pore size distribution of all samples. As the AL/B rises, the distribution first shifts to the left (pore size decreases) and then to the right (pore size increases). The specific pore proportion distribution of FAG is shown in Figure 11. Based on pore size range, pores are classified into micropores (d < 0.01 μm), mesopores (0.01–0.05 μm), capillary pores (0.05–1 μm), and macropores (d > 1 μm) [54]. Following 7 d of curing, pores in samples with varying AL/B were primarily composed of micropores, mesopores, and capillary pores, with macropores accounting for a smaller proportion. As the AL/B increases, the proportion of mesopores initially goes down and subsequently goes up, while the proportions of capillaries and macropores decrease. This is because, as the AL/B increases, the proportions of H₂O, OH⁻, and Na⁺ in the alkaline solution correspondingly rise, promoting the generation of more N-A-S-H gel [55], which ultimately reduces the proportion of pore size. Excessive alkaline solution may disrupt the continuity of the gel phase and make the mesopore proportion larger. A similar phenomenon was also observed at 28 d.

3.3. SEM Testing Analysis

In this study, the microstructural characteristics under different curing ages (7 d and 28 d) and AL/B (0.25, 0.45, 0.65) were analyzed. Figure 12 illustrates the corresponding results. Compared with FAG45-7d (Figure 12a), the sample of FAG45-28d (Figure 12c) contains more N-A-S-H gel, more sufficient solubility of FA particles, and fewer microcracks, which indicates when the curing age goes up, polymerization reaction continues, amorphous aluminosilicate gel is significantly generated and filled with pores, and the microstructure tends to densify, gradually realizing the transformation of FAG from porous loose to dense strengthened [56]. FAG25-28d (Figure 12b) shows loose microstructure and abundant unreacted FA due to insufficient alkali supply, while FAG65-28d (Figure 12d) presents numerous micropores and broken gel phases caused by excessive alkaline residues, which further verifies the optimal matching condition at AL/B = 0.45 summarized in Section 3.1.1.

3.4. XRD Testing Analysis

The XRD results for FAG are shown in Figure 13. FAG exhibits quartz, mullite, sodium feldspar, and calcite as its primary crystalline phases, and the wide dispersion peak in the range of 20°~40° 2 θ is characterized by amorphous N-A-S-H gel [57]. The XRD diffuse peak intensity at 7 d was relatively low, indicating limited gel formation at early curing age. As the curing age increased to 28 d, the peak shape gradually became more pronounced, corresponding to an increase in N-A-S-H gel content and suggesting that when curing ages increase, the alkali activation of FAG becomes more sufficient. Furthermore, the intensity of the characteristic N-A-S-H gel peak first increased and then decreased as AL/B rose, reaching a peak at AL/B = 0.45, which matches the variation rule of gel formation efficiency explained in Section 3.1.1. However, excessive alkaline solution further inhibits the depolymerization–polycondensation reaction. A dense amorphous gel phase can generate on the surface of FAG when AL/B = 0.45, at which point gel formation reaches its optimal state.

4. Mesoscopic Damage Mechanism Discussion

4.1. Statistical Damage Model

Bai et al. [38] proposed the “intrinsic mechanical property exertion mechanism” theory, interpreting the deformation and failure of concrete as a self-organizing behavior where the stress skeleton of the microstructure of the material undergoes optimal adjustment to adapt to changes in external load conditions. There are two types of effects within the microstructure during the deformation and failure process of concrete: degradation effect and strengthening effect, which correspond to the initiation and propagation of microcracks and the optimization and adjustment of the stress skeleton, respectively.

On this basis, a corresponding statistical damage model for concrete under uniaxial compression was further established [39,58,59,60] (Figure 14). Uniaxial compression failure is essentially caused by lateral tensile damage caused by Poisson effect. The introduction of equivalent tensile damage strain ${\mathsf{\epsilon }}^{+}$ is introduced to satisfy ${\mathsf{\epsilon }}^{+}=-\mathrm{v}\mathsf{\epsilon }$ ($\nu$ is Poisson’s ratio). This model divides the uniaxial compression of concrete into two stages: uniform damage and local failure, in which the critical state plays a key role. The entire deformation and failure process is interpreted from the perspective of effective stress, and two mesoscopic-scale damage modes, namely fracture damage and yield damage, are considered in this process, corresponding to degradation effects and strengthening effects, respectively. In Figure 14, A, B, and C represent the proportional limit state, peak nominal stress, and critical state, respectively. q(ε⁺) and p(ε⁺) are the probability density functions reflecting fracture damage and yield damage, respectively. For analytical simplicity, q(ε⁺) and p(ε⁺) can be assumed to follow a triangular probability distribution. The constitutive expression for the uniform damage stage is as follows:

$$\sigma =E(1-D_{\mathrm{y}})(1-D_{\mathrm{R}})\epsilon$$

(1)

$${\sigma }_{\mathrm{E}}=E(1-D_{\mathrm{y}})\epsilon$$

(2)

$$D_{\mathrm{y}}={\int }_0^{{\epsilon }^{+}}p\left({\epsilon }^{+}\right)d{\epsilon }^{+}-{\displaystyle \frac{{\int }_0^{{\epsilon }^{+}}p\left({\epsilon }^{+}\right){\epsilon }^{+}d{\epsilon }^{+}}{{\epsilon }^{+}}}$$

(3)

$$D_{\mathrm{R}}={\int }_0^{{\epsilon }^{+}}q\left({\epsilon }^{+}\right)d{\epsilon }^{+}$$

(4)

$$E_{\mathrm{v}}={\int }_0^{{\epsilon }^{+}}p\left({\epsilon }^{+}\right)d{\epsilon }^{+}$$

(5)

$$q\left({\epsilon }^{+}\right)=\left\{\begin{array}{cc}0& \left({\epsilon }^{+}\le {\epsilon }_{\mathrm{a}}\right)\hfill \\ {\displaystyle \frac{2H\left({\epsilon }^{+}-{\epsilon }_{\mathrm{a}}\right)}{{\left({\epsilon }_{\mathrm{b}}-{\epsilon }_{\mathrm{a}}\right)}^2}}& \left({\epsilon }_{\mathrm{a}}<{\epsilon }^{+}\le {\epsilon }_{\mathrm{b}}\right)\hfill \end{array}\right.$$

(6)

$$p\left({\epsilon }^{+}\right)=\left\{\begin{array}{cc}0& \left({\epsilon }^{+}\le {\epsilon }_{\mathrm{a}}\right)\hfill \\ {\displaystyle \frac{2\left({\epsilon }^{+}-{\epsilon }_{\mathrm{a}}\right)}{\left({\epsilon }_{\mathrm{h}}-{\epsilon }_{\mathrm{a}}\right)\left({\epsilon }_{\mathrm{b}}-{\epsilon }_{\mathrm{a}}\right)}}& \left({\epsilon }_{\mathrm{a}}<{\epsilon }^{+}\le {\epsilon }_{\mathrm{h}}\right)\hfill \\ {\displaystyle \frac{2\left({\epsilon }_{\mathrm{b}}-{\epsilon }^{+}\right)}{\left({\epsilon }_{\mathrm{b}}-{\epsilon }_{\mathrm{h}}\right)\left({\epsilon }_{\mathrm{b}}-{\epsilon }_{\mathrm{a}}\right)}}& \left({\epsilon }_{\mathrm{h}}<{\epsilon }^{+}\le {\epsilon }_{\mathrm{b}}\right)\hfill \end{array}\right.$$

(7)

$$H=D_{\mathrm{R}}\left({\epsilon }_{\mathrm{b}}\right)$$

(8)

where: $\sigma$ and ${\sigma }_{\mathrm{E}}$ are the nominal and effective stresses, respectively; $E_0$ is the elastic modulus; $D_{\mathrm{R}}$ and $D_{\mathrm{y}}$ represent the damage variables for fracture and yield, respectively; and $E_{\mathrm{v}}$ represents the evolution factor, ranging from 0 to 1. ${\epsilon }_{\mathrm{a}}$, ${\epsilon }_{\mathrm{b}}$, and ${\epsilon }_{\mathrm{h}}$ are the initial damage strain, the critical state strain, and the peak strain of $p\left({\epsilon }^{+}\right)$, respectively, and $H$ represents the fracture damage value at the critical state.

The advantages of this model lies in the fact that it can characterize the two-stage features of distributed damage accumulation and local catastrophic failure; it can reflect the cumulative process of damage from “quantitative change” to “qualitative change” in the uniform damage stage; more importantly, the model can reasonably explain the lag phenomenon of the critical state of local catastrophic failure revealed by deformation localization [61], acoustic emission [62], and electrical resistivity [63]. That is, the critical state corresponds to the maximum effective stress state and occurs later than the peak nominal stress state. When the critical state is reached, the stress skeleton of the microstructure is optimally adjusted, the potential mechanical properties are fully exerted to the limit, and then the local catastrophic failure stage is entered.

4.2. Mesoscopic Damage Mechanisms

Genetic algorithm parameter inversion and multiple regression predictive analysis is conducted on the stress–strain curve in Figure 15, with specific values shown in

Table 5. Characteristic parameters.

Age	AL/B	εa/×10−4	εh/×10−4	εb/×10−4	H	RE	R2
7 d	0.25	6.616	13.768	26.166	0.451	1.000	0.9997
	0.35	4.860	10.000	24.870	0.230	1.848	0.9988
	0.45	4.653	9.360	21.310	0.189	2.708	0.9997
	0.55	5.314	10.327	22.001	0.241	1.510	0.9984
	0.65	9.621	14.752	33.894	0.260	0.971	0.9992
28 d	0.25	7.563	9.924	29.148	0.466	1.000	0.9994
	0.35	6.577	8.985	15.286	0.327	3.196	0.9977
	0.45	2.293	7.694	13.505	0.197	10.363	0.9985
	0.55	2.612	7.909	15.464	0.245	7.099	0.9976
	0.65	2.904	8.407	16.119	0.364	5.311	0.9998

. Here, $R_{\mathrm{E}}={\displaystyle \frac{E_{\mathrm{A},i}}{E_{\mathrm{A},0}}}$, where $R_{\mathrm{E},\mathrm{A}}$ is the elastic modulus influence factor of FAG specimens under different alkali-binder ratios; $E_{\mathrm{A},i}$ is the elastic modulus of FAG specimens under different alkali-binder ratios; and $E_{\mathrm{A},0}$ is the elastic modulus of the control group (alkali-binder ratio of 0.45).

As illustrated in Figure 15, the nominal stress–strain and effective stress–strain curves that are anticipated by the statistical damage constitutive model are shown. The uniform damage stage is a useful tool for the analysis of the distinctive curves in both. The experimental result is in good agreement with the nominal stress–strain curve, encompassing both ascending and descending segments. Effective stress is defined as the outcome of optimizing and adjusting the predicted concrete stress skeleton. It has been demonstrated that effective stress exhibits a monotonically increasing trend until reaching its greatest value during the critical state [60]. Moreover, a comparison of the experimental results with the model predictions (Figure 16) reveals that the peak stress and peak strain of the curve predicted differ from the experimental curve by approximately ±10%. Consequently, the accuracy of the model in predicting the stress–strain relationship during the damage process of FAG is further verified. A detailed analysis of Figure 15 reveals that FAG exhibits identical trends at both 7 d and 28 d. As the AL/B increases, both the effective stress and nominal stress aligned with the critical state of the two sample groups initially increase and then decrease, reaching their maximum values at AL/B = 0.45. Consequently, FAG under AL/B = 0.45 exhibits optimal experimental mechanical properties and potential mechanical load-bearing capacity during uniaxial compression.

The mesoscopic characteristic factors listed in Table 5 are categorized into yield damage-related characteristic factors and fracture damage-related characteristic factors. The characteristic factors ${\epsilon }_{\mathrm{a}}$, ${\epsilon }_{\mathrm{h}}$, and ${\epsilon }_{\mathrm{b}}$ related to yield damage show variation trends as illustrated in Figure 17, while the characteristic factor $H$ related to fracture damage shows its variation trend in Figure 18. As shown in the figures, regardless of the 7 d or 28 d, the values of ${\epsilon }_{\mathrm{a}}$, ${\epsilon }_{\mathrm{h}}$, ${\epsilon }_{\mathrm{b}}$, and $H$ all exhibit a pattern of initially declining and then rising near AL/B = 0.45. This indicates that the damage mechanism of FAG exhibits a distinct threshold effect, revealing the nonlinear characteristics of the uniform damage process in FAG. With a rise from 0.25 to 0.45 in AL/B, ε_a, ε_h, and ε_b gradually decrease, indicating that optimizing AL/B triggers internal damage in FAG earlier and rapidly reaches a critical state. Specifically, the decrease in ε_a indicates that as AL/B approaches 0.45, the stress skeleton of the FAG enters the strain threshold for structural optimization earlier; that is, the accelerated alkali-activated reaction enables the matrix structure of the geopolymer to complete adaptive adjustments at smaller strains. The decrease in ε_b reflects a reduction in the critical damage strain, indicating that the bonding strength between gel phase and aggregate interface increases when AL/B = 0.45, making localized failure more readily activated at lower strain levels. The evolution law of ε_h further corroborates the aforementioned mechanism: the sample with AL/B = 0.45, corresponding to the minimum value, exhibits the shortest duration of the damage homogenization stage, enabling FAG to enter the strengthening stage more rapidly.

The shape of the function $q\left({\epsilon }^{+}\right)$ is determined by the H value, which is an important indication of fracture damage that is directly associated with the initiation and propagation of microcracks. As shown in Figure 18, the minimum value of the fracture factor H occurs at AL/B = 0.45, indicating that the microstructure exhibits densification characteristics and the minimum number of microcracks. Combining the synergistic changes of ε_a and ε_b, the fracture damage probability density function $q\left({\epsilon }^{+}\right)$ demonstrates distinct regularities in its triangular distribution law. When AL/B is less than 0.45, the triangle vertex gradually shifts leftward with increasing AL/B (decreasing ε_h), and the distribution range narrows (decreasing ε_b–ε_a difference), indicating more localized damage progression. Conversely, when AL/B exceeds 0.45, the vertex shifts rightward and the distribution range expands, which originates from the change of matrix compactness controlled by the depolymerization–polycondensation degree elaborated in Section 3.1.1.

Figure 19 illustrates the evolution curve of the factor E_v. As a key factor characterizing the material damage process, E_v reflects the evolution of the microstructure and the changes in potential mechanical properties under external loading. Its value fluctuates between 0 and 1. When it reaches 1, it indicates that the limit of the potential mechanical properties of the material has been reached, the stressed skeleton has stabilized to its ideal state, and the maximum value of the effective stress has been attained; subsequently, it will go into the stage of local failure. Figure 19 shows that as AL/B increases, the E_v curves of FAG cured for 7 d and 28 d both exhibit a tendency of first fast followed by slow development near AL/B = 0.45, indicating a threshold effect on the triggering rate of the critical point of material damage. The E_v curve attains the critical state more rapidly with a rise from 0.25 to 0.45 in AL/B; whereas when AL/B exceeds 0.45, the E_v curve progresses more slowly. This indicates that excessively high AL/B weakens the gel phase interface, thereby slowing the rate of damage accumulation. Additionally, the morphological changes in the E_v curve reveal the influence mechanism of AL/B on FAG ductility: under low AL/B (0.25, 0.35) and excessively high AL/B (0.55, 0.65) conditions, the E_v curves of both 7 d and 28 d exhibit slow development characteristics, indicating the material possesses high deformation capacity. When AL/B is 0.45, the localized failure stage occurs earlier in the sample, the ductility significantly decreases, and the critical strain for damage also decreases accordingly.

The initiation and propagation of microcracks during the uniform damage stage are closely correlated with the D_R curve [58]. The D_R evolution curves for FAG samples are displayed in Figure 20. As AL/B increases, the growth rates of the D_R curves for both 7 d and 28 d demonstrate no apparent law. However, it has been observed that the curve terminus is first reached at AL/B = 0.45, indicating that the microcrack propagation rate exhibits a nonlinear dependence on AL/B. A substantial forward shift in the terminus of the D_R curve is evident as AL/B rises from 0.25 to 0.45. It has been demonstrated that this is attributable to the effective acceleration of the geopolymerization reaction process by AL/B, which in turn promotes microstructural densification. This, in turn, results in a synchronous acceleration of microcrack initiation and damage rate. Consequently, samples enter a state of local disaster earlier. When AL/B exceeds 0.45, the terminus of the curve lags behind, indicating that FAG damage and optimization adjustments progress slowly, manifesting as reaching the critical state at a later point.

Figure 21 shows the stress ratio (σ_cr/σ_p) and strain ratio (ε_cr/ε_p) of the FAG sample at peak and critical states. The ratios σ_cr/σ_p and ε_cr/ε_p both follow a quadratic parabolic evolution trend with the increase of AL/B, with the optimal AL/B value of 0.45. Meanwhile, the fitting curves corresponding to 28 d exhibit higher fitting accuracy. The data in Figure 21a suggest that the median value of σ_cr/σ_p between the critical state and peak state on the nominal stress–strain curve is 0.78, with a range of 0.65 to 0.91. The connection between ε_cr/ε_p as a function of AL/B is depicted in Figure 21b, with a median value of 1.51 and fluctuations between 1.36 and 1.65. The results show that the lowering stage of the stress–strain curve is when the critical state occurs, meaning that during uniaxial compression, the initiation of macroscopic cracks in the FAG sample occurs later than the peak stress. Further analysis reveals that under the influence of AL/B, σ_cr/σ_p exhibits a pattern of initially rising and subsequently falling, while ε_cr/ε_p shows the opposite behavior. This indicates that AL/B significantly affects the triggering position of the critical state. The stronger the mechanical properties exhibited, the closer the critical state approaches the peak value. In the constitutive model of recycled aggregate concrete proposed by Xiao et al. [64], a limit state corresponding to 85% of the peak stress on the descending branch of the stress–strain curve is defined to fully characterize the deformation capacity. The critical state adopted in this study shares a similar physical implication with the aforementioned limit state and possesses a more in-depth physical mechanism. We recommend taking the critical state as the final failure point of the constitutive model. This treatment can not only fully account for the ductility during the uniform damage stage, but also avoid overestimating the size effect induced by localized failure.

In fact, peak stress is a characteristic state on the stress–strain curve of concrete, and its formation mechanism is a complex issue involving the entire process of concrete from microstructure setting and hardening, stress deformation, to instability and failure; it is jointly determined by two aspects: microstructural mechanical characteristics (affected by components, micro morphology, porosity, etc.) and mesoscopic damage evolution (including microcrack initiation, propagation and optimal adjustment of the microstructure stress skeleton). For the FAG at 28 d, the connection ranging from the mesoscopic damage mechanism to the macroscopic stress–strain behavior is depicted in Figure 22. As the AL/B ratio increases, the figure indicates an initial rise in E, followed by a subsequent decline. Significant law is exhibited by the triangular distribution laws of fracture damage q(ε⁺) and yield damage p(ε⁺). When AL/B less than 0.45, the vertices of the triangle gradually shift to the left with increasing AL/B (ε_h decreases), and the distribution range narrows (the difference between ε_b and ε_a diminishes), indicating that damage development becomes more localized. When AL/B exceeds 0.45, the peak shifts to the right and the distribution range expands, reflecting the loosening of gel structure caused by an excessively alkaline environment. These results elucidate the rationale for the initial steepening and subsequent flattening of the macroscopic stress–strain curve with the growth of AL/B. The laws of E, yield damage, fracture damage, and the change in the stress–strain curve with AL/B are more fully demonstrated in this, as well as the close relationship between the mesoscopic damage evolution mechanism and the macroscopic stress–strain behavior of FAG.

5. Conclusions

This article designed and conducted mechanical performance tests on FAG with different AL/B. Uniaxial compression tests and microstructural analyses (NMR, SEM, XRD) were performed on FAG samples for 7 d and 28 d. By integrating experimental results with a statistical damage constitutive model, the mesoscopic evolution and strength development mechanism of FAG were examined in relation to AL/B and curing age. The following are the primary conclusions:

(1)

The macroscopic mechanical properties of FAG are closely related to the AL/B, exhibiting consistent variation laws at 7 d and 28 d alike: the σ_p and E of FAG first increase and then decrease with the increase of AL/B, reaching their maximum values at AL/B = 0.45; conversely, the ε_p reaches its minimum value at AL/B = 0.45. At the curing age of 28 d, the σ_p and E of specimens with AL/B = 0.45 are 11.33–365.60% and 45.98–936.28% higher than those of other AL/B groups, respectively, while their deformability decreases by approximately 20.83–58.70%. Under the experimental conditions adopted in this study, the optimal AL/B of FAG is 0.45. Both excessively low and high AL/B hinder the full development of polymerization reactions within FAG, leading to degradation of mechanical properties.

(2)

The aluminosilicate phase is a reaction product of FAG, as evidenced by experimental results from NMR, SEM, and XRD, significantly influencing the microstructural evolution of FAG. With increased AL/B, the porosity initially falls and subsequently rises, attaining its lowest value at AL/B = 0.45, which closely aligns with the strength variation law. When AL/B = 0.45, FA particles exhibit higher dissolution, and the alkali activation reaction is sufficient. This condition results in the highest density microstructure and the maximum quantity of N-A-S-H gel formation. With increasing curing age, the XRD diffuse peak intensity increases. As the AL/B increases, the intensity of the characteristic N-A-S-H gel peak first increases and then decreases, reaching its peak at AL/B = 0.45.

(3)

The strength of concrete is determined by both microstructural mechanical characteristics and mesoscopic damage evolution. This study demonstrates the impact of AL/B and curing age on the evolution laws of mesoscopic damage in FAG, as derived from statistical damage theory. For curing ages of 7 d and 28 d, the values of ε_a, ε_h, ε_b and H show a trend of decreasing first and then increasing around AL/B = 0.45. With the rise of the AL/B, the triangular distribution curves of yield damage and fracture damage first shift leftward and then rightward gradually. This verifies that the damage mechanism of FAG has an obvious threshold effect and reveals the nonlinear characteristics of the uniform damage evolution of FAG. Moreover, σ_cr/σ_p increases first and then decreases with the growth of AL/B, while ε_cr/ε_p decreases first and then increases, which further clarifies that the critical strain lags behind the peak strain. All these results demonstrate that the macroscopic nonlinear stress–strain behavior of FAG is closely correlated with its mesoscopic damage evolution.

(4)

This study systematically elucidates the influence of AL/B and curing age on the multi-scale strength formation mechanism of FAG, which contributes to promoting the efficient resource utilization of fly ash-based solid waste in multiple fields such as green building materials, road engineering, and mine backfilling. It should be noted that, due to the limitations of the research scope, this paper has not yet examined the durability, semi-quantitative XRD analysis, or tensile and flexural properties of FAG. Subsequent studies will focus on the aforementioned aspects to provide more comprehensive data support for the engineering application of FAG.