A method for designing a mixture ratio of alkali-activated mortar and alkali-activated mortar

Abstract

The application provides a kind of alkali-activated mortar mix design method and alkali-activated mortar, and relates to the technical field of building materials, comprising: obtaining the particle size distribution data of full solid phase component and constructing actual particle size distribution function;Based on the closest particle packing model, an ideal particle size distribution function is established, and the optimal volume fraction of each component is obtained by optimization solution under the volume fraction constraint;Determine the mass mix ratio based on the optimal volume fraction and apparent density;Based on the linear relationship between fluidity and water-binder ratio, extrapolate to zero fluidity state to determine the reference water-binder ratio.The application realizes the closest packing of full solid phase component and the quantitative determination of water consumption, improves the mortar density, mechanical properties and the scientificity of mix design.

Description

Technical Field

[0001] This application relates to the field of building materials technology, specifically to a method for designing the mix proportion of alkali-activated mortar and alkali-activated mortar. Background Technology

[0002] Alkali-activated cementitious materials are green building materials formed by the polymerization reaction of industrial solid waste as the main precursor under the action of an alkaline activator. In existing alkali-activated mortar mix design processes, empirical trial mixing methods are typically relied upon, resulting in long design cycles and significant material waste. Although some studies have introduced particle packing theory for optimization, they often only focus on the gradation design of aggregates and main cementitious materials, treating solid alkali activators and active admixtures as non-packed or liquid phase components, failing to incorporate them as independent powders into the overall particle packing system. This makes it difficult to achieve optimal mortar density in the multi-component composite system, thus affecting the activation efficiency and mechanical properties of the weakly alkaline system. Furthermore, existing technologies often use fixed water-cement ratios or empirical adjustments when determining mortar water content, lacking quantitative determination methods based on rheological properties, making it difficult to accurately balance workability and volume stability after hardening. Therefore, there is an urgent need for an alkali-activated mortar mix design method that can achieve the densest packing of all solid components and quantitatively determine the baseline water-cement ratio. Summary of the Invention

[0003] To address the problems of insufficient density and lack of quantitative means for determining water demand in existing alkali-activated mortar mix design due to the failure to incorporate all solid components into the packing system, this application proposes an alkali-activated mortar mix design method and alkali-activated mortar to achieve quantitative design of alkali-activated mortar mix proportion and maximize system density.

[0004] To achieve the above objectives, this application adopts the following technical solution: A method for designing the mix proportion of alkali-activated mortar includes: acquiring particle size distribution data of the all-solid components of the alkali-activated mortar, wherein the all-solid components include a cementitious precursor, a solid alkali activator, an active admixture, and aggregates, and each component participates in the particle size distribution calculation as an independent powder to construct the actual particle size distribution function of the all-solid components; establishing an ideal particle size distribution function based on the densest particle packing model, and under a preset volume fraction constraint, optimizing the solution to make the actual particle size distribution function approximate the ideal particle size distribution function to obtain the optimal volume fraction of each component in the all-solid components; determining the mass mix proportion of the alkali-activated mortar based on the optimal volume fraction and the apparent density of each component; and establishing a linear relationship between flowability and water-cement ratio based on flowability test data at different water-cement ratios, and extrapolating to a zero flowability state to determine the reference water-cement ratio of the alkali-activated mortar.

[0005] The above scheme incorporates all solid-phase components, including solid alkali activators and active admixtures, as independent powders into the particle size distribution calculation and packing optimization system. This breaks the limitation of traditional design that only optimizes aggregates and main cementitious materials, allowing trace amounts of functional powders to fill the gaps between the main particles, thus achieving the densest packing of the entire system at the mathematical model level. At the same time, by establishing a linear relationship between fluidity and water-cement ratio and extrapolating to a zero fluidity state, it provides a quantitative method for determining the benchmark water-cement ratio without relying on empirical trial mixing, ensuring the scientific nature and repeatability of mix design.

[0006] Preferably, the cementitious precursor includes fly ash and slag, the active admixture is active MgO, and the aggregate is fine aggregate; the actual particle size distribution function is a weighted sum of the particle size distribution functions of each component material according to their respective volume fractions; wherein, the actual particle size distribution function represents the cumulative passing rate of particles with a particle size smaller than a certain particle size value in the system, and the particle size distribution function of each component material represents the cumulative passing rate of particles with a particle size smaller than the stated particle size value in that component.

[0007] Preferably, the ideal particle size distribution function satisfies the continuous gradation packing model, and the ideal particle size distribution function is a cumulative distribution function constructed based on the power function relationship of particle size, wherein the exponent of the power function is the particle distribution coefficient.

[0008] Preferably, the optimization solution aims to maximize the goodness of fit between the actual particle size distribution function and the ideal particle size distribution function, and the goodness of fit is determined by the ratio of the residual sum of squares to the total sum of squares.

[0009] Preferably, the volume fraction constraint conditions include: the sum of the volume fractions of all components in the total solid phase component is 1.0, and each component satisfies the following volume fraction ranges: fly ash 0.08~0.23, slag 0.08~0.23, solid alkali activator 0.05~0.15, active MgO 0.004~0.01, and fine aggregate 0.50~0.65.

[0010] Preferably, a linear relationship between flowability and water-cement ratio is established based on flowability test data at different water-cement ratios, and extrapolated to a zero flowability state to determine the reference water-cement ratio of the alkali-activated mortar. This includes: calculating the relative flowability based on the flowability test data, where the relative flowability is the ratio of the flowability in the flowability test data to the lower diameter of the truncated cone mold used for testing, minus one; establishing a linear relationship between the relative flowability and the water-cement ratio, where the water-cement ratio in the linear relationship is equal to the product of the fitting coefficient and the relative flowability plus the reference water-cement ratio; and substituting the relative flowability of zero into the linear relationship to obtain the reference water-cement ratio.

[0011] Preferably, the flowability in the flowability test data is obtained by testing a standard truncated cone mold, and the flowability is the average of the maximum spread and the spread in the vertical direction.

[0012] Preferably, the method further includes: adding a preset increment to the baseline water-cement ratio, while controlling the increase in fluidity to not exceed a preset fluidity threshold, to determine the target water-cement ratio of the alkali-activated mortar.

[0013] Preferably, the solid alkali activator is one or more of sodium carbonate, sodium sulfate, and sodium metasilicate in a proportional composite composition; the aggregate is continuously graded natural river sand with a median particle size within a preset particle size range.

[0014] In addition, this application also provides an alkali-activated mortar, which is prepared by the alkali-activated mortar mix design method described above; the solid phase components of the alkali-activated mortar include fly ash, slag, solid alkali activator, active MgO and fine aggregate, and the goodness of fit between the particle size distribution of the system and the ideal particle size distribution function is greater than or equal to a preset threshold.

[0015] The aforementioned alkali-activated mortar products employ a fully solid-phase, densest packing design method, resulting in an internal particle size distribution that closely approximates the ideal packing curve and significantly reduces porosity. Consequently, they achieve excellent mechanical properties and long-term volume stability while ensuring safety in low-alkalinity environments.

[0016] Beneficial effects: The alkali-activated mortar mix design method provided in this application incorporates components traditionally considered non-bulk phases, such as solid alkali activators and active admixtures, into a densest particle packing model as independent powders. This constructs an actual particle size distribution function encompassing all solid components, and solves for the ideal particle size distribution function as the optimization objective. This full-component packing optimization strategy eliminates inter-particle voids caused by micro-particle gradation imbalances from a physical structure perspective, significantly improving the packing density of the mortar system and thus mitigating the slow strength development problem caused by excessive porosity in weakly alkaline systems. Simultaneously, this method innovatively establishes a linear fitting relationship between relative fluidity and water-cement ratio, and quantitatively obtains the benchmark water-cement ratio by extrapolating to a zero-fluidity state, replacing the traditional empirical trial mixing method. This not only significantly reduces the number of trials and material consumption but also achieves precise control of water usage, effectively balancing workability and the durability of the hardened body.

[0017] This application employs a weakly basic, multi-component composite solid activator system, which is used as an independent powder in gradation optimization. While ensuring the system's pH value remains within a safe range and reducing the risk of corrosion during construction, the system increases the number of contact points between solid particles through the closest packing effect, promoting the formation of a spatial network of gel products and solving the problem of insufficient activation efficiency of a single weakly basic component. Furthermore, the alkali-activated mortar designed based on this method possesses engineering applicability with "single-component dry mixing and on-site water addition." Combined with a quantitatively determined target water-cement ratio, the stability of material performance across different batches is ensured, which is conducive to promoting the large-scale application of alkali-activated materials in fields such as building repair. Attached Figure Description

[0018] Figure 1 This is a flowchart of the alkali-activated mortar mix design method according to an embodiment of this application; Figure 2 This is a comparison diagram of the particle size distribution curve of the all-solid phase components and the ideal packing model in an embodiment of this application; Figure 3 This is a graph showing the linear fit between relative flowability and water-cement ratio in an embodiment of this application. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application.

[0020] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0021] Example 1 like Figure 1 As shown in this embodiment, a method for designing the mix proportion of alkali-activated mortar is provided. This method achieves quantitative design of the mix proportion through independent powder packing optimization of all solid components and linear extrapolation mechanism of flowability. Specifically, the method for designing the mix proportion of alkali-activated mortar includes the following steps: Step S1: Obtain the particle size distribution data of the solid components of the alkali-activated mortar. The solid components include cementitious precursors, solid alkali activators, active admixtures, and aggregates. Each component is treated as an independent powder and participates in the particle size distribution calculation to construct the actual particle size distribution function of the solid components.

[0022] In this embodiment, the process of obtaining particle size distribution data is not a simple raw material inspection, but a digital reconstruction of the physical structure of the system. Specifically, solid alkali activators and active admixtures must be considered as powder particles with independent particle size characteristics, rather than being treated as liquid solvents or negligible trace chemical additives in traditional designs. For example, when characterizing the particle size of solid alkali activators, they should be tested as dry powders to obtain their true particle size distribution curves; similarly, active admixtures also need to be collected as independent solid units. This approach breaks through the limitations of existing technologies that only design the gradation of aggregates and main cementitious materials, ensuring that all solid phase materials occupying volume are included in the calculation scope of the packing model. By weighted superposition of the particle size distribution data of the above components, the constructed actual particle size distribution function can truly reflect the particle composition characteristics of the mortar system in the unwatered state, providing an accurate data foundation for achieving the densest packing of the entire system.

[0023] Step S2: Based on the densest particle packing model, establish an ideal particle size distribution function. Under the preset volume fraction constraint, optimize the solution to make the actual particle size distribution function approximate the ideal particle size distribution function, and obtain the optimal volume fraction of each component in the whole solid phase.

[0024] Specifically, the ideal particle size distribution function represents the theoretically lowest porosity and highest packing density particle gradation state. The optimization process essentially involves finding an optimal combination of volume fractions, under the premise of satisfying engineering performance constraints, so that the actual gradation curve of the all-solid phase components geometrically matches the theoretically closest packing curve to the greatest extent possible. It should be understood that this approximation is a mathematical optimization process, aiming to minimize the deviation between the actual and ideal distributions. The optimal volume fraction determined in this way can ensure the density of the internal skeleton of the hardened mortar body at the physical structure level, thereby reducing internal voids caused by particle gradation imbalance. This is crucial for improving the mechanical properties and durability of the weakly alkali-activated system.

[0025] Step S3: Based on the optimal volume fraction and the apparent density of each component, determine the mass mix ratio of the alkali-activated mortar.

[0026] Specifically, since industrial production and construction measurement are usually based on mass, while the calculation results of the packing model are presented as volume fractions, a conversion of physical quantities is required. Using the pre-determined apparent densities of each solid component, the optimal volume fraction obtained in step S2 is converted into the mass of each material per unit volume of mortar. This conversion process ensures that the theoretically densest packing design can be seamlessly transformed into an executable engineering mix proportion, guaranteeing the feasibility of the design scheme in actual production.

[0027] Step S4: Establish a linear relationship between fluidity and water-cement ratio based on fluidity test data under different water-cement ratios, and extrapolate to the zero fluidity state to determine the reference water-cement ratio for alkali-activated mortar.

[0028] Specifically, the determination of the baseline water-cement ratio no longer relies on empirical trial mixing or fixed value selection, but is based on quantitative derivation of rheological properties. By testing the fluidity of mortar mixtures with multiple different water-cement ratios, a linear regression model between the fluidity index and the water-cement ratio is established. Extrapolating this linear relationship to a state of zero fluidity yields the baseline water-cement ratio. From a physical perspective, the zero fluidity state corresponds to the critical point where the water in the mortar mixture just fills the voids between particles and forms a saturated surface dry film. At this point, the water usage is entirely determined by the packing structure of the particle system, eliminating subjective interference from human experience. The baseline water-cement ratio determined using this method can accurately match the densest packing skeleton constructed in step S2, avoiding both increased porosity and decreased strength due to excessive water usage, and insufficient workability due to insufficient water usage, thus achieving precise control and stability assurance of mortar performance.

[0029] Example 2 Building upon Example 1, this example further defines the specific algorithm implementation and parameter constraints for the all-solid packing optimization. The cementing precursors include fly ash and slag, the active admixture is active MgO, and the aggregate is fine aggregate. This component selection constitutes a typical multi-component composite system for alkali-activated mortar. Fly ash and slag serve as the main aluminosilicate sources providing cementing properties, active MgO acts as a micro-expansion component to compensate for shrinkage and participate in later strength development, and fine aggregate forms the mechanical framework. It should be understood that although this example lists the specific materials mentioned above, in other embodiments, the cementing precursors may also include other aluminosilicate solid wastes such as steel slag and silica fume, and the active admixture may also be other mineral powders with pozzolanic activity or micro-expansion function, as long as they participate in the packing calculation as independent powder particles.

[0030] The actual particle size distribution function is a weighted sum of the particle size distribution functions of each component material according to their respective volume fractions. Specifically, for example... Figure 2 As shown, the actual particle size distribution function The calculation formula is as follows: In the formula, For the first The volume fraction of a component material in the overall mixture, ranging from 0 to 1, and the sum of all volume fractions is 1.0; For the first The particle size of the component is smaller than Particle cumulative throughput; This represents the total number of solid components in the mortar system, as described in this embodiment. (i.e., fly ash, slag, solid alkali activator, activated MgO, and fine aggregate). The physical meaning of this formula is that it treats the gradation of a multi-component mixed system as a linear superposition of the gradations of each individual component, provided that each component remains dispersed and does not agglomerate during the mixing process. The actual distribution function constructed in this way can accurately characterize the true particle composition of the entire solid-phase system, including trace amounts of functional powders.

[0031] The ideal particle size distribution function satisfies the continuous gradation packing model. The ideal particle size distribution function is a cumulative distribution function constructed based on the power function relationship of particle size, where the exponent of the power function is the particle distribution coefficient. In this embodiment, the Dinger-Funk model is used as the theoretical objective of the closest packing, and its expression is: In the formula, Particle size; The particle distribution coefficient is used to control the shape of the gradation curve. For mortar systems, the value is usually taken between 0.37 and 0.5 to obtain the optimal bulk density. The maximum particle size of the system is determined by the maximum particle size of the fine aggregate. The minimum particle size of the system is determined by the finest particle size of the active MgO or solid alkali activator. For particles smaller than The ideal cumulative percentage of particles. For example... Figure 2 As shown, the ideal particle size distribution curve is a smooth S-shaped curve, representing the particle gradation state with the theoretical lowest porosity. Solid alkali activator and activated MgO were incorporated into... The definition and overall gradation calculation enable the theoretical model to cover particles of all sizes from micrometers to millimeters, avoiding the gradation discontinuity caused by neglecting fine powders in traditional models.

[0032] The optimization solution aims to maximize the goodness of fit between the actual particle size distribution function and the ideal particle size distribution function. The goodness of fit is determined by the ratio of the sum of squared residuals to the sum of squared total squares. Specifically, the coefficient of determination is used. As an evaluation indicator, its calculation formula is as follows: In the formula, This represents the number of statistical samples within the particle size range; for The corresponding actual cumulative screening pass rate, This is the arithmetic mean of the cumulative undersize passing rate of particles across all particle size ranges in the mortar system. The closer the value is to 1, the higher the degree of agreement between the actual gradation curve and the ideal closest packing curve. In this embodiment, the value is set to... This serves as an engineering threshold for a suitable mix proportion. The setting of this threshold is not merely a mathematical pursuit, but rather a performance inflection point derived from extensive experimental verification: when... When the porosity inside the mortar decreases significantly, the 28-day compressive strength can typically reach a stable level of over 45 MPa; while when Even with increased cementitious material usage, the strength improvement is extremely limited, indicating that the performance bottleneck of the system has shifted from chemical composition to physical stacking structural defects.

[0033] The volume fraction constraints include: the sum of the volume fractions of all components in the total solid phase is 1.0, and each component must meet the following volume fraction ranges: fly ash 0.08~0.23, slag 0.08~0.23, solid alkali activator 0.05~0.15, active MgO 0.004~0.01, and fine aggregate 0.50~0.65. These constraint ranges comprehensively consider both chemical reaction requirements and physical packing requirements. For example, the lower limit of the volume fraction of fly ash and slag (0.08%) is to ensure sufficient aluminosilicate precursors to form a stable gel network, while the upper limit (0.23%) is to avoid excessive unreacted particles becoming weak points in strength. The volume fraction of solid alkali activator is controlled between 0.05 and 0.15%, providing the necessary alkalinity environment without causing poor volume stability due to excessive salt crystallization. The trace addition of active MgO is mainly used to adjust micro-stress and compensate for shrinkage; exceeding this range may lead to excessive expansion and cracking. The proportion of fine aggregate (0.50-0.65%) maintains a balance between the stability and workability of the mortar skeleton. During the optimization process, the algorithm searches within the above-mentioned constraint space to achieve... The combination of the largest volume fractions yields the optimal blending ratio that balances chemical efficacy and physical density.

[0034] Based on the aforementioned ideal packing curve of Dinger-Funk as the fitting target, a nonlinear regression fitting was performed on this ideal particle size distribution using the actual particle size distribution function to obtain the volume fraction of each component. The mix design results of alkali-activated repair mortar based on the maximum density theory are shown in Table 1. The final mix proportion was appropriately adjusted based on the theoretical calculation results, taking into account the convenience of construction. Furthermore, to further explore the influence of different precursor ratios on the performance of alkali-activated mortar, fly ash / slag mass ratios were set at 70% / 30% (F70G30), 50% / 50% (F50G50), and 30% / 70% (F30G70).

[0035] Table 1. Mix design of alkali-activated repair mortar based on the closest packing theory. To verify the necessity of involving all solid components in packing optimization, the following comparative example was set up: In the comparative example, only fly ash, slag, and fine aggregate were included in the Dinger-Funk model for gradation optimization, while solid alkali activator and active MgO were considered as non-packing phases, and their dosage was added at a fixed empirical level, without participating in volume fraction calculation or gradation adjustment. Test results showed that the gradation fit of the comparative example was good. The value was only 0.88, lower than the threshold of 0.92 set in this application; the 28-day compressive strength of the prepared mortar was 36.5 MPa, significantly lower than the 48.2 MPa of the optimized mortar in this embodiment. Microstructural analysis showed that, due to the lack of consideration of the particle filling effect of solid alkali activator and active MgO in the comparative example, there was an obvious pore enrichment zone at the interface between the cementitious material and fine aggregate, which weakened the overall structural compactness. This comparative result strongly proves that incorporating traditionally neglected trace functional powders as independent components into the all-solid-phase packing system is not a simple application of mathematical models, but a key technical means to solve the insufficient compactness of weakly alkaline systems and improve mechanical properties, demonstrating a significant level of creativity.

[0036] Example 3 Building upon Example 1, this example further defines the specific implementation process of the baseline water-cement ratio quantitative determination method based on linear extrapolation of flowability. This method elevates the determination of the water-cement ratio from the traditional empirical trial mixing level to the rheological quantitative level, ensuring the repeatability and precise control of mix design by establishing a standardized testing and calculation system.

[0037] Specifically, the process of determining the baseline water-cement ratio includes the following sub-steps: Step S41: Calculate the relative flowability based on the flowability test data. The relative flowability is the ratio of the flowability in the flowability test data to the lower diameter of the truncated cone mold used in the test, minus one. The flowability d is obtained by measuring the maximum diameter of the mortar mixture after it is lifted from the truncated cone mold and its diameter in the vertical direction, and taking the arithmetic mean of the two. Based on this, the concept of relative flowability R_flow is introduced, and its calculation formula is as follows: In the formula, Relative fluidity is a dimensionless parameter. For actual flowability; The lower diameter of the truncated cone mold is used. Relative flowability, rather than absolute flowability, is used as the variable because it eliminates the direct influence of the mold geometry on the flowability value, normalizing the flow behavior to the degree of deformation relative to the initial mold dimensions. When Time means This means that the mortar mixture just fills the bottom of the mold without any radial expansion, which corresponds to the critical yield point where the mortar is transitioning from a plastic state to a solid state. This normalization process makes the data from different laboratories and different batches comparable, laying the foundation for establishing a universal linear model.

[0038] Step S42: Establish a linear relationship between relative fluidity and water-cement ratio. In this linear relationship, the water-cement ratio equals the product of the fitting coefficient and the relative fluidity plus the baseline water-cement ratio. Specifically, at least four different water-cement ratios are selected to prepare mortar mixtures, and their relative fluidity is tested for each. The alkali-activated cement paste mix proportions used in this embodiment are shown in Table 2.

[0039] Table 2. Alkali-activated paste mix proportions like Figure 3 As shown, relative fluidity The x-axis represents the water-to-gel ratio. A scatter plot was drawn on the ordinate, and a linear regression was performed to obtain the following linear equation: In the formula, The fitting coefficients reflect the sensitivity of this specific all-solid phase gradation system to water content, i.e., the increment of water-cement ratio required to increase unit fluidity. The intercept is when The water-to-binder ratio at that time. From a rheological mechanism perspective, This represents the theoretical minimum amount of water required to fill the voids between all-solid particles and form a saturated dry film. At this point, the frictional force and gravity within the slurry are in equilibrium, and macroscopic flow has not yet occurred. This parameter is entirely determined by the all-solid packing structure determined in step S2, eliminating subjective interference from human experience. In this embodiment, the fitted value... The value is 0.309, and the correlation coefficient is... A value above 0.97 indicates a highly significant linear correlation between the water-cement ratio and relative fluidity in this gradation system. The test results of the rheological parameters of alkali-activated paste under different water-cement ratios are shown in Table 3.

[0040] Table 3. Test results of rheological parameters of alkali-activated paste with different water-cement ratios (F50G50) Step S43: Substitute the relative fluidity of zero into the linear relationship to obtain the baseline water-cement ratio. As mentioned earlier, directly... Substituting into the above linear equation, the baseline water-cement ratio can be obtained. This value serves as a scientific benchmark for determining the actual water usage during construction.

[0041] However, relying solely on the baseline water-cement ratio Often, mortar in a zero-flow state is too dry and hard to meet the workability requirements of actual engineering projects because it cannot be poured or finished normally. Therefore, this embodiment also includes a step of adjusting the target water-cement ratio: adding a preset increment to the baseline water-cement ratio, while controlling the increase in flowability to not exceed a preset flowability threshold, to determine the target water-cement ratio of the alkali-activated mortar. Specifically, the target water-cement ratio... The calculation follows the following dual control principle: In the formula, This is a preset increment, ranging from 0.02 to 0.06. This increment is set to provide the necessary thickness of the lubricating water film, enabling the mortar to possess basic plastic deformation capabilities. Simultaneously, it is essential to verify whether the measured flowability at this water-cement ratio falls within the acceptable range. Within the range of mm, the relative fluidity is approximately 0.05 to 0.15. Exceeding this threshold indicates excessive water usage, which may lead to slurry segregation, bleeding, or increased porosity after hardening, thereby weakening mechanical properties and durability. Conversely, falling below this threshold indicates insufficient workability, making it difficult to guarantee the bonding quality of the repair interface. This dual constraint mechanism of incremental and threshold values ​​ensures both ease of construction and strict control over the performance degradation risk caused by excessive water usage, achieving an optimal balance between workability and mechanical properties.

[0042] To verify the superiority of this method, the following comparative example was set up: In the comparative example, the traditional empirical method was used to fix the water-cement ratio at 0.45 for mix design, and the remaining raw materials and preparation process were exactly the same as in this embodiment. Test results showed that, because the influence of raw material particle size distribution fluctuations and environmental temperature and humidity changes on water demand was not considered, the flowability of the mortar prepared in the comparative example fluctuated by as much as 35 mm between different batches, and the standard deviation of the 28-day compressive strength reached 4.2 MPa, showing significant dispersion. In contrast, the target water-cement ratio determined by the method in this embodiment (…) The fluidity of the corresponding mortar was consistently controlled at around 106 mm, and the standard deviation of the 28-day compressive strength for both the same batch and across batches was only 1.1 MPa, with the average strength increasing by approximately 12% compared to the control group. This comparative result fully demonstrates that the quantitative design method based on linear extrapolation of fluidity can effectively eliminate the blindness of experience-based trial mixing, significantly improve the stability and reliability of alkali-activated mortar performance, and is particularly suitable for engineering repair scenarios with stringent requirements for quality consistency.

[0043] Example 4 Building upon Examples 1 to 3, this example further specifies the exact selection and specifications of key raw materials to support the universality and feasibility of the all-solid-phase packing optimization method under different material systems. The solid alkali activator is one or more components of sodium carbonate, sodium sulfate, and sodium metasilicate in a specific ratio. Specifically, although the aforementioned examples treated the solid alkali activator as an independent powder in particle size distribution calculations, in practical engineering applications, the choice of its chemical composition directly determines the activation efficiency and reaction kinetics characteristics, thus affecting the setting of constraints in mix design. This application provides three preferred composite forms to meet different performance requirements: The first form is a single-component sodium carbonate (Na2CO3) system, which is weakly alkaline and has a long hydration induction period, suitable for low-heat repair scenarios where early strength requirements are not high but long-distance transportation or large-volume casting is required; The second form is a binary composite system of sodium carbonate and sodium sulfate (Na2SO4), which utilizes the micro-expansion effect generated by the reaction of sulfate ions with the calcium source in the system to form ettringite, which can compensate to some extent for the slow early strength development of weakly alkaline systems, and is suitable for conventional structural repair; The third form is a ternary composite system of sodium carbonate, sodium sulfate, and sodium metasilicate (Na2O·2SiO2), in which sodium metasilicate, as a fast-dissolving active silicon source, can significantly shorten the induction period of gel formation and improve the early polymerization degree, suitable for emergency repairs or engineering scenarios with strict requirements for early strength. It should be understood that, regardless of the chemical composite form used, they all exist in a dry powder state at the physical level and have definite particle size distribution characteristics. Therefore, they can all be used as independent solid phase units to be substituted into the particle size distribution data acquisition in step S1 and the packing model optimization calculation in step S2, without changing the core logic of the mix design method of this application.

[0044] The aggregate is continuously graded natural river sand with a median particle size within a preset range. In this embodiment, the fine aggregate is preferably Zone II continuously graded natural river sand conforming to GB / T14684-2011, with a median particle size controlled between 0.8 mm and 1.0 mm. Zone II sand has a relatively flat particle size distribution curve and a reasonable mix of coarse and fine particles, effectively avoiding excessive porosity caused by a single particle size. The median particle size range of 0.8 mm to 1.0 mm is ideal for forming a good macro-skeleton-micro-filled interlocking structure with micron-sized cementing components such as fly ash, slag, and solid alkali activators. When this gradation parameter is input into the Dinger-Funk ideal packing model, it provides accurate aggregate end boundary conditions for the algorithm, ensuring that the optimized volume fraction combination not only mathematically approximates the theoretical optimal curve but also possesses high physical feasibility. Using sand sources with a median particle size deviating from this range may lead to a difference in the goodness of fit R between the actual gradation curve and the ideal curve. 2 This decrease in density and mechanical properties of the mortar can negatively impact its compactness.

[0045] It should be noted that the above-mentioned limitations on the chemical composition of the solid alkali activator and the physical specifications of the fine aggregate are merely preferred embodiments listed in this application to fully disclose the technical solution, and do not constitute an exclusive limitation on the scope of protection of this application. In practical applications, as long as a certain solid alkali activator or aggregate can be characterized in independent powder form for its particle size distribution and meets the basic requirements of chemical compatibility and engineering applicability, it can replace the specific materials in this embodiment and be substituted into the aforementioned packing optimization process and water-cement ratio determination method. This flexibility in material selection is a major advantage of the mix design method of this application, which distinguishes it from traditional empirical formulations, enabling it to be widely adapted to the production and construction needs of alkali-activated mortar under different regional and raw material source conditions.

[0046] Example 5 This embodiment provides an alkali-activated mortar, which is prepared using the alkali-activated mortar mix design method described in any one of Examples 1 to 4 above. Specifically, this product is a concrete manifestation of the aforementioned quantitative design method at the physical level of engineering materials, and its microstructure and macroscopic properties are directly controlled by the precise matching of the packing state of the all-solid phase components and the water-cement ratio.

[0047] In this embodiment, the solid-phase components of the alkali-activated mortar include fly ash, slag, solid alkali activator, active MgO, and fine aggregate. The goodness of fit between the particle size distribution and the ideal particle size distribution function of the system is greater than or equal to a preset threshold. Taking a preferred F50G50 type alkali-activated mortar as an example, its specific mass proportion is: 300 kg / m³ of fly ash. 3 300kg / m³ of slag 3 Solid alkali activator 90kg / m 3 12 kg / m³ of active MgO 3 Fine aggregate 1200kg / m 3 This mix proportion was not obtained through traditional empirical trial mixing, but was strictly calculated using the all-solid packing optimization process described in Example 2. Actual measurements verified that the particle size distribution curve of this formulation system has a fitting coefficient of determination R0 with the ideal closest packing curve of the Dinger-Funk mixture. 2 The goodness of fit reached 0.929, significantly higher than the 0.90 level of conventional design methods. This high goodness of fit indicates that all solid particles, including the solid alkali activator and active MgO, achieved efficient spatial interlocking and filling, minimizing the initial porosity inside the hardened body and laying the physical structural foundation for excellent mechanical properties.

[0048] Based on the aforementioned densest packing structure and the target water-cement ratio determined in Example 3, this alkali-activated mortar exhibits stable and excellent comprehensive performance. Standard testing showed that the flowability of the freshly mixed mortar was 106 mm, within the optimal construction window of 105 ± 5 mm, proving that the water content determined by linear extrapolation based on flowability can accurately balance workability and density requirements. The 28-day compressive strength of the hardened mortar reached 48.2 MPa, meeting the high-strength repair requirement of ≥45 MPa; the bond strength with the old concrete substrate reached 1.6 MPa, meeting the interfacial bonding requirement of ≥1.5 MPa. It should be understood that these performance improvements are not solely due to improved raw material quality, but rather stem from structural optimization at the methodological level: the all-solid-phase packing eliminates internal defects caused by trace powder gradation imbalances, allowing for more dense growth of the gel products under the weakly alkali-activated system; and precise control of the baseline water-cement ratio avoids capillary channels left by excess water evaporation, thereby simultaneously improving strength and durability.

[0049] Furthermore, this alkali-activated mortar is particularly suitable for the reinforcement and repair of concrete structures. Because it uses solid alkali activators and active admixtures as independent powders in the mix design, all dry-mix components can be pre-mixed in the factory to create a single-component dry powder mortar product. On-site, only a measured amount of water needs to be added according to the designed target water-cement ratio and stirred before use, eliminating the need for on-site preparation of highly corrosive alkaline solutions as with traditional two-component alkali-activated materials. This construction method not only completely avoids the corrosion risks and safety burden on construction personnel caused by liquid strong alkali, but also significantly simplifies the on-site mixing process, eliminates performance fluctuations caused by human measurement errors, and ensures the consistency and reliability of the repair project quality. In summary, the alkali-activated mortar product provided in this embodiment forms a close technical loop with the aforementioned mix design method in terms of material composition, microstructure, macroscopic properties, and ease of construction, fully demonstrating the technical value of this method in practical engineering applications.

[0050] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for designing the mix proportion of alkali-activated mortar, characterized in that, include: The particle size distribution data of the solid phase components of alkali-activated mortar are obtained. The solid phase components include cementitious precursors, solid alkali activators, active admixtures and aggregates. Each component is treated as an independent powder and participates in the particle size distribution calculation to construct the actual particle size distribution function of the solid phase components. An ideal particle size distribution function is established based on the densest particle packing model. Under the preset volume fraction constraint, the actual particle size distribution function is made to approximate the ideal particle size distribution function through optimization, thereby obtaining the optimal volume fraction of each component in the whole solid phase composition. Based on the optimal volume fraction and the apparent density of each component, the mass mix ratio of the alkali-activated mortar is determined; A linear relationship between flowability and water-cement ratio was established based on flowability test data at different water-cement ratios, and extrapolated to a zero flowability state to determine the reference water-cement ratio of the alkali-activated mortar.

2. The method for designing the mix proportion of alkali-activated mortar according to claim 1, characterized in that, The cementitious precursor includes fly ash and slag, the active admixture is active MgO, and the aggregate is fine aggregate; The actual particle size distribution function is a weighted sum of the particle size distribution functions of each component material according to their respective volume fractions; wherein, the actual particle size distribution function represents the cumulative throughput of particles smaller than a certain particle size value in the system, and the particle size distribution function of each component material represents the cumulative throughput of particles smaller than the stated particle size value in that component.

3. The method for designing the mix proportion of alkali-activated mortar according to claim 2, characterized in that, The ideal particle size distribution function satisfies the continuous gradation packing model. The ideal particle size distribution function is a cumulative distribution function constructed based on the power function relationship of particle size, where the exponent of the power function is the particle distribution coefficient.

4. The method for designing the mix proportion of alkali-activated mortar according to claim 2, characterized in that, The optimization solution aims to maximize the goodness of fit between the actual particle size distribution function and the ideal particle size distribution function. The goodness of fit is determined by the ratio of the sum of squared residuals to the sum of squared total squares.

5. The method for designing the mix proportion of alkali-activated mortar according to claim 2, characterized in that, The volume fraction constraints include: the sum of the volume fractions of all components in the total solid phase is 1.0, and each component satisfies the following volume fraction ranges: fly ash 0.08~0.23, slag 0.08~0.23, solid alkali activator 0.05~0.15, active MgO 0.004~0.01, and fine aggregate 0.50~0.

65.

6. The method for designing the mix proportion of alkali-activated mortar according to claim 1, characterized in that, A linear relationship between flowability and water-cement ratio is established based on flowability test data at different water-cement ratios, and extrapolated to a zero flowability state to determine the reference water-cement ratio of the alkali-activated mortar, including: The relative flowability is calculated based on the flowability test data. The relative flowability is the ratio of the flowability in the flowability test data to the lower diameter of the truncated cone mold used in the test, minus one. Establish a linear relationship between the relative fluidity and the water-cement ratio, wherein the water-cement ratio is equal to the product of the fitting coefficient and the relative fluidity plus the reference water-cement ratio; Substituting the relative fluidity of zero into the linear relationship yields the baseline water-cement ratio.

7. The method for designing the mix proportion of alkali-activated mortar according to claim 6, characterized in that, The flowability in the flowability test data is obtained through standard truncated cone mold testing, and the flowability is the average of the maximum spread and the spread in the vertical direction.

8. The method for designing the mix proportion of alkali-activated mortar according to claim 6, characterized in that, The method further includes: The target water-cement ratio of the alkali-activated mortar is determined by adding a preset increment to the baseline water-cement ratio, while controlling the increase in fluidity to not exceed a preset fluidity threshold.

9. The method for designing the mix proportion of alkali-activated mortar according to claim 1, characterized in that, The solid alkali activator is one or more of sodium carbonate, sodium sulfate, and sodium metasilicate in a certain proportion; the aggregate is continuously graded natural river sand with a median particle size within a preset particle size range.

10. An alkali-activated mortar, characterized in that, The alkali-activated mortar mix design method according to any one of claims 1 to 9 was used to prepare the mortar. The solid phase components of the alkali-activated mortar include fly ash, slag, solid alkali activator, active MgO and fine aggregate, and the goodness of fit between the particle size distribution of the system and the ideal particle size distribution function is greater than or equal to a preset threshold.

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