Method for optimizing mechanical properties of recycled concrete

Abstract

The application provides a recycled concrete mechanical property optimization method, and relates to the technical field of recycled concrete materials. The specific steps include: obtaining surface morphology data and three-dimensional shape data of recycled aggregates and natural aggregates, determining surface fractal dimension and three-dimensional shape coefficient and combining them as a structure characteristic vector; setting multiple volume content ratios to prepare samples, measuring bulk density, interface transition zone porosity and compressive strength and establishing a sample data set; determining a candidate content interval through first-round screening, training a ratio-performance mapping model; and using a multi-objective optimization algorithm to optimize the candidate optimal volume content ratio in the candidate interval. The application solves the technical problems of traditional mix design, such as ignoring the micro differences of aggregates and relying on experience and trial and error, and realizes efficient and accurate optimization of the mechanical properties of recycled concrete through quantitative characterization of aggregate structure characteristics and data-driven optimization.

Description

Technical Field

[0001] This invention relates to the field of recycled concrete materials technology, specifically a method for optimizing the mechanical properties of recycled concrete. Background Technology

[0002] With the deepening of the utilization of construction solid waste resources, recycled concrete technology has become an important research direction in the field of green building materials. The quality of its mix design directly determines the utilization efficiency of recycled aggregates and the mechanical properties of concrete. However, existing recycled concrete mix design methods often treat recycled aggregates as simple quality substitutes for natural aggregates, ignoring the essential differences in microscopic morphology and macroscopic form that exist in recycled aggregates due to the adhesion of old cement mortar to their surfaces. This substitution approach leads to mix design focusing only on the single variable of admixture ratio, failing to establish a quantitative relationship between aggregate structural characteristics and concrete packing behavior, interfacial transition zone quality, and macroscopic mechanical properties. This results in a lack of reliable materials science basis for optimizing the admixture ratio, often relying on a large number of trial-and-error experiments, which is inefficient and makes it difficult to obtain the truly optimal mix ratio.

[0003] As the skeleton material of concrete, the microstructure and macromorphology of aggregates significantly influence interfacial bonding performance and packing density. Therefore, accurate characterization of aggregate structural characteristics is a prerequisite for optimizing mix proportions. However, in characterizing the structural characteristics of recycled aggregates, existing technologies typically use a single morphological parameter to roughly classify aggregate quality, lacking a systematic method for integrating multi-dimensional morphological information such as surface roughness, angularity, porosity distribution, and particle sphericity and convexity. More importantly, existing characterization results are mostly absolute values, failing to consider the relative structural differences between recycled and natural aggregates. This makes it difficult to compare the performance and transfer the mix proportions of aggregates from different sources and batches within a unified quantitative framework, severely restricting the engineering universality and repeatability of mix design methods.

[0004] Furthermore, the performance optimization of recycled concrete is essentially a multi-objective synergistic problem involving packing behavior, interfacial structure, and macroscopic strength, with complex nonlinear conflicts often existing between various performance indicators. However, in terms of multi-objective optimization strategies, existing research on recycled concrete often employs single-objective optimization or linear weighting methods based on empirical weights, artificially compressing multiple performance indicators such as bulk density, interfacial transition zone porosity, and compressive strength into a single objective function, thus obscuring the inherent conflict characteristics and trade-offs between the various performance indicators. Simultaneously, existing optimization processes typically involve blind searches across the entire admixture range, failing to pre-select invalid regions that do not meet basic engineering performance requirements. This results in optimization algorithms consuming significant computational resources in infeasible regions, and the sparse distribution of training samples directly reduces the predictive reliability of the surrogate model. Consequently, the final "optimal solution" is often difficult to verify through physical experiments, lacking sufficient engineering practicality. Summary of the Invention

[0005] The purpose of this invention is to provide a method for optimizing the mechanical properties of recycled concrete to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for optimizing the mechanical properties of recycled concrete, comprising the following steps: Step 1: Obtain surface morphology data and three-dimensional morphology data of recycled aggregate and natural aggregate, and determine the parameters used to characterize the aggregate structure based on the data, and construct the aggregate structure feature vector; Step 2: Set multiple sets of volumetric admixture ratios of recycled aggregate and natural aggregate, prepare corresponding mixed aggregate samples and concrete samples, and determine the bulk density, interfacial transition zone porosity and compressive strength corresponding to each set of volumetric admixture ratios to establish a sample dataset. Step 3: Based on the sample dataset, construct and train the volumetric admixture ratio-performance mapping model. The volumetric admixture ratio-performance mapping model takes the volumetric admixture ratio and aggregate structure feature vector as input, and outputs the predicted values ​​of bulk density, interfacial transition zone porosity and compressive strength. Step 4: Based on the volumetric doping ratio-performance mapping model, multi-objective optimization is used to optimize the volumetric doping ratio. Multiple performance indicators, including bulk density, porosity of the interface transition zone, and compressive strength, are used as optimization objectives to output candidate optimal volumetric doping ratios.

[0007] Furthermore, the surface morphology data includes the roughness index, angularity coefficient, and surface porosity distribution of the aggregate surface; The method for determining the fractal dimension of aggregate surface based on the surface morphology data includes: fusing the roughness index, the angularity coefficient, and the surface porosity distribution to obtain a comprehensive surface morphology index, and determining the fractal dimension of aggregate surface based on the comprehensive surface morphology index.

[0008] Furthermore, the three-dimensional morphological data includes the sphericity, aspect ratio, and convexity index of the aggregate; The method for determining the three-dimensional morphological coefficients based on the three-dimensional morphological data includes: constructing a three-dimensional morphological vector from the sphericity, aspect ratio, and convexity index; normalizing the three-dimensional morphological vector; and weighting and fusing the normalized components to obtain the three-dimensional morphological coefficients.

[0009] Furthermore, setting several sets of volumetric admixture ratios of recycled aggregate and natural aggregate includes: setting a lower limit and an upper limit for the volumetric admixture ratio of recycled aggregate, and selecting several set values ​​for the volumetric admixture ratio of recycled aggregate within the range defined by the lower limit and the upper limit; wherein, the volumetric admixture ratio of each set of natural aggregate is complementary to the volumetric admixture ratio of the corresponding set of recycled aggregate.

[0010] Furthermore, when establishing the sample dataset, preset admission conditions are set, including: a lower threshold for bulk density, an upper threshold for porosity in the interface transition zone, and a lower threshold for compressive strength. For any sample data in the sample dataset, if its bulk density is lower than the lower limit threshold of bulk density, or its interface transition zone porosity is higher than the upper limit threshold of interface transition zone porosity, or its compressive strength is lower than the lower limit threshold of compressive strength, the sample data is determined not to meet the preset admission conditions and is removed.

[0011] Furthermore, the proportion-performance mapping model, with volumetric admixture ratio and structural feature vector as input, includes: determining surface feature parameters and three-dimensional morphological feature parameters of recycled aggregate and natural aggregate respectively based on their structural feature vectors, and constructing aggregate property boundary parameters to characterize the differences between the two aggregates based on the surface feature parameters and three-dimensional morphological feature parameters; and using the volumetric admixture ratio and the aggregate property boundary parameters together as input to the proportion-performance mapping model.

[0012] Furthermore, when using multi-objective optimization to optimize the volumetric doping ratio, the doping range is determined first; The method for determining candidate doping ranges includes: performing continuity analysis on the volume doping ratio groups retained after screening by the preset admission criteria; determining one or more continuous doping ranges based on the comparison results of the doping difference between adjacent volume doping ratio groups and the preset continuity threshold; and determining candidate doping ranges from the continuous doping ranges according to the preset range selection criteria.

[0013] Furthermore, several sets of volumetric content ratios are generated within the candidate content range as candidate samples. The volumetric content ratios and aggregate property boundaries corresponding to each candidate sample are input into the trained proportion-performance mapping model to obtain the predicted values ​​of bulk density, interface transition zone porosity, and compressive strength. With the optimization objectives of maximizing the predicted bulk density, minimizing the predicted porosity of the interface transition zone, and maximizing the predicted compressive strength, the candidate samples are subjected to multi-objective optimization iterative updates to obtain the non-dominated solution set or Pareto optimal solution set. The volumetric doping ratio with optimal overall performance is determined from the non-dominated solution set or Pareto optimal solution set and used as a candidate optimal volumetric doping ratio.

[0014] Compared with the prior art, the beneficial effects of the present invention are: This invention constructs a surface fractal dimension and a three-dimensional morphology coefficient to fuse multi-dimensional structural information such as surface roughness, angularity, porosity distribution, particle sphericity, aspect ratio, and convexity of recycled and natural aggregates into a standardized structural feature vector. This achieves quantitative calibration and unified characterization of complex aggregate structural features. This characterization system not only overcomes the limitations of single-parameter information but also constructs aggregate attribute boundaries through the ratio calculation of surface fractal ratio and three-dimensional morphology ratio. This eliminates absolute numerical fluctuations caused by different testing conditions and aggregate sources, ensuring stable comparability of model inputs across data sources and significantly improving the adaptability and engineering transferability of mix design methods for different batches of aggregates.

[0015] The first-round screening and continuity detection mechanism proposed in this invention sets a three-dimensional admission threshold based on the benchmark performance of natural aggregates and the safety strength level of the target project. It automatically identifies and removes invalid admixture points with deteriorated performance from the full range of samples, and then extracts the longest continuous qualified proportion segment as the candidate admixture range. This process strictly limits model training and optimization search to a data-intensive, reliable, and gradually changing effective domain. It avoids model extrapolation distortion caused by sparse samples and provides a continuous and complete feasible solution space for multi-objective optimization algorithms, fundamentally solving the problems of wasted computational resources and unreliable optimization results caused by blindly searching the entire range in traditional methods.

[0016] This invention employs a multi-objective evolutionary algorithm based on non-dominated sorting, with the combined objectives of maximizing bulk density, minimizing porosity in the interface transition zone, and maximizing compressive strength. Through a dual selection mechanism of dominance level and crowding distance, it systematically explores the Pareto optimal frontier within the candidate admixture range. Finally, it uses the ideal point method to select the candidate volumetric admixture ratio with the best overall performance from the non-dominated solution set. This method eliminates the need to pre-set subjective weights for each objective, fully preserving the conflict characteristics and trade-offs between performance indicators. The output candidate optimal ratio represents the best compromise solution for the three indicators under physical constraints, and can be directly used as a core reference for engineering mix design. Combined with subsequent small-scale physical verification, the implementation mix ratio can be quickly determined, significantly shortening the traditional lengthy "trial mixing-testing-adjustment" cycle and significantly improving the intelligence level and engineering implementation efficiency of recycled concrete mix design. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a graph showing the trend of packing density as a function of doping amount provided in an embodiment of the present invention; Figure 3 A graph showing the trend of porosity in the interface transition zone as a function of dosage, provided in an embodiment of the present invention; Figure 4 This is a graph showing the trend of compressive strength as a function of dosage, provided in an embodiment of the present invention. Figure 5 The multi-objective optimization iterative convergence curve provided in the embodiments of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0019] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0020] Example: Please see Figures 1 to 5 The present invention provides a technical solution: A method for optimizing the mechanical properties of recycled concrete, comprising the following steps: Step 1: Obtain surface morphology data and three-dimensional morphology data of recycled aggregate and natural aggregate, and determine the parameters used to characterize the aggregate structure based on the data, and construct the aggregate structure feature vector.

[0021] In the field of mechanical property research on recycled concrete, natural and recycled aggregates are the core components of concrete, and their microstructural characteristics directly determine the macroscopic mechanical performance of concrete. However, there are fundamental differences in the microstructural characteristics between recycled and natural aggregates. Natural aggregates, after natural weathering and water erosion, have relatively dense, smooth surfaces and regular shapes. In contrast, recycled aggregates, due to the mechanical actions such as crushing and screening during their production process, often have hardened cement mortar adhering to their surfaces, resulting in a rougher surface, more angular features, higher porosity, and more irregular particle shapes compared to natural aggregates. These fundamental differences in surface morphology and three-dimensional form directly affect the packing state of aggregates in concrete mixtures and the interfacial bonding performance with cement paste, ultimately significantly impacting the macroscopic mechanical and workability properties of recycled concrete. Therefore, if recycled aggregates are simply regarded as substitutes for natural aggregates while ignoring their inherent structural characteristics, it will be difficult to accurately predict and optimize the performance of mixed aggregate concrete.

[0022] Therefore, this embodiment first quantitatively characterizes the structural features of the two aggregates. By obtaining key parameters that reflect the surface roughness and geometric shape of the aggregates, a calculable and comparable structural feature vector is established, laying the foundation for establishing the mapping relationship between aggregate properties and concrete performance.

[0023] Specifically, surface morphology data is used to characterize the microscopic roughness of aggregate surfaces, while three-dimensional morphology data describes the overall geometry of aggregate particles. By calculating the surface fractal dimension and three-dimensional morphology coefficients based on these two types of data, the complex structural information of aggregates can be transformed into standardized numerical indicators, providing a unified quantitative evaluation benchmark for aggregates from different sources and batches. Finally, the surface fractal dimension and three-dimensional morphology coefficients are combined into a structural feature vector. This vector, as a compact expression of aggregate properties, includes both the microscopic texture information of the aggregate surface and the macroscopic morphological information at the particle scale, comprehensively reflecting the influence mechanism of aggregates on concrete interface properties and packing behavior.

[0024] Furthermore, the surface morphology data specifically includes the roughness index, angularity coefficient, and surface porosity distribution of the aggregate surface.

[0025] In the quantitative characterization system of aggregate structure, surface morphology data is the core set of parameters reflecting the microscopic physical state of the aggregate surface. In this embodiment, roughness index, angularity coefficient, and surface porosity distribution are selected as the three components of surface morphology data. This selection is based on an in-depth analysis of the surface differences between recycled and natural aggregates, as well as the clear physical meaning of the influence path of each parameter on concrete performance.

[0026] The roughness index quantifies the severity of surface undulations in aggregates, and its value directly reflects the height and density of micro-protrusions on the aggregate surface. Recycled aggregates, due to the adhering layer of old cement mortar, typically have a significantly higher roughness index than natural aggregates. An increased roughness index can, on the one hand, increase the mechanical interlocking force between the aggregate and the cement paste, improving interfacial bond strength; on the other hand, excessive roughness can also lead to localized stress concentration in the cement paste around the aggregate, easily inducing microcracks in the interfacial transition zone. Therefore, the roughness index is a key indicator for evaluating the dual impact of aggregate surface texture on interfacial performance.

[0027] The angularity factor describes the degree to which the aggregate particle profile deviates from an ideal sphere, reflecting the sharpness of the aggregate edges and corners. A higher angularity factor indicates a more irregular aggregate profile and sharper corners. During concrete mixing, aggregates with a high angularity factor increase the mechanical interlocking between particles and enhance the skeletal support effect during stacking. However, this also increases the need for cement paste encapsulation, leading to decreased workability. For recycled aggregates, the angular effect produced by the crushing process contrasts sharply with the smooth profile of natural aggregates, making the angularity factor a crucial parameter for distinguishing the morphological characteristics of these two types of aggregates.

[0028] Surface porosity distribution is used to characterize the number, size, and spatial distribution of open pores on the aggregate surface. The old cement mortar layer on the surface of recycled aggregate is rich in capillary pores and microcracks. These pores absorb mixing water during concrete hardening, leading to a localized increase in the water-cement ratio in the interfacial transition zone, forming a loose and porous weakened layer that severely affects interfacial bonding quality. By quantitatively obtaining the surface porosity distribution, the potential impact of aggregates on the workability of fresh concrete and the pore structure of the hardened interfacial transition zone can be predicted.

[0029] The three parameters described above characterize the microstructural features of the aggregate surface from different dimensions: the roughness index reflects the amplitude characteristics of surface undulations, the angularity coefficient reflects the geometric characteristics of the contour morphology, and the surface porosity distribution reflects the compactness of the surface material. These three parameters complement each other and are not interchangeable, together constituting complete surface morphology data. Based on this three-dimensional parameter system, the surface fractal dimension can be determined by constructing surface morphology feature points and calculating their Euclidean distances to the origin, thereby achieving quantitative calibration and unified characterization of the complex morphology of the aggregate surface.

[0030] Furthermore, the method for determining the fractal dimension of the aggregate surface based on the surface morphology data includes: fusing the roughness index, the angularity coefficient, and the surface porosity distribution to obtain a comprehensive surface morphology index, and determining the fractal dimension of the aggregate surface based on the comprehensive surface morphology index.

[0031] This embodiment uses a method combining multi-parameter fusion and fractal calibration to calculate the surface fractal dimension. The core idea is to map the three-dimensional morphology parameters of the aggregate surface into a comprehensive index, and then convert it into a fractal dimension with clear physical meaning through fractal calibration coefficients.

[0032] First, the roughness index, angularity coefficient, and surface porosity distribution of the aggregate are used as coordinate components in three-dimensional space to construct the surface morphology feature points of the aggregate. Let the roughness index of the aggregate be... The values ​​are obtained by measuring multiple points on the aggregate surface using laser profile scanning or a stylus-type roughness tester and taking the arithmetic mean. The unit is 1. Let the angle coefficient be... Its value is obtained by calculating the curvature variation characteristics of the projected contour of aggregate particles using image analysis technology. It is a dimensionless parameter, typically ranging from 0 to 1, with larger values ​​indicating sharper edges; assuming the surface porosity distribution is... The values ​​were obtained by combining scanning electron microscope images with image binarization processing, statistically analyzing the proportion of surface pore area to the total field of view, and expressed as a percentage. These three parameters were then used as coordinate components in three-dimensional space to construct the surface morphology feature points of the aggregate. ,Right now The location of the surface morphology feature point in the three-dimensional parameter space uniquely determines the overall state of the aggregate surface morphology. Three-dimensional space, rather than a single parameter, is chosen for characterization because the complex morphology of the aggregate surface cannot be fully described by any single index. Roughness, angularity, and porosity correspond to different physical mechanisms, and their combined effect determines the interfacial interaction behavior between the aggregate and the cement paste.

[0033] In this embodiment, the roughness index was measured using a MarSurf M300 stylus roughness tester. Three contour lines were taken along the long axis of the aggregate, with a sampling length of 5.6 mm and an evaluation length of 17.5 mm. The angularity coefficient was analyzed using ImageJ image analysis software to statistically measure the curvature changes of the two-dimensional projected contour of the aggregate. The surface porosity distribution was obtained using a ZEISS EVO18 scanning electron microscope at 500x magnification to acquire backscattered electron images, which were then binarized using ImageJ to statistically analyze the pore area ratio. Fifty samples were measured for each of the above three parameters, and the arithmetic mean was taken. Please refer to Table 1, which lists the original measurement data of 10 representative samples in this embodiment.

[0034] Table 1: Raw data of aggregate surface morphology measurement As shown in Table 1, the roughness index of the natural aggregate samples ranged from 10.85 to 14.25 μm, which is consistent with the statistical mean of 12.35 μm for 50 samples. The roughness index of the recycled aggregate samples ranged from 24.35 to 33.42 μm, which is consistent with the statistical mean of 28.67 μm. Moreover, the three parameters of each recycled aggregate sample were systematically higher than those of the natural aggregate, which is consistent with the objective law that recycled aggregate is rougher, has sharper edges and more pores due to the old cement mortar adhering to its surface.

[0035] Next, the surface morphology feature points are calculated. To the origin Euclidean distance The calculation formula is: The physical significance of this distance lies in unifying three morphological parameters with different dimensions and orders of magnitude under a unified geometric scale for comprehensive measurement. A larger distance indicates a higher overall surface roughness of the aggregate, meaning a more complex surface morphology and a greater deviation from the ideal smooth state. Using Euclidean distance instead of simple summation avoids the weight imbalance caused by differences in dimensions and numerical scales between parameters, ensuring that the three parameters have equal geometric contribution weights in the comprehensive index.

[0036] To eliminate the influence of absolute values ​​on the comparability of different types of aggregates, the obtained Euclidean distance was used. relative to the preset reference distance The specific formula for performing ratio calculations is as follows: in, The preset reference distance is determined based on the Euclidean distance of surface morphological feature points of standard smooth quartz sand particles, serving as a reference for ideal smooth aggregate. The resulting ratio... This is the comprehensive surface morphology index of aggregates. This index is a dimensionless quantity. A value greater than 1 indicates that the surface roughness of the aggregate is higher than that of the reference smooth aggregate, equal to 1 indicates that it is comparable to the reference, and less than 1 indicates that it is smoother.

[0037] Since the classical definition of fractal dimension involves a self-similarity index under scale transformation, its mathematical expression is usually logarithmic. Therefore, this embodiment focuses on the comprehensive index of surface morphology. The natural logarithmic transformation is performed using the following formula: The role of logarithmic transformation is to compress exponential morphological differences into a linear scale, making the numerical distribution of aggregate surface morphology index more uniform, which is convenient for subsequent model training and optimization calculations. At the same time, logarithmic transformation can reduce the skewness of data, improve the comparability between different samples, and provide a reliable data foundation for the subsequent construction of performance mapping models.

[0038] Then, the transformed values With the preset fractal calibration coefficients Multiplying them together yields the surface fractal dimension of the aggregate. The specific formula is as follows: Among them, fractal calibration coefficients It is a constant greater than 0, and its physical meaning is to map the dimensionless logarithmic composite exponent to the range of values ​​of the standard fractal dimension. The scaling factor within the range. The specific value of this coefficient is determined as follows: a set of calibration aggregate samples with typical surface morphology (including natural river sand, manufactured sand, and recycled aggregates from different sources) are selected, and the measured surface fractal dimension values ​​are obtained using classical fractal dimension determination methods such as box counting. Simultaneously, the scaling factor of each sample is calculated. The value was determined by least squares fitting. The optimal value of is such that the result calculated by this formula is... The mean square error between the measured fractal dimension and the actual fractal dimension is minimized.

[0039] Fractal calibration coefficients The calibration ensures the consistency between the surface fractal dimension obtained by this method and classical fractal theory, making... It has a clear physical meaning: when When the value approaches 2.0, it indicates that the aggregate surface is close to an ideal smooth plane; when... When the value approaches 3.0, it indicates that the aggregate surface is extremely rough and complex, almost filling the three-dimensional space. The surface fractal dimension of recycled aggregates is usually distributed between 2.3 and 2.8, while the surface fractal dimension of natural aggregates is usually distributed between 2.1 and 2.4.

[0040] Through the steps described above, this embodiment combines three independent morphological parameters—roughness index, angularity coefficient, and surface porosity distribution—into a single surface fractal dimension with a clear fractal geometric meaning. A larger parameter indicates a higher degree of irregularity and complexity on the aggregate surface, suggesting that the aggregate may have a larger specific surface area and stronger mechanical interlocking potential when mixed with cement paste, but it may also introduce more interfacial defects. This quantitative index provides crucial numerical basis for subsequent steps in evaluating the differences in surface characteristics between recycled and natural aggregates, and for establishing a correlation model between recycled and natural aggregates and the macroscopic properties of concrete.

[0041] Furthermore, the three-dimensional morphological data specifically refers to the sphericity, aspect ratio, and convexity index of the aggregate.

[0042] In the quantitative characterization system of aggregate structural characteristics, three-dimensional morphological data is the core set of parameters reflecting the overall geometric shape of aggregate particles. Unlike surface morphology data, which focuses on microscopic texture, three-dimensional morphological data focuses on the macroscopic contour features at the particle scale, directly determining the aggregate's packing behavior in concrete, its ability to form a skeleton structure, and the stress transfer path under load. In this embodiment, sphericity, aspect ratio, and convexity index are selected as the three components of three-dimensional morphological data, which is determined based on an in-depth analysis of the correlation mechanism between aggregate morphological parameters and concrete mechanical properties.

[0043] Sphericity is used to quantify how close aggregate particles are to an ideal sphere, and is a core indicator describing the three-dimensional spatial uniformity of particles. Sphericity is typically calculated based on the particle's dimensions in three orthogonal directions, defined as the ratio of the surface area of ​​a sphere of equal volume to the actual surface area of ​​the particle, or the ratio of the diameter of a sphere equal to the particle's volume to the particle's maximum Freret diameter. Sphericity values ​​range from 0 to 1; a value closer to 1 indicates that the particles are closer to a sphere, making them easier to flow and compact in concrete mixing; a lower value indicates that the particles are flatter or more elongated, which can lead to directional alignment during packing and affect the isotropy of the concrete. For recycled aggregates, particles produced by crushing processes often have lower sphericity, while natural river sand, after long-term erosion by water flow, generally has higher sphericity. Differences in sphericity directly affect the aggregate's compact packing density and porosity, thus determining the amount of cement paste required in concrete.

[0044] The aspect ratio describes the extent of aggregate particle extension along its longest and second longest axes, reflecting the tendency of the particles to become flattened or needle-like. The aspect ratio is defined as the ratio of the largest Feretta diameter of the particle to the second largest Feretta diameter perpendicular to that direction. A larger aspect ratio indicates a more needle-like or flaky particle shape. These particles are prone to stress concentration in concrete under stress and are detrimental to the uniform distribution and workability of the mixture. Relevant standards typically set upper limits on the needle-like and flaky content of coarse aggregates, precisely because of the significant impact of the aspect ratio on the mechanical and workability properties of concrete. Recycled aggregates, due to dissociation along the interface between old mortar and natural aggregates during crushing, often produce more needle-like and flaky particles, and their aspect ratio distribution differs systematically from that of natural aggregates.

[0045] The convexity index characterizes the degree to which the outline of aggregate particles closely resembles their convex hulls, reflecting the degree of concavity and complexity of the particle surface. The convexity index is defined as the ratio of the actual area (or volume) of the particle to the area (or volume) of its convex hull, ranging from 0 to 1. A value closer to 1 indicates a more convex particle outline with fewer surface concavities; a lower value indicates more concavities, grooves, or indentations on the particle surface. The convexity index has a significant impact on aggregate packing behavior: particles with high convexity exhibit more uniform contact point distribution and better skeleton stability during packing; particles with low convexity are prone to mechanical interlocking due to interlocking of concave areas, increasing porosity during packing. Recycled aggregates, with old mortar adhering to their surfaces, often have a lower convexity index than natural aggregates, leading to decreased packing efficiency in mixed aggregates.

[0046] The three parameters described above characterize the three-dimensional geometric features of aggregate particles from different dimensions: sphericity reflects the overall spatial balance of the particles, aspect ratio reflects the extension characteristics of the principal plane of the particles, and convexity index reflects the complexity of the particle contour. Together, they constitute complete three-dimensional morphological data, encompassing both the isometric information of the particles and the directional characteristics and surface depression information of non-isometric particles. Based on this three-dimensional parameter system, subsequent steps can be taken to construct a three-dimensional morphological vector and perform normalized weighted processing to determine the three-dimensional morphological coefficients, thereby achieving quantitative calibration and unified characterization of the macroscopic morphology of aggregates.

[0047] Furthermore, the specific method for determining the three-dimensional morphology coefficient based on the three-dimensional morphology data of the aggregate is as follows: the sphericity, aspect ratio, and convexity index of the aggregate are constructed into a three-dimensional morphology vector. The components of the obtained three-dimensional morphology vector are subjected to minimum-maximum normalization. The normalized sphericity, aspect ratio, and convexity index are weighted and summed. The product of the summation result and the preset morphology adjustment coefficient is used as the three-dimensional morphology coefficient.

[0048] In this embodiment, sphericity, aspect ratio, and convexity index describe the shape characteristics of aggregate particles from different dimensions. Their numerical dimensions, value ranges, and weights influencing concrete performance are all different. Directly using these three independent parameters as input to the subsequent model would not only increase model complexity but also make it difficult to intuitively compare the overall superiority or inferiority of the three-dimensional morphology of different aggregates. Therefore, this embodiment employs a method combining vector construction, normalization fusion, and morphological calibration. The three independent morphological parameters of aggregate particles are unified in dimensions, weighted, and then converted into a comprehensive morphological index with a unified scale and engineering comparability—the three-dimensional morphological coefficient—through a morphological adjustment coefficient.

[0049] Let the sphericity of the aggregate be... The aspect ratio is convexity index is These three parameters are used to construct a three-dimensional shape vector. ,Right now The coordinates of this vector in the three-dimensional morphological space uniquely determine the geometric morphology of the aggregate particles. This embodiment chooses to construct a three-dimensional morphological vector based on three parameters to characterize the geometric morphology of the aggregate because the actual shape of the aggregate has a multi-dimensional impact on concrete performance: sphericity determines the space-filling efficiency of the particles, aspect ratio affects the directional arrangement of the particles and stress transfer, and convexity index restricts the contact pattern between particles and the stability of the skeleton. The combined effect of these three factors determines the compact packing characteristics of the mixed aggregate and the quality of the interfacial transition zone in the concrete.

[0050] Since the range of values ​​for sphericity and convexity indices is [missing information] The aspect ratio typically ranges from 100 to 1000. Direct numerical calculations can lead to dimensional conflicts and weight imbalances. Therefore, this embodiment focuses on the three-dimensional shape vector. Each component is subjected to min-max normalization and mapped uniformly to... The standard range.

[0051] Normalization first requires determining the lower and upper limits of the range of values ​​for each parameter. For sphericity... With convexity index Both are dimensionless parameters, with a theoretical lower limit of 0 (extremely irregular shape) and a theoretical upper limit of 1 (ideal smooth sphere). Therefore, the theoretical extreme values ​​can be directly used as the normalization boundaries for both. With convexity index The normalization formula is as follows: For aspect ratio Since the aspect ratio has no theoretical upper limit, a reasonable normalization upper limit needs to be set based on engineering practice experience. According to aggregate morphology research and concrete engineering specifications, when the aspect ratio exceeds 3.0, the particles exhibit significant needle-like and flaky characteristics, seriously affecting the workability and mechanical properties of concrete, and are usually considered unqualified aggregates. Therefore, in this embodiment, the normalization upper limit of the aspect ratio is set to 3.0, and the lower limit is set to 1.0 (ideal equiaxed particles). The normalization formula is as follows: If the actual measured aspect ratio is greater than 3.0, then it will be truncated to the upper limit of 3.0. If the actual measured aspect ratio is less than 1.0, then it will be truncated to the lower limit of 1.0. Therefore, the aspect ratio is... The range of values ​​is mapped to sphericity. and convexity index Same standard interval .

[0052] The role of min-max normalization is to eliminate the dimensional and numerical scale differences between different morphological parameters, so that the three parameters are comparable and balanced in subsequent weighted fusion; at the same time, normalization is based on theoretical extreme values ​​or engineering limits to ensure that the processed values ​​have clear physical boundary meanings and do not depend on subsequent sample statistics.

[0053] Subsequently, the three normalized morphological parameters are weighted and summed to obtain the morphological composite index. The formula is: in, The weighting coefficients for sphericity, aspect ratio, and convexity index are respectively, satisfying... and The weighting coefficients are determined based on the degree of influence of each morphological parameter on the core performance of concrete. In this embodiment, sphericity has the most direct impact on bulk density and is therefore assigned a higher weight. The value ranges from 0.35 to 0.45; the aspect ratio has a significant impact on the porosity and compressive strength of the interface transition zone, and is assigned a medium weight. The value ranges from 0.30 to 0.40; the convexity index has a moderating effect on skeleton stability and stress transfer, and is assigned a lower weight. The value ranges from 0.20 to 0.30. In engineering practice, the specific weight values ​​can be optimized and calibrated through orthogonal experiments or response surface analysis, with bulk density, porosity of the interface transition zone, and compressive strength as the response targets.

[0054] Finally, the overall pattern index Adjustment coefficient with preset shape Multiplying them together yields the three-dimensional morphology coefficient of the aggregate. The specific formula is as follows: Among them, the morphological adjustment coefficient This is a constant greater than 0, and its physical meaning is to map the dimensionless morphology index to a standard numerical range that is convenient for engineering applications. The calibration method for this coefficient is as follows: a set of calibration aggregate samples with typical morphologies are selected, including near-ideal spherical river sand, flattened manufactured sand, and irregular recycled aggregate. Their measured bulk density values ​​are determined through a close-packing test, and the morphology index of each sample is calculated simultaneously. ,by A linear regression was performed with ... The initial calibration values ​​are then fine-tuned by combining them with the prediction errors of the interfacial transition zone porosity and compressive strength, ultimately minimizing the combined prediction errors of bulk density, interfacial transition zone porosity, and compressive strength. The value serves as the optimal form adjustment coefficient.

[0055] Through the above steps, this embodiment combines the three independent morphological parameters—sphericity, aspect ratio, and convexity index—into a single dimensionless three-dimensional morphological coefficient. The higher the value, the more favorable the overall morphology of the aggregate is to the compact packing and interfacial properties of the concrete; the lower the value, the more morphological defects there are, requiring compensation by adjusting the admixture ratio. This comprehensive index provides a simple, effective, and comparable numerical basis for quantifying the differences in three-dimensional morphology between recycled and natural aggregates in subsequent steps, and for using it as a key input parameter in the proportion-performance mapping model.

[0056] Step 2: Set multiple sets of volumetric admixture ratios of recycled aggregate and natural aggregate, prepare corresponding mixed aggregate samples and concrete samples, and determine the bulk density, interfacial transition zone porosity and compressive strength corresponding to each set of volumetric admixture ratios to establish a sample dataset.

[0057] After quantitatively characterizing the structural features of recycled and natural aggregates, the core objective of this step is to establish a quantitative relationship between the proportion of recycled aggregate and key performance indicators of concrete, providing a data foundation for the subsequent screening of candidate content ranges and the training of the proportion-performance mapping model. Traditional recycled concrete mix design often relies on empirical formulas or limited experimental points, making it difficult to fully reveal the continuous influence of recycled aggregate content on concrete performance throughout the feasible range. Therefore, this embodiment adopts a systematic experimental design method, setting multiple gradient points within a preset volumetric content range to comprehensively acquire performance response data of the mixed aggregate and concrete at different content levels.

[0058] This step first sets several sets of volumetric admixture ratios for recycled and natural aggregates. The volumetric admixture ratio is the core control variable in this embodiment; it is defined as the percentage of the volume of recycled aggregate relative to the total volume of the mixed aggregate. The reason for using volumetric admixture instead of mass admixture is that the packing state of aggregates and the mix design of concrete essentially follow the principle of volumetric filling. There is a significant difference in apparent density between recycled and natural aggregates. If the admixture is controlled by mass ratio, it will lead to a deviation in the actual volumetric proportion, thus affecting the accurate judgment of the packing structure and the formation mechanism of the interface transition zone. Therefore, using the volumetric admixture ratio as a control parameter can more directly reflect the spatial filling relationship and skeletal structural characteristics of aggregate particles.

[0059] After determining the volumetric admixture ratios for each group, corresponding mixed aggregate samples and concrete samples were prepared according to these ratios. The mixed aggregate samples were loosely packed masses obtained by thoroughly mixing recycled and natural aggregates at a predetermined volume ratio, used for compact packing tests. The concrete samples were concrete specimens prepared according to the same mixed aggregate volume ratio, with fixed amounts of cement, water, and admixtures, using standard molding processes, and used for subsequent determination of porosity and compressive strength in the interfacial transition zone. The preparation of both groups of samples followed the same volumetric admixture ratio to ensure parameter correspondence and traceability throughout the entire process from aggregate packing to concrete hardening.

[0060] Next, the bulk density of each group of mixed aggregate samples was obtained through a close packing test. Bulk density refers to the mass of mixed aggregate per unit volume in a close-packed state, and it is a core indicator for measuring the compactness of the aggregate particle system. Recycled aggregates, due to their rough surfaces, numerous edges and corners, and irregular shapes, typically have a higher porosity in a loose state than natural aggregates. However, through reasonable particle size distribution and admixture optimization, the irregular shapes of recycled aggregates can fill the voids between natural aggregates, forming a denser skeletal structure. The close packing test typically uses a vibrating table or tamping method to bring the aggregate particles to their densest arrangement under a specified compaction effort. The mass is then weighed and divided by the container volume to obtain the bulk density at that volumetric admixture ratio. A higher bulk density indicates a more compact skeletal structure of the mixed aggregates, which is beneficial for improving the strength and durability of concrete.

[0061] Simultaneously, the porosity and compressive strength of the interfacial transition zone were measured for each group of concrete samples at a preset curing age. The interfacial transition zone is a thin layer of approximately tens of micrometers thick between the aggregate and cement paste in concrete. It is the weakest link in concrete, and its porosity and density directly determine the macroscopic mechanical properties and permeability of the concrete. The old cement mortar adhering to the surface of recycled aggregate has a high water absorption rate and a rough surface texture, which will change the water-cement ratio and the distribution of hydration products in the interfacial transition zone, thus affecting its pore structure. The porosity of the interfacial transition zone is usually determined using backscattered electron imaging technology combined with image analysis. At a preset curing age (such as 28 days standard curing age), the cut section of the concrete sample is scanned, and the proportion of pore area within the interfacial transition zone is statistically analyzed. Compressive strength is the most basic indicator for measuring the mechanical properties of concrete. Axial pressure is applied to concrete specimens of specified dimensions according to standard test methods until failure, and their ultimate bearing capacity is recorded and the compressive strength value is calculated. The higher the compressive strength, the stronger the concrete's ability to withstand loads.

[0062] Finally, a sample dataset was established to correlate volumetric doping ratios with bulk density, interfacial transition zone porosity, and compressive strength. This dataset maps each volumetric doping ratio to its corresponding three performance indicators, serving not only as the direct basis for the initial screening but also as the training sample source for the ratio-performance mapping model. The size, coverage, and accuracy of the sample dataset directly affect the prediction accuracy and reliability of the subsequent model's optimization results.

[0063] Through the systematic experimental design and data acquisition in this step, this embodiment establishes a complete and quantifiable correspondence between recycled aggregate content and concrete performance, laying a solid experimental data foundation for subsequent data mining of the optimal content range and construction of an accurate performance prediction model.

[0064] Furthermore, setting several sets of volumetric admixture ratios of recycled aggregate and natural aggregate includes: setting a lower limit and an upper limit for the volumetric admixture ratio of recycled aggregate, and selecting several set values ​​for the volumetric admixture ratio of recycled aggregate within the range defined by the lower limit and the upper limit; wherein, the volumetric admixture ratio of each set of natural aggregate is complementary to the volumetric admixture ratio of the corresponding set of recycled aggregate.

[0065] This embodiment uses the equidistant sub-interval division method to determine the volumetric admixture ratio sequence of recycled aggregate. Its core purpose is to cover the complete feasible range of recycled aggregate replacing natural aggregate with a systematic sampling strategy, to ensure the representativeness and continuity of experimental data, and to provide balanced sample support for the subsequent establishment of the ratio-performance mapping relationship.

[0066] In engineering practice, the proportion of recycled aggregate has clear physical boundaries. The lower limit is usually set at 0, i.e., a benchmark natural aggregate concrete with no recycled aggregate at all, serving as a performance reference point. The upper limit, however, needs to comprehensively consider the stability of the recycled aggregate source, the range of performance fluctuations, and the quality requirements of the target project, and is usually set between 0.3 and 0.7. If the upper limit is too low, the utilization potential of recycled aggregate cannot be fully explored; if it is too high, the concrete performance will degrade too quickly, making it difficult to meet the safety requirements of the project. The specific upper limit should be determined based on the local recycled aggregate production technology level and existing engineering application experience, and should be set after verification through preliminary tests.

[0067] The range between the lower and upper limits is divided equally into multiple sub-intervals. The fineness of this division directly determines the number of test groups and sample density. Too few sub-intervals will cause performance abrupt changes at key proportion points to be missed, while too many will significantly increase test costs and time. In this embodiment, based on the non-linearity of the impact of recycled aggregate substitution ratio on concrete performance, the total range is typically divided into 8 to 15 sub-intervals. This ensures that the intervals between adjacent proportion points can capture both the gradual trend of performance changes and identify possible inflection point characteristics.

[0068] Using the left endpoint of each sub-interval as the set value for the volumetric content ratio of recycled aggregate in each group ensures the strict monotonically increasing nature of the ratio sequence and a constant difference between adjacent ratio points, facilitating subsequent continuous testing and determination of candidate content ranges. For example, if the lower limit is set to 0, the upper limit to 0.6, and the number of sub-intervals is set to 10, then the width of each sub-interval is 0.06, and the set values ​​for the volumetric content ratio of recycled aggregate are 0, 0.06, 0.12, 0.18, 0.24, 0.30, 0.36, 0.42, 0.48, and 0.54, for a total of 10 groups. Although the upper limit endpoint of the last group, 0.60, is not directly used as the set value, its performance can be obtained through trend extrapolation or supplementary experiments.

[0069] For each set of recycled aggregate volume fraction settings, the set value for the natural aggregate volume fraction is determined by the difference between the value 1 and the recycled aggregate ratio. This setting is based on the principle of aggregate volume normalization, meaning that the sum of the volume fractions of recycled and natural aggregates in the mixed aggregate is always 1. This ensures that all mix designs are compared within the same aggregate volume framework, eliminating the interference of aggregate volume variations on performance. Continuing with the previous example, when the recycled aggregate ratio is 0.24, the corresponding natural aggregate ratio is 0.76; when the recycled aggregate ratio is 0.54, the corresponding natural aggregate ratio is 0.46.

[0070] Table 2: Sample Data on Volume Admixture Ratio and Concrete Performance Please refer to Table 2. In this embodiment, the volumetric admixture ratio of recycled aggregate is set according to the equidistant sub-interval division method described above. The lower limit is 0.00 (i.e., the natural aggregate benchmark group), and the upper limit is 0.84. The total interval is equally divided into 14 sub-intervals. The left endpoint value of each sub-interval is used as the set value of the volumetric admixture ratio of 15 groups of recycled aggregate. The volumetric admixture ratio of natural aggregate is determined by the difference between 1 and the ratio of recycled aggregate.

[0071] As shown in Table 2, as the volumetric admixture ratio of recycled aggregate increased from 0.00 to 0.84, the compact packing density of the mixed aggregate increased from 1685... Gradually decreased to 1491 The porosity of the interfacial transition zone continuously increased from 3.82% to 17.95%, and the compressive strength decreased from 52.4 MPa to 17.2 MPa. All three performance indicators showed a significant nonlinear deterioration trend, and the deterioration rate accelerated significantly in the high content range (above 0.60). This sample dataset fully records the quantitative response relationship between the proportion of recycled aggregate and the key performance of concrete.

[0072] Please see Figure 2 , Figure 3 and Figure 4 The three figures show the relationship between the proportion of recycled aggregate and three key properties of concrete. As can be seen from the figure, with the increase of the proportion of recycled aggregate, the bulk density and compressive strength both show an approximately linear decreasing trend, while the porosity of the interfacial transition zone shows an accelerated increasing trend. Especially after the content exceeds 0.60, the deterioration rate of all three properties is significantly accelerated, indicating that the negative impact of recycled aggregate on concrete performance tends to be significant in the high content range.

[0073] Through the above-mentioned equidistant sub-interval division and normalized proportion setting, this embodiment constructs a volumetric admixture ratio sequence that covers the complete substitution interval, is evenly distributed, and has clear boundaries. This provides a standardized test scheme basis for the subsequent preparation of mixed aggregate samples and concrete samples, determination of corresponding performance indicators, and establishment of sample datasets.

[0074] Step 3: Based on the sample dataset, construct and train the volumetric admixture ratio-performance mapping model. The volumetric admixture ratio-performance mapping model takes the volumetric admixture ratio and aggregate structure feature vector as input, and outputs the predicted values ​​of bulk density, interfacial transition zone porosity and compressive strength.

[0075] Furthermore, when establishing the sample dataset, preset admission conditions are set, including: a lower threshold for bulk density, an upper threshold for porosity in the interface transition zone, and a lower threshold for compressive strength. For any sample data in the sample dataset, if its bulk density is lower than the lower limit threshold of bulk density, or its interface transition zone porosity is higher than the upper limit threshold of interface transition zone porosity, or its compressive strength is lower than the lower limit threshold of compressive strength, the sample data is determined not to meet the preset admission conditions and is removed.

[0076] The preset admission criteria set in this embodiment adopt a "single-index veto system." That is, for any sample data in the sample dataset, if any one of the three indices—bulk density, interfacial transition zone porosity, or compressive strength—exceeds the corresponding threshold boundary, the sample data is determined not to meet the admission criteria and is discarded. The core purpose of this strict screening mechanism is to ensure that all samples entering the subsequent modeling and optimization process are within the engineering-feasible performance range, and to prevent any ratio scheme with severely degraded single performance from interfering with model training.

[0077] The three threshold indicators are set based on different engineering benchmarks, and each has a clear physical meaning and calibration method.

[0078] The lower limit threshold for bulk density is set based on the compacted bulk density of natural aggregate under a preset compaction work. Natural aggregate, as a high-quality aggregate proven through long-term engineering, has a compacted bulk density that represents a benchmark level of aggregate packing efficiency. In this embodiment, the compacted bulk density of natural aggregate measured under standard compaction work (such as the ASTM standard compaction procedure of three-layer loading and 25 tamping passes per layer) is used as a reference benchmark. The lower limit threshold for bulk density is typically set to 80% to 90% of this benchmark value. If the bulk density of a certain mix of aggregates is lower than this threshold, it indicates that the incorporation of recycled aggregates has severely damaged the packing efficiency of the aggregate skeleton, leading to excessive porosity and a surge in cement paste filling. This not only deteriorates economics but also easily causes durability problems such as shrinkage cracking, and therefore, it is discarded.

[0079] The upper limit threshold for the porosity of the interfacial transition zone is set based on the measured porosity of the interfacial transition zone of a reference concrete prepared with natural aggregate at the same age. The reference concrete is prepared using natural aggregate with the same mix proportion as the test group (only the aggregate type differs), and cured under standard curing conditions to a preset age (usually 28 days). Its interfacial transition zone porosity is measured using mercury intrusion porosimetry or backscattered electron imaging analysis. This measured value represents the porosity level of a high-quality interfacial structure, and the upper limit threshold for the interfacial transition zone porosity is typically set to 120% to 150% of this reference value. If the interfacial transition zone porosity of a recycled concrete mix exceeds this threshold, it indicates that the old cement mortar layer on the surface of the recycled aggregate has caused severe porosity in the interfacial zone, resulting in a significant decrease in bond strength and impermeability, failing to meet structural durability requirements, and therefore is rejected.

[0080] The lower limit threshold for compressive strength is set based on the safety strength level of the target project. This threshold directly corresponds to the concrete strength grade requirements specified in the engineering design documents, such as C30, C40, etc., and takes into account an appropriate safety margin (usually 90% to 95% of the strength grade value). If the compressive strength of recycled concrete in a certain mix proportion is lower than this threshold, even if its bulk density and porosity in the interface transition zone are acceptable, it is directly judged as not meeting the structural bearing capacity requirements, has no engineering application value, and must be rejected.

[0081] The combined effect of these three thresholds forms a three-dimensional performance feasible domain boundary. The lower limit threshold for bulk density constrains the mix design from the perspective of aggregate packing and economy; the upper limit threshold for porosity in the interface transition zone constrains the mix design from the perspective of microstructure and durability; and the lower limit threshold for compressive strength constrains the mix design from the perspective of macroscopic mechanics and safety. These three thresholds are independent and indispensable, collectively ensuring that the selected qualified samples meet the basic thresholds for engineering applications across multiple performance dimensions. This lays a data quality foundation for subsequently establishing a reliable proportion-performance mapping model and performing effective multi-objective optimization.

[0082] Furthermore, the proportion-performance mapping model, with volumetric admixture ratio and structural feature vector as input, includes: determining surface feature parameters and three-dimensional morphological feature parameters of recycled aggregate and natural aggregate respectively based on their structural feature vectors, and constructing aggregate property boundary parameters to characterize the differences between the two aggregates based on the surface feature parameters and three-dimensional morphological feature parameters; and using the volumetric admixture ratio and the aggregate property boundary parameters together as input to the proportion-performance mapping model.

[0083] Step 4: Based on the volumetric doping ratio-performance mapping model, multi-objective optimization is used to optimize the volumetric doping ratio. Multiple performance indicators, including bulk density, porosity of the interface transition zone, and compressive strength, are used as optimization objectives to output candidate optimal volumetric doping ratios.

[0084] Furthermore, when using multi-objective optimization to optimize the volumetric doping ratio, the doping range is determined first; The method for determining candidate doping ranges includes: performing continuity analysis on the volume doping ratio groups retained after screening by the preset admission criteria; determining one or more continuous doping ranges based on the comparison results of the doping difference between adjacent volume doping ratio groups and the preset continuity threshold; and determining candidate doping ranges from the continuous doping ranges according to the preset range selection criteria.

[0085] Furthermore, several sets of volumetric content ratios are generated within the candidate content range as candidate samples. The volumetric content ratios and aggregate property boundaries corresponding to each candidate sample are input into the trained proportion-performance mapping model to obtain the predicted values ​​of bulk density, interface transition zone porosity, and compressive strength. With the optimization objectives of maximizing the predicted bulk density, minimizing the predicted porosity of the interface transition zone, and maximizing the predicted compressive strength, the candidate samples are subjected to multi-objective optimization iterative updates to obtain the non-dominated solution set or Pareto optimal solution set. The volumetric doping ratio with optimal overall performance is determined from the non-dominated solution set or Pareto optimal solution set and used as a candidate optimal volumetric doping ratio.

[0086] After constructing the sample dataset, the core task of this embodiment is to screen and refine the original experimental data. From the sample points covering the entire dosage range, a dosage range that meets both basic engineering performance requirements and has continuous optimization value is defined. Based on the data within this range, a predictive model that can accurately map the quantitative relationship between dosage ratio and performance indicators is constructed. This step plays a crucial role in the overall technical solution: on the one hand, it controls the quality and focuses the range of the original sample data generated in the previous steps; on the other hand, it provides a reliable solution boundary and a high-precision performance prediction tool for the subsequent multi-objective optimization search.

[0087] In the sample dataset constructed in the aforementioned steps, not all concrete performance ratios meet the basic requirements for engineering applications. When the recycled aggregate content is too high, due to the low strength, high water absorption, and increased defects in the interface transition zone of the recycled aggregate itself, the bulk density and compressive strength of the concrete may decrease significantly, while the porosity in the interface transition zone may increase sharply, leading to a deterioration of the overall performance of the concrete to a level unworthy of engineering application. If these clearly substandard aggregate ratios are included in subsequent model training and optimization, it will not only reduce the prediction accuracy of the model within the effective aggregate range but may also cause the optimization algorithm to waste computational resources in invalid regions, or even output an "optimal solution" that is practically unusable. Therefore, the purpose of the first round of screening is to quickly filter out those clearly infeasible aggregate ratios by setting entry conditions based on engineering standards and benchmark performance, focusing the scope of subsequent analysis on the acceptable performance range.

[0088] The core logic of the first round of screening is to comprehensively judge each volumetric doping ratio in the sample dataset based on its corresponding three performance indicators. Only when the bulk density, interfacial transition zone porosity, and compressive strength simultaneously meet their respective threshold requirements is the ratio group considered a qualified sample; if any indicator exceeds the corresponding threshold, the ratio group and all its performance data are eliminated. This "one-vote veto" screening strategy strictly ensures the engineering usability of the selected samples and avoids misleading the model by ratio schemes with severely degraded performance in one aspect but acceptable performance in others.

[0089] After the first round of screening, the remaining volumetric admixture ratio groups are all qualified samples that meet the preset admission criteria. However, these qualified samples may not be continuously distributed on the ratio axis, but rather present as several mutually separated ratio segments. For example, in the low-admixture and medium-admixture regions, there may be two continuous intervals with qualified performance, interrupted by an admixture point or interval that does not meet the admission criteria. This fragmentation phenomenon usually corresponds to a qualitative change in the internal skeleton structure and interface characteristics of concrete when the recycled aggregate admixture reaches a certain critical value, leading to a step-like deterioration in performance. To ensure the continuity and stability of subsequent optimization solutions, this embodiment further performs continuity testing on the screened qualified samples, and determines the ratio segment that is continuously distributed on the ratio axis and contains the largest number of qualified samples as the candidate admixture interval. The continuous qualified segment containing the largest number of samples is selected as the candidate interval because, on the one hand, this interval usually corresponds to the main feasible range of recycled aggregate admixture, with the richest sample information support; on the other hand, the performance changes within this interval are relatively gradual, which is conducive to building a stable and reliable prediction model, and also provides a continuous and complete solution space for the multi-objective optimization algorithm.

[0090] After determining the candidate doping level range, this embodiment uses sample data within this range to train a proportion-performance mapping model. Following the initial screening and continuity testing, four sets of volumetric doping proportion samples are retained within the candidate doping level range, denoted as Group 1 to Group 4, forming the model training dataset. The input samples for this dataset are three-dimensional vectors. ,in This refers to the volumetric proportion of recycled aggregate. The surface fractal ratio, The output sample is a three-dimensional vector, representing the morphological aspect ratio. ,in This is the predicted bulk density value. This represents the predicted porosity value for the interface transition zone. This is the predicted value for compressive strength.

[0091] Because the numerical scales of the components in the input layer differ, this embodiment performs min-max normalization on the input samples to uniformly map each component to... The output sample directly uses the original measured values ​​as the network's target output, and is directly mapped to the original physical dimension space by the linear activation function of the output layer to ensure that the dimensions of the loss function calculation are consistent with those of the engineering performance indicators. For the input sample, the normalization formula for the j-th component is: in, This is the original measured value of this component. and These are the minimum and maximum values ​​of the component in the training set samples, respectively. The input value is the normalized value.

[0092] In this embodiment, the model employs a fully connected feedforward neural network, with the input layer containing three neurons (volume doping ratio r, surface fractal ratio). 3D morphology ratio The system employs a three-layer hidden layer with 64, 128, and 64 neurons respectively, all using the ReLU activation function. The output layer contains three neurons (predicted packing density, predicted porosity of the interface transition zone, and predicted compressive strength), using a linear activation function. The loss function is mean squared error (MSE), the optimizer is Adam, the initial learning rate is 0.001, the batch size is 4, the maximum number of training epochs is 500, and the early stopping mechanism terminates training if the validation loss shows no improvement after 50 consecutive epochs. The quantitative criterion for no improvement in validation loss is: in 50 consecutive iterations, the absolute decrease in validation loss relative to the previous iteration is less than a preset convergence threshold. When the early stopping condition is met, the network training is considered to have reached convergence, the model has stable generalization ability, and training can be terminated while the current network weight parameters are saved. If the early stopping condition is not triggered after 500 iterations, training is forcibly terminated, and the network weights corresponding to the iteration with the lowest validation loss are taken as the final model parameters. The criteria for determining training completion are: the training loss and validation loss decrease synchronously and tend to stabilize, and the difference between the two remains within a preset reasonable range; the model has reliable prediction ability on both the training and validation sets.

[0093] This embodiment employs leave-one-out cross-validation, using the first four groups of samples within the candidate doping level range as the validation set in turn, and the remaining three groups as the training set, repeating the process four times to ensure that each group participates in the validation. The convergence of training loss and validation loss during the training process is shown in Table 3.

[0094] Table 3: Model Training Loss Convergence Data Table As shown in Table 3, the training loss decreased from the initial 125.30 to the final 0.45, and the validation loss decreased from 130.50 to 1.10. Both converged synchronously and the difference remained stable, indicating that the model did not exhibit overfitting. Back-substituting the trained model into the first four groups of samples, the relative errors between the predicted and measured bulk density values ​​were 0.11%–0.15%, the predicted porosity of the interface transition zone was 0.51%–0.79%, and the predicted compressive strength was 0.57%–0.79%. The prediction accuracy of all three performance indicators meets the requirements for engineering applications.

[0095] After training is completed, the volumetric doping ratio to be evaluated is first... Boundary of aggregate properties with the current batch Combined into a three-dimensional input vector Subsequently, based on the maximum and minimum values ​​of each input component recorded during the training phase, the input vector is subjected to min-max normalization to obtain a normalized input vector. The normalized input vector is fed into the trained fully connected feedforward neural network, and then passed through the input layer and three hidden layers for forward propagation calculation. The predicted packing density value with the original physical dimensions is directly obtained from the output layer. Predicted porosity values ​​in the interface transition zone and predicted compressive strength During the multi-objective optimization iteration process, for each group of candidate volumetric doping ratios, the complete process of "normalized input - network forward calculation - output predicted value" is repeatedly executed to quickly obtain the three performance predicted values ​​corresponding to the candidate ratio, which serve as the fitness basis for non-dominated ranking and crowding distance calculation, thereby replacing physical experiments to achieve efficient virtual evaluation of ratio performance.

[0096] The core function of this model is to establish a mathematical mapping relationship between input variables (volume admixture ratio and structural feature vector) and output variables (predicted bulk density, predicted interfacial transition zone porosity, and predicted compressive strength). Traditional regression analysis methods can usually only handle the relationship between a single independent variable and a dependent variable, making it difficult to simultaneously consider the synergistic effects of admixture ratio and aggregate structural characteristics on multiple performance indicators. However, the proportion-performance mapping model constructed in this embodiment uses the volume admixture ratio of recycled aggregate and the structural feature vectors of both types of aggregate as input. This allows for a thorough study of the differentiated influence of recycled aggregates of different qualities at different admixture levels on concrete performance, thereby achieving high-precision prediction of performance indicators under any given admixture ratio and aggregate property combination. The model outputs three continuous values, corresponding to the predicted bulk density, predicted interfacial transition zone porosity, and predicted compressive strength, respectively. These three indicators comprehensively evaluate the overall performance of concrete at a specific admixture ratio from three dimensions: skeleton density, interfacial microstructure, and macroscopic mechanical properties.

[0097] The proportion-performance mapping model trained in this embodiment will act as a surrogate model for the objective function in the subsequent multi-objective optimization process. Since multi-objective optimization algorithms typically require numerous iterative searches and performance evaluations within the solution space, relying on real physical experiments for each evaluation would incur enormous time and economic costs. However, with a pre-trained mapping model, the optimization algorithm can quickly calculate the predicted performance value corresponding to any doping point within the candidate doping range, thus achieving global optimization with extremely low computational cost. Therefore, the prediction accuracy and generalization ability of the proportion-performance mapping model directly determine the reliability and engineering practical value of the final optimization results.

[0098] This embodiment introduces a continuity detection mechanism after the initial screening. Its core purpose is to extract the longest and densest continuous proportion segment from the discretely distributed qualified samples, serving as a reliable data foundation for subsequent model training and optimization. The necessity of this design stems from the inherent learning characteristics of the proportion-performance mapping model. This model essentially establishes a nonlinear mapping relationship from volumetric doping ratio to performance indicators within the input space. If the training samples are sparsely distributed on the proportion axis or have large blank areas, the model will be unable to accurately interpolate and predict the performance response of the blank areas, leading to increased prediction errors or even the generation of non-physical spurious trends.

[0099] First, all remaining qualified volumetric admixture ratio groups after the initial screening are sorted in ascending order according to the numerical value of the recycled aggregate volumetric admixture ratio, forming an ordered ratio sequence. This sorting operation makes the ratio points present a clear relative positional relationship on the number axis, laying the foundation for subsequent difference calculation and fracture identification. The sorted sequence is denoted as […]. ,in, Let represent the volumetric proportion of recycled aggregate in the i-th qualified proportion group, and satisfy . .

[0100] Subsequently, the differences between pairs of the sorted proportion sequences were calculated. For each pair of adjacent volumetric admixture proportions, the absolute value of the difference in the volumetric admixture proportion of recycled aggregate was calculated. The absolute value of this difference quantifies the distance between adjacent qualified samples on the scale axis, reflecting the density of the sample distribution. The obtained absolute value of the difference is then compared with a preset continuity threshold. If a comparison is made, If the adjacent proportion groups are determined to be continuously distributed, they belong to the same continuous proportion segment; if If a breakpoint is found between the two, the proportional sequence is interrupted at this point, and the preceding and following points belong to different continuous proportional segments.

[0101] Continuity threshold The threshold value directly determines the sensitivity of breakpoint identification. This threshold is usually set based on the original interval width when dividing the equally spaced sub-intervals in step 2, generally taking 1.5 to 2.0 times the original interval width. For example, if the range of 0 to 0.6 is divided into 10 sub-intervals in step 2, and the original interval width is 0.06, then the continuity threshold can be set to 0.09 to 0.12. The logic behind this setting is that after the first round of screening to remove unqualified samples, the interval between adjacent qualified samples usually does not exceed an integer multiple of the original interval width; if the interval exceeds 1.5 to 2.0 times the original width, it indicates that there are multiple consecutive unqualified samples that have been centrally removed, forming a substantial data gap area. The model lacks training support in this area and should not be included in the candidate interval.

[0102] After comparing all adjacent pairs, all breakpoints divide the ordered proportion sequence into several non-overlapping continuous proportion segments. Within each continuous proportion segment, the proportion groups are closely adjacent on the proportion axis with controllable spacing, providing sufficient sample density to support continuous model learning. Finally, the continuous proportion segment containing the largest number of volumetric dopant proportion groups is selected as the candidate dopant interval. The core consideration of this selection strategy is that the number of samples directly determines the sufficiency of model training and the stability of prediction. The longest continuous proportion segment means the largest sample capacity and the widest coverage, providing the richest data support for the subsequent training of the proportion-performance mapping model, while reserving the broadest search space for the optimization algorithm.

[0103] If multiple consecutive proportion segments contain the same number of volumetric admixture proportion groups, the proportion segment located in the lower recycled aggregate admixture range should be selected first. The engineering significance of this supplementary rule is that the lower admixture range is closer to the performance benchmark of natural aggregate concrete, the reliability of the sample data is higher, and the application risk in actual engineering is lower, which is in line with the gradual strategy of promoting the use of recycled aggregates.

[0104] Through the progressive processing method described above—sorting, continuity detection, breakpoint identification, and maximum segment selection—this embodiment automatically identifies and extracts the optimal continuous doping interval as a candidate doping interval from the qualified ratio group after the first round of screening. This process avoids the subjectivity and arbitrariness of manually defining intervals while ensuring the continuity and stability of performance within the candidate intervals, laying a scientific and standardized spatial foundation for subsequent model training and optimization.

[0105] In this embodiment, the input design of the ratio-performance mapping model is not simply to directly concatenate the obtained surface fractal dimension and three-dimensional morphological coefficient. Instead, the surface fractal dimension and three-dimensional morphological coefficient are obtained from the structural feature vectors, and the ratio operation is used to construct the aggregate attribute boundary. Its core purpose is to eliminate the absolute numerical fluctuation caused by the difference in aggregate source and extract the relative structural difference information between the two types of aggregates, thereby enhancing the model's generalization and adaptability to aggregates from different batches and different origins.

[0106] Specifically, surface fractal ratio Defined as the fractal dimension of the surface of recycled aggregate fractal dimension of natural aggregate surface The ratio, that is This ratio uses the surface fractal dimension of natural aggregate as a reference, normalizing the surface roughness of recycled aggregate to a relative scale. When When the surface roughness of recycled aggregate is higher than that of natural aggregate, the interfacial mechanical interlocking force is enhanced, but the risk of stress concentration is increased; when When, it indicates that the surface textures of the two are similar; when If the surface of the recycled aggregate is abnormally smooth, it indicates that the surface may be due to a special processing technique. A ratio is used instead of an absolute difference because the absolute values ​​of the surface fractal dimension measured in different laboratories or under different testing conditions may have systematic biases. The ratio form can effectively offset these systematic biases, making the model input comparable across data sources.

[0107] Similarly, three-dimensional shape ratio Defined as the three-dimensional morphology coefficient of recycled aggregate Compared with the three-dimensional morphology coefficient of natural aggregate The ratio, that is This ratio uses the overall morphological level of natural aggregates as a reference to quantify the relative advantages and disadvantages of recycled aggregates in terms of morphological indicators such as sphericity, aspect ratio, and convexity. When the overall morphology of recycled aggregate is superior to that of natural aggregate, it shows better packing efficiency and skeleton stability; when At that time, their morphological levels were comparable; when If the ratio is too high, it indicates that the morphological defects of the recycled aggregate are relatively prominent and need to be compensated for through proportion optimization.

[0108] The surface fractal ratio and the three-dimensional morphology ratio are combined into a two-dimensional array. This constitutes the aggregate property boundary. This boundary uniquely determines the relative position of the structural features of the recycled aggregate relative to the natural aggregate in a two-dimensional plane, providing a compact and information-intensive representation of aggregate properties. Compared to directly using four independent parameters (the surface fractal dimension and three-dimensional morphology coefficients of the two aggregates), the aggregate property boundary compresses the input dimension from four to two, reducing model complexity and the risk of overfitting, while retaining key information distinguishing the performance differences between different aggregate sources.

[0109] Finally, the volumetric admixture ratio r and the aggregate property boundary are... Together, they serve as inputs to the proportional-performance mapping model, forming a three-dimensional input vector, i.e. The volumetric admixture ratio r directly controls the ratio of recycled aggregate to natural aggregate, and the boundary of aggregate properties. This characterizes the relative structural differences between the two types of aggregates under this mix design. The synergistic effect of the two allows the model to simultaneously respond to the dual effects of mix design adjustment and aggregate replacement, predicting the evolution of concrete performance under different admixtures of aggregates from different sources.

[0110] The key advantage of the input design strategy in this embodiment lies in achieving decoupled expression of aggregate properties and proportioning parameters. The volumetric admixture ratio, as an engineering-controllable variable, is the direct object of optimization search; the aggregate property boundary, as an inherent material property, remains constant after a specific batch of aggregates is selected, providing a stable structural prior for the model. When the aggregate source is changed, only the new aggregate property boundary needs to be re-measured and calculated, without retraining the entire model, significantly improving the method's engineering applicability and deployment flexibility.

[0111] After determining the candidate admixture range and training the proportion-performance mapping model, this embodiment enters the final objective optimization stage. The core task of this stage is to search for the optimal volumetric admixture ratio that can simultaneously take into account multiple performance indicators within the engineering-feasible mix proportion range. Since the performance optimization of recycled concrete is essentially a typical multi-objective conflict problem, the increase in bulk density is often at odds with the control of porosity in the interfacial transition zone, while the maximization of compressive strength is constrained by the combined effects of the former two. Therefore, it is impossible to obtain the global optimal solution through simple iteration of a single objective. It is necessary to use multi-objective optimization algorithms to conduct systematic exploration on the Pareto front.

[0112] This embodiment uses the candidate doping range as the solution boundary, a approach with dual significance. From a computational efficiency perspective, compared to blindly searching within the entire 0-1 scale range, the candidate doping range has already eliminated a large number of infeasible regions through the initial screening and continuity testing, compressing the optimization space into a reliable and data-intensive local range, significantly reducing ineffective searches and computational burden. From a model reliability perspective, the scale-performance mapping model is only fully trained within the candidate doping range, and its prediction accuracy is statistically guaranteed within this range. Predictions outside this boundary fall into the category of extrapolation, with uncontrollable errors. Therefore, strictly limiting the search boundary is a necessary measure to ensure the credibility of the optimization results.

[0113] Based on the trained proportion-performance mapping model, the optimization algorithm can quickly obtain performance predictions for any candidate mix proportion without performing physical experiments. This model acts as a "virtual experimental platform" in the optimization process, compressing the traditional trial-test-adjustment cycle that takes days or even weeks in mix design into millisecond-level computational responses, making large-scale, high-precision mix optimization possible. This data-driven strategy, replacing physical experiments, is a key technological breakthrough in improving the efficiency and intelligence of recycled concrete mix design.

[0114] The joint optimization objective adopted in this embodiment includes three dimensions: maximizing bulk density, minimizing porosity in the interface transition zone, and maximizing compressive strength. Increasing bulk density relies on the tight interlocking of aggregate particles, but excessive pursuit of density may lead to the breakage and detachment of the old mortar layer on the surface of recycled aggregate, thus increasing the porosity in the interface transition zone. Minimizing the porosity in the interface transition zone requires controlling the amount of recycled aggregate or optimizing its surface properties, but low amounts limit the utilization efficiency of recycled resources. Compressive strength, as a comprehensive reflection of macroscopic performance, is influenced by both bulk density and interface quality, and its optimal region often lies in the compromise between two individual optimalities. Therefore, the goal of the multi-objective optimization algorithm is not to find the ideal solution that simultaneously achieves the theoretical extreme values ​​for all three, but rather to explore a set of Pareto optimal solutions that achieve the best trade-off among various performance aspects, allowing engineering decision-makers to flexibly choose according to specific project priorities.

[0115] The execution flow of the multi-objective optimization algorithm follows the basic paradigm of evolutionary optimization. First, an initial sample group is randomly generated within the candidate admixture range, with each sample corresponding to a set of volumetric admixture ratios of recycled and natural aggregates. The volumetric admixture ratio of each sample and its corresponding aggregate attribute boundary are input into the proportion-performance mapping model to obtain predicted values ​​for the three performance attributes, and the fitness of each sample in the multi-objective space is calculated accordingly. Then, non-dominated sorting is used to divide the samples into different dominance levels, and samples within the same level are further analyzed using crowding distance to maintain diversity. Based on the joint selection of dominance level and crowding distance, excellent samples are selected as parents, and offspring are generated through crossover and mutation operations. Parents and offspring are merged and selected again, iterating until a preset upper limit for iteration rounds is reached. Finally, the sample with the best overall performance is selected from the non-dominated solution set of the last generation population, and its corresponding volumetric admixture ratio is the candidate optimal volumetric admixture ratio.

[0116] The candidate optimal volumetric admixture ratio is not the only absolutely optimal solution, but rather the optimal estimate obtained based on training data and model predictions under the current aggregate properties. In practical engineering applications, this candidate ratio can be used as a central point, and small-scale physical verification tests can be conducted within its neighborhood to correct model prediction errors and confirm actual performance, ultimately determining the mix proportion for engineering implementation. This closed-loop strategy of "model prediction-experimental verification" leverages the efficient exploration advantages of data-driven methods while retaining the final authority of physical experiments, ensuring the scientific rigor and reliability of recycled concrete mix design.

[0117] Furthermore, the specific method of using a multi-objective optimization algorithm for interval optimization is as follows: set the upper limit of sample size and iteration rounds, randomly generate an initial sample group within the candidate admixture range, where each sample corresponds to a set of volume admixture ratios of recycled aggregate and natural aggregate, input the volume admixture ratio of each sample and its corresponding aggregate attribute boundary into the trained proportion-performance mapping model, and obtain the predicted bulk density, predicted porosity of the interface transition zone, and predicted compressive strength of the sample.

[0118] This embodiment employs a multi-objective optimization algorithm based on an evolutionary strategy for interval optimization. Its overall process follows the standard evolutionary optimization paradigm of "initialization-evaluation-selection-evolution-convergence". First, it is necessary to set the sample size and the upper limit of the number of iterations.

[0119] The sample size, i.e., the number of individuals in each generation of the population, directly determines the density of the search space coverage and the ability to maintain diversity. If the sample size is too small, the population diversity is insufficient, and the algorithm is prone to premature convergence to a local optimum; if the sample size is too large, the computational burden increases, and the evaluation time per iteration increases significantly. In this embodiment, the sample size is set between 50 and 100 based on the width of the candidate dosing range and the complexity of the problem. When the range is wide or the aggregate properties differ significantly, the upper limit is used to enhance the exploration capability; when the range is narrow or the aggregate properties are similar, the lower limit is used to improve convergence efficiency.

[0120] The upper limit of the number of iterations is one of the core criteria for algorithm termination, preventing infinite loops and controlling overall computational cost. Too few iterations result in insufficient evolution and poor solution set quality; too many iterations lead to diminishing returns in later stages, wasting computational resources. This embodiment sets the upper limit of the number of iterations to 100 to 200, supplemented by an auxiliary convergence criterion: when the rate of change of the non-dominated solution set is less than 1% within 20 consecutive iterations, the iteration can be terminated early, balancing search sufficiency and computational economy.

[0121] An initial sample group is randomly generated within the candidate aggregate content range. Each sample corresponds to a set of volumetric aggregate content ratios of recycled and natural aggregates. The purpose of random generation is to cover the entire candidate range unbiasedly, avoiding search bias caused by human pre-setting. Specifically, the generation method involves using the lower limit of the candidate aggregate content range... With upper limit Between these points, random numbers of the sample size are randomly selected according to a uniform distribution. Each random number... This refers to the volumetric proportion of recycled aggregate in a sample, while the corresponding volumetric proportion of natural aggregate is... .

[0122] To ensure uniform coverage of the initial population, this embodiment divides the candidate interval into sub-intervals of the same sample size, and only one sample is drawn from each sub-interval. This avoids sample clustering or large blank areas that may occur with pure random sampling, making the initial population more evenly distributed on the scale axis and improving the quality of the starting point for subsequent evolution.

[0123] For each sample in the initial sample ensemble, its volumetric doping ratio is determined. Boundary of aggregate properties as described above Together they form a three-dimensional input vector The trained proportion-performance mapping model is then input into the dataset. Based on the nonlinear mapping relationship learned within the candidate doping range, the model quickly outputs three performance prediction values ​​for that sample, namely the packing density prediction value. Predicted porosity values ​​in the interface transition zone and predicted compressive strength .

[0124] This prediction process is entirely based on forward computation of a trained model, requiring no physical experiments, and a single evaluation typically takes only milliseconds. Compared to the lengthy process of traditional mix design, where each mix requires specimen preparation and 28 days of standard curing before testing, the speed advantage of model prediction is extremely significant. This makes it possible to evaluate the performance of hundreds or thousands of candidate mixes within a limited time, which is a key technological support for achieving efficient and intelligent optimization.

[0125] The three predicted values ​​together constitute the coordinate position of the sample in the multi-object space, that is... The packing density and compressive strength are taken as negative values ​​to unify them into a minimization problem. This coordinate position is directly used for subsequent non-dominated ranking and crowding distance calculations, determining the survival probability and selection priority of samples during the evolutionary process.

[0126] Furthermore, with the joint optimization objectives of maximizing the predicted bulk density, minimizing the predicted porosity of the interface transition zone, and maximizing the predicted compressive strength, the fitness value of each sample on each optimization objective is calculated. Based on the fitness value, each sample in the initial sample group is non-dominated and sorted to determine the dominance level of each sample. The crowding distance of each sample within the same dominance level is calculated. Samples are selected sequentially according to the order of dominance level from low to high and crowding distance within the same dominance level from large to small, until the number of selected samples reaches the set sample size. The selected samples are used as parent samples to form the parent sample group.

[0127] In this embodiment, when performing multi-objective optimization, the three dissimilar optimization objectives first need to be unified into a comparable fitness framework. Maximizing the predicted bulk density and compressive strength is transformed into a minimization problem by taking negative values, while minimizing the predicted porosity of the interface transition zone maintains its original direction. For the i-th sample, its three-dimensional fitness vector... Defined as: in This is the predicted packing density value for this sample. This represents the predicted porosity value for the interface transition zone. This is the predicted compressive strength value. Each component of this vector follows the principle that the smaller the value, the better, thus unifying the originally disparate multi-objective problems into a standard minimization space for measurement.

[0128] Based on the fitness vector described above, a non-dominated ranking is performed on the sample population. For any two samples i and j, if sample i is not inferior to sample j in all three objective components and is strictly superior to sample j in at least one objective component, then sample i is said to dominate sample j. The number of times each sample is dominated by other samples is counted. Samples with zero domination counts constitute the first domination level. These samples have no competitors with better overall performance in the current population, and they together form the Pareto front currently searched. After temporarily removing the samples in the first domination level, samples with zero domination counts are searched again from the remaining samples to form the second domination level. This process continues until all samples are assigned a unique domination level. ,in .

[0129] The lower the dominance level value, the higher the overall superiority of the sample in the multi-objective space. The samples in the first dominance level are the non-dominated solution set of the current population. There is no absolute superiority or inferiority relationship between any single objective among them. Each item represents an optimal trade-off between packing density, porosity of the interface transition zone, and compressive strength.

[0130] To prevent excessive clustering of non-dominated solutions within local segments of the Pareto front and to maintain population diversity in the target space, this embodiment calculates crowding distance for samples within the same dominance level. Crowding distance quantifies the sparsity of the solutions surrounding a sample, reflecting the search potential of the region containing that sample.

[0131] For the k-th dominance level, all samples within this level are sorted in ascending order according to a certain objective function value. The crowding distance of the boundary samples (the best and worst samples under this objective) is set to infinity to ensure that extreme solutions are always preserved. For the intermediate sample i, its crowding distance contribution on this objective is the absolute value of the difference between the corresponding objective values ​​of the two adjacent samples. Combining the three objectives, the crowding distance of sample i is... The calculation formula is: in, and Let be the function values ​​of two adjacent samples of sample i after sorting them in ascending order on the m-th target. and These are the maximum and minimum values ​​of the m-th target within this dominance level, respectively. The denominator is normalized using the range of target values ​​to ensure that the contributions of the three targets with different dimensions to the congestion distance are comparable. The larger the value, the sparser the solution distribution around sample i, and preserving this sample helps to explore search regions that have not yet been fully explored.

[0132] The selection of the parent sample group follows a dual priority rule. First, samples are selected from low to high dominance levels, prioritizing lower-level samples with better overall performance. This ensures the algorithm's convergence trend towards the Pareto optimal front. When the number of samples within the same dominance level exceeds the remaining available slots, they are sorted from largest to smallest crowding distance, prioritizing sparsely distributed samples that can represent new exploration directions. This prevents the solution set from prematurely clustering in local segments of the frontier, ensuring the breadth of the search space coverage.

[0133] Samples are selected sequentially according to the aforementioned dual rules until the number of selected samples reaches the set sample size N. These selected samples constitute the parent sample group. As a gene pool for evolutionary operations, the parent sample group contains individuals with the best overall performance and the widest distribution in the current population. It will generate offspring through subsequent crossover and mutation operations, driving the population to continuously evolve towards a better and more uniform region.

[0134] Furthermore, crossover and mutation operations are performed sequentially on the parent sample group to generate a child sample group. The parent sample group and the child sample group are merged. The merged sample group is then subjected to non-dominated sorting and crowding distance calculation again. Samples are selected sequentially according to the dominance level from low to high and the crowding distance within the same dominance level from large to small until a set sample size is reached, generating a new parent sample group. The crossover, mutation, and merging selection operations are repeated until the upper limit of the iteration rounds is reached. The sample with the best overall performance is selected from the non-dominated solution set of the final parent sample group, and the volume doping ratio corresponding to this sample is used as the candidate optimal volume doping ratio.

[0135] After constructing the parent sample population through non-dominated sorting and crowding distance calculation, the algorithm enters the evolutionary generation stage. Crossover generates new volumetric blending ratios by recombining information between parent samples, allowing the inheritance and combination of superior traits from different parents and opening up new possible directions in the blending space. Mutation introduces random perturbations into the existing samples to maintain the genetic diversity of the population and prevent the algorithm from prematurely converging to local optima and losing its global exploration ability. The offspring sample population generated after crossover and mutation also needs to undergo three performance predictions using a proportion-performance mapping model to obtain complete fitness information.

[0136] Merging the parent and offspring sample groups is a key aspect of the elite preservation strategy. If offspring are simply used to directly replace parents, superior individuals that may have emerged during evolution could be lost during crossover and mutation, leading to a decline in the overall population quality. By merging the two generations into a unified population and then re-performing non-dominated ordination and crowding distance calculations, we can ensure a fair comparison between high-quality solutions discovered in previous generations and the exploration results of the new generation within the same competitive framework. Subsequently, samples are selected sequentially according to a dual rule: from low to high dominance level and from large to small crowding distance within the same level, until a predetermined sample size is reached, generating a new parent sample group. This environmental selection mechanism strictly guarantees that each generation's parent sample group consists of elite individuals from all currently existing individuals, ensuring a stable improvement in population quality with each iteration.

[0137] The crossover, mutation, and merge selection operations are repeatedly performed until the preset iteration limit is reached. During the iteration process, the population gradually approaches the Pareto optimal front. Early iterations are mainly exploratory, with the population extensively searching the matching space to quickly locate potential high-performance regions; mid-term iterations are mainly developmental, with a large number of mutations and recombinations occurring around superior individuals to finely mine local optima; in later iterations, the population tends to stabilize, the non-dominated solution set gradually converges, and the shape of the front becomes clearly discernible.

[0138] Please see Figure 5 The figure shows the convergence curve of the multi-objective optimization iteration. The vertical axis represents the minimum normalized distance from each sample in the non-dominated solution set to the ideal point, and the horizontal axis represents the iteration round. As can be seen from the figure, in the first 50 iterations, the minimum normalized distance rapidly decreases from the initial value of about 0.85 to below 0.30, indicating that the algorithm effectively located the approximate region of the Pareto front in the early stage. Between the 50th and 120th iterations, the rate of decrease gradually slows down, and the curve enters a plateau transition period. After 120 iterations, the minimum normalized distance tends to stabilize (about 0.102), and the rate of change is less than 1% for 20 consecutive iterations, satisfying the auxiliary convergence criterion, indicating that the non-dominated solution set has basically converged, and further iterations are unlikely to achieve significant improvement. This convergence characteristic verifies the rationality of the upper limit of the iteration rounds (150 rounds) set in this embodiment, ensuring a good balance between computational efficiency and solution set quality in the optimization results.

[0139] The algorithm terminates when the iteration reaches the maximum number of rounds. At this point, the first dominant level of the final parent sample group is the non-dominated solution set, where each sample represents an optimal trade-off between packing density, interfacial transition zone porosity, and compressive strength. No single objective can be improved without compromising other objectives. To determine the unique candidate optimal volumetric doping ratio from this set, this embodiment introduces the ideal point method for final decision-making.

[0140] The ideal point is composed of the theoretical optimal values ​​of each individual property in the non-dominated solution set. For the predicted bulk density and compressive strength, the maximum value in the non-dominated solution set is taken as the ideal component; for the predicted porosity in the interface transition zone, the minimum value in the non-dominated solution set is taken as the ideal component. Let the ideal point be... ,in , , i traverses the non-dominated solution set.

[0141] For each sample i in the non-dominated solution set, calculate its normalized Euclidean distance to the ideal point. The specific formula is as follows: In this formula, each denominator represents the range of the predicted values ​​of each objective in the non-dominated solution set, which is used to eliminate dimensional differences. The smaller the value, the closer the overall performance of the sample is to the ideal state where all individual performance metrics are simultaneously optimal. (Selection) The smallest sample is selected as the sample with the best overall performance, and its corresponding volumetric doping ratio is selected as the candidate optimal volumetric doping ratio.

[0142] The candidate optimal volumetric admixture ratio is a Pareto optimal compromise solution obtained through data-driven optimization under the current aggregate properties. It is not the extreme optimal of a single performance, but rather achieves the best overall balance among the three indicators of bulk density, porosity in the interfacial transition zone, and compressive strength.

[0143] To verify the practical feasibility of the candidate optimal volumetric admixture ratio, this embodiment prepared three sets of parallel verification specimens according to this ratio. The specimen preparation process is as follows: ordinary Portland cement strength grade 42.5, dosage 380 kg / m³; tap water 190 kg / m³, water-cement ratio 0.50; polycarboxylate superplasticizer 5.7 kg / m³, solid content 20%, water reduction rate 25%; the volumetric admixture ratio of recycled aggregate to natural aggregate is 0.145:0.855. Mixing process: first, cement, superplasticizer and 80% of the mixing water are added to a forced concrete mixer and mixed for 60 seconds, then the pre-wetted aggregate (10 minutes) is added and mixed for 90 seconds, and finally the remaining 20% ​​of the mixing water is added and mixed for 60 seconds. The slump of the mixture is controlled at 80±10 mm, and it is placed in a mold and vibrated. The vibration frequency is 50 Hz, the amplitude is 0.5 mm, the vibration time is 30 seconds, and the specimen size is 150 mm × 150 mm × 150 mm cube. The standard curing conditions were a temperature of 20±2 degrees Celsius and a relative humidity of not less than 95%, cured for 28 days. After the curing period, performance was determined using the same testing equipment and operating procedures as the 15 groups of specimens described above: Bulk density was determined using a 10-liter metal graduated cylinder according to the three-layer tamping method of GB / T14685, with each layer tamped 25 times. The tamping rod was a 16 mm diameter round steel bar. Porosity of the interface transition zone was obtained using a ZEISS EVO18 scanning electron microscope at 2000x magnification, 15 kV accelerating voltage, and a working distance of 10 mm. The image resolution was 2048×1536 pixels. After binarization, the threshold grayscale value was 128, and the pore area ratio of 20 fields of view was statistically analyzed. Compressive strength was tested using a YAW-3000 microcomputer-controlled electro-hydraulic servo pressure testing machine according to GB / T50081, continuously and uniformly loading the specimen at a rate of 5.0 kN / s until failure. The ultimate failure load was recorded, and the results were calculated using the formula... The compressive strength was calculated, where F is the failure load in Newtons and A is the bearing area of ​​the specimen in square millimeters, taken as 22,500 square millimeters. The comparison between the model predictions and the verified measured values ​​is shown in Table 4.

[0144] Table 4: Comparison of predicted and measured values ​​in the verification experiment As shown in Table 4, the relative errors between the model predictions and the measured values ​​for the three performance indicators are all less than 2%, and the measured values ​​all meet the preset threshold requirements. This result indicates that the proportion-performance mapping model established in this embodiment has good generalization ability and prediction accuracy. The candidate optimal volumetric admixture ratio r=0.145 is reliable in practical engineering and can be directly used as the core reference for the mix design of recycled concrete.

[0145] Furthermore, the crossover operation specifically involves: randomly selecting two samples from the parent sample group each time as paired samples, performing linear interpolation between the volume doping ratios of the two paired samples to generate a new volume doping ratio, using the new volume doping ratio as an intermediate offspring sample, and repeating the random selection and linear interpolation operation until the number of intermediate offspring samples generated reaches the set sample size, thus obtaining an intermediate offspring sample group.

[0146] The crossover operation used in this embodiment belongs to the linear recombination operator in real-number encoded genetic algorithms. In the evolutionary optimization process, the core role of the crossover operation is to generate new individuals through the recombination of information between parent individuals, allowing the inheritance and combination of the excellent matching characteristics of the parents, thereby exploring potential high-performance solutions between the regions where the parents are located in the candidate dosing space. Since the volume dosing ratio is a continuous real variable, this embodiment uses linear interpolation to generate offspring, ensuring that the newly generated volume dosing ratio always lies within a continuous interval between the parent ratios, maintaining the physical feasibility and numerical stability of the solution.

[0147] Let N be the number of samples in the current parent sample ensemble. Two distinct samples are randomly selected as paired samples each time. Let the volumetric doping ratio of the first paired sample be denoted as . The volumetric doping ratio of the second paired sample is ,in and All are within the candidate doping range Inside, and Generate a conforming... Uniformly distributed random numbers in an interval The volumetric doping ratio of offspring samples was calculated using linear interpolation. The specific formula is as follows: in, These are interpolation coefficients, and their values ​​range from 0 to 1. When... hour, ;when hour, ;when hour, It is exactly the arithmetic mean of the proportions of the two parents. The randomness of the model allows offspring to be evenly distributed along the line connecting the proportions of the two parent generations, fully exploring all possible ratios on that line segment and avoiding blind spots caused by fixed step sizes.

[0148] because and All are within the candidate doping range Inside, and Based on the properties of convex combinations, the generated It will inevitably fall into Within the interval, no additional boundary correction is required to directly determine the effective volumetric doping ratio. This characteristic is a significant advantage of choosing linear interpolation as the crossover operator, fundamentally avoiding the problem of out-of-bounds invalid solutions that may arise from traditional discrete crossover, ensuring that each generated offspring sample has clear engineering significance.

[0149] The newly generated volume doping ratio As an intermediate offspring sample, its corresponding natural aggregate volumetric content ratio is automatically determined as follows: The offspring sample inherits the proportioning information from the two parent samples, and its aggregate property boundaries are consistent with those of the parents. Subsequently, its three performance prediction values ​​can be directly evaluated through a proportion-performance mapping model.

[0150] The above random selection and linear interpolation operations are repeated until the number of offspring samples generated reaches the set sample size N, thus forming an intermediate offspring sample population. In actual implementation, this embodiment allows the same parent sample to participate in multiple pairings, that is, a random selection method with replacement is adopted. This ensures that superior individuals in the parent population have a higher chance of spreading their genetic characteristics, while also maintaining genetic fluidity within the population and preventing the premature loss of high-quality pairing information during evolution.

[0151] Furthermore, the mutation operation specifically involves adding a random perturbation to the volume doping ratio of each sample in the intermediate progeny sample group and performing boundary correction to form mutated progeny samples. After all intermediate progeny samples have undergone mutation, the progeny sample group is obtained.

[0152] The mutation operation used in this embodiment is a local fine-tuning of the intermediate offspring sample group generated by crossover. Its core purpose is to maintain the genetic diversity of the population and prevent the algorithm from getting trapped in local optima due to over-reliance on parental information. The crossover operation mainly searches along the lines connecting the proportions of the parents, and its exploration range is limited by the distribution boundary of the parental population. The mutation operation, on the other hand, introduces random perturbations into the existing solutions, allowing individuals to jump out of their current neighborhood and explore a wider matching space, thereby enhancing the algorithm's ability to find the global optimum.

[0153] Let the volumetric doping ratio of a selected sample in the intermediate offspring sample population be . Generate a conforming Uniformly distributed random numbers in an interval and a preset disturbance intensity coefficient. Then the random disturbance quantity The calculation formula is: in, and These represent the upper and lower limits of the candidate doping range, respectively. This represents the total width of the candidate interval. Introducing the interval width as a scaling factor allows the perturbation amplitude to automatically adapt to candidate intervals of different widths, ensuring that the variable interval length matches the search space scale. Perturbation intensity coefficient. This is a constant greater than 0, typically set between 0.05 and 0.15, and its physical meaning is the proportion of the maximum relative step size of a single mutation to the total width of the interval. When When the value is large, the mutated individual jumps a greater distance, enhancing its global exploration ability, but may disrupt the already obtained optimal matching structure; when When the value is small, the mutation searches finely within the local range, which is beneficial for in-depth development of potential optimal regions, but the ability to escape local extrema is weakened.

[0154] The random perturbation is superimposed on the original sample's volumetric doping ratio to obtain the mutated volumetric doping ratio. The mathematical expression is: Due to random numbers The range of values ​​is After superposition May exceed the candidate doping range The boundary. To ensure the feasibility of the solution, this embodiment performs boundary truncation correction on the out-of-bounds results, as shown in the following mathematical expression: After boundary correction This refers to the volumetric content ratio of the mutated offspring sample, and the corresponding volumetric content ratio of natural aggregate is adjusted accordingly. This sample inherited the aggregate property boundaries of the corresponding intermediate offspring sample, with only its volumetric admixture ratio experiencing local perturbation. Subsequently, its three performance prediction values ​​were also evaluated using a proportion-performance mapping model.

[0155] The core idea of ​​this embodiment is to correlate the microstructural characteristics and proportioning parameters of aggregates with the macroscopic properties of concrete across scales, achieving intelligent optimization of recycled concrete mix proportions through data-driven approaches. First, the structural differences between recycled and natural aggregates are quantified using surface fractal dimension and three-dimensional morphology coefficients. Then, a sample dataset covering feasible intervals is established through systematic experiments. After admission screening and continuity testing, a proportion-performance mapping model is trained within the data-dense candidate intervals to replace time-consuming physical experiments. Finally, a multi-objective evolutionary algorithm based on non-dominated sorting is employed to simultaneously optimize bulk density, porosity of the interface transition zone, and compressive strength based on model predictions. Through cross-recombination and mutation perturbation, the algorithm continuously approaches the Pareto front, selecting the volumetric admixture ratio with optimal overall performance. This method overcomes the limitations of traditional trial mix design methods, which rely on experience and are time-consuming. It achieves accurate decision-making on recycled aggregate admixture content with lower experimental costs, providing an efficient and reliable technical path for the engineering application of recycled concrete.

[0156] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0157] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0158] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0159] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for optimizing the mechanical properties of recycled concrete, characterized in that, The specific steps include: Step 1: Obtain surface morphology data and three-dimensional morphology data of recycled aggregate and natural aggregate, and determine the parameters used to characterize the aggregate structure based on the data, and construct the aggregate structure feature vector; Step 2: Set multiple sets of volumetric admixture ratios of recycled aggregate and natural aggregate, prepare corresponding mixed aggregate samples and concrete samples, and determine the bulk density, interfacial transition zone porosity and compressive strength corresponding to each set of volumetric admixture ratios to establish a sample dataset. Step 3: Based on the sample dataset, construct and train the volumetric admixture ratio-performance mapping model. The volumetric admixture ratio-performance mapping model takes the volumetric admixture ratio and aggregate structure feature vector as input, and outputs the predicted values ​​of bulk density, interfacial transition zone porosity and compressive strength. Step 4: Based on the volumetric doping ratio-performance mapping model, multi-objective optimization is used to optimize the volumetric doping ratio. Multiple performance indicators, including bulk density, porosity of the interface transition zone, and compressive strength, are used as optimization objectives to output candidate optimal volumetric doping ratios.

2. The method for optimizing the mechanical properties of recycled concrete according to claim 1, characterized in that, The surface morphology data includes the roughness index, angularity coefficient, and surface porosity distribution of the aggregate surface; The method for determining the fractal dimension of aggregate surface based on the surface morphology data includes: fusing the roughness index, the angularity coefficient, and the surface porosity distribution to obtain a comprehensive surface morphology index, and determining the fractal dimension of aggregate surface based on the comprehensive surface morphology index.

3. The method for optimizing the mechanical properties of recycled concrete according to claim 1, characterized in that, The three-dimensional morphological data includes the sphericity, aspect ratio, and convexity index of the aggregate; The method for determining the three-dimensional morphological coefficients based on the three-dimensional morphological data includes: constructing a three-dimensional morphological vector from the sphericity, aspect ratio, and convexity index; normalizing the three-dimensional morphological vector; and weighting and fusing the normalized components to obtain the three-dimensional morphological coefficients.

4. The method for optimizing the mechanical properties of recycled concrete according to claim 1, characterized in that, The setting of several sets of volumetric admixture ratios of recycled aggregate and natural aggregate includes: setting a lower limit and an upper limit of the volumetric admixture ratio of recycled aggregate, and selecting several set values ​​of the volumetric admixture ratio of recycled aggregate within the range defined by the lower limit and the upper limit; wherein, the volumetric admixture ratio of each set of natural aggregate is complementary to the volumetric admixture ratio of the corresponding set of recycled aggregate.

5. The method for optimizing the mechanical properties of recycled concrete according to claim 1, characterized in that, When establishing a sample dataset, preset admission conditions are set, including: a lower threshold for bulk density, an upper threshold for porosity in the interface transition zone, and a lower threshold for compressive strength. For any sample data in the sample dataset, if its bulk density is lower than the lower limit threshold of bulk density, or its interface transition zone porosity is higher than the upper limit threshold of interface transition zone porosity, or its compressive strength is lower than the lower limit threshold of compressive strength, the sample data is determined not to meet the preset admission conditions and is removed.

6. The method for optimizing the mechanical properties of recycled concrete according to claim 1, characterized in that, The proportion-performance mapping model, with volumetric admixture ratio and structural feature vector as input, includes: determining surface feature parameters and three-dimensional morphological feature parameters of recycled aggregate and natural aggregate respectively based on their structural feature vectors; constructing aggregate property boundary parameters to characterize the differences between the two aggregates based on the surface feature parameters and three-dimensional morphological feature parameters; and using the volumetric admixture ratio and the aggregate property boundary parameters together as input to the proportion-performance mapping model.

7. The method for optimizing the mechanical properties of recycled concrete according to claim 5, characterized in that, When using multi-objective optimization to find the optimal volumetric doping ratio, the doping range should be determined first. The method for determining candidate doping ranges includes: performing continuity analysis on the volume doping ratio groups retained after screening by the preset admission criteria; determining one or more continuous doping ranges based on the comparison results of the doping difference between adjacent volume doping ratio groups and the preset continuity threshold; and determining candidate doping ranges from the continuous doping ranges according to the preset range selection criteria.

8. The method for optimizing the mechanical properties of recycled concrete according to claim 7, characterized in that, Several sets of volumetric admixture ratios are generated within the candidate admixture range as candidate samples. The volumetric admixture ratio and aggregate property boundary corresponding to each candidate sample are input into the trained proportion-performance mapping model to obtain the predicted values ​​of bulk density, interface transition zone porosity, and compressive strength. With the optimization objectives of maximizing the predicted bulk density, minimizing the predicted porosity of the interface transition zone, and maximizing the predicted compressive strength, the candidate samples are subjected to multi-objective optimization iterative updates to obtain the non-dominated solution set or Pareto optimal solution set. The volumetric doping ratio with optimal overall performance is determined from the non-dominated solution set or Pareto optimal solution set and used as a candidate optimal volumetric doping ratio.

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