Multi-objective optimization method for strain hardening alkali-activated concrete material

Abstract

The invention belongs to the technical field of optimization design of concrete materials, and particularly relates to a multi-objective optimization method of a strain hardening alkali-activated concrete material, which comprises the following steps: selecting an experimental material, setting a plurality of alkali-activated mortar mixing ratios, and predicting the performance of alkali-activated mortar based on a response surface method; performing parameter analysis based on the response curved surface model, and constructing a response index prediction model; based on the response index prediction model, defining basic parameters; the response indexes are considered, alkali-activated mortar multi-objective optimization is carried out through an NSGA-II algorithm, and a Pareto leading edge is obtained; determining an optimal compromise solution set based on a Pareto leading edge; based on the optimal compromise solution set, determining the objective weight of each response index by adopting an entropy weight method; based on the determined objective weight of each response index, performing multi-target evaluation on the alkali-activated mortar mix proportion in the optimal compromise solution set by adopting an ideal approximation algorithm to obtain an optimized alkali-activated mortar mix proportion; and the performance optimization of the strain hardening alkali-activated concrete material is indirectly realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of optimized design of concrete materials, and particularly relates to a multi-objective optimization method for strain-hardening alkali-activated concrete materials. Background Art

[0002] With the continuous development of engineering materials, Engineered Cementitious Composites (ECC) have been widely studied due to their excellent tensile ductility, tensile strain hardening and multiple crack cracking characteristics, and show great application potential in various structural engineering projects. However, traditional ECC highly relies on Portland cement, resulting in a large amount of carbon emissions during its production process, which is contrary to the current goal of sustainable development. Therefore, it is urgent to develop more environmentally friendly alternative materials. Alkali-activated materials are new cementitious materials prepared by using industrial solid wastes (slag, fly ash, red mud, carbide slag, etc.) as precursors and activating them with alkaline substances such as sodium hydroxide. They not only have good mechanical properties, durability and chemical corrosion resistance, but also reduce carbon emissions by 55%-76% compared with cement. Many related studies have been carried out on replacing cement with alkali-activated materials to prepare concrete, which proves the feasibility of alkali-activated materials as cement substitutes. At present, there are few studies on using alkali-activated materials to prepare strain-hardening concrete, and its preparation method and optimization design theory have not been proposed. Summary of the Invention

[0003] To solve the above technical problems, the present invention proposes a multi-objective optimization method for strain-hardening alkali-activated concrete materials and concrete materials. In order to obtain the optimal mix ratio with high compressive strength, low fracture toughness, low carbon emissions and low cost, realize the precise control of the matrix performance, provide a theoretical basis for material design, and ensure the stability and reliability of material performance.

[0004] On the one hand, to achieve the above object, the present invention provides

[0005] A multi-objective optimization method for strain-hardening alkali-activated concrete materials, comprising:

[0006] Select experimental materials, set several mix ratios of alkali-activated mortar, and conduct performance prediction of alkali-activated mortar based on the response surface method;

[0007] Conduct parameter analysis based on the response surface model and construct a response index prediction model;

[0008] Define basic parameters based on the response index prediction model;

[0009] Based on the basic parameters, considering the response index, conduct multi-objective optimization of alkali-activated mortar through the NSGA-II algorithm to obtain the Pareto front;

[0010] determining an optimal compromise solution set based on the Pareto front;

[0011] Based on the optimal compromise solution set, the objective weight of each response indicator is determined using the entropy weight method;

[0012] Based on the determined objective weights of each response index, an approximate ideal algorithm is used to perform a multi-objective evaluation on the alkali-activated mortar mix ratio in the optimal compromise solution set to obtain the optimized alkali-activated mortar mix ratio.

[0013] Optionally, the experimental materials include silica fume content, sodium carbonate replacement amount and sand-to-binder ratio of quartz sand.

[0014] Optional parameter analysis based on response surface model includes:

[0015]

[0016] Among them, y is the response index; β0 is the intercept term; x i is the experimental variable; k is the number of experimental factors; β1 is the regression coefficient of the linear effect; β jj is the second-order effect regression coefficient; β ij is the factor x i and x j The regression coefficient of the interaction effect between them; ε is the statistical error.

[0017] Optionally, building a response indicator prediction model includes:

[0018] Carbon emissions CE, calculated as follows:

[0019] CE=526+9.86x1-194x2-4766x3,

[0020] Cost is calculated as follows:

[0021] Cost=1976+730x1-570x2-3507x3,

[0022] Liquidity FL is calculated as follows:

[0023]

[0024] Fracture toughness K m , calculated as follows:

[0025]

[0026] The matrix evaluation index MEI is calculated as follows:

[0027]

[0028] Among them, x1, x2, and x3 are the silica fume content, sand-cement ratio, and sodium carbonate content.

[0029] Optionally, multi-objective optimization of alkali-activated mortar is carried out by the NSGA-II algorithm, and the obtained Pareto front includes:

[0030] Select fluidity, matrix evaluation index, cost, and carbon emission as the indexes for multi-objective optimization;

[0031] Through the NSGA-II algorithm for multi-objective optimization of alkali-activated mortar, determine the response index prediction model, initialize the population size, and obtain the Pareto front through iterative calculation.

[0032] Optionally, based on the optimal compromise solution set, the objective weights of each response index are determined by the entropy weight method, including:

[0033] The normalized decision matrix is:

[0034]

[0035] Among them, y ij refers to the response value of the i-th solution under the j-th index, and r ij is the normalized value of the i-th solution under the j-th index;

[0036] Calculate the information entropy of each index as:

[0037]

[0038] Among them, E j is the information entropy of the j-th index, and ln(m) is a constant for normalizing the entropy;

[0039] Calculate the entropy surplus value as:

[0040] d j = 1 - E j ,

[0041] Among them, the entropy surplus value d j is the information utility value of the j-th index;

[0042] Calculate the weight w j of each index as:

[0043]

[0044] Optionally, the multi-objective evaluation of the mix proportion of alkali-activated mortar in the optimal compromise solution set is carried out by using the technique for order preference by similarity to an ideal solution, including:

[0045] Construct a decision matrix,

[0046]

[0047] Among them, Y is the decision matrix, m is the number of alternative solutions, n is the number of evaluation indexes of alternative solutions, and y mn is the value of the m-th alternative solution on the n-th evaluation index;

[0048] Matrix standardization,

[0049]

[0050] Construct a weighted standardized matrix,

[0051] v ij = w j ·z ij ,

[0052] Among them, v ij is the weighted standardized matrix, w j is the weight assigned to each index, and z ij is the standardized matrix.

[0053] Technical effects of the present invention: The present invention discloses a multi-objective optimization method for strain-hardened alkali-activated concrete materials. The use of central composite sequential design and response surface analysis methods can effectively reduce the number of tests and reduce the trial-and-error cost, having advantages in economy and efficiency; the use of genetic algorithm and entropy weight method - technique for order preference by similarity to an ideal solution algorithm can consider multiple concrete performance indexes simultaneously, and then design concrete materials with balanced performance, having engineering application value; the multi-objective optimization method of the present invention has good generalization ability and can be applied to the design of various materials and solve various engineering problems; the present invention is to obtain the optimal mix ratio with high compressive strength, low fracture toughness, low carbon emissions and low cost, realize precise control of the matrix performance, provide a theoretical basis for material design, and ensure the stability and reliability of material performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The drawings constituting a part of this application are used to provide a further understanding of this application. The schematic embodiments of this application and their descriptions are used to explain this application and do not constitute an improper limitation to this application. In the drawings:

[0055] Figure 1 is a schematic flow chart of a multi-objective optimization method for strain-hardened alkali-activated concrete materials according to an embodiment of the present invention;

[0056] Figure 2 is a schematic diagram of a three-factor central composite sequential design according to Embodiment III of the present invention;

[0057] Figure 3 is a flowchart of the operation of NSGA-II according to an embodiment of the present invention;

[0058] Figure 4 Schematic diagram of the microscopic design principle and optimization path of SHAAC according to an embodiment of the present invention;

[0059] Figure 5 Schematic diagram of the comparison of the matrix and fiber bridging strengths in the high-ductility composite mortar developed using PE fibers according to an embodiment of the present invention, where (a) shows an approximately linear positive correlation between the matrix compressive strength and the fiber bridging strength, and (b) shows the square of the matrix fracture toughness and the toughness J at the crack tip tip showing a linear positive correlation;

[0060] Figure 6 Schematic diagram of the XRD image of the precursor according to an embodiment of the present invention;

[0061] Figure 7 Particle size distribution and scanning electron microscope images (SEM) of the raw materials according to an embodiment of the present invention; a is the particle size distribution of GGBS, FA, SF, and QS; b - e are the microtopographies of GGBS, FA, SF, and QS respectively; f is the microtopography of the PE fiber;

[0062] Figure 8 Dimensions of the test specimens and material preparation process for the mechanical properties test of AAM according to an embodiment of the present invention, where a is a cubic specimen; b is a prismatic specimen; c is a dumbbell-shaped specimen; d is the preparation and curing process of AAM;

[0063] Figure 9 Results of NSGA-II according to an embodiment of the present invention, where a is the Pareto front; b is the hypervolume;

[0064] Figure 10 Results of the Pareto front evaluation based on the entropy weight method - TOPSIS algorithm according to an embodiment of the present invention, where a is a 3D scatter plot; b is a bar chart of the performance response indicators of the selected elements in the solution set;

[0065] Figure 11 Mechanical properties test results of AAM for verification according to an embodiment of the present invention, where a is the compressive strength; b is the fracture toughness; c is the matrix evaluation index; d is the comparison chart of the predicted value and the actual value;

[0066] Figure 12 Schematic diagram of the axial tensile stress - strain curve of SHAAC according to an embodiment of the present invention, where a - c are the tensile stress - strain curves of Rank 1, Rank 100, and Rank 200 respectively; d is the tensile strength; e is the ultimate tensile strength; f is the tensile strain energy density;

[0067] Figure 13This is the comprehensive performance evaluation result of Embodiment M45 and SHAAC of the present invention. Among them, a is the comprehensive mechanical property index considering cost; b is the comprehensive mechanical property index considering carbon emissions. Detailed implementation manners

[0068] It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0069] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than here.

[0070] To address this challenge, the present invention introduces the principle of microstructural design to enhance the toughness and ductility of the matrix by regulating its microstructure. This design concept is mainly realized by adjusting the composition of the alkali activator, optimizing the interfacial properties between the aggregate and the matrix, etc., effectively improving the mechanical behavior of the material. During the matrix optimization process of SHAAC, multiple variables have an important impact on its performance. For example, the type and content of the alkali activator, the incorporation ratio of admixtures (such as fly ash and slag), and parameters such as the sand-cement ratio all play a decisive role in the mechanical properties of the matrix. Systematically adjusting these variables and studying their effects within different ranges helps to find the optimal combination scheme, thereby achieving precise control of the matrix performance. This in-depth research can provide a theoretical basis for material design, ensuring the stability and reliability of material performance. In summary, the present invention combines advanced material design principles with statistical optimization tools, aiming to improve the tensile performance of SHAAC, providing scientific support and technical guidance for the development of high-performance, low-cost, and environmentally friendly building materials.

[0071] The strain-hardening alkali-activated concrete material used in this embodiment is:

[0072] Using an alkali-activated mortar matrix to replace the cement mortar matrix;

[0073] Using sodium silicate anhydrous, sodium carbonate, and borax as solid alkaline activators to replace traditional liquid activators, where the molar ratios of SiO2 to Na2O in the sodium silicate anhydrous are 1.0 and 2.0 respectively;

[0074] Under tensile load, the strain-hardening alkali-activated concrete material has multi-crack cracking and strain-hardening characteristics, with a tensile strain reaching 5% and a tensile strength reaching 7 MPa. The cost and carbon emissions are reduced by 9.91% and 35.3% respectively compared with traditional strain-hardening concrete.

[0075] Such as Figure 1As shown in the figure, a multi-objective optimization method for strain-hardening alkali-activated concrete materials is provided in this embodiment, including:

[0076] Select experimental materials, set several mix ratios of alkali-activated mortar, and conduct performance prediction of alkali-activated mortar based on the response surface method;

[0077] Conduct parameter analysis based on the response surface model and construct a response index prediction model;

[0078] Based on the response index prediction model, define basic parameters, where the basic parameters refer to the initialization parameters of NSGA-II, such as the number of iterations, population size, etc.;

[0079] Based on the basic parameters, considering the response index, conduct multi-objective optimization of alkali-activated mortar through the NSGA-II algorithm to obtain the Pareto front;

[0080] Determine the optimal compromise solution set based on the Pareto front;

[0081] Based on the optimal compromise solution set, use the entropy weight method to determine the objective weights of each response index;

[0082] Based on the determined objective weights of each response index, conduct multi-objective evaluation of the mix ratio of alkali-activated mortar in the optimal compromise solution set using the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) algorithm to obtain the optimized mix ratio of alkali-activated mortar.

[0083] Furthermore, the experimental materials include the silica fume content, the replacement amount of sodium carbonate, and the sand-to-binder ratio of quartz sand.

[0084] Furthermore, the parameter analysis based on the response surface model includes:

[0085]

[0086] where y is the response index; β0 is the intercept term; x i is the experimental variable; k is the number of experimental factors; β1 is the regression coefficient of the linear effect; β jj is the regression coefficient of the second-order effect; β ij is the regression coefficient of the interaction effect between factor x i and x j ; and ε is the statistical error.

[0087] Furthermore, constructing the response index prediction model includes:

[0088] Carbon emissions CE, calculated as follows:

[0089] CE = 526 + 9.86x1 - 194x2 - 4766x3,

[0090] Cost, calculated as follows:

[0091] Cost = 1976 + 730x1 - 570x2 - 3507x3,

[0092] The fluidity FL is calculated as follows:

[0093]

[0094] Fracture toughness K m , which is calculated as follows:

[0095]

[0096] The matrix evaluation index MEI is calculated as follows:

[0097]

[0098] where x1, x2, and x3 are the silica fume content, sand-cement ratio, and sodium carbonate content.

[0099] Furthermore, multi-objective optimization of alkali-activated mortar is carried out by the NSGA-II algorithm, and the Pareto front obtained includes:

[0100] The fluidity, matrix evaluation index, cost, and carbon emissions are selected as the indexes for multi-objective optimization;

[0101] Through the NSGA-II algorithm for multi-objective optimization of alkali-activated mortar, a response index prediction model is determined, the population size is initialized, and through iterative calculation, the Pareto front is obtained.

[0102] Furthermore, based on the optimal compromise solution set, the entropy weight method is used to determine the objective weights of each response index, including:

[0103] The standardized decision matrix is:

[0104]

[0105] where y ij refers to the response value of the i-th scheme under the j-th index, and r ij is the standardized value of the i-th scheme under the j-th index;

[0106] The information entropy of each index is calculated as:

[0107]

[0108] where E i is the information entropy of the j-th index, and ln(m) is a constant for normalizing the entropy;

[0109] The entropy redundancy value is calculated as:

[0110] dj = 1 - E j ,

[0111] where the entropy remainder value d j is the information utility value of the j-th index;

[0112] Calculate the weight w of each index j as follows:

[0113] Furthermore, the multi-objective evaluation of the alkali-activated mortar mix proportion in the optimal compromise solution set using the technique for order preference by similarity to an ideal solution includes:

[0114] Construct a decision matrix,

[0115]

[0116] where Y is the decision matrix, m is the number of alternative solutions, n is the number of evaluation indexes of the alternative solutions, and y mn is the value of the m-th alternative solution on the n-th evaluation index;

[0117] Matrix standardization,

[0118]

[0119] Construct a weighted standardized matrix,

[0120] v ij = w j ·z ij ,

[0121] where v ij is the weighted standardized matrix, w j is the weight assigned to each index, and z ij is the standardized matrix.

[0122] A specific application example of the present invention is as follows:

[0123] From the aspects of precursors, activators, and aggregates, the silica fume content, sodium carbonate substitution amount, and sand-cement ratio of quartz sand were selected as experimental variables respectively. Twenty mix proportions of alkali-activated mortar (AAM) were set using the Central Composite Circumscribed (CCC) experimental design, and the influence laws of these experimental variables on response indexes such as the fluidity, compressive strength, fracture toughness, cost, and carbon emissions of the one-step alkali-activated matrix were studied by the Response Surface Methodology (RSM). In addition, the entropy weight method - Technique for Order Preference by Similarity to an Ideal Solution (The entropy based-TOPSIS Method) was used to optimize the response indexes multi-objectively to obtain the optimal mix proportion with high compressive strength, low fracture toughness, low carbon emissions, and low cost. Finally, the tensile properties of the strain-hardening alkali-activated concrete (SHAAC) prepared with the optimal matrix were verified.

[0124] The Response Surface Methodology (RSM) is a statistical method for optimizing experimental results. Specifically, it is to establish a mathematical model to describe the relationship between experimental factors and response indexes, so as to find the optimal combination of experimental factors. When there are complex interaction effects or second-order effects for variables, the relationship between the response index and the experimental factor can usually be expressed by Equation (1):

[0125]

[0126] where y is the response index; β0 is the intercept term (i.e., the constant term); x i is the experimental variable; k is the number of experimental factors; β1 is the regression coefficient of the linear effect; β jj is the regression coefficient of the second-order effect; β ij represents the regression coefficient of the interaction effect between factor x i and x i ; ε is the statistical error.

[0127] In the present invention, the Central Composite Circumscribed (CCC) design is adopted to design the experimental grouping, providing a higher fitting degree for the model of the multi-factor experiment through quadratic terms and interaction terms. In addition, it can effectively reduce the number of experiments and reduce the waste of experimental resources. Figure 2 Shows the three-factor central composite circumscribed design, including the center point, axial points, and factor points, where the position of the axial points is determined by the parameter α, and its value is calculated according to Equation (2). The number of experiments N is determined according to Equation (3):

[0128] α = (2 k ) 1 / 4 (2),

[0129] N = 2 k+2k + n c (3),

[0130] where n c is the number of center points.

[0131] The standard response surface method usually focuses on single - objective optimization. For multi - objective optimization, other specific strategies are needed to handle the optimization problems of multiple response variables. The multi - objective optimization algorithm proposed by the multi - objective genetic algorithm aims to optimize multiple conflicting objective functions simultaneously and seek a set of optimal solutions (i.e., the Pareto front), rather than a single optimal solution. NSGA - II adopts the concepts of non - dominated sorting and crowding distance. Compared with other multi - objective optimization algorithms, its advantage lies in the efficient Pareto dominance sorting and the ability to maintain population diversity. Figure 3 Shows the running steps of NSGA - II.

[0132] The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) algorithm is a ranking method for multi - objective decision - making and is applicable to decision - making problems that need to comprehensively consider multiple factors. This method should first obtain the optimal solution and the worst solution of each index, and at the same time establish a two - dimensional data space of the distance between each index and the optimal / worst solution. In this space, the solution that is closest to the ideal solution and farthest from the negative ideal solution is considered the optimal solution. The specific steps of the TOPSIS algorithm are as follows:

[0133] Establish the decision matrix. First, all types of response indexes should be uniformly transformed into the maximization or minimization type to meet the decision - making requirements of the TOPSIS algorithm. For a decision matrix with m alternative solutions and n evaluation indexes for each solution, its form is as follows:

[0134]

[0135] where y mn is the value of the m - th alternative solution on the n - th evaluation index.

[0136] Matrix normalization. To eliminate the influence of index units or dimensions, the decision matrix needs to be normalized. The vector normalization method is adopted, that is, the numerical value of each index is divided by the norm of the index. The normalized matrix Z=(z ij ) is shown in Equation (5):

[0137]

[0138] Construct the weighted normalized matrix. The importance of each index may be different, so a weight w j needs to be assigned to each index. The weighted normalized matrix V is:[[]]

[0139] v ij = w j · z ij (6),

[0140] where the weight w j is the importance of the j-th index and satisfies z ij is the standardized matrix.

[0141] Determine the ideal solution and the negative ideal solution. The ideal solution V + and the negative ideal solution V - represent the optimal value and the worst value of each index respectively. The ideal solution takes the maximum value of the index, and the negative ideal solution takes the minimum value. The definitions of the ideal solution V + and the negative ideal solution V - are shown in Eqs. (7) and (8):

[0142] V + = (max{v 11 , v 21 , …, v m1}, max{v 12 , v 22 , …, v m2}, …, max{v 1n , v 2n , …, v mn ) (7),

[0143] V - = (min{v 11 , v 21 , …, v m1 , min{v 12 , v 22 , …, v m2 , …, min{v 1n , v 2n , …, v mn ) (8),

[0144] Calculate the distances between each solution and the ideal solution and the negative ideal solution. Use the Euclidean distance formula to calculate the distances between each solution and the ideal solution and the negative ideal solution respectively.

[0145] Distance from the ideal solution

[0146]

[0147] Distance from the negative ideal solution

[0148]

[0149] Calculate the relative closeness. By calculating the relative closeness C i to evaluate each solution. The relative closeness is the ratio of the distance between the solution and the negative ideal solution to the total distance, and the formula is as follows:

[0150]

[0151] where C i is the relative closeness, and the value of C i ranges from 0 to 1. The larger the value, the closer the solution is to the ideal solution.

[0152] However, the weights of TOPSIS usually need to rely on subjective judgment, which may affect the final decision-making result. Therefore, the present invention uses the entropy weight method to objectively assign weights to reduce the influence of human factors in decision-making and enhance the objectivity of decision-making. The specific steps are as follows:

[0153] Standardize the decision matrix. To ensure the dimensional consistency of each index, first perform standardization processing on the decision matrix Y. It should be noted that to ensure that the value of each index is between 0 and 1, so as to reflect the discreteness of the data, the standardization method here is different from the standardization method in formula (5). The standardized decision matrix R=(r ij ) The calculation formula is as follows:

[0154]

[0155] where each r ij represents the standardized value of the i-th solution under the j-th index.

[0156] Calculate the information entropy of each index. The specific formula is as follows:

[0157]

[0158] where E j reflects the information entropy of the j-th index, and ln(m) is a constant for normalizing the entropy.

[0159] Calculate the entropy redundancy value. The larger the entropy redundancy value, the richer the information, the greater the change, and the higher the importance of the index. The specific formula is:

[0160] d j =1 - E j (14),

[0161] where the entropy redundancy value d j represents the information utility value of the j-th index.

[0162] Calculate the weights of each index. The specific formula is as follows:

[0163]

[0164] This step is to ensure that the sum of all weights is 1, that is

[0165] Figure 4 The microscopic design principle shown indicates that for SHAAC to achieve the tensile mechanical behaviors of multi-slit cracking and pseudo strain hardening, the following conditions need to be met: I. Strength criterion, that is, the maximum bridging stress σ0 of the fiber is not less than the matrix cracking strength σ c , as shown in Equation (16); II. Energy criterion, that is, the residual bridging energy J′ of the fiber b is not less than the toughness J at the crack tip of the matrix tip , as shown in Equation (17).

[0166] σ0 ≥ σ c (16),

[0167]

[0168] where K m is the matrix fracture toughness, calculated from fracture experiment data; E m is the matrix elastic modulus.

[0169] Based on the above criteria, two pseudo strain hardening coefficients (PSH s and PSH e ) can be used to evaluate the pseudo strain hardening potential of high-ductility materials such as SHAAC. The higher the PSH coefficient, the stronger the tensile strain hardening ability of SHAAC. The definitions of the strength coefficient PSH s and the energy coefficient PSH e are shown in Equations (18) and (19):

[0170]

[0171] It can be seen from Figure 4 that the improvement of the pseudo strain hardening coefficient can be achieved by reducing the matrix fracture toughness and strength and increasing the residual bridging energy and bridging strength of the fiber. The present invention aims to improve the tensile properties of SHAAC by regulating the properties of the matrix. It can be seen from Figure 5 that Figure 5 (a) shows an approximately linear positive correlation between the matrix compressive strength and the fiber bridging strength, Figure 5 (b) shows that the square of the matrix fracture toughness is also linearly positively correlated with the toughness J at the crack tip tip . Therefore, the objective of the present invention is to increase the matrix compressive strength while reducing the matrix fracture toughness in order to improve the tensile properties of SHAAC.

[0172] The precursors used in this invention are ground granulated blast-furnace slag (GGBS, grade S105), fly ash (FA, class F, grade I), and silica fume (SF). The chemical compositions of the precursors were obtained by X-ray fluorescence spectrometry (XRF), and this data, together with the density and loss on ignition, is presented in Table 1. The crystalline phase compositions of the precursors were analyzed by X-ray diffraction analysis (XRD), as Figure 6 shown. A large amount of amorphous phase was contained in the precursors, indicating their good reactivity. In addition, crystalline phases such as quartz and mullite were contained in FA, and two different structural SiO2 crystalline phases were contained in SF. Quartz sand (QS) was used as the fine aggregate to reduce the shrinkage of the paste and regulate the workability and mechanical properties of the paste. Figure 7 shows the particle size distributions and microtopographies of the precursors and QS. The particle sizes of the precursors and QS both satisfy "wide overall distribution and narrow local distribution", which is beneficial to dense packing. Sodium silicate anhydrous with modulus (molar ratio of SiO2 to Na2O) of 1.0 and 2.0 respectively was used as the main alkaline activator, and sodium carbonate anhydrous was used as a supplementary activator to partially replace sodium silicate anhydrous with an equivalent Na2O content. In addition, borax (Na2B4O7·10H2O) was used as a retarder to prolong the setting time of the paste and simultaneously improve the mechanical properties of the alkali-activated mortar. PE fiber was used as the reinforcing material for AAM to prepare SHAAC, and its microtopography is as Figure 7 shown in f of. The diameter of the PE fiber is 24 μm, the length is 12 mm, the elastic modulus is 120 GPa, and the strength is 3000 MPa.

[0173] Table 1

[0174]

[0175] Some parameters of the AAM designed in this invention were limited, including the water-binder ratio (m 水 / (m 前驱体 +m 激发剂 was fixed at 0.28; the dosage of the alkali activator (mass ratio of activator equivalent Na2O to the precursor) was fixed at 7Na2O%; the modulus of the sodium silicate alkali activator was fixed at 1.5, obtained by mixing sodium silicate anhydrous with modulus of 1.0 and 2.0; the mass ratio of GGBS to FA was fixed at 6:4; the borax content was fixed at 1Na2O%. The Design-Expert software was used to conduct CCC design on the mix proportion, and the SF content (mass proportion in the precursor), sand-binder ratio (mass ratio of quartz sand to the precursor), and the dosage of Na2CO3 (replacement amount of sodium carbonate for the sodium silicate activator) were selected as the experimental factors. The experimental factors, codes, and levels of CCC are summarized in Table 2.

[0176] Table 2

[0177]

[0178] A total of 20 mix proportions were designed based on CCC, including 6 center points, to improve the accuracy of experimental error estimation, better control the complexity of the model, and improve the stability of prediction. The specific AAM mix proportions are shown in Table 3.

[0179] Table 3

[0180]

[0181] For the mechanical property test of AAM, cube specimens with dimensions of 50 mm×50 mm×50 mm, prism specimens with dimensions of 40 mm×40 mm×160 mm, and dumbbell-shaped specimens for the tensile test of SHAAC were used. For the prism specimens, after curing, a prefabricated crack with a depth of 12 mm and a width of 1 mm needs to be cut in the middle using a cutting machine, as specifically shown in Figure 8 a of Figure 8 b of Figure 8 c of Figure 8 d of. The specific preparation process of AAM: Add the precursors (GGBS, FA, and SF), aggregates (QS), activators (sodium metasilicate anhydrous and Na2CO3), and borax into a planetary mixer and stir at a speed of 75 r / min for 3 min, then add water and stir at a speed of 75 r / min for 3 min until it becomes a paste, and finally switch to the high-speed mode (165 r / min) and continue to stir for 5 min until the slurry is homogeneous and has satisfactory fluidity; Pour the uniformly stirred AAM into the mold for molding. After final setting, cover it with a film and cure it in the laboratory environment (25±2℃) for 24 h and then demold. After sealing the specimens, place them in an oven at 80℃ for 24 h, and then place them in the laboratory environment to air dry naturally for 7 d, and then carry out the mechanical property test. The specific process is shown in Figure 8 c of

[0182] Through analysis, it is considered that the larger the MEI of AAM, the more beneficial it is to improve the tensile properties of SHAAC. In addition, fluidity is also one of the important factors determining the mechanical properties of SHAAC. The fluidity of AAM determines the pouring difficulty and pouring quality of SHAAC. Good fluidity can reduce the holes and defects in the formed SHAAC and improve the mechanical properties. And the cost and carbon emission index directly determine the engineering application prospect of AAM. Therefore, the present invention selects fluidity, matrix evaluation index, cost, and carbon emission as the indexes for multi-objective optimization. Use NSGA-II to perform multi-objective optimization on AAM, select carbon emission CE, cost Cost, fluidity FL, and matrix evaluation index MEI as the objective functions, and the parameter range is the same as the experimental setting range. The initial population size is selected as 200. After 200 iterations of calculation, the Pareto front is obtained as shown in Figure 9As shown in a of [reference]. The Pareto front is presented as a 3D scatter plot, where CE, Cost, and FL are used as the X, Y, and Z axes respectively, and MEI is shown in the form of color mapping. Figure 9 b of [reference] shows the hypervolume corresponding to each iteration during the operation of NSGA-II. The hypervolume can be used to test the convergence of the algorithm. It can be seen from the figure that after 200 iterations, the hypervolume tends to be stable, indicating that the algorithm converges. At this time, a better Pareto front cannot be generated anymore. The obtained Pareto front is the compromise optimal for multiple objectives and exists in the form of a set. Therefore, further decision-making is required to achieve the optimal AAM index.

[0183] Results and analysis of the entropy weight method - Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) algorithm. First, the entropy weight method is used to objectively assign weights to each index, and the results are shown in Table 4. According to the obtained entropy weights, the TOPSIS algorithm is used to further analyze the elements in the Pareto front, and the optimal ratio is sorted according to the scores. The results are as Figure 10 shown in a of [reference]. Table 5 shows the AAM decision variables and performance response index information with serial numbers Rank 1, 20, 40, …, 200 for the entropy weight method - TOPSIS algorithm. The performance response indexes of Rank 1, 20, 40, …, 200 AAM are plotted in Figure 10 b of [reference] after normalization. It can be seen from the figure that the value of MEI plays a major decision-making role. The higher the MEI, the higher the TOPSIS score of AAM. In addition, AAMs with higher scores usually contain less silica sand.

[0184] Table 4

[0185]

[0186] Table 5

[0187]

[0188] To verify the optimization results, three groups of AAM ratios shown in Table 5 (i.e., Rank 1, Rank 100, and Rank 200) are taken to conduct the compressive test and fracture test of AAM respectively. In addition, 2% of PE fibers with the mentioned dosage are additionally incorporated into AAM to prepare strain-hardening alkali-activated concrete (SHAAC), and the corresponding axial tensile test is carried out.

[0189] As Figure 11 shown, [reference] shows the compressive strength, fracture toughness, and matrix evaluation indexes of the AAM for verification. Figure 11 a of [reference] shows that Rank 1 has the highest compressive strength, reaching 106.4 MPa. The compressive strengths of Rank 100 and Rank 200 are relatively close, both about 100 MPa.Figure 11 b shows the fracture toughness test results, indicating that Rank 1 has the lowest fracture toughness, further demonstrating the effect of lower sand-cement ratio and higher sodium carbonate content on reducing the matrix fracture toughness. Figure 11 c shows the situation of matrix evaluation indicators. Rank 1 has the highest MEI, which is 43.2% and 74.6% higher than Rank 100 and Rank 200 respectively. Figure 11 d compares the predicted values and actual values of the matrix evaluation indicators calculated by AAM based on the matrix evaluation indicator MEI, indicating that the prediction formula has high prediction accuracy. The error between the predicted values and actual values of Rank 1 and Rank 100 is within 5%, while the error of Rank 200 is within the acceptable range of 20%.

[0190] Figure 12 shows the axial tensile stress-strain curve of SHAAC. Figure 12 a-c respectively show the tensile stress-strain curves of Rank 1, Rank 100, and Rank 200. It can be seen from the figure that Rank 1 with higher MEI has smaller sawtooth stress fluctuations during the tensile process and a more gentle stress redistribution process. Figure 12 d shows the tensile strength of SHAAC. The figure shows that Rank 100 has the highest tensile strength, which may be related to its higher sand-cement ratio. Figure 12 e shows the ultimate tensile strain of SHAAC. As the ranking decreases, the tensile deformation ability gradually decreases, which also verifies the optimization path of SHAAC, that is, higher MEI can make SHAAC exhibit better strain hardening / deformation ability. Figure 12 d also shows that Rank 1 has the highest strain energy density, that is, it has the highest toughness.

[0191] Combined with the compressive strength of AAM matrix (σ c ), the tensile strength of SHAAC (σ t ), the ultimate tensile strain (ε t ), and the strain energy density (g se ) and other mechanical property indicators, as well as indicators such as carbon emissions (CE) and cost (Cost), comprehensively evaluate the performance of the material. Use the ratio of mechanical property parameters to cost / carbon emissions as the economic and environmental protection indicators. In addition, for the convenience of display and calculation, the cost and carbon emissions of the classic engineered cementitious composite (M45[]) are selected as reference values to normalize the cost and carbon emission indicators of SHAAC. Table 6 shows the detailed results of each performance indicator of M45 and SHAAC. Table 7 shows the results of performance indicators considering cost and carbon emissions.

[0192] Table 6

[0193]

[0194] Table 7

[0195]

[0196] Figure 13 is a radar chart showing the comprehensive performance evaluation of M45 and SHAAC, where Figure 13 a is the comprehensive mechanical property index considering cost, Figure 13 b is the comprehensive mechanical property index considering carbon emissions. It can be seen from the figure that SHAAC still has mechanical property indexes far higher than those of traditional ECC (M45) after considering cost and carbon emissions. In addition, Rank 1 has the largest envelope area after considering cost, indicating that it has the best performance in terms of cost. When considering carbon emissions, it can be found that Rank 1 and Rank 100 have similar envelope areas, indicating that they perform equally well in terms of environmental protection.

[0197] The present invention discloses a strain-hardening alkali-activated concrete material and a multi-objective optimization method for the concrete material. The use of the central composite sequential design and response surface analysis method can effectively reduce the number of tests and lower the trial-and-error cost, having advantages in economy and efficiency; the use of the genetic algorithm and the entropy weight method - technique for order preference by similarity to an ideal solution algorithm can consider multiple concrete performance indexes simultaneously, and thus design a concrete material with balanced performance, having engineering application value; the multi-objective optimization method of the present invention has good generalization ability and can be applied to the design of various materials and the solution of various engineering problems; the present invention aims to obtain an optimal mix ratio with high compressive strength, low fracture toughness, low carbon emissions and low cost, realize precise control of the matrix performance, provide a theoretical basis for material design, and ensure the stability and reliability of material performance.

[0198] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present application should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A multi-objective optimization method for strain-hardening alkali-activated concrete materials, characterized in that Including: Select experimental materials, set several mix proportions of alkali-activated mortar, and conduct performance prediction of alkali-activated mortar based on the response surface method; Conduct parameter analysis based on the response surface model and construct a response index prediction model; Define basic parameters based on the response index prediction model; Based on the basic parameters, considering the response index, conduct multi-objective optimization of alkali-activated mortar through the NSGA-II algorithm to obtain the Pareto front; Determine the optimal compromise solution set based on the Pareto front; Based on the optimal compromise solution set, use the entropy weight method to determine the objective weights of each response index; Based on the determined objective weights of each response index, use the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) to conduct multi-objective evaluation of the mix proportions of alkali-activated mortar in the optimal compromise solution set to obtain the optimized mix proportions of alkali-activated mortar.

2. The multi-objective optimization method for concrete materials according to claim 1, wherein the experimental materials include silica fume content, sodium carbonate substitution amount, and sand-to-binder ratio of quartz sand.

3. The multi-objective optimization method for concrete materials according to claim 1, wherein the parameter analysis based on the response surface model includes: Among them, y is the response index; β0 is the intercept term; x i is the experimental variable; k is the number of experimental factors; β1 is the regression coefficient of the linear effect; β jj is the regression coefficient of the second-order effect; β ij is the regression coefficient of the interaction effect between factor x i and x j ; ε is the statistical error.

4. The multi-objective optimization method for concrete materials according to claim 1, wherein constructing the response index prediction model includes: Carbon emission CE, calculated as follows: CE = 526 + 9.86x1 - 194x2 - 4766x3, Cost, calculated as follows: Cost = 1976 + 730x1 - 570x2 - 3507x3, Flowability FL, calculated as follows: Fracture toughness K m , is calculated as follows: Matrix evaluation index MEI, calculated as follows: wherein, x1, x2, and x3 are silica fume content, sand-to-binder ratio, and sodium carbonate content respectively.

5. The multi-objective optimization method for concrete materials according to claim 4, wherein conducting multi-objective optimization of alkali-activated mortar through the NSGA-II algorithm to obtain the Pareto front includes: Select flowability, matrix evaluation index, cost, and carbon emission as the indexes for multi-objective optimization; Conduct multi-objective optimization of alkali-activated mortar through the NSGA-II algorithm, determine the response index prediction model, initialize the population size, and obtain the Pareto front through iterative calculation.

6. The multi-objective optimization method for concrete materials according to claim 1, wherein using the entropy weight method to determine the objective weights of each response index based on the optimal compromise solution set includes: The standardized decision matrix is: where r ij is the standardized value of the i-th solution under the j-th index, and y ij refers to the response value of the i-th solution under the j-th index; Calculate the information entropy of each index as: Among them, E j is the information entropy of the j-th index, and ln(m) is a constant for normalizing the entropy; Calculate the entropy surplus value as: Among them, the entropy residual value d j is the information utility value of the j-th index; Calculate the weight w of each index j It is as follows:

7. The multi-objective optimization method of the concrete material according to claim 1, characterized in that, Using the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) to conduct multi-objective evaluation of the mix proportions of alkali-activated mortar in the optimal compromise solution set includes: Construct a decision matrix, Among them, Y is the decision matrix, m is the number of alternative solutions, n is the number of evaluation indicators for alternative solutions, and y mn is the value of the m-th alternative solution on the n-th evaluation indicator; Matrix standardization, Construct a weighted standardized matrix, v ij = W j ·z ij , Among them, v ij is the weighted normalization matrix, s is the weight assigned to each index, and z ij is the normalized matrix.

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