Mass concrete multi-objective anti-cracking optimization design method

Abstract

The application discloses a mass concrete multi-target anti-cracking optimization design method, and relates to the technical field of computer-aided design of building engineering.The method first divides an anti-cracking control area, sets an allowable threshold of cracking risk corresponding to an age period, selects uncertain parameters to construct an interval ellipsoid model, and determines the most unfavorable working condition of parameter fluctuation; then, taking the risk threshold as a constraint, a design parameter feasible region is solved through a reverse mapping algorithm, control stages are divided according to the hydration heat evolution law, and weight coefficients of multiple types of optimization targets are configured; finally, a multi-target optimization is completed in the feasible region to obtain a candidate scheme set, and the final scheme is output after being verified by a construction process constraint; the application adopts a forward design logic to replace a traditional reverse trial-and-error mode, can shorten a design cycle, avoid missing detection of high-risk areas, adapt the output scheme to on-site parameter fluctuation, meet cracking control requirements at different ages, conform to construction conditions, and can be directly applied to engineering.

Description

Technical Field

[0001] This invention relates to the field of computer-aided design technology for building engineering, specifically a multi-objective crack resistance optimization design method for large-volume concrete. Background Technology

[0002] Mass concrete is a common form of core load-bearing structure in engineering projects such as bridge abutments, high-rise building foundations, and hydraulic dams. The heat released during cement hydration creates a temperature gradient within the structure, leading to thermal stress. When this stress exceeds the tensile strength of the concrete, cracks will occur, affecting the structure's durability and long-term safety. As the volume of engineering structures continues to increase, the design difficulty for temperature control and crack resistance continues to rise. Optimization design methods based on numerical simulation are gradually replacing traditional experience-based design and have become a commonly used technique in the industry.

[0003] Currently, most industry practices employ a reverse trial-and-error design process. Designers first formulate initial mix proportions, temperature control, and pouring schemes based on engineering experience. Then, they verify the cracking risk through simulation calculations. If the risk does not meet the standards, parameters are manually adjusted and recalculated, iterating repeatedly until the scheme is satisfactory. This approach involves numerous iterations and adjustments, resulting in a long design cycle. The final scheme quality is significantly influenced by the designer's experience, making it prone to overlooking high-risk areas and failing to achieve a good overall effect. Furthermore, existing optimizations are mostly based on fixed parameters, without fully considering the fluctuations in material properties and environmental conditions at the construction site. Schemes that pass theoretical calculations are prone to exceeding cracking risk standards in practical applications. Moreover, the optimization process does not take into account construction constraints, and some theoretical schemes cannot be directly adopted due to actual site limitations. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a multi-objective crack resistance optimization design method for large-volume concrete. This method replaces the traditional reverse trial-and-error design mode by using a forward design approach that presets regional crack resistance risk thresholds and solves the feasible region of design parameters in reverse. It combines an interval ellipsoidal model to quantify the most unfavorable working conditions of field parameter fluctuations, dynamically configures multi-objective optimization weights according to the hydration heat evolution stage, and embeds a construction process constraint verification link to form a complete crack resistance optimization design process. This method can directly lock in the parameter range that meets crack resistance requirements, reduce the number of manual iterations, and output a solution that adapts to field parameter fluctuations, conforms to the crack control laws at different ages, and ensures that all parameters meet the field construction conditions. It can be directly applied to the crack resistance design of various large-volume concrete structures.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a multi-objective crack resistance optimization design method for large-volume concrete, the specific steps of which are as follows: S1. Based on the constraints and stress characteristics of the structure to be designed, divide it into multiple crack resistance control zones and set the crack risk tolerance threshold for each zone at the corresponding age. S2. Determine the set of design parameters and their range of values, select uncertain parameters to construct an interval ellipsoid model, and determine the most unfavorable working condition for parameter fluctuations; S3. Using the risk tolerance threshold of each region as a constraint, solve the feasible region of design parameters that satisfy all constraints through the parameter-risk inverse mapping algorithm. S4. Divide the control into multiple control stages according to the evolution law of hydration heat, and assign weight coefficients to multiple optimization objectives for each stage; S5. Within the feasible region of the design parameters, perform multi-objective optimization based on the weight coefficients of each stage to obtain a Pareto optimal candidate solution set. S6. Call the construction process constraint rule library, verify the candidate solution set, eliminate out-of-limit solutions, sort and output the final optimized solution.

[0006] Furthermore, in S1, the crack control area is divided into three categories: the base constraint area, the internal core area, and the surface exposed area. These three categories correspond to different constraint levels and temperature load levels, enabling differentiated management by region. The crack risk tolerance threshold is characterized by the stress reserve coefficient, which is the ratio of the tensile strength of the concrete at the same age in the corresponding area to the maximum principal tensile stress in that area. The three categories correspond to different allowable thresholds for the stress reserve coefficient, which can avoid local design redundancy or insufficient risk management caused by using a uniform threshold.

[0007] Furthermore, in S2, the hydration heat rate, thermal conductivity, elastic modulus, and ambient temperature are selected as uncertainty parameters. The interval ellipsoid model is centered on the nominal value of each parameter, with the fluctuation range of each parameter as the half-axis length of the corresponding coordinate axis. The orientation of the ellipsoid is adjusted in combination with the physical correlation between parameters to form an ellipsoidal space that encloses all parameter fluctuation combinations. The ellipsoid range covers most of the actual fluctuation range of the parameters, which can ensure the adaptability of the scheme without excessively increasing the conservatism. The parameter combination corresponding to the boundary of the ellipsoid is taken as the most unfavorable working condition and used for constraint determination in the feasible region solution. Using this as the constraint boundary can ensure that all schemes in the feasible region meet the crack resistance requirements within the normal fluctuation range of parameters.

[0008] Furthermore, before executing S3, the mutual information method is used to quantitatively calculate the impact of each design parameter on the cracking risk. After eliminating weakly correlated parameters with an impact of less than 5%, the feasible region solution and subsequent optimization calculations are then performed. After eliminating weakly correlated parameters, the cumulative contribution of the remaining parameters to the cracking risk remains at a high level, which can reduce the solution dimension and computational load without affecting the calculation accuracy.

[0009] Furthermore, in S3, the parameter-risk inverse mapping algorithm is executed as follows: Within the range of design parameter values, sample points are obtained using the Latin hypercube sampling method. These sample points are then substituted into the most unfavorable operating condition to calculate the cracking risk value for each control region. A Kriging surrogate model that fits the mapping relationship between design parameters and cracking risk is trained. The surrogate model's fitting accuracy meets engineering calculation requirements and can replace finite element simulation for rapid calculation. Using the risk tolerance threshold as the boundary, a bisection method is used sequentially for each design parameter dimension to iteratively search for the critical value of the parameter whose cracking risk equals the tolerance threshold. This gradually shrinks the parameter space. The dimension-by-dimensional search method can quickly lock the boundary range, reducing the number of iterations compared to a full-domain search. When the relative deviation of the feasible region boundary obtained from two consecutive iterations is less than 1%, the iteration converges and the feasible region is output. Within the feasible region, any combination of parameters under the most unfavorable operating condition ensures that the cracking risk of each control region does not exceed the corresponding tolerance threshold, providing a stable safety constraint boundary for subsequent optimization.

[0010] Furthermore, in S4, the control phase is divided into three stages: the temperature rise period, the peak temperature difference period, and the cooling period. The optimization objectives include three categories: crack resistance performance, engineering cost, and construction period. The temperature rise period corresponds to the time from the completion of pouring to the peak internal temperature. With the control of the highest temperature as the core, the crack resistance performance objective has a weight of 0.7 to 0.8, and the remaining weight is allocated to engineering cost and construction period objectives. This can prioritize the control of the peak internal temperature and reduce the constraint stress level in the later cooling stage. The peak temperature difference period is the time from the peak internal temperature to the maximum internal-to-surface temperature difference. With the control of the internal-to-surface temperature difference as the focus, the crack resistance performance objective has a weight of 0.55 to 0.65. This can specifically prevent surface temperature difference cracks and balance the control requirements of internal temperature and surface temperature difference. The cooling period corresponds to the time from the peak internal-to-surface temperature difference to the structural temperature tending to stabilize in the environment. It has both cooling rate control and engineering economy. The crack resistance performance objective has a weight of 0.45 to 0.55. This can reasonably balance engineering investment and construction progress while ensuring the prevention of penetrating cracks.

[0011] Furthermore, in S5, the multi-objective optimization adopts the differential evolution algorithm. The initialization of the algorithm population and the iteration process of each generation are limited to the feasible region of the design parameters. There is no need to set additional constraint penalty terms, which can simplify the algorithm logic and improve the optimization efficiency. When the number of iterations reaches the preset maximum value, or no new non-dominated solution is generated for 20 consecutive generations, the iteration terminates and outputs the Pareto optimal candidate solution set. The dual convergence judgment rule can avoid meaningless iterative calculations while ensuring the distribution of solutions.

[0012] Furthermore, in S6, the construction process constraint rule library includes four types of constraint rules: feasible range of mix proportion, limit value of cooling water pipe layout, range of pouring layer thickness, and adjustable range of pouring temperature. These four types of constraints correspond to the four construction stages: material production, on-site layout, pouring operation, and temperature control implementation, respectively, which can comprehensively cover the main constraints on the implementation of the scheme. During verification, each parameter of the candidate scheme is compared with the corresponding rule limit value, and the scheme with any parameter exceeding the limit value is eliminated. The remaining schemes are sorted according to the multi-objective weighted comprehensive score calculated by the target weight of each stage and then output. The scheme with better comprehensive performance can be directly given by sorting according to the comprehensive score, which reduces the workload of designers in subsequent comparison and selection.

[0013] Compared with existing technologies, this multi-objective crack resistance optimization design method for large-volume concrete has the following advantages: I. This invention replaces the traditional reverse trial-and-error design mode by pre-setting the risk tolerance threshold of each crack resistance control zone and using the forward design logic of reverse solving the feasible domain of design parameters. It eliminates the need for repeated manual adjustment and iterative calculation of parameters and can directly lock in the parameter range that meets the crack resistance requirements of each zone. This shortens the design cycle and avoids the problem of missing high-risk areas that is prone to occur in experience-based design.

[0014] Second, this invention uses a combination design that quantifies adverse working conditions with parameter fluctuations through an interval ellipsoid model, optimizes target weights by matching them in stages, and embeds construction process constraints for verification. This allows the output optimization scheme to adapt to fluctuations in on-site material and environmental parameters, improving the scheme's fault tolerance. The optimization results are more in line with the crack control laws at different ages, and all parameters meet the on-site construction conditions, making it directly applicable to engineering implementation.

[0015] Other advantages, objectives and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination or study, or may be learned from the practice of the invention. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0017] Figure 1 This is a flowchart illustrating the overall steps of the multi-objective crack resistance optimization design method for large-volume concrete according to the present invention. Figure 2 The flowchart for solving the feasible region of design parameters using the parameter-risk inverse mapping method of this invention is shown below. Figure 3 This is a flowchart of the phased multi-objective weight configuration and Pareto scheme generation process of the present invention. Detailed Implementation

[0018] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0019] This embodiment takes the large-volume concrete pier cap of a cross-river bridge as the application object, completes the five steps of this method in sequence, and finally obtains a crack-resistant optimization scheme that can be directly used for on-site construction, thus verifying the feasibility of this method.

[0020] In this embodiment, the foundation has a planar dimension of 32m × 22m and a height of 5m. It uses C35 strength grade concrete, and the foundation is a rock foundation with a high degree of constraint, making it a typical large-volume concrete structure. The overall implementation process is as follows: Figure 1 As shown, the specific execution steps are as follows: First, the crack control zones and risk thresholds were defined. Based on the foundation constraints, internal stress characteristics, and surface exposure of the foundation, the structure was divided into three types of crack control zones. The first type is the foundation-constrained zone, which is the 0.5m height range where the bottom of the foundation contacts the bedrock. This area is most constrained by external factors, and the concrete shrinkage during the cooling stage is limited by the foundation, making it prone to penetrating cracks. The second type is the internal core zone, which is the core area in the middle of the foundation far from the outer boundary. It has the highest degree of hydration heat accumulation and the largest internal temperature peak. The third type is the surface-exposed zone, which is the 0.3m depth range between the top and sides of the foundation. It is directly affected by ambient temperature fluctuations and is prone to surface temperature difference and drying shrinkage cracks. For projects with more complex structural forms, special control zones such as corner constraint zones and areas around openings can be added, with the same classification logic as the above three types of zones.

[0021] Cracking risk is characterized by the stress reserve factor, calculated using the following formula: ; in, This is the stress reserve coefficient; The tensile strength of concrete at the corresponding age is calculated based on the splitting tensile test data of the same batch of concrete and the strength growth law over age. The maximum principal tensile stress in the corresponding region is output from temperature stress simulation calculations. The smaller the value, the higher the risk of structural cracking. Based on the secondary structural safety level of the foundation and referring to general industry requirements for crack-resistant design, allowable cracking risk thresholds are set for the three types of areas at corresponding ages. The base-constrained area has the highest degree of constraint, and a 90-day age threshold is set for this area. The allowable threshold value is 1.3; the temperature load is most significant in the internal core area, and a 90-day age is set. The allowable threshold value is 1.2; the early risk of surface exposure is prominent, and a 14-day age limit is set. The allowable threshold value is 1.15. The threshold value can be flexibly adjusted according to the structural safety level; the higher the safety level, the larger the allowable threshold value.

[0022] After completing the regional division and threshold setting, the range of design parameters involved in the optimization was further determined, and an uncertainty parameter model was constructed. First, the set of design parameters involved in the optimization was determined, covering three dimensions: material mix proportions, temperature control measures, and construction technology. Specifically, it included five items: total cementitious material usage, fly ash content, placement temperature, horizontal spacing of cooling water pipes, and cooling water flow rate. The initial value ranges for each parameter were determined based on commonly used engineering ranges, material performance requirements, and equipment capabilities. Specifically, the total cementitious material usage range was 320~380 kg / m³, the fly ash content range was 20%~40%, the placement temperature range was 26~30℃, the horizontal spacing of cooling water pipes ranged from 1.0~1.5 m, and the cooling water flow rate ranged from 0.5~1.2 m / s.

[0023] Parameters that significantly impact cracking risk and exhibit large on-site fluctuations are selected as uncertainty parameters, specifically including hydration heat rate, thermal conductivity, elastic modulus, and daily average ambient temperature. At the construction site, only the fluctuation range of these parameters can usually be obtained, making it impossible to determine their accurate probability distribution function. Therefore, an interval ellipsoid model is used for quantitative description. The mathematical expression of the interval ellipsoid is as follows: ; In the formula, The vector of uncertain parameters corresponds to four parameters in order: hydration heat rate, thermal conductivity, elastic modulus, and daily average ambient temperature. This is the nominal value vector of each parameter, which is the reference design value of the parameter. The nominal values ​​of hydration heat rate, thermal conductivity, and elastic modulus are from the thermal and mechanical property test report of the same batch of materials, and the nominal value of the ambient daily average temperature is from the local meteorological statistics data of the same period over the past ten years. The matrix is ​​ellipsoidal in shape, with its order matching the number of uncertain parameters. The eigenvalues ​​correspond to the reciprocal square of the fluctuation range of each parameter. The fluctuation range is taken as the sum of the range of experimental data and the bias from engineering experience, ensuring the ellipsoid covers all possible parameter fluctuation ranges. The eigenvector directions correspond to the relevant directions of the parameters, and the matrix elements are adjusted according to the physical correlations between the parameters. For example, the hydration heat rate is positively correlated with the early elastic modulus; a faster hydration rate indicates faster early strength development. Therefore, the off-diagonal elements of the matrix are adjusted to be positive, aligning the ellipsoid with the correlation characteristics of the parameters.

[0024] The resulting ellipsoidal space encompasses all possible combinations of parameter fluctuations. Thirty sets of parameter combinations are uniformly extracted from the ellipsoidal boundary, and each is substituted into the finite element model to calculate the corresponding cracking risk. The parameter combination with the highest risk value is taken as the most unfavorable condition, serving as the unified constraint boundary condition for subsequent feasible region solutions. Using the most unfavorable condition as a constraint ensures that any solution within the feasible region can meet crack resistance requirements within the parameter fluctuation range.

[0025] Before solving for the feasible region, the design parameters are first subjected to sensitivity screening to eliminate weakly correlated parameters, thereby reducing the dimensionality of the solution and improving computational efficiency. The sensitivity calculation uses the mutual information method, and the formula for calculating mutual information is as follows: in, For design parameters Risk of cracking Mutual information value between them Let the joint probability density of the two be... and These are their respective marginal probability densities, which are calculated using the kernel density estimation method. The kernel density estimation uses a Gaussian kernel function, and the bandwidth is determined by the Silverman criterion, which is a common method for processing sample probability densities in the engineering field. , The mutual information value represents the differential element of the corresponding variable. A larger mutual information value indicates a stronger influence of that parameter on cracking risk. The proportion of each parameter's mutual information value to the total mutual information value is calculated, and weakly correlated parameters with an influence of less than 5% are removed. The 5% threshold is determined based on the engineering calculation accuracy requirements. Parameters below this threshold have an overall impact of less than 1% on cracking risk and can be ignored. Removing them has minimal impact on calculation accuracy but significantly reduces the computational load in subsequent solutions. In this embodiment, the mutual information proportions of the five design parameters are all higher than the threshold, and all are retained for subsequent calculations.

[0026] Next, the feasible region of the design parameters is solved in reverse, using a parameter-risk inverse mapping algorithm, such as... Figure 2 As shown, it is specifically divided into two stages: surrogate model training and boundary iterative shrinkage.

[0027] The first stage is surrogate model training. Within the initial value range of the design parameters, sample points are extracted using the Latin hypercube sampling method. The number of samples is 10 times the parameter dimension; in this example, there are 5-dimensional parameters, resulting in 50 sets of sample points. Latin hypercube sampling ensures that the samples are evenly distributed across all parameter dimensions, covering the entire parameter space with a smaller sample size, making it more efficient than random sampling. For each set of sample points, the parameter conditions of the aforementioned most unfavorable working condition are substituted, and the stress reserve coefficients of the three control regions are calculated through finite element simulation to obtain the corresponding cracking risk values. Using the design parameters of all sample points as input and the cracking risk values ​​of each region as output, the Kriging surrogate model is trained to fit the nonlinear mapping relationship between the design parameters and the cracking risk. The Kriging surrogate model has both global trend fitting and local deviation correction capabilities, making it suitable for handling highly nonlinear mapping problems in engineering. After the model training is completed, the coefficient of determination is used to verify the accuracy. The coefficient of determination ranges from 0 to 1. The closer it is to 1, the higher the model fitting accuracy. In engineering, the coefficient of determination is generally required to be no less than 0.95. At this time, the error of the model replacing the simulation is within an acceptable range, and the model is judged to be qualified. Otherwise, additional sample points are added and the model is retrained.

[0028] The second stage is boundary iteration and contraction. Using the crack risk tolerance threshold for each region as the constraint boundary, the critical value is iteratively searched for each design parameter dimension using a bisection method. When searching a single parameter dimension, the remaining parameters are fixed as nominal values. The upper and lower limits of the current parameter's interval are used as the initial endpoints of the iteration. The midpoint is used to calculate the corresponding crack risk value. The interval range is narrowed based on the relationship between the risk value and the threshold. This iteration is repeated until the deviation between the calculated risk value and the tolerance threshold is less than 0.001. This deviation threshold corresponds to the engineering-acceptable calculation accuracy, balancing calculation efficiency and result accuracy. The parameter value at this point is the critical boundary of the current dimension. The critical boundaries of all parameter dimensions together form the initial feasible region. Since the initial boundary obtained by the dimension-by-dimensional search is rectangular, while the actual feasible region is irregular in shape, additional sampling and verification are needed at the boundary of the initial feasible region. If there are regions that do not meet the risk constraints, the boundary is further contracted. When the relative deviation of the feasible region boundary obtained from two consecutive iterations is less than 1%, the iteration is considered converged, and the final feasible region of the design parameters is output. Within the final feasible region, under the most unfavorable working conditions, the cracking risk of any combination of design parameters does not exceed the corresponding allowable threshold in all control areas.

[0029] After obtaining the feasible region, multi-objective weights are configured in stages. For example... Figure 3 As shown, based on the general laws of heat release and cracking risk evolution of large-volume concrete, and combined with engineering measured statistical data, the entire age of concrete from pouring to temperature stabilization is divided into three cracking control stages. For the main control risk type of each stage, weight coefficients of three optimization objectives, namely crack resistance performance, engineering cost, and construction period, are configured respectively.

[0030] The first stage is the temperature rise period, corresponding to the time from the completion of pouring to the peak internal temperature, which in this implementation is approximately 0-7 days after pouring. During this stage, the cement hydration reaction is intense, the internal heat release rate is greater than the surface heat dissipation rate, and the temperature continues to rise. The main risk is that the maximum internal temperature is too high, leading to an excessive cooling rate later. Therefore, crack resistance control is the core focus, with the target weight of crack resistance set at 0.75, engineering cost weight at 0.15, and construction cost weight at 0.1.

[0031] The second stage is the peak temperature difference period, which roughly corresponds to 7 to 14 days after pouring. At this time, the internal hydration heat release rate slows down and the temperature gradually enters the plateau stage. The surface cools down faster due to the heat dissipation of the environment, and the internal and external temperature difference continues to expand. The risk of surface cracking is the most prominent. Therefore, the focus is on the control of internal and external temperature difference. The weight of the crack resistance target is set at 0.6, the engineering cost weight is 0.25, and the construction cost weight is 0.15.

[0032] The third stage is the cooling period, corresponding to the time from the peak of the internal surface temperature difference to the period when the structural temperature tends to stabilize in the environment. In this implementation, this period is approximately 14 to 90 days after pouring. During this stage, the heat release from hydration is basically completed, and the structure as a whole slowly dissipates heat and cools down. The constraint effect of the base gradually becomes apparent. The main risk is through-cage cracks caused by excessively rapid cooling. At this time, the temperature change tends to be gradual, and the project economy and construction efficiency can be appropriately balanced. The target weight of crack resistance is set at 0.5, the weight of project cost is 0.3, and the weight of construction time is 0.2.

[0033] The weight values ​​are determined based on the importance of the main control risks at each stage, ensuring that the optimization results match the crack control requirements at different ages and avoiding redundancy or insufficient risk in local stage designs caused by fixed weights.

[0034] After weight configuration, multi-objective optimization is performed within the feasible region of the design parameters. This embodiment uses a differential evolution algorithm for calculation. During algorithm population initialization, the parameter values ​​of all individuals are limited to the feasible region to avoid generating invalid solutions. The population size is set to 80, a common configuration for differential evolution algorithms with 5-dimensional parameters. During iteration, each individual corresponds to a set of design parameter combinations. Based on the aforementioned phased weight coefficients, the weighted comprehensive score of the multi-objective optimization over the entire cycle is calculated, with the optimal comprehensive score as the evolutionary direction. When the number of iterations reaches a preset 100, or no new non-dominated solution is generated for 20 consecutive generations, the algorithm is considered converged, the iteration terminates, and a uniformly distributed Pareto optimal candidate solution set is output. The convergence threshold of 20 generations refers to the general settings for multi-objective optimization, which can prevent the algorithm from getting trapped in local optima too early while ensuring convergence efficiency. All solutions in the candidate solution set satisfy the crack resistance risk constraint. Different solutions focus on improving crack resistance reserves, reducing engineering costs, or shortening the construction period, and can be selected according to the actual needs of the project.

[0035] Finally, the construction process constraints are verified and the solution is output. A construction process constraint rule library is pre-built. The rule library is compiled based on the on-site equipment capabilities, material supply conditions, and industry construction specifications, and includes four categories of constraint rules. The first category is the feasible range of mix proportions. The dosage of cementitious materials and admixtures must conform to the conventional concrete mix proportion design range to avoid theoretically optimal but unsuitable mix proportions for production. The second category is the limit value for cooling water pipe layout. The spacing and diameter of water pipes must match the conventional construction specifications and operating space requirements on site. Too small a spacing will increase construction difficulty, while too large a spacing will not guarantee the cooling effect. The third category is the range of pouring layer thickness. The layer thickness must be adapted to the effective vibration depth of the vibrating equipment, usually not exceeding 1.25 times the length of the vibrator. This limit comes from the general requirements of concrete construction technology and can ensure the compaction of concrete. The fourth category is the adjustable range of placement temperature. The placement temperature must be within the adjustable range achievable by the on-site mixing and transportation system to avoid temperature requirements that cannot be achieved on site.

[0036] The rule base is invoked to validate each Pareto candidate solution set, comparing each parameter with its corresponding rule limit, and eliminating solutions where any parameter exceeds the limit. For the remaining solutions that meet the construction requirements, a multi-objective weighted comprehensive score is calculated according to the phased objective weights. The solutions are then sorted from highest to lowest score, and the top-ranked solution is selected as the final optimized design solution. Simultaneously, 3 to 5 alternative solutions can be output for designers to compare.

[0037] This embodiment, by fully implementing the above process, yields an optimized solution that eliminates the need for repeated manual parameter adjustments, significantly shortening the design cycle compared to traditional reverse trial-and-error methods. Furthermore, all parameters meet the requirements of on-site construction conditions. Even under the most unfavorable parameter fluctuations, the solution ensures that the cracking risk in each area meets the standards, demonstrating stronger fault tolerance than traditional deterministic designs and adaptability to complex on-site conditions.

[0038] This method is not limited to bridge abutment structures, but is also applicable to the crack resistance optimization design of various large-volume concrete structures such as high-rise building raft slabs, hydraulic engineering dam bodies, and large equipment foundations. The region division, threshold settings, and parameter ranges can be adjusted according to the constraint characteristics and design requirements of different structures.

[0039] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A multi-objective crack resistance optimization design method for large-volume concrete, characterized in that, The specific steps of this method are as follows: S1. Based on the constraints and stress characteristics of the structure to be designed, divide it into multiple crack resistance control zones and set the crack risk tolerance threshold for each zone at the corresponding age. S2. Determine the set of design parameters and their range of values, select uncertain parameters to construct an interval ellipsoid model, and determine the most unfavorable working condition for parameter fluctuations; S3. Using the risk tolerance threshold of each region as a constraint, solve the feasible region of design parameters that satisfy all constraints through the parameter-risk inverse mapping algorithm. S4. Divide the control into multiple control stages according to the evolution law of hydration heat, and assign weight coefficients to multiple optimization objectives for each stage; S5. Within the feasible region of the design parameters, perform multi-objective optimization based on the weight coefficients of each stage to obtain a Pareto optimal candidate solution set. S6. Call the construction process constraint rule library, verify the candidate solution set, eliminate out-of-limit solutions, sort and output the final optimized solution.

2. The multi-objective crack resistance optimization design method for large-volume concrete according to claim 1, characterized in that, In S1, the crack control area is divided into three categories: the base confinement area, the internal core area, and the surface exposed area. The crack risk tolerance threshold is characterized by the stress reserve coefficient, which is the ratio of the tensile strength of the concrete at the same age in the corresponding area to the maximum principal tensile stress in that area. The three types of areas correspond to different stress reserve coefficient tolerance thresholds.

3. The multi-objective crack resistance optimization design method for large-volume concrete according to claim 1, characterized in that, In S2, the hydration heat rate, thermal conductivity, elastic modulus, and ambient temperature are selected as uncertainty parameters. The interval ellipsoid model is centered on the nominal value of each parameter, and the fluctuation range of each parameter is taken as the half-axis length of the corresponding coordinate axis. The orientation of the ellipsoid is adjusted in combination with the physical correlation between parameters to form an ellipsoid space that encloses all parameter fluctuation combinations. The parameter combination corresponding to the ellipsoid boundary is taken as the most unfavorable working condition and used for constraint determination in the feasible region solution.

4. The multi-objective crack resistance optimization design method for large-volume concrete according to claim 1, characterized in that, Before executing S3, the mutual information method is used to quantitatively calculate the impact of each design parameter on the cracking risk. After eliminating weakly correlated parameters with an impact of less than 5%, the feasible region solution and subsequent optimization calculations are then performed.

5. The multi-objective crack resistance optimization design method for large-volume concrete according to claim 1, characterized in that, In S3, the parameter-risk inverse mapping algorithm is executed as follows: within the range of design parameter values, sample points are obtained using the Latin hypercube sampling method, and the cracking risk value of each sample point corresponding to each control area is calculated by substituting it into the most unfavorable working condition. A Kriging surrogate model that fits the mapping relationship between design parameters and cracking risk is then trained. Using the risk tolerance threshold as the boundary, the bisection method is used sequentially for each design parameter dimension to iteratively search for the critical value of the parameter where the cracking risk equals the tolerance threshold, thereby gradually shrinking the parameter space. When the relative deviation of the feasible region boundary obtained by two consecutive iterations is less than 1%, the iteration converges and the feasible region is output; under the most unfavorable working condition, the cracking risk of each control area in any combination of parameters within the feasible region does not exceed the corresponding allowable threshold.

6. The multi-objective crack resistance optimization design method for large-volume concrete according to claim 1, characterized in that, In S4, the control phase is divided into three stages: the temperature rise period, the peak temperature difference period, and the cooling period. The optimization objectives include three categories: crack resistance performance, engineering cost, and construction period. The temperature rise period corresponds to the time from the completion of pouring to the peak internal temperature, with crack resistance performance accounting for 0.7 to 0.8% of the target weight, and the remaining weight is allocated to engineering cost and construction period. The peak temperature difference period is the time from the peak internal temperature to the maximum internal surface temperature difference, with crack resistance performance accounting for 0.55 to 0.65% of the target weight. The cooling period corresponds to the time from the peak internal surface temperature difference to the time when the structural temperature tends to stabilize, with crack resistance performance accounting for 0.45 to 0.55% of the target weight.

7. The multi-objective crack resistance optimization design method for large-volume concrete according to claim 1, characterized in that, In S5, the multi-objective optimization adopts the differential evolution algorithm. The initialization of the algorithm population and the iteration process of each generation are limited to the feasible domain of the design parameters. When the number of iterations reaches the preset maximum value, or no new non-dominated solution is generated for 20 consecutive generations, the iteration terminates and outputs the Pareto optimal candidate solution set.

8. The multi-objective crack resistance optimization design method for large-volume concrete according to claim 1, characterized in that, In S6, the construction process constraint rule library includes four types of constraint rules: feasible range of mix proportion, limit value of cooling water pipe layout, range of pouring layer thickness, and adjustable range of pouring temperature. During verification, each parameter of the candidate scheme is compared with the corresponding rule limit value. Schemes with any parameter exceeding the limit value are eliminated. The remaining schemes are sorted and output according to the multi-objective weighted comprehensive score calculated by the target weight of each stage.

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