Prediction method for compression resistance of self-adaptive shrinkage compensation self-compacting concrete

Abstract

The invention discloses a method for predicting compression resistance of self-adaptive shrinkage compensation self-compacting concrete, and belongs to the technical field of building materials. The method comprises the steps of firstly collecting environment and raw material data, and extracting key parameters through feature engineering; then constructing an integrated learning prediction model fusing a support vector machine and an adaptive lifting algorithm; finally, the mixing amount of intelligent materials such as a water-retaining agent and a shrinkage reducing agent is dynamically optimized based on the real-time environmental parameters, and self-adaptive design of the mix proportion is achieved. The method can accurately predict the compressive strength and the working performance of the concrete in different environments, effectively coordinate the mechanical properties and the working performance, and significantly reduce the test period and the void risk.

Description

Technical Field

[0001] This invention belongs to the field of building materials technology, and specifically relates to an adaptive method for predicting the compressive strength of shrinkage-compensated self-compacting concrete. Background Technology

[0002] The development of concrete-filled steel tube arch bridges is rapid, and they offer numerous advantages: versatility, allowing for consideration of various spans; high load-bearing capacity, increasing the load-bearing capacity of the arch ribs to meet diverse engineering needs; strong adaptability, as the arch rib structure minimizes horizontal thrust at the arch foot, making them suitable for use in challenging soil conditions; and aesthetically pleasing designs, with concrete-filled steel tube arch bridges offering diverse and attractive forms, sometimes even serving as scenic bridges in designated areas. Self-compacting concrete, due to its excellent fluidity and vibration-free properties, is widely used in the pouring construction of concrete-filled steel tube arch bridges. Ideally, it fills the cavity under its own weight and bonds tightly to the inner wall of the steel tube, forming a synergistic composite structure. The combined effect of the steel tube and concrete can achieve a synergistic effect greater than the sum of its parts ("1+1>2").

[0003] Self-compacting concrete is a special type of concrete with high fluidity and excellent anti-segregation properties. During pouring, it can flow and fill every corner of the formwork by its own weight and fully wrap the reinforcing steel without relying on external vibration for compaction. This ensures uniform and dense structure, avoids the defects that may be caused by traditional vibration, improves construction efficiency, and reduces noise. It is especially suitable for complex engineering structures, such as the core tube of high-rise buildings, precast components, or in-tube casting of arch bridges.

[0004] Adjusting the performance of self-compacting concrete is mainly achieved by adjusting the water-cement ratio, sand ratio, and admixture dosage. These measures can effectively regulate the workability of concrete. However, a problem arises: its mechanical properties are inversely proportional to its workability. Therefore, it is necessary to coordinate its mechanical and workability properties, ensuring that the workability of self-compacting concrete meets the standard of not clogging pipes while its mechanical properties also meet design requirements. However, this involves a significant workload, and each test block requires 28 days of curing, resulting in a long testing cycle and substantial time, manpower, and material resources. This is difficult to meet the needs of construction sites.

[0005] In summary, there is an urgent need to develop a new method for predicting the compressive strength of self-compacting concrete. This method should not only ensure that the designed concrete mix proportions meet the requirements of long-distance, high-lift pumping construction, but also adapt to complex external environmental conditions. By intelligently controlling its workability maintenance, hydration process, and shrinkage compensation behavior, it can achieve full-process volume stability from the plastic stage to the hardening stage, thereby significantly reducing or even eliminating void defects. Summary of the Invention

[0006] The purpose of this invention is to propose an adaptive method for predicting the compressive strength of shrinkage-compensated self-compacting concrete, and to solve the problem of how to achieve real-time, dynamic, and adaptive design of the mix proportion of self-compacting concrete. Based on real-time environmental data and raw material conditions, the optimal mix proportion can be generated before construction through AI prediction and optimization, thereby ensuring that the concrete performance meets the requirements of pumping construction and achieves the specified strength and volume stability in complex and variable environments.

[0007] By extracting features from production data related to concrete raw materials through feature engineering and integrating two ensemble learning methods, the compressive strength of shrinkage-compensated self-compacting concrete can be accurately and quickly predicted.

[0008] The technical solution of the present invention is as follows:

[0009] An adaptive method for predicting the compressive strength of shrinkage-compensated self-compacting concrete includes the following steps:

[0010] S1. Collect real-time temperature T and humidity RH in the construction area, and combine them with meteorological data of the project location and construction period forecasts to determine the expected range of T and RH and their upper and lower threshold limits.

[0011] S2. Delete samples with missing or duplicate 28-day compressive strength attributes in the concrete raw material production data; perform outlier analysis on the first type of data attributes of the remaining samples, and delete the sample if more than 3 attribute values ​​are outliers in the same sample; fill in missing values ​​in the first type of data with 0; perform dummy variable encoding on the production condition type variables in the second type of data to obtain the cleaned modeling dataset.

[0012] S3. The cleaned data is Z-score standardized to eliminate dimensions; features significantly related to 28-day compressive strength are extracted using Pearson correlation coefficient, and the amounts of fine sand, medium sand, and coarse sand are combined into fine aggregate amount, the amounts of small stone and medium stone are combined into coarse aggregate amount, and the amounts of water and recycled water are combined into water amount. The remaining features are kept as is. Finally, all feature data are normalized to form a modeling feature set.

[0013] S4. Use ε-SVR to relax variables. , The regularization penalty coefficient C balances model complexity and training error. The features are mapped to a high-dimensional space using the RBF kernel function. The 28-day compressive strength and 60-day shrinkage rate are simultaneously regressed within the ε-insensitive band. Cross-validation is used to optimize the hyperparameters C, γ, and ε so that the coefficient of determination R² on the test set is greater than 0.85 and the root mean square error RMSE is lower than a preset threshold. This yields the SVR surrogate model for subsequent mix ratio optimization.

[0014] S5. Using the ε-SVR surrogate model obtained in step S4 as the prediction engine, run it in a programmable environment simulation chamber at real-time T and RH, with water-retaining agent x1, shrinkage-reducing agent x2, and phase change material microcapsules x3 as decision variables, construct a multi-objective optimization function, using a weighted sum form:

[0015]

[0016] Where Xs=[x1, x2, x3] is the decision variable vector, x1, x2, x3 represent the dosage of water-retaining agent, shrinkage-reducing agent, and phase change material, respectively, T and RH are the real-time input temperature and humidity, and f 6h f is the prediction function for the 6-hour collapse expansion. 28d Let w1 and w2 be the prediction function for 28-day compressive strength, and w1 + w2 = 1, where w1 and w2 are the weighting coefficients.

[0017] The optimal Xs=[x1, x2, x3] was obtained by solving the formula. The mixture was then tested and molded according to this ratio. The slump expansion at 6 hours, the compressive strength at 28 days, and the shrinkage rate at 60 days were verified in an environmental chamber. The measured data were fed back into the sample library and the model was retrained periodically to form a closed loop.

[0018] Furthermore, the standardization described in step S3 is performed using the following formula:

[0019] ;

[0020] in, The mean of the sample; For the i-th observation; The standard deviation is the sample standard deviation.

[0021] The Pearson correlation coefficient is calculated using the following formula:

[0022] ;

[0023] Where r is the sample Pearson correlation coefficient, with a value of [-1, 1], and the closer it is to 1, the stronger the linear correlation; n is the sample size; and the absolute value... The standard deviation is the sample standard deviation. This is the sample mean; Let be the i-th observation.

[0024] Furthermore, step S4 specifically includes:

[0025] S41. Model Structure:

[0026] Using ε-SVR, slack variables are introduced. , And the regularization penalty coefficient C, simultaneously regressing 28-day compressive strength and 60-day shrinkage within the ε-insensitive band; the original features are processed by the RBF kernel function:

[0027] ;

[0028] Mapping to a high-dimensional space to complete nonlinear fitting;

[0029] S42. Optimization Objective:

[0030] The objective function to be optimized is:

[0031] ;

[0032] Where w is the weight vector; C is the regularization penalty coefficient, used to balance model complexity and training error; and These are slack variables;

[0033] The constraints are as follows:

[0034] ;

[0035] in, For the weight vector, It is a bias term. and These are slack variables, allowing sample points to deviate. Insensitive zone It is a penalty parameter used to balance model complexity and training error. It is an insensitive loss parameter. It is a kernel function that maps the input to a high-dimensional feature space. It is the first The true value of each sample It is the number of training samples;

[0036] S43. SVR Prediction Function:

[0037] ;

[0038] ;

[0039] S44. Prediction accuracy is quantified using regression evaluation indicators:

[0040] ;

[0041] ;

[0042] The calculated model must satisfy R 2 > 0.85 and RMSE is below the preset threshold;

[0043] S45. Hyperparameter optimization:

[0044] Perform 5-fold grid cross-validation on (C, γ, ε) and use R² and RMSE as convergence criteria to obtain the optimal parameter combination;

[0045] S46. Model Output:

[0046] An ε-SVR surrogate model was obtained that can simultaneously output 28-day compressive strength and 60-day shrinkage rate, which can be directly used for subsequent multi-objective optimization of mix proportions.

[0047] Furthermore, the multi-objective optimization function in step S5 satisfies the following conditions: 28-day compressive strength ≥ design value, initial slump expansion ≥ 650 mm, 0.05% ≤ x1 ≤ 0.3%, 1% ≤ x2 ≤ 3.4%, and 2% ≤ x3 ≤ 8%.

[0048] The entire design process forms a closed loop through rigorous verification and adjustments. The optimized mix proportions are placed in an environmental simulation chamber to reproduce actual construction conditions for verification testing, evaluating whether the changes in workability over time and strength development match the model predictions. If deviations exist, fine-tuning is performed, and the new data generated from this experiment is fed back into the model to continuously optimize its predictive accuracy. This step not only confirms the feasibility of the theoretical design but also endows the entire system with self-learning and continuous improvement capabilities, ensuring the high reliability and advanced nature of the invention in practical applications.

[0049] The workability of concrete largely depends on the proper control of admixtures. The composition, type, and concentration of the water-reducing agent mother liquor must meet specific requirements to ensure excellent mechanical and workability. By controlling the slump spread to above 650mm 6 hours after mixing, the concrete maintains good pumpability after being transported to the construction site, thereby reducing the risk of pumping pipeline blockage and effectively ensuring the safety and stability of structural construction.

[0050] The technical solution provided by this invention can bring the following beneficial effects:

[0051] (1) Achieving precise environmental adaptability and fundamentally improving the volume stability of concrete. By pre-defining the threshold range of environmental parameters and establishing a response model of intelligent material dosage and performance output, the mix design of this invention is no longer fixed. It can accurately calculate the required intelligent component dosage for specific high-temperature, dry or humid environments, thereby actively counteracting the main shrinkage driving factors in that environment (such as rapid evaporation of moisture and overheating of hydration), significantly reducing the risk of voids caused by volume deformation incompatibility, and ensuring the integrity of the structure.

[0052] (2) Imparting "dynamic self-adaptive" intelligent characteristics to concrete, ensuring workability throughout the construction process. The core innovation of this invention lies in the fact that the dosage of intelligent materials is a function of environmental parameters. This means that the concrete mix proportion has "dynamic self-adaptive" capabilities. Under high-temperature conditions, the system will automatically increase the dosage of water-retaining agent or phase change material microcapsules to maintain workability; under non-high-temperature conditions, there is no need to use excessive amounts. This intelligent response ensures that the concrete maintains excellent and stable rheological properties throughout the entire construction window from discharge to pouring, effectively avoiding pump blockage or incomplete pouring caused by excessive loss of workability.

[0053] (3) Non-numerical production process experience and knowledge are transformed into features that can be identified and quantified by machine learning models, enabling the models to accurately capture the quantitative impact of different production conditions on concrete performance. The entire process organically combines knowledge from the field of materials science with data statistics techniques, forming a set of repeatable and verifiable data governance standards. Its ultimate beneficial effect is reflected in directly driving the efficiency improvement of downstream applications: the reliability, accuracy, and guiding value of strength prediction models, mix proportion optimization schemes, or quality control strategies built based on high-quality preprocessed data are substantially enhanced, providing solid and reliable data support for the intelligent production, refined quality control, and cost optimization of self-compacting concrete. Attached Figure Description

[0054] Figure 1 This is a flowchart of an adaptive shrinkage-compensated self-compacting concrete compressive strength prediction method provided in an embodiment of this application.

[0055] Figure 2 This is the predictive compressive strength model of the present invention. Detailed Implementation

[0056] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0057] The example uses a series of concrete production data from China Railway Group. To accurately predict the compressive strength of self-compacting concrete produced subsequently, this example provides an adaptive method for predicting the compressive strength of shrinkage-compensated self-compacting concrete. This method includes the following steps:

[0058] Step 1:

[0059] The environment is measured, and real-time temperature data (T) and humidity data (RH) of the construction area are collected. Then, by collecting meteorological data and construction period forecasts of the project site, the expected range of temperature and humidity changes is determined, and the upper and lower limits of the thresholds are determined.

[0060] Step Two:

[0061] Production data related to concrete raw materials that contained missing or duplicate 28-day compressive strength attributes were deleted. Outlier analysis was performed on the deleted data using statistical methods. For each production data sample, if more than three attribute values ​​in the first category were outliers, that data sample was deleted. Missing first-category attributes were represented by 0. Dummy variables were used to encode the typological variables of production conditions in the second category of production data, resulting in the cleaned modeling dataset.

[0062] Step 3:

[0063] The raw material data of self-compacting concrete is preprocessed. The obtained data is standardized to eliminate the influence of dimensions. Then, the Pearson correlation coefficient is input. Features that are significantly correlated with 28-day compressive strength are extracted through the Pearson correlation coefficient. Cement dosage, water-reducing agent dosage, etc. are directly retained as features. Other attributes are combined according to the Pearson correlation coefficient and in accordance with industry experience. Fine sand dosage, medium sand dosage, and coarse sand dosage are combined into fine aggregate dosage, small stone dosage and medium stone dosage are combined into coarse aggregate dosage, and water dosage and recycled water dosage are combined into water dosage. The remaining features are left as is. Finally, all feature data are normalized to form a modeling feature set.

[0064] standardization:

[0065] ;

[0066] ;

[0067] in, The mean of the sample; For the i-th observation; This represents the sample standard deviation.

[0068] Pearson correlation coefficient analysis:

[0069] ;

[0070] Where r is the sample Pearson correlation coefficient, with a value of [-1, 1], and the closer it is to 1, the stronger the linear correlation; n is the sample size; and the absolute value... The standard deviation is the sample standard deviation. This is the sample mean; Let be the i-th observation.

[0071] Step 4: Build and train the ε-SVR agent model:

[0072] 1. Model Structure:

[0073] Using ε-SVR, slack variables are introduced. , And the regularization penalty coefficient C, simultaneously regressing 28-day compressive strength and 60-day shrinkage within the ε-insensitive band; the original features are processed by the RBF kernel function:

[0074] ;

[0075] Mapping to a high-dimensional space completes nonlinear fitting.

[0076] 2. Optimization Objective:

[0077] The objective function to be optimized is:

[0078] ;

[0079] Where w is the weight vector; C is the regularization penalty coefficient, used to balance model complexity and training error; and These are slack variables.

[0080] The constraints are as follows:

[0081] ;

[0082] in, For the weight vector, It is a bias term. and These are slack variables, allowing sample points to deviate. Insensitive zone It is a penalty parameter used to balance model complexity and training error. It is an insensitive loss parameter. It is a kernel function that maps the input to a high-dimensional feature space. It is the first The true value of each sample It represents the number of training samples.

[0083] 3. SVR prediction function:

[0084] ;

[0085] ;

[0086] 4. Prediction accuracy is quantified using regression evaluation indicators:

[0087] ;

[0088] ;

[0089] The calculated model must satisfy R 2 > 0.85 and RMSE is lower than the preset threshold.

[0090] 5. Hyperparameter optimization:

[0091] Perform 5-fold grid cross-validation on (C, γ, ε) and obtain the optimal parameter combination using the above R² and RMSE as convergence criteria.

[0092] 6. Model Output:

[0093] An ε-SVR surrogate model was obtained that can simultaneously output 28-day compressive strength and 60-day shrinkage rate, which can be directly used for subsequent multi-objective optimization of mix proportions.

[0094] Step 5:

[0095] Using the ε-SVR surrogate model generated in step four, the compressive strength of self-compacting concrete was predicted based on the test set data. The model utilized existing laboratory conditions and external environment, and then predicted compressive performance based on the input mix proportions. Finally, all mix proportions were poured and cured for 28 days to conduct compressive performance tests. The test results were compared with the predicted results to verify the accuracy of the prediction model.

[0096] Using the ε-SVR surrogate model generated in step four, the strength of the concrete mix design tested in the laboratory is predicted:

[0097] Experimental Design and Data Acquisition: Experimental points were designed using a full factorial experiment or Latin hypercube sampling method in a programmable environment simulation chamber. Variables included:

[0098] Input characteristics: environmental variables, temperature T, humidity RH.

[0099] Material variables: water-retaining agent, dosage range 0.05%-0.3%; shrinkage-reducing agent, dosage range 1%-3.4%; phase change material microcapsules, dosage range 2%-8%; dosage is calculated as a percentage of the mass of cementitious materials. Record the baseline mix proportion parameters (such as water-cement ratio and sand ratio).

[0100] Output target: Measured concrete properties, including initial slump flow, slump flow after 6 hours, T500 time, 28-day compressive strength, and 60-day shrinkage rate.

[0101] Based on the absolute volume method, a static benchmark mix proportion was designed according to specifications to meet the minimum performance requirements under standard curing conditions. Specific parameters are: total amount of cementitious materials (kg / m³). 3 The following parameters were used: water-cement ratio (%), sand ratio (%), and water-reducing agent dosage (%). These parameters served as the benchmark for performance comparison and the starting point for dynamic optimization calculations.

[0102] This step is the core of achieving adaptive ratio calculation.

[0103] Establish an optimized mathematical model:

[0104] Let vector X S =[x1, x2, x3], representing the dosage of water-retaining agent, shrinkage-reducing agent, and phase change material, respectively.

[0105] Defined as a multi-objective weighted sum:

[0106] ;

[0107] Xs=[x1, x2, x3] is the decision variable vector, where x1, x2, and x3 represent the dosages of water-retaining agent, shrinkage-reducing agent, and phase change material, respectively; T and RH are real-time environmental parameters (temperature and humidity); f 6h f is the prediction function for the 6-hour collapse expansion. 28d The function for predicting 28-day compressive strength is denoted by w1 and w2, which are weighting coefficients, and w1 + w2 = 1. T and RH are real-time input environmental parameters.

[0108] Constraints:

[0109] (Strength constraints);

[0110] (Initial working constraints);

[0111] (Upper and lower limits of smart material doping).

[0112] Execute optimization algorithm:

[0113] Based on the dynamic mix proportions output above, trial mixing was carried out, and in an environmental simulation chamber, the temperature was set to the real-time environmental parameter T to verify the workability loss, shrinkage, and strength of the concrete over time.

[0114] The new data points obtained in this validation experiment are used as new samples and added to the original database of the procedure. The SVR model is retrained periodically using the updated database. This closed-loop mechanism ensures that the prediction model can continuously adapt to new materials and new environmental patterns, and its prediction accuracy and application scope continue to expand and improve over time.

[0115] The method will be described in detail below through specific embodiments to verify its rationality and accuracy.

[0116]

[0117] The workability and mechanical properties of the prepared concrete were tested by various external factors. The prepared concrete met the design requirements and met the pumping requirements. The results are shown in the table below, using the above raw materials and environmental parameters as inputs for prediction.

[0118]

[0119] As can be seen from the table above, the predicted concrete mix proportions are relatively accurate in terms of workability and mechanical properties compared with the measured results. The predicted results for workability (spreadability index) are between 0.1% and 1.1%, the predicted results for mechanical properties (compressive strength) are between 0.1% and 0.3%, and the predicted results for 60-day shrinkage rate are less than 14.2%.

[0120] The embodiments described above are merely illustrative of the technical solutions of the present invention and are not intended to limit the present invention. Those skilled in the art can make various reasonable changes and modifications to the above embodiments without departing from the essential spirit of the present invention and the scope of protection defined by the claims. The scope of protection of the present invention should be determined by the claims and covers all equivalent substitutions and obvious variations.

Claims

1. An adaptive method for predicting the compressive strength of shrinkage-compensated self-compacting concrete, characterized in that, Includes the following steps: S1. Collect real-time temperature T and humidity RH in the construction area, and combine them with meteorological data of the project location and construction period forecasts to determine the expected range of T and RH and their upper and lower threshold limits. S2. Delete samples with missing or duplicate 28-day compressive strength attributes in the concrete raw material production data; perform outlier analysis on the first type of data attributes of the remaining samples, and delete the sample if more than 3 attribute values ​​are outliers in the same sample; fill in missing values ​​in the first type of data with 0; perform dummy variable encoding on the production condition type variables in the second type of data to obtain the cleaned modeling dataset. S3. The cleaned data is Z-score standardized to eliminate dimensions; features significantly related to 28-day compressive strength are extracted using Pearson correlation coefficient, and the amounts of fine sand, medium sand, and coarse sand are combined into fine aggregate amount, the amounts of small stone and medium stone are combined into coarse aggregate amount, and the amounts of water and recycled water are combined into water amount. The remaining features are kept as is. Finally, all feature data are normalized to form a modeling feature set. S4. Use ε-SVR to relax variables. , The regularization penalty coefficient C balances model complexity and training error. The features are mapped to a high-dimensional space using the RBF kernel function. The 28-day compressive strength and 60-day shrinkage rate are simultaneously regressed within the ε-insensitive band. Cross-validation is used to optimize the hyperparameters C, γ, and ε so that the coefficient of determination R² on the test set is greater than 0.85 and the root mean square error RMSE is lower than a preset threshold. This yields the SVR surrogate model for subsequent mix ratio optimization. S5. Using the ε-SVR surrogate model obtained in step S4 as the prediction engine, run it in a programmable environment simulation chamber at real-time T and RH, with water-retaining agent x1, shrinkage-reducing agent x2, and phase change material microcapsules x3 as decision variables, construct a multi-objective optimization function, using a weighted sum form: ； Where Xs=[x1, x2, x3] is the decision variable vector, x1, x2, x3 represent the dosage of water-retaining agent, shrinkage-reducing agent, and phase change material, respectively, T and RH are the real-time input temperature and humidity, and f 6h f is the prediction function for the 6-hour collapse expansion. 28d Let w1 and w2 be the prediction function for 28-day compressive strength, and w1 + w2 = 1, where w1 and w2 are the weighting coefficients. The optimal Xs=[x1, x2, x3] was obtained by solving the formula. The mixture was then tested and molded according to this ratio. The slump expansion at 6 hours, the compressive strength at 28 days, and the shrinkage rate at 60 days were verified in an environmental chamber. The measured data were fed back into the sample library and the model was retrained periodically to form a closed loop.

2. The method according to claim 1, characterized in that, The standardization described in step S3 is performed as follows: ； in, The mean of the sample; For the i-th observation; The standard deviation is the sample standard deviation. The Pearson correlation coefficient is calculated using the following formula: ； Where r is the sample Pearson correlation coefficient, with a value of [-1, 1], and the closer it is to 1, the stronger the linear correlation; n is the sample size; and the absolute value... The standard deviation is the sample standard deviation. This is the sample average; Let be the i-th observation.

3. The method according to claim 1, characterized in that, Step S4 is as follows: S41. Model Structure: Using ε-SVR, slack variables are introduced. , And the regularization penalty coefficient C, simultaneously regressing 28-day compressive strength and 60-day shrinkage within the ε-insensitive band; The original features are processed by the RBF kernel function: ； Mapping to a high-dimensional space to complete nonlinear fitting; S42. Optimization Objective: The objective function to be optimized is: ； Where w is the weight vector; C is the regularization penalty coefficient, used to balance model complexity and training error; and These are slack variables; The constraints are as follows: ； in, For the weight vector, It is a bias term. and These are slack variables, allowing sample points to deviate. Insensitive zone It is a penalty parameter used to balance model complexity and training error. It is an insensitive loss parameter. It is a kernel function that maps the input to a high-dimensional feature space. It is the first The true value of each sample It is the number of training samples; S43. SVR Prediction Function: ； ； S44. Prediction accuracy is quantified using regression evaluation indicators: ； ； The calculated model must satisfy R 2 > 0.85 and RMSE is below the preset threshold; S45. Hyperparameter optimization: Perform 5-fold grid cross-validation on (C, γ, ε) and obtain the optimal parameter combination using R² and RMSE as convergence criteria; S46. Model Output: An ε-SVR surrogate model was obtained that can simultaneously output 28-day compressive strength and 60-day shrinkage rate, which can be directly used for subsequent multi-objective optimization of mix proportions.

4. The method according to claim 1, characterized in that, The multi-objective optimization function in step S5 satisfies the following conditions: 28-day compressive strength ≥ design value, initial slump spread ≥ 650 mm, 0.05% ≤ x1 ≤ 0.3%, 1% ≤ x2 ≤ 3.4%, and 2% ≤ x3 ≤ 8%.

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