Concrete carbonation can weaken its strength, cause the corrosion of steel reinforcement, and shorten its service life. Predicting the concrete carbonation depth is a critical aspect of assessing concrete durability. Currently, mathematical models for the concrete carbonation depth, exemplified by the Fick model, suffer from a low fitting accuracy and limited applicability due to the complexity and variability of concrete materials and service environments. In light of this, this work proposes an improved Fick model that incorporates a correction term to effectively enhance the curve fitting accuracy. The correction term in the improved model provides a reasonable adjustment for deviations in the development pattern of the concrete carbonation depth from the Fick model under different conditions, thereby broadening the applicability of the new model compared to the Fick model. Several sets of experimental data on the concrete carbonation depth are used to validate the universality and superiority of the new model. The results of the case studies indicate that the average prediction error and standard deviation of the new model are significantly smaller than those of the Fick model. For the first two examples, in most situations, the average prediction error and standard deviation of the new model are less than 50% of those of the Fick model, with the lowest average prediction error being only 4% and the lowest standard deviation being only 2% of the Fick model’s respective values. For the third example, the new model demonstrates superior predictive capability for the later-stage concrete carbonation depth compared to the Fick model and the ANN model. Specifically, for the carbonation depth of the concrete on the 56th day, the relative error between the predicted value of the new model and the measured value is only 2%, which is much smaller than the 27% of the Fick model and the 12% of the ANN model. These results demonstrate the unique advantage of the proposed model in predicting the carbonation depth, especially when only a limited amount of experimental data are available.

To accurately quantify the variation in concrete carbonation depth, selecting an appropriate mathematical curve model is crucial. Currently prevalent models, such as the Fick model and exponential models, confront limitations in prediction accuracy and range of application. Given that a single curve model struggles to precisely describe the pattern of concrete carbonation, this work introduces a mixed-curve-based prediction model for carbonation depth, effectively integrating the Fick model with a hyperbolic model. Compared to the Fick model, the additional term in the mixed-curve model can be viewed as a reasonable correction to better adapt to the complex and varied conditions of concrete carbonation. This hybrid model transcends the limitations of individual models, enhancing fitting precision and broadening the scope of applicability. The new model boasts a concise structure with only two fitting parameters, facilitating ease of application. To validate its superiority, rigorous comparisons were conducted between the proposed model and existing ones, leveraging experimental data from 10 distinct concrete carbonation scenarios. By comparing the average error, standard deviation, and coefficient of determination across these cases, the new model demonstrates a clear advantage over the Fick model and the exponential model. In terms of fitting errors, the average error and standard deviation of the new model are notably lower than those of the other two models. In terms of the coefficient of determination, the values achieved by the new model in all examples are closer to 1 than those of both the Fick model and the exponential model, underscoring the new model’s superior fitting quality and remarkable stability. This research indicates that the combined model presented in this paper holds promising prospects for widespread application in predicting concrete carbonation depth.

To accurately quantify the time-varying pattern of concrete’s compressive strength, selecting an appropriate curve model is of paramount importance. Currently, widely adopted models such as polynomial, hyperbolic, and exponential models all possess limitations, particularly in terms of low fitting accuracy during the ultra-early-age stage. This paper innovatively introduces a mathematical model that utilizes a combined curve approach. This model boasts a simplified structure with only two fitting parameters. Compared to traditional models, when utilizing three or more sets of experimental data on compressive strength across different ages, the new model is capable of yielding more precise strength predictions. Due to its minimal reliance on experimental data, the new model exhibits high practicality and convenience in real-world applications. To validate its superiority, a detailed comparison between the new model and existing models was conducted based on several sets of experimental data. The results demonstrate that the new model has significant advantages in terms of mean fitting error and standard deviation, making its predictions the most reliable. For most cases, the standard deviation of the new model is reduced by approximately 30% to 80% compared to the second-best model, underscoring its exceptional stability and consistency. Additionally, the predicted long-term compressive strength values of the new model are closer to the design strength grade of the concrete. This model can also be successfully applied to predict the tensile strength of concrete during its ultra-early age. It has been demonstrated that the combined model proposed in this paper shows promising application prospects in evaluating the time-varying behavior of concrete strength.

The stochastic finite element method is an important tool for structural reliability analysis. In order to improve the calculation efficiency, a stochastic finite element method based on the Krylov subspace is proposed for the static reliability analysis of structures. The first step of the proposed method is to preprocess the static response equation considering randomness to reduce the condition number of the coefficient matrix. The second step of the proposed method is to construct a Krylov subspace based on the preprocessed static response equation. Then, the static displacement of random sampling is expressed as a linear combination of subspace basis vectors to achieve the purpose of a fast solution. Finally, statistics and failure probability are calculated according to the static response obtained from thousands of random samples. Three numerical examples are given to compare the proposed method with the stochastic finite element method based on the Neumann series. The results show that the stochastic finite element method based on the Krylov subspace is more accurate and efficient than the stochastic finite element method based on the Neumann series.

In structural stochastic dynamic analysis, the consideration of the randomness in the physical parameters of the structure necessitates the establishment of numerous stochastic finite element models and the subsequent computation of their corresponding vibration modes. When the complete analysis is applied to calculate the vibration modes for each sample of the stochastic finite element model, a substantial computational expense is incurred. To enhance computational efficiency, this work presents an extended subspace iteration method aimed at rapidly determining the vibration modal parameters of statically indeterminate structures. The essence of this proposed method revolves around efficiently constructing reduced basis vectors during the subspace iteration process, utilizing flexibility disassembly perturbation and the Krylov subspace. This extended subspace iteration method proves particularly advantageous for the modal analysis of finite element models that incorporate a multitude of random variables. The proposed modal random analysis method has been validated using both a truss structure and a beam structure. The results demonstrate that the proposed method achieves substantial savings in computational time. Specifically, for the truss structure, the calculation time of the proposed method is approximately 1.2% and 65% of that required by the comprehensive analysis method and the combined approximation method, respectively. For the beam structure, on average, the computational time of the proposed method is roughly 2.1% of a full analysis and approximately 48.2% of the Ritz vector method’s time requirement. Compared to existing stochastic modal analysis algorithms, the proposed method offers improved computational accuracy and efficiency, particularly in scenarios involving high-discreteness random analyses.

Carbon Fiber Reinforced Polymer (CFRP)-strengthened steel plate systems demonstrate remarkable advantages in civil engineering structural rehabilitation, with their overall performance critically reliant on the interfacial bond behavior between CFRP and steel plates. This paper systematically reviews the typical failure modes, key factors influencing interfacial bond performance, and corresponding testing methodologies. Research indicates that interfacial shear stress dominates the failure process. Enhanced strengthening efficacy can be achieved by employing CFRP plates with optimized adhesive layer thickness (recommended 0.5–1.5 mm) and double-sided bonding configurations. Concurrently, substrate surface treatment and environmental factors (temperature–humidity, corrosion, etc.) significantly affect interfacial bond performance. Current research primarily focuses on the single-factor and strength failure performance of standard specimens, lacking a systematic understanding of the long-term durability and failure mechanisms of complex structures under multi-field coupling effects. This review further summarizes the distinctive features and application scenarios of innovative strengthening systems—including prestressed, unbonded, and shape memory alloy composite systems—to provide guidance for engineering selection and standardized design.