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For a reinforced concrete beam subjected to fatigue loads, the structural stiffness and bearing capacity will gradually undergo irreversible degeneration, leading to damage. Moreover, there is an inherent relationship between the stiffness and bearing capacity degradation and fatigue damage. In this study, a series of fatigue tests are performed to examine the degradation law of the stiffness and bearing capacity. The results pertaining to the stiffness show that the stiffness degradation of a reinforced concrete beam exhibits a very clear monotonic decreasing "S" curve, i.e., the stiffness of the beam decreases significantly at the start of the fatigue loading, it undergoes a linear decline phase in the middle for a long loading period, and before the failure, the bearing capacity decreases drastically again. The relationship between the residual stiffness and residual bearing capacity is determined based on the assumption that the residual stiffness and residual bearing capacity depend on the same damage state, and then, the bearing capacity degradation model of the reinforced concrete beam is established based on the fatigue stiffness. Through the established model and under the premise of the known residual stiffness degradation law, the degradation law of the bearing capacity is determined by using at least one residual bearing capacity test data, for which the parameters of the stiffness degradation function are considered as material constants. The results of the bearing capacity show that the bearing capacity degradation of the reinforced concrete beam also exhibits a very clear monotonic decreasing "S" curve, which is consistent with the stiffness degradation process and in good agreement with the experiment. In this study, the stiffness and bearing capacity degradation expressions are used to quantitatively describe their occurrence in reinforced concrete beams. In particular, the expression of the bearing capacity degradation can mitigate numerous destructive tests and save cost. The stiffness and bearing capacity degradation expressions for a reinforced concrete beam can be used to predict the deformation and bearing capacity of a structure during the service process and determine the structural fatigue damage and degree of degradation. [ABSTRACT FROM AUTHOR]

• The self-magnetic flux leakage effect eliminates the need for any processing on the RC beam. • The whole process failure test of RC beams under four-point bending loading was carried out. • The RC beams' stress and crack development over the entire loading process were analyzed. • A dimensionless parameter A σ was defined to quantitatively calculate the reinforcement stress of RC beams. The self-magnetic flux leakage (SMFL) effect has been widely studied because it not only can identify early damage evaluation of ferromagnetic materials but is highly sensitive to the stress state. To promote the application of the SMFL effect in the health detection of reinforced concrete (RC) bridge, the whole process failure experiment of the RC beams under four-point bending loading was carried out and a method for detecting and quantitatively evaluating reinforcement stress in RC beams was established. A three-axis automatic displacement device based on metal magnetic memory was used to collect the magnetic signals of the RC beams under different loads, the magnetic signals under different values (LOVs) and multiple scanning paths were analyzed. Based on the magnetic signals under different stress states, a dimensionless parameter A σ was defined to quantitatively calculate the steel bars stress of RC beams. The experimental results show that in the pure bending section of RC beam, the steel bars stress, and the dimensionless parameter A σ emerged with a linear relationship. Furthermore, the effect of parameter lift-off values (LOV) on the test results was discussed. [ABSTRACT FROM AUTHOR]

Both corrosion defects and stress can cause magnetic field mutations, so the effect of stress must be considered in the magnetic detection of steel corrosion. This paper focuses on exploring the influence law of tension on magnetic signals of the corroded specimens. Based on the spontaneous magnetic leakage mechanism of steel bar corrosion and the stress magnetization model, the magnetic memory detection of corroded reinforced concrete under tension was carried out. The magnetic characteristics of corroded specimens before and after loading were analyzed. The corrosion positions of the specimens can be determined according to the representative mutation points (RMP) of the Byc(0) curves, and the magnetic index I2 was proposed to roughly determine the corrosion degree of the specimens when the specimens were not subjected to tensions. The experimental results showed that the RMP of Byc(F) curves can still represent corrosion positions when the specimens were under tension. The theoretical derivation showed that the magnetic field change caused by tensile force is limited, and the maximum value of the magnetic field change caused by tensile force can be obtained. Based on this, the corresponding I3-F curves were obtained through the test. The magnetic field change caused by the most unfavorable tensions was calculated to analyze its influence on corrosion magnetic detection. Compared with I2, the relationship between I3 and the corrosion degree was more discrete, indicating that tensile forces affected the quantitative detection of corrosion. Still, the magnetic field caused by corrosion played a leading role. The verification showed that the measured corrosion positions of reinforced concrete specimens were in good agreement with those detected by the magnetic memory method. [ABSTRACT FROM AUTHOR]

• Bending strength of corroded RC beams evaluated via innovative NDT technique SMFL. • SMFL index K for quantitative evaluation was proposed theoretically. • Quantitative correlation between index K and bending strength loss rate β was established. • Bending strength of corroded RC beams was quantitatively evaluated via K based on Bayesian model. The self-magnetic flux leakage (SMFL), a non-destructive testing (NDT) technique, was applied innovatively to the quantitative statistical evaluation of the bending strengths of corroded reinforced concrete (RC) beams. In this study, the variations of the SMFL and bending strength caused by steel bar corrosion were analyzed theoretically and experimentally. Based on theoretical analysis, a SMFL index K that is not affected by the initial magnetization and magnetization history was proposed. The bending strength loss rate β of the corroded RC beams could be evaluated quantitatively using index K. 1775 K data from 18 corroded RC beams with different corrosion degrees were extracted, and the experimental correlation between K and β was established based on the experimental data and a theoretical correction. The results indicated that the magnitudes of K from different beams were similar, which proved that K eliminated the difference between the initial magnetization and magnetization history between different individuals. K and β were approximately exponentially related, and their correlation was not significantly affected by the stirrups. In view of the discreteness of the experimental sample K , β was statistically evaluated via K based on a Bayesian model. The posterior probability distribution of β in different value intervals when K was in a certain value interval was given. Thus, the quantitative classification of β was realized. This work is beneficial for the engineering evaluation of the bending strengths of corroded RC beams and provides an innovative research idea. [ABSTRACT FROM AUTHOR]

• The detection and evaluation of reinforcement elastic stress in RC beams were studied. • The magnetic signal gradient was quantitatively modeled and verified by experiments. • A method based on Bayesian theory was developed to estimate the elastic stress. • This method can be reliably applied for rapid and economic stress detection in RC beams. This study developed a method for detection and quantitative evaluation of the elastic stress of the reinforcement in reinforced concrete (RC) beams. By combining the minimum energy and magnetic dipole theories, a quantitative model of the magnetic signal gradient and magnetization angle was established. The spatial distribution of the magnetic signals and variation of the average gradient with stress in the pure bending section of the RC beams were obtained through four-point bending experiments. The results show that the law of the average gradient with the stress is consistent with that predicted by the theoretical model. Based on the Bayesian theory, a method to evaluate the elastic stress was established, which can be applied for grading the elastic stress of the reinforcement within a certain range of accuracy. [ABSTRACT FROM AUTHOR]

The non-destructive quantitative evaluation of the rebar corrosion degree is an urgent problem to be solved for corroded reinforced concrete structures. In this study, a non-destructive quantification method for the rebar localized corrosion cross-sectional area was proposed based on the dynamic linkage mechanism of the induced magnetic and self-magnetic flux leakage fields of rebar. As verified by data from the experiment and the finite element simulation, this quantification method could eliminate the adverse influence of the magnetic property differences of the rebar. The results indicated that different quantitative indices for corrosion evaluation could be created based on this method, and an index created by two transformations with the same geometric characteristics had better quantification capability. The four quantitative indices I 1 , I 2 , I 3 , and I 4 created in this study were all linearly related to the rebar localized corrosion cross-sectional area ratio S , and index I 3 had the relatively best quantitative capability and applicability. This quantification method provided an innovative solution for the non-destructive quantitative evaluation of rebar corrosion. • The dynamic linkage mechanism between the IM and SMFL fields of corroded rebar was demonstrated. • An SMFL-based non-destructive quantification method for the rebar corrosion degree was proposed. • Four quantitative indices were created based on this quantification method. • All of the created quantitative indices were linearly related to the corrosion cross-sectional area of rebar. [ABSTRACT FROM AUTHOR]

Accurate measurement and assessment of rebar corrosion are critical for the safety and durability of reinforced concrete (RC) structures. The non-destructive self-magnetic flux leakage (SMFL) technology is often employed but still has some difficulties in achieving this goal, especially when the RC structure is under load. Therefore, an SMFL measurement experiment and corresponding finite element simulation of six loaded corroded RC beams were carried out in this study. Then, a dimensionless SMFL quantitative index G i for assessing the corrosion degree of the loaded RC beam was proposed. The experimental and simulated index G i has a similar linear correlation with the corrosion degree of the longitudinal tensile rebars of the RC beams. The corrosion-induced increasing ratio of index G i was up to 500% while that of the load-induced does not exceed 10.6%, which indicates that load has little effect on the SMFL-based corrosion degree assessment of RC beams. Furthermore, a universal grading assessment standard of the corrosion degree of loaded RC beams was established based on the Bayesian model and a G i data set extracted from 500 random simulation combinations of corrosion distribution and load. According to this standard, the corrosion level of the loaded RC beam can be directly determined via the value of G i with an accuracy between 70% and 100%. This work is beneficial for the engineering assessment of the rebar corrosion of loaded RC beams and provides an innovative research idea for this research field. • The SMFL characteristics of RC beams with stress-corrosion coupling were explored. • The proposed SMFL index G i is linearly related to the corrosion degree η of RC beams. • The effect of stress on the linear relationship between G i and η is minimal. • A G i -based corrosion grading standard of loaded RC beam was proposed. [ABSTRACT FROM AUTHOR]

Various structural failure modes exhibit great differences in occurrence probabilities, failure consequences and intrinsic characteristics, etc. Utilising these differences can enhance the effectiveness and efficiency of damage identification research, which has currently received little coverage. Therefore, a new idea, developing mode-specific damage detection methods, is suggested in the paper, with validation on beam structures. Firstly, structural behaviour was investigated from the perspective of stochastic traits and the structure design theory. It was concluded that developing damage detection methods for probabilistically dominant modes had potential to enhance the effectiveness of the identification significantly. Secondly, the strategy was applied to simply supported beams for the purpose of verification. When following the flexural mode, a major failure pattern of the beams, the structures demonstrated a very interesting feature – linearized deflection curves. Hence, damage severity and location indices were defined and an analytical model was built by quantifying the feature and then linking the indices to the curvature of the beams. Thirdly, experiments on reinforced concrete (RC) beams were conducted. The results showed that both the flexural mode and the characteristic of the linearized deflection curves were observed on all specimens; that there was a strong correlation between the damage severity index and the state of the defects on the beams; that the location indices corresponding to damaged and intact sections varied completely differently in quality and quantity. Thus, implementing the mode-specific strategy improves the specificity and efficiency of the damage identification dramatically. [ABSTRACT FROM AUTHOR]

• Magnetic parameter S was used to measure steel bar stress. • SMFL signals tended to be flat during the increase of the stress. • Magnetic parameter S has a highly linear relationship with the stress. • The lift-off value and initial stress value have slight influence on the measurement results. The measurement of the working stress of steel bars in concrete depends on an embedded sensor, which is difficult to replace once it is damaged. Innovatively, the magnetic characteristic "spatial difference parameter" was used to quantify the working stress of steel bars inside reinforced concrete (RC) bridges, which completely avoided the shortcomings of embedded sensors. The correlation between the stress of steel bars and the magnetic parameters was analyzed based on experimental results from nine steel bars. To be more suitable for practical engineering, the influences of the parameter lift-off value (LOV) and the initial stress value (ISV) on the experiment results were discussed. The results showed that the relative error of the measurement was almost less than 20%. The LOV and ISV did not significantly reduce the accuracy of the measurement results, which provided a good foundation for the application in the stress measurement for the actual RC bridges. [ABSTRACT FROM AUTHOR]