[Objective] Accurate assessment of concrete fatigue life under fatigue load is essential to ensure the safety and stability of structures, especially the fatigue failure behavior dominated by stress and strain. The fatigue loading surface function is established to describe the fatigue state of concrete based on the constraint relationship in the stress-strain fatigue criterion. The fatigue loading surface function of concrete exhibits a monotonic variation with fatigue cycles, enabling the establishment of an equivalent function to represent the concrete fatigue state. The fatigue loading surface function of concrete can be described as a linear equivalent expression, and the coefficients can be calibrated by the characteristic points in the fatigue loading process. [Methods] Based on the constraint relationship between fatigue stress-strain and fatigue cycles, the equivalent fatigue cycles can be calculated from the fatigue stress-strain data. The equivalent fatigue cycles can effectively express the fatigue stress-strain state of the material, and the fatigue life indirectly represents the fatigue failure stress-strain state in the fatigue failure criterion of materials with the static constitutive curve as the limit value. The degree of fatigue accumulation of materials can be quantified by comparing the equivalent fatigue cycles and fatigue life. The evaluation method based on equivalent fatigue cycles overcomes the shortcomings of the current evaluation methods based on the classic fatigue criteria and fatigue envelope lines. Therefore, in this work, the fatigue loading surface function is constructed, and its evolution law is studied through the analogical form of the fatigue failure criterion of materials with a static constitutive curve as the limit value, thus proposing a description method for equivalent calibration and solving the equivalent fatigue cycles. The fatigue loading surface function is proposed to describe the fatigue state and determine the constraint relationship between fatigue stress and strain and fatigue cycles based on the fatigue failure criterion of materials with a static constitutive curve as the limit value. The equivalent fatigue loading surface function and coefficients can be obtained by the equivalent description method of feature point calibration. The R-square is introduced to ensure an equivalent description, and the maximum R-square directly relates to the optimal equivalent description results. Therefore, the maximum R-square algorithm is proposed based on the evolution law of the fatigue loading surface function. The linear equivalent form of the fatigue loading surface function is proposed to meet the equivalent description and practical application requirements. [Results] Therefore, equivalent calibration can be achieved by selecting the optimal maximum R-square, and the coefficients of the fatigue loading surface function can be determined from the experimental results of the fatigue loading process. The equivalent fatigue loading surface function, feature point calibration, and maximum determinable coefficient algorithms were developed to achieve the equivalent fatigue state description of materials. Through the equivalent calibration results, the equivalent fatigue cycles can be obtained using the corresponding fatigue stress-strain. Furthermore, the fatigue stress-strain state of concrete can be quantified by the equivalent fatigue cycles, and corresponding evaluation processes and indicators are obtained through further study. [Conclusions] The proposed method provides an effective approach for the fatigue life analysis of concrete.
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