A method for evaluating the failure probability of parallel steel wires under the action of a corrosive environment

Abstract

The present invention discloses a method for evaluating the failure probability of parallel steel wires under the action of a corrosive environment. The method includes: based on the traditional S-N curve, establishing a fatigue reliability evaluation model for bridge cable structures considering the corrosion effect, and then inversely deducing the corrosion quantity of parallel steel wires in the cable structure based on the Bayesian network method, and giving the failure probability of each parallel steel wire. The method of the present invention can obtain the influence of the fatigue stress amplitude of parallel steel wires, the corrosion quantity of parallel steel wires, and the service life on the fatigue reliability of the cable system. Moreover, it realizes the evaluation of the cable fatigue reliability from the failure state of parallel steel wires and the inverse deduction of the failure state of parallel steel wires from the cable fatigue reliability.

Description

Technical Field

[0001] The present invention relates to the field of safety assessment of cables for long-span bridges and their parallel steel wires. Specifically, it relates to a method for evaluating the failure probability of parallel steel wires under the action of a corrosive environment. Background Art

[0002] In cable-supported bridges, the cable structure is the main load-bearing component of the entire cable-supported bridge. Its safety and durability play a crucial role in the normal operation of the bridge. The cable structure is composed of numerous parallel steel wires, indicating that the performance of the parallel steel wires determines the performance of the cable structure. Therefore, it is first necessary to obtain the performance of the parallel steel wires to accurately evaluate the reliability of the cable structure. In particular, the parallel steel wires are affected by cyclic loads during service, resulting in fatigue failure problems, which will cause their service life to be much lower than the normal service life. Therefore, many researchers have carried out fatigue tests on parallel steel wires and obtained their fatigue life curves, namely S-N curves. However, the parallel steel wires are also affected by environmental corrosion during service, leading to a further decrease in their fatigue life. Currently, for the fatigue life of parallel steel wires in a corrosive environment, corrosion-fatigue tests are often carried out on single parallel steel wires, without fully considering the influence of single parallel steel wires on the fatigue reliability of the cable structure. In addition, in the actual engineering site, the result is often known, that is, the reliability of the cable structure system is known, which makes it difficult to capture the failure probability of each parallel steel wire component. Therefore, how to consider the influence of the state of parallel steel wires on the fatigue reliability of the cable structure and reverse the corrosion conditions of each parallel steel wire based on the known influence of the fatigue reliability of the cable structure is an urgent problem to be solved currently. Summary of the Invention

[0003] Aiming at the defects of the existing methods for evaluating the fatigue reliability of bridge cables and deriving the failure probability of parallel steel wires, the present invention derives the S-N curve of parallel steel wires in a corrosive environment, realizes the evaluation of the fatigue reliability of cables from the failure state of parallel steel wires and the reverse derivation of the failure state of parallel steel wires from the fatigue reliability of cables, and solves the problem of system-level reliability evaluation.

[0004] To achieve the above object, the method for evaluating the failure probability of parallel steel wires under the action of a corrosive environment according to the present invention includes the following steps:

[0005] Based on the fatigue life test of domestic 1860-grade low-relaxation prestressed steel strands, obtain the fatigue life curve:

[0006] logN + mlog(S) = logA

[0007] wherein, N is the total number of cycles under stress; S is the fatigue stress amplitude; logA = 13.84; m = 3.5.

[0008] Considering the corrosion of parallel steel wires, the fatigue-life equation of parallel steel wires under corrosion conditions was derived:

[0009] N = A1(S) -m

[0010] A1 = A / K f ; K f = 1.2 + 5.77C(t); C(t) = kt r

[0011] C(t) represents the pitting depth function; t is the service life; k is the corrosion depth (mm) after one year of service; r is the corrosion rate; K f is the fatigue reduction coefficient.

[0012] Based on the fatigue reliability theory, a fatigue reliability model based on the traditional S-N curve was established:

[0013]

[0014] Based on the fatigue reliability theory, a fatigue reliability model considering the corrosion of parallel steel wires was established:

[0015]

[0016] p f = Φ(-β)

[0017] f(S) is the probability distribution of the equivalent structural stress; n tot is the number of cycles per day; t is the service life of the structure; D f is the fatigue damage at failure, which can be represented by a lognormal distribution, i.e., LN(0, 0.294); p f is the fatigue failure probability; β is the reliability index; Φ(·) is the standard normal distribution function.

[0018]

[0019]

[0020] Furthermore, based on Bayes' theorem, the failure probabilities of each parallel steel wire can be deduced inversely:

[0021]

[0022] In the formula, P(A i ) is the failure probability of the i-th parallel steel wire, which can be calculated according to the constructed fatigue reliability model; P(S) is the failure probability of the cable structure system; P(A i , S) is only the probability that the failure of the i-th parallel steel wire causes the failure of the cable structure system; P(A i$P_i$ is the probability of failure of the cable structure system caused by the failure of the $i$-th parallel wire; $Q$ is the total number of parallel wires in the cable.

[0023] The beneficial effects of the present invention are as follows:

[0024] By considering the S-N curve of parallel wires in a corrosive environment, the present invention establishes a corresponding reliability evaluation model and determines the failure probability of each parallel wire based on the Bayesian network. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is Bayes' theorem.

[0026] Figure 2 is a schematic diagram of the safety status of parallel wires in the cable cross-section.

[0027] Figure 3 is the calculation result of the case. DETAILED DESCRIPTION OF THE INVENTION

[0028] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and cases.

[0029] Based on the fatigue life test of domestic 1860-grade low-relaxation prestressed steel strands, the fatigue life curve is obtained:

[0030] logN + mlog(ΔS) = logA

[0031] where $N$ is the total number of cycles under stress; $\Delta S$ is the fatigue stress amplitude; logA = 13.84; m = 3.5.

[0032] Considering the corrosion situation of parallel wires, the fatigue-life equation of parallel wires under corrosion is derived:

[0033] N = A1(S) -m

[0034] A1 = A / K f ; K f = 1.2 + 5.77C(t); C(t) = kt r

[0035] C(t) represents the pitting depth function; t is the service life; k is the corrosion depth (mm) after one year of service; r is the corrosion rate; K f is the fatigue reduction coefficient. Table 1 shows the atmospheric corrosion rates of carbon steel materials in different cities in China.

[0036]

[0037] Based on the fatigue reliability theory, a fatigue reliability model based on the traditional S-N curve was established:

[0038]

[0039] Based on the fatigue reliability theory, a fatigue reliability model considering the corrosion of parallel wires was established:

[0040]

[0041] p f = Φ(-β)

[0042] f(S) is the probability distribution of the equivalent structural stress; n tot is the number of cycles per day; t is the service life of the structure; D f is the fatigue damage at failure, which can be represented by a lognormal distribution, i.e., LN(0, 0.294); p f is the fatigue failure probability; β is the reliability index; Φ(·) is the standard normal distribution function.

[0043]

[0044]

[0045] Furthermore, based on Bayes' theorem, the failure probabilities of each parallel wire can be deduced inversely:

[0046]

[0047] In the formula, P(A i ) is the failure probability of the i-th parallel wire, which can be calculated according to

[0015] ; P(S) is the failure probability of the cable structure system; P(A i , S) is only the probability that the failure of the cable structure system is caused by the failure of the i-th parallel wire; P(A i |S) is the probability that the failure of the cable structure system is caused by the failure of the i-th parallel wire; Q is the total number of parallel wires in the cable.

[0048] Figure 1 is Bayes' theorem

[0049] Assume that the bridge suspender structure is composed of 7 parallel wires, and the safety status of the parallel wires in the cable cross-section is as Figure 2 shown.

[0050] The present invention uses a calculation case to analyze the influence of the number of corroded wires on the fatigue reliability of the cable system under different fatigue stress amplitudes and cycle numbers, as shown in Table 2.

[0051]

[0052] Figure 2 For the case calculation results. For the calculation cases, the fatigue stress amplitudes of parallel wires are all ln(15) MPa, and the number of cycles are all ln(5000). In the case, the fatigue reliability of the cable system changes with the number of corroded wires and time as shown in Figure 2 (a). It can be seen from Figure 2 (a) that when the number of corroded wires is fixed, with the increase of service time, the fatigue reliability of the cable system drops rapidly. Taking the case where the number of corroded wires is 1 as an example, when the service time is 50 years, the fatigue reliability of the cable system is 3.944; when the service time is 100 years, the fatigue reliability of the cable system is 1.611; when the service time is 150 years, the fatigue reliability of the cable system is 0.244; when the service time is 200 years, the fatigue reliability of the cable system is -0.721. In addition, when the service time is fixed, with the increase of the number of corroded wires, the fatigue reliability of the cable system gradually drops. Taking the service time of 100 years as an example, when the number of corroded wires is 1, the fatigue reliability of the cable system is 1.611; when the number of corroded wires is 2, the fatigue reliability of the cable system is 1.510; when the number of corroded wires is 3, the fatigue reliability of the cable system is 1.474; when the number of corroded wires is 4, the fatigue reliability of the cable system is 1.440; when the number of corroded wires is 5, the fatigue reliability of the cable system is 1.418; when the number of corroded wires is 6, the fatigue reliability of the cable system is 1.401; when the number of corroded wires is 7, the fatigue reliability of the cable system is 1.388.

[0053] Furthermore, taking the service time of 100 years as an example, according to the Bayesian network method, the safety states of each parallel wire can be inversely deduced, as shown in Figure 2 (b). Specifically, when the failure probability of the cable system is 1, the failure probabilities of each wire can be obtained under different calculation cases of the number of corroded wires.

[0054] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for evaluating the failure probability of parallel steel wires under the action of a corrosive environment, characterized in that, Including the following steps: Based on the traditional S-N curve, establish a fatigue reliability model of the cable structure considering the action of the corrosion environment; determine the service state of parallel wires under the fatigue reliability model of the cable structure considering the action of the corrosion environment based on the Bayesian network, and obtain the failure probability of each parallel wire; specifically including: Based on the traditional S-N curve, establish a fatigue reliability evaluation model for the bridge cable structure as follows: ， ， Wherein, N is the total number of cycles under stress; A and m are constants related to the material, and logA = 13.84 and m = 3.5 respectively; p f is the fatigue failure probability; D f is the fatigue damage at failure; S is the fatigue stress, n tot is the number of cycles per day; t is the service life of the structure; f(S) is the probability distribution of the equivalent structural stress; Considering the case where parallel wires are corroded, establish a fatigue reliability evaluation model for the bridge cable structure based on the traditional S-N curve: ， ， ， ， ， Among them, K f is the fatigue reduction coefficient: C(t) represents the pitting depth function; t is the service life; k is the corrosion depth (mm) after one year of service; r is the corrosion rate; Determine the service state of each parallel wire based on the Bayesian network, that is, the failure probability of each parallel wire, specifically: ， ， ， Wherein, P(A i ) is the failure probability of the i-th parallel wire, which is obtained according to the fatigue reliability model of the cable structure under the constructed corrosion environment; P(S) is the failure probability of the cable structure system; P(A i , S) is the probability that the failure of the i-th parallel wire leads to the failure of the cable structure system; P(A i |S) is the probability of failure caused by the failure of the i-th parallel wire when the cable structure system fails, and Q is the total number of parallel wires in the cable.

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