Large-span box girder bridge time-varying reliability evaluation method considering concrete fatigue creep

Abstract

The invention discloses a large-span box girder bridge time-varying reliability evaluation method considering concrete fatigue creep. The method comprises the steps that concrete static creep and shrinkage strain are calculated; calculating concrete fatigue creep strain generated by the vehicle load; constructing a concrete unified constitutive model considering a multi-factor coupling effect; establishing a long-term performance fine analysis numerical model of the large-span box girder bridge; establishing a large-span box girder bridge time-varying reliability calculation method; establishing a limit state equation of reliability analysis; and evaluating the structural time-varying reliability considering the concrete fatigue creep effect. According to the method, the time-varying reliability of the large-span box girder bridge under the coupling action of factors such as concrete static creep, cyclic creep and shrinkage can be accurately evaluated, and technical support can be provided for health diagnosis, maintenance and reinforcement of bridges of the same type.

Description

Technical Field

[0001] The present invention relates to the field of structural state evaluation, and particularly to a reliability evaluation method for long-span box girder bridges considering concrete fatigue creep. Background Art

[0002] Typical diseases such as excessive deflection of the main span and cracking of the beam body commonly occur in long-span box girder bridges during operation, seriously reducing the normal service performance of the structure and even inducing safety accidents such as bridge collapse. Research shows that insufficient estimation of time-varying effects is the main reason for excessive deflection of long-span box girder bridges during the operation period.

[0003] Currently, in the time-varying reliability analysis of long-span box girder bridges, deterioration factors such as static creep, shrinkage, and stress relaxation of concrete under dead load are usually considered. However, under the repeated action of frequent vehicle loads, stress fluctuations will be generated in the beam cross-section, thereby inducing fatigue creep in the concrete. Its essence is the irreversible macroscopic deformation manifested by the fatigue development of existing micro-cracks in the concrete. Research shows that the continuous action of fatigue (repeated) loads will accelerate the development of creep and increase the long-term deformation of the structure. Under the current situation of increasing traffic volume, especially serious overloading, the vehicle-induced fatigue creep effect is relatively significant, and its influence should be considered in the reliability evaluation of long-span box girder bridges.

[0004] Therefore, considering the coupling effects of factors such as static creep, fatigue creep, and shrinkage of concrete on the long-term performance of long-span box girder bridges and establishing corresponding reliability evaluation methods are of great significance for the health assessment and maintenance and reinforcement of the same type of bridges during the service period. Summary of the Invention

[0005] Object of the Invention: The object of the present invention is to provide a reliability evaluation method for long-span box girder bridges considering concrete fatigue creep.

[0006] Technical Solution: The present invention includes the following steps:

[0007] (1) Calculate the static creep and shrinkage strain of concrete;

[0008] (2) Calculate the concrete fatigue creep strain generated by vehicle loads;

[0009] (3) Construct a unified constitutive model of concrete considering multi-factor coupling effects;

[0010] (4) Establish a refined analysis numerical model for the long-term performance of long-span box girder bridges;

[0011] (5) Establish a time-varying reliability evaluation method for long-span box girder bridges;

[0012] (6) Establish a limit state equation for reliability analysis;

[0013] (7) Evaluate the time-varying reliability of the structure considering the concrete fatigue creep effect.

[0014] Further, the step (1) includes the following steps:

[0015] (1.1) Divide the calculation time into T time steps Δt i , i = 1, 2 ……, T. According to the Kelvin chain model, transform the integral creep formula into a rate-type creep law with built-in variables. The increment of the static creep strain of concrete within the time step Δt i = t i - t i-1 is: That is:

[0016]

[0017] where Δσ i is the stress increment within the time step Δt i ; N is the number of Kelvin units; τ μ is the delay time, μ = 1, 2,......, N; γ μ is the internal variable of the Kelvin unit considering the stress history of the previous time step; λ μ is the coefficient related to the delay time τ μ and the time step Δt i ; A μ is the discrete spectrum, and its expression is:

[0018]

[0019] where C (k) is the k-th derivative of C(t, t0) = J(t, t0) - 1 / E μ with respect to time t, J(t, t0) is the creep function, and E μ is the elastic modulus of the μ-th Ke1vin unit; in practical applications, k taking 3 can meet the accuracy requirements;

[0020] (1.2) According to the CEB-FIP model, the increment of the concrete shrinkage strain within the time step Δt i is: That is:

[0021]

[0022] where t s is the starting shrinkage age; ε sh0 represents the nominal shrinkage strain; β RH is the coefficient affected by the relative environmental humidity; β s (t i - t s ) and βs (t i-1 -t s ) represent the coefficients of the development of concrete shrinkage during the time period t i -t s and t i-1 -t s respectively.

[0023] Furthermore, step (2) includes, within a time step Δt i , the increment of concrete fatigue creep strain generated by vehicle loads is:

[0024]

[0025] where C1 = 46×10 -6 , m = 4, obtained through optimization analysis based on test data; σ is the average stress of concrete, approximated by the stress generated by the structural dead loads (self-weight, prestress, and attached structures); the stress amplitude Δσ = σ max -σ mia , σ max and σ mia are the maximum and minimum values of the normal stress of the cross-section; f c represents the standard compressive strength of concrete; ΔN c represents the traffic volume passing through the bridge within the time step Δt i .

[0026] Since different types of vehicles drive randomly on the bridge, the stress amplitude Δσ varies with time. For ease of analysis, the cyclic stresses generated by various vehicles are averaged over time to obtain an equivalent fatigue load with a constant amplitude.

[0027] Furthermore, the calculation steps of the equivalent fatigue load with a constant amplitude include:

[0028] (2.1) Based on the highway toll system near the bridge site, obtain the annual vehicle load data. For ease of analysis, classify the vehicles passing through the bridge according to their weights;

[0029] (2.2) Based on the measured traffic information, adopt a simplified traffic pattern to approximate the complex operation mode of vehicles on the bridge, and determine whether various types of vehicles pass through the bridge side by side or one by one;

[0030] (2.3) According to the determined vehicle load and traffic pattern, and combined with the moment influence lines of various types of vehicles, calculate the stress amplitude Δσ. The expression for the constant amplitude of the equivalent fatigue load is:

[0031]

[0032] where t Nis the duration for N cycles, C is a constant parameter; Δσ(t) is the change amplitude generated by the actual vehicle load; Δσ represents the constant amplitude of the equivalent fatigue load.

[0033] Further, step (3) includes, within each time step Δt i the total strain increment Δε of the concrete i is composed of the elastic strain increment i generated by the stress change Δσ the static creep strain increment the fatigue creep strain increment and the shrinkage strain increment Δε i is expressed as:

[0034]

[0035] The unified constitutive model of concrete considering the multi - factor coupling effect can be expressed as:

[0036]

[0037] where t i-1 / 2 represents the mid - point moment of the time step Δt i and E″(t i-1 / 2 ) is the effective incremental modulus of the concrete, and its expression is:

[0038]

[0039] where E0 is the instantaneous elastic modulus of the concrete.

[0040] Further, step (4) includes the following steps:

[0041] (4.1) According to the unified constitutive model of concrete, the creep analysis of complex structures can be simplified as an elastic problem for solution. Embedding this constitutive model as a user - subroutine into the general finite - element program DIANA can realize the calculation of the long - term performance of the structure;

[0042] (4.2) To improve the calculation efficiency, only a finite - element model of a 1 / 2 box - girder bridge is established using DIANA software. The mechanical behavior of the thin - wall box girder is simulated by eight - node combined degenerated shell elements, and ordinary steel bars are simulated by a series of steel bar meshes embedded in the shell elements. There are two layers of steel bar meshes in the top plate, web plate, and bottom plate of the box girder; for prestressed steel bars, they are determined by defining position key points and shape functions, and the prestressed tendon elements can be automatically generated by the program; the initial material properties of concrete and steel bars are defined by their standard values, and the constitutive relations of ordinary steel bars and prestressed steel bars both adopt the bilinear model;

[0043] (4.3) In order to describe the complex stress history of the cantilever box girder construction process, the stage analysis technique in the DIANA program is used to achieve this. In the initial stage of the simulation, the segments are first passivated and then activated in sequence according to the actual construction progress and closing sequence.

[0044] Furthermore, the step (5) includes using the importance sampling method (IS) to calculate the reliability of the structure, and establishing the sampling center at the maximum possible failure point of the structure, namely the "design point". Assume that n random variables x that affect the reliability of the structure i (i=1,2,...,n) form a vector x and calculate the failure probability P of the structure f , whose expression is:

[0045]

[0046] Where g(x) represents the limit state equation of the structure. I[g(x)] is an indicative function. If g(x)≤1, I[g(x)]=1 and g(x)>0, I[g(x)]=0. f(x) represents the joint probability density function, which is defined as where f i (x i ) indicates that the mean is μ i and the standard deviation is σ i The random variable x i The probability density function of ρ(x) is the density function of IS, which is defined as where ρ i (x i ) indicates that the value corresponding to x i In order to avoid cluster sampling and select samples with actual physical meaning, the truncated Latin hypercube (TLHS) is used to generate M groups of sample values X of the random variable x. k (k=1, 2, ..., M), P f It can be estimated as:

[0047]

[0048] Determining the "design point" (i.e., sampling center) is an important issue in the importance sampling method. Since the structure function function is an implicit form of the input variables, the "design point" needs to be obtained through a series of iterative calculations.

[0049] Furthermore, the steps of obtaining the "design point" through a series of iterative calculations include:

[0050] (5.1) Based on the distribution of random variables, the truncated Latin hypercube technique is used to generate m groups of sample values X k (k=1,2,...,m,each group of samples X kInput the finite element model and calculate the corresponding g(X k ) value;

[0051] (5.2) Among the m groups of samples in an iterative analysis, if there exists X k such that g(X k ) ≤ 0, then select the sample value X k corresponding to the maximum value of f(X * ) as the candidate design point; otherwise, select the sample value X k corresponding to the minimum value of g(X * ) as the candidate design point;

[0052] (5.3) Replace the mean μ i of each random variable X i with , and then apply the truncated Latin hypercube technique to obtain new m groups of sample values X k (k = 1, 2,..., m), and substitute them into the finite element model for calculation, so as to obtain a new design point X * ;

[0053] (5.4) Perform cyclic analysis according to the above process. When g(X * ) ≈ 0, and the increment of each random variable corresponding to in the previous and subsequent iterations is less than the specified allowable error ω i , then the final X * is the approximate design point sought, and the iterative calculation terminates at this time;

[0054] (5.5) Set the distribution center of the random variable at the final design point X * , and then input the generated M groups of sample values X k (k = 1, 2,..., M) into the finite element model for calculation to obtain the corresponding g(X k ) values, while f(X k ) and ρ(X k ) are respectively expressed as:

[0055]

[0056] Furthermore, step (6) includes that in the deflection reliability analysis, the maximum deflection of the prestressed concrete bridge should not exceed L / 600, where L is the main span. Here, it is used as the deflection threshold, and the limit state equation can be expressed as:

[0057] g(t) = [w] - [w max (t)]

[0058] where: [w] is the deflection threshold; [w max (t)] represents the mid-span deflection of the main span when operating for t years.

[0059] Further, step (7) includes establishing two numerical models to verify the influence of fatigue creep on the reliability of long-span box girder bridges: in the first numerical model, only the influence of concrete static creep, shrinkage, and steel strand stress relaxation on long-term deformation is considered, and the subroutine for evaluating fatigue creep effects is deactivated; for the second numerical simulation, the influence of these factors on the time-varying effects of box girder bridges is considered simultaneously.

[0060] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: in the time-varying reliability analysis of long-span box girder bridges, the concrete fatigue creep effect generated by vehicle loads is taken into account, realizing the accurate assessment of the structural state throughout the service life; it can be realized programmatically, with simple and fast operation, and has wide engineering application value; it provides technical support for improving the design method of prestressed concrete box girder bridges. Description of the Drawings

[0061] Figure 1 is the flowchart of the present invention;

[0062] Figure 2 is the contour diagram of the long-span box girder bridge; (a) is the elevation view of the completed bridge; (b) is the typical cross-sectional dimensions;

[0063] Figure 3 is the delay spectrum Aμ of the CEB-FIP90 model;

[0064] Figure 4 is the annual traffic flow of the long-span box girder bridge;

[0065] Figure 5 The simplified traffic pattern of vehicle loads;

[0066] Figure 6 The finite element model of the long-span box girder bridge;

[0067] Figure 7 The flowchart for determining the approximate "design point";

[0068] Figure 8 The time-varying reliability of the long-span box girder bridge considering fatigue creep effects. Detailed Embodiments

[0069] The technical solution of the present invention will be further described below with reference to the drawings.

[0070] The present invention includes: calculating the static creep and shrinkage strain of concrete; calculating the concrete fatigue creep strain generated by vehicle loads; constructing a unified constitutive model of concrete considering the coupling effects of multiple factors; establishing a refined numerical model for the long-term performance analysis of long-span box girder bridges; establishing a time-varying reliability assessment method for long-span box girder bridges; establishing the limit state equation for reliability analysis; and evaluating the time-varying reliability of the structure considering the concrete fatigue creep effect.

[0071] Taking the three-span variable cross-section prestressed concrete continuous box girder bridge with a main span of 150 m as an example, this bridge is composed of two identical and independent single-box single-cell box girders, which respectively carry vehicles moving in opposite directions, such as Figure 2 shown. The top slab and bottom slab of a single box girder are 14.6 m and 7.4 m wide respectively. According to the 1.8th-degree parabola, the height of the box girder and the thickness of the bottom slab are reduced from 9.0 m and 0.9 m at the pier to 3.3 m and 0.32 m at the mid-span respectively, and the thickness of the web changes linearly from 0.9 m at the pier to 0.5 m at the mid-span. The box girder is constructed by cantilever casting with C55 concrete. The main span contains 37 beam segments, and each of the two side spans contains 18 beam segments. The box girder adopts a three-way prestressing system, and the prestressing tendons are high-strength low-relaxation steel strands with a standard strength f pk of 1860 MPa.

[0072] Taking the mid-span cross-section of the main span of this bridge as an example, clarify the reliability assessment method of long-span box girder bridges considering concrete fatigue creep, such as Figure 1 shown, and obtain the evolution law of the time-varying reliability of the structure during the entire service life.

[0073] (1) Calculate the static creep and shrinkage strain of concrete

[0074] Divide the calculation time into T time steps Δt i , i = 1, 2 ……, T. According to the Kelvin chain model, transform the integral creep formula into a rate-type creep law with built-in variables. During the time step Δt i = t i - t i-1 The increment of static creep strain of concrete is:

[0075]

[0076] where Δσ i is the stress increment during the time step Δt i ; N is the number of Kelvin units; τ μ is the delay time, μ = 1, 2,......, N; γ μ is the internal variable of the Kelvin unit considering the stress history of the previous time step; λ μ is the coefficient related to the delay time τ μ and the time step Δt i ; A μ is the discrete spectrum, and its expression is:

[0077]

[0078] where C (k)C(t, t0) = J(t, t0) - 1 / E μ is the k-th derivative with respect to time t, J(t, t0) is the creep function, and E μ is the elastic modulus of the μ-th Kelvin element; in practical applications, taking k = 3 can meet the accuracy requirements;

[0079] According to the CEB - FIP model, within the time step Δt i the increment of concrete shrinkage strain is:

[0080]

[0081] where t s is the start age of shrinkage; ε sh0 represents the nominal shrinkage strain; β RH is the coefficient affected by the relative humidity of the environment; β s (t i - t s ) and β s (t i-1 - t s ) respectively represent the coefficients of concrete shrinkage development during the time periods t i - t s and t i-1 - t s interval.

[0082] In the case, the static creep of concrete is described by the CEB - FIP90 model, and the delay spectrum A μ under different loading ages is calculated and used in the static creep analysis of the current time step as shown in Figure 3 .

[0083] (2) Calculate the concrete fatigue creep strain caused by vehicle load

[0084] Within the time step Δt i the increment of concrete fatigue creep strain caused by vehicle load is:

[0085]

[0086] where C1 = 46×10 -6 , m = 4, obtained through optimization analysis based on test data; σ is the average stress of concrete, approximated by the stress generated by the structural dead load (self - weight, prestress, and attached structures); the stress amplitude Δσ = σσ max - σσ min , σ max and σ min are the maximum and minimum values of the normal stress of the cross - section; f c represents the standard compressive strength of concrete; ΔNc represents the traffic flow passing through the bridge within the time step Δt i through the bridge.

[0087] Since different types of vehicles move randomly on the bridge, the stress amplitude Δσ varies with time. For the convenience of analysis, the cyclic stresses generated by various vehicles are averaged over time to obtain an equivalent fatigue load with a constant amplitude.

[0088] The calculation steps of the equivalent fatigue load with a constant amplitude include:

[0089] Based on the highway toll system near the bridge site, annual vehicle load data is obtained. For the convenience of analysis, the vehicles passing through the bridge are classified according to their weights;

[0090] Based on the measured traffic information, a simplified traffic pattern is used to approximate the complex operation mode of vehicles on the bridge, and it is determined whether various types of vehicles pass through the bridge side by side or one by one;

[0091] According to the determined vehicle load and traffic pattern, and combined with the bending moment influence lines of various types of vehicles, the stress amplitude Δσ is calculated. The expression for the constant amplitude of the equivalent fatigue load is:

[0092]

[0093] where t N is the duration of N cycles, C is a constant parameter; Δσ(t) is the varying amplitude generated by the actual vehicle load; Δσ represents the constant amplitude of the equivalent fatigue load.

[0094] In the case, based on the highway toll system near the bridge site, the annual traffic flow of the bridge is obtained. As Figure 4 shown, the vehicles passing through the bridge are divided into five types according to their weights, and a simplified traffic pattern is used to simulate the complex operation mode of vehicles on the bridge. As Figure 5 shown, except that 92% of the heavy trucks pass through the bridge one by one, other vehicles of the same type can drive side by side in the lane.

[0095] (3) Construct a unified constitutive model of concrete considering the coupling effect of multiple factors

[0096] Within each time step Δt i the total strain increment Δε of concrete i is composed of the elastic strain increment i caused by the stress change Δσ the static creep strain increment the fatigue creep strain increment and the shrinkage strain increment Δε i is expressed as:[[]]

[0097]

[0098] The unified constitutive model of concrete considering the multi - factor coupling effect can be expressed as:

[0099]

[0100] Where t i-1 / 2 represents the mid - point moment of the time step Δt i , and E″(t i-1 / 2 ) is the effective incremental modulus of concrete, and its expression is:

[0101]

[0102] Where E0 is the instantaneous elastic modulus of concrete.

[0103] (4) Establish a numerical model for the refined analysis of the long - term performance of long - span box - girder bridges

[0104] According to the unified constitutive model of concrete, the creep analysis of complex structures can be simplified as an elastic problem for solution. Embedding this constitutive model as a user subroutine into the general finite - element program DIANA can realize the calculation of the long - term performance of the structure;

[0105] To improve the calculation efficiency, the finite - element model of only 1 / 2 of the box - girder bridge is established using DIANA software. The mechanical behavior of the thin - wall box girder is simulated by eight - node combined degenerated shell elements, and ordinary steel bars are simulated by a series of steel bar meshes embedded in the shell elements. There are two layers of steel bar meshes in the top slab, web and bottom slab of the box girder; for prestressed steel bars, they are determined by defining the position key points and shape functions, and the prestressed tendon elements can be automatically generated by the program; the initial material properties of concrete and steel bars are defined by their standard values, and the constitutive relationships of ordinary steel bars and prestressed steel bars both adopt the bilinear model;

[0106] To describe the complex stress time - history during the cantilever construction process of the box girder, the stage analysis technology in the DIANA program is used. In the initial stage of the simulation, the segments are first deactivated, and then activated successively according to the actual construction progress and closure sequence.

[0107] In the case, a finite - element model of the long - span box - girder bridge is established using DIANA software, as Figure 6 shown.

[0108] (5) Establish a time - varying reliability assessment method for long - span box - girder bridges;

[0109] The importance sampling method (IS) is used to calculate the reliability of the structure, and the sampling center is established at the most likely failure point of the structure, namely the "design point". Let the n random variables x that affect the structural reliability i(i = 1, 2,..., n) form the vector x, and calculate the failure probability P of the structure f , and its expression is:

[0110]

[0111] Among them, g(x) represents the limit state equation of the structure. I[g(x)] is the indicator function. If g(x) ≤ 0, I[g(x)] = 1; if g(x) > 0, I[g(x)] = 0. f(x) represents the joint probability density function, which is defined as where f i (x i ) represents the probability density function of the random variable x i with a mean of μ i and a standard deviation of σ i ; ρ(x) is the density function of IS, which is defined as where ρ i (x i ) represents the importance sampling density function corresponding to x i . To avoid clustering sampling and ensure that the selected samples have practical physical meanings, the truncated Latin hypercube (TLHS) is used to generate M sets of sample values X k (k = 1, 2,..., M) of the random variable x. P f can be estimated as:

[0112]

[0113] Determining the "design point" (i.e., the sampling center) is an important issue in the importance sampling method. Since the structure function is in an implicit form of input variables, the "design point" needs to be obtained through a series of iterative calculations. The steps include:

[0114] According to the distribution of the random variables, use the truncated Latin hypercube technique to generate m sets of sample values X k (k = 1, 2,..., m), and input each set of samples X k into the finite element model to calculate the corresponding g(X k ) value;

[0115] In the m sets of samples in one iterative analysis, if there exists X k such that g(X k ) ≤ 0, then select the sample value X k corresponding to the maximum value of f(X * ) as the candidate design point; otherwise, select the sample value X k corresponding to the minimum value of g(X * ) as the candidate design point;

[0116] For each random variable X i , the mean μi is replaced, and then the truncated Latin hypercube technique is applied to obtain m new sets of sample values X (k = 1, 2,..., m), which are substituted into the finite element model for calculation, so as to obtain the new design point X k ; * ;

[0117] Analyze cyclically according to the above process. When g(X * ) ≈ 0, and the increment of each random variable corresponding to in the two consecutive iterations is less than the specified allowable error ω i , then the final X * is the approximate design point sought, and the iterative calculation terminates at this time;

[0118] Set the distribution center of the random variable at the final design point X * , and then input the M sets of sample values X k (k = 1, 2,..., M) generated respectively into the finite element model for calculation to obtain the corresponding g(X k ) values, while f(X k ) and ρ(X k ) are respectively expressed as:

[0119]

[0120] In the case, the importance sampling method is used to calculate the structural reliability, and the process of obtaining the approximate "design point" is as Figure 7 shown. Take m = 20 and M = 200. It takes about 15 iterations to reach convergence and obtain the approximate "design point".

[0121] (6) Establish the limit state equation for reliability analysis;

[0122] In the deflection reliability analysis, the maximum deflection of the prestressed concrete bridge should not exceed L / 600, where L is the main span. Here, it is used as the deflection threshold, and the limit state equation can be expressed as:

[0123] g(t) = [w] - [w max (t)]

[0124] where: [w] is the deflection threshold; [w max (t)] represents the mid-span deflection of the main span when operating for t years.

[0125] In the case, the main span L of the long-span box girder bridge is 150 m, the deflection threshold [w] is 0.25 m, and the mid-span deflection [W max (t)] of the main span when the bridge operates for t years is obtained through numerical analysis.

[0126] (7) Evaluate the time-varying reliability of structures considering the fatigue creep effect of concrete.

[0127] To verify the influence of fatigue creep on the reliability of long-span box girder bridges, two numerical models were established: in the first numerical model, only the effects of concrete static creep, shrinkage, and steel strand stress relaxation on long-term deformation were considered, and the subroutine for evaluating the fatigue creep effect was deactivated; for the second numerical simulation, the effects of these factors on the time-varying effect of the box girder bridge were considered simultaneously.

[0128] In the case, the time-history curves of the deflection reliability index were obtained by two numerical simulations, as Figure 8 shown. Based on the first numerical simulation, the reliability index at the completion of the bridge was 7.4, indicating that the structure had high reliability. With the development of concrete static creep, shrinkage, and the increase of prestress loss, the reliability index decreased rapidly, but within the entire design reference period, the reliability index was higher than the target value of 1.5; when the second numerical model was run, the reliability calculation results considering the fatigue creep effect of concrete were obtained, as Figure 8 shown. Due to the contribution of fatigue creep to long-term deformation being taken into account, the reliability index decreased accordingly, and the bridge was lower than the target level after about 35 years of service.

Claims

1. A time-varying reliability assessment method for long-span box girder bridges considering concrete fatigue creep, characterized in that: The method includes the following steps: (1) Calculate the static creep and shrinkage strain of concrete; (2) Calculate the fatigue creep strain of concrete generated by vehicle loads; (3) Construct a unified constitutive model of concrete considering the coupling effect of multiple factors; (4) Establish a refined numerical model for the long-term performance analysis of long-span box girder bridges; (5) Establish a time-varying reliability assessment method for long-span box girder bridges; (6) Establish a limit state equation for reliability analysis; (7) Evaluate the time-varying reliability of the structure considering the fatigue creep effect of concrete.

2. The time-varying reliability assessment method for long-span box girder bridges considering concrete fatigue creep according to claim 1, characterized in that: The step (1) includes the following steps: (1.1) Divide the calculation time into T time steps Δt i , where i = 1, 2..., T. According to the Kelvin chain model, transform the integral creep formula into a rate-type creep law with built-in variables. During the time step Δt i = t i - t i-1 , the increment of static creep strain of concrete is as follows: where, Δσ i is the stress increment within the time step Δt i ; N is the number of Kelvin elements; τ μ is the delay time, μ = 1, 2,......, N; γ μ is the internal variable of the Kelvin element considering the stress history of the previous time step; λ μ is the coefficient related to the delay time τ μ and the time step Δt i ; A μ is the discrete spectrum, and its expression is: Among them, C (k) is the k-th derivative of C(t, t0) = J(t, t0) - 1 / E μ with respect to time t, J(t, t0) is the creep function, and E μ is the elastic modulus of the μ-th Kelvin unit; in practical applications, k is taken as 3; (1.2) According to the CEB-FIP model, the increment of concrete shrinkage strain within the time step Δt i is as follows: Among them, t s is the starting shrinkage age; ε sh0 represents the nominal shrinkage strain; β RH is the coefficient affected by the relative environmental humidity; β s (t i -t s ) and β s (t i-1 -t s ) respectively represent the coefficients of the concrete shrinkage development during the time periods t i -t s and t i-1 -t s .

3. The time-varying reliability assessment method for long-span box girder bridges considering concrete fatigue creep according to claim 1, wherein: The step (2) includes within the time step Δt i the increment of concrete fatigue creep strain induced by the vehicle load, which is Among them, C1 = 46×10 -6 , m = 4, obtained through optimized analysis based on test data; σ is the average stress of concrete, approximated by the stress generated by the structural dead load; the stress amplitude Δσ = σ max -σ min , σ max and σ min are the maximum and minimum values of the normal stress of the cross-section; f c represents the standard compressive strength of concrete; ΔN c represents the traffic flow passing through the bridge within the time step Δt i . Average the cyclic stresses generated by various vehicles over time to obtain an equivalent fatigue load with a constant amplitude.

4. The time-varying reliability assessment method for long-span box girder bridges considering concrete fatigue creep according to claim 3, characterized in that: The calculation steps of the equivalent fatigue load include: (2.1) Based on the highway toll system near the bridge site, obtain the annual vehicle load data. For ease of analysis, classify the vehicles passing through the bridge according to their weights; (2.2) Based on the measured traffic information, adopt a simplified traffic pattern to approximate the complex operation mode of vehicles on the bridge, and determine whether various types of vehicles pass through the bridge side by side or one by one; (2.3) According to the determined vehicle load and traffic pattern, and combined with the moment influence lines of various vehicles, calculate the stress amplitude Δσ. The expression for the constant amplitude of the equivalent fatigue load is: where t N is the duration for N cycles, C is a constant parameter; Δσ(t) is the change amplitude generated by the actual vehicle load; Δσ represents the constant amplitude of the equivalent fatigue load.

5. The time-varying reliability assessment method for long-span box girder bridges considering concrete fatigue creep according to claim 1, characterized in that: The said step (3) includes, within each time step Δt i the total strain increment Δε of the concrete i is composed of the elastic strain increment i caused by the stress change Δσ the static creep strain increment the fatigue creep strain increment and the shrinkage strain increment Δε i is expressed as: The unified constitutive model of concrete considering the coupling effect of multiple factors can be expressed as: where t i-1 / 2 represents the midpoint time of the time step Δt i , and E″(t i-1 / 2 ) is the effective incremental modulus of concrete, and the expression is: Among them, E0 is the instantaneous elastic modulus of concrete.

6. The time-varying reliability assessment method for long-span box girder bridges considering concrete fatigue creep according to claim 1, characterized in that: The step (4) includes the following steps: (4.1) According to the unified constitutive model of concrete, simplify the complex creep analysis of the structure into an elastic problem for solution. Embed the constitutive model as a user subroutine into the general finite element program DLANA to calculate the long-term performance of the structure; (4.2) Use the DIANA software to establish only the finite element model of the 1 / 2 box girder bridge. Among them, the mechanical behavior of the thin-walled box girder is simulated by eight-node combined degenerated shell elements, and the ordinary steel bars are simulated by a series of steel bar meshes embedded in the shell elements. There are two layers of steel bar meshes on the top plate, web and bottom plate of the box girder; for the prestressed steel bars, determine them by defining the position key points and shape functions, and the program automatically generates the prestressed tendon elements; the initial material properties of concrete and steel bars are defined by their standard values, and the constitutive relations of ordinary steel bars and prestressed steel bars both adopt the bilinear model; (4.3) Use the stage analysis in the DIANA program to describe the complex stress time history during the cantilever construction process of the box girder. In the initial stage of the simulation, first blunt the segments, and then activate them in sequence according to the actual construction progress and closure sequence.

7. The time-varying reliability assessment method for long-span box girder bridges considering concrete fatigue creep according to claim 1, characterized in that: The step (5) includes calculating the reliability of the structure by the importance sampling method, establishing the sampling center at the most probable failure point of the structure, i.e., the design point, and assuming that n random variables x i (i = 1, 2,..., n) form a vector x, and calculating the failure probability P f , and the expression is: where \(g(x)\) represents the limit state equation of the structure; \(I[g(x)]\) is the indicator function, if \(g(x)\leq0\), \(I[g(x)] = 1\) and if \(g(x)>0\), \(I[g(x)] = 0\); \(f(x)\) represents the joint probability density function, defined as where \(f\) i (X i ) represents a random variable \(x\) i with mean \(\mu\) i and standard deviation \(\sigma\) i of the probability density function; \(\rho(x)\) is the density function of IS, defined as where \(\rho\) i (x i ) represents the importance sampling density function corresponding to \(x\) i ; \(M\) sets of sample values \(X\) k (\(k = 1, 2,\cdots,M\)) of the random variable \(x\) are generated by truncated Latin hypercube, and \(P\) f is estimated as: Determining the design point is an important issue in the importance sampling method. Since the structural performance function is in an implicit form of input variables, the design point is obtained through a series of iterative calculations.

8. The time-varying reliability assessment method for long-span box girder bridges considering concrete fatigue creep according to claim 7, characterized in that: The steps of obtaining the design point through iterative calculations include: (5.1) According to the distribution of the random variable, apply the truncated Latin hypercube technique to generate m sets of sample values X k (k = 1, 2,..., m), and input each set of samples X k into the finite element model to calculate the corresponding g(X k ) values; (5.2) Among the m groups of samples in an iterative analysis, if there exists X k such that g(X k ) ≤ 0, then select the sample value X k corresponding to the maximum value of f(X * ) as the design point to be selected; otherwise, select the sample value X k corresponding to the minimum value of g(X * ) as the design point to be selected; (5.3) Replace the mean value μ of each random variable X i with i and then apply the truncated Latin hypercube technique to obtain new m sets of sample values X (k = 1, 2,..., m), and substitute them into the finite element model for calculation, so as to obtain the new design point X k ; * ​ (5.4) Analyze cyclically according to the above process. When g(X * ) ≈ 0, and the increment of each random variable corresponding to in the previous and subsequent two iterations is less than the specified allowable error ω i , then the final X * is the approximate design point sought. At this time, the iterative calculation terminates; (5.5) Set the distribution center of the random variable at the final design point X * , and then input the M groups of generated sample values X k (k = 1, 2,..., M) into the finite element model for calculation respectively to obtain the corresponding g(X k ) values, while f(X k ) and ρ(X k ) are expressed as follows:

9. The time-varying reliability assessment method for long-span box girder bridges considering concrete fatigue creep according to claim 1, wherein: The step (6) includes that in the deflection reliability analysis, the maximum deflection of the prestressed concrete bridge should not exceed L / 600, where L is the main span. Here, it is used as the deflection threshold, and the limit state equation is expressed as: g(t) = [w] - [w max (t)] Where: [w] is the deflection threshold; [w max (t) represents the mid-span deflection of the main span at the operation time of t years.

10. The time-varying reliability assessment method for long-span box girder bridges considering concrete fatigue creep according to claim 1, characterized in that: The said step (7) includes establishing two numerical models to verify the influence of fatigue creep on the reliability of long-span box girder bridges: in the first numerical model, only the influence of concrete static creep, shrinkage and steel strand stress relaxation on long-term deformation is considered, and the subroutine used to evaluate the fatigue creep effect is deactivated; for the second numerical simulation, the influence of these factors on the time-varying effect of the box girder bridge is considered simultaneously.

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