A method for calculating bridge cable force reliability considering variation of initial cable force of suspender

Abstract

The present application relates to a kind of method for considering the reliability of bridge cable force calculation considering initial cable force variation of suspender, comprising the following steps, establish the finite element model of positive installation, obtain the stage variation by the difference of suspender cable force of before and after construction stage, obtain the influence variation of single suspender under the action of its unit load on suspender cable force, construct influence matrix;Monte Carlo method sampling is carried out to initial cable force of suspender, obtain the random initial cable force sample set under the tension accuracy of a certain suspender;The final bridge cable force under each sample is calculated, whether the final bridge cable force under each sample reaches the deviation requirement range of target bridge cable force is judged, obtains the reliability of bridge suspender bridge cable force under the tension accuracy of a certain suspender.The present application establishes the relationship between initial cable force of suspender and bridge cable force by influence matrix, simplifies the process of calculating bridge cable force, on this basis, the reliability of bridge cable force is calculated by combining Monte Carlo method sampling, shorten the calculation time, improve the analysis efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of arch bridge construction monitoring, in particular to a method for calculating bridge cable force reliability considering variation of initial cable force of hanger. BACKGROUND

[0002] In the actual construction process of the arch bridge, due to the universal existence of factors such as errors of tensioning tools, human errors of workers, and errors of cable force measuring tools, it is difficult to achieve that the final bridge cable force reaches the deviation range of the target bridge cable force under the condition that no deviation occurs in other parameters except the initial cable force.

[0003] In order to understand the probability (bridge cable force reliability) that the bridge cable force reaches the deviation requirement of the target bridge cable force under the condition of variation of the initial cable force of the hanger, the common method is to calculate the bridge cable force reliability by combining the finite element method with the Monte Carlo method sampling. First, the deterministic finite element analysis needs a certain time, and the large number of sample calculations combined with the Monte Carlo method sampling cause the method to have the disadvantage of long time consumption. SUMMARY

[0004] In view of the problems in the prior art, the purpose of the present application is to provide a method for calculating bridge cable force reliability considering variation of initial cable force of hanger, which shortens the calculation time of bridge cable force reliability and improves the analysis efficiency.

[0005] In order to achieve the above purpose, the present application adopts the following technical scheme:

[0006] A method for calculating bridge cable force reliability considering variation of initial cable force of hanger, comprising the following steps,

[0007] According to the actual construction scheme of the arch bridge, a forward finite element model considering the construction stage is established;

[0008] According to the established forward finite element model, the hanger tension and the hanger cable force under the subsequent construction stage are extracted therefrom to obtain the influence variation of a single hanger on the hanger cable force under the action of its unit load, and an influence matrix related to the actual construction stage and the hanger cable force variation is constructed;

[0009] According to the initial cable force of the hanger, the Monte Carlo method sampling is performed on the initial cable force of the hanger considering the random variation thereof to obtain a random initial cable force sample set under the tensioning accuracy of a certain hanger;

[0010] Based on the constructed influence matrix and the obtained random initial cable force sample set, the final bridge cable force under each sample is calculated, and it is judged whether the final bridge cable force under each sample reaches the deviation requirement range of the target bridge cable force, and finally the bridge hanger bridge cable force reliability under the tensioning accuracy of a certain hanger is obtained.

[0011] Further, the obtaining method of the forward finite element model is that according to the bridge parameters, load conditions and boundary conditions provided by the design, combined with the construction plan and construction method of the construction unit, the units, boundaries and loads are activated and passivated in sequence according to the construction stages by using the Midas / civil finite element software, and the forward finite element model considering the construction stages is obtained.

[0012] Further, the construction method of the influence matrix is that the forward finite element model is calculated to obtain the calculation results of the crane cable force in each construction stage under the crane tension and the subsequent construction stage, the stage change amount of the crane cable force in each construction stage is obtained by subtracting the crane cable force in the previous construction stage from the crane cable force in the subsequent construction stage, and the stage change amount of the crane cable force in each construction stage is divided by the initial tension cable force applied by the construction stage to obtain the influence of the unit initial tension cable force on the crane cable force of the whole bridge, and the influence matrix [A] of the unit initial tension cable force on the crane cable force is formed. j×k , which represents the influence of the unit initial tension cable force of the k crane tension stages in the construction process on the j crane cable force.

[0013] Further, the obtaining method of the random sample set is that {x} represents the initial tension cable force of the crane tension in the ideal situation, which is a k-dimensional column vector, and the Monte Carlo method sampling considering random variation is performed on {x} to obtain the random sample set [X] under the crane tension accuracy. k×n , wherein n represents the sampling number.

[0014] Further, the obtaining method of the crane cable force after the crane tension is as follows, based on the influence matrix [A] j×k , the random sample set [X] k×n , the crane cable force after the crane tension is calculated by the equation [A] j×k [X] k×n =[B] j×n , [B] j×n represents the crane cable force of the j cranes after the crane tension under n times of sampling.

[0015] Further, in the construction stage, if the crane tension is followed by the removal of the temporary support and the construction of the second permanent load, the influence of the temporary support removal and the second permanent load on the crane cable force needs to be calculated respectively, and the influence of the two is added to the crane cable force after the crane tension to obtain the crane cable force in the bridge.

[0016] Further, when calculating the influence of the temporary support removal on the crane cable force, the influence matrix of the crane cable force under the unit temporary support reaction force and the reaction force of each temporary support after the crane tension needs to be calculated.

[0017] Furthermore, when calculating the reaction force of each temporary support after the suspension rod is tensioned, it is necessary to add the reaction force of the temporary support before the suspension rod is tensioned to the change in the reaction force of the temporary support during the suspension rod tensioning period.

[0018] Furthermore, the reliability of the bridge suspender cable force in the completed bridge is obtained as follows: It is determined whether the cable force of the bridge suspender corresponding to each sampling is within the target deviation range for the completed bridge cable force. The number of times the target deviation range is reached is denoted as m. Then, under a certain suspender tensioning accuracy, the reliability of the bridge cable force in the completed bridge is:

[0019] Furthermore, during the actual tensioning of the suspenders, the initial tensioning accuracy is controlled to be below 3% to ensure that the final cable force of the completed bridge meets the specifications.

[0020] In summary, the present invention has the following advantages:

[0021] Existing techniques typically involve direct deterministic finite element analysis (FEM) calculations combined with Monte Carlo sampling of a large sample size (often tens of thousands) to analyze the reliability of the cable forces in completed bridges. This process is time-consuming and inefficient. In contrast, the method of this invention establishes the relationship between the initial tension of the suspenders and the cable forces in the completed bridge through an influence matrix, simplifying the calculation process. Furthermore, by combining this with Monte Carlo sampling, the time required to calculate the reliability of the cable forces in the completed bridge is only a few minutes, significantly reducing computation time and improving analysis efficiency. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the process of determining the reliability of cable forces in a completed bridge according to an embodiment of the present invention.

[0023] Figure 2 This is a diagram showing the numbering of the booms in an embodiment of the present invention.

[0024] Figure 3 This is a model diagram of an arch bridge according to an embodiment of the present invention. Detailed Implementation

[0025] Based on the known initial tension of the suspenders during arch bridge construction, this invention introduces a stochastic analysis method to consider the probability that the suspender tension will meet the target deviation requirement in the final bridge state, assuming deviations occur during the actual construction process.

[0026] The present invention will now be described in further detail.

[0027] like Figure 1 As shown, a method for calculating the cable force reliability of a completed bridge considering the variation in initial tension of the suspenders includes the following steps:

[0028] S1, according to the relevant design data and actual construction scheme, using Midas / civil finite element software to establish the finite element model considering the construction stage;

[0029] S2, according to the model established in S1, the cable tension of the crane boom and the cable tension of the crane boom in the subsequent construction stage are extracted, the difference between the cable tension of the crane boom in the subsequent construction stage and the cable tension of the crane boom in the previous construction stage is obtained, the change value of each construction stage is obtained. Take the crane boom tensioning and the temporary support unloading (if any) construction stage as an example, divide the change value obtained by the load applied to it to obtain the change value of a single crane boom or a single support under the action of unit load, and form a row indicating the internal force change value of each crane boom or temporary support in a certain construction stage. The influence matrix of the internal force change value of each construction stage under a certain crane boom number or temporary support number is indicated.

[0030] S3, according to the initial tensioning cable force of the crane boom, considering the random variation, the Monte Carlo method is used to sample the initial tensioning cable force of the crane boom under a certain crane boom tensioning accuracy to obtain a random initial tensioning cable force sample set.

[0031] S4, based on the influence matrix obtained in S2 and the random initial tensioning cable force sample set obtained in S3, the final bridge cable force under each sample is calculated, and whether the final bridge cable force under each sample reaches the target bridge cable force deviation requirement range is judged, and finally the bridge crane boom bridge cable force reliability under a certain crane boom tensioning accuracy is obtained.

[0032] For S1 step, the specific operation process is as follows:

[0033] According to the bridge parameters, load conditions, boundary conditions and other information provided by the design, combined with the construction plan and construction method of the construction unit, the Midas / civil finite element software is used to activate and passivate units, boundaries, loads and other information in sequence according to the construction stage to obtain the finite element model considering the construction stage.

[0034] For S2 step, the specific operation process is as follows:

[0035] The finite element model established in S1 step is calculated to obtain the crane boom tensioning and the cable tension of the crane boom in the subsequent construction stage. The difference between the cable tension of the crane boom in the subsequent construction stage and the cable tension of the crane boom in the previous construction stage is obtained. Take the crane boom tensioning as an example to explain the calculation of the influence matrix of the crane boom under the action of unit initial tensioning cable force. The change value of each crane boom cable force in the crane boom tensioning construction stage is divided by the initial tensioning cable force applied to it to obtain the influence of the crane boom under the action of unit initial tensioning cable force. Then the above calculation is carried out for each crane boom tensioning to form the influence matrix of the crane boom under the action of unit initial tensioning cable force. j×k, which represents the influence matrix of the unit initial cable force of the jth crane cable corresponding to the kth crane initial cable force tensioning stage in the construction process.

[0036] For S3, the specific operation process is as follows:

[0037] {x} represents the initial cable force of the crane tensioning in the ideal case, which is a k-dimensional column vector. The Monte Carlo method sampling considering random variation is performed on {x} to obtain a random sample set [X] under a certain crane tensioning accuracy. k×n , where n represents the number of samples.

[0038] For S4, the specific operation process is as follows:

[0039] Based on the influence matrix [A] obtained in S2 j×k , the random sample set [X] obtained in S3 k×n , the equation [A] j×k [X] k×n = [B] j×n The crane cable force of the bridge after all crane tensioning can be calculated, [B] j×n , which represents the crane cable force of the jth crane after all crane tensioning corresponding to n times of sampling, and further superimposes the influence of temporary support removal and construction secondary constant load on the crane cable force to obtain the bridge cable force in the bridge state. Then it is judged whether the bridge crane bridge cable force corresponding to each sampling is within the target bridge cable force deviation requirement range, where the number of times reaching the target bridge cable force deviation requirement range is m, then the bridge bridge cable force reliability under a certain crane tensioning accuracy is

[0040] Taking a certain arch bridge as an example, the main bridge is 460m long (50+180+180+50), and there are 68 cranes in the whole bridge, as shown in Figure 2 . The main girder adopts steel box girder form, and the arch rib adopts steel arch form. Combined with relevant design data and actual construction process, a forward finite element model considering construction stage is established as shown in Figure 3 . A total of 3862 nodes are established in the model, and the whole bridge is discretized into 6736 units. The beam element is used to simulate the main girder, arch rib and bridge tower, and the cable element in the only tension element is used to simulate the crane and pull rod. The substructure is simplified as general support, and the main girder temporary support is established by elastic support of only tension node. The connection between main girder and arch rib, inclined rod and arch rib, main and secondary arch rib, crane and main girder, and crane and arch rib is connected by rigid type connection in elastic connection. The construction process is shown in Table 1.

[0041] Table 1 Construction process division table

[0042] Stage Working condition 1 Construction of middle pier, side pier and erection of temporary support of main girder, erection and installation of main girder 2 Welding construction and closure of steel main girder 3 Installation and erection of arch rib support 4 Erection and installation of main and auxiliary arch rib 5 Welding construction and closure of arch rib 6 Installation of middle pier bridge tower 7 Dismantling of arch rib support on steel main girder 8 Tensioning of tie rod between curved rods 9 Tensioning of suspender 10 Dismantling of temporary support under steel main girder 11 Construction of secondary dead load

[0043] In the 9th construction stage, the suspender is stretched in the order of 1#→35#→18#→52#→2#→36#→19#→53#→3#→…→17#→51#→34#→68#.

[0044] Firstly, the initial cable force of each suspender is shown in Table 2. Firstly, the cable force of all the suspenders in each suspender stretching step is extracted from the established finite element model. Due to the limited space, only part of the data is shown in Table 3. The cable force change value of each stretching step is obtained by subtracting the cable force of the previous step from that of the current step. Then, the influence matrix of the unit initial cable force on the cable force of the suspender is obtained by dividing the cable force change value by the initial cable force of the suspender, as shown in Table 4. Taking the influence of the unit initial cable force of the 2# cable on the 1# cable as an example, the cable force change of the 1# cable when the 2# cable is stretched is obtained by subtracting the cable force of the 1# cable in the 4th column of the 1st row in Table 3 from the cable force of the 1st column of the 1st row in Table 3, i.e. 195.5t. Then, the change amount of the 1# cable under the unit initial cable force of the 2# cable is obtained by dividing the change by the initial cable force of the 2# cable in Table 2, i.e. 209.4t, i.e. -1.03E-01.

[0045] Table 2 Initial cable force of suspender

[0046] Cable number Initial tensioning cable force (t) Cable number Initial tensioning cable force (t) 1# 217.0 35# 216.9 2# 209.4 36# 209.3 3# 181.3 37# 181.3 4# 147.6 38# 147.6 5# 125.9 39# 125.9 6# 115.1 40# 115.1 7# 115.0 41# 115.0 8# 120.5 42# 120.5 9# 130.1 43# 130.2 10# 142.7 44# 142.7 11# 140.7 45# 140.7 12# 160.2 46# 160.3 13# 176.8 47# 176.8 14# 205.8 48# 205.7 15# 234.4 49# 234.3 16# 256.3 50# 256.2 17# 270.7 51# 270.6 18# 225.0 52# 224.9 19# 229.7 53# 229.6 20# 217.2 54# 217.1 21# 181.7 55# 181.6 22# 154.8 56# 154.7 23# 146.1 57# 146.0 24# 149.2 58# 149.1 25# 157.2 59# 157.1 26# 163.6 60# 163.5 27# 166.3 61# 166.2 28# 158.1 62# 158.1 29# 171.1 63# 171.1 30# 187.5 64# 187.4 31# 220.3 65# 220.2 32# 250.4 66# 250.4 33# 268.7 67# 268.7 34# 277.8 68# 277.8

[0047] Table 3 Cable force matrix of suspender in stretching step

[0048]

[0049]

[0050] Table 4 Influence matrix of unit initial cable force on cable force of suspender

[0051]

[0052] As can be seen from the construction process division table in Table 1, the temporary support of the steel main beam is removed after the suspender is stretched, which is a single construction step on the surface, but it is the removal of hundreds of temporary support counterforces. The size of each temporary support counterforce is closely related to the previous suspender stretching construction step. The change of the suspender cable force in this construction step is not simply linear, so it cannot be obtained by simply subtracting the previous construction step from the current construction step. Therefore, two steps need to be completed. Firstly, the size of each temporary support counterforce when the temporary support of the steel main beam is removed, i.e. after the suspender is stretched, is obtained. Secondly, the influence matrix of the unit counterforce of the temporary support of the steel main beam on the cable force of the suspender during the removal process is obtained, and then the change amount of the cable force of the suspender caused by the removal process is obtained.

[0053] For the first step, the same as before, the step reaction of all the steel girder temporary supports in each suspender tensioning step is extracted from the finite element model. Due to the length of the paper, only part of it is shown here, as shown in Table 5. The step reaction of each suspender tensioning step is subtracted from the previous step reaction to obtain the change value of the reaction of each temporary support, which is then divided by the initial tensioning cable force applied in the step to obtain the change value of the reaction of each temporary support per unit initial tensioning cable force, as shown in Table 6. The calculation process is not repeated here.

[0054] Table 5 Temporary support reaction matrix in suspender tensioning step

[0055]

[0056] Table 6 Influence matrix of unit initial tensioning cable force on temporary support reaction

[0057]

[0058]

[0059] At this point, the change value of the suspender cable force and the temporary support reaction during the suspender tensioning period can be obtained by the above-mentioned influence matrix and the initial tensioning cable force. It is worth noting that in order to obtain the temporary support reaction after the completion of the suspender tensioning, the reaction of the temporary support before the suspender tensioning, i.e. at the completion of the 8th construction step, still needs to be added, as shown in Table 7, and the suspender does not exist at the 8th construction step, so there is no suspender cable force. The suspender cable force and the temporary support reaction after the completion of all suspender tensioning are shown in Tables 8 and 9, respectively. Taking the 1# cable force in Table 8 as an example to explain the calculation process of each suspender cable force, first multiply each suspender initial tensioning cable force in Table 2 by the influence of each suspender tensioning unit initial tensioning cable force on the 1# suspender force (the first row) in Table 4, then add them up, i.e. 217.0 x (1.00E+00) + 216.9 x (4.84E-08) + 225.0 x (4.45E-08) + 224.9 x (4.45E-08) + 209.4 x (-1.03E-01) + … + 270.7 x (4.52E-05) + 270.6 x (2.02E-03) + 277.8 x (7.06E-05) + 277.8 x (9.13E-05) = 187.2 t.

[0060] Table 7 Temporary support reaction of steel girder in the 8th construction step

[0061]

[0062]

[0063] Table 8 Suspender cable force after the completion of all suspender tensioning

[0064]

[0065]

[0066] Table 9 Temporary support reaction force when all hangers are tensioned

[0067]

[0068] For the second step, the single-step construction process is discretized into the unloading of 308 temporary supports, the reaction forces of each temporary support in the finite element model after the hanger tensioning is completed are extracted, and the reaction forces are equivalent to replace the elastic support of the only tensioned node. A unit force is applied to each support to obtain the influence matrix of the temporary support unit reaction force on the hanger cable force. Due to the limited space, only part of it is shown in Table 10.

[0069] Table 10 Influence matrix of temporary support unit reaction force on hanger cable force

[0070]

[0071] By combining the calculation results in Table 9 and the influence matrix of each temporary support reaction force in Table 10, the change value of the hanger cable force during the unloading construction step of the steel girder temporary support can be calculated. The calculation method is similar to Table 8. First, multiply each temporary support reaction force in Table 9 by the influence of the unloading of each temporary support unit reaction force on the 1# hanger cable force in Table 10 (the first row), then add up to obtain the change value of the 1# hanger cable force caused by the unloading of the steel girder temporary support. Multiply by the second row and add up to obtain the change value of the 2# hanger cable force. Similarly, the change value of the 68 hanger cable forces caused by the unloading of the steel girder temporary support is obtained. Add the change value to the corresponding hanger in Table 8, and finally obtain the hanger cable force by linear superposition of the construction second-phase dead load single-step construction step change value (Table 11). The purpose of this method is to calculate the bridge structure response by the influence matrix method to approximately replace the true response function of the bridge structure. Therefore, the difference between the calculation value of the influence matrix method and the finite element model calculation result needs to be compared to investigate whether this method can accurately describe the bridge structure response when the hanger is tensioned to the completed bridge. The results are shown in Table 12.

[0072] Table 11 Change value of hanger cable force in construction second-phase dead load single-step construction step

[0073]

[0074]

[0075] Table 12 Accuracy verification of calculation results by influence matrix method

[0076]

[0077]

[0078]

[0079] From the above table, it can be seen that the bridge completion cable force calculated by the influence matrix method has small difference with the finite element analysis result, the maximum difference appears in No. 54 cable, which is -0.21%, that is, the bridge structure response obtained by the influence matrix method has good effect, and the bridge completion cable force reliability can be further calculated.

[0080] Next, based on the initial tension cable force of the suspender in Table 2, Monte Carlo sampling is carried out. The variation of the initial tension cable force of the suspender conforms to the normal distribution, and the initial tension cable force of the suspender in Table 2 is taken as the mean value. 10000 times sampling is carried out respectively under the conditions that the variation coefficient of the initial tension cable force is 1%, 2%, 3%, 4% and 5%. Then, the above calculation is respectively performed on the 10000 samples. The suspender bridge completion cable force reliability is expressed as the probability that all the suspender bridge completion cable forces are controlled within the maximum deviation value of the construction under the bridge state. The requirements for the maximum deviation value in the standards “Highway Engineering Quality Inspection and Evaluation Standard First Volume Civil Engineering” (JTG F80 / 1-2017) and “Highway Bridge Construction Monitoring Technical Specification” (JTG / T 3650-01-2022) are ±10% of the target bridge completion cable force. The target bridge completion cable force is shown in Table 13. The frequency that all the suspender bridge completion cable forces are controlled within the maximum deviation value of the construction of the target bridge completion cable force in the 10000 sampling results is further calculated, which is approximately the suspender bridge completion cable force reliability p under the corresponding variation coefficient. The calculation results are shown in Table 14.

[0081] Table 13 Target bridge completion cable force of suspender

[0082] Cable number Cable force (t) Cable number Cable force (t) 1 190.0 35 210.0 2 190.0 36 210.0 3 190.0 37 220.0 4 190.0 38 220.0 5 190.0 39 220.0 6 190.0 40 220.0 7 190.0 41 230.0 8 190.0 42 230.0 9 180.0 43 230.0 10 180.0 44 230.0 11 180.0 45 240.0 12 180.0 46 240.0 13 170.0 47 240.0 14 170.0 48 240.0 15 170.0 49 250.0 16 170.0 50 250.0 17 170.0 51 250.0 18 170.0 52 250.0 19 170.0 53 270.0 20 170.0 54 270.0 21 180.0 55 270.0 22 180.0 56 270.0 23 180.0 57 290.0 24 180.0 58 290.0 25 190.0 59 290.0 26 190.0 60 290.0 27 190.0 61 300.0 28 190.0 62 300.0 29 200.0 63 300.0 30 200.0 64 300.0 31 200.0 65 300.0 32 200.0 66 300.0 33 210.0 67 300.0 34 210.0 68 300.0

[0083] Table 14 Bridge completion cable force reliability under different tensioning accuracy of initial tension cable force

[0084]

[0085] From the above table, it can be seen that the tensioning accuracy of the initial tension cable force has a sensitive influence on the suspender bridge completion cable force. When the variation coefficient of the initial tension cable force is less than 3%, the bridge completion cable force reliability is still high. When the variation coefficient of the initial tension cable force is 4%, the bridge completion cable force reliability is 63.1%, which is reduced by 31.9% compared with the case that the variation coefficient is 3%. When the variation coefficient of the initial tension cable force is 5%, the bridge completion cable force reliability is only 20.2%, which is reduced by 74.8% compared with the case that the variation coefficient is 3%. The probability that all the suspender bridge completion cable forces reach the deviation requirement range of the target bridge completion cable force is already very small. According to the result, when the suspender is actually tensioned, the initial tension cable force tensioning accuracy should be controlled to be less than 3% to ensure that the final bridge completion cable force can meet the specification requirements.

[0086] The present application has the following advantages:

[0087] (1) The calculation of the reliability of the completed bridge cable force is conducive to improving the grasp of the overall situation of the suspender cable force by the construction monitoring unit in the case of variation of the initial suspender cable force.

[0088] (2) With the improvement of the suspender tensioning accuracy, the construction difficulty will also increase, and the construction cost will also increase. The calculation result of the reliability of the completed bridge cable force is conducive to helping the construction unit to find a balance between the suspender tensioning accuracy and the construction cost.

[0089] (3) The existing technology directly performs deterministic finite element calculation, which often takes several minutes. A large number of samples (often tens of thousands) are combined with the Monte Carlo method to analyze the reliability of the completed bridge cable force, which requires a large amount of time. The method of the present application establishes the relationship between the initial suspender cable force and the completed bridge cable force through the influence matrix, simplifies the process of calculating the completed bridge cable force, and on this basis, the time required for calculating the reliability of the completed bridge cable force by combining the Monte Carlo method is only a few minutes, which greatly shortens the calculation time and improves the analysis efficiency.

[0090] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited by the above embodiments, and any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present application are equivalent replacement methods and are included in the protection scope of the present application.

Claims

1. A method for calculating the reliability of the cable force of a completed bridge considering the variation of the initial tension of the suspenders, characterized in that: Includes the following steps, Based on the actual construction plan of the arch bridge, a finite element model of the arch bridge was established, taking into account the construction stages. Based on the established finite element model, the cable force of the suspender under tension and subsequent construction stages is extracted. The influence of a single suspender on the cable force under its unit load is obtained, and the influence matrix related to the actual construction stage and the change of cable force is constructed. Based on the initial tension force of the suspender, considering its random variation, Monte Carlo sampling is performed on the initial tension force of the suspender to obtain a random initial tension force sample set under a certain tensioning accuracy of the suspender. Based on the constructed influence matrix and the obtained random initial tension sample set, the final bridge cable force under each sample is calculated. The final bridge cable force under each sample is judged to see whether it reaches the target bridge cable force deviation requirement range. Finally, the reliability of the bridge cable force of the bridge suspender under a certain suspender tensioning accuracy is obtained. The influence matrix is ​​constructed as follows: A finite element model is calculated to obtain the cable force calculation results for each construction stage during the tensioning and subsequent construction phases of the suspenders. The stage variation of the cable force is obtained by subtracting the cable forces from those of the preceding and following construction stages. This stage variation is then divided by the initial tension applied to the suspenders during that construction stage to obtain the influence of a unit initial tension on the overall bridge suspender cable force, thus forming the influence matrix on the suspender cable force under a unit initial tension. , indicating the construction process k The effect of the unit initial tension force on the suspender during the initial tensioning stage of the suspender cable on the... j Influence matrix of the root shunt cable force; The random sample set is obtained by using... This represents the initial tension force of the suspender during construction under ideal conditions. k dimensional column vector, for Monte Carlo sampling, which takes into account random variation, is used to obtain a random sample set under a certain tensioning accuracy of the boom. ,in n Indicates the number of samples; The method for obtaining the cable force of the suspender after tensioning is as follows, based on the influence matrix. Random sample set Through equation The cable tension of the bridge's hangers was calculated after all hangers were tensioned. This indicates that after all the suspension rods have been tensioned, n The sampling corresponding to j The cable force matrix of the root suspender.

2. The method for calculating the reliability of bridge cable forces considering the variation of initial tension cable force in suspenders, as described in claim 1, is characterized in that: The formal finite element model is obtained by using Midas Civil finite element software to activate and deactivate elements, boundaries, and loads sequentially according to the construction stage, based on the bridge parameters, load conditions, and boundary conditions provided in the design, combined with the construction plan and construction methods of the construction unit, to obtain a formal finite element model that takes into account the construction stage.

3. The method for calculating the reliability of bridge cable forces considering the variation of initial tension cable force in suspenders, as described in claim 1, is characterized in that: During the construction phase, if the tensioning of the suspenders includes the dismantling of temporary supports and the construction of the second-phase dead load, it is necessary to calculate the impact of the dismantling of temporary supports and the construction of the second-phase dead load on the suspender cable force separately, and then add the impact of the two to the suspender cable force of the bridge after all suspenders are tensioned to obtain the suspender cable force of the completed bridge.

4. The method for calculating the reliability of bridge cable forces considering the variation of initial tension cable force in suspenders, as described in claim 3, is characterized in that: When determining the impact of temporary support dismantling on the suspender cable force, it is necessary to obtain the influence matrix of the reaction force of each temporary support and the reaction force of a unit temporary support on the suspender cable force after the suspender is tensioned.

5. The method for calculating the reliability of bridge cable forces considering the variation of initial tension cable force in suspenders according to claim 4, characterized in that: To determine the reaction forces of each temporary support after the suspension rod is tensioned, we need to add the reaction forces of the temporary supports before the suspension rod is tensioned to the changes in the reaction forces of the temporary supports during the tensioning process.

6. The method for calculating the reliability of bridge cable forces considering the variation of initial tension cable force in suspenders according to claim 1, characterized in that: The reliability of the bridge suspender cable force in the completed bridge is obtained as follows: It is determined whether the cable force of the bridge suspender corresponding to each sampling is within the target deviation range for the completed bridge cable force. The number of times the target deviation range is met is recorded as follows: m Under a certain tensioning accuracy of the suspender, the reliability of the cable force of the completed bridge is: .

7. The method for calculating the reliability of the completed bridge cable force considering the variation of the initial tension of the suspenders, as described in claim 1, is characterized in that: When actually tensioning the suspenders, the initial tensioning accuracy should be controlled to be below 3% to ensure that the final cable force of the completed bridge meets the specifications.

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