Method for calculating reliability of finished bridge cable force by considering variation of initial tension cable force of suspender

Abstract

The invention relates to a method for calculating the reliability of finished bridge cable force by considering the variation of the initial tension cable force of a suspender, which comprises the following steps of: establishing a forward finite element model, obtaining a stage variation through the difference of the cable force of the suspender in the later and previous construction stage, obtaining the variation of the influence of a single suspender on the cable force of the suspender under the action of unit load, and constructing an influence matrix; carrying out Monte Carlo method sampling on the initial tension force of the suspender to obtain a random initial tension force sample set under a certain suspender tension precision; and calculating the final finished bridge cable force under each sample, judging whether the final finished bridge cable force under each sample reaches the target finished bridge cable force deviation requirement range or not, and obtaining the finished bridge cable force reliability of the bridge suspender under a certain suspender tension precision. According to the method, the relation between the initial cable tension of the lifting rod and the finished bridge cable force is established through the influence matrix, the process of calculating the finished bridge cable force is simplified, on this basis, the Monte Carlo method is combined for sampling and calculating the reliability of the finished bridge cable force, the calculation time is shortened, and the analysis efficiency is improved.

Description

Technical Field

[0001] The invention relates to the technical field of arch bridge construction monitoring, and in particular to a method for calculating the reliability of a completed bridge cable force by considering the variation of the initial cable force of a suspender rod. Background Art

[0002] In the actual construction process of arch bridges, due to the common existence of factors such as errors in tensioning tools, human errors in workers, and errors in cable tension measurement tools, it is still difficult to achieve the final bridge cable tension within the deviation range of the target bridge cable tension even if there is no deviation in other parameters except the initial tension.

[0003] In order to understand the probability that the completed cable force reaches the target completed cable force deviation requirement (completed cable force reliability) when the initial cable force of the hanger varies, a common practice is to use the finite element method to calculate the completed cable force and combine it with the Monte Carlo method to calculate the reliability of the completed cable force by sampling. First, it takes a certain amount of time to perform deterministic finite element analysis, and combined with the large number of sample calculations using the Monte Carlo method, this method has the disadvantage of being time-consuming. Summary of the invention

[0004] In view of the problems existing in the prior art, the purpose of the present invention is to provide a method for calculating the reliability of the cable force of a completed bridge by taking into account the variation of the initial cable force of the hanger, thereby shortening the calculation time of the reliability of the cable force of the completed bridge and improving the analysis efficiency.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A method for calculating the reliability of cable force of a completed bridge by considering the variation of initial cable force of suspenders comprises the following steps:

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

[0008] According to the established forward finite element model, the cable forces of the suspenders under the suspender tension and subsequent construction stages are extracted, the influence variation of the single suspender on the cable forces under its unit load is obtained, and the influence matrix related to the actual construction stage and the cable forces variation is constructed;

[0009] According to the initial tension of the hanger rod, the random variation of the initial tension of the hanger rod is considered, and the random initial tension sample set under a certain hanger rod tensioning accuracy is obtained;

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

[0011] Furthermore, the formal finite element model is obtained by using the Midas / civil finite element software to activate and passivate the units, boundaries, and loads in sequence according to the construction stages, based on the bridge parameters, load conditions, and boundary conditions provided by the design, combined with the construction plan and construction methods of the construction unit, to obtain the formal finite element model considering the construction stages.

[0012] Furthermore, the influence matrix is ​​constructed by operating the forward finite element model to obtain the calculation results of the suspender cable forces at each construction stage during the suspender tensioning and subsequent construction stages, and by subtracting the suspender cable forces at the previous and subsequent construction stages, the stage variation of the suspender cable forces at each construction stage is obtained, and the stage variation of each suspender cable force is divided by the initial tension applied to it at the construction stage to obtain the influence of the unit initial tension on the suspender cable forces of the entire bridge, thus forming an influence matrix [A] on the suspender cable forces under the unit initial tension of the suspender. j×k , which represents the influence matrix of the unit initial cable force of k hangers on the cable force of j hangers during the initial cable tensioning stage of k hangers during the construction process.

[0013] Furthermore, the random sample set is obtained by taking {x} as the initial tension of the hanger during construction under ideal conditions, which is a k-dimensional column vector, and performing Monte Carlo sampling on {x} with random variation to obtain a random sample set [X] under a certain hanger tensioning accuracy. k×n , where n represents the number of samples.

[0014] Furthermore, the cable force of the suspender after the suspender is tensioned is obtained as follows: based on the influence matrix [A] j×k , random sample set [X] k×n , through equation [A] j×k [X] k×n =[B] j×n Calculate the bridge suspender cable tension after all suspenders are tensioned, [B] j×n It represents the cable tension of the j hangers after all hangers corresponding to n samplings are tensioned.

[0015] Furthermore, during the construction phase, if the tensioning of the hanger includes the dismantling of temporary supports and the construction of the second-phase constant load, it is necessary to separately calculate the influence of the dismantling of the temporary supports and the construction of the second-phase constant load on the hanger cable tension, and add the influence of the two to the hanger cable tension of the bridge after all the hangers are tensioned to obtain the hanger cable tension of the completed bridge.

[0016] Furthermore, when calculating the influence of temporary support removal on the suspension rod cable force, it is necessary to calculate the influence matrix of each temporary support reaction force and the unit temporary support reaction force on the suspension rod cable force after the suspension rod is tensioned.

[0017] Furthermore, when calculating the reaction force of each temporary support after the suspension rod is tensioned, the reaction force of the temporary support before the suspension rod is tensioned plus the change in the reaction force of the temporary support during the tensioning of the suspension rod is required.

[0018] Furthermore, the reliability of the bridge suspender cable force is obtained as follows: it is determined whether the bridge suspender cable force corresponding to each sampling is within the target bridge suspender cable force deviation requirement range, where the number of times the target bridge suspender cable force deviation range is reached is recorded as m. Under a certain suspender tensioning accuracy, the reliability of the bridge suspender cable force is

[0019] Furthermore, when the hanger is actually tensioned, the tensioning accuracy of the initial cable force is controlled to be below 3% to ensure that the final cable force of the completed bridge can meet the regulatory requirements.

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

[0021] The existing technology usually directly performs deterministic finite element calculations and analyzes the reliability of the cable force of the completed bridge by combining a large number of samples (often tens of thousands) sampled by the Monte Carlo method, which takes a lot of time and has low analysis efficiency. The method of the present invention establishes the relationship between the initial cable force of the suspender and the cable force of the completed bridge through the influence matrix, which simplifies the process of calculating the cable force of the completed bridge. On this basis, the time required to calculate the reliability of the cable force of the completed bridge by combining the Monte Carlo method sampling is only a few minutes, which greatly shortens the calculation time and improves the analysis efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 The present invention is a flowchart for obtaining the reliability of the cable force of a completed bridge according to an embodiment of the present invention.

[0023] Figure 2 This is a numbering diagram of the suspension rod according to an embodiment of the present invention.

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

[0025] Based on the known initial cable tension of arch bridge hanger construction, the present invention introduces a random analysis method to consider the probability that the hanger cable tension will reach the target bridge cable tension deviation requirement in the final bridge state when the initial cable tension of the hanger deviates during the actual construction process.

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

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

[0028] S1. Based on the relevant design data and the actual construction plan, the finite element model of the installation considering the construction stage is established using the Midas / civil finite element software;

[0029] S2. According to the model established in S1, the cable forces of the suspenders in the suspender tensioning and subsequent construction stages are extracted, and the stage variation is obtained by subtracting the cable forces of the suspenders in the subsequent construction stages. For the construction stages of the suspender tensioning and temporary support unloading (if any), the influence variation of a single suspender or a single support on the cable forces of the suspenders under the unit load is obtained by dividing the aforementioned stage variation by the magnitude of the load applied thereto, and the influence matrix is ​​constructed, in which the rows represent the variation of the internal forces of each suspender or temporary support in a certain construction stage, and the columns represent the variation of the internal forces in each construction stage under a certain suspender number or temporary support number;

[0030] S3. According to the initial cable force of the hanger, the Monte Carlo method is used to sample the initial cable force of the hanger considering its random variation, and a random initial cable force sample set under a certain hanger tensioning accuracy is obtained.

[0031] S4. Based on the influence matrix obtained in S2 and the random initial cable tension sample set obtained in S3, the final cable tension under each sample is calculated, and it is judged whether the final cable tension under each sample reaches the target cable tension deviation range, and finally the reliability of the bridge suspender cable tension under a certain suspender tensioning accuracy is obtained.

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

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

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

[0035] The finite element model established in step S1 is operated to obtain the calculation results of the cable forces of the suspenders in each construction stage during the suspender tensioning and subsequent construction stages. The cable forces of the suspenders in each construction stage are subtracted from the cable forces of the previous and subsequent construction stages to obtain the change values ​​of the cable forces of the suspenders. Taking the suspender tensioning as an example, the calculation of the influence matrix of the cable forces of the suspenders under the action of the unit initial tension is explained: the change values ​​of the cable forces of each suspender in the tensioning construction stage of a certain suspender are divided by the initial tension applied to it in the tensioning construction stage to obtain the influence of the cable forces of the suspenders of the whole bridge under the action of the unit initial tension of the suspender. Then, the above calculations are performed for each suspender tensioning to form the influence matrix of the cable forces of the suspenders under the action of the unit initial tension of the suspender [A] j×k, which represents the influence matrix of the unit initial cable force of k hangers on the cable force of j hangers during the initial cable tensioning stage of k hangers during the construction process.

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

[0037] {x} represents the initial tension of the hanger during construction under ideal conditions, which is a k-dimensional column vector. Monte Carlo sampling is performed on {x} to obtain a random sample set [X] under a certain hanger tension accuracy. k×n , where n represents the number of samples.

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

[0039] Influence matrix obtained based on S2 [A] j×k , S3 obtains the random sample set [X] k×n , through equation [A] j×k [X] k×n =[B] j×n The cable tension of the bridge suspenders after all suspenders are tensioned can be calculated. [B] j×n It represents the cable tension of j suspenders after all the suspenders corresponding to n samplings are tensioned. The influence of temporary support removal and the second-phase constant load on the cable tension of the suspenders is further added to obtain the completed cable tension of the bridge in the completed state. Then, it is judged whether the completed cable tension of the bridge suspenders corresponding to each sampling is within the target cable tension deviation requirement range. The number of times that the target cable tension deviation range is reached is recorded as m. Under a certain suspender tensioning accuracy, the reliability of the bridge cable tension is

[0040] Take an arch bridge as an example. The main bridge is 460m long (50+180+180+50). There are 68 hangers in the whole bridge. The hangers are numbered as follows: Figure 2 The main beam adopts the form of steel box beam, and the arch rib adopts the form of steel arch. Combining relevant design data and actual construction process, a positive finite element model considering the construction stage is established. Figure 3 As shown in the figure. A total of 3862 nodes are established in the model, and the whole bridge is discretized into 6736 units. Beam units are used to simulate the main beam, arch ribs and bridge towers, and cable units in the tension-only units simulate the hangers and tie rods. The lower structure is simplified to general support, and the temporary support of the main beam is established with elastic support of the tension-only nodes. The connections between the main beam and the arch rib, the diagonal rod and the arch rib, the main and secondary arch ribs, the hanger and the main beam, and the hanger and the arch rib are all rigid type connections in the elastic connection. The construction process is shown in Table 1.

[0041] Table 1 Construction process division table

[0042] stage Working conditions 1 Construction of middle piers and side piers and erection of temporary supports for main beams, erection and installation of main beams 2 Steel main beam welding construction and closure 3 Install the arch rib bracket 4 Erection and installation of main and secondary arch ribs 5 Arch rib welding construction and closure 6 Installation of the middle pier tower 7 Removal of arch rib supports on steel main beams 8 Tension rods between the tension rods 9 Tensioning suspender 10 Dismantle the temporary support under the steel main beam 11 Construction Phase II Dead Load

[0043] During the 9th construction phase, the hangers were tensioned in the order of 1#→35#→18#→52#→2#→36#→19#→53#→3#→……→17#→51#→34#→68#.

[0044] First, taking the case where the variation of the initial tension of the hanger is not considered as an example, it is demonstrated how to establish a connection between the initial tension of the hanger and the cable tension of the completed bridge through the influence matrix method. The initial tension of each hanger in the construction of this bridge is shown in Table 2. First, the current step tension of all hangers in each hanger tensioning step is extracted from the established finite element model. Due to limited space, only part of it is shown here, as shown in Table 3. The cable force change value of each tensioning step is obtained by subtracting the cable force of the previous and subsequent tensioning steps, and then divided by the initial tension of the hanger applied in the current step, and the influence matrix of the hanger cable force under the unit initial tension is obtained as shown in Table 4. Taking the influence of the initial tension of the 2# cable on the tension of the 1# cable as an example, the calculation process of the numbers in Table 4 is explained. The change in the tension of the 1# cable when the 2# cable is tensioned is obtained by subtracting the tension of the 4th column and row 1 from the tension of the 5th column and row 195.5t in Table 3 from the tension of the 4th column and row 217.0t. Then, this change is divided by the initial tension of the 2# cable, 209.4t, in Table 2, to obtain the change in the tension of the 1# cable under the initial tension of the 2# cable, -1.03E-01.

[0045] Table 2 Initial tension of suspender

[0046] Search number Initial tension (t) Search number Initial tension (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 the hanger tensioning step

[0048]

[0049]

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

[0051]

[0052] It can be seen from the construction process division table in Table 1 that the temporary support of the steel main beam is dismantled after the suspension rod is tensioned. On the surface, this is only a single construction step, but it is the dismantling of hundreds of temporary support reaction forces. The reaction force of each temporary support is closely related to the previous suspension rod tensioning construction step. The change of the suspension rod cable force in this construction step is not purely linear, so it cannot be obtained by simply subtracting the previous and subsequent construction steps. To this end, two steps need to be completed. The first step is to obtain the reaction force of each temporary support when the temporary support of the steel main beam is dismantled, that is, after the suspension rod is tensioned; the second step is to obtain the influence matrix of the unit reaction force of each temporary support on the suspension rod cable force during the dismantling process of the temporary support of the steel main beam, and then obtain the change in the suspension rod cable force caused by the dismantling process.

[0053] For the first step, as before, the reaction forces of all temporary supports of the steel main beam in each hanger tensioning step are extracted from the finite element model. Due to space reasons, only part of them are shown here, as shown in Table 5. The reaction force change value of each tensioning step support is obtained by subtracting the reaction force of the previous and subsequent tensioning steps, and then divided by the initial tensioning force of the hanger applied in the current step to obtain the reaction force change value of each temporary support under the unit initial tensioning force, as shown in Table 6. The calculation process will not be repeated here.

[0054] Table 5 Reaction matrix of temporary support when the suspender is tensioned

[0055]

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

[0057]

[0058]

[0059] At this point, the influence matrix and initial cable tension obtained above can be used to obtain the change in the cable tension of the suspender and the reaction force of the temporary support of the steel main beam during the suspender tensioning period. It is worth noting that in order to obtain the reaction force of each temporary support after the suspender tensioning is completed, it is still necessary to add the reaction force of the temporary support before the suspender tensioning, that is, when the 8th construction step is completed, as shown in Table 7. However, the suspender has not appeared at the 8th construction step, so there is no suspender cable tension. The suspender cable tension and temporary support reaction force obtained by calculation when all suspenders are tensioned are shown in Tables 8 and 9 respectively. Taking the No. 1 cable tension in Table 8 as an example to illustrate the calculation process of each hanger cable tension, firstly, multiply the initial tension of each hanger in Table 2 by the influence of the initial tension of each hanger unit in Table 4 on the No. 1 hanger cable tension (first row) and then add them up, that is, 217.0×(1.00E+00)+216.9×(4.84E-08)+225.0×(4.45E-08)+224.9×(4.45E-08)+209.4×(-1.03E-01)+……+270.7×(4.52E-05)+270.6×(2.02E-03)+277.8×(7.06E-05)+277.8×(9.13E-05)=187.2t.

[0060] Table 7 Reaction force of temporary support for steel main beam in the 8th construction step

[0061]

[0062]

[0063] Table 8: Cable tension of suspenders when all suspenders are tensioned

[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 force of each temporary support in the finite element model after the hanger tensioning is completed is extracted, and the reaction force is used to replace the elastic support of the tension node only. A unit force is applied to each support, and the influence matrix of the temporary support unit reaction force on the hanger cable force is obtained. Due to limited space, only part of it is shown here, as shown in Table 10.

[0069] Table 10 The influence matrix of temporary support unit reaction force on the suspension cable force

[0070]

[0071] Based on the calculation results in Table 9 and the reaction influence matrix of each temporary support in Table 10, the change value of the suspension cable tension in the construction step of the temporary support unloading of the steel main beam can be calculated. The calculation method is similar to that in Table 8. First, the reaction forces of each temporary support in Table 9 are multiplied by the influence of the unit reaction force of each temporary support unloading on the 1# suspension cable tension in Table 10 (first row), and then the accumulation is performed to obtain the change value of the 1# suspension cable tension caused by the unloading of the temporary support of the steel main beam. The change value of the 2# suspension cable tension is obtained by multiplying it by the second row and accumulating it. Similarly, the change value of the 68 suspension cable tensions caused by the unloading of the temporary support of the steel main beam is obtained. Add this change value to the corresponding hanger in Table 8, and finally obtain the hanger cable force when the bridge is completed by linearly superimposing the change value of the single-step construction step of the second phase of constant load (Table 11). The purpose of this method is to calculate the bridge structure response by the influence matrix method to approximately replace the real response function of the bridge structure. For this purpose, it is necessary to compare the calculated values ​​of the influence matrix method with the calculation results of the finite element model to examine whether this method can accurately describe the bridge structure response when the hanger is tensioned to the completion of the bridge. The results are shown in Table 12.

[0072] Table 11 Changes in the cable force of the single-step construction step of the second phase of the construction with constant load

[0073]

[0074]

[0075] Table 12 Verification of the accuracy of the calculation results of the influence matrix method

[0076]

[0077]

[0078]

[0079] It can be seen from the above table that the cable forces of the completed bridge calculated by the influence matrix method are slightly different from the results of finite element analysis. The largest difference occurs in cable No. 54, which is -0.21%. This shows that the influence matrix method is effective in calculating the response of the bridge structure, and the reliability of the cable forces of the completed bridge can be further calculated.

[0080] Next, Monte Carlo sampling is performed based on the initial tension of the suspender in Table 2. The variation of the initial tension of the suspender conforms to the normal distribution. Taking the initial tension of the suspender in Table 2 as the mean, 10,000 samples are taken for the cases where the coefficient of variation of the initial tension is 1%, 2%, 3%, 4%, and 5%, respectively. Then, the above calculation is performed on each of the 10,000 samples. The reliability of the suspender cable force represents the probability that all the suspender cable forces are controlled within the maximum allowable deviation value of the construction under the bridge state. The maximum deviation value requirements in the standards "Highway Engineering Quality Inspection and Assessment Standards Volume 1 Civil Engineering" (JTG F80 / 1-2017) and "Technical Code for Highway Bridge Construction Monitoring" (JTG / T 3650-01-2022) are ±10% of the target bridge cable force. The target bridge cable force is shown in Table 13. The frequency of all the suspender cable forces being controlled within the maximum allowable deviation value of the target bridge cable force construction in the 10,000 sampling results is further calculated, which is approximated as the reliability p of the suspender cable force under the corresponding coefficient of variation. The calculation results are shown in Table 14.

[0081] Table 13 Target cable forces of suspenders

[0082] Search number Cable force(t) Search 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 Reliability of cable force in completed bridge under different tensioning accuracy of initial cable force

[0084]

[0085] As can be seen from the above table, the tensioning accuracy of the initial tension cable is sensitive to the cable tension of the suspender bridge. When the variation coefficient of the initial tension cable is below 3%, the reliability of the bridge cable is still relatively high. When the variation coefficient of the initial tension cable is 4%, the reliability of the bridge cable is 63.1%, which is 31.9% lower than the case with a variation coefficient of 3%. When the variation coefficient of the initial tension cable is 5%, the reliability of the bridge cable is only 20.2%, which is 74.8% lower than the case with a variation coefficient of 3%. The probability that all the suspender bridge cable forces reach the target bridge cable force deviation requirement range is very small. According to this result, when the bridge is actually tensioning the suspender, the tensioning accuracy of the initial tension cable should be controlled below 3% to ensure that the final bridge cable force can meet the specification requirements.

[0086] The present invention has the following advantages:

[0087] (1) The calculation of the cable tension reliability of the completed bridge is conducive to improving the construction monitoring unit's understanding of the overall situation of the suspender cable tension when the initial tension of the suspender cable varies.

[0088] (2) As the accuracy of hanger tensioning increases, the construction difficulty will also increase, and the construction cost will also increase. The calculation results of the cable force reliability of the completed bridge are helpful to help construction units find a balance between the hanger tensioning accuracy and the construction cost.

[0089] (3) The existing technology often takes several minutes to directly perform deterministic finite element calculations, and it takes a lot of time to analyze the reliability of the cable force of the completed bridge by combining a large number of samples (often tens of thousands) sampled by the Monte Carlo method. However, the method in this paper establishes the relationship between the initial cable force of the hanger and the cable force of the completed bridge through the influence matrix, which simplifies the process of calculating the cable force of the completed bridge. On this basis, the time required to calculate the reliability of the cable force of the completed bridge by combining the Monte Carlo method sampling is only a few minutes, which greatly shortens the calculation time and improves the analysis efficiency.

[0090] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A method for calculating the reliability of bridge cable force by considering the variation of initial cable force of suspenders, characterized in that: The following steps are included: According to the actual construction plan of the arch bridge, a positive finite element model considering the construction stage is established; According to the established forward finite element model, the cable forces of the suspenders under the suspender tension and subsequent construction stages are extracted, the influence variation of the single suspender on the cable forces under its unit load is obtained, and the influence matrix related to the actual construction stage and the cable forces variation is constructed; According to the initial tension of the hanger rod, the random variation of the initial tension of the hanger rod is considered, and the random initial tension sample set under a certain hanger rod tensioning accuracy is obtained; Based on the constructed influence matrix and the obtained random initial cable force sample set, the final cable force under each sample is calculated, and it is judged whether the final cable force under each sample reaches the target cable force deviation range. Finally, the reliability of the bridge hanger cable force under a certain hanger tensioning accuracy is obtained.

2. The method for calculating the reliability of the cable force of a completed bridge by considering the variation of the initial cable force of the suspender rod according to claim 1 is characterized in that: The method of obtaining the full-scale finite element model is to use the Midas / civil finite element software to activate and deactivate units, boundaries, and loads in sequence according to the construction stage based on the bridge parameters, load conditions, and boundary conditions provided by the design, combined with the construction plan and construction methods of the construction unit, to obtain the full-scale finite element model considering the construction stage.

3. The method for calculating the reliability of the cable force of a completed bridge by considering the variation of the initial cable force of the suspender rod according to claim 1 is characterized in that: The influence matrix is ​​constructed by operating the forward finite element model to obtain the calculation results of the suspender cable forces at each construction stage during the suspender tensioning and subsequent construction stages. The stage change of the suspender cable forces at each construction stage is obtained by subtracting the suspender cable forces at the previous and subsequent construction stages. The stage change of each suspender cable force is divided by the initial tension applied to it at that construction stage to obtain the influence of the unit initial tension on the suspender cable forces of the entire bridge, thus forming an influence matrix [A] on the suspender cable forces under the unit initial tension of the suspender. j×k , which represents the influence matrix of the unit initial cable force of k hangers on the cable force of j hangers during the initial cable tensioning stage of k hangers during the construction process.

4. The method for calculating the reliability of the cable force of a completed bridge by considering the variation of the initial cable force of the suspender rod according to claim 3 is characterized in that: The random sample set is obtained by taking {x} as the initial tension of the hanger during construction under ideal conditions, which is a k-dimensional column vector, and performing Monte Carlo sampling on {x} with random variation to obtain a random sample set [X] under a certain hanger tensioning accuracy. k×n , where n represents the number of samples.

5. The method for calculating the reliability of the cable force of a completed bridge by considering the variation of the initial cable force of the suspender rod according to claim 4 is characterized in that: The method to obtain the cable force of the suspender after the suspender is tensioned is as follows: based on the influence matrix [A] j×k , random sample set [X] k×n , through equation [a] j×k [X] k×n =[B] j×n Calculate the bridge suspender cable tension after all suspenders are tensioned, [B] j×n It represents the cable tension of the j hangers after all hangers corresponding to n samplings are tensioned.

6. The method for calculating the reliability of the cable force of a completed bridge by considering the variation of the initial cable force of the suspender rod according to claim 1 is characterized in that: During the construction phase, if the tensioning of the hanger includes the dismantling of temporary supports and the construction of the second-phase constant load, it is necessary to calculate the influence of the dismantling of the temporary supports and the construction of the second-phase constant load on the hanger cable tension respectively, and add the influence of the two to the hanger cable tension of the bridge after all the hangers are tensioned to obtain the hanger cable tension of the completed bridge.

7. The method for calculating the reliability of the cable force of a completed bridge by considering the variation of the initial cable force of the suspender rod according to claim 6 is characterized in that: When calculating the influence of temporary support disassembly on the hanger cable force, it is necessary to calculate the influence matrix of each temporary support reaction force and the unit temporary support reaction force on the hanger cable force after the hanger is tensioned.

8. The method for calculating the reliability of the cable force of a completed bridge by considering the variation of the initial cable force of the suspender rod according to claim 7, characterized in that: When calculating the reaction force of each temporary support after the hanger is tensioned, the reaction force of the temporary support before the hanger is tensioned plus the change in the reaction force of the temporary support during the hanger tensioning period are required.

9. The method for calculating the reliability of the cable force of a completed bridge by considering the variation of the initial cable force of the suspender rod according to claim 1, characterized in that: The reliability of the bridge suspender cable force is obtained as follows: determine whether the bridge suspender cable force corresponding to each sampling is within the target bridge suspender cable force deviation requirement range, where the number of times the target bridge suspender cable force deviation range is reached is recorded as m. Under a certain suspender tensioning accuracy, the reliability of the bridge suspender cable force is 10. The method for calculating the reliability of the cable force of a completed bridge by considering the variation of the initial cable force of the suspender rod according to claim 1, characterized in that: When actually tensioning the hanger, the tensioning accuracy of the initial cable force is controlled to be below 3% to ensure that the final cable force of the completed bridge meets the regulatory requirements.

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