Inverse analysis method for internal forces of rope buckle and back rope under postural driving

Abstract

By providing a method for backward analysis of the internal forces of rope buckles and back ropes under posture driving in the field of bridge construction safety control, it provides strong technical guarantees for rope force adjustment and abnormal rope warning, and greatly improves the stability and safety of arch bridge structures during the cantilever construction process. [Solution] A parametric nonlinear mechanical calculation model is established for rope buckles, back ropes, and cable towers, and the initial rope force, initial apparent damage state, temperature, and spatial posture of each rope are obtained based on different equilibrium states of the tensile process of the arch rib segment. Using each rope spatial posture vector as the target, the parametric nonlinear mechanical calculation model is repeatedly updated to calculate the rope force value of each rope, and a special virtual rope force change vector and rope force apparent loss ratio vector are further calculated to further obtain the rope force value of the non-new rope in the current equilibrium state.

Description

[Technical Field]

[0001] The present invention relates to the field of bridge construction safety control, and more particularly to a method for inverse analysis of the internal forces of rope buckles and back ropes under posture driving. [Background technology]

[0002] Cantilever construction is an efficient and widely used method for constructing large-span or ultra-large-span arch bridges. During this process, cable towers, as temporary structures, not only provide support for the arch ribs, but also maintain the stability and safety of the structure during construction through the rational arrangement of rope buckles and back ropes. While rope buckles are primarily used to provide support for the main arch section construction, back ropes are used to balance the forces exerted by the rope buckles, thereby maintaining the structure's equilibrium. This force balance is achieved through precise calculations and careful adjustment of rope forces.

[0003] However, during construction, after the next arch rib segment is pulled, the spatial posture of the front arch rib segment changes, and the rope force conditions of the rope buckle and back rope also change. These changes are not only affected by the arch rib's own weight and the construction load, but also by factors such as manufacturing errors, variations in construction control, and slack in the rope structure, making it difficult to accurately evaluate the rope force conditions of the rope buckle and back rope, and making it impossible to ensure safety throughout the entire construction process.

[0004] Therefore, how to accurately calculate each rope force value and identify the abnormal rope position becomes a problem that must be solved immediately by those skilled in the art. Summary of the Invention [Problem to be solved by the invention]

[0005] In this regard, the present invention provides a method for reverse analysis of the internal forces of the rope buckle and back rope under posture driving, so as to accurately obtain the rope force value of each rope after balancing the tension of each arch rib segment, and accurately identify the abnormal rope position and rope force value. In order to achieve the above objectives, the present invention provides the following technical solutions: [Means for solving the problem]

[0006] The present invention discloses a method for backward analysis of the internal force of the rope buckle and the back rope under posture driving, and the specific steps are as follows:

[0007] The method for reverse analysis of the internal force of the rope buckle and the back rope under posture driving is characterized in that the specific steps are as follows:

[0008] Step 1: Obtain the initial geometry data, elastic modulus, and volumetric weight of the cable tower, the initial geometry data, elastic modulus, and volumetric weight of the arch rib, and the initial length, cross-sectional area, elastic modulus, and volumetric weight of each rope, and establish and initialize a parametric nonlinear mechanical calculation model.

[0009] Step 2: Number the rope buckles and back ropes, and number the rope buckles, back ropes and cable tower equilibrium states at different times according to the tension process of the arch rib segments.

[0010] Step 3: Obtain the initial rope force values ​​of the newly added ropes in the current equilibrium state, update the initial rope force value matrix, obtain the temperature value and spatial posture vector of each rope, and calculate the temperature change vector and spatial posture change vector of each rope.

[0011] Step 4: Detect the apparent damage state of each rope before tensioning, obtain the initial apparent damage state data, and obtain the rope force initial loss value according to the correspondence between the damage type and the rope force (for example, the correspondence between the rope force and factors such as the number of broken rope threads, the degree of rust on the rope cross section, and the slip distance when the rope is tensioned and locked), and then calculate the rope force apparent loss ratio vector of each rope based on the initial rope force value.

[0012] Step 5: Add a new rope to the current parametric nonlinear mechanics calculation model, and use the spatial posture change vector of each rope in the current equilibrium state as the rope force adjustment target. Make the difference between each rope spatial deformation of the parametric nonlinear mechanics calculation model and the spatial posture change vector reach the target accuracy, update the parametric nonlinear mechanics calculation model, and calculate the rope force vector of each rope in the parametric nonlinear mechanics calculation model.

[0013] Step 6: In the updated parametric nonlinear mechanical calculation model, the total number of ropes is set as the number of cycles, and non-overlapping ropes are specified one by one so that unit virtual damage occurs each time, and the damage to the remaining ropes is set to zero, thereby obtaining a rope force change vector corresponding to the occurrence of unit virtual damage in a single rope buckle each time, and further obtaining a rope force change matrix corresponding to the virtual unit damage.

[0014] Step 7: Based on the rope force change matrix, the rope force vector of each rope in the model, and the initial rope force value matrix, calculate a special virtual rope force change vector value for each rope, which indicates the ratio of the rope force change amount to the initial rope force value after unit displacement damage occurs in each rope.

[0015] Step 8: According to the special virtual rope force change vector and the rope force apparent loss ratio vector of each rope, calculate the nominal actual rope force change vector of each rope, and each element of the nominal actual rope force change vector indicates the ratio of the rope force change value and the actual rope force value, which is combined with the initial rope force to further obtain the rope force value of the non-new rope in the current equilibrium state.

[0016] Step 9: Repeat steps 3 to 8 until the arch rib segment tensioning process is completed.

[0017] Furthermore, the equilibrium state and the initial rope force value are confirmed based on design drawings and on-site measurements.

[0018] Furthermore, X=[X 1k ,X 2k ,…,X nk ,X (n+1)b ,X (n+2)b ,…,X wb ,] Rope buckles and back ropes are numbered according to this formula.

[0019] Here, k indicates that rope X is a rope buckle, b indicates that rope X is a back rope, n is the total number of rope buckles, and W is the total number of rope buckles and back ropes.

[0020] Furthermore, the spatial attitude vector is acquired by scanning with a total station or a three-dimensional laser.

[0021] Furthermore, the initial apparent damage conditions include thread breakage, rust, and jig slippage, and step 4 quantifies and takes into account the initial apparent damage conditions including thread breakage, rust, jig slippage, etc.

[0022] Furthermore, step 5 further includes updating the temperature and initial apparent damage state of each rope in the parametric nonlinear dynamics calculation model based on the temperature change vector and rope force apparent loss ratio vector of each rope.

[0023] Furthermore, step 6 includes: considering that virtual damage of unit displacement occurs only in the i-th rope buckle, calculating the rope force change vector of each rope based on the parametric nonlinear mechanics calculation model; and when calculating all i values ​​one by one, considering the rope force change vector of each rope when virtual damage of unit displacement occurs only in the i-th rope buckle, and obtaining a rope force change matrix corresponding to the virtual unit damage. [Effects of the Invention]

[0024] From the above technical solution, it can be seen that, compared with the prior art, the present invention discloses and provides a method for reverse analysis of the internal force of the rope buckle and the back rope under posture driving.

[0025] An accurate model iterative calculation mechanism is established, and the change in the measured rope spatial posture is repeatedly used as the target. Automatic iterative calculations are performed using a parametric nonlinear mechanical model until the rope force state and the measured posture accurately match. This realizes real-time monitoring and dynamic adjustment of the rope force state during construction. This not only effectively responds to changes in rope force caused by factors such as manufacturing errors, variations in construction control, and loose rope structure, but also accurately locates abnormal rope positions and quantitatively analyzes abnormal rope force values. This provides solid technical guarantee for rope force adjustment and abnormal rope warning, greatly improving the structural stability and safety of arch bridges during cantilever construction. This has important theoretical significance and application value in the field of bridge construction, and will have a significant impact on the safety assurance and optimization of large-span arch bridge construction. [Brief explanation of the drawings]

[0026] In order to more clearly describe the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the accompanying drawings that need to be used in the embodiments or prior art description. It is obvious that the accompanying drawings in the following description are only embodiments of the present invention, and those skilled in the art can obtain other accompanying drawings based on the accompanying drawings provided without exerting any creative efforts.

[0027] [Figure 1] 1 is a schematic diagram of the steps of the present invention; [Figure 2] 1 is a schematic diagram of the main arch arrangement of an arch bridge according to an embodiment of the present invention. [Figure 3] FIG. 10 is a schematic diagram of the distribution of cable towers, back ropes, and rope buckles during the half arch rib construction stage of an embodiment of the present invention. [Figure 4] 1 is a schematic diagram of a parametric nonlinear dynamics calculation model according to an embodiment of the present invention; [Figure 5] FIG. 1 is a schematic diagram of the equilibrium state of the first embodiment of the present invention. [Figure 6] FIG. 2 is a schematic diagram of the equilibrium state of the second embodiment of the present invention. [Figure 7] FIG. 3 is a schematic diagram of the equilibrium state of the third embodiment of the present invention. [Figure 8] FIG. 4 is a schematic diagram of the equilibrium state of the fourth embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0028] The following clearly and completely describes the technical solutions in the embodiments of the present invention in combination with the accompanying drawings in the embodiments of the present invention, and obviously, the described embodiments are only some embodiments of the present invention, not all embodiments, and all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without any creative efforts fall within the protection scope of the present invention.

[0029] The embodiment of the present invention discloses a method for backward analysis of the internal force of the rope buckle and the back rope under posture driving, as shown in Figure 1, the specific steps are as follows:

[0030] Step 1: Obtain the initial geometric data, elastic modulus, and volume weight of the cable tower, the initial geometric data, elastic modulus, and volume weight of the arch rib, and the initial length, cross-sectional area, elastic modulus, and volume weight of each rope. Then, calculate the parametric nonlinear mechanical calculation model M corresponding to the Gth arch rib segment casting shown in Figure 4. k where k is the number of iterations of the model, G represents the construction step where the current model is located, and then initialize the model to obtain the model M k is established by examining design drawings and on-site measured structural data, and taking into account factors such as self-weight, vertical effect, and temperature changes.

[0031] Step 2: Number the rope buckles and back ropes, and number the rope buckles, back ropes and cable tower equilibrium states at different times according to the tension process of the arch rib segments.

[0032] Step 3: Obtain the initial rope force value of the newly added rope in the current equilibrium state and calculate the initial rope force matrix S o Update the temperature value and spatial posture vector of each rope, calculate the temperature change vector and spatial posture change vector of each rope, and obtain the temperature change matrix △T and spatial posture change matrix △D.

number

[0033] Here, 1k, 2k, and Wb indicate the numbers of each rope, and W is the total number of ropes including rope buckles and back ropes.

[0034] Step 4: Detect the apparent damage state of each rope before tensioning, obtain the initial apparent damage state data, and obtain the rope force initial loss value according to the correspondence between the damage type and the rope force (for example, the correspondence between the rope force and factors such as the number of broken rope threads, the degree of rust on the rope cross section, and the slip distance when the rope is tensioned and locked). Then, calculate the rope force apparent loss ratio vector h0 for each rope based on the initial rope force value. i Calculate the matrix h0=[ h0 1k , h0 2k ,...,h0 Wb ], where i denotes the number of any one of the ropes in the current equilibrium state, and i ⊂ (1, 2, 3, ... W).

[0035] Step 5: Add a new rope to the current parametric nonlinear dynamics calculation model, and use the spatial posture change vector of each rope in the current equilibrium state as the rope force adjustment target. In the parametric nonlinear dynamics calculation model, the difference between each rope's spatial deformation and the spatial posture change vector reaches the target accuracy. Update the parametric nonlinear dynamics calculation model, and calculate the rope force vector matrix S of each rope in the parametric nonlinear dynamics calculation model, S = [S 1k ,S 2k ,…, S wb ,] T is.

[0036] Step 6: In the updated parametric nonlinear dynamics calculation model, a special virtual unit displacement vector D i Based on this, the total number of ropes is used as the number of cycles, and by specifying non-overlapping ropes one by one so that unit virtual damage occurs each time, and specifying damage to the remaining ropes as zero, a rope force change vector corresponding to the occurrence of unit virtual damage in a single rope buckle is obtained each time, and further a rope force change matrix ΔS' corresponding to the virtual unit damage is obtained.

[0037] Step 7: Rope force change matrix △S', rope force vector matrix S for each rope in the model, initial rope force value matrix So Based on this, the special virtual rope force change vector matrix h value of each rope is calculated, and h = [h 1k , h 2k ,…, h wb ,], a special virtual rope force change vector indicates the ratio of the rope force change amount after unit displacement damage occurs in each rope to the initial rope force value.

[0038]

number

[0039] Step 8: Based on the special virtual rope force change vector matrix h and the rope force apparent loss ratio vector matrix h0 of each rope, the nominal actual rope force change vector h of each rope is calculated. i Calculate ' and h i '=1-(1-h0 i) )(1-h i ) and h i ' denotes the ratio of the rope force remaining value of the i-th rope buckle to the initial rope force value, which is used to calculate the rope force value of the non-new rope in the current equilibrium state.

[0040] Step 9: Repeat steps 3 to 8 until the arch rib segment tensioning process is completed.

[0041] In one specific embodiment, the equilibrium state and the initial rope force value are confirmed based on design drawings and on-site measurements.

[0042] In one specific embodiment, the rope buckles, back ropes are numbered according to the formula: X=[X 1k ,X 2k ,…,X nk ,X (n+1)b ,X (n+2)b ,…,X wb ,]

[0043] Here, k indicates that rope X is a rope buckle, b indicates that rope X is a back rope, n is the total number of rope buckles, and W is the total number of rope buckles and back ropes. Note that the first construction step is numbered by performing rope buckle and then back rope, the second construction step continues to number based on the change in the previous step, and newly added ropes are numbered by performing rope buckle and then back rope.

[0044] In one specific embodiment, the spatial attitude vector is obtained by a total station or a 3D laser scan.

[0045] In one specific example, the initial apparent damage conditions considered include thread breakage, rust, and jig slippage.

[0046] In one specific embodiment, step 5 further includes updating the temperature and initial apparent damage state of each rope in the parametric nonlinear dynamics calculation model based on the temperature change vector and rope force apparent loss ratio vector of each rope.

[0047] In one specific embodiment, step 6 includes considering that the virtual damage of unit displacement occurs only in the i-th rope buckle, and the virtual damage of unit displacement occurred in other ropes is 0, and calculating the rope force change vector matrix ΔS of each rope based on a parametric nonlinear dynamics calculation model. i Calculate ΔS i =[ΔS i 1k , ΔS i 2k ,...,ΔS i Wb ] T When calculating all i values ​​one by one, consider the rope force change vector matrix of each rope when a virtual damage of unit displacement occurs only in the i-th rope buckle, and obtain the rope force change matrix ΔS' corresponding to the virtual unit damage, ΔS'=[ΔS' 1k ,ΔS' 2k ,...,ΔS'Wb ].

[0048] In one specific example, the construction of arch ribs in an arch bridge will be taken as an example for further detailed interpretation.

[0049] Take the arch bridge shown in Figure 2. The calculated main span of this bridge is 600 meters, the calculated arch height is 125 meters, the vector cross ratio is 1 / 4.8, and the arch axis coefficient m is 1.9. The two ribs of the beam are arranged laterally in the form of parallel arches, with a width-to-span ratio of 1:26. The arch ribs are made of concrete box cross-section, with the box height at the arch base being 12 meters and the box width being 6.5 meters, and the box height at the dome being 8 meters and the box width being 6.5 meters. The lateral center distance between the arch ribs is 16.5 meters. The thickness of the arch box web gradually changes from 45 cm at the dome to 95 cm at the arch base. The thickness of the top plate is 65 cm, and the thickness of the bottom plate gradually changes from 65 cm at the dome to 130 cm at the arch base. The arch rib concrete is C60. The arch rib of the main arch of this bridge is constructed using a cable-suspended diagonal suspension system. The single-span main arch is divided into 24 suspension segments and one closing segment, and the arch rib is suspended by a single arch rib. Here, the main arch rib is constructed symmetrically on both sides, and the numbering rule for the rope buckles and back ropes of a single span is as shown in Figure 3.

[0050] The first equilibrium state is as shown in Figure 5. This construction step is when the first segment is erected and tension is completed, that is, when the cable tower is kept vertical by actual measurement and the arch rib of the first segment reaches the expected position in the drawing, rope X 1k , Rope X 2b The rope force of is the determined value (determined during the tension construction process), and then the next segment is constructed, and the equilibrium state of No. 2 is reached, as shown in Figure 6. In the equilibrium state of No. 2, the rope X 2b , Rope X 3k When pulling the rope and determining the rope force value, 1kThe rope force value of is unknown. Accordingly, as shown in Figures 7 and 8, when moving from equilibrium state 2 to equilibrium state 3, or from equilibrium state 3 to equilibrium state 4, the non-current tensile rope force in the equilibrium state corresponding to the current construction step is unknown. Obtaining the rope force of this portion of the rope is relatively complicated. To avoid the complex rope force measurement process and reduce detection costs, the spatial state of each rope is obtained based on total station measurement or 3D laser scanning, and a parametric nonlinear mechanical calculation model is combined to invert the rope force of the unknown rope. Analysis shows that if equilibrium state 1 can estimate the rope force of each rope in equilibrium state 2, the rope force of each rope in the previous equilibrium state is known when the next equilibrium state is completed.

[0051] Take the equilibrium state of No. 4 as an example. The rope force value of each rope in the equilibrium state of No. 3 is known. When the equilibrium state of No. 4 is completed, the rope under tension control is rope X. 5k , Rope X 6b (These rope forces are known), and the initial rope force vector matrix S0 is S0 = [ΔS0 1k ,ΔS0 2b ,ΔS0 3k ,ΔS0 4k ,ΔS0 5k ,ΔS0 6b ] T , and the initial apparent damage state of each rope in the equilibrium state of No. 4 is inspected and quantified by non-destructive detection means, and the rope force apparent loss ratio vector matrix h0 of each rope is h0=[ h0 1k ,h0 2b ,h0 3k ,h0 4k ,h0 5k ,h0 6b ] and get Rope X 5k , Rope X 6b The rope force value of is known at equilibrium state 4, but rope X 1k , Rope X 2b , Rope X 3k , Rope X 4kThe spatial position change information of these ropes is obtained by a method such as a total station or three-dimensional laser scanning, that is, the spatial coordinate change vector ΔD of these ropes is known, and the model M 3 By forcing the displacement of each rope in the model M 4 Iteratively update the model M to reach the target expectation. 4 obtain the rope force vector matrix S for each rope corresponding to this model, and 4 When virtual unit damage occurs only in the i-th rope buckle, the rope force change vector matrix ΔS of each rope corresponding to the virtual unit damage occurs only in the i-th rope buckle. i Obtain all ΔS i Construct a rope force change matrix ΔS' corresponding to the virtual unit damage,

number

[0052] Vector matrix S of the same vector matrix S o , combined with the approximate linear relationship existing in the matrix △S' and the special virtual rope force change vector matrix h to be sought,

number

[0053] Further solving is performed to obtain a vector matrix h, and then the nominal and actual rope force change vector h' of each rope is obtained, and finally the vector h' calculates the rope force value of the non-new rope in the current equilibrium state.

[0054] Each embodiment in this specification will be described step by step, and each embodiment will be described focusing on the differences from other embodiments, and the same or similar parts between the embodiments may be referred to. The description of the device disclosed in the embodiment will be relatively simple since it corresponds to the method disclosed in the embodiment, and for related points, please refer to the description of the method.

[0055] The above description of the disclosed embodiments will enable those skilled in the art to make or use the present invention. Many modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be embodied in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not intended to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for reverse analysis of internal forces of rope buckles and back ropes under posture drive, relating to rope buckles, back ropes, cable towers and arch ribs used in the cantilever construction method of large span or ultra-long span arch bridges, comprising: The specific steps are: Step 1: Obtaining the initial geometric data, elastic modulus, and volume weight of the cable tower, the initial geometric data, elastic modulus, and volume weight of the arch rib, and the initial length, cross-sectional area, elastic modulus, and volume weight of each rope, and establishing and initializing a parametric nonlinear mechanical calculation model; Step 2: numbering the rope buckles and back ropes, and numbering the rope buckles, back ropes and cable tower equilibrium states at different times according to the tension process of the arch rib segments; Step 3: obtaining the initial rope force values ​​of the ropes newly added in the current equilibrium state, updating the initial rope force value matrix, obtaining the temperature values ​​and spatial posture vectors of each rope, and calculating the temperature change vector and spatial posture change vector of each rope; Step 4: detecting the apparent damage state of each rope before tension, obtaining initial apparent damage state data, obtaining rope force initial loss value according to the corresponding relationship between damage type and rope force, and further calculating the rope force apparent loss ratio vector of each rope according to the initial rope force value; Step 5: adding a new rope to the current parametric nonlinear dynamics calculation model, using the spatial posture change vector of each rope in the current equilibrium state as a rope force adjustment target, adjusting the difference between each rope spatial deformation of the parametric nonlinear dynamics calculation model and the spatial posture change vector to a target accuracy, updating the parametric nonlinear dynamics calculation model, and calculating the rope force vector of each rope in the parametric nonlinear dynamics calculation model; Step 6: In the updated parametric nonlinear dynamics calculation model, the total number of ropes is set as the number of cycles, and each time, non-overlapping ropes are designated so that a unit virtual damage occurs, and the damage of the remaining ropes is designated as zero, thereby obtaining a rope force change vector corresponding to the occurrence of a unit virtual damage in a single rope buckle, and further obtaining a rope force change matrix corresponding to the virtual unit damage; Step 7: based on the rope force change matrix, the rope force vector of each rope in the model, and the initial rope force value matrix, calculate a special virtual rope force change vector value for each rope, which indicates the ratio of the rope force change amount to the initial rope force value after unit displacement damage occurs in each rope; Step 8: according to the special virtual rope force change vector and the rope force apparent loss ratio vector of each rope, calculate the nominal actual rope force change vector of each rope, and combine with the initial rope force to further obtain the rope force value of the non-new rope in the current equilibrium state; and step 9, repeating steps 3 to 8 until the arch rib segment tensioning process is completed.

2. The method for reverse analysis of the internal force of a rope buckle and a back rope under posture driving as described in claim 1, characterized in that the equilibrium state and the initial rope force value are confirmed based on design drawings and on-site measurements.

3. X=[X 1k ,X 2k ,…,X nk ,X (n+1)b ,X (n+2)b ,…,X wb ,] According to the formula, the rope buckle and back rope are numbered. Here, k indicates that the rope X is a rope buckle, b indicates that the rope X is a back rope, n is the total number of rope buckles, and W is the total number of rope buckles and back ropes. The method for reverse analysis of the internal force of rope buckles and back ropes under posture driving as described in claim 1.

4. The method for inverse analysis of the internal force of a rope buckle and a back rope under posture driving as claimed in claim 1, characterized in that the spatial posture vector is obtained by a total station or a three-dimensional laser scan.

5. The method for reverse analysis of the internal force of a rope buckle and a back rope under posture driving as described in claim 1, characterized in that the initial apparent damage conditions include thread breakage, rust, and jig slippage.

6. The method for inverse analysis of the internal force of a rope buckle and a back rope under posture driving as described in claim 1, characterized in that step 5 further includes updating the temperature of each rope in the parametric nonlinear dynamics calculation model and the initial apparent state before tensioning based on the temperature change vector of each rope and the apparent loss ratio vector of the rope force.

7. 2. The method for backward analysis of internal forces of rope buckles and back ropes under posture driving as described in claim 1, wherein step 6 includes: considering that virtual damage of unit displacement occurs only in the i-th rope buckle, calculating the rope force change vector of each rope based on the parametric nonlinear mechanical calculation model; and when calculating all i values ​​one by one, considering the rope force change vector of each rope when virtual damage of unit displacement occurs only in the i-th rope buckle, and obtaining a rope force change matrix corresponding to the virtual unit damage.

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