A method and system for analyzing the stability of a cast-in-place support of a steel pipe concrete tied-arch

Abstract

This invention discloses a method and system for stability analysis of cast-in-place scaffolding for steel-concrete composite tied arches. The method includes: considering the stress characteristics of a three-arch ribbed tied arch structure on a wide bridge deck, decoupling the load in the scaffolding area along the transverse direction to construct a dynamic non-uniform initial load combination that reflects the entire construction process. Based on the disc-lock scaffolding structure, a differentiated finite element model is established for the arch foot reinforcement section and the standard section, simultaneously coupling parameters such as foundation stiffness, inelastic deformation, temperature effects, and node performance to achieve realistic simulation of multi-physics mechanical behavior. Combining the symmetrical, multi-stage pouring path to divide the work into multiple stages, the model parameters and load conditions are dynamically corrected based on on-site monitoring data to complete a comprehensive evaluation of the scaffolding's stability throughout its entire lifecycle. Simultaneously, using pouring deformation monitoring as feedback, a multi-factor coupled optimization model is constructed to iteratively optimize the scaffolding layout and pre-camber parameters, and sensitivity analysis of key parameters is conducted.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering construction technology, and more specifically, relates to a method and system for stability analysis of cast-in-place supports for steel-concrete tied arches. Background Technology

[0002] As the main load-bearing structure during construction, the stability of the support system directly affects the alignment control of the main structure, construction quality, and even the overall safety of the project. The transverse stress of a wide-deck, three-arch, ribbed, tied-arch structure is complex, with concentrated loads on the arch ribs and uniform load distribution on the bridge deck. Traditional support system designs do not perform zonal load-bearing analysis for the multiple arch ribs, and often use a simplified uniform load calculation model, which is difficult to match the actual non-uniform stress characteristics. This easily leads to local load calculation deviations and results in unreasonable safety reserves in the support system.

[0003] Currently, bridge support construction often relies on empirical methods for classifying work conditions, which cannot accurately correspond to the temporal changes of symmetrical, phased pouring of the arch ribs. The load transfer paths and stress evolution patterns at each construction stage are difficult to clearly demonstrate. Furthermore, existing analytical models typically ignore actual influencing factors such as differences in foundation stiffness, inelastic deformation of the support preload, temperature effects, and joint mechanical properties. This results in significant discrepancies between simulation results and the actual stress state on site. Stability assessments rely solely on a single indicator, lacking a comprehensive, multi-dimensional evaluation approach that fails to fully identify potential instability risks during construction.

[0004] In terms of support parameter design and optimization, traditional methods rely on specification limits and engineering experience, lacking a dynamic feedback mechanism based on on-site monitoring data. Support layout parameters and pre-camber settings often employ conservative designs, easily leading to material waste or insufficient alignment control. Currently, there is a lack of unified quantitative methods for sensitivity analysis of key support design parameters, making it impossible to clearly define the impact of parameters such as upright spacing, crossbar spacing, and cross-sectional dimensions on overall stability, and hindering precise control during construction. These problems collectively result in shortcomings in the construction of cast-in-place supports for wide-deck three-arch rib-tied arch bridges, including incomplete safety assessments, inaccurate parameter design, and untimely risk control. These issues severely restrict the safety management level and quality improvement of cast-in-place bridge construction, necessitating a targeted and practical support stability analysis and optimization method to provide reliable technical support for engineering construction. Summary of the Invention

[0005] This invention aims to solve problems such as load simulation distortion, insufficient model accuracy, one-sided stability evaluation, and rough parameter design of cast-in-place supports for three-arch rib-tied arch bridges on wide decks, improve the safety management and control capabilities of the entire support construction process, and provide reliable analysis and optimization methods for cast-in-place bridge construction.

[0006] To address the aforementioned deficiencies or improvement needs of existing technologies, as a first aspect of this invention, the present invention provides a method for stability analysis of cast-in-place supports for steel-concrete composite tied arches, comprising: S1. In view of the stress characteristics of the three-arch rib tied arch structure of the wide bridge deck, the load decoupling of the support area along the transverse direction of the bridge is implemented in the partitioned load, and the construction dynamic load of each partition is represented in the form of time-varying function to construct a dynamic non-uniform initial load combination that can reflect the entire construction process. S2. Based on the structural characteristics of the socket-type disc-lock scaffold, a differentiated parametric finite element model of the arch foot densified section and the standard section is established. The foundation stiffness, scaffold preload inelastic deformation, temperature effect and nodal mechanical performance parameters are synchronously coupled into the model. Based on the dynamic non-uniform initial load combination, the multi-physics mechanical behavior of the scaffold system is realistically simulated. S3. Combine the symmetrical phased pouring construction path of the tie-arch to divide the calculation conditions into multiple stages. Based on the real-time monitoring data of the construction site, dynamically correct the working parameters and load conditions of the finite element model, and comprehensively evaluate the stability of the support system at each construction stage and throughout the entire process. S4. Based on the real-time monitoring data of casting deformation, a multi-factor coupled optimization model is constructed by coupling load characteristics, model parameters and stage evaluation results. The support layout parameters and pre-camber parameters are iteratively optimized, and the sensitivity analysis of key parameters is completed.

[0007] Furthermore, the specific process of implementing zoned load decoupling in the support area along the transverse bridge direction in S1 is as follows: Based on the stress characteristics of the cast-in-place construction of the three-rib tied arch on the wide bridge deck, and taking the arch rib axis and the lane division boundary of the bridge deck as the benchmark, the overall load-bearing area of ​​the support in the transverse direction of the bridge is divided into multiple independent stress units, including the main load-bearing zone corresponding to the three arch ribs, the bridge deck flange zone and the intermediate transition zone. By defining the transverse and longitudinal bridge coordinate variables and the coordinate boundaries of each zone, the spatial range of each independent stress zone is clarified, ensuring that all zones together constitute the overall transverse bridge bearing area of ​​the support and that there is no spatial overlap between any zones. For each independent stress zone, spatial distribution variables of the self-weight load of the arch, the self-weight load of the cast-in-place layer of the bridge deck, the load of construction machinery and equipment, and the load of construction personnel activities are defined respectively. The static load variables of any spatial point in each zone are obtained by superimposing the loads, thereby characterizing the overall effect of the superposition of various loads at that location. By introducing construction time variables and total construction period, the static loads of each zone are extended into real-time time-varying load functions. A continuous time-varying load expression is constructed through time domain integral transformation, thereby obtaining the time-varying function of the overall load field of the support. A two-dimensional Laplace operator is introduced to perform spatial decoupling operations on the load field, and the decoupling control equations for the zoned loads are constructed. The time-varying load function is decomposed into the transverse spatial distribution characteristic function, the longitudinal spatial distribution characteristic function, and the time-domain variation characteristic function using the separation of variables method. The load orthogonality condition is used to achieve complete decoupling of the loads in each zone, ensuring that there is no coupling interference between the loads in different zones, and finally completing the independent decoupling characterization of the transverse load of the support.

[0008] Furthermore, the construction process of the dynamic non-uniform initial load combination in S1 is as follows: Combining the characteristics of cast-in-place construction of wide-deck three-arch rib-tied arch, the support structure is divided into several independent stress zones that do not overlap in the transverse direction of the bridge, and the spatial range and coordinate definition standards of each zone are clearly defined. Based on each zone, a static load variable is defined. This variable is formed by the superposition of various loads generated by the self-weight of the arch, the cast-in-place layer of the bridge deck, construction machinery and equipment, and personnel activities. It is used to characterize the magnitude of the static load at spatial points in each zone. By introducing a time variable, the total construction period and the time nodes of each stage are defined, and a time-series coupling function is constructed to realize the dynamic evolution of the load with the construction process. At the same time, a spatial distribution correction function is introduced to correct the differences in the spatial distribution of the load and reflect the non-uniform characteristics of the load in each zone. By constructing a dynamic time-varying load function and combining it with the spatial distribution gradient characteristics, the static load is coupled with the time-series function and the spatial correction function to form a load system that takes into account both dynamic time sequence and spatial non-uniformity. Then, through global spatial superposition, a dynamic load combination covering the entire support is constructed.

[0009] Furthermore, the construction process of the parametric finite element model in S2 is as follows: Taking the overall structural parameters of the support as the core, we comprehensively consider key parameters such as the longitudinal span of the support bridge, the height of the uprights, the cross-sectional area of ​​the members, the moment of inertia of the cross section, the elastic modulus of the material, and the shear modulus, and clarify the definition and function of each parameter. Based on the structure of the support frame, it is broken down into four core components: uprights, horizontal bars, ground braces, and diagonal braces. Each component is simulated using corresponding finite element units to clarify the stress characteristics and connection methods of each component, ensuring coordinated stress and displacement among the components. A material constitutive model is introduced, and the stress-strain relationship is used to describe the mechanical response of the support frame material from elastic to plastic stages, capturing the stress state of the structure. A load mapping mechanism is established to deeply couple dynamic non-uniform loads with the finite element model. The load mapping function is used to connect the load and the model. At the same time, the linkage verification of model parameters is completed to ensure that the model parameters can be adjusted and updated in real time. Finally, a parametric finite element model that can truly reflect the stress state of the support and adapt to the construction process is constructed.

[0010] Furthermore, the process of dividing the multi-stage calculation conditions in S3 is as follows: Based on the symmetrical phased pouring construction path of the tied arch and the on-site construction rhythm, and combined with the time nodes, load distribution forms and support stress characteristics of each construction stage, the calculation conditions of multiple stages are divided. The entire construction process is divided into four independent and sequentially connected conditions: preliminary preparation, foundation construction, arch pouring, and final acceptance, which correspond to the support erection, foundation construction, segmented pouring of the arch, and final verification, respectively. The composition and distribution characteristics of the loads under each working condition change differently with the construction process. In the early preparation working condition, the load is mainly the self-weight of the support and a small amount of equipment load, and the load distribution is uniform. In the foundation construction working condition, the load of the newly poured material is added, and it shows a local concentrated distribution. In the arch pouring working condition, the load increases dynamically with the progress of symmetrical pouring, and the spatial distribution shows a non-uniform characteristic. In the final acceptance working condition, the load gradually decreases and tends to stabilize, thus fully covering the entire construction process and simulating the actual stress state of the support at each stage.

[0011] Furthermore, the process of dynamically correcting the working parameters and load conditions of the finite element model in S3 is as follows: set up These are spatial coordinate variables, corresponding to the horizontal, vertical, and center directions of the bridge, respectively. Construction time is a variable; The structural displacement field obtained from on-site monitoring is used to characterize the actual deformation of the structure; Calculate the displacement field for the finite element model to characterize the theoretical deformation of the model; define the displacement residual. , used to characterize the overall deviation between measured and calculated results; Parameter correction forward calculation The expression is obtained directly from the spatial gradient field of the displacement residuals. ,in For three-dimensional gradient operators, , For the overall computational domain of the support structure, For the volume of a spatial infinitesimal element, this formula directly yields a correction operator that reflects the overall stiffness deviation of the structure by integrating the residual gradient over the entire domain. The correction expression for the operating condition parameters is as follows: ,in To correct the operating parameters of the previous model, To correct the working parameters of the model, the parameter correction process is entirely driven by monitoring residuals, realizing synchronous adaptive updates of model stiffness and constraint conditions; Load space adaptive correction regularization The displacement residual is determined by the two-dimensional integral of the displacement residual in the load plane and the structural geometric characteristics, and the specific expression is as follows: ,in The area of ​​load application The formula is a plane area. By integrating the area, the displacement deviation is transformed into a correction ratio for the load distribution, so that the load conditions match the measured deformation. The corrected expression for the load field is: ,in For the original dynamic non-uniform load, To correct the load; Substituting the corrected working parameters and load conditions into the model and recalculating, we obtain the displacement field of the new generation model. and update the displacement residuals. Repeat the iterative calculation until... , To calculate the convergence threshold, the model parameters must now perfectly match the actual stress state on site, thus completing the entire dynamic correction process.

[0012] Furthermore, the specific process of comprehensive evaluation in S3 is as follows: Eigenvalue buckling analysis was performed on the stent system to solve the buckling control equation. ,in Here is the linear elastic stiffness matrix of the structure. For the first Critical buckling characteristic value during the construction phase. For the first Initial stress-stiffness matrix of the stage For the first buckling mode vectors of the stage; Geometric and material nonlinear analyses were performed to obtain load-displacement curves for each construction stage. ,in For the first Actual loads applied during the stage The maximum structural displacement at the corresponding stage; the first extreme point of the curve is extracted. Ultimate bearing capacity of staged support system Calculate the stable reserve ratio This directly reflects the structure's ability to resist instability at that stage; Extract the calculated stress values ​​of all load-bearing members at each construction stage. ,in Numbering the construction phases Number the members according to their material design strength. Based on the strength verification formula Complete the strength and safety assessment of all members; extract the displacement calculation values ​​of key nodes at each stage. ,in Key nodes are numbered according to the allowable structural displacement. As a control benchmark, a stiffness verification formula is used. Complete the structural stiffness and stability determination; The critical buckling characteristic value, ultimate bearing capacity reserve ratio, member stress, and nodal displacement were calculated simultaneously for all construction stages, and all stages met the requirements. , , , At that time, the stent was deemed to be stable and up to standard at that stage.

[0013] By summarizing the stability assessment results of all construction stages, a full-process stability evaluation function is constructed. in This represents the total number of construction phases. For the first Maximum stress in members at each stage For the first Maximum node displacement in a stage.

[0014] Furthermore, the sensitivity analysis process for the key parameters in S4 is as follows: First, the core parameter set for sensitivity analysis is determined, including the spacing between support uprights, the step distance of crossbars, the density of diagonal bracing, the cross-sectional dimensions of uprights, and the pre-camber value. The critical buckling characteristic value, the stability reserve ratio, the maximum member stress, and the maximum nodal displacement are selected as key response indicators for the stability of the support. The single-parameter variable method is adopted. While keeping the other parameters unchanged at the design reference value, the single parameter is made to change uniformly at a fixed step size within its design value range, and the response index value corresponding to the step size of each parameter change is calculated. Based on the changes in parameters and response indicators, a formula for calculating sensitivity coefficients is constructed. The sensitivity coefficients of each core parameter to each response indicator are then calculated to form a sensitivity coefficient matrix. Based on the absolute value of the obtained sensitivity coefficient, a grading standard is set, and each parameter is divided into three levels: high sensitivity, medium sensitivity, and low sensitivity, so as to quantify the degree of influence of each parameter on stent stability.

[0015] As a second aspect of the present invention, a method for stability analysis of cast-in-place supports for steel-concrete composite tied arches is also provided, comprising: The load decoupling construction unit is used to decouple the load in the support area along the transverse direction of the bridge, based on the stress characteristics of the three-arch rib tied arch structure of the wide bridge deck. The dynamic construction load of each zone is represented in the form of a time-varying function, and a dynamic non-uniform initial load combination that can reflect the entire construction process is constructed. The support simulation coupling unit is used to establish a differentiated parametric finite element model of the arch foot densified section and the standard section based on the structural characteristics of the socket-type disc-lock support. The foundation stiffness, support preload inelastic deformation, temperature effect and nodal mechanical performance parameters are synchronously coupled into the model. Based on the dynamic non-uniform initial load combination, the multi-physics mechanical behavior of the support system is realistically simulated. The multi-condition stability evaluation unit is used to divide the calculation conditions into multiple stages based on the symmetrical phased pouring construction path of the tie-arch, dynamically correct the condition parameters and load conditions of the finite element model based on real-time monitoring data at the construction site, and comprehensively evaluate the stability of the support system at each construction stage and throughout the entire process. The parameter optimization and analysis unit is used to construct a multi-factor coupled optimization model based on real-time monitoring data of casting deformation, coupled with load characteristics, model parameters and stage evaluation results, to iteratively optimize the support layout parameters and pre-camber parameters, and to complete the sensitivity analysis of key parameters.

[0016] As a third aspect of the invention, a computer-readable storage medium is also provided, on which a computer program is stored, which is executed by a processor, according to any one of the methods for stability analysis of cast-in-place steel-concrete composite tied-arch supports.

[0017] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: 1. The stability analysis method for cast-in-place steel-concrete tied-arch supports of the present invention, by considering the stress characteristics of a three-arch tied-arch structure on a wide bridge deck, implements zoned load decoupling in the bearing area of ​​the support along the transverse direction, represents the dynamic construction load of each zone as a time-varying function, superimposes various static loads, and introduces time-series coupling and spatial distribution correction functions to construct a dynamic non-uniform initial load combination reflecting the entire construction process. This method can accurately distinguish the differences in load distribution among zones, avoid interference from zoned load coupling, and ensure that the load input is consistent with the actual stress state of the symmetrical, phased casting of the three arch ribs on site. It effectively solves the problem of traditional load characterization not conforming to reality, provides an accurate and reliable load basis for subsequent support stability analysis, and ensures the initial accuracy of mechanical analysis.

[0018] 2. The stability analysis method for cast-in-place steel-concrete composite tied-arch supports of the present invention establishes differentiated parametric finite element models of the arch foot reinforced section and standard section based on the structural characteristics of the socket-type disc-lock support. The method synchronously couples the foundation stiffness, inelastic deformation of the support preload, temperature effects, and nodal mechanical performance parameters to the model. Combined with dynamic non-uniform initial load combinations, it achieves realistic simulation of multi-physics mechanical behavior. The method divides the calculation into multiple stages and dynamically corrects model parameters and load conditions based on real-time on-site monitoring data, comprehensively evaluating the stability of the support at each stage and throughout the entire process. This method can realistically reproduce the stress and deformation state of the support at different construction stages, correct model deviations in real time, avoid the problem of traditional models being disconnected from reality, and ensure that the stability evaluation results are objective and comprehensive, covering the safety judgment requirements of the entire construction process.

[0019] 3. The stability analysis method for cast-in-place steel-concrete composite tied-arch supports of the present invention uses real-time monitoring data of casting deformation as feedback, and constructs a multi-factor coupled optimization model by coupling load characteristics, model parameters, and stage evaluation results. Iterative optimization of support layout parameters and pre-camber parameters is performed, and a single-parameter variable method is used to complete the sensitivity analysis of key parameters and classify sensitivity levels. This method can optimize design parameters while ensuring support stability, clarify the influence of each key parameter on support stability, solve the problems of insufficient targeting and parameter redundancy in traditional support design, provide quantitative basis for construction control, improve the economy of support design and the accuracy of construction control, and ensure the safety of support construction. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating a method for stability analysis of a cast-in-place support for a steel-concrete composite tie-arch according to an embodiment of the present invention. Figure 2 This is a finite element model diagram of an embodiment of the present invention; Figure 3 This is a schematic diagram of displacement calculation according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the system units in an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0022] Example 1 Please refer to Figure 1 This embodiment 1 provides a method for stability analysis of cast-in-place supports for steel-concrete composite tied arches, including: S1. In view of the stress characteristics of the three-arch rib tied arch structure of the wide bridge deck, the load decoupling of the support area along the transverse direction of the bridge is implemented in the partitioned load, and the construction dynamic load of each partition is represented in the form of time-varying function to construct a dynamic non-uniform initial load combination that can reflect the entire construction process. S2. Based on the structural characteristics of the socket-type disc-lock scaffold, a differentiated parametric finite element model of the arch foot densified section and the standard section is established. The foundation stiffness, scaffold preload inelastic deformation, temperature effect and nodal mechanical performance parameters are synchronously coupled into the model. Based on the dynamic non-uniform initial load combination, the multi-physics mechanical behavior of the scaffold system is realistically simulated. S3. Combine the symmetrical phased pouring construction path of the tie-arch to divide the calculation conditions into multiple stages. Based on the real-time monitoring data of the construction site, dynamically correct the working parameters and load conditions of the finite element model, and comprehensively evaluate the stability of the support system at each construction stage and throughout the entire process. S4. Based on the real-time monitoring data of casting deformation, a multi-factor coupled optimization model is constructed by coupling load characteristics, model parameters and stage evaluation results. The support layout parameters and pre-camber parameters are iteratively optimized, and the sensitivity analysis of key parameters is completed.

[0023] Please refer to Figure 2 as well as Figure 3 This embodiment 1 further elaborates on the above steps.

[0024] (1) Load decoupling construction During the cast-in-place construction phase of a wide-deck three-arch rib tied arch, the stress distribution of the support system along the transverse direction is extremely uneven. The load is highly concentrated below the arch ribs, while the stress on the bridge deck area is relatively uniform. Traditional monolithic load analysis methods cannot reflect this regional stress difference, nor can they reproduce the dynamic changes in load as construction progresses, thus affecting the authenticity of support stress simulation and stability evaluation. To solve this problem, firstly, based on the stress characteristics of cast-in-place construction of a wide-deck three-arch rib tied arch, and using the arch rib axis and the lane division boundary of the bridge deck as a benchmark, the support bearing area along the transverse direction is divided into the main bearing zone corresponding to the three arch ribs, the bridge deck flange zone, and the intermediate transition zone, forming mutually independent transverse stress units. set up The transverse overall load-bearing area of ​​the support structure is used to characterize the entire load-bearing range of the support in the transverse direction of the bridge. The transverse coordinate variable is used to characterize different positions of the support structure in the transverse direction. , , These are the transverse coordinate variables corresponding to the axes of the three arch ribs, respectively, representing the positions of the axes of the three arch ribs; The coordinate variable is the left boundary of the support bridge; The coordinate variable is the right boundary of the support bridge. Based on the above coordinate division Each independent stress zone , … ,in , , The three arch ribs form the main load-bearing zone, while the rest are bridge deck flange zones and intermediate transition zones; each zone satisfies... , This is a partition set union operation, used to represent all partitions together forming a whole carrying area; each partition simultaneously satisfies , For set intersection operation, and Different partitions are numbered, with values ​​ranging from 1 to 2. to , used to indicate that there is no spatial overlap between any partitions; Introducing longitudinal bridge coordinate variables Used to characterize different positions of the longitudinal bridge of the support; for arbitrary partitions ,definition Spatial points within this partition The self-weight load of the arch at that location; Spatial points within this partition The self-weight load of the cast-in-place bridge deck at the location; Spatial points within this partition The load on the construction machinery and equipment at the location; Spatial points within this partition The load of construction workers' activities at the site; Spatial points within the partition The total load at the location satisfies , This refers to the static load variable of the spatial point corresponding to this partition, used to characterize the overall effect of the superposition of various loads at this location; Introducing construction time variables Used to characterize the progress of construction procedures; The total construction period is [missing information]. The range of values ​​is Extending spatial loads into time-varying functions It is used to characterize the real-time load of spatial points within the partition as the construction progresses; the overall support load field satisfies , The load field is a time-varying function; a continuous time-varying load expression is constructed using time-domain integral transform. , The initial spatial load for the partition. Let be the load change rate function. For integration time; Introducing the two-dimensional Laplacian operator Used for spatial decoupling calculations of the load field. The second-order partial derivative of the transverse bridge direction, The second-order partial derivatives in the longitudinal direction of the bridge are used to construct the decoupling control equations. , The characteristic function for decoupling zoned loads is derived; the method of separation of variables is employed. , The characteristic function of the transverse spatial distribution of the bridge The characteristic function of the longitudinal spatial distribution of the bridge is... It is a time-domain characteristic function.

[0025] Utilizing the load orthogonality condition The equation demonstrates that there is no coupling interference between different zone loads, thus achieving independent decoupling of the transverse load.

[0026] Building upon the decoupling of zoned loads, a dynamic non-uniform initial load combination tailored to the entire construction process is further constructed. Based on the static loads of each zone, and considering the start and end times of load application in each zone, a time-series coupling function is constructed to ensure that load changes align with the actual construction rhythm, thus forming a zoned dynamic time-varying load. Specifically: Let... This represents the total number of independent stress zones in the transverse direction of the support bridge. This is the partition number, and its value is... to , For the first Each zone is an independent load-bearing zone, and each zone does not overlap and completely covers the overall load-bearing area of ​​the support bridge in the transverse direction. ; The transverse coordinate variable is used to characterize different positions of the support structure in the transverse direction. For longitudinal bridge coordinate variables, used to characterize different positions of the support structure in the longitudinal direction of the bridge; For any spatial point coordinate variable of the support, used to locate the specific spatial position of the load action; For the first Each partition any point in the inner space The static load variable is formed by the superposition of the self-weight of the arch, the self-weight of the cast-in-place bridge deck, the load of construction machinery and equipment, and the load of construction personnel within the zone. It is used to characterize the static superposition value of various loads at this spatial point; the construction time variable is introduced. Used to characterize the progress of construction procedures, with a value range of [value range missing]. , The total construction period is a variable used to characterize the entire duration of the support structure construction. Corresponding to the start time of construction Corresponding construction completion time; Introducing timing coupling function , used to characterize the The relationship between the application of loads in each zone and the construction process is established, enabling the dynamic evolution of loads according to construction procedures. Its expression is: ,in For the first The time at which the partition load begins to be applied is a variable. For the first The time variable when the application of the partition load is completed. and The sequence of construction procedures is set to ensure that the timing of load application in each zone is consistent with the actual construction pace. By coupling the static load of the partition with the time-series coupling function, the dynamic time-varying load function of the i-th partition is obtained. This function is used to characterize any spatial point within the i-th partition. The real-time load magnitude at construction time t enables continuous dynamic change of the load as the construction progresses. To characterize the spatial non-uniformity of the load, a spatial distribution correction function is introduced. This is used to correct the spatial distribution gradient difference of the load in the i-th partition, and its expression is: ,in For zoned loads on the transverse bridge coordinates The first-order partial derivative, For the longitudinal coordinates of the zonal load The first-order partial derivatives are used to extract the gradient characteristics of the load spatial distribution, reflecting the non-uniform distribution of the load within each partition. By coupling the dynamic time-varying load function with the spatial distribution correction function, the corrected partitioned dynamic load function is obtained. This function takes into account both the dynamic temporal variation of the load and the spatial non-uniform distribution characteristics. Using a global spatial superposition method, all partitioned corrected dynamic load functions are superimposed to construct a dynamic non-uniform initial load combination, the expression of which is: ,in A time-varying function of dynamic non-uniform initial load combination, used to characterize any spatial point of the support frame. The total initial load at construction time t; used to achieve the global spatial superposition of dynamic loads in all zones.

[0027] (2) Stent simulation coupling The stress distribution of the wide-deck three-arch rib structure varies significantly. Traditional single finite element models cannot accurately match the stress characteristics of different areas, especially the load concentration at the arch foot. Ordinary models cannot take into account the stress differences between the reinforced section and the standard section at the arch foot, which can easily lead to a disconnect between simulation results and actual stress. Therefore, it is necessary to construct differentiated parametric finite element models that incorporate various actual influencing factors to ensure that the simulation results are consistent with the actual site conditions.

[0028] When constructing a finite element model, first set This is a set of overall structural parameters for the stent, used to coordinate all key structural parameters of the stent. ,in The longitudinal span variable of the support structure is used to characterize the longitudinal extension length of the support structure. The height of the support column is a variable used to characterize the vertical support height of the support. This represents the cross-sectional area variable of the support member, used to characterize the size of the load-bearing cross section of the member; The moment of inertia of the cross section of the support member is a variable used to characterize the member's ability to resist bending deformation; The elastic modulus of the support material is a variable used to characterize the material's stiffness properties. The shear modulus of the support material is used to characterize the material's ability to resist shear deformation. All of the above parameters are determined by the actual design drawings of the support and the material performance test report to achieve the matching between the model and the actual structure. Meanwhile, taking into full account the structural characteristics of the socket-type disc-lock scaffold, and considering the load concentration in the arch foot area, the model is divided into two parts: the arch foot densified section and the standard section. The arch foot densified section corresponds to the stress concentration area of ​​the scaffold, with appropriate densification of the mesh and reinforcement of the node connection stiffness. The standard section is set according to the conventional scaffold structure, so as to reflect the stress differences in different areas and ensure that the model can truly reflect the stress characteristics of different parts of the scaffold.

[0029] Based on the structural composition of the support system, it is broken down into four core components: uprights, horizontal bars, base braces, and diagonal braces. Parametric finite element units (FEMs) are constructed for each component: uprights and horizontal bars are simulated using beam elements to characterize their bending, shear, and axial stress characteristics; base braces are simulated using beam elements to provide horizontal and vertical support at the bottom of the support system; and diagonal braces are simulated using beam elements to enhance the overall stability of the support system. The parameters of each component's FEM are correlated one-to-one with the corresponding structural parameters to ensure that the element characteristics are consistent with the actual components. Define mesh cell size variables Used to characterize the fineness of the finite element mesh, determined through mesh convergence verification. The optimal value is determined to ensure both computational accuracy and efficiency, avoiding excessive computation due to overly dense meshes or excessively sparse meshes that lead to excessive computational errors. The parametric finite element units of each component are assembled according to the actual structural connection relationship, and the constraint relationship between the components is established: the bottom of the upright is subject to fixed constraints to limit horizontal, vertical and rotational displacements; rigid connection constraints are used between the horizontal bar and the upright, and between the diagonal brace and the upright and horizontal bar to ensure that each component is subjected to force in a coordinated manner and conforms to the actual connection state of the support. During the model construction process, multiple key influencing factors were simultaneously incorporated to compensate for the shortcomings of traditional models that ignore actual working conditions. On the one hand, the influence of foundation stiffness on the stress of the support was fully considered. Combined with the actual bearing capacity of the foundation at the construction site, the foundation stiffness parameters were integrated into the model to avoid deviations in stress calculation caused by neglecting foundation settlement. On the other hand, the influence of temperature effects was included. Combined with the changes in ambient temperature during construction, the impact of temperature on the mechanical properties of the support material was simulated. At the same time, the inelastic deformation generated during the preloading process of the support was considered. These factors were deeply coupled with the model, making the model more consistent with the actual construction conditions on site.

[0030] In a preferred embodiment, a material constitutive model is also introduced. ,in For the stress variable of the support material, The strain variable of the support material is used to describe the stress-strain relationship of the material in the elastic stage. Combined with the material's plastic yield criterion, the mechanical response of the support structure in the entire stage from elastic to plastic is simulated. Dynamic non-uniform loads are mapped through a load mapping function. Mapped to the finite element model, where For dynamic load combinations, The load mapping coefficient is determined by the correspondence between model nodes and load application locations, achieving precise coupling between load and model; After the model is built, perform parameter linkage verification and adjust arbitrary structural parameters. One of the steps involves updating the geometric dimensions and material properties of the corresponding components in the model simultaneously, ensuring that the model has parametric adjustment capabilities and can quickly adapt to changes in the support structure under different construction conditions, ultimately forming a parametric finite element model that can accurately reflect the actual structure, stress, and deformation characteristics of the support.

[0031] Meanwhile, after establishing the differentiated parametric finite element model, the determined dynamic non-uniform initial load combination is applied to the corresponding nodes and regions of the model according to the load mapping relationship, so that the spatial distribution and temporal changes of the load are completely consistent with the construction and pouring process. In the simulation calculation, the foundation stiffness parameter directly constrains the bottom boundary conditions of the support, reflecting the deformation and bearing characteristics of the foundation itself; the inelastic deformation generated by the preloading of the support is introduced into the model in the form of initial displacement, correcting the initial shape of the support before being subjected to force; the temperature effect is applied through the temperature load field, reflecting the influence of environmental temperature changes on the expansion and contraction and internal forces of the members; the mechanical properties of the nodes are realized by setting the node stiffness and constraint stiffness, restoring the real force transmission and rotation characteristics of the disc-locked nodes.

[0032] Multiphysics coupled simulation simultaneously performs mechanical and deformation calculations, outputting stress values ​​for uprights, crossbars, and diagonal braces, displacement amplitudes of key nodes, overall deflection morphology of the support structure, and stress development trends of local components stage by stage. This comprehensively presents the mechanical changes of the support structure throughout the entire symmetrical, phased pouring process. This simulation process no longer simplifies actual boundaries and the influence of multiple factors, accurately reflecting the stress and deformation characteristics of the support structure under complex site conditions. It outputs quantitative results that can be directly used for stability assessment, providing data support for safety evaluations in subsequent construction stages.

[0033] (3) Multi-condition stability evaluation Based on the actual construction of the wide-deck three-arch rib-tied arch and the stress characteristics of the socket-type disc-lock scaffold, in addition to completing the load analysis and model construction, it is also necessary to divide the calculation conditions into multiple stages according to the pouring path and on-site conditions throughout the construction process. The model parameters are corrected by real-time monitoring data, and a multi-dimensional stability evaluation is carried out to ensure the safety and controllability of the scaffold throughout the construction process. This is also a key link between load analysis and stability evaluation, filling the gap of traditional models that only focus on a single condition and ignore the dynamic changes in construction.

[0034] Specifically, firstly, based on the construction drawings and the on-site construction schedule, the construction path for the symmetrical, multi-stage pouring of the tied arch was determined, clarifying the time nodes, load distribution, and stress characteristics of the supports for each pouring stage. This served as the core basis for the multi-stage calculation of working conditions. The total construction period was... The construction process is divided into four core stages: the preliminary preparation stage, the foundation construction stage, the arch pouring stage, and the final acceptance stage. Each stage is divided into four calculation conditions, which are independent of each other and connected in an orderly manner to ensure coverage of the entire construction process.

[0035] Working condition one is the preliminary preparation condition, corresponding to the site clearing, equipment arrival, and scaffolding erection stages in the early stages of construction. At this time, the scaffolding only bears its own structural weight and a small amount of construction equipment load, and the load distribution is relatively uniform. The load under this condition is defined as... , It consists only of the weight of the support itself and the weight of the construction equipment, without any additional construction load, and is used to simulate the initial stress state of the support.

[0036] Working condition two corresponds to the foundation construction phase, including foundation pouring, pole erection, and scaffold reinforcement. In this case, the load includes the weight of the scaffold itself, the weight of the foundation pouring materials, and the loads from construction personnel and equipment. The load under this working condition is defined as follows: , The load is formed by the superposition of the weight of the foundation construction materials, the weight of the construction equipment, and the load of personnel activities. The load distribution shows a localized concentration characteristic, mainly concentrated in the foundation construction area.

[0037] Working condition three is the arch casting condition, corresponding to the core stage of symmetrical multi-stage casting of tied arches. In this case, the load includes the weight of the arch casting materials, the load of construction equipment, and the load of personnel. The load under this condition is defined as follows: , Based on the dynamic changes in the pouring progress, the load gradually increases as the pouring area expands, exhibiting a non-uniform distribution characteristic. The focus is on simulating the load variation pattern during the arch pouring process.

[0038] Condition 4 is the final acceptance condition, corresponding to the stability check of the support after pouring. At this time, the load mainly consists of the remaining construction equipment load and the load of materials not yet cleared. The load under this condition is defined as follows: , The pressure gradually decreases as the finishing work progresses, eventually stabilizing, and is used to verify the stability of the support system after construction is completed.

[0039] Based on the division of working conditions, and combined with real-time monitoring data from the construction site, the working parameters and load conditions of the finite element model are dynamically corrected. Let... These are spatial coordinate variables, corresponding to the horizontal, vertical, and center directions of the bridge, respectively. Construction time is a variable; The structural displacement field obtained from on-site monitoring is used to characterize the actual deformation of the structure; Calculate the displacement field for the finite element model to characterize the theoretical deformation of the model; define the displacement residual. , used to characterize the overall deviation between measured and calculated results; Parameter correction forward calculation The expression is obtained directly from the spatial gradient field of the displacement residuals. ,in For three-dimensional gradient operators, , For the overall computational domain of the support structure, For the volume of a spatial infinitesimal element, this formula directly yields a correction operator that reflects the overall stiffness deviation of the structure by integrating the residual gradient over the entire domain. The correction expression for the operating condition parameters is as follows: ,in To correct the operating parameters of the previous model, To correct the working parameters of the model, the parameter correction process is entirely driven by monitoring residuals, realizing synchronous adaptive updates of model stiffness and constraint conditions; Load space adaptive correction regularization The displacement residual is determined by the two-dimensional integral of the displacement residual in the load plane and the structural geometric characteristics, and the specific expression is as follows: ,in The area of ​​load application The formula is a plane area. By integrating the area, the displacement deviation is transformed into a correction ratio for the load distribution, so that the load conditions match the measured deformation. The corrected expression for the load field is: ,in For the original dynamic non-uniform load, To correct the load; Substituting the corrected working parameters and load conditions into the model and recalculating, we obtain the displacement field of the new generation model. and update the displacement residuals. Repeat the iterative calculation until... , To calculate the convergence threshold, the model parameters must now perfectly match the actual stress state on site, thus completing the entire dynamic correction process.

[0040] After the model was corrected, a multi-dimensional comprehensive stability evaluation was conducted based on the defined working conditions for each construction stage. During the evaluation, eigenvalue buckling analysis was first performed on the support system to solve the buckling control equations. ,in Here is the linear elastic stiffness matrix of the structure. For the first Critical buckling characteristic value during the construction phase. For the first Initial stress-stiffness matrix of the stage For the first buckling mode vectors of the stage; Geometric and material nonlinear analyses were performed to obtain load-displacement curves for each construction stage. ,in For the first Actual loads applied during the stage The maximum structural displacement at the corresponding stage; the first extreme point of the curve is extracted. Ultimate bearing capacity of staged support system Calculate the stable reserve ratio This directly reflects the structure's ability to resist instability at that stage; Extract the calculated stress values ​​of all load-bearing members at each construction stage. ,in Numbering the construction phases Number the members according to their material design strength. Based on the strength verification formula Complete the strength and safety assessment of all members; extract the displacement calculation values ​​of key nodes at each stage. ,in Key nodes are numbered according to the allowable structural displacement. As a control benchmark, a stiffness verification formula is used. Complete the structural stiffness and stability determination; The critical buckling characteristic value, ultimate bearing capacity reserve ratio, member stress, and nodal displacement were calculated simultaneously for all construction stages, and all stages met the requirements. , , , At that time, the stent was deemed to be stable and up to standard at that stage.

[0041] By summarizing the stability assessment results of all construction stages, a full-process stability evaluation function is constructed. in This represents the total number of construction phases. For the first Maximum stress in members at each stage For the first Maximum node displacement in a stage.

[0042] In addition, during the evaluation process, a comprehensive verification of the overall and local stability of the support was carried out simultaneously. The stress state of the support in the arch foot density area and the load concentration area was focused on. The internal force distribution and deformation law of the support under dynamic load were analyzed to fully understand the stability performance of the support at different construction stages.

[0043] By integrating the stability evaluation results of each construction stage, a complete stability evaluation system for the support structure is formed. This system covers both the stability determination of each individual construction stage and the overall stability assessment of the entire construction process. It provides accurate and reliable evaluation basis for subsequent adjustment of construction parameters and safety management, ensuring the structural safety of the support structure and the smooth progress of construction throughout the entire construction cycle.

[0044] (4) Parameter optimization and analysis In the cast-in-place construction of a three-arch ribbed tied arch bridge with a wide deck, the rationality of the scaffold layout parameters and pre-camber setting directly affects the load-bearing capacity and construction safety of the scaffold. Traditional analyses often neglect dynamic changes and parameter sensitivity during construction, resulting in a lack of scientific basis for optimization and adjustment, making it difficult to optimize the scaffold design. Therefore, it is necessary to use real-time monitoring data of casting deformation as feedback, combined with the previously established dynamic load and parameter system, to construct a multi-factor coupled optimization model. This model iteratively optimizes the scaffold layout parameters and pre-camber parameters, while simultaneously conducting sensitivity analysis of key parameters to ensure that the scaffold design not only conforms to actual construction conditions but also meets stability requirements.

[0045] The process uses the measured data of vertical settlement, lateral displacement, and arch-base shape of key nodes of the support as direct feedback inputs. It unifies and couples the previously determined dynamic non-uniform spatial load distribution, stiffness parameters of the finite element model, foundation constraints, mechanical properties of nodes, and stability verification indicators at each stage to establish a multi-objective optimization model.

[0046] The model uses the longitudinal and transverse spacing of the support uprights, the step distance of the horizontal bars, the spacing of the diagonal braces, the cross-sectional specifications of the uprights, and the pre-camber value of the arch rib segments as design variables. It uses the maximum stress, the overall displacement limit, the critical buckling safety factor, and the linear deviation as constraints, and the economic efficiency of structural materials and the uniformity of deformation as optimization objectives.

[0047] The difference between the simulated displacement and the field-monitored displacement is used as an iterative correction term. In each iteration, the load distribution, foundation stiffness, boundary constraints, and member stiffness parameters of the model are automatically updated, and mechanical calculations are carried out again to gradually narrow the gap between the calculated and measured values.

[0048] After multiple rounds of iterative convergence, the optimal support layout parameters and pre-camber parameters that meet the stability requirements, alignment control requirements, and construction feasibility are output and can be directly used for on-site support erection and alignment control.

[0049] Furthermore, we define the core parameter set for sensitivity analysis. ,in To establish spacing for the support structure, The step distance of the horizontal bar. For the density of diagonal bracing, These are the dimensions of the upright cross-section. This is the pre-camber value; Selecting the set of key response indicators for stent stability ,in This is the critical buckling characteristic value. To stabilize the reserve ratio, For the maximum stress in the member, This represents the maximum nodal displacement. The single-parameter variable method is adopted, fixing all other parameters as design baseline values, and only allowing a single parameter to follow its design range. To undergo uniform change, where The parameter change step size is Calculate the response index value corresponding to each change step size. ,in This represents the number of parameter change steps. Construct expressions for calculating the sensitivity coefficients of each parameter. ,in For the first The parameter for the first Sensitivity coefficient of each response indicator In response to changes in the indicators, The baseline value for the response indicator, The change in the parameter The baseline value of the parameter is used; the larger the absolute value of the sensitivity coefficient, the more significant the impact of the parameter on the corresponding response index. The sensitivity coefficients of each core parameter to the four response indicators were calculated separately, resulting in a sensitivity coefficient matrix. Matrix elements Corresponding to the The parameter for the first Sensitivity coefficient of each response indicator; Define the sensitivity level determination criteria, when When, the parameter is determined to be a highly sensitive parameter; when When the parameter is deemed to be of moderate sensitivity, it is considered to be of medium sensitivity. When this condition is met, the parameter is determined to be a low-sensitivity parameter.

[0050] Through the above sensitivity analysis, the influence of each design parameter on the buckling stability, load-bearing capacity reserve, member strength and structural stiffness of the support can be quantitatively identified. In the optimization iteration, priority should be given to controlling the accuracy of the values ​​of highly sensitive parameters, guiding the key monitoring and control of critical design variables in on-site construction, and providing a basis for lightweight and economical selection of support schemes. This avoids insufficient safety redundancy or material waste caused by blind adjustment of parameters, making the optimization process of the optimization model more engineering-oriented and reliable.

[0051] Example 2 Please refer to Figure 4 This embodiment 2 provides a method for stability analysis of cast-in-place supports for steel-concrete composite tied arches, including: The load decoupling construction unit is used to decouple the load in the support area along the transverse direction of the bridge, based on the stress characteristics of the three-arch rib tied arch structure of the wide bridge deck. The dynamic construction load of each zone is represented in the form of a time-varying function, and a dynamic non-uniform initial load combination that can reflect the entire construction process is constructed. The support simulation coupling unit is used to establish a differentiated parametric finite element model of the arch foot densified section and the standard section based on the structural characteristics of the socket-type disc-lock support. The foundation stiffness, support preload inelastic deformation, temperature effect and nodal mechanical performance parameters are synchronously coupled into the model. Based on the dynamic non-uniform initial load combination, the multi-physics mechanical behavior of the support system is realistically simulated. The multi-condition stability evaluation unit is used to divide the calculation conditions into multiple stages based on the symmetrical phased pouring construction path of the tie-arch, dynamically correct the condition parameters and load conditions of the finite element model based on real-time monitoring data at the construction site, and comprehensively evaluate the stability of the support system at each construction stage and throughout the entire process. The parameter optimization and analysis unit is used to construct a multi-factor coupled optimization model based on real-time monitoring data of casting deformation, coupled with load characteristics, model parameters and stage evaluation results, to iteratively optimize the support layout parameters and pre-camber parameters, and to complete the sensitivity analysis of key parameters.

[0052] Example 3 This embodiment 3 also provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement any step of a method for stability analysis of a cast-in-place support for a steel-concrete composite tied arch.

[0053] The computer-readable storage medium may include various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0054] For a description of the computer-readable storage medium provided in this application, please refer to the above method embodiments; further details will not be repeated here.

[0055] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for stability analysis of cast-in-place supports for steel-concrete composite tied arches, characterized in that, include: S1. In view of the stress characteristics of the three-arch rib tied arch structure of the wide bridge deck, the load decoupling of the support area along the transverse direction of the bridge is implemented in the partitioned load, and the construction dynamic load of each partition is represented in the form of time-varying function to construct a dynamic non-uniform initial load combination that can reflect the entire construction process. S2. Based on the structural characteristics of the socket-type disc-lock scaffold, a differentiated parametric finite element model of the arch foot densified section and the standard section is established. The foundation stiffness, scaffold preload inelastic deformation, temperature effect and nodal mechanical performance parameters are synchronously coupled into the model. Based on the dynamic non-uniform initial load combination, the multi-physics mechanical behavior of the scaffold system is realistically simulated. S3. Combine the symmetrical phased pouring construction path of the tie-arch to divide the calculation conditions into multiple stages. Based on the real-time monitoring data of the construction site, dynamically correct the working parameters and load conditions of the finite element model, and comprehensively evaluate the stability of the support system at each construction stage and throughout the entire process. S4. Based on the real-time monitoring data of casting deformation, a multi-factor coupled optimization model is constructed by coupling load characteristics, model parameters and stage evaluation results. The support layout parameters and pre-camber parameters are iteratively optimized, and the sensitivity analysis of key parameters is completed.

2. The method for stability analysis of a cast-in-place steel-concrete composite tied-arch support according to claim 1, characterized in that, The specific process of implementing zoned load decoupling in the support area along the transverse bridge direction in S1 is as follows: Based on the stress characteristics of the cast-in-place construction of the three-rib tied arch on the wide bridge deck, and taking the arch rib axis and the lane division boundary of the bridge deck as the benchmark, the overall load-bearing area of ​​the support in the transverse direction of the bridge is divided into multiple independent stress units, including the main load-bearing zone corresponding to the three arch ribs, the bridge deck flange zone and the intermediate transition zone. By defining the transverse and longitudinal bridge coordinate variables and the coordinate boundaries of each zone, the spatial range of each independent stress zone is clarified, ensuring that all zones together constitute the overall transverse bridge bearing area of ​​the support and that there is no spatial overlap between any zones. For each independent stress zone, spatial distribution variables of the self-weight load of the arch, the self-weight load of the cast-in-place layer of the bridge deck, the load of construction machinery and equipment, and the load of construction personnel activities are defined respectively. The static load variables of any spatial point in each zone are obtained by superimposing the loads, thereby characterizing the overall effect of the superposition of various loads at that location. By introducing construction time variables and total construction period, the static loads of each zone are extended into real-time time-varying load functions. A continuous time-varying load expression is constructed through time domain integral transformation, thereby obtaining the time-varying function of the overall load field of the support. A two-dimensional Laplace operator is introduced to perform spatial decoupling operations on the load field, and the decoupling control equations for the zoned loads are constructed. The time-varying load function is decomposed into the transverse spatial distribution characteristic function, the longitudinal spatial distribution characteristic function, and the time-domain variation characteristic function using the separation of variables method. The load orthogonality condition is used to achieve complete decoupling of the loads in each zone, ensuring that there is no coupling interference between the loads in different zones, and finally completing the independent decoupling characterization of the transverse load of the support.

3. The method for stability analysis of cast-in-place steel-concrete composite tied-arch supports according to claim 1, characterized in that, The construction process of the dynamic non-uniform initial load combination in S1 is as follows: Combining the characteristics of cast-in-place construction of wide-deck three-arch rib-tied arch, the support structure is divided into several independent stress zones that do not overlap in the transverse direction of the bridge, and the spatial range and coordinate definition standards of each zone are clearly defined. Based on each zone, a static load variable is defined. This variable is formed by the superposition of various loads generated by the self-weight of the arch, the cast-in-place layer of the bridge deck, construction machinery and equipment, and personnel activities. It is used to characterize the magnitude of the static load at spatial points in each zone. By introducing a time variable, the total construction period and the time nodes of each stage are defined, and a time-series coupling function is constructed to realize the dynamic evolution of the load with the construction process. At the same time, a spatial distribution correction function is introduced to correct the differences in the spatial distribution of the load and reflect the non-uniform characteristics of the load in each zone. By constructing a dynamic time-varying load function and combining it with the spatial distribution gradient characteristics, the static load is coupled with the time-series function and the spatial correction function to form a load system that takes into account both dynamic time sequence and spatial non-uniformity. Then, through global spatial superposition, a dynamic load combination covering the entire support is constructed.

4. The method for stability analysis of a cast-in-place support for a steel-concrete composite tied-arch as described in claim 1, characterized in that, The construction process of the parametric finite element model in S2 is as follows: Taking the overall structural parameters of the support as the core, we comprehensively consider key parameters such as the longitudinal span of the support bridge, the height of the uprights, the cross-sectional area of ​​the members, the moment of inertia of the cross section, the elastic modulus of the material, and the shear modulus, and clarify the definition and function of each parameter. Based on the structure of the support frame, it is broken down into four core components: uprights, horizontal bars, ground braces, and diagonal braces. Each component is simulated using corresponding finite element units to clarify the stress characteristics and connection methods of each component, ensuring coordinated stress and displacement among the components. A material constitutive model is introduced, and the stress-strain relationship is used to describe the mechanical response of the support frame material from elastic to plastic stages, capturing the stress state of the structure. A load mapping mechanism is established to deeply couple dynamic non-uniform loads with the finite element model. The load mapping function is used to connect the load and the model. At the same time, the linkage verification of model parameters is completed to ensure that the model parameters can be adjusted and updated in real time. Finally, a parametric finite element model that can truly reflect the stress state of the support and adapt to the construction process is constructed.

5. The method for stability analysis of cast-in-place steel-concrete composite tied-arch supports according to claim 1, characterized in that, The process of dividing the multi-stage calculation conditions in S3 is as follows: Based on the symmetrical phased pouring construction path of the tied arch and the on-site construction rhythm, and combined with the time nodes, load distribution forms and support stress characteristics of each construction stage, the calculation conditions of multiple stages are divided. The entire construction process is divided into four independent and sequentially connected conditions: preliminary preparation, foundation construction, arch pouring, and final acceptance, which correspond to the support erection, foundation construction, segmented pouring of the arch, and final verification, respectively. The composition and distribution characteristics of the loads under each working condition change differently with the construction process. In the early preparation working condition, the load is mainly the self-weight of the support and a small amount of equipment load, and the load distribution is uniform. In the foundation construction working condition, the load of the newly poured material is added, and it shows a local concentrated distribution. In the arch pouring working condition, the load increases dynamically with the progress of symmetrical pouring, and the spatial distribution shows a non-uniform characteristic. In the final acceptance working condition, the load gradually decreases and tends to stabilize, thus fully covering the entire construction process and simulating the actual stress state of the support at each stage.

6. The method for stability analysis of a cast-in-place support for a steel-concrete composite tied-arch as described in claim 1, characterized in that, The process of dynamically correcting the working parameters and load conditions of the finite element model in S3 is as follows: set up These are spatial coordinate variables, corresponding to the horizontal, vertical, and center directions of the bridge, respectively. Construction time is a variable; The structural displacement field obtained from on-site monitoring is used to characterize the actual deformation of the structure; Calculate the displacement field for the finite element model to characterize the theoretical deformation of the model; define the displacement residual. , used to characterize the overall deviation between measured and calculated results; Parameter correction forward calculation The expression is obtained directly from the spatial gradient field of the displacement residuals. ,in For three-dimensional gradient operators, , For the overall computational domain of the support structure, For the volume of a spatial infinitesimal element, this formula directly yields a correction operator that reflects the overall stiffness deviation of the structure by integrating the residual gradient over the entire domain. The correction expression for the operating condition parameters is as follows: ,in To correct the operating parameters of the previous model, To correct the working parameters of the model, the parameter correction process is entirely driven by monitoring residuals, realizing synchronous adaptive updates of model stiffness and constraint conditions; Load space adaptive correction regularization The displacement residual is determined by the two-dimensional integral of the displacement residual in the load plane and the structural geometric characteristics, and the specific expression is as follows: ,in The area of ​​load application The formula is a plane area. By integrating the area, the displacement deviation is transformed into a correction ratio for the load distribution, so that the load conditions match the measured deformation. The corrected expression for the load field is: ,in For the original dynamic non-uniform load, To correct the load; Substituting the corrected working parameters and load conditions into the model and recalculating, we obtain the displacement field of the new generation model. and update the displacement residuals. Repeat the iterative calculation until... , To calculate the convergence threshold, the model parameters must now perfectly match the actual stress state on site, thus completing the entire dynamic correction process.

7. The method for stability analysis of a cast-in-place steel-concrete composite tied-arch support according to claim 1, characterized in that, The specific process of comprehensive evaluation in S3 is as follows: Eigenvalue buckling analysis was performed on the stent system to solve the buckling control equation. ,in Here is the linear elastic stiffness matrix of the structure. For the first Critical buckling characteristic value during the construction phase. For the first Initial stress-stiffness matrix of the stage For the first buckling mode vectors of the stage; Geometric and material nonlinear analyses were performed to obtain load-displacement curves for each construction stage. ,in For the first Actual loads applied during the stage The maximum structural displacement at the corresponding stage; the first extreme point of the curve is extracted. Ultimate bearing capacity of staged support system Calculate the stable reserve ratio This directly reflects the structure's ability to resist instability at that stage; Extract the calculated stress values ​​of all load-bearing members at each construction stage. ,in Numbering the construction phases Number the members according to their material design strength. Based on the strength verification formula Complete the strength and safety assessment of all members; Extracting displacement calculation values ​​of key nodes at each stage ,in Key nodes are numbered according to the allowable structural displacement. As a control benchmark, a stiffness verification formula is used. Complete the structural stiffness and stability determination; The critical buckling characteristic value, ultimate bearing capacity reserve ratio, member stress, and nodal displacement were calculated simultaneously for all construction stages, and all stages met the requirements. , , , At that time, the stent was deemed to be stable and up to standard during this stage; By summarizing the stability assessment results of all construction stages, a full-process stability evaluation function is constructed. in This represents the total number of construction phases. For the first Maximum stress in members at each stage For the first Maximum node displacement in a stage.

8. The method for stability analysis of a cast-in-place support for a steel-concrete composite tied-arch as described in claim 1, characterized in that, The process of sensitivity analysis of key parameters in S4 is as follows: First, determine the set of core parameters for sensitivity analysis. These core parameters include the spacing between support uprights, the step distance of horizontal bars, the density of diagonal bracing, the cross-sectional dimensions of the uprights, and the pre-camber value. Critical buckling characteristic value, stability reserve ratio, maximum member stress, and maximum nodal displacement were selected as key response indicators for the stability of the support. The single-parameter variable method is adopted. While keeping the other parameters unchanged at the design reference value, the single parameter is made to change uniformly at a fixed step size within its design value range, and the response index value corresponding to the step size of each parameter change is calculated. Based on the changes in parameters and response indicators, a formula for calculating sensitivity coefficients is constructed. The sensitivity coefficients of each core parameter to each response indicator are then calculated to form a sensitivity coefficient matrix. Based on the absolute value of the obtained sensitivity coefficient, a grading standard is set, and each parameter is divided into three levels: high sensitivity, medium sensitivity, and low sensitivity, so as to quantify the degree of influence of each parameter on stent stability.

9. A method for stability analysis of cast-in-place supports for steel-concrete composite tied arches, characterized in that, include: The load decoupling construction unit is used to decouple the load in the support area along the transverse direction of the bridge, based on the stress characteristics of the three-arch rib tied arch structure of the wide bridge deck. The dynamic construction load of each zone is represented in the form of a time-varying function, and a dynamic non-uniform initial load combination that can reflect the entire construction process is constructed. The support simulation coupling unit is used to establish a differentiated parametric finite element model of the arch foot densified section and the standard section based on the structural characteristics of the socket-type disc-lock support. The foundation stiffness, support preload inelastic deformation, temperature effect and nodal mechanical performance parameters are synchronously coupled into the model. Based on the dynamic non-uniform initial load combination, the multi-physics mechanical behavior of the support system is realistically simulated. The multi-condition stability evaluation unit is used to divide the calculation conditions into multiple stages based on the symmetrical phased pouring construction path of the tie-arch, dynamically correct the condition parameters and load conditions of the finite element model based on real-time monitoring data at the construction site, and comprehensively evaluate the stability of the support system at each construction stage and throughout the entire process. The parameter optimization and analysis unit is used to construct a multi-factor coupled optimization model based on real-time monitoring data of casting deformation, coupled with load characteristics, model parameters and stage evaluation results, to iteratively optimize the support layout parameters and pre-camber parameters, and to complete the sensitivity analysis of key parameters.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program is executed by a processor according to any one of claims 1-8, a method for stability analysis of cast-in-place steel-concrete composite tied arch supports.

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