Coordinated parametric design method for negative moment region of uhp bridges based on finite element analysis

Abstract

This invention relates to the field of computer-aided design technology, and more particularly to a collaborative parametric design method for the negative bending moment zone of UHPC bridges based on finite element analysis. A five-dimensional design parameter vector is constructed and iteratively optimized. Simulations are performed for multiple cooling scenarios, and a two-stage collaborative optimization is executed: the first stage extracts the most unfavorable temperature drop envelope for optimization, fixing static structural parameters such as thickness and reinforcement in the converged solution, and outputting design drawings; the second stage, with the static parameters fixed, performs dimensionality reduction and independent optimization only on the dynamic intervention parameters for multiple cooling scenarios, generating a field-triggered dynamic control parameter table. This invention can solve or at least alleviate the problems of decoupling between static structural parameters and dynamic intervention parameters in the negative bending moment zone of UHPC bridges, and the disconnect between optimization objectives and material conditions, providing a collaborative parametric design method for the negative bending moment zone of UHPC bridges based on finite element analysis.

Description

Technical Field

[0001] This invention relates to the field of computer-aided design technology, and in particular to a collaborative parametric design method for the negative bending moment zone of UHPC bridges based on finite element analysis. Background Technology

[0002] Under heavy-load operation, long-span continuous beam bridges and composite beam bridges experience long-term longitudinal tensile stress in the bridge deck of the negative bending moment zone above the mid-support. Ordinary concrete has low tensile strength, making it prone to penetrating cracks in these areas, leading to steel corrosion and reduced structural durability. Ultra-high performance concrete (UHPC), with its high tensile strength, good toughness, and low permeability, has been gradually applied to bridge decks in the negative bending moment zone and longitudinal and transverse wet joints. However, UHPC exhibits significant nonlinear time-varying behavior during early hydration and hardening. The superposition of chemical self-shrinkage and thermal contraction after steam curing makes it prone to cracking at a young age. The peak tensile stress generated by the release of self-weight during system replacement also has an adverse effect on the young matrix. Traditional structural design methods, such as increasing reinforcement ratio, embedding constant prestressing tendons, and the mid-support jacking method, typically rely on empirical parameter values ​​and employ passive interventions with fixed time sequences, which are difficult to match with the time-varying physical behavior of UHPC.

[0003] Currently, the industry mainly adopts two approaches to address the above problems: First, introducing elastic recovery devices or delayed tensioning processes to offset prestress loss through discrete mechanical compensation; second, adjusting construction procedures (such as pouring before negative bending moment, or pouring after jacking up supports) to pre-set initial compressive stress in the structure. These methods have achieved certain results under traditional NC systems, but their design process is essentially based on empirical values ​​of a few independent parameters, without establishing a unified design variable system covering UHPC layer thickness, reinforcement ratio, initial micro-tensioning control stress, hydraulic return step length, and prestressed stepped tensioning increment. This results in various intervention methods being independent of each other, making it difficult to achieve synergy in the time and spatial domains. When dealing with time-varying nonlinear materials like UHPC, situations of delayed intervention timing or mismatched compensation amounts are prone to occur.

[0004] From the perspective of computer-aided design, the root cause of the above shortcomings lies in the fact that the existing engineering design process lacks a mathematical framework that incorporates static structural parameters and dynamic intervention parameters into the same optimization objective function. Furthermore, the CAD design stage lacks a mechanism for incorporating material micro-phase transformations, temperature drop inflection points, and other state conditions into multi-condition optimization and pre-simulation. Although finite element simulation is widely used in bridge structural analysis, it is mostly used for forward verification and has not yet formed a reverse optimization process with crack width and tensile stress as objectives and UHPC time-varying tensile strength and normal deformation threshold as constraints. Existing topology optimization methods mainly focus on the static distribution and void generation of single materials, which differs mathematically from the parametric design involved in this invention. They also lack the ability to optimize and pre-simulate dynamic intervention parameters during construction, and there is no compilation of optimization results into a condition-triggered multi-condition strategy library that can be called on-site based on state events. Therefore, the parametric design of the negative bending moment zone has long remained in an iterative stage of "first empirical design, then simulation verification," limiting both design efficiency and structural synergy performance. Summary of the Invention

[0005] To achieve the above-mentioned objectives, this invention provides a collaborative parametric design method for the negative bending moment zone of UHPC bridges based on finite element analysis. This method aims to solve or at least alleviate the problems in the prior art where the static structural parameters and dynamic intervention parameters of UHPC bridges in the negative bending moment zone are designed independently, and the optimization objectives and material conditions lack coordination.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a collaborative parametric design method for the negative bending moment zone of UHPC bridges based on finite element analysis, comprising:

[0007] The UHPC layer thickness, longitudinal and transverse reinforcement ratios, initial micro-tension control stress, hydraulic step fall step length and prestressed step tension increment are constructed into a five-dimensional design parameter vector and normalized.

[0008] In the finite element preprocessing, a finite element model is established based on the subset of static structural variables in the design parameter vector. The UHPC solid elements in the model are given a tensile-compressive plastic damage constitutive model, a time-varying strength function and corresponding boundary conditions, and multi-condition loads are applied.

[0009] The comprehensive damage obtained by weighting the dimensionless crack width prediction function and the maximum tensile stress function in the negative bending moment region is used as the optimization objective. The stress envelope constraint and deformation threshold constraint are used as boundary conditions. The Lagrange multiplier method or the exterior point penalty function method are used to construct the augmented objective function with a penalty term and perform iterative optimization.

[0010] Based on historical meteorological databases and UHPC hydration heat-temperature drop prediction curves, a two-stage collaborative optimization is performed on multi-condition cooling scenarios: the first stage is the static parameter determination stage, which performs overall optimization of all variables for the most unfavorable temperature drop envelope condition with superimposed extreme values, fixes the values ​​of the subset of static structural variables in the converged solution, and outputs the determined construction drawings and physical structure data through the static construction output channel.

[0011] The second stage is the dynamic strategy library generation stage. Under the premise that the values ​​of the static structural variable subset are fixed, simulations are performed for multiple cooling conditions. Only the dynamic intervention variable subset is optimized independently. The obtained optimization solutions are merged into a condition-triggered multi-condition strategy library through the dynamic collaborative control output channel, which serves as the parameter call data source for the on-site control terminal during the construction period.

[0012] To further realize the present invention, the following technical solutions may be preferred:

[0013] Preferably, the design parameter vector is divided into a static structural variable subset and a dynamic intervention variable subset. The former includes the UHPC layer thickness and longitudinal and transverse reinforcement ratios, while the latter includes the initial micro-tension control stress, hydraulic step fall step size, and prestressed step tension increment. The geometric entity configurations and boundary conditions corresponding to the two subsets are solved simultaneously in the finite element model. Each component in the design parameter vector is mapped to the dimensionless interval [0,1] in a linear normalization manner according to the process search interval of its respective physical quantity before participating in the calculation of the objective function and constraint function.

[0014] Preferably, the crack width prediction function is established based on the theoretical calculation method of crack width for UHPC-NC composite bridge deck structures, and the maximum tensile stress function covers the top surface of the bridge deck in the negative bending moment zone of the mid-support point.

[0015] Preferably, the stress envelope constraint requires that the tensile stress on the top surface of the UHPC under any transient condition does not exceed the tensile strength at the current age, and the deformation threshold constraint requires that the normal springback deformation of the hydraulic support is within a preset sub-millimeter threshold.

[0016] Preferably, the time-varying intensity function is the evolution relationship between the tensile strength, compressive strength and elastic modulus of UHPC as a function of age, which is obtained by fitting measured material data through cubic spline interpolation.

[0017] Preferably, in the second stage, a set of working condition samples is generated using the Monte Carlo method or exhaustive search method for different cooling gradient working conditions. For each sample, a different comprehensive damage function weight coefficient is used in the optimization iteration: when the cooling gradient is greater than a set threshold, the optimization upper limit of the hydraulic step fall step is relaxed; when the cooling gradient is not greater than a set threshold, the optimization upper limit of the prestressed step tension increment is relaxed.

[0018] Preferably, the index conditions of the condition-triggered multi-condition strategy library include strain and temperature state events of the UHPC core area and the interface between the old and new components. The state events include the initial solidification phase transition point criterion calibrated by the abrupt change of the first derivative of strain and the temperature drop inflection point criterion calibrated by the temperature drop inflection point. The strategy library is used for parameter calls during the construction phase to replace real-time finite element calculations at the construction site.

[0019] Preferably, the calculation steps of the first derivative of the strain are as follows: the original strain time history signal obtained by optical fiber sensing is first subjected to moving average filtering to eliminate high-frequency noise, and then the first-order difference operation is performed on the filtered time series. The confirmation condition of the phase transition abrupt point is that the first-order difference value is continuously greater than the calibration threshold for a period of time exceeding a preset time window.

[0020] Preferably, the static structural output channel includes the UHPC layer thickness distribution, reinforcement arrangement, and prestressed tendon trajectory line, which are used to import into three-dimensional mechanical design software to generate structural drawings; the dynamic collaborative control output channel includes a synchronization sequence composed of hydraulic depressurization timestamps and prestressing tension timestamps, as well as a feedforward time advance for compensating for the response delay of the actuator.

[0021] Preferably, the iterative optimization is performed in a fixed parameterized design variable space using the moving asymptote method or the sequential quadratic programming method. When the norm change of the design parameter vector within a set number of consecutive iterations is less than a set threshold, it is determined to be converged. The converged solution is then submitted to the strength verification module for review. If the review fails, the constraint parameters are adjusted and the optimization is performed again.

[0022] The beneficial effects of this invention are:

[0023] This invention establishes a unified normalized design parameter vector at the computer-aided design level, covering UHPC layer thickness, longitudinal and transverse reinforcement ratios, initial micro-tension control stress, hydraulic step fall step size, and prestressed step tension increment. It uses the comprehensive damage, weighted by crack width prediction and the maximum tensile stress function, as the optimization objective, and the time-varying tensile strength envelope and normal deformation threshold of UHPC as optimization constraints. This changes the traditional approach of separately processing static structural parameters and dynamic intervention parameters and relying on manual experience for value selection. It enables the collaborative design of the negative bending moment zone to be solved uniformly within the same algorithm framework, which helps reduce the peak tensile stress on the top surface of the bridge deck during the temperature drop period in the negative bending moment zone, the peak tensile stress during system replacement transients, and the microcrack density at the UHPC-NC interface.

[0024] This invention introduces a multi-condition simulation and pre-running mechanism during the CAD design phase. It generates diverse cooling condition samples using historical meteorological databases and UHPC temperature drop prediction curves. For each sample, it determines the weight of the comprehensive damage objective function and the optimization upper limit of the design variables, and organizes the calculation results into a condition-triggered multi-condition strategy library. This strategy library is delivered synchronously with the design drawings. During the construction phase, the distributed fiber optic sensing network on-site reads measured state events such as the initial condensation phase transition and temperature drop inflection point, and then calls the parameters accordingly. The output of this invention consists of two parts: static structural data and the multi-condition strategy library. The former is used for model reconstruction in 3D mechanical design software, while the latter serves as the parameter data source for the on-site control terminal during the construction period, thus forming a complete data flow from the CAD design end to the construction execution end. Attached Figure Description

[0025] Figure 1 This is a flowchart of the overall algorithm of the present invention.

[0026] Figure 2 This is a schematic diagram illustrating the principle of the five-dimensional design parameter vector composition and normalization mapping of the present invention.

[0027] Figure 3 This is a schematic diagram of the finite element model of the negative bending moment region and the arrangement of sensing nodes in this invention.

[0028] Figure 4 This is a schematic diagram of the two-stage collaborative optimization process of the present invention.

[0029] Figure 5 This is a schematic diagram of the weight mapping principle of the dual-system collaborative control strategy of the present invention.

[0030] Figure 6 This is a schematic diagram of the dual-channel data flow from the CAD design end to the construction execution end of the present invention. Detailed Implementation

[0031] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] Example 1

[0034] The computer-aided design system of this embodiment includes a parametric preprocessing module, a finite element solution kernel, a nonlinear optimization module, a multi-condition simulation module, a data output module, and a verification interface module. Each module is coupled via an internal bus and has a reserved communication interface for delivering the generated multi-condition strategy library to the control terminal at the construction site in the form of a data file. The overall process is as follows: Figure 1 As shown, the dual-channel data interaction relationship between the various modules of the CAD design end and the construction execution end is as follows: Figure 6 As shown.

[0035] The parametric preprocessing module reads in the geometric information and material parameters of the bridge's negative bending moment zone and constructs a five-dimensional design parameter vector. .in, The thickness of the UHPC layer is in mm. The longitudinal and transverse reinforcement ratios are expressed in % (%). The initial micro-tension control stress is expressed in MPa. The hydraulic step drop step length is in mm / step. The increment of prestressed stepped tension is expressed as a percentage / level of the design tension force. It constitutes a subset of static structural variables, reflecting the crack resistance reserve of the structural body; This constitutes a subset of dynamic intervention variables, reflecting the ability to actively intervene in the early shrinkage and system replacement processes of UHPC. The physical meaning of each component of the five-dimensional vector, the process search interval, and the normalized mapping relationship are as follows: Figure 2 As shown. To eliminate the influence of different physical quantities in units of measurement, the design parameter vector is searched according to the process range. Perform linear normalization:

[0036] i = 1,2,…,5

[0037] After normalization, all components fall within the [0,1] interval. The comprehensive damage objective function, constraint function, and norm convergence criterion are all calculated in the normalized space. The final result is output after being mapped back to engineering dimensions through inverse normalization.

[0038] The finite element solution kernel is built on a general-purpose finite element analysis platform, and the model layout is as follows: Figure 3As shown. The UHPC layer and NC bridge deck in the negative bending moment region are discretized using eight-node solid elements, the main steel beams using four-node shell elements, and the prestressed steel strands using embedded rod elements. The UHPC and NC interfaces are coupled at common nodes to simulate shear bonding. A hydraulic servo jacking element is set at the mid-support position, and the jacking displacement and self-locking state are simulated by stiffness coefficient and displacement boundary conditions. The UHPC material constitutive model adopts the tensile-compressive plastic damage constitutive model (CDP). The compressive strength, tensile strength, and elastic modulus are taken according to the time-varying strength function with age. The time-varying strength function is obtained by fitting the measured data of the early strength evolution of UHPC material through cubic spline interpolation.

[0039] The nonlinear optimization module has a built-in comprehensive damage objective function:

[0040]

[0041] in, The crack width prediction function is calculated using the empirical formula of the nominal stress method: In the formula, the effective protective layer thickness is... With reinforcement ratio From static structure variables , The converted stress of the tensile reinforcement is... Extracted from finite element calculation results, The elastic modulus of the steel reinforcement; This is the maximum tensile stress function on the top surface of the bridge deck in the negative bending moment zone at the mid-support point. , These are dynamic weighting coefficients that vary with the simulated operating conditions. Constraints include stress envelope constraints. ,in, The tensile strength of UHPC at its current age; deformation threshold constraint. ; and lateral constraints such as the feasible region of reinforcement ratio and the UHPC thickness process range. To incorporate these constraints into the nonlinear optimization, a comprehensive objective functional with constraint penalty terms is constructed using the Lagrange multiplier method:

[0042]

[0043] in, Lagrange multipliers constrained by inequality For the equation side constraint multiplier;

[0044] When using the exterior point penalty function method, the augmented objective function can be written as:

[0045]

[0046] in, As a penalty factor, it increases geometrically from the initial value during iteration. The value is gradually increased until the constraint violation is less than a set threshold. The optimization algorithm uses the moving asymptote method or sequential quadratic programming method to find the optimal value in a fixed parametric design variable space. The convergence criterion is the change in the L2 norm of the normalized design parameter vector in K consecutive iterations. Less than the set threshold In this embodiment, =1×10 -4 It is important to emphasize that this method does not use the density method to gradually eliminate the topology optimization path of the cells. The design variables remain as continuous parameter values ​​throughout the optimization process, and irregular holes are not generated.

[0047] The multi-condition simulation module runs during the CAD design phase. It is responsible for extracting typical annual ambient temperature and humidity curves for the target region from the meteorological database, and calculating a family of temperature drop prediction curves by combining the UHPC hydration heat prediction model with boundary heat transfer conditions. This module performs a two-stage collaborative optimization process, as follows: Figure 4 As shown. The first stage is the static parameter determination stage, which extracts the most unfavorable envelope working condition with a large temperature drop gradient and performs five-dimensional global optimization. After obtaining the convergent solution, the subset of static structural variables that determine the solid geometry and reinforcement will be used. The value is fixed; the second stage is the dynamic strategy library generation stage, in Under the premise of keeping the values ​​constant, the Monte Carlo method is used to sample and generate N working condition samples according to the three-dimensional parameter space composed of the cooling gradient, the cooling start time and the ambient temperature difference. In this embodiment, N=50, and only a subset of dynamic intervention variables are made available to these N samples. The space for optimization.

[0048] For each sample, query the pre-defined weight allocation mapping table and adjust the overall damage objective function. , weight and , The upper limit of optimization for the current sample. Increase the threshold when the cooling gradient exceeds the set threshold. The upper limit of optimization and its sensitivity in the objective function make hydraulic fallback play a major role in macroscopic displacement compensation; when the cooling gradient does not exceed the set threshold, the increase... The optimization upper limit and sensitivity of the parameters enable prestressed stepped tensioning to play a major role in flexible stress compensation. In the second stage, after each working condition sample completes independent optimization, the convergent solutions of the dynamic parameters are grouped according to the cooling gradient and merged into a condition-triggered multi-working-condition strategy library. The strategy library entries include: trigger condition intervals and corresponding... , , Feedforward time advance Δt and synchronization timestamp template.

[0049] The data output module integrates the results of parametric preprocessing and multi-condition simulation and outputs the following: Static structural output generates UHPC thickness distribution, reinforcement arrangement, and prestressed tendon trajectory lines, which are imported into 3D mechanical design software in STEP format for model reconstruction, generating structural drawings of precast components or wet joints; the multi-condition strategy library is output in the form of tables and instruction files, including index condition ranges, corresponding dynamic parameter values, synchronization timestamp templates, and suggested values ​​for feedforward timing. Both types of output are processed through... Figure 6 The static structural output channel and dynamic collaborative control output channel shown are respectively distributed to the 3D mechanical design software and the field control terminal, forming a complete data flow from the CAD design end to the construction execution end. The strategy library is delivered together with the construction drawings, and during construction, the field control terminal calls parameters based on the measured status events read by the distributed fiber optic sensing network; the design method involved in this invention does not make any modifications to static parameters such as thickness and reinforcement during construction.

[0050] In terms of system hardware configuration, the solution server uses a multi-core processor and a large capacity of memory, and is equipped with a GPU-accelerated computing card to improve the computational efficiency of large-scale finite element solutions and multi-condition optimization.

[0051] Example 2

[0052] Based on the system configuration described in Embodiment 1, this embodiment further illustrates the collaborative parametric design method for the negative bending moment zone of UHPC bridges based on finite element analysis. In the pre-parametric processing stage, the computer reads the geometric and material parameters of the target bridge, sets the initial value and search interval of the five-dimensional design parameter vector X, and maps it to the [0,1] space according to the aforementioned linear normalization formula. The process starting point is described in [link to documentation]. Figure 1 The initial values ​​were selected based on existing engineering experience, and the search interval was determined by considering both process feasibility and material mechanical properties. A time-varying strength function was assigned to the UHPC material, which was obtained by cubic spline interpolation fitting of measured tensile strength, compressive strength, and elastic modulus data of indoor standard cured specimens at different ages.

[0053] After the finite element model is established, a lifting displacement boundary condition is applied to the central support point to convert the negative bending moment region into a pre-compression or zero-stress state. Once the lifting displacement reaches the design value, the displacement degrees of freedom of the corresponding nodes are locked, forming a rigid support boundary. In the finite element model, the UHPC element is then activated using the element birth and death technique to simulate its casting process, and the initial strain of the UHPC element is set to zero.

[0054] The two-stage procedure (e.g., during the multi-condition pre-simulation phase) is executed automatically. Figure 4(As shown): The first step is to determine static parameters. The most unfavorable working condition with superimposed extreme values ​​is extracted and optimized using a five-dimensional parameter vector. After convergence, the UHPC thickness x1 and reinforcement ratio x2 are fixed as constants, eliminating the correlation between entity parameters and random weather conditions. The second step is to obtain a Monte Carlo working condition sample set based on meteorological database sampling of cooling gradients. For ordinary working condition samples, the optimization module, with the thickness and reinforcement ratio fixed, follows... Figure 5 The weight allocation mapping shown determines the weights and the upper limit of the optimization. After constructing the augmented objective function, only the dynamic parameters are considered. , , Independent iterative optimization is performed until the norm change of the normalized design parameter vector is less than the convergence threshold. The optimization process for a single sample is completed in the offline CAD stage, and the optimization solutions of all N samples are merged into a condition-triggered multi-condition strategy library according to the cooling gradient interval. The basis for the two-stage output design is that the thickness of the bridge deck cannot be changed by weather conditions, so a fixed construction drawing must be output uniformly; while for ordinary weather conditions, only the dynamic intervention parameters are independently optimized and pre-stored, which can simplify the response during the construction period to a parameter call process in seconds, without having to recalculate the finite element method online.

[0055] Regarding the identification of the initial condensation phase transition point, this implementation method employs the following data processing flow: A distributed fiber optic grating array acquires the original strain time history signal of the UHPC core area at a high sampling rate. The signal is first filtered by moving average to eliminate high-frequency noise in the fiber sensing, and then a first-order difference operation is performed on the filtered time series to obtain the first derivative of the strain. When the absolute value of the first derivative of the strain remains greater than the calibrated abrupt change threshold for a duration exceeding a preset time window, it is determined to be the initial condensation phase transition point. This identification rule is preset in the control terminal as a trigger condition in the multi-condition strategy library.

[0056] During the steam curing heating period, the sensing network detected an increase in the UHPC core temperature and a shift in internal strain towards the positive direction. The control terminal's strategy library query result was a "passive hold" state, maintaining the current output unchanged and allowing the material to expand freely to release non-uniform thermal stress. After steam curing, the temperature drop inflection point was identified by the sensing interface module. After inflection point identification, the control terminal retrieved the corresponding cooling condition range from the multi-condition strategy library based on the real-time cooling gradient read from the optical fiber and called the corresponding dynamic parameter set. The corresponding weight allocation logic and calibration results for each condition are as follows: Figure 5 As shown. When the cooling gradient exceeds the set threshold, the parameter set with hydraulic recoil as the main compensation method is invoked; when the cooling gradient does not exceed the set threshold, the parameter set with prestressed stepped tensioning as the main compensation method is invoked. A stress relaxation stabilization period is provided between each step of the operation. The sensing interface module monitors the stability of the strain feedback signal, and only proceeds to the next step after the strain feedback has stabilized.

[0057] After the UHPC compressive strength reaches the design value, the system replacement stage begins. The hydraulic decompression and prestressing tension synchronization control curves for this stage were generated and saved as strategy library entries during the CAD multi-condition pre-simulation stage. The constraint is that the tensile stress on the top surface of the bridge deck under any transient condition during the system replacement process does not exceed the tensile strength of the UHPC at its current age. During the pre-simulation stage, preliminary values ​​are taken based on the hydraulic pump station response time constant, pipeline pressure build-up delay, and tensioning pump station pressurization time constant provided by the equipment manufacturer. Further corrections are made when necessary, incorporating data from on-site joint commissioning, and the feedforward time advance Δt is calculated accordingly. Δt is used to advance the prestressing pressure increase command relative to the hydraulic decompression action, compensating for the physical response delay of the two actuators at the pre-simulation level. It should be noted that the mechanical hysteresis of the hydraulic pump and the on-site synchronization accuracy are ultimately determined by the hardware selection and joint commissioning of the on-site electromechanical system, and are not technical problems directly solved by the CAD design method of this invention.

[0058] After the iterative optimization converges, the strength verification module performs a secondary verification of the model corresponding to X*. The verification includes stress verification under the serviceability limit state, bending moment verification under the ultimate limit state of bearing capacity, shear stress verification at the UHPC-NC interface, and calculation of long-term creep loss. After successful verification, the data output module outputs data in two ways: static structural data and multi-condition strategy library data (see [link]). Figure 6 (Dual channels shown); if the review fails, the constraint parameters are adjusted, usually by relaxing the upper limit of the reinforcement ratio or fine-tuning the lower limit of the UHPC thickness, and then re-optimizing (see...). Figure 4 The first stage of the loop.

[0059] Example 3

[0060] The verification case uses a multi-span continuous beam bridge as the engineering background. The main bridge span is approximately (80+5×190+80)m, the total bridge deck width is approximately 37m, and the negative bending moment zone UHPC layer covers an area of ​​approximately 25m on both sides of the central support. The bridge deck thickness is designed to be within the range of 35mm to 55mm. The computing platform uses a dual-processor server with large-capacity memory and an accelerated computing card. The finite element solution kernel uses general-purpose finite element analysis software, and the optimization module is based on a Python environment.

[0061] The initial values ​​of the design parameter vector are set as follows: Approximately 40mm Approximately 2.8%, Approximately 0.9 MPa equivalent compressive stress, Approximately 0.6 mm / grade Approximately 6% of the design tension per grade. The search range is: ∈[35, 55]mm, ∈[2.0%, 4.0%], Equivalent compressive stress ∈ [0.4, 2.0] MPa, ∈[0.3, 1.5]mm / level, ∈[3%, 12%] / level. Each component is mapped to [0,1] according to the aforementioned linear normalization formula before participating in the iterative calculation.

[0062] In the multi-condition simulation phase, approximately 50 cooling condition samples were generated using the Monte Carlo method. The cooling gradient sampling range was 1.5 to 7.5℃ / h, and the ambient temperature difference sampling range was 8℃ to 28℃. The actual simulation calculations strictly followed a two-stage collaborative optimization process. The first stage involved a five-dimensional global optimization for the most unfavorable envelope condition. After obtaining a convergent solution, the values ​​of the static structural variables were fixed. In this verification, the values ​​determined from the construction drawings were... Approximately 45mm Approximately 3.1%; the single calculation for global optimization in this stage takes approximately tens of minutes. In the second stage, given that the thickness and reinforcement values ​​are fixed, the generated samples for ordinary cooling conditions are only processed for dynamic intervention variables (…). , , Independent optimization was performed. Since the number of variables was reduced to three dimensions and there was no need to re-mesh the static geometric mesh, the time consumed in a single optimization was significantly reduced to the order of minutes. The total time for the second-stage pre-simulation was approximately several hours, and all calculations were completed on an offline server during the CAD design phase. Results show that the dynamic intervention variables exhibit a distinct stepped distribution under different working conditions and are grouped into a condition-triggered multi-working-condition strategy library according to the cooling gradient interval. The comprehensive damage objective function value F(X*) is approximately 0.31 (normalized with an initial value of 1.00). In the converged solution representing the normal working condition, the dynamic parameter part is approximately [1.1MPa, 0.8mm / level, 7% / level]ᵀ.

[0063] For on-site measurement data verification, the data collection locations were the distributed fiber optic nodes at the core area of ​​the UHPC at the central support point and the interface, with a sampling frequency of approximately 50Hz. The measured data showed that the initial solidification phase transition point was identified by the sensing network approximately 11 hours after UHPC casting. Compared to the time determined by a penetration resistance meter for the same batch of specimens in the laboratory, the deviation was within ten minutes, falling within the measurement error range. Within several minutes of identifying the initial solidification phase transition point, the on-site control terminal invoked the corresponding strategy from the strategy library. The values ​​are obtained and sent to the prestressing system to initiate micro-tensioning; actual measurements are performed. The corresponding equivalent compressive stress is approximately 1.1 MPa, which is basically consistent with the value taken from the strategy library. The slight deviation is mainly caused by the friction loss under the anchor.

[0064] During the steam curing phase, the measured peak temperature of the UHPC core was approximately 74℃, while the finite element prediction was approximately 73.5℃, with a deviation within 2%. The average core temperature decrease rate during the cooling period was approximately 4.8℃ / h, with the instantaneous value reaching approximately 6.2℃ / h from the 3rd to the 5th hour, exceeding the set threshold of 5℃ / h. Based on this, the field control terminal automatically switched to the parameter set corresponding to the cooling condition with hydraulic sag as the primary compensation method (this parameter set had been calculated during the CAD pre-simulation phase and stored in the multi-condition strategy library); the measured hydraulic sag step size was adjusted from 0.8mm / step to approximately 1.1mm / step during this period. The rate was adjusted from 7% per level to approximately 5% per level. After 5 hours, the cooling rate dropped back to approximately 3.1℃ / h, and the field control terminal switched back to the parameter set corresponding to the default cooling condition. , The system reverts to its normal settings. The above switching process has a response time in seconds and does not involve any online finite element recalculation, demonstrating... Figure 6 The actual effect of the dual-channel output architecture shown.

[0065] During the system replacement phase, the synchronization error of the actuator response to hydraulic depressurization and prestressing tension was controlled within the upper limit of the engineering design tolerance of 0.2 seconds in multiple sets of measurements. The baseline value of the feedforward time advance Δt was approximately 0.35 seconds. Considering factors such as mechanical dead zone and fluctuations in the bulk modulus of hydraulic oil, the measured response delay of the actuator was within the range of 0.3 to 0.4 seconds. The measured extreme value of the tensile stress on the top surface of the bridge deck under the replacement transient was controlled within approximately +1.1 MPa, which did not exceed the tensile strength of UHPC at that age (measured at approximately 6 MPa), satisfying the stress envelope constraint. The measured peak value of the normal springback deformation was within 1 mm, which did not exceed the deformation threshold.

[0066] The control group used a traditional passive prestressing process. Under the same working conditions, the measured peak tensile stress during the temperature drop period was about 3.9 MPa, and the measured instantaneous tensile stress during the support fall was about 4.6 MPa, which is close to two-thirds to three-quarters of the tensile strength of UHPC at that age (about 6 MPa), indicating a risk of further cracking. In this embodiment, the peak tensile stress during the temperature drop period was about 0.9 MPa, and the measured extreme value of the instantaneous tensile stress during the support fall was about 1.1 MPa.

[0067] The density of microcracks at the bridge deck interface was determined using a magnifying glass counting method after spraying a whitening agent onto the surface. Ten test areas, each approximately 5m × 37m on either side of the central support, were selected. The average microcrack density in the control group was approximately 0.4 cracks / m. In this embodiment, under the same temperature difference monitoring environment, no macroscopically visible cracks were observed on the bridge deck, and the average microcrack density decreased to below 0.1 cracks / m, significantly suppressing the dispersion of construction quality. Twenty-eight days after the system replacement, the UHPC-NC interface was non-destructively tested using the ultrasonic wave velocity method. The average wave velocity in the control group was approximately 3920 m / s with a coefficient of variation of approximately 7%. The average wave velocity in this embodiment was approximately 4265 m / s with a coefficient of variation of approximately 4%, indicating improved interface density and uniformity.

[0068] Predicted through equivalent long-term creep numerical analysis, the effective prestress retention rate of this scheme is higher than that of the control group. Approximately 6 months after operation, several transverse visible cracks were detected in the negative bending moment zone of the bridge deck in the control group, with a maximum width of approximately 0.11 mm; no visible cracks were detected in this scheme during the same period. The effective prestress retention rate read by the fiber optic sensing network was approximately 92% of the initial value in this scheme, compared to approximately 79% in the control group. Twelve months after operation, the effective prestress in this scheme continued to slowly decrease to approximately 91% due to normal structural creep, compared to approximately 76% in the control group.

[0069] It should be noted that the core focus of this invention is the multi-condition collaborative optimization and strategy library generation process during the CAD design phase; electromechanical issues such as mechanical hysteresis compensation of hydraulic pumps at the construction site and synchronous control accuracy of servo actuators are resolved by the hardware selection and joint debugging of the on-site electromechanical system, and are not technical problems directly addressed by this invention.

[0070] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A collaborative parametric design method for the negative bending moment zone of UHPC bridges based on finite element analysis, characterized in that, include: The UHPC layer thickness, longitudinal and transverse reinforcement ratios, initial micro-tension control stress, hydraulic stepped fall-back step size, and prestressed stepped tension increment are constructed as a five-dimensional design parameter vector and normalized. In the finite element preprocessing, a tensile-compressive plastic damage constitutive model and a time-varying strength function are applied to the UHPC. The comprehensive damage weighted by crack width and maximum tensile stress is used as the objective, and the stress envelope and deformation threshold are used as constraints for iterative optimization. The optimization is carried out in two stages based on meteorological data and temperature drop prediction curves: the first stage optimizes all variables for the most unfavorable working condition, and outputs construction drawings after fixing the UHPC layer thickness and reinforcement ratio; the second stage, under the premise of fixed static parameters, optimizes only the dynamic intervention parameters independently for multiple cooling working conditions, generating a condition-triggered multi-working-condition strategy library.

2. The method according to claim 1, characterized in that, The design parameter vector is divided into a subset of static structural variables and a subset of dynamic intervention variables. The former includes the thickness of the UHPC layer and the longitudinal and transverse reinforcement ratios, while the latter includes the initial micro-tension control stress, the hydraulic step fall step length, and the prestressed step tension increment. Each component is mapped to the dimensionless interval [0,1] in a linear normalization manner according to its respective process search interval and then participates in the calculation of the objective function and constraint function.

3. The method according to claim 1, characterized in that, The crack width prediction function is established based on the theoretical calculation method of crack width of UHPC-NC composite bridge deck structure, and the maximum tensile stress function covers the top surface of the bridge deck in the negative bending moment zone of the middle support.

4. The method according to claim 1, characterized in that, The stress envelope constraint requires that the tensile stress on the top surface of the UHPC under any transient condition does not exceed the tensile strength at the current age, and the deformation threshold constraint requires that the normal springback deformation of the hydraulic support is within a preset sub-millimeter threshold.

5. The method according to claim 1, characterized in that, The time-varying intensity function represents the evolution of UHPC tensile strength, compressive strength, and elastic modulus over age, and is obtained by fitting measured material data through cubic spline interpolation.

6. The method according to claim 1, characterized in that, In the second stage, a set of working condition samples is generated using the Monte Carlo method or exhaustive search method for different cooling gradient working conditions. For each sample, different comprehensive damage function weight coefficients are used in the optimization iteration: when the cooling gradient is greater than a set threshold, the optimization upper limit of the hydraulic step fall step is relaxed; when the cooling gradient is not greater than the set threshold, the optimization upper limit of the prestressed step tension increment is relaxed. The obtained optimization solutions are merged into the multi-working condition strategy library according to the cooling gradient interval.

7. The method according to claim 6, characterized in that, The indexing conditions of the multi-condition strategy library include strain and temperature state events of the UHPC core area and the interface between the old and new components. The state events include the initial solidification phase transition point criterion calibrated by the abrupt change of the first derivative of strain and the temperature drop inflection point criterion for the start of the temperature drop shrinkage period. The strategy library is used for parameter calls during the construction phase to replace real-time finite element calculations at the construction site.

8. The method according to claim 7, characterized in that, The calculation steps for the first derivative of the strain are as follows: first, the original strain time history signal obtained by optical fiber sensing is first subjected to moving average filtering to eliminate high-frequency noise, and then the first-order difference operation is performed on the filtered time series. The confirmation condition for the phase transition abrupt point is that the first-order difference value is continuously greater than the calibrated threshold for a duration exceeding the preset time window.

9. The method according to claim 1, characterized in that, The construction drawings include the UHPC layer thickness distribution, reinforcement arrangement, and prestressed tendon trajectory lines, which are used to import into three-dimensional mechanical design software to generate structural drawings; the entries in the multi-condition strategy library include dynamic intervention parameter values, synchronous timestamp templates for hydraulic depressurization and prestressing tensioning, and feedforward time advance for compensating for the response delay of the actuator.

10. The method according to claim 1, characterized in that, The iterative optimization adopts the moving asymptote method or the sequential quadratic programming method. When the norm change of the design parameter vector within a set number of consecutive iterations is less than a set threshold, it is determined to be converged. The converged solution is submitted to the strength verification module for review. If the review fails, the constraint parameters are adjusted and optimization is performed again.

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