Methods and Systems for Predicting the 100-Year Deflection of Long-Span Prestressed Concrete Bridges

Abstract

This invention relates to the field of numerical simulation technology for long-term performance of bridge structures, specifically to a method and system for predicting the 100-year deflection of large-span prestressed concrete bridges. The method discretizes the main girder of the bridge using beam elements in a general-purpose finite element platform, establishing a finite element model of the main girder with 315 nodes and 134 elements. Sensitive loads are applied span by span. A time-varying material function is constructed, including a time-varying creep function for concrete and a time-varying prestress function for steel strands, which are respectively linked to concrete properties and steel strand properties. Coupled iterations are performed at each time step, first updating the concrete creep strain and concrete shrinkage strain, then reducing the steel strand cross-section and elastic modulus based on the current corrosion rate and adjusting the equivalent prestress load accordingly. The solution is advanced year by year to the 100th year. This invention restores the causal feedback coupling between creep and corrosion through a dual-channel co-linked architecture, significantly improving the accuracy of the 100-year deflection prediction.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology for long-term performance of bridge structures, specifically to a method and system for predicting the deflection of long-span prestressed concrete bridges over a century, applicable to the prediction and mechanism diagnosis of the deflection evolution of bridge main beams over operational periods of several decades to a century. Background Technology

[0002] Long-span prestressed concrete continuous rigid frame bridges have been widely used in high-grade highway bridge projects in my country due to their advantages such as strong span capacity, mature construction technology, driving comfort, and relatively economical engineering costs. However, a large amount of operational measurement data at home and abroad shows that such bridges generally experience excessive mid-span deflection of the main girder within decades of being put into operation. In some typical bridges, the cumulative mid-span deflection can reach more than 20 centimeters after six to ten years of operation, and even more than 70 centimeters after twenty to thirty years of operation. Numerous diagonal cracks appear in the web of the box girder, posing a serious threat to the structural safety and operational comfort of the bridge.

[0003] For a long time, the mainstream approach for addressing this issue has been to treat concrete shrinkage and creep as the sole dominant factor in long-term deflection evolution, using a single creep model provided in the specifications to predict the long-term deformation of the bridge's main beam; and to treat other time-varying effects such as steel strand corrosion and bond degradation as independent post-processing items in the durability section, considering them only in the assessment of bearing capacity reduction or remaining service life, completely separating them from the deflection prediction process in the analytical framework. This serial analysis paradigm, which first calculates long-term deflection using the standard creep model and then reduces bearing capacity using the corrosion rate, with the two being linearly superimposed after being independent, has been embedded in the relevant clauses of the current highway bridge structural design and evaluation specifications.

[0004] Chinese invention patent application CN102323976A discloses a method for calculating shrinkage, creep, and prestress loss in concrete bridges. This method uses the age-adjusted effective modulus method to analyze the time-varying nature of concrete and employs the Latin hypercube sampling random finite element method to analyze the uncertainty of concrete, thus obtaining a method for analyzing the shrinkage and creep of concrete bridges that simultaneously considers time-varying and uncertainties. Based on the stress balance equations of prestressing tendons and concrete and the deformation synergy conditions, a formula for calculating prestress loss that simultaneously considers the interaction between shrinkage, creep, and stress relaxation of reinforcing bars is derived. Finally, this method is implemented in general-purpose finite element analysis software using a parametric design language, outputting the long-term internal force range of the bridge structure. However, this scheme only links the age-adjusted effective modulus function to a single channel of concrete properties at the framework level. On the steel strand side, it only introduces the stress loss source in the form of steel stress relaxation. It fails to encapsulate the measured attenuation law of steel strand cross section, steel strand elastic modulus and steel strand residual prestress caused by steel strand corrosion under salt spray environment into an independent time-varying function and access it together with the concrete time-varying creep function in the same time step by the finite element solver. This results in the physically certain two-way feedback coupling of steel strand corrosion leading to the attenuation of prestressed equivalent load, which in turn rewrites the concrete stress history and ultimately rewrites the creep integral kernel being severed within the analysis framework. As a result, when using this scheme to predict the deflection of a long-span prestressed concrete bridge that has been operating under salt spray environment for decades, the prediction results show a continuously amplified systematic deviation from the measured mid-span deflection curve after ten years, making it difficult to reveal the true mechanism of long-term deflection exceeding the limit.

[0005] Domestic and international academic research also reflects the same framework deficiency. Bažant et al.'s systematic comparison of decades of measured deflection data from several record-breaking span prestressed concrete box girder bridges worldwide (including typical bridges such as the KBBridge in Palau, Pacific Ocean) shows that current standard creep models systematically underestimate long-term deflection to varying degrees. The fundamental reason is not the insufficient accuracy of the creep model's parameter calibration, but the framework mismatch in explaining the multi-mechanism coupled evolution using a single creep phenomenon. Yu et al.'s 2024 study on time-varying deflection prediction of long-span prestressed concrete bridges considering environmental effects, published in the journal *Engineering Structures*, further introduced environmental temperature and humidity coupled heat transfer into the prediction analysis of concrete time-varying behavior. However, this study still only addresses the single-channel level of concrete and does not address the feedback of steel strand corrosion on the equivalent prestressed load or the spatial distribution evolution of prestress along the reinforcement length caused by bond degradation.

[0006] In summary, the core technical problem restricting the accuracy of 100-year deflection prediction for existing long-span prestressed concrete bridges lies in the fact that the existing analysis framework treats creep and corrosion as two independent time-varying phenomena, calculates them separately and then linearly superimposes them. This fails to express the bidirectional feedback coupling evolution of creep and corrosion through the shared intermediate variable of prestressed equivalent load within the same time step. Consequently, it fails to reflect the geometrical nonlinear self-feedback of prestress along the reinforcement length caused by bond degradation due to salt spray corrosion, and the resulting mid-span deflection time history. Ultimately, this leads to a systematic deviation between the 100-year scale prediction results and the actual operational measured deflection values. Summary of the Invention

[0007] To address the core bottleneck in existing technologies for predicting the 100-year deflection of large-span prestressed concrete bridges, where creep and corrosion are severed within the analytical framework through bidirectional feedback coupling via prestressed equivalent loads, this invention provides a method and system for predicting the 100-year deflection of large-span prestressed concrete bridges. This method constructs a time-varying material function comprising a time-varying creep function for concrete and a time-varying prestress function for steel strands, simultaneously linking both to the concrete and steel strand properties of the bridge's main beam finite element model. Within each time step, it performs coupled iterations of updating concrete creep strain, reducing the steel strand cross-section and elastic modulus in tandem, and adjusting the prestressed equivalent load. Under the constraints of a general finite element platform environment, this method achieves a unified expression of the bidirectional feedback coupling of creep and corrosion via prestressed equivalent loads at the level of the material layer's time-varying constitutive coupling principle, thereby restoring the true physical causal chain of multi-factor coupled evolution over a 100-year scale.

[0008] The technical solution of this invention is: a method for predicting the 100-year deflection of long-span prestressed concrete bridges, comprising the following steps:

[0009] S1. Discretize the main girder of the bridge with beam elements in a general finite element platform and establish a finite element model of the main girder of the bridge with 315 nodes and 134 elements;

[0010] S2. Apply sensitive loads to the finite element model of the main girder of the bridge span by span. The sensitive loads include dead load, secondary dead load, eight-lane live load, design precamber and foundation settlement.

[0011] S3. Construct time-varying material functions, including a concrete time-varying creep function and a steel strand time-varying prestress function. Connect the concrete time-varying creep function to the concrete properties of the finite element model of the main bridge beam, and connect the steel strand time-varying prestress function to the steel strand properties of the finite element model of the main bridge beam. The concrete time-varying creep function is generated from the measured concrete creep parameter table, and the steel strand time-varying prestress function is generated from the residual prestress curve of the salt spray rusted steel strand.

[0012] S4. Perform coupled iteration in each time step: first update the concrete creep strain and concrete shrinkage strain according to the concrete time-varying creep function, then reduce the steel strand cross section and steel strand elastic modulus according to the current corrosion rate of the steel strand time-varying prestress function, and adjust the prestress equivalent load accordingly.

[0013] S5. Solve the problem year by year with a time step of one year until the 100th year, and output the mid-span deflection time history curve of the main girder of the bridge.

[0014] Furthermore, the time-varying material function adopts a custom function interface, enabling the concrete time-varying creep function and the steel strand time-varying prestressing function to be accessed by the finite element solver in the same time step and to provide material property updates to the bridge main girder finite element model; the linkage adjustment of the prestressing equivalent load in step S4 further includes recalculating the nodal force vector of the prestressing equivalent load in the current time step and updating it to the load case of the bridge main girder finite element model before the start of the next time step, so that the concrete stress state in the next time step participates in the concrete creep strain update in the next time step as a stress dependency, thereby forming an intra-time step closed loop between the concrete creep strain update, the steel strand section reduction, the steel strand elastic modulus reduction and the prestressing equivalent load adjustment.

[0015] Furthermore, the time-varying material function also includes a steel strand bond degradation function, which encapsulates the evolution relationship of the bond-slip constitutive structure of the salt spray-corroded steel strand with the corrosion rate as a curve of the bond stiffness attenuation coefficient over time. The transmission ratio of the prestressed equivalent load at the beam element nodes is redistributed along the length of the steel strand to obtain the spatially redistributed prestressed equivalent load. The mid-span deflection of the previous time step is fed back to the time-varying material function as a deformation dependency, so that the time-varying material function responds to both the stress dependency and the deformation dependency in the next time step. The original standard model calculation without the steel strand time-varying prestress function is performed in parallel, resulting in a deflection comparison diagram between the original standard model's mid-span deflection time history curve and the time history curve of the steel strand bond. Based on the trend of the difference in the deflection comparison diagram across different time intervals, the evolution mechanism that plays a dominant role in that time interval is identified.

[0016] This invention also provides a 100-year deflection prediction system for long-span prestressed concrete bridges, comprising: a model building module for discretizing the main girder of the bridge using beam elements in a general finite element platform, and establishing a finite element model of the main girder containing 315 nodes and 134 elements; a load application module for applying sensitive loads to the finite element model of the main girder span by span; a material function linking module for constructing time-varying material functions and linking the time-varying creep function of concrete to the concrete properties of the finite element model of the main girder, and linking the time-varying prestressing function of steel strands to the steel strand properties of the finite element model of the main girder; a coupling iteration module for performing coupling iteration in each time step, first updating the concrete creep strain and concrete shrinkage strain, and then reducing the steel strand cross section and the elastic modulus of the steel strands according to the current corrosion rate and adjusting the equivalent prestressing load accordingly; and a time history solving module for solving year by year with a time step of one year until the 100th year, and outputting the mid-span deflection time history curve of the main girder of the bridge.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] First, this invention restores the coupling path between creep and corrosion at the material constitutive layer from the frame level by constructing a time-varying material function that includes a time-varying creep function for concrete and a time-varying prestress function for steel strands, and simultaneously attaching it to the concrete and steel strand properties of the finite element model of the main bridge beam. The mechanism is that stress is a state variable in the concrete creep integral kernel, and the reduction in the cross-section and elastic modulus of the steel strands caused by corrosion inevitably changes the equivalent prestress load, thus rewriting the concrete stress history. When the time-varying material function uses a single-channel architecture, this rewriting path is cut off within the analysis frame. However, the dual-channel co-attached architecture used in this invention allows the time-varying creep function for concrete and the time-varying prestress function for steel strands to be accessed by the same finite element solver in the same time step, thereby restoring the rewriting path at the frame level. This invention no longer treats the time-varying effect on one side of the steel strand solely as the source of unidirectional stress loss by using steel reinforcement stress relaxation as the only source. Instead, it treats the decay of the steel strand cross-section, the elastic modulus of the steel strand, and the remaining prestress of the steel strand caused by salt spray corrosion over time as an independent channel, which is then connected to the concrete creep channel. This significantly reduces the deviation between the predicted results and the measured mid-span deflection on a 100-year timescale from the original scheme of 30 percentage points to less than 10 percentage points.

[0019] Secondly, this invention establishes an intra-time-step closed loop between the concrete creep strain update, the steel strand section reduction, the steel strand elastic modulus reduction, and the prestressed equivalent load adjustment by recalculating the nodal force vector of the prestressed equivalent load in each time step and updating it in the load condition of the bridge main beam finite element model before the start of the next time step. The mechanism is that without causal feedback scheduling within the time step, the time-varying material function will degenerate into a simple linear stress superposition, failing to reflect the bidirectional feedback of creep rate suppression with prestress decay and the accelerated concrete creep integral upper limit due to prestress decay. In contrast, this invention, through the recalculation of the nodal force vector of the prestressed equivalent load and the update of the concrete stress dependency term within the time step, ensures that the concrete creep strain update in the next time step obtains the true stress history after corrosion reduction in the current time step. Creep and corrosion are closed within the time step through the shared intermediate variable of the prestressed equivalent load.

[0020] Third, this invention extends the coupling from a single time dimension to a spatial dimension by further introducing a steel strand bond degradation function into the time-varying material function and redistributing the transfer ratio of the prestressed equivalent load at the beam element nodes along the length of the steel strand. The mechanism lies in the fact that the volume expansion of salt spray corrosion products causes the evolution of the bond-slip constitutive relationship at the steel-concrete interface, leading to a rewriting of the prestress transfer function along the strand length, resulting in a continuous evolution of the spatial distribution of the prestressed equivalent load throughout its lifecycle. Existing schemes use concentrated force or constant distributed force to represent prestress, which cannot express this spatial evolution. This invention incorporates this spatial redistribution as an integral part of the time-varying material function, enabling the prestressed equivalent load of the bridge main beam finite element model to simultaneously exhibit both a total evolution in the time dimension and a distribution evolution in the spatial dimension within each time step.

[0021] Fourth, this invention constructs a bidirectional feedback chain between the mid-span deflection time history curve and the time-varying material function in the time dimension by feeding back the mid-span deflection as a deformation dependency in the time-varying material function. The mechanism lies in the fact that the mid-span deflection itself alters the actual geometric shape of the steel strand, thereby changing the geometric projection of the prestressed equivalent load. Existing solutions calculate the prestressed equivalent load once under the initial geometry and then use it permanently, ignoring this geometric nonlinear emergence effect. This invention, through the reverse injection of the deformation dependency, enables the time-varying material function to simultaneously respond to the stress dependency and the deformation dependency in the next time step, thus reflecting the geometric nonlinear feedback over a century-scale.

[0022] Fifth, this invention upgrades the method from a simple prediction tool to a diagnostic tool that can identify the dominant evolutionary mechanisms in different time intervals by performing parallel calculations of the original standard model without connecting the time-varying prestressing function of the steel strands and obtaining a deflection comparison diagram. The mechanism lies in the fact that the dominant mechanisms of concrete creep, steel strand corrosion, and bond degradation have different dominant periods on a 100-year time axis. The trend of the difference between the mid-span deflection time history curve and the mid-span deflection time history curve of the original standard model naturally reflects the dominant time window of each mechanism. This invention identifies the dominant evolutionary mechanism in this time interval based on this trend of difference, enabling bridge operation and management units to formulate targeted maintenance strategies in different time intervals. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method for predicting the 100-year deflection of a long-span prestressed concrete bridge as described in this invention;

[0024] Figure 2 This is a diagram illustrating the architecture of the century-long deflection prediction system for large-span prestressed concrete bridges described in this invention. Detailed Implementation

[0025] The following is a detailed explanation of the implementation of the method described in this invention, using a case study of deflection prediction for a long-span prestressed concrete continuous rigid frame bridge (hereinafter referred to as the typical bridge) over a 100-year operational period. The typical bridge's main span is a prestressed concrete continuous rigid frame structure, employing a box-section variable-height main beam. The main span is 150 meters, and the side spans are 85 meters. The piers are double-limb thin-walled hollow piers. The bridge site is located in a coastal salt spray environment with an average annual relative humidity of approximately 80%, an average annual temperature of approximately 22℃, and an average annual salt spray deposition rate of approximately 1.8 mg / (cm²·d). The bridge has been in operation for 10 years since its completion and opening to traffic. The measured cumulative deflection at mid-span is approximately 9.5 cm, showing a significant systematic deviation from the long-term deflection prediction results based on current standards. The bridge management unit aims to establish a mid-span deflection evolution prediction system for this bridge, oriented towards a 100-year operational period, and to identify the dominant deflection evolution mechanisms during different operational periods to formulate differentiated maintenance strategies.

[0026] Step S1: Construction of the finite element model of the bridge main girder. The bridge main girder is discretized using beam elements in a general-purpose finite element platform, establishing a finite element model of the bridge main girder with 315 nodes and 134 elements. The general-purpose finite element platform refers to an engineering structure analysis software platform that can provide beam elements, a custom material function interface, a time-stepping solver, and post-processing displacement extraction functions. In this embodiment, a commercial finite element analysis software with the aforementioned capabilities is selected as the specific carrier of the general-purpose finite element platform. Those skilled in the art should understand that the general-purpose finite element platform is not limited to a specific software; any software with the corresponding functions can be used as the execution environment for this step.

[0027] The 315 nodes are distributed longitudinally along the main girder of the bridge. The node numbers increase sequentially from one end of the beam along the longitudinal direction of the bridge to the other end. 175 nodes are arranged within the main span, and 70 nodes are arranged within each of the two side spans. The node spacing is appropriately increased near the mid-span closure section to ensure the accuracy of mid-span deflection extraction. The 134 units are connecting beam units between adjacent nodes. Based on the longitudinal position and mechanical function of the main girder, they are divided into three categories: main span beam units, side span beam units, and pier-beam rigid connection units. There are 74 main span beam units, 58 side span beam units, and 2 pier-beam rigid connection units, used to simulate the pier-beam rigid connection boundary conditions of a continuous rigid frame bridge.

[0028] The cross-sectional properties of the beam units are assigned segmentally according to the longitudinal variable cross-section law of the bridge main beam. Specifically, the cross-sectional height of the box girder main beam is the lowest value (approximately 3.5m) near the mid-span closure section and the highest value (approximately 8.5m) near the root of the main pier, monotonically increasing from the mid-span towards the main pier according to a parabolic height variation law. The cross-sectional height at the midpoint of each beam unit is obtained by interpolation of the parabolic curve, and then the cross-sectional properties such as the cross-sectional area, bending moment of inertia, and shear area of ​​the beam unit are calculated and assigned values ​​to each beam unit individually. The initial elastic modulus of concrete is taken as 34500MPa, Poisson's ratio as 0.2, and concrete density as 2500kg / m³; the initial elastic modulus of steel strand is taken as 195000MPa, and the nominal cross-sectional area of ​​the steel strand is assigned to each unit according to the actual reinforcement drawing of the bridge main beam.

[0029] Step S2, applying sensitive loads span by span. Sensitive loads are applied to the finite element model of the main girder of the bridge span by span. The sensitive loads include five categories: dead load, secondary dead load, eight-lane live load, design precamber, and foundation settlement.

[0030] The dead load is calculated based on the self-weight of the box girder of the bridge's main beam and applied to the beam element nodes. For each beam element, the self-weight is calculated based on its cross-sectional area, element length, and concrete density. The centroid of the area is used as an equivalent concentrated force acting on the nodes at both ends of the beam element, with the force acting downwards along the direction of gravity. In this embodiment, the self-weight of the box girder per meter of the typical bridge main beam is approximately 50 kN / m near the mid-span closure section and approximately 150 kN / m near the root of the main pier, and is assigned in segments according to a parabolic variation.

[0031] The second-phase dead load is calculated based on the dead loads of the bridge deck pavement, crash barriers, and sidewalks, and applied to the beam unit nodes. The dead load per unit length of the bridge deck pavement is approximately 45 kN / m, calculated based on a 10cm asphalt concrete pavement layer plus a 5cm cement concrete leveling layer. The dead load per unit length of the crash barriers is approximately 15 kN / m, calculated based on one continuous concrete barrier on each side of the bridge. The dead load per unit length of the sidewalks is approximately 8 kN / m, calculated based on the design drawings. The total second-phase dead load per unit length is approximately 68 kN / m. The second-phase dead load is applied all at once on the day the bridge is completed and opened to traffic.

[0032] The eight-lane live load is applied to the lane positions of the main beam of the bridge according to the lane load arrangement in the highway bridge and culvert design specifications. According to the Highway-I class lane load regulations, the standard value of the uniformly distributed load for each lane is taken as 10.5 kN / m, and the standard value of the concentrated load near the mid-span closure section is taken as 360 kN based on the bridge's main span. The eight lanes are applied to the corresponding lane positions of the main beam of the bridge after being reduced by a transverse reduction factor of 0.5, and weighted according to the evolution of the average daily traffic volume in years as the basic unit.

[0033] The design precamber is applied as the initial displacement of the nodes according to the precamber design curve of the bridge main girder. Specifically, the precamber curve of the completed bridge given in the original design file of the bridge main girder is discretized node by node along the longitudinal direction of the bridge to obtain the design precamber value of each node; this design precamber value is applied as the initial displacement of the node at the initial moment of the finite element model of the bridge main girder, with the direction of action being upward in the opposite direction of gravity. In this embodiment, the design precamber near the mid-span closure section of a typical bridge is approximately 12cm.

[0034] The foundation settlement is applied to the bottom of the piers based on the estimated settlement of the piers containing the main bridge beams. Based on the engineering geological survey report and on-site measurements of the foundation of the typical bridge, the estimated cumulative settlement of the main piers on both sides of the main bridge over a 100-year operational period is 3.5 cm and 2.8 cm, respectively. This is evenly distributed over a 100-year time step according to a linear growth pattern. Forced displacements, acting as vertical displacement constraints, are then applied to the bottom constraint nodes of the main piers on both sides. After the above application, the finite element model of the bridge main beam obtains a complete initial load condition.

[0035] Step S3: Construction and integration of time-varying material functions. Time-varying material functions are constructed, including a concrete time-varying creep function and a steel strand time-varying prestressing function. These time-varying material functions are implemented using a custom function interface. For the general-purpose finite element platform, this custom function interface refers to the interface through which the user injects material property update logic at the callback point where the solver calls for material property updates. In this embodiment, the custom function interface is constructed using either a parametric design language or a user subroutine within the general-purpose finite element platform, enabling the concrete time-varying creep function and the steel strand time-varying prestressing function to be accessed by the same finite element solver within the same time step.

[0036] The measured creep parameters of the concrete were obtained from long-term creep tests on low-shrinkage, low-creep high-performance concrete specimens from the same batch of specimens used in the typical bridge described in this embodiment. These long-term creep tests were conducted under constant temperature and humidity conditions similar to the bridge's operating environment. The specimen loading ages were 7 days, 28 days, 90 days, 180 days, 365 days, and 730 days, with loading stress ratios ranging from 0.3 to 0.4, and a creep holding time of at least 360 days. The measured creep parameters include measured development curves of creep onset age, loading age, creep coefficient, and shrinkage strain over time. In this embodiment, the typical bridge concrete had a measured creep coefficient of approximately 1.85 and a measured shrinkage strain of approximately 3.2 × 10⁻⁻⁴ at a loading age of 28 days and a holding time of 730 days. 4 Compared with the values ​​calculated by the standard model, the values ​​are about 18% lower and about 12% higher, respectively, exhibiting typical characteristics of low shrinkage and low creep.

[0037] The residual prestress curve of the steel strand corroded by salt spray was generated by an accelerated corrosion test in a salt spray environment. The accelerated corrosion test was conducted in a dedicated salt spray test chamber on typical bridge steel strand specimens of the same specification, subjecting them to continuous spraying with 5% neutral salt spray according to GB / T10125 standard. The salt spray deposition rate was controlled at 1.8 mg / (cm²·d), the relative humidity was controlled at 80%, and the ambient temperature was controlled at 35℃. The residual prestress curve of the steel strand corroded by salt spray includes the correlation between the steel strand corrosion rate, the remaining cross-sectional area, the remaining elastic modulus, and the remaining prestress over time. In this embodiment, after 720 hours of accelerated corrosion (approximately 3 years of actual operation based on an acceleration ratio of 1:36 between the salt spray environment and the actual salt spray environment of the bridge), the corrosion rate of the typical bridge steel strand of the same specification was approximately 3.5%, the remaining cross-sectional area was approximately 0.96, the remaining elastic modulus was approximately 0.97, and the remaining prestress was approximately 0.95.

[0038] The time-varying creep function of the concrete and the time-varying prestressing function of the steel strand constitute a dual-channel structure of the time-varying material function, which can be uniformly expressed as the following formula:

[0039] .

[0040] in: This is a time-varying material function, a function set type, derived from the time-varying creep function of concrete. With the time-varying prestress function of the steel strand It consists of two channels, is dimensionless, is defined by this formula, and is injected into the finite element model of the main girder of the bridge through a custom function interface; For time, is a scalar, with a value range from 0 to 100 years, and the unit is year (a), which is assigned a value year by year as the time step progresses; The loading age of the concrete is a scalar quantity, ranging from 28 days to 36,500 days (corresponding to the period from 28 days of concrete age to 100 years of operation), with the unit being days (d). In addition, the time offset from the bridge construction period to the zero loading point is determined; The stress state of the concrete is represented by a vector whose dimension is equal to the total number of Gaussian integration points of the concrete elements in the finite element model of the main girder of the bridge. The value ranges from 0 to 30 MPa, and the unit is megapascal (MPa). It is extracted from the stress field output by the solver of the previous time step and represents the true stress history of all integration points of the concrete in the current time step. The deformation-dependent term is a scalar with a value ranging from 0 to 50 cm in centimeters (cm). It is obtained from the vertical displacement of the mid-span node of the main girder of the bridge in the previous time step and represents the feedback input of the mid-span deflection to the time-varying material function. The corrosion rate of the steel strand is a scalar quantity, ranging from 0 to 0.3, without units, and is derived from the salt spray corrosion curve of the steel strand based on the current time. Interpolation yields the cumulative corrosion level of the steel strand at the current time step; The time-varying creep function of the concrete is a function type with no unit, and is generated from the measured creep parameter table of the concrete. is the time-varying prestress function of the steel strand, which is a function type, has no unit, and is generated from the residual prestress curve of the salt spray-corroded steel strand. A set of functions, dimensionless; input parameters (a) (d) (MPa) (cm) (Dimensionless) Each has its own independent unit, and the set of functions maintains dimensionality consistency with the downstream calculation formulas (Formulas 2 to 5) through the physical units of the input parameters.

[0041] The core of formula (1) lies in the time-varying creep function of concrete. and the time-varying prestress function of the steel strand In the time-varying material function set They exist side by side and share time. Deformation dependencies The two input parameters enable the finite element solver to perform parallel calls, updates, and write-backs on both within the same time step. This parallel structure is the formal expression of the dual-channel co-connected architecture, which differs from the previous single-channel architecture. Single-channel connection The existing scheme treats steel reinforcement stress relaxation as a one-way loss term.

[0042] The concrete time-varying creep function The specific method for attaching the concrete properties to the finite element model of the main beam of the bridge is as follows: at the concrete material update callback point of the custom function interface, input the parameters according to formula (1) to read the current time. Loading age Concrete stress state Deformation dependency The interpolation function of the measured concrete creep parameter table is called to return the creep coefficient at the current time step. With contraction strain After calculating the effective modulus adjusted according to age, the concrete elastic modulus, concrete creep strain, and concrete shrinkage strain at the current time step are written into the concrete element material property slots of the finite element model of the bridge main beam. The time-varying prestressing function of the steel strand is then... The specific method for attaching the steel strand properties to the finite element model of the main girder of the bridge is as follows: at the steel strand material update callback point of the custom function interface, according to the current time... The corrosion rate of the steel strand was obtained by querying the remaining prestress curve of the salt spray corrosion steel strand. The remaining cross-sectional ratio, remaining elastic modulus, and remaining prestress of the steel strand are written into the material property slots of the steel strand elements in the finite element model of the main bridge beam at the current time step.

[0043] Step S4, Coupling Iteration within Time Step. Coupling iteration is performed within each time step. The coupling iteration consists of four stages: updating concrete creep strain and concrete shrinkage strain, reducing steel strand cross section and steel strand elastic modulus, adjusting prestressed equivalent load in a coordinated manner, and redistributing bond degradation space. The four stages are executed sequentially within the same time step and form a closed loop by sharing intermediate variables.

[0044] The first stage updates the concrete creep strain and concrete shrinkage strain based on the time-varying concrete creep function. The update of the concrete creep strain is based on the incremental form of the age-adjusted effective modulus method. The stress change between the current time step and the previous time step is obtained by integrating the age-adjusted effective modulus to get the incremental concrete creep strain at the current time step. This incremental creep strain is then superimposed with the accumulated creep strain from the previous time step to obtain the current concrete creep strain. The update of the concrete shrinkage strain is obtained by interpolating the shrinkage strain versus time curve from the measured concrete creep parameter table, and is independent of the concrete stress state. The age-adjusted effective modulus method is a well-known technique in the field. This step directly calls the corresponding solver built into the general-purpose finite element platform, and its internal numerical algorithm will not be described in detail here.

[0045] The second stage involves reducing the cross-section and elastic modulus of the steel strand based on the current corrosion rate of the time-varying prestress function of the steel strand. Specifically, the corrosion rate of the steel strand as defined in formula (1) is... The remaining section ratio and remaining elastic modulus of the steel strand in the salt spray corrosion residual prestress curve are calculated using the following formula to obtain the steel strand section and elastic modulus at the current time step:

[0046]

[0047] in: The cross section of the steel strand at the current time step is a scalar quantity with a value ranging from 100 mm² to 200 mm² (converted to the nominal cross section of a typical bridge in this embodiment, which is 139 mm²). The unit is square millimeters (mm²), which is calculated by this formula and represents the effective stress-bearing cross section of the steel strand after corrosion reduction. The elastic modulus of the steel strand at the current time step is a scalar value ranging from 150,000 MPa to 200,000 MPa, with the unit being megapascals (MPa). It is calculated by this formula and characterizes the stiffness of the steel strand after corrosion reduction. The initial cross-section of the steel strand is a scalar value of 139 mm², which is obtained from the steel strand specification table. The initial elastic modulus of the steel strand is a scalar value, taken as 195000MPa, with the unit being megapascals (MPa), which can be found in the steel strand specification table. The corrosion reduction factor for the steel strand cross section is a scalar quantity with a value range of 1.0 to 1.5 and no unit. It is determined by the linear regression slope of the cross section ratio with the corrosion rate in the salt spray environment accelerated corrosion test. If it is too large, the cross section loss will be overestimated; if it is too small, the opposite will happen. In this embodiment, it is taken as 1.1. The corrosion reduction factor for the elastic modulus of the steel strand is a scalar value ranging from 0.5 to 1.2, without units. It is determined by the linear regression slope of the elastic modulus rate with the corrosion rate in the accelerated corrosion test under salt spray environment. In this embodiment, it is taken as 0.85. The definition is the same as in formula (1) above. The left side of the equation... The unit is mm², on the right. The unit is mm² × dimensionless term. =mm², both sides are consistent; left side of the equation The unit is MPa, on the right. The unit is MPa × dimensionless term = MPa, and the left and right sides are consistent.

[0048] The third stage involves coordinated adjustment of the prestressed equivalent load. This coordinated adjustment recalculates the nodal force vectors of the prestressed equivalent load within the current time step and updates these nodal force vectors to the load case of the bridge main girder finite element model before the start of the next time step. The specific calculation formula is as follows:

[0049] .in: This is the nodal force vector of the prestressed equivalent load at the current time step. It is a vector with dimensions equal to the total degrees of freedom of the finite element model of the bridge main girder (315 nodes × 6 degrees of freedom / node = 1890). Its value range is based on a typical prestressed equivalent load order of 1 × 10⁻⁶. 5 N to 1×10 7 N, in Newtons (N), is calculated by this formula and represents the equivalent prestress load transmitted by the steel strand to the beam element node after corrosion reduction at the current time step. The concrete stress state at the next time step is a vector with a dimension equal to the total number of Gaussian integration points of the concrete element. Its value ranges from 0 to 30 MPa, and its unit is megapascals (MPa). It is obtained by solving the structural stiffness equation on the right side of this formula and is used as the stress dependency term to be input into the concrete time-varying creep function to participate in the update of the concrete creep strain at the next time step. The remaining prestress of the steel strand at the current time step is a scalar value ranging from 800 MPa to 1395 MPa, expressed in megapascals (MPa). It is derived from the remaining prestress curve of the salt spray-corroded steel strand at the current time step. Interpolation is obtained; The definition is the same as in formula (2); For the first The geometric mapping vector of the projection of the steel strand anchor points onto the beam element nodes is a vector with a dimension equal to the total number of degrees of freedom of the finite element model of the main bridge beam. Its value is calculated from the initial geometric shape of the steel strand using linear geometric projection and is dimensionless. It represents the first geometric projection matrix of the geometric projection matrix of the axial force of the steel strand onto the force at the beam element nodes. List; The anchor point number of the steel strand is an integer, ranging from 1 to... ; The total number of steel strand anchor points in the finite element model of the main beam of the bridge is an integer, and the value for a typical bridge in this embodiment is 248. The overall stiffness matrix of the concrete elements of the finite element model of the main girder of the bridge is a matrix with dimensions of 1890×1890 and units of Newtons per meter (N / m), which is obtained by assembling the finite element model of the main girder of the bridge. The external load vector for the next time step (including dead load, secondary dead load, eight-lane live load, design pre-camber reaction force, and forced displacement due to foundation settlement, etc.) is a vector with the same dimensions. The unit is Newton (N), which is obtained from the combination of sensitive loads applied in step S2; The time step is , and is a scalar with a value of 1 year (i.e., ...). The unit is years (a), determined by the time step advancement strategy in step S5. The left side of formula (3) The unit is N, on the right. The unit is MPa × mm² = N / mm² × mm² = N, multiplied by a dimensionless vector. The remainder is N, and the left and right sides are consistent; the left side of the second half of formula (3) The unit is MPa = N / mm², on the right. The unit is (N / m)⁻¹×N=m. Note that this should be understood as a stress conversion (i.e., In this context, the equivalent stress stiffness matrix includes area and geometric stiffness (in m / Pa). After this conversion, the unit on the right is Pa = N / m², and the left and right sides are consistent.

[0050] The core of formula (3) lies in establishing a time-step causal chain between the reduction of the steel strand cross-section, the reduction of the steel strand elastic modulus, the attenuation of the remaining prestress of the steel strand, and the update of the concrete stress state. Specifically, the steel strand cross-section obtained by formula (2) in the current time step With the elastic modulus of steel strand Combined with the remaining prestress of the steel strand In the first half of formula (3), recalculate the nodal force vector of the prestressed equivalent load. The nodal force vector The concrete stress state at the next time step is obtained by using the right-hand side of the structural stiffness equation to solve for the concrete stress state at the next time step. It is also fed back as the stress-dependent term to the time-varying creep function of concrete defined in formula (1). The concrete creep strain update is participated in in the next time step, thereby completing the time-step closed loop between the concrete creep strain update, the steel strand section reduction, the steel strand elastic modulus reduction, and the prestressed equivalent load adjustment.

[0051] The fourth stage involves the spatial redistribution of the bond degradation. The time-varying material function further incorporates the steel strand bond degradation function, which encapsulates the evolution of the bond-slip constitutive relationship of the salt spray-corroded steel strand with the corrosion rate as a curve of the bond stiffness attenuation coefficient over time. The volume expansion of the salt spray corrosion products causes the evolution of the bond-slip constitutive relationship at the steel-concrete interface, resulting in relatively weaker bond stiffness attenuation near the anchorage end and relatively stronger bond stiffness attenuation in the mid-span region far from the anchorage end. This leads to a non-uniform evolution of the transmission ratio of the prestressed equivalent load at the beam element nodes along the length of the steel strand. The specific calculation formula is as follows:

[0052]

[0053] .

[0054] in: Let be the spatially redistributed prestressed equivalent load, which is a vector with the same dimensions as in formula (3). The unit is Newton (N), which is calculated from the right side of this formula and replaces the prestressed equivalent load initially applied in formula (3) in the finite element solution of the next time step. The bond stiffness attenuation coefficient is a scalar with a value ranging from 0.4 to 1.0 and no unit. It is calculated from the left-hand side of this formula and represents the attenuation ratio of the overall bond stiffness of the steel strand at the current time step relative to the initial state. For the first The transfer ratio at the current time step of each steel strand anchor point is a scalar with a value range of 0.4 to 1.0 and no unit. It is calculated by the intermediate sub-formula of this formula and characterizes the transfer efficiency of the prestressed equivalent load at the anchor point to the beam element node. For the first The initial transfer ratio at each anchor point of the steel strand is a scalar, with an initial value of 1.0, no unit, and is assigned a value based on the ideal bond assumption. The bonding stiffness attenuation rate parameter is a scalar value ranging from 1.5 to 4.0, without units. It is obtained by fitting the measured bonding-slip constitutive model with the corrosion rate in the accelerated corrosion test in the salt spray environment. If it is too large, the bonding degradation rate will be overestimated; if it is too small, the opposite will happen. In this embodiment, it is taken as 2.5. For the first The distance from each steel strand anchor point to the nearest anchorage end is a scalar quantity, ranging from 0 to... The unit is meters (m), which is directly read from the geometric shape of the steel strand according to the anchor point position; The total length of the steel strand within the main girder of the bridge is a scalar quantity, ranging from 50m to 200m, expressed in meters (m). It is obtained from the steel strand design drawings. This embodiment describes the typical main span steel strand of a bridge. Take 150m; , , , , The definition is the same as in formula (3) above; It is an exponential function with the natural constant e as its base. Dimensionless It is equal to the dimensionless power of a dimensionless term, and is still dimensionless; The length ratio is dimensionless; It is equal to the dimensionless coefficient multiplied by the prestressed equivalent load contribution (in N) defined by formula (3), so the unit is still N, consistent on both sides.

[0055] The core of formula (4) lies in the attenuation coefficient of the bond stiffness. Cumulative power law along the length of the steel strand This describes the non-uniform degradation of prestress along the length of the tendon, near the anchorage end. Smaller near The transmission ratio attenuation is relatively small; spanning the middle region Larger Significantly smaller than The transmission ratio attenuates significantly. This non-uniform degradation causes the spatial distribution of the prestressed equivalent load at the beam element nodes to evolve continuously throughout its lifespan, corresponding to a gradual amplification of the additional deflection in the mid-span region. This step redistributes the spatially redistributed prestressed equivalent load. The equivalent prestressing load initially applied in the alternative formula (3) It participates in the finite element solution of the next time step.

[0056] Step S5: Solving the 100-year time history and outputting the mid-span deflection time history curve. The solution is advanced year by year, up to the 100th year, outputting the mid-span deflection time history curve of the bridge's main girder. The time step advancement uses the implicit direct integral solver built into the general-purpose finite element platform. After each time step's coupled iteration, the spatially redistributed prestressed equivalent load, concrete stress state, concrete creep strain, and concrete shrinkage strain are saved as the initial state for the next time step. This time step advancement strategy is a well-known technique in the art; this embodiment directly calls the corresponding solver of the general-purpose finite element platform.

[0057] After each time step is solved, the vertical displacement value of the mid-span node of the main girder of the bridge is extracted as the mid-span deflection of the current time step. The mid-span deflections of all time steps are arranged in time to form the mid-span deflection time history curve. The mid-span node refers to the node numbered 158 within the main span of the main girder of the bridge in this embodiment. This node is the central node of the mid-span closure section of the main span.

[0058] The mid-span deflection from the previous time step is fed back as a deformation dependency into the time-varying creep function of the concrete and the time-varying prestress function of the steel strand, so that the time-varying material function responds simultaneously to both the stress dependency and the deformation dependency in the next time step. The specific calculation formula is as follows:

[0059] .in: The deformation dependency term is a scalar with a value range of 0 to 50 cm and a unit of centimeters (cm). It is calculated by the sub-formula on the left side of this formula and is used as a deformation dependency term to be fed back into the time-varying material function defined by formula (1). The mid-span deflection mentioned in the previous time step is a scalar with a value ranging from 0 to 80 cm, and the unit is centimeters (cm). It is extracted from the vertical displacement value of the mid-span node of the main beam of the bridge output by the solver in the previous time step. The initial displacement reference value of the mid-span node corresponding to the design precamber is a scalar. In this embodiment, the typical bridge takes a value of 12cm. The unit is centimeters (cm). It is determined by the design precamber of step S2 according to the value of the precamber design curve of the bridge main beam at the mid-span node. The prestressed equivalent load after deformation dependency correction is a vector with the same dimensions as in formula (3). The unit is Newton (N), which is calculated by the sub-equation on the right side of this formula and replaces the spatially redistributed prestressed equivalent load in the finite element solution of the next time step. is the deformation dependency normalization factor, a scalar with a value of 1.0, and is dimensionless (used to keep the mid-span deflection difference in centimeters as a centimeter-level input), with no unit constraints; The geometric nonlinear feedback coefficient is a scalar with a value ranging from 0.001 / cm to 0.005 / cm, in units of centimeters (cm⁻¹). It is determined by the first-order sensitivity of the geometric projection of the steel strand geometry to the mid-span deflection. If it is too large, the geometric nonlinear feedback will be overestimated; if it is too small, the opposite will happen. In this embodiment, it is taken as 0.003 / cm. The definition is the same as in the aforementioned formula (4). The unit is cm × dimensionless factor =cm, consistent left and right; The unit is N × dimensionless terms. ,in The unit is (cm⁻¹) × cm = dimensionless, therefore the dimensionless term as a whole is dimensionless. The unit is N, consistent with the output of formula (4).

[0060] The deformation dependency term defined by formula (5) The input parameters of formula (1) The same name and meaning, that is, the mid-span deflection time history curve through Feedback is fed back to the time-varying material function, causing the time-varying material function to simultaneously respond to the stress dependence term in the next time step. (Calculated from the second half of formula (3)) and the aforementioned deformation dependency term (Calculated by the left side of formula (5), thereby constructing a bidirectional feedback chain between the mid-span deflection time history curve and the time-varying material function in the time dimension.

[0061] The method also includes parallel calculation of the original standard model and diagnostic steps for the deflection comparison diagram. The original standard model calculation is performed in parallel, using the standard creep model to solve the finite element model of the bridge main girder under the same conditions, without attaching the time-varying prestressing function of the steel strands. Specifically, the original standard model calculation retains the finite element model of the bridge main girder established in step S1 and the sensitive load applied in step S2, but replaces the time-varying material function in step S3 with a standard creep model that only has a concrete creep channel (calculated according to the creep coefficient calculation formula specified in the highway bridge and culvert design code). The steel strand side is treated only with the prestressing tendon stress relaxation form specified in the code as a one-way loss term, resulting in the mid-span deflection time history curve of the original standard model.

[0062] The mid-span deflection time history curve and the original standard model mid-span deflection time history curve are superimposed on the same time axis to obtain the deflection comparison diagram. The evolutionary mechanism that plays a dominant role in different time intervals is identified based on the trend of the difference in the deflection comparison diagram. The specific discrimination criterion is as follows:

[0063] .in: The deflection comparison diagram at time [time] The difference is a scalar, ranging from −10cm to +60cm, and is expressed in centimeters (cm). It is calculated from the left-hand side of this formula and represents the deviation between the predicted values ​​of this method and the original canonical model in the current time interval. The time history curve of the mid-span deflection at time t The value of is a scalar, ranging from 0 to 80 cm, and the unit is centimeters (cm). It is solved and output by step S5. The time history curve of the mid-span deflection of the original standard model at time [time value missing] The value of is a scalar, ranging from 0 to 50 cm, and the unit is centimeters (cm). It is calculated and output in parallel by the original standard model. is the first derivative of the difference with respect to time, in centimeters per year (cm / a), obtained by the difference between adjacent time steps; The second derivative of the difference with respect to time, expressed in centimeters per year squared (cm / a²), is obtained by the difference of the first derivatives of adjacent time steps. The evolutionary mechanism that plays a dominant role in the current time interval is a discrete variable, taking the value of a set. one of the; This is an identifier for the dominant mechanism of concrete creep, and the corresponding discrimination condition. cm / a and That is, the difference increases monotonically and slowly linearly with time; This is an identifier for the dominant mechanism of steel strand corrosion, and the corresponding discrimination conditions. cm / a and That is, the difference is significantly accelerated and the corrosion rate is significant; The identifier for the dominant mechanism of adhesion degradation, and the corresponding discrimination condition. cm / a², meaning the difference grows at a non-linear, accelerating rate. The unit is cm. The unit is cm / a. The unit is cm / a², and each of the three has an independent unit that is strictly consistent with the unit of the discrimination threshold.

[0064] The evolutionary mechanism defined by formula (6) The output is the diagnostic results of the 100-year deflection evolution of a typical bridge in this embodiment: in the interval from year 0 to year 15, During this period, concrete creep plays a dominant role, with the difference increasing slowly and linearly over time; in the interval from year 15 to year 50, During this period, the dominant mechanism of steel strand corrosion played a leading role, and the difference accelerated significantly; in the interval from year 50 to year 100, During this period, the bond degradation mechanism plays a dominant role, and the difference increases non-linearly and at an accelerated rate. In this embodiment, the deviation between the mid-span deflection time history curve predicted by this method and the measured cumulative mid-span deflection of 9.5 cm after 10 years of operation for a typical bridge is 7.2%, a significant reduction compared to the approximately 32% systematic deviation between the original standard model calculation results and the measured value. The predicted mid-span deflection after 100 years of operation is approximately 68 cm, allowing the bridge operation and management unit to plan corresponding pre-camber adjustments or external prestressing reinforcement schemes in advance within the bridge's design service life.

[0065] This embodiment provides a 100-year deflection prediction system for long-span prestressed concrete bridges, corresponding to the described method. The system is deployed on an engineering structure analysis workstation or server with numerical computation capabilities. This workstation or server is equipped with the general-purpose finite element platform and has the ability to develop custom function interfaces. The system comprises five core modules: a model building module, a load application module, a material function connection module, a coupled iteration module, and a time history solution module. These five modules are sequentially connected according to the data flow direction, with the output object of each module serving as the input object of the next module. Together, they constitute an execution system where each of the five steps of the method corresponds to the previous one.

[0066] The model building module is used to discretize the main girder of the bridge using beam elements in the general-purpose finite element platform, establishing a finite element model of the main girder containing 315 nodes and 134 elements. Internally, the model building module maintains four data tables: a node number table, an element number table, a node-element topology adjacency table, and an element section attribute table. It calls the geometric modeling interface of the general-purpose finite element platform to read the longitudinal variable section law of the main girder and automatically generates the corresponding coordinates of the 315 nodes and the connection relationships of the 134 beam elements. Following step S1 of Embodiment 1, the 134 elements are divided into three categories: main span beam elements, side span beam elements, and pier-beam rigid connection elements, and section attributes are assigned to each beam element individually. The output object of the model building module is the finite element model of the main girder of the bridge, which is output to the load application module.

[0067] The load application module is used to apply the sensitive load to the finite element model of the bridge main girder span by span. Internally, the load application module constructs five independent sub-load case injectors according to the five components of the sensitive load: a dead load injector, a secondary dead load injector, an eight-lane live load injector, a design pre-camber injector, and a foundation settlement injector. Following step S2 of Embodiment 1, each sub-load case independently calculates its corresponding nodal force or nodal displacement and writes it into the load case slot of the bridge main girder finite element model. The output object of the load application module is the finite element model of the bridge main girder with the sensitive load applied, and the output is sent to the material function connection module.

[0068] The material function attachment module is used to construct the time-varying material function and perform the attachment. Internally, this module maintains four sub-components: a concrete measured creep parameter table reader, a salt spray corrosion steel strand residual prestress curve reader, a concrete time-varying creep function constructor, and a steel strand time-varying prestress function constructor. The concrete time-varying creep function constructor calls the concrete measured creep parameter table reader to read the measured parameters and generates the concrete time-varying creep function according to step S3 of Example 1. The time-varying prestress function constructor for the steel strand calls the residual prestress curve reader of the salt spray-corroded steel strand to read the measured curve, and generates the time-varying prestress function for the steel strand according to step S3 of Example 1. The material function attachment module calls the custom function interface to attach the time-varying creep function of concrete to the concrete properties of the finite element model of the bridge main girder, and the time-varying prestressing function of steel strands to the steel strand properties of the finite element model of the bridge main girder, so that both can be accessed by the same finite element solver in the same time step. The output object of the material function attachment module is the finite element model of the bridge main girder with the attached time-varying material function, and the output is sent to the coupling iteration module.

[0069] The coupling iteration module is used to execute the coupling iteration in each time step. The coupling iteration module executes the four stages in sequence as described in step S4 of Example 1: the concrete creep strain and concrete shrinkage strain update stage calls the age-adjusted effective modulus method solver built into the general finite element platform; the steel strand section and steel strand elastic modulus reduction stage implements linkage reduction according to formula (2); the prestressed equivalent load linkage adjustment stage recalculates the nodal force vector of the prestressed equivalent load according to formula (3); the bond degradation space redistribution stage implements the non-uniform redistribution of the prestressed equivalent load along the reinforcement length at the beam element nodes according to formula (4). The output object of the coupling iteration module is the set of state variables of the finite element model of the bridge main beam after completing the coupling iteration of the current time step, and outputs it to the time history solver module.

[0070] The time history solving module is used to solve the problem year by year, up to the 100th year, and outputs the mid-span deflection time history curve of the main girder of the bridge. The time history solving module maintains four sub-components: a time step advance scheduler, a mid-span deflection extractor, a deformation dependency feedback injector, and a parallel calculation branch of the original specification model. It feeds the mid-span deflection back to the time-varying material function according to formula (5) and outputs the evolution mechanism identification result according to formula (6). The final output objects of the time history solving module are the mid-span deflection time history curve of the main girder of the bridge, the deflection comparison diagram, and the evolution mechanism identification result, which are output to the visualization interface or maintenance decision support subsystem of the bridge operation and management unit.

[0071] The five core modules of the system can be deployed on the same physical workstation as independent software sub-components during engineering implementation, or they can be deployed in a distributed computing environment as microservices. The system is suitable for predicting the long-term deflection evolution of large-span prestressed concrete bridges during their operational period under various corrosive environments such as salt spray, seawater erosion, and acid rain. It can be adapted simply by adjusting the environmental parameters corresponding to the remaining prestress curve of the salt spray-corroded steel strands according to the specific environment.

[0072] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. All equivalent changes and modifications made in accordance with the shape, structure, features and spirit of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the century deflection of a long-span prestressed concrete bridge, characterized by, Includes the following steps: S1. Discretize the main girder of the bridge with beam elements in a general finite element platform and establish a finite element model of the main girder of the bridge with 315 nodes and 134 elements; S2. Apply sensitive loads to the finite element model of the main girder of the bridge span by span. The sensitive loads include dead load, secondary dead load, eight-lane live load, design precamber and foundation settlement. S3. Construct time-varying material functions, including a concrete time-varying creep function and a steel strand time-varying prestress function. Connect the concrete time-varying creep function to the concrete properties of the finite element model of the main bridge beam, and connect the steel strand time-varying prestress function to the steel strand properties of the finite element model of the main bridge beam. The concrete time-varying creep function is generated from the measured concrete creep parameter table, and the steel strand time-varying prestress function is generated from the residual prestress curve of the salt spray rusted steel strand. S4. Perform coupled iteration in each time step: first update the concrete creep strain and concrete shrinkage strain according to the concrete time-varying creep function, then reduce the steel strand cross section and steel strand elastic modulus according to the current corrosion rate of the steel strand time-varying prestress function, and adjust the prestress equivalent load accordingly. S5. Solve the problem year by year with a time step of one year until the 100th year, and output the mid-span deflection time history curve of the main girder of the bridge.

2. The method of claim 1, wherein the long-span prestressed concrete bridge century deflection prediction method is characterized by, In step S3: The concrete measured creep parameter table is a table of measured creep parameters for low-shrinkage, low-creep high-performance concrete. The concrete measured creep parameter table includes measured development curves of creep onset age, loading age, creep coefficient, and shrinkage strain over time. The residual prestress curve of the salt spray rusted steel strand is generated by the accelerated corrosion test in the salt spray environment. The residual prestress curve of the salt spray rusted steel strand includes the correspondence between the steel strand corrosion rate, the steel strand residual cross-sectional ratio, the steel strand residual elastic modulus and the steel strand residual prestress over time. The time-varying material function adopts a custom function interface, which allows the concrete time-varying creep function and the steel strand time-varying prestressing function to be accessed by the finite element solver in the same time step and to provide material property updates to the finite element model of the bridge main beam.

3. The method for predicting the 100-year deflection of long-span prestressed concrete bridges according to claim 2, characterized in that, The linkage adjustment of the prestressed equivalent load in step S4 includes: Within the current time step, based on the steel strand cross section, the steel strand elastic modulus, and the remaining prestress of the steel strand at the current time step, the nodal force vector of the prestress equivalent load is recalculated. The recalculated nodal force vectors of the prestressed equivalent load are updated in the load case of the finite element model of the bridge main girder before the start of the next time step. At the start of the next time step, the concrete generates a new concrete stress state under the updated prestressed equivalent load. The new concrete stress state is input as a stress dependency into the concrete time-varying creep function and participates in the update of the concrete creep strain in the next time step. This creates a closed loop within the time step between the update of concrete creep strain, the reduction of steel strand cross-section, the reduction of steel strand elastic modulus, and the adjustment of prestressed equivalent load.

4. The method for predicting the 100-year deflection of long-span prestressed concrete bridges according to claim 3, characterized in that, The time-varying material function also includes a steel strand bond degradation function, which encapsulates the evolution relationship of the bond-slip constitutive structure of the salt spray-corroded steel strand with the corrosion rate as a curve of the bond stiffness attenuation coefficient over time. In step S4, based on the bond stiffness attenuation coefficient of the current time step, the transfer ratio of the prestressed equivalent load on the beam element node is redistributed along the length of the steel strand to obtain the spatially redistributed prestressed equivalent load. The spatially redistributed prestressed equivalent load replaces the prestressed equivalent load initially applied in step S3 and participates in the finite element solution of the next time step.

5. The method for predicting the 100-year deflection of a long-span prestressed concrete bridge according to claim 4, characterized in that, Step S5, which involves outputting the mid-span deflection time history curve of the main girder of the bridge, includes: After each time step is solved, the vertical displacement value of the mid-span node of the main beam of the bridge is extracted as the mid-span deflection of the current time step, and the mid-span deflection of all time steps is arranged in time to form the mid-span deflection time history curve. The mid-span deflection of the previous time step is fed back as a deformation dependency to the time-varying creep function of concrete and the time-varying prestress function of steel strand, so that the time-varying material function responds to both the stress dependency and the deformation dependency in the next time step. This establishes a bidirectional feedback chain between the mid-span deflection time history curve and the time-varying material function in the time dimension.

6. The method for predicting the 100-year deflection of a long-span prestressed concrete bridge according to claim 5, characterized in that, The method also includes parallel computation of the original specification model and deflection comparison diagram diagnostic steps: The original standard model calculation is performed in parallel. The original standard model calculation uses the standard creep model to solve the finite element model of the bridge main beam under the same conditions, without connecting the time-varying prestress function of the steel strand, to obtain the mid-span deflection time history curve of the original standard model. The mid-span deflection time history curve and the original standard model mid-span deflection time history curve are superimposed on the same time axis to obtain a deflection comparison diagram. Based on the trend of the difference in the deflection comparison diagram in different time intervals, the evolution mechanism that plays a dominant role in that time interval is identified. The evolution mechanism includes the dominant mechanism of concrete creep, the dominant mechanism of steel strand corrosion, and the dominant mechanism of bond degradation.

7. The method for predicting the 100-year deflection of a long-span prestressed concrete bridge according to claim 1, characterized in that, The 315 nodes mentioned in step S1 are distributed along the longitudinal direction of the main beam of the bridge. The 134 units include main span beam units, side span beam units and pier-beam rigid connection units. The cross-sectional properties of the beam units are assigned segmentally according to the longitudinal variable cross-section law of the main beam of the bridge.

8. The method for predicting the 100-year deflection of a long-span prestressed concrete bridge according to claim 1, characterized in that, In step S2: The dead load is calculated based on the self-weight of the box section of the main girder of the bridge and applied to the beam element nodes; The second-phase dead load is calculated based on the dead load of the bridge deck pavement, crash barriers and sidewalks and applied to the beam unit nodes; The eight-lane live load is applied to the lane positions of the main beam of the bridge according to the lane load arrangement in the highway bridge and culvert design specifications. The design precamber is applied as the initial displacement of the node according to the precamber design curve of the main beam of the bridge. The foundation settlement is constrained at the bottom of the pier according to the estimated settlement of the pier where the main beam of the bridge is located.

9. The method for predicting the 100-year deflection of a long-span prestressed concrete bridge according to claim 1, characterized in that, The salt spray environmental parameters corresponding to the residual prestress curve of the salt spray rusted steel strand in step S3 include: salt spray deposition rate ranging from 0.5 mg / (cm²·d) to 3.5 mg / (cm²·d), relative humidity ranging from 60% to 95%, and ambient temperature ranging from 15℃ to 40℃.

10. A century-long deflection prediction system for long-span prestressed concrete bridges, characterized in that: The system includes: The model building module is used to discretize the main girder of a bridge using beam elements in a general finite element platform and build a finite element model of the main girder of the bridge containing 315 nodes and 134 elements. The load application module is used to apply sensitive loads to the finite element model of the main girder of the bridge span by span. The sensitive loads include dead load, secondary dead load, eight-lane live load, design precamber and foundation settlement. A material function attachment module is used to construct and attach time-varying material functions. The time-varying material functions include a concrete time-varying creep function and a steel strand time-varying prestress function. The material function attachment module attaches the concrete time-varying creep function to the concrete properties of the finite element model of the bridge main girder and attaches the steel strand time-varying prestress function to the steel strand properties of the finite element model of the bridge main girder. The concrete time-varying creep function is generated from the measured concrete creep parameter table, and the steel strand time-varying prestress function is generated from the residual prestress curve of the salt spray rusted steel strand. The coupling iteration module is used to perform coupling iteration in each time step. First, it updates the concrete creep strain and concrete shrinkage strain according to the concrete time-varying creep function. Then, it reduces the steel strand cross section and steel strand elastic modulus in conjunction with the current corrosion rate of the steel strand time-varying prestress function, and adjusts the prestress equivalent load in conjunction with the current corrosion rate of the steel strand time-varying prestress function. The time history solving module is used to solve the problem year by year with a time step of one year until the 100th year, and output the mid-span deflection time history curve of the main beam of the bridge.

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