Simulation method of non-perfectly bonded prestressed beam considering corrosion effect

Abstract

The application discloses a simulation method of non-complete bonding prestressed beams considering corrosion, which is based on the non-complete bonding theory and the vector finite element method, introduces a corrosion damage model, can accurately reflect the influence of longitudinal reinforcement corrosion on the mechanical properties of prestressed beams, quantifies the weakening effect of the corrosion degree on the bonding strength by establishing a longitudinal reinforcement-concrete interface bonding slip constitutive model, constructs a dynamic balance equation of the corroded prestressed beam under the vector finite element framework, and solves the equation by using an explicit time integration algorithm, and introduces the longitudinal reinforcement effective section loss and the concrete protective layer cracking effect caused by corrosion to form a complete analysis method of the corroded prestressed beam. The method can simulate the stress behavior of the prestressed beam at different corrosion stages, and provides a theoretical basis and technical support for the performance evaluation and life prediction of existing prestressed concrete structures.

Description

Technical Field

[0001] This invention relates to the field of civil engineering technology, and in particular to a method for simulating incompletely bonded prestressed beams that takes into account the effects of corrosion. Background Technology

[0002] Prestressed concrete structures are widely used in bridges, buildings, and other engineering fields due to their excellent crack resistance and load-bearing capacity. However, during long-term service, prestressed steel bars will corrode due to environmental factors and material deterioration, leading to a decline in structural performance.

[0003] Steel corrosion mainly affects the load-bearing performance of prestressed beams in the following ways: (1) Effective section loss: The volume of the corrosion products (rust) is about 2 to 4 times the original steel bar volume. The resulting expansion stress causes the concrete cover to crack and peel off. At the same time, the effective section of the steel bar is reduced, and the bearing capacity is reduced.

[0004] (2) Degradation of bond performance: Corrosion destroys the mechanical interlocking between the longitudinal reinforcement (steel bar / prestressed tendon) and the concrete, resulting in a significant reduction in bond strength, which in turn affects the transmission of prestress and the beam's cooperative stress performance.

[0005] (3) Deterioration of material properties: Corrosion not only affects the yield strength and ductility of longitudinal reinforcement (steel bars / prestressed tendons), but also affects the stiffness of the overall structure through crack propagation and concrete damage.

[0006] Traditional methods for analyzing prestressed beams are mostly based on the assumption of perfect bonding, which cannot accurately reflect the bond-slip effect caused by corrosion. Although the vector finite element method can handle large deformation problems, existing studies have not systematically considered the impact of corrosion damage on the mechanical behavior of prestressed beams.

[0007] Patent document CN121919951A discloses a method, equipment, and storage medium for deformation calculation and life assessment of prestressed beam bridges based on the coupling of creep, corrosion, and hydrodynamic fatigue. This method establishes a hydrodynamic simulation model of the beam bridge containing a time-varying creep constitutive model and prestressing tendons, updating parameters such as concrete creep, prestress relaxation, prestressing tendon corrosion depth, and hydrodynamic fatigue cracking depth annually. Based on the corrosion-fatigue competition criterion, the failure area of ​​the prestressing tendons is determined, and the interfacial bonding performance is calculated. Subsequently, a coupled simulation of hydrodynamic and long-term effects is performed to extract mid-span deflection, relative displacement of the piers, and prestress amplitude, thereby assessing the corrosion-hydraulic fatigue life of the prestressing tendons.

[0008] Patent document CN122021196A discloses a method for simulating prestressed beams based on incomplete bonding theory and vector finite element method, including: calculating the mechanical response of the prestressed beam section under different loads based on the incomplete bonding theory model to construct the moment-rotation relationship; discretizing the prestressed beam structure containing the prestressed beam section into multiple mass points using the vector finite element method, and connecting the multiple mass points with massless beam elements to construct a global structural analysis model; using the moment-rotation relationship as the force-deformation relationship of the massless beam elements in the global structural analysis model, calculating the displacement response of each mass point in the global structural analysis model, updating the internal forces according to the deformation of the massless beam elements and the moment-rotation relationship during the calculation process, and outputting the simulation results of the prestressed beam structure.

[0009] Therefore, establishing a simulation method for prestressed beams that can simultaneously consider the characteristics of incomplete bonding and the effects of corrosion damage is of great significance for accurately assessing the remaining life and safety status of existing prestressed concrete structures. Summary of the Invention

[0010] The purpose of this invention is to overcome the shortcomings of the prior art and provide a simulation method for incompletely bonded prestressed beams that takes into account the effect of corrosion. This method can accurately simulate the impact of corrosion on the mechanical properties of prestressed beams and provide an effective tool for the performance evaluation of existing prestressed concrete structures.

[0011] To achieve the above objectives, the present invention adopts the following technical solution: A method for simulating incompletely bonded prestressed beams that takes into account corrosion includes the following steps: Step S1: Based on the depth of rust Establish a constitutive model of bond-slip at the longitudinal reinforcement-concrete interface that takes into account the corrosion effect; Step S2, based on the depth of corrosion Calculate the corrosion rate Various reduction coefficients , , and cracking damage factors ; Based on the corrosion rate, section stiffness reduction factor, corrosion bond strength reduction factor, mass reduction factor, and cracking damage factor, the loss of elastic modulus, section stiffness, and bond strength caused by corrosion are calculated. Step S3: Discretize the prestressed beam into a finite number of mass points and vector beam elements. Combine the longitudinal reinforcement-concrete interface bond-slip constitutive model established in step S1, and the elastic modulus loss, section stiffness loss and bond strength loss obtained in step S2, to construct the dynamic equilibrium equation of the corroded prestressed beam. Step S4: Based on the internal forces, external forces, and damping forces acting on each mass point at the current moment, the dynamic equilibrium equation of the corroded prestressed beam is solved using the explicit time integration method to obtain the displacement, velocity, and acceleration response of each mass point at the current moment.

[0012] Specifically, based on the corrosion depth, a constitutive model of bond-slip at the longitudinal reinforcement-concrete interface considering the corrosion effect is established, where the longitudinal reinforcement includes steel bars and / or prestressed tendons. In this model, let For bonding stress, s For the amount of slip, the bond stress-slip constitutive relation can be expressed as: In the formula, The corrosion depth of the longitudinal reinforcement (steel bars / prestressed tendons) is related to the corrosion rate of the longitudinal reinforcement (steel bars / prestressed tendons) section. The relationship is: ;in, This is the initial diameter of the longitudinal reinforcement (steel bars / prestressed tendons).

[0013] The bond strength loss caused by corrosion is addressed by introducing a corrosion bond strength reduction factor. Consider that its expression is: In the formula , and These are material parameters.

[0014] Specifically, the discretization of the rusted prestressed beam involves discretizing the rusted prestressed beam along its length into... A point mass and Each vector-based beam element, and each mass point... Having position ,speed acceleration and quality The effective mass loss caused by corrosion is expressed by a mass reduction factor. Consider that its expression is: In the formula, , and These are material parameters.

[0015] Specifically, the section stiffness loss caused by corrosion is measured by the section stiffness reduction factor. Consider that its expression is: In the formula , The initial moment of inertia of the cross section, This is the stiffness attenuation parameter, and its value range is... .

[0016] Specifically, the expansion of corrosion products generates radial pressure on the concrete cover. When this pressure exceeds the tensile strength of the concrete, the cover cracks. (Corrosion expansion pressure) It can be represented as: In the formula, The elastic modulus of concrete. The volume of the corrosion products. This represents the original volume of the longitudinal reinforcement (steel bars / prestressed tendons). The volume of the surrounding concrete; when the radial stress caused by corrosion reaches the tensile strength of the concrete. At that time, the protective layer cracked, and the cracking conditions were: In the formula, For circumferential stress, The outer radius of the protective layer, The radius of the longitudinal reinforcement (steel bars / prestressed tendons); after the protective layer cracks, the loss of elastic modulus caused by corrosion effect is addressed by introducing a cracking damage factor. Consider that its expression is: In the formula , This represents the critical corrosion depth at which cracking occurs. These are damage evolution parameters.

[0017] Specifically, the dynamic equilibrium equation of the corroded prestressed beam is expressed as: In the formula: This represents the internal force vector of the corrosion element; This is the external load vector; The damping force vector; internal forces of the corrosion element. The calculations, taking into account the corrosion effect, yielded the following: In the formula, and These represent the pure tensile / compressive deformation and pure bending deformation of the vector beam element at the current time step, respectively. Indicates the loss of elastic modulus. Indicates the loss of cross-sectional stiffness. The bond strength loss is represented by the explicit central difference method, based on the mass of the particles. The data of internal forces, external forces, and damping forces acting on each mass point are input, and the dynamic equilibrium equations of the corroded prestressed beam are solved by time integration. The update formulas for the displacement and velocity of mass point i at time t+Δt are: ; Acceleration is calculated from the equilibrium equations: Time step Stability conditions must be met: In the formula, The minimum period of the system is determined by the stiffness of the cross-section after corrosion.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) By combining the corrosion effect with the theory of incomplete bonding, a simulation method for prestressed beams that takes corrosion into account was established, which can accurately reflect the mechanical behavior of prestressed beams at different corrosion stages.

[0019] (2) The influence of corrosion on bond strength, cross-sectional stiffness, mass and elastic modulus of concrete is quantitatively described by the reduction factor, so that the model has a clear physical meaning.

[0020] (3) Based on the vector finite element method, it can handle large deformation and geometric nonlinear problems caused by corrosion and is suitable for simulation of the whole process from the elastic stage to the failure stage.

[0021] (4) The algorithm uses explicit time integration, which is computationally efficient, easy to program and implement, and convenient for engineering applications.

[0022] The method of this invention can be widely applied in the following fields: (1) Performance evaluation of existing prestressed concrete bridges: By detecting the degree of corrosion of longitudinal reinforcement (steel bars / prestressed tendons), this method is used to simulate the actual bearing capacity of the structure, providing a basis for bridge maintenance decisions.

[0023] (2) Prediction of the service life of prestressed concrete structures: Combine environmental factors and corrosion rate to predict the mechanical properties of the structure after different service years and formulate a reasonable maintenance plan.

[0024] (3) Design for strengthening prestressed beams with rust: simulate the stress performance of the structure before and after strengthening, optimize the strengthening scheme, and improve the strengthening effect. Attached Figure Description

[0025] Figure 1 This is a flowchart of a method for simulating the behavior of a prestressed concrete beam structure considering the slippage of longitudinal reinforcement under the influence of corrosion, according to the present invention.

[0026] Figure 2 This is a vector finite element program flowchart of a method for simulating the behavior of prestressed concrete beam structures considering longitudinal reinforcement slippage under the influence of corrosion, according to the present invention.

[0027] Figure 3 This is a load-displacement comparison diagram of an embodiment of the present invention before and after corrosion. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0029] like Figure 1 As shown, the simulation method for incompletely bonded prestressed beams considering corrosion in this embodiment includes the following steps: Step S1: Establish a bond-slip constitutive model of the longitudinal reinforcement-concrete interface considering corrosion effects by taking into account the geometric parameters, material parameters, corrosion parameters, and boundary conditions of the prestressed beam. Step S2, based on the depth of corrosion Calculate the corrosion rate Various reduction coefficients , , and cracking damage factors ; Based on the corrosion rate, section stiffness reduction factor, corrosion bond strength reduction factor, mass reduction factor, and cracking damage factor, the loss of elastic modulus, section stiffness, and bond strength caused by corrosion are calculated. Step S3: Discretize the prestressed beam into a finite number of mass points and vector beam elements. Combine the longitudinal reinforcement-concrete interface bond-slip constitutive model established in step S1, and the elastic modulus loss, section stiffness loss and bond strength loss obtained in step S2, to construct the dynamic equilibrium equation of the corroded prestressed beam. Step S4: Based on the internal forces, external forces, and damping forces acting on each mass point at the current moment, solve the dynamic equilibrium equation of the corroded prestressed beam using the explicit time integration method to obtain the displacement, velocity, and acceleration response of each mass point at the current moment.

[0030] To verify the effectiveness of the present invention, a rusted prestressed concrete beam is used as an example for illustration.

[0031] Basic parameters of a beam: beam length Cross-sectional dimensions Concrete strength grade Prestressed steel bars are used The initial tension of the steel strand is 1200kN.

[0032] Corrosion parameters: Average corrosion depth of longitudinal reinforcement (steel bars / prestressed tendons) after 20 years of service. (Moderate corrosion), protective layer thickness .

[0033] like Figure 2 The following are the calculation steps provided in this embodiment: Phase 1: Initial Data Input and Parameter Preprocessing (1) Data input: Import the initial geometric parameters of the prestressed beam (beam length) Cross-sectional dimensions Initial diameter of longitudinal reinforcement Material parameters (concrete strength, steel strand elastic modulus, etc.), external loading regime, and detected corrosion depth. .

[0034] (2) Calculate corrosion evolution parameters: Based on corrosion depth Calculate the corrosion rate of the longitudinal reinforcement. .

[0035] (3) Solve for the reduction factor: Based on the calculated corrosion rate Based on environmental empirical parameters, the corrosion bond strength reduction factor was calculated sequentially. Mass reduction factor Section stiffness reduction factor and cracking damage factors .

[0036] Phase Two: Model Discretization and State Initialization (4) Structural Discretization: Using the vector finite element method, the corroded prestressed beam is discretized along its length. A point mass and Vector-type beam elements.

[0037] (5) Parameter allocation and initialization: Update the cross-sectional bond strength of each element using the calculated reduction coefficient. Moment of inertia ,quality Elastic modulus .

[0038] Initialize all particles in displacement at time ,speed acceleration Set the time step to 0. .

[0039] Phase 3: Explicit Time Integration Dynamic Solution (Time Step Loop) (6) Calculate internal forces: At the current time step Based on the displacement of the current node, and considering the corrosion effect, calculate the displacement of each mass point. internal force vector .

[0040] (7) Calculate external forces and damping: Determine the external force vector at the current time step based on the loading regime. And calculate the damping force vector. .

[0041] (8) Solve the dynamic equilibrium equations: , , Substitute the equations of dynamic equilibrium of the corroded prestressed beam to calculate the acceleration of each mass point at the current time step. .

[0042] (9) State Update: The explicit central difference method is used to update the calculated state of the particle. The speed of time and Displacement at any given moment.

[0043] (10) Time step progression: Determine whether the total loading time or structural failure criterion has been met. If not, return to step (6); if met, end the loop.

[0044] Phase Four: Results Output and Evaluation (11) Extract response results: Extract the displacement data of the mid-span mass point and the corresponding external load during the entire loading process, and plot the load-deflection curve.

[0045] (12) Performance evaluation: such as Figure 3 As shown, by comparing the output curve of the corroded beam with that of the uncorroded beam, it can be concluded that the ultimate bearing capacity of the corroded beam in this embodiment is reduced by about 8% and the stiffness is reduced by about 5%, thus completing the simulation analysis process.

[0046] Furthermore, the terms "upper," "lower," "inner," "outer," "front," and "rear" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Unless otherwise specifically stated, the relative steps, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention.

[0047] Of course, the above description is only a specific embodiment of the present invention and is not intended to limit the scope of the present invention. All equivalent changes or modifications made to the structure, features and principles described in the claims of the present invention should be included in the scope of the claims of the present invention.

[0048] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for simulating incompletely bonded prestressed beams considering corrosion, characterized in that, Includes the following steps: Step S1: Establish a bond-slip constitutive model of the longitudinal reinforcement-concrete interface considering corrosion effects by taking into account the geometric parameters, material parameters, corrosion parameters, and boundary conditions of the prestressed beam. Step S2: Calculate the corrosion rate, cross-sectional stiffness reduction factor, corrosion bond strength reduction factor, mass reduction factor, and cracking damage factor based on the corrosion depth. Based on the corrosion rate, section stiffness reduction factor, corrosion bond strength reduction factor, mass reduction factor, and cracking damage factor, the loss of elastic modulus, section stiffness, and bond strength caused by corrosion are calculated. Step S3: Discretize the prestressed beam into a finite number of mass points and vector beam elements. Combine the longitudinal reinforcement-concrete interface bond-slip constitutive model established in step S1, and the elastic modulus loss, section stiffness loss and bond strength loss obtained in step S2, to construct the dynamic equilibrium equation of the corroded prestressed beam. Step S4: Based on the internal forces, external forces, and damping forces acting on each mass point at the current moment, solve the dynamic equilibrium equation of the corroded prestressed beam using the explicit time integration method to obtain the displacement, velocity, and acceleration response of each mass point at the current moment.

2. The method for simulating incompletely bonded prestressed beams considering corrosion according to claim 1, characterized in that, The constitutive model expression for the bond-slip at the longitudinal reinforcement-concrete interface is as follows: In the formula, For bonding stress, s For slip, The corrosion depth of the longitudinal reinforcement is given, and its relationship with the corrosion rate of the longitudinal reinforcement section is as follows: In the formula, The initial diameter of the longitudinal reinforcement. This represents the corrosion rate.

3. The simulation method for incompletely bonded prestressed beams considering corrosion according to claim 1, characterized in that, The discretization of the rusted prestressed beam involves discretizing the rusted prestressed beam along its length. A point mass and Each vector beam element has position, velocity, acceleration, and mass.

4. The method for simulating incompletely bonded prestressed beams considering corrosion according to claim 1, characterized in that, The loss of bond strength is analyzed by introducing a corrosion bond strength reduction factor, which is expressed as follows: In the formula Indicates the loss of bond strength. and For material parameters, The initial diameter of the longitudinal reinforcement. This represents the depth of corrosion of the longitudinal reinforcement.

5. The method for simulating incompletely bonded prestressed beams considering corrosion according to claim 1, characterized in that, The section stiffness loss is analyzed using a section stiffness reduction factor, the expression of which is: In the formula This represents the section stiffness reduction factor. Let the initial moment of inertia of the cross section be... For stiffness attenuation parameters, This represents the depth of corrosion of the longitudinal reinforcement. This is the initial diameter of the longitudinal reinforcement.

6. The method for simulating incompletely bonded prestressed beams considering corrosion according to claim 1, characterized in that, The aforementioned loss of elastic modulus is analyzed by introducing a cracking damage factor when the concrete protective layer cracks due to corrosion. Its expression is as follows: In the formula Indicates the cracking damage factor. This represents the critical corrosion depth at which cracking occurs. For damage evolution parameters, This refers to the elastic modulus of concrete.

7. The method for simulating incompletely bonded prestressed beams considering corrosion according to claim 6, characterized in that, When the radial stress caused by corrosion reaches the tensile strength of concrete When the protective layer cracks, the cracking conditions are as follows: In the formula, For circumferential stress, The outer radius of the protective layer, Where is the radius of the reinforcing bar.

8. The method for simulating incompletely bonded prestressed beams considering corrosion according to claim 1, characterized in that, The dynamic equilibrium equation of the corroded prestressed beam is expressed as follows: In the formula, This represents the internal force vector of the corrosion element; This is the external load vector; The damping force vector, This indicates the position of the i-th particle. Let represent the mass of the i-th particle.

9. The method for simulating a non-fully bonded prestressed beam considering corrosion according to claim 8, characterized in that, Internal forces of the corrosion unit The calculations, taking into account the corrosion effect, yielded the following: In the formula, and These represent the pure tensile / compressive deformation and pure bending deformation of the vector beam element at the current time step, respectively. Indicates the loss of elastic modulus. Indicates the loss of cross-sectional stiffness. This represents the loss of bond strength. The internal force vector of each mass point is updated by substituting the damaged section parameters into the element deformation compatibility equation.

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