Reinforcement Method and System for Precast π-Shaped Slabs at Wharf

Abstract

This invention provides a method and system for reinforcing precast π-shaped slabs in wharf construction, relating to the field of structural design technology in building engineering. The invention establishes a three-dimensional finite element model of the π-shaped slab and divides it into disordered and non-disordered reinforcement regions. In the non-disordered region, a strain distribution model is constructed using the plane section assumption and the principle of internal force equilibrium to calculate the reinforcement area. In the disordered region, a dynamic steel corrosion model is constructed, and the model is corrected using a corrosion compensation equation to calculate the reinforcement area. Finally, a multi-objective optimization function is constructed using life-cycle durability constraints to optimize the reinforcement area in the disordered region, obtaining the optimized reinforcement area. The reinforcement areas of the two regions are then combined to obtain the optimal reinforcement scheme for the π-shaped slab. This invention, by combining finite element analysis and a dynamic steel corrosion model, achieves the scientific division and multi-objective optimization design of the reinforcement region of the π-shaped slab.

Description

Technical Field

[0001] This invention relates to the field of structural design technology in building engineering, specifically to a method and system for reinforcing precast π-shaped slabs for wharves. Background Technology

[0002] With the continuous expansion of port and wharf construction, precast π-shaped slabs, as an important component of wharf bridges, have attracted widespread attention for their structural safety and durability. Traditional π-shaped slab reinforcement design relies heavily on experience and static analysis methods, which are insufficient to fully reflect the complex stress state under actual working conditions. In particular, there are design blind spots regarding the arrangement of reinforcing bars and corrosion issues in areas of disordered reinforcement. Furthermore, the durability degradation caused by reinforcing bar corrosion seriously affects the service life of wharf structures. Existing design methods lack effective prediction and compensation measures for the dynamic process of reinforcing bar corrosion, making it difficult to achieve optimal reinforcement configuration. With the development of computer-aided engineering technology and finite element analysis methods, combined with digital simulation and multi-objective optimization technology, it is expected to achieve refined management and optimization of precast π-shaped slab reinforcement design, improving structural safety and durability and meeting the high standards required for modern wharf construction.

[0003] In existing technologies, traditional π-shaped slab reinforcement methods rely primarily on static stress analysis, making it difficult to accurately distinguish between disordered and non-disordered reinforcement areas within the π-shaped slab. This results in reinforcement design failing to provide differentiated optimization for different stress areas, lacking a fine division of stress states, and often overlooking the cross-sectional area loss and reduced durability of steel bars due to chloride ion corrosion in the harsh environment of wharves. This fails to reflect the impact of steel bar corrosion on structural performance in a timely manner, making it difficult to guarantee the service life of the structure.

[0004] Therefore, it is necessary to provide a method and system for reinforcing precast π-shaped slabs for wharves to solve the aforementioned problem.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for reinforcing precast π-shaped slabs for wharves, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for reinforcing precast π-shaped slabs for wharves, comprising the following steps:

[0009] Step 1: Obtain the geometric and material parameters of the π-shaped plate to be manufactured, perform finite element modeling of the π-shaped plate based on finite element analysis software, apply simulated loads to the constructed 3D finite element model of the π-shaped plate, and establish a discrimination index function based on the stress distribution to determine the disordered reinforcement region and the non-disordered reinforcement region in the π-shaped plate to be manufactured.

[0010] Step 2: For the non-disordered reinforcement region in the π-shaped slab, construct the plane section strain distribution model using the plane section assumption principle and the internal force equilibrium principle, and calculate the reinforcement area in the non-disordered reinforcement region based on the established plane section strain distribution model;

[0011] Step 3: Based on the principle of chloride ion migration and diffusion, a dynamic steel corrosion model is comprehensively constructed in the reinforcement disorder area. A corrosion compensation equation for the thickness of the steel protective layer and the steel diameter is established. The dynamic steel corrosion model is compensated based on the modified equation. The reinforcement area in the reinforcement disorder area is calculated using the compensated dynamic steel corrosion model.

[0012] Step 4: Based on the life-cycle durability constraint optimization principle, construct a multi-objective optimization function to optimize the reinforcement area in the disordered reinforcement region, so as to determine the optimal reinforcement area in the disordered reinforcement region. Summarize the reinforcement areas of the π-shaped slab to be manufactured to obtain the optimal reinforcement area of ​​the π-shaped slab to be manufactured.

[0013] Furthermore, the π-shaped plate was modeled using finite element analysis software, and the method used was as follows:

[0014] Obtain the geometric and material parameters of the π-shaped plate. The geometric parameters include the plate width, total height, total length, flange thickness, and web thickness. The material parameters include the elastic modulus, Poisson's ratio, and compressive strength. First, draw the two-dimensional cross-sectional profile of the π-shaped plate in the finite element analysis software, including the shape of the flange and web. Then, stretch it along the length to form a three-dimensional solid. Mesh the three-dimensional solid of the π-shaped plate. Discretize the concrete using three-dimensional eight-node linear solid elements. Locally refine the mesh at the flange-web connection, edge, and support area. The mesh size should be selected to balance computational efficiency and accuracy requirements, and controlled to be between one-fifth and one-tenth of the plate thickness.

[0015] Boundary conditions were set for the three-dimensional geometric model of the π-shaped plate after meshing. The bottom of the flange and the bottom of the web of the π-shaped plate, which are in contact with the foundation, were selected as the supports of the π-shaped plate. All nodes in the contact surface at the supports were selected and their degrees of freedom were constrained. Specifically, in the finite element software, "displacement constraints" were applied to the support nodes to fix the vertical displacement while keeping the translational and rotational degrees of freedom free. Spring elements were connected between the support nodes and the reference point, and the spring stiffness was defined according to the design support stiffness parameters to complete the construction of the three-dimensional finite element model of the π-shaped plate.

[0016] Furthermore, simulated loads were applied to the three-dimensional finite element model of the π-shaped plate, and a discriminant index function was established based on the stress distribution to determine the disordered and non-disordered reinforcement regions in the π-shaped plate to be manufactured. The method used was as follows:

[0017] The simulated load applied to the three-dimensional finite element model of the π-shaped plate mainly consists of the self-weight load of the π-shaped plate and the water pressure of the environment in which the π-shaped plate is located. First, the material density is input into the finite element analysis software, and the vertical downward direction is specified as the direction of gravitational acceleration. The finite element analysis software automatically calculates the volume force based on the model volume to realize the self-weight load. For the π-shaped plate of the wharf, the water pressure is usually a lateral uniform pressure that varies linearly with the water depth. The application method is surface pressure, and the direction is perpendicular to the water-receiving surface. The application of non-uniform water pressure is realized by defining a function of water pressure changing with depth.

[0018] For each mesh element in the 3D finite element model of the π-shaped plate, the average side length of all mesh elements in the model is calculated. A neighborhood radius of 2 to 3 times the average side length of the mesh elements is used as the neighborhood radius of each mesh element. With the geometric center point of each mesh element as the center, all mesh elements within this radius are automatically searched and included in the neighborhood calculation.

[0019] Based on the defined neighborhood radius of each mesh element and the known simulated load applied by the finite element analysis software, the local stress of each mesh element is obtained. The mean and standard deviation of the local stress are calculated within the neighborhood of that mesh element to reflect the stress level and the degree of stress variation in that region. The formula used is as follows:

[0020]

[0021]

[0022] in, In the model, the first The average local stress of each mesh element Indicates the first Within the neighborhood of the first grid cell Local stress in each mesh element The index of the grid cell within the neighborhood. This represents the total number of grid cells in the neighborhood. This refers to the index of the mesh element in the model. In the model, the first The standard deviation of local stress in each grid cell;

[0023] A discriminant index function is constructed based on the calculated mean and standard deviation of local stress, and a stress disorder threshold is established. This discriminant index function is then used to distinguish between disordered and non-disordered reinforcement regions in the model. The formula used is as follows:

[0024]

[0025] in, In the model, the first Stress disorder value of each mesh element , These are the weighting coefficients, and ;

[0026] The stress disorder value obtained by calculating the discriminant index function Compared with the preset stress disturbance threshold Compare and statistically analyze all The mesh elements are marked as areas of disordered reinforcement; all The mesh elements are marked as reinforced non-disordered regions.

[0027] Furthermore, the method used to construct the plane section strain distribution model is as follows:

[0028] Based on the constructed three-dimensional finite element model of the π-shaped plate, the cross-sectional geometric parameters of the π-shaped plate are determined. Assuming the cross-section is under bending, the neutral axis of the π-shaped plate is defined as a distance measured from the edge of the compression side towards the height of the cross-section, representing the location of the cross-section where the strain is zero. The ultimate compressive strain of the top surface of the concrete is obtained. Then, using the principle of plane section strain distribution assumption, the strain is linearly distributed along the cross-sectional height. The strain of the tie rod at any point on the cross-section is:

[0029]

[0030] in, Indicates the position at the height of the π-shaped plate section. The strain value of the reinforcing steel at the point of contact with the compression edge, i.e., the cross-section at the distance from the compression edge. The strain value at the location, This represents the ultimate compressive strain value at the top surface of the concrete, typically taken as 0.003 in design. This is the vertical distance from the location of the reinforcing bar to the compression edge of the cross-section. It is the height of the neutral axis of the π-shaped plate, which divides the cross-section into a compression zone and a tension zone;

[0031] Based on the stress-strain relationship between concrete and reinforcing steel, the stress in the reinforcing steel is calculated according to its strain, using the following formula:

[0032]

[0033] in, Indicates the position at the height of the π-shaped plate section. The stress value borne by the reinforcing steel at that location. This refers to the elastic modulus of the reinforcing steel. The yield strength of the steel reinforcement represents the stress value at which the steel reinforcement begins to yield. It is a sign function used to determine the direction of stress in steel reinforcement. This represents the yield strain of the steel reinforcement, corresponding to the strain value at the yield strength of the steel reinforcement.

[0034] Similarly, based on the principle of plane section strain distribution assumption, the position at the height of the π-shaped plate section is first obtained. To calculate the concrete stress at the point of concrete strain, the actual constitutive relationship between the concrete and the reinforcing steel is used. The formula used is:

[0035]

[0036] in, Indicates the position at the height of the π-shaped plate section. The stress value borne by the concrete at that point, This refers to the axial compressive strength of concrete. This represents the peak strain of the concrete. Indicates the position at the height of the π-shaped plate section. The strain value of the concrete at that location. This is the exponent, which is usually 2.

[0037] Furthermore, the reinforcement area in the non-disordered reinforcement region is calculated based on the constructed plane section strain distribution model. The method used is as follows:

[0038] After applying the simulated load, the axial force and bending moment of the π-shaped plate section are output using finite element analysis software. Based on the principle of axial force balance and bending moment balance in internal force equilibrium, the area of ​​the compression reinforcement and the area of ​​the tension reinforcement are calculated and summarized to obtain the reinforcement area in the non-disordered reinforcement region. The formula used is as follows:

[0039]

[0040]

[0041] in, This represents the axial force experienced by the π-shaped plate section under simulated load. This represents the bending moment experienced by the π-shaped plate section under simulated load. This represents the resultant force of the concrete in the compression zone of the cross section. This indicates the pressure exerted by the reinforcing steel bars located in the compression zone of the cross section. This indicates the tensile force generated by the reinforcing steel located in the tensile zone of the cross-section. The width of the π-shaped plate cross-section is... For the area of ​​the reinforcing rib, For the area of ​​the reinforcing bar, The stress generated by the strain of the reinforcing steel in the compression zone. The stress generated by the strain in the reinforcing steel in the tensile zone. This is the distance from the point of application of the resultant force in the concrete to the edge under compression. This is the distance from the point of application of the resultant force of the reinforcing steel in the compression zone to the compression edge. This is the distance from the point of application of the resultant force of the reinforcing steel in the tensile zone to the compression edge;

[0042] Based on a plane section strain distribution model with axial force and bending moment as inputs and tension and compression reinforcement areas as outputs, and considering the neutral axis height, the model checks whether the axial force and bending moment equilibrium equations are satisfied. If not, adjustments are made. Repeat the calculation and iterative solution until equilibrium is reached. Once it is confirmed that the strain of the steel reinforcement meets the minimum design strain requirement, the sum of the area of ​​the tension reinforcement and the area of ​​the compression reinforcement is the reinforcement area in the non-disordered reinforcement region. .

[0043] Furthermore, a dynamic steel corrosion model was comprehensively constructed in the disordered reinforcement region based on the principle of chloride ion migration and diffusion. The method used was as follows:

[0044] To simulate the migration process of chloride ions in concrete within the disordered reinforcement region, a mathematical model of chloride ion diffusion is established using Fick's second law. This model assumes that chloride ions mainly migrate from the surface to the interior along the concrete thickness direction via diffusion, and that the diffusion process is controlled by the diffusion coefficient of the concrete material. Its basic differential equation is:

[0045]

[0046] in, Indicates in At any given time, the depth from the concrete surface is Chloride ion concentration at the location, The chloride ion diffusion coefficient of concrete is given. Let be the partial derivative of chloride ion concentration with respect to time, representing the concentration at a fixed position. The rate of change of chloride ion concentration at a given location over time. Chloride ion concentration versus spatial position The second partial derivative at a point represents the curvature of the concentration along the depth direction, i.e., the rate of change of the concentration gradient.

[0047] Assume the chloride ion concentration on the concrete surface is . ,Right now Furthermore, the concrete initially does not contain chloride ions, i.e. Therefore, the corrosion initiation time of the reinforcing steel. Defined as such At the time of its establishment, among which The critical chloride ion concentration for corrosion. The thickness of the concrete cover for the reinforcing steel is given, and the initial radius of the reinforcing steel is obtained. A dynamic model of steel corrosion is constructed by combining the mathematical model of chloride ion diffusion. The formula used is as follows:

[0048]

[0049]

[0050]

[0051] in, Indicates that the reinforcing steel is in The corrosion rate at time t, The current time is the time variable of the corrosion process. This is the corrosion initiation time. The corrosion rate coefficient is... The corrosion sensitivity index is used to represent the nonlinear effect of chloride ion concentration on the corrosion rate. Indicates that the reinforcing steel is in The radius at time t, Let be the initial radius of the reinforcing bar. Indicates that the reinforcing steel is in The cross-sectional area at time t.

[0052] Furthermore, a corrosion compensation equation for the thickness of the concrete cover and the diameter of the reinforcing bar is established. Based on this modified equation, the dynamic reinforcing bar corrosion model is compensated using the following method:

[0053] To address the impact of the non-uniformity of the concrete cover thickness and rebar diameter on the corrosion rate in areas of disordered reinforcement, a compensation factor is introduced to establish a corrosion compensation equation based on the concrete cover thickness and rebar diameter. The formula used is as follows:

[0054]

[0055] in, Indicates the corrosion compensation factor. , These are the standard design protective layer thickness and rebar diameter, , This is an empirical coefficient. The diameter of the reinforcing bar is, and ;

[0056] The dynamic steel reinforcement corrosion model is compensated based on the established corrosion compensation equation, and the formula used is as follows:

[0057]

[0058]

[0059]

[0060] in, , , These represent the corrosion correction rate, the reinforcement correction radius, and the reinforcement correction cross-sectional area after compensation, respectively.

[0061] Furthermore, the reinforced area in the disordered reinforcement region was calculated using the compensated dynamic steel corrosion model, based on the following method:

[0062] Count the number of mesh elements in areas with disordered reinforcement. Assuming the concrete cover thickness, rebar diameter, and corrosion initiation time are uniform within each grid cell, and calculating the theoretical rebar quantity for each grid cell, the reinforcement area within each grid cell is:

[0063]

[0064] in, Indicates in In the disordered reinforcement area within a certain time period, the first The reinforcement area of ​​each grid cell Indicates the first in the area of ​​disordered reinforcement The number of steel bars in each grid cell. Indicates the first in the area of ​​disordered reinforcement In each grid cell, a single reinforcing bar... Corrosion correction cross-sectional area at time t, This is the index of the mesh element in the disordered reinforcement region, and ;

[0065] The total reinforcement area of ​​the disordered reinforcement region is obtained by summing the reinforcement areas of each grid element within the disordered reinforcement region, based on the following formula:

[0066]

[0067] in, Indicates in The area of ​​reinforcement in the disordered reinforcement zone within a given time period.

[0068] Furthermore, based on the life-cycle durability constraint optimization principle, a multi-objective optimization function is constructed to optimize the reinforcement area in the disordered reinforcement region to determine the optimal reinforcement area for the π-shaped slab to be manufactured. The method used is as follows:

[0069] Based on the life-cycle durability constraint optimization principle, the initial reinforcement area configuration of the disordered reinforcement region is determined. The reinforcement areas in both the disordered and non-disordered reinforcement regions are summarized as variables to be optimized. A multi-objective optimization function is constructed by combining the structural remaining durability life function and the reinforcement cost function, ensuring that the structure meets the ultimate bearing capacity within the target life and that the initial reinforcement area of ​​the disordered reinforcement region is greater than or equal to its minimum value specified in the code. The formula on which the multi-objective optimization function is constructed is as follows:

[0070]

[0071]

[0072]

[0073] in, This represents the objective function value, used to minimize the weighted sum of lifetime and cost. , These represent the lifespan weighting coefficient and the cost weighting coefficient, respectively. It is the expected lifespan of the structure. Cost per unit area of ​​reinforcement This represents the initial reinforcement area for the disordered reinforcement region. Indicates the structural bearing capacity at the end of its lifespan. The minimum ultimate bearing capacity required by the design. This represents the minimum standard value for the reinforcement area in areas with disordered reinforcement.

[0074] The specific optimization process is as follows: Initialize the initial reinforcement area of ​​the disordered reinforcement region and summarize it with the reinforcement area of ​​the non-disordered reinforcement region; calculate the expected life of the structure and the structural bearing capacity at the end of the life; adjust the initial reinforcement area of ​​the disordered reinforcement region based on the constraints to minimize the objective function value; finally, output the optimal reinforcement area of ​​the disordered reinforcement region and the optimal reinforcement area of ​​the π-shaped plate, based on the following formula:

[0075]

[0076] in, This represents the optimal reinforcement area for a π-shaped slab. This represents the optimal reinforcement area for areas with disordered reinforcement.

[0077] The present invention also provides a reinforcement system for precast π-shaped slabs at wharves, the reinforcement system being used to perform the above-described reinforcement method for precast π-shaped slabs at wharves, comprising:

[0078] The reinforcement area discrimination module is used to obtain the geometric and material parameters of the π-shaped plate to be manufactured, perform finite element modeling of the π-shaped plate based on finite element analysis software, apply simulated load to the constructed three-dimensional finite element model of the π-shaped plate, and establish discrimination index function based on stress distribution to determine the disordered reinforcement area and the non-disordered reinforcement area in the π-shaped plate to be manufactured.

[0079] The module for calculating the reinforcement area in the non-disordered region is used to construct a plane section strain distribution model for the non-disordered reinforcement area in a π-shaped slab using the plane section assumption principle and the internal force balance principle. Based on the established plane section strain distribution model, the reinforcement area in the non-disordered reinforcement area is calculated.

[0080] The module for calculating the reinforcement area in disordered regions constructs a dynamic steel corrosion model in disordered reinforcement regions based on the principle of chloride ion migration and diffusion. It establishes a corrosion compensation equation for the thickness of the steel protective layer and the diameter of the steel bar, compensates the dynamic steel corrosion model based on the modified equation, and uses the compensated dynamic steel corrosion model to calculate the reinforcement area in disordered reinforcement regions.

[0081] The optimal reinforcement area determination module constructs a multi-objective optimization function based on the life-cycle durability constraint optimization principle to optimize the reinforcement area in the disordered reinforcement region, so as to determine the optimal reinforcement area in the disordered reinforcement region. The reinforcement areas of the π-shaped slab to be manufactured are summarized to obtain the optimal reinforcement area of ​​the π-shaped slab to be manufactured.

[0082] Compared with the prior art, the beneficial effects of the present invention are:

[0083] This invention introduces a stress distribution discrimination method based on finite element analysis, which enables precise division of disordered and non-disordered reinforcement regions in precast π-shaped slabs of wharves. This effectively solves the problem that traditional static analysis methods cannot accurately reflect complex stress states. By adopting differentiated reinforcement design for different regions, it not only improves the scientificity and rationality of structural reinforcement, but also enhances the overall safety performance and load-bearing capacity of the structure.

[0084] Furthermore, this invention constructs a dynamic steel reinforcement corrosion model based on the principle of chloride ion migration and diffusion, and corrects the corrosion process through a corrosion compensation equation. It can dynamically predict the loss of steel reinforcement cross-sectional area and its impact on structural durability. Combined with life-cycle durability constraints and multi-objective optimization technology, it achieves the optimal configuration of reinforcement area, significantly improving the service life and economic benefits of the wharf π-shaped slab. Attached Figure Description

[0085] Figure 1 This is a schematic diagram of the overall method flow of the present invention.

[0086] Figure 2 This is a schematic diagram of the system module flow of the present invention. Detailed Implementation

[0087] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0088] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0089] Example:

[0090] Please see Figure 1 A method for reinforcing precast π-shaped slabs at wharves, comprising the following steps:

[0091] Step 1: Obtain the geometric and material parameters of the π-shaped plate to be manufactured, perform finite element modeling of the π-shaped plate using finite element analysis software, apply simulated loads to the constructed 3D finite element model of the π-shaped plate, and establish a discriminant index function based on the stress distribution to determine the disordered and non-disordered reinforcement regions in the π-shaped plate to be manufactured.

[0092] In a specific embodiment of the present invention, step 1 is the foundation and prerequisite for the entire method of optimizing the reinforcement of precast π-shaped slabs at the wharf. Obtaining the geometric and material parameters of the π-shaped slab and performing three-dimensional modeling based on finite element analysis software is a prerequisite for subsequent stress analysis, reinforcement area identification, and reinforcement optimization design. By establishing a high-precision finite element model, the stress distribution and deformation characteristics of the π-shaped slab under actual working conditions can be accurately reflected, thereby providing scientific and reliable data support for identifying disordered and disordered reinforcement areas, as well as subsequent durability analysis and optimization design. If the geometric or material parameters are not selected accurately or the model is not constructed reasonably, it will directly affect the accuracy and engineering applicability of the entire reinforcement analysis results.

[0093] Furthermore, the π-shaped plate was modeled using finite element analysis software, and the method used was as follows:

[0094] Obtain the geometric and material parameters of the π-shaped plate. The geometric parameters include the plate width, total height, total length, flange thickness, and web thickness. The material parameters include the elastic modulus, Poisson's ratio, and compressive strength. First, draw the two-dimensional cross-sectional profile of the π-shaped plate in the finite element analysis software, including the shape of the flange and web. Then, stretch it along the length to form a three-dimensional solid. Mesh the three-dimensional solid of the π-shaped plate. Discretize the concrete using three-dimensional eight-node linear solid elements. Locally refine the mesh at the flange-web connection, edge, and support area. The mesh size should be selected to balance computational efficiency and accuracy requirements, and controlled to be between one-fifth and one-tenth of the plate thickness.

[0095] Boundary conditions were set for the three-dimensional geometric model of the π-shaped plate after meshing. The bottom of the flange and the bottom of the web of the π-shaped plate, which are in contact with the foundation, were selected as the supports of the π-shaped plate. All nodes in the contact surface at the supports were selected and their degrees of freedom were constrained. Specifically, in the finite element software, "displacement constraints" were applied to the support nodes to fix the vertical displacement while keeping the translational and rotational degrees of freedom free. Spring elements were connected between the support nodes and the reference point, and the spring stiffness was defined according to the design support stiffness parameters to complete the construction of the three-dimensional finite element model of the π-shaped plate.

[0096] It should be noted that the simulated loads applied to the π-shaped plate mainly simulate the self-weight load of the π-shaped plate and the water pressure load. The purpose is to realistically reflect the actual working conditions of the π-shaped plate under the wharf environment. This load application method fully considers the weight of the structure itself and the lateral pressure of the surrounding water environment on the structure, ensuring the authenticity and accuracy of the stress state of the finite element model. The self-weight loading is realized by automatically calculating the volume force, and the surface pressure is applied by using the linear variation of water pressure with depth. This realizes the reasonable distribution and non-uniformity simulation of the load, which helps to obtain accurate stress distribution results.

[0097] By using the mean stress to reflect the local stress level and the standard deviation to reflect the severity of stress changes, we can accurately identify areas with complex stress states and large stress fluctuations, i.e., areas with disordered reinforcement. The advantage of doing this is that after dividing the π-shaped plate into disordered and non-disordered areas, we can adopt different reinforcement strategies for different areas, optimize the arrangement of steel bars, avoid waste of resources, and improve the load-bearing capacity and durability of key areas.

[0098] Furthermore, simulated loads were applied to the three-dimensional finite element model of the π-shaped plate, and a discriminant index function was established based on the stress distribution to determine the disordered and non-disordered reinforcement regions in the π-shaped plate to be manufactured. The method used was as follows:

[0099] The simulated load applied to the three-dimensional finite element model of the π-shaped plate mainly consists of the self-weight load of the π-shaped plate and the water pressure of the environment in which the π-shaped plate is located. First, the material density is input into the finite element analysis software, and the vertical downward direction is specified as the direction of gravitational acceleration. The finite element analysis software automatically calculates the volume force based on the model volume to realize the self-weight load. For the π-shaped plate of the wharf, the water pressure is usually a lateral uniform pressure that varies linearly with the water depth. The application method is surface pressure, and the direction is perpendicular to the water-receiving surface. The application of non-uniform water pressure is realized by defining a function of water pressure changing with depth.

[0100] For each mesh element in the 3D finite element model of the π-shaped plate, the average side length of all mesh elements in the model is calculated. A neighborhood radius of 2 to 3 times the average side length of the mesh elements is used as the neighborhood radius of each mesh element. With the geometric center point of each mesh element as the center, all mesh elements within this radius are automatically searched and included in the neighborhood calculation.

[0101] Based on the defined neighborhood radius of each mesh element and the known simulated load applied by the finite element analysis software, the local stress of each mesh element is obtained. The mean and standard deviation of the local stress are calculated within the neighborhood of that mesh element to reflect the stress level and the degree of stress variation in that region. The formula used is as follows:

[0102]

[0103]

[0104] in, In the model, the first The average local stress of each mesh element Indicates the first Within the neighborhood of the first grid cell Local stress in each mesh element The index of the grid cell within the neighborhood. This represents the total number of grid cells in the neighborhood. This refers to the index of the mesh element in the model. In the model, the first The standard deviation of local stress in each grid cell;

[0105] A discriminant index function is constructed based on the calculated mean and standard deviation of local stress, and a stress disorder threshold is established. This discriminant index function is then used to distinguish between disordered and non-disordered reinforcement regions in the model. The formula used is as follows:

[0106]

[0107] in, In the model, the first Stress disorder value of each mesh element , These are the weighting coefficients, and ;

[0108] The stress disorder value obtained by calculating the discriminant index function Compared with the preset stress disturbance threshold Compare and statistically analyze all The mesh elements are marked as areas of disordered reinforcement; all The grid cells are labeled as reinforced non-disordered regions. In the formula for constructing the discriminant index function, the mean stress reflects the average stress intensity within a grid cell and its neighborhood, serving as a fundamental quantity for measuring the overall stress level of the region. A higher mean stress usually indicates that the region bears a larger load and that the internal forces of the structure are more concentrated. The standard deviation of stress reflects the variability or non-uniformity of stress within the grid neighborhood, reflecting the "disorder" or "fluctuation" characteristics of the stress distribution. A high standard deviation indicates that the stress in the region changes drastically, with a large stress gradient or stress concentration, which may lead to cracks or localized damage. It is an important indicator for assessing the potential weaknesses of the structure. Furthermore, the formula introduces weighting coefficients to weight the mean stress and standard deviation, and the design follows... The principle indicates that the mean stress has a higher weight in determining the importance of a region, while also taking into account the influence of stress fluctuations.

[0109] Step 2: For the non-disordered reinforcement region in the π-shaped slab, construct a plane section strain distribution model using the plane section assumption principle and the internal force balance principle, and calculate the reinforcement area in the non-disordered reinforcement region based on the established plane section strain distribution model.

[0110] In a specific embodiment of the present invention, based on the classical plane section assumption theory, the strain distribution of the π-shaped plate section under bending state is simplified to a linear change along the section height. By determining the position of the neutral axis of the section, the strain-stress conversion of concrete and steel reinforcement is realized. Specifically, the local stress is calculated using the actual constitutive relationship of concrete and steel reinforcement. Combined with the balance equation of axial force and bending moment, the height of the neutral axis is iteratively adjusted to ensure the balance of internal forces and deformation coordination of the section. Combined with the axial force and bending moment output by the finite element simulation, the distribution of internal forces and reinforcement area of ​​the section are solved by mathematical iteration method.

[0111] Furthermore, the method used to construct the plane section strain distribution model is as follows:

[0112] Based on the constructed three-dimensional finite element model of the π-shaped plate, the cross-sectional geometric parameters of the π-shaped plate are determined. Assuming the cross-section is under bending, the neutral axis of the π-shaped plate is defined as a distance measured from the edge of the compression side towards the height of the cross-section, representing the location of the cross-section where the strain is zero. The ultimate compressive strain of the top surface of the concrete is obtained. Then, using the principle of plane section strain distribution assumption, the strain is linearly distributed along the cross-sectional height. The strain of the tie rod at any point on the cross-section is:

[0113]

[0114] in, Indicates the position at the height of the π-shaped plate section. The strain value of the reinforcing steel at the point of contact with the compression edge, i.e., the cross-section at the distance from the compression edge. The strain value at the location, This represents the ultimate compressive strain value at the top surface of the concrete, typically taken as 0.003 in design. This is the vertical distance from the location of the reinforcing bar to the compression edge of the cross-section. It is the height of the neutral axis of the π-shaped plate, which divides the cross-section into a compression zone and a tension zone;

[0115] Based on the stress-strain relationship between concrete and reinforcing steel, the stress in the reinforcing steel is calculated according to its strain, using the following formula:

[0116]

[0117] in, Indicates the position at the height of the π-shaped plate section. The stress value borne by the reinforcing steel at that location. This refers to the elastic modulus of the reinforcing steel. The yield strength of the steel reinforcement represents the stress value at which the steel reinforcement begins to yield. It is a sign function used to determine the direction of stress in steel reinforcement. This represents the yield strain of the steel reinforcement, corresponding to the strain value at the yield strength of the steel reinforcement.

[0118] Similarly, based on the principle of plane section strain distribution assumption, the position at the height of the π-shaped plate section is first obtained. To calculate the concrete stress at the point of concrete strain, the actual constitutive relationship between the concrete and the reinforcing steel is used. The formula used is:

[0119]

[0120] in, Indicates the position at the height of the π-shaped plate section. The stress value borne by the concrete at that point, This refers to the axial compressive strength of concrete. This represents the peak strain of the concrete. Indicates the position at the height of the π-shaped plate section. The strain value of the concrete at that location. This is the exponent, which is usually 2.

[0121] It should be noted that by considering the force contributions of different areas of concrete and steel reinforcement, the internal force distribution of the compression and tension parts of the section is completely described. Furthermore, axial force and bending moment data under actual load can be obtained through finite element analysis software. The position of the neutral axis is adjusted by mathematical iteration to ensure the balance of internal forces and the consistency of deformation of the section, thereby achieving accurate calculation of the reinforcement area.

[0122] Furthermore, the reinforcement area in the non-disordered reinforcement region is calculated based on the constructed plane section strain distribution model. The method used is as follows:

[0123] After applying the simulated load, the axial force and bending moment of the π-shaped plate section are output using finite element analysis software. Based on the principle of axial force balance and bending moment balance in internal force equilibrium, the area of ​​the compression reinforcement and the area of ​​the tension reinforcement are calculated and summarized to obtain the reinforcement area in the non-disordered reinforcement region. The formula used is as follows:

[0124]

[0125]

[0126] in, This represents the axial force experienced by the π-shaped plate section under simulated load. This represents the bending moment experienced by the π-shaped plate section under simulated load. This represents the resultant force of the concrete in the compression zone of the cross section. This indicates the pressure exerted by the reinforcing steel bars located in the compression zone of the cross section. This indicates the tensile force generated by the reinforcing steel located in the tensile zone of the cross-section. The width of the π-shaped plate cross-section is... For the area of ​​the reinforcing rib, For the area of ​​the reinforcing bar, The stress generated by the strain of the reinforcing steel in the compression zone. The stress generated by the strain in the reinforcing steel in the tensile zone. This is the distance from the point of application of the resultant force in the concrete to the edge under compression. This is the distance from the point of application of the resultant force of the reinforcing steel in the compression zone to the compression edge. This is the distance from the point of application of the resultant force of the reinforcing steel in the tensile zone to the compression edge;

[0127] Based on a plane section strain distribution model with axial force and bending moment as inputs and tension and compression reinforcement areas as outputs, and considering the neutral axis height, the model checks whether the axial force and bending moment equilibrium equations are satisfied. If not, adjustments are made. Repeat the calculation and iterative solution until equilibrium is reached. Once it is confirmed that the strain of the steel reinforcement meets the minimum design strain requirement, the sum of the area of ​​the tension reinforcement and the area of ​​the compression reinforcement is the reinforcement area in the non-disordered reinforcement region. .

[0128] Step 3: Based on the principle of chloride ion migration and diffusion, a dynamic steel corrosion model is comprehensively constructed in the reinforcement disorder area. A corrosion compensation equation is established for the thickness of the steel protective layer and the steel diameter. The dynamic steel corrosion model is compensated based on the modified equation. The reinforcement area in the reinforcement disorder area is calculated using the compensated dynamic steel corrosion model.

[0129] In a specific embodiment of the present invention, a dynamic steel reinforcement corrosion model under time variables is constructed based on the chloride ion migration and diffusion mechanism and corrosion kinetics. This model can accurately reflect the gradual decrease of the cross-sectional area of ​​the steel reinforcement over time, and reflect the true situation of corrosion development of the steel reinforcement during its service life. The purpose of this approach is that the disordered reinforcement area of ​​the π-shaped slab is affected by environmental loads and chemical erosion, which leads to significant changes in the thickness of the protective layer and the diameter of the steel reinforcement in the disordered reinforcement area, and directly affects the chloride ion diffusion path and corrosion rate. Therefore, using Fick's second law to describe chloride ion diffusion is a widely accepted concrete corrosion mechanism model that can scientifically predict the diffusion behavior of chloride ions based on environmental and material parameters, and fundamentally reflect the initiation time and development law of steel reinforcement corrosion.

[0130] Furthermore, a dynamic steel corrosion model was comprehensively constructed in the disordered reinforcement region based on the principle of chloride ion migration and diffusion. The method used was as follows:

[0131] To simulate the migration process of chloride ions in concrete within the disordered reinforcement region, a mathematical model of chloride ion diffusion is established using Fick's second law. This model assumes that chloride ions mainly migrate from the surface to the interior along the concrete thickness direction via diffusion, and that the diffusion process is controlled by the diffusion coefficient of the concrete material. Its basic differential equation is:

[0132]

[0133] in, Indicates in At any given time, the depth from the concrete surface is Chloride ion concentration at the location, The chloride ion diffusion coefficient of concrete is given. Let be the partial derivative of chloride ion concentration with respect to time, representing the concentration at a fixed position. The rate of change of chloride ion concentration at a given location over time. Chloride ion concentration versus spatial position The second partial derivative at a point represents the curvature of the concentration along the depth direction, i.e., the rate of change of the concentration gradient.

[0134] Assume the chloride ion concentration on the concrete surface is . ,Right now Furthermore, the concrete initially does not contain chloride ions, i.e. Therefore, the corrosion initiation time of the reinforcing steel. Defined as such At the time of its establishment, among which The critical chloride ion concentration for corrosion. The thickness of the concrete cover for the reinforcing steel is given, and the initial radius of the reinforcing steel is obtained. A dynamic model of steel corrosion is constructed by combining the mathematical model of chloride ion diffusion. The formula used is as follows:

[0135]

[0136]

[0137]

[0138] in, Indicates that the reinforcing steel is in The corrosion rate at time t, The current time is the time variable of the corrosion process. This is the corrosion initiation time. The corrosion rate coefficient is... The corrosion sensitivity index is used to represent the nonlinear effect of chloride ion concentration on the corrosion rate. Indicates that the reinforcing steel is in The radius at time t, Let be the initial radius of the reinforcing bar. Indicates that the reinforcing steel is in The cross-sectional area at time t.

[0139] It should be noted that the reason for compensating and correcting the constructed dynamic steel corrosion model is that the greater the thickness of the protective layer of the steel, the longer the distance for chloride ions to diffuse to the surface of the steel, the later the corrosion initiation time, and the relatively lower the corrosion rate. When the protective layer is thinner, chloride ions can reach the surface of the steel more easily and quickly, and the degree of corrosion is aggravated. Secondly, the change in the diameter of the steel will change the ratio of the surface area to the cross-sectional area of ​​the steel, thereby affecting the cross-sectional area loss rate caused by corrosion. Thinner steel bars have more obvious cross-sectional loss under the same corrosion rate, affecting the structural bearing capacity. Therefore, a corrosion compensation equation is constructed to compensate and correct the model.

[0140] The specific mechanism for model compensation correction based on the compensation factor is as follows: the protective layer thickness ratio term in the corrosion compensation equation... In the case of actual protective layer thickness Below standard design value When this ratio is greater than 1, the corrosion rate is further amplified, indicating that chloride ions are more likely to corrode steel bars. The sensitivity of the corrosion rate to changes in protective layer thickness was controlled; in the steel bar diameter ratio item In the middle, the diameter of the reinforcing bar Compared with standard diameter The ratio adjusts the corrosion rate, reflecting the differences in corrosion response of steel bars of different diameters under the same corrosive environment. The influence of adjusting the diameter of the reinforcing steel on the corrosion rate; obtaining empirical coefficients through experimental calibration. , The specific method is as follows: Corrosion rate data are collected under different protective layer thicknesses and rebar diameters through accelerated corrosion tests or natural exposure tests. The measured corrosion rates are compared with model predictions, and the optimal corrosion rate is determined using the least squares method. and value.

[0141] Furthermore, a corrosion compensation equation for the thickness of the concrete cover and the diameter of the reinforcing bar is established. Based on this modified equation, the dynamic reinforcing bar corrosion model is compensated using the following method:

[0142] To address the impact of the non-uniformity of the concrete cover thickness and rebar diameter on the corrosion rate in areas of disordered reinforcement, a compensation factor is introduced to establish a corrosion compensation equation based on the concrete cover thickness and rebar diameter. The formula used is as follows:

[0143]

[0144] in, Indicates the corrosion compensation factor. , These are the standard design protective layer thickness and rebar diameter, , This is an empirical coefficient. The diameter of the reinforcing bar is, and ;

[0145] The dynamic steel reinforcement corrosion model is compensated based on the established corrosion compensation equation, and the formula used is as follows:

[0146]

[0147]

[0148]

[0149] in, , , These represent the corrosion correction rate, the reinforcement correction radius, and the reinforcement correction cross-sectional area after compensation, respectively.

[0150] Furthermore, the reinforced area in the disordered reinforcement region was calculated using the compensated dynamic steel corrosion model, based on the following method:

[0151] Count the number of mesh elements in areas with disordered reinforcement. Assuming the concrete cover thickness, rebar diameter, and corrosion initiation time are uniform within each grid cell, and calculating the theoretical rebar quantity for each grid cell, the reinforcement area within each grid cell is:

[0152]

[0153] in, Indicates in In the disordered reinforcement area within a certain time period, the first The reinforcement area of ​​each grid cell Indicates the first in the area of ​​disordered reinforcement The number of steel bars in each grid cell. Indicates the first in the area of ​​disordered reinforcement In each grid cell, a single reinforcing bar... Corrosion correction cross-sectional area at time t, This is the index of the mesh element in the disordered reinforcement region, and ;

[0154] The total reinforcement area of ​​the disordered reinforcement region is obtained by summing the reinforcement areas of each grid element within the disordered reinforcement region, based on the following formula:

[0155]

[0156] in, Indicates in The area of ​​reinforcement in the disordered reinforcement zone within a given time period.

[0157] Step 4: Based on the life-cycle durability constraint optimization principle, construct a multi-objective optimization function to optimize the reinforcement area in the disordered reinforcement region, so as to determine the optimal reinforcement area in the disordered reinforcement region. Summarize the reinforcement areas of the π-shaped slab to be manufactured to obtain the optimal reinforcement area of ​​the π-shaped slab to be manufactured.

[0158] In a specific embodiment of the present invention, since the π-shaped slab of the port terminal is an important load-bearing component, its use environment is complex and its maintenance cost is high. In order to extend the service life of the structure and control the cost, the design must comprehensively consider durability and reinforcement cost. Both are indispensable. Moreover, there are problems such as uneven reinforcement arrangement and high corrosion risk in the disordered reinforcement area. If the reinforcement area is blindly increased during the design, it will cause waste. If it is too low, it will affect the safety performance. A multi-objective optimization method is adopted to achieve precise configuration of reinforcement area, thereby improving structural performance and economic benefits.

[0159] It should be noted that the multi-objective optimization function is a weighted combination of the structural life function and the reinforcement cost function of the steel reinforcement. The structural life function is defined as the time it takes for the ultimate bearing capacity of the structure to decrease to the design requirement ultimate bearing capacity. Therefore, the structural life function needs to satisfy the maximum time under the condition that the ultimate bearing capacity is equal to the design requirement. The corresponding life time can be solved by numerical methods using a corrosion kinetic model and combining the relationship between bearing capacity and time. The reinforcement cost function is represented by the product of the reinforcement area and the reinforcement cost per unit area. That is, the total reinforcement cost is equal to the cost per unit reinforcement area multiplied by the sum of the initial reinforcement area and the initial area of ​​the reinforcement disordered region, thus reflecting the economic input under different reinforcement configuration schemes.

[0160] Furthermore, based on the life-cycle durability constraint optimization principle, a multi-objective optimization function is constructed to optimize the reinforcement area in the disordered reinforcement region to determine the optimal reinforcement area for the π-shaped slab to be manufactured. The method used is as follows:

[0161] Based on the life-cycle durability constraint optimization principle, the initial reinforcement area configuration of the disordered reinforcement region is determined. The reinforcement areas in both the disordered and non-disordered reinforcement regions are summarized as variables to be optimized. A multi-objective optimization function is constructed by combining the structural remaining durability life function and the reinforcement cost function, ensuring that the structure meets the ultimate bearing capacity within the target life and that the initial reinforcement area of ​​the disordered reinforcement region is greater than or equal to its minimum value specified in the code. The formula on which the multi-objective optimization function is constructed is as follows:

[0162]

[0163]

[0164]

[0165] in, This represents the objective function value, used to minimize the weighted sum of lifetime and cost. , These represent the lifespan weighting coefficient and the cost weighting coefficient, respectively. It is the expected lifespan of the structure. Cost per unit area of ​​reinforcement This represents the initial reinforcement area for the disordered reinforcement region. Indicates the structural bearing capacity at the end of its lifespan. The minimum ultimate bearing capacity required by the design. This represents the minimum standard value for the reinforcement area in areas with disordered reinforcement.

[0166] The specific optimization process is as follows: Initialize the initial reinforcement area of ​​the disordered reinforcement region and summarize it with the reinforcement area of ​​the non-disordered reinforcement region; calculate the expected life of the structure and the structural bearing capacity at the end of the life; adjust the initial reinforcement area of ​​the disordered reinforcement region based on the constraints to minimize the objective function value; finally, output the optimal reinforcement area of ​​the disordered reinforcement region and the optimal reinforcement area of ​​the π-shaped plate, based on the following formula:

[0167]

[0168] in, This represents the optimal reinforcement area for a π-shaped slab. This represents the optimal reinforcement area for areas with disordered reinforcement.

[0169] Please see Figure 2 The present invention also provides a reinforcement system for precast π-shaped slabs at wharves, the reinforcement system being used to perform the above-described reinforcement method for precast π-shaped slabs at wharves, comprising:

[0170] The reinforcement area discrimination module is used to obtain the geometric and material parameters of the π-shaped plate to be manufactured, perform finite element modeling of the π-shaped plate based on finite element analysis software, apply simulated load to the constructed three-dimensional finite element model of the π-shaped plate, and establish discrimination index function based on stress distribution to determine the disordered reinforcement area and the non-disordered reinforcement area in the π-shaped plate to be manufactured.

[0171] The module for calculating the reinforcement area in the non-disordered region is used to construct a plane section strain distribution model for the non-disordered reinforcement area in a π-shaped slab using the plane section assumption principle and the internal force balance principle. Based on the established plane section strain distribution model, the reinforcement area in the non-disordered reinforcement area is calculated.

[0172] The module for calculating the reinforcement area in disordered regions constructs a dynamic steel corrosion model in disordered reinforcement regions based on the principle of chloride ion migration and diffusion. It establishes a corrosion compensation equation for the thickness of the steel protective layer and the diameter of the steel bar, compensates the dynamic steel corrosion model based on the modified equation, and uses the compensated dynamic steel corrosion model to calculate the reinforcement area in disordered reinforcement regions.

[0173] The optimal reinforcement area determination module constructs a multi-objective optimization function based on the life-cycle durability constraint optimization principle to optimize the reinforcement area in the disordered reinforcement region, so as to determine the optimal reinforcement area in the disordered reinforcement region. The reinforcement areas of the π-shaped slab to be manufactured are summarized to obtain the optimal reinforcement area of ​​the π-shaped slab to be manufactured.

[0174] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0175] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0176] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0177] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for reinforcing precast π-shaped slabs for wharves, characterized in that, The specific steps include: Step 1: Obtain the geometric and material parameters of the π-shaped plate to be manufactured, perform finite element modeling of the π-shaped plate based on finite element analysis software, apply simulated loads to the constructed 3D finite element model of the π-shaped plate, and establish a discrimination index function based on the stress distribution to determine the disordered reinforcement region and the non-disordered reinforcement region in the π-shaped plate to be manufactured. Step 2: For the non-disordered reinforcement region in the π-shaped slab, construct the plane section strain distribution model using the plane section assumption principle and the internal force equilibrium principle, and calculate the reinforcement area in the non-disordered reinforcement region based on the established plane section strain distribution model; Step 3: Based on the principle of chloride ion migration and diffusion, a dynamic steel corrosion model is comprehensively constructed in the reinforcement disorder area. A corrosion compensation equation for the thickness of the steel protective layer and the steel diameter is established. The dynamic steel corrosion model is compensated based on the modified equation. The reinforcement area in the reinforcement disorder area is calculated using the compensated dynamic steel corrosion model. Step 4: Based on the life-cycle durability constraint optimization principle, construct a multi-objective optimization function to optimize the reinforcement area in the disordered reinforcement region, so as to determine the optimal reinforcement area in the disordered reinforcement region. Summarize the reinforcement areas of the π-shaped slab to be manufactured to obtain the optimal reinforcement area of ​​the π-shaped slab to be manufactured. A dynamic steel corrosion model is comprehensively constructed in the disordered reinforcement region based on the principle of chloride ion migration and diffusion. The method used is as follows: In order to simulate the migration process of chloride ions in concrete in the disordered reinforcement area, a mathematical model of chloride ion diffusion is established using Fick's second law. This model assumes that chloride ions migrate from the surface to the interior along the thickness direction of concrete by diffusion. The diffusion process is controlled by the diffusion coefficient of concrete material. A basic differential equation is established to describe the migration mode of chloride ions. Assume the chloride ion concentration on the concrete surface is . ,Right now Furthermore, the concrete initially does not contain chloride ions, i.e. Therefore, the corrosion initiation time of the reinforcing steel. Defined as such At the time of its establishment, among which The critical chloride ion concentration for corrosion. The thickness of the concrete cover for the reinforcing bars is determined, and the initial radius of the reinforcing bars is obtained. A dynamic model of reinforcing bar corrosion is then constructed by combining the mathematical model of chloride ion diffusion. A corrosion compensation equation was established for the thickness of the concrete cover and the diameter of the reinforcing bars. Based on this modified equation, a dynamic reinforcing bar corrosion model was compensated. The compensated dynamic reinforcing bar corrosion model was then used to calculate the reinforcement area in the disordered reinforcement region. The method used was as follows: To address the impact of the non-uniformity of the concrete cover thickness and rebar diameter on the corrosion rate in areas with disordered reinforcement, a compensation factor is introduced to establish a corrosion compensation equation for the concrete cover thickness and rebar diameter. The dynamic steel corrosion model is compensated based on the established corrosion compensation equation to obtain the corrosion correction rate, steel correction radius and steel correction cross-sectional area after compensation. Count the number of mesh elements in areas with disordered reinforcement. Assuming that the thickness of the concrete cover, the diameter of the steel bars, and the corrosion initiation time are uniform in each grid cell, the theoretical number of steel bars is counted for each grid cell, and the reinforcement area in each grid cell is calculated. The reinforcement areas of each grid cell within the disordered reinforcement region are summed to obtain the total reinforcement area of ​​the disordered reinforcement region.

2. The reinforcement method for precast π-shaped slabs at a wharf according to claim 1, characterized in that, The finite element modeling of the π-shaped plate was performed using finite element analysis software, and the method used was as follows: Obtain the geometric and material parameters of the π-shaped plate. The geometric parameters include the plate width, total height, total length, flange thickness, and web thickness. The material parameters include the elastic modulus, Poisson's ratio, and compressive strength. First, draw the two-dimensional cross-sectional profile of the π-shaped plate in the finite element analysis software, including the shape of the flange and web. Then, stretch it along the length to form a three-dimensional solid. Mesh the three-dimensional solid of the π-shaped plate. Discretize the concrete using three-dimensional eight-node linear solid elements. Locally refine the mesh at the flange-web connection, edge, and support area. The mesh size should be selected to balance computational efficiency and accuracy requirements, and controlled to be between one-fifth and one-tenth of the plate thickness. Boundary conditions were set for the three-dimensional geometric model of the π-shaped plate after meshing. The bottom of the flange and the bottom of the web of the π-shaped plate, which are in contact with the foundation, were selected as the supports of the π-shaped plate. All nodes in the contact surface at the supports were selected and their degrees of freedom were constrained. Specifically, in the finite element software, "displacement constraints" were applied to the support nodes to fix the vertical displacement while keeping the translational and rotational degrees of freedom free. Spring elements were connected between the support nodes and the reference point, and the spring stiffness was defined according to the design support stiffness parameters to complete the construction of the three-dimensional finite element model of the π-shaped plate.

3. The reinforcement method for precast π-shaped slabs at a wharf according to claim 2, characterized in that, Simulated loads were applied to the three-dimensional finite element model of the π-shaped plate. Based on the stress distribution, a discriminant index function was established to determine the disordered and non-disordered reinforcement regions in the π-shaped plate to be manufactured. The method used was as follows: The simulated load applied to the three-dimensional finite element model of the π-shaped plate consists of the self-weight load of the π-shaped plate and the water pressure of the environment in which the π-shaped plate is located. First, the material density is input into the finite element analysis software, and the vertical downward direction is specified as the direction of gravitational acceleration. The finite element analysis software automatically calculates the volume force based on the model volume to realize the self-weight load. For the π-shaped plate of the wharf, its water pressure is a lateral uniform pressure that varies linearly with the water depth. The application method is surface pressure, and the direction is perpendicular to the water receiving surface. The application of non-uniform water pressure is realized by defining a function of water pressure changing with depth. For each mesh element in the 3D finite element model of the π-shaped plate, the average side length of all mesh elements in the model is calculated. A neighborhood radius of 2 to 3 times the average side length of the mesh elements is used as the neighborhood radius of each mesh element. With the geometric center point of each mesh element as the center, all mesh elements within this radius are automatically searched and included in the neighborhood calculation. Based on the defined neighborhood radius of each grid cell, and combined with the known simulated load applied by the finite element analysis software, the local stress of each grid cell is obtained. The mean and standard deviation of the local stress are calculated within the neighborhood of the grid cell to reflect the stress level and the degree of stress variation in the region. A discriminant index function is constructed based on the calculated mean and standard deviation of local stress, and a stress disorder threshold is set. The discriminant index function is used to distinguish between disordered and non-disordered reinforcement regions in the model. The stress disorder value calculated by the discrimination index function is compared with the preset stress disorder threshold. All mesh elements whose stress disorder value exceeds the threshold are counted and marked as reinforcement disorder areas. All mesh elements whose stress disorder values ​​do not exceed the threshold are statistically analyzed and marked as reinforced non-disordered regions.

4. The reinforcement method for precast π-shaped slabs at a wharf according to claim 3, characterized in that, The method used to construct the plane section strain distribution model is as follows: Based on the constructed three-dimensional finite element model of the π-shaped plate, the cross-sectional geometric parameters of the π-shaped plate are determined. When the cross-section is subjected to bending, the neutral axis of the π-shaped plate is defined as a distance measured from the edge of the compression side towards the height of the cross-section, representing the cross-sectional position where the strain is zero. The ultimate compressive strain of the top surface of the concrete is obtained. Then, using the principle of plane section strain distribution assumption, the strain is linearly distributed along the height of the cross-section, and the strain of the tie rod at any point of the height of the π-shaped plate cross-section is calculated. Based on the stress-strain relationship between concrete and steel reinforcement, the stress in the steel reinforcement is calculated based on the strain of the steel reinforcement. Similarly, based on the principle of plane section strain distribution assumption, the position at the height of the π-shaped plate section is first obtained. The concrete strain is determined by using the actual constitutive relationship between the concrete and the reinforcing steel to calculate the concrete stress.

5. The reinforcement method for precast π-shaped slabs at a wharf according to claim 4, characterized in that, The method used to calculate the reinforcement area in the non-disordered region of the reinforcement based on the constructed plane section strain distribution model is as follows: After applying the simulated load, the axial force and bending moment of the π-shaped plate section are output by the finite element analysis software. Based on the axial force balance and bending moment balance in the internal force balance principle, the area of ​​the compression reinforcement and the area of ​​the tension reinforcement are calculated and summarized to obtain the reinforcement area in the non-disordered reinforcement area. Based on a plane section strain distribution model with axial force and bending moment as inputs and tension and compression reinforcement areas as outputs, and considering the neutral axis height, the model checks whether the axial force and bending moment equilibrium equations are satisfied. If not, adjustments are made. Repeat the calculation and iterative solution until equilibrium is reached, confirming that the strain of the steel reinforcement meets the minimum design strain requirement. Then, the sum of the area of ​​the tension reinforcement and the area of ​​the compression reinforcement is the reinforcement area in the non-disordered reinforcement region. .

6. The reinforcement method for precast π-shaped slabs at a wharf according to claim 5, characterized in that, Based on the life-cycle durability constraint optimization principle, a multi-objective optimization function is constructed to optimize the reinforcement area in the disordered reinforcement region, in order to determine the optimal reinforcement area of ​​the π-shaped slab to be manufactured. The method used is as follows: Based on the life-cycle durability constraint optimization principle, the initial reinforcement area configuration of the disordered reinforcement region is determined. The reinforcement areas in the disordered and non-disordered reinforcement regions are summarized as variables to be optimized. A multi-objective optimization function is constructed by combining the structural remaining durability life function and the reinforcement cost function. It is ensured that the structure meets the ultimate bearing capacity within the target life and that the initial reinforcement area of ​​the disordered reinforcement region is greater than or equal to its minimum value specified in the code. The multi-objective optimization function is constructed to optimize the reinforcement area of ​​the disordered reinforcement region. The specific optimization process is as follows: Initialize the initial reinforcement area of ​​the disordered reinforcement region and summarize it with the reinforcement area of ​​the non-disordered reinforcement region. Calculate the expected life of the structure and the structural bearing capacity at the end of the life. Adjust the initial reinforcement area of ​​the disordered reinforcement region based on the constraints to minimize the objective function value. Finally, output the optimal reinforcement area of ​​the disordered reinforcement region and the optimal reinforcement area of ​​the π-shaped plate.

7. A reinforcement system for precast π-shaped slabs at a wharf, characterized in that, The reinforcement system is used to perform the reinforcement method for precast π-shaped slabs at the wharf as described in any one of claims 1-6, including: The reinforcement area discrimination module is used to obtain the geometric and material parameters of the π-shaped plate to be manufactured, perform finite element modeling of the π-shaped plate based on finite element analysis software, apply simulated load to the constructed three-dimensional finite element model of the π-shaped plate, and establish discrimination index function based on stress distribution to determine the disordered reinforcement area and the non-disordered reinforcement area in the π-shaped plate to be manufactured. The module for calculating the reinforcement area in the non-disordered region is used to construct a plane section strain distribution model for the non-disordered reinforcement area in a π-shaped slab using the plane section assumption principle and the internal force balance principle. Based on the established plane section strain distribution model, the reinforcement area in the non-disordered reinforcement area is calculated. The module for calculating the reinforcement area in disordered regions constructs a dynamic steel corrosion model in disordered reinforcement regions based on the principle of chloride ion migration and diffusion. It establishes a corrosion compensation equation for the thickness of the steel protective layer and the diameter of the steel bar, compensates the dynamic steel corrosion model based on the modified equation, and uses the compensated dynamic steel corrosion model to calculate the reinforcement area in disordered reinforcement regions. The optimal reinforcement area determination module constructs a multi-objective optimization function based on the life-cycle durability constraint optimization principle to optimize the reinforcement area in the disordered reinforcement region, so as to determine the optimal reinforcement area in the disordered reinforcement region. The reinforcement areas of the π-shaped slab to be manufactured are summarized to obtain the optimal reinforcement area of ​​the π-shaped slab to be manufactured.

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