Gate pier ultimate bearing capacity determination method and system based on finite element analysis

Abstract

The application provides a kind of gate pier ultimate bearing capacity determination method and system based on finite element analysis, it is related to ultimate bearing capacity analysis technical field, the application includes: establishing gate pier three-dimensional finite element model and defining material constitutive model and boundary condition;Obtain historical extreme load event sequence, sequentially applied to model according to time sequence, update state field variable by nonlinear finite element analysis, simulate cumulative damage;Lock state field variable, obtain damaged finite element model;Potential limit working condition load is applied on the damage model, nonlinear analysis is carried out by using incremental loading method, until the structure is unstable, the previous convergence step load value is used as real-time ultimate bearing capacity;Real-time bearing capacity is compared with design reference bearing capacity, bearing capacity degradation rate is calculated, historical degradation trajectory is constructed, degradation trend is fitted, safety evaluation and decision are carried out in combination with safety threshold.The application realizes the accurate evaluation and early warning of gate pier bearing capacity considering historical damage.

Description

Technical Field

[0001] This invention relates to the field of ultimate bearing capacity analysis technology, specifically to a method and system for determining the ultimate bearing capacity of gate piers based on finite element analysis. Background Technology

[0002] As a key structure in water conservancy projects for regulating water flow and ensuring flood control safety, the structural reliability of hydraulic gates is of paramount importance. Gate piers are the core load-bearing components supporting the gate and transmitting the entire water load. During long-term service, they repeatedly endure high hydrostatic pressure, pulsating loads, and enormous support reactions transmitted by the gate under extreme flood discharge conditions. Although these historical extreme load events are short-lived, they can induce microcracks within the concrete material, leading to irreversible stiffness degradation and plastic deformation. The cumulative effect of this damage significantly weakens the actual ultimate bearing capacity of the gate piers, posing a potential threat to their long-term safety.

[0003] In current technical practices, the safety assessment of gate piers largely relies on design code calculations based on the intact structural state or conventional finite element analysis. These methods typically only verify a single design condition, generally ignoring the cumulative damage caused by historical load sequences. In other words, traditional methods treat a damaged structure that has undergone years of flood discharge fatigue as a brand-new, intact structure for load-bearing capacity assessment. This simplistic approach fails to reflect time-varying effects such as material stiffness degradation and residual stress, leading to overly optimistic assessment results that fail to accurately reflect the real-time safety status of the structure throughout its life cycle, thus creating potential safety hazards for the project. Therefore, there is an urgent need in this field for a refined assessment method that can quantify the cumulative damage from historical loads and accurately calculate the real-time ultimate bearing capacity of damaged gate piers. This method aims to overcome the two major technical bottlenecks of traditional assessments—ignoring damage history and calculating failure at limit points—and provide a scientific basis for the safe operation and maintenance and decision-making of hydraulic structures.

[0004] 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

[0005] The purpose of this invention is to provide a method and system for determining the ultimate bearing capacity of gate piers based on finite element analysis, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for determining the ultimate bearing capacity of a gate pier based on finite element analysis, comprising the following steps:

[0008] Step 1: Based on the structural drawings of the gate pier, establish its three-dimensional finite element model and define the material constitutive model and boundary conditions;

[0009] Step 2: Obtain the sequence of historical extreme load events experienced by the gate pier during the target time period; apply each historical extreme load event to the three-dimensional finite element model in chronological order, and iteratively update the state field variables of the three-dimensional finite element model through nonlinear finite element analysis.

[0010] Step 3: After simulating all historical extreme load event sequences, lock all state field variables in the finite element model to obtain a damaged finite element model that reflects the current damage state of the gate pier.

[0011] Step 4: Apply the load of the potential ultimate condition to the damaged finite element model and perform nonlinear finite element analysis using the incremental loading method until the model no longer converges due to structural instability. Then, determine the load value corresponding to the previous incremental step as the real-time ultimate bearing capacity of the gate pier under the current damage state.

[0012] Step 5: Compare the real-time ultimate bearing capacity with the design reference bearing capacity of the gate pier to obtain the current bearing capacity degradation rate of the gate pier; calculate the bearing capacity degradation rate of the gate pier after each historical extreme load event simulation, form a historical bearing capacity degradation trajectory in chronological order, and perform fitting analysis on the relationship between the bearing capacity degradation rate and time, so as to conduct a safety assessment of the gate pier based on the current and predicted bearing capacity degradation rates.

[0013] Furthermore, the definition of the material constitutive model and boundary conditions specifically includes:

[0014] In establishing the initial three-dimensional finite element model of the gate pier based on the structural drawings, a plastic damage model is used to define the nonlinear mechanical behavior of concrete material. The uniaxial stress-strain relationship under compressive and tensile conditions is analyzed, specifically including:

[0015] When the compressive strain of concrete is not greater than the ultimate compressive strain of concrete, the specific logic for obtaining the compressive stress of concrete under compression is as follows:

[0016] Based on the preset compressive damage factor, the difference between 1 and the compressive damage factor is used as the compressive influence coefficient to characterize the remaining effective integrity of the material; the product of the initial elastic modulus of concrete and the compressive strain of concrete is used as the theoretical parameter of compressive stress to characterize the theoretical elastic stress of concrete in the ideal linear elastic state; the product of the compressive influence coefficient and the theoretical parameter of compressive stress is used as the numerator, which characterizes the effective stress of concrete after compressive damage.

[0017] The ratio of the theoretical compressive stress parameter to the standard value of the uniaxial compressive strength of concrete is taken as the first influencing parameter. This first influencing parameter is a dimensionless ratio. The square term of the difference between it and 1 is analyzed to reflect the degree to which the material response deviates from the linear elastic behavior. The sum of 1 and this square term is used for normalization adjustment and is used as the denominator term.

[0018] The ratio of the numerator to the denominator is the compressive stress of the concrete.

[0019] When the tensile strain of concrete is not greater than the ultimate tensile strain of concrete, the specific logic for obtaining the tensile stress of concrete during tensile behavior is as follows:

[0020] Based on the preset tensile damage factor, the difference between 1 and the tensile damage factor is used as the tensile influence coefficient to characterize the degradation of the material's effective stiffness due to tensile damage; and the product of the initial elastic modulus of concrete and tensile strain is used as the theoretical parameter of tensile stress to characterize the theoretical elastic stress of concrete in the tensile direction.

[0021] The product of the tensile influence coefficient and the theoretical parameter of tensile stress is the tensile stress of concrete.

[0022] When defining boundary conditions, the connection section between the gate pier and the bottom plate is set as a fixed constraint to simulate the embedment effect of the foundation. At the same time, a coupling point is established downstream of the gate pier for subsequent application of concentrated force transmitted by the gate. The magnitude of the concentrated force is determined by inputting the characteristic water level into the gate stress calculation model.

[0023] Furthermore, obtaining the historical extreme load event sequence specifically includes:

[0024] The time interval from the time the gate pier was put into operation to the present time is defined as the target time period; relevant data of all load events experienced by the gate pier within the target time period are collected, and the load events include at least flood discharge and water blocking;

[0025] The relevant data includes at least characteristic water level data; characteristic water level data of the gate pier for each load event within the target time period is extracted, including at least the upstream water level process line, the downstream water level process line, and the gate opening and support reaction force determined therefrom; based on the relevant data, load events judged as historical extreme load events are selected from all load events according to the preset screening criteria; the screening criteria are: if the equivalent hydrostatic pressure load borne by the gate pier in a load event reaches or exceeds the preset threshold, then this load event is judged as a historical extreme load event;

[0026] The selected historical extreme load events are sorted in chronological order of occurrence to form a sequence of historical extreme load events.

[0027] For each historical extreme load event in the sequence, the hydrostatic pressure load intensity acting on the gate pier during that historical extreme load event is calculated based on its corresponding characteristic water level data. The specific logic is as follows:

[0028] The net head at point z is calculated by the difference between the upstream head and the downstream water level at height z; the product of the water density, gravitational acceleration and net head is the hydrostatic pressure load intensity at height z; z represents the coordinate value along the height of the gate pier.

[0029] At the same time, the distribution of uplift pressure and gate support reaction force corresponding to this historical extreme load event were determined;

[0030] The relevant data for each historical extreme load event should include at least its characteristic water level, the calculated hydrostatic pressure load intensity, the uplift pressure distribution, and the gate support reaction force.

[0031] Furthermore, applying loads to the initial three-dimensional finite element model specifically includes:

[0032] The relevant data of historical extreme load events are applied sequentially to the initial three-dimensional finite element model in chronological order, specifically including:

[0033] For the first historical extreme load event in the sequence, its corresponding hydrostatic load intensity distribution, uplift pressure distribution and gate support reaction force are applied to the initial three-dimensional finite element model to perform the first nonlinear static analysis.

[0034] After completing the nonlinear static analysis of the first historical extreme load event, the finite element model is updated to generate an updated finite element model. After each update, all external loads and constraints in the updated finite element model are reset to the initial state. This update is achieved by modifying the state field variables of all integration points in the initial three-dimensional finite element model to the results at the end of the analysis of the first historical extreme load event. The state field variables include at least the compressive damage factor and tensile damage factor of concrete, the plastic strain field of the material, and the stress field of the structure.

[0035] The next historical extreme load event is applied to the updated finite element model for a new round of nonlinear static analysis.

[0036] Repeat the above steps until all historical extreme load events in the historical extreme load event sequence have been simulated.

[0037] After simulating all historical extreme load events, the final updated finite element model state is defined as the damaged finite element model.

[0038] Furthermore, the incremental loading method specifically includes:

[0039] The load applied under the potential limit condition is as follows: On the upstream face of the gate pier with the damaged finite element model, a monotonically increasing hydrostatic pressure load is applied. This load is controlled by a load scaling factor. The magnitude of the hydrostatic pressure load intensity at this time is the product of the hydrostatic pressure load intensity at the corresponding height and the load scaling factor.

[0040] The nonlinear finite element analysis using the incremental loading method employs the arc length method for control. The key parameters are determined based on the current state of the damaged finite element model, including the initial arc length radius, scaling factor, and maximum allowable number of iterations.

[0041] When using the arc-length method for incremental loading, the equilibrium equation and constraint equation are solved simultaneously in each incremental step. The specific logic of the equilibrium equation is that the internal force vector of the damaged finite element model is equal to the currently applied external load vector. The internal force vector is a function of the displacement vector, representing the total resultant force generated inside the gate pier to resist the external force after the displacement deformation of the k-th incremental step. The external load vector applied in the k-th incremental step is the product of the preset reference load vector and the load scaling factor of the k-th incremental step, where k is the index of the incremental step.

[0042] The arc length constraint equation defines the geometric constraint relationship between the displacement increment and the load factor increment within the increment step. The first term is the sum of squares of the displacement increments in the k-th increment step, i.e., the square of the L2 norm of the displacement vector. The second term is a scalarized measure of the load increment in the k-th increment step. The third term is the square of the dynamic arc length radius in the k-th increment step. The sum of the first and second terms equals the third term, which is the geometric constraint relationship.

[0043] The second term is characterized by the product of three influencing parameters, which are the square of the load factor increment at the kth increment step, the square of the preset scaling factor, and the sum of the squares of the reference load vector, i.e., the square of the L2 norm of the reference load vector.

[0044] Furthermore, determining the current real-time ultimate bearing capacity specifically includes:

[0045] The criterion for determining whether the calculation will no longer converge due to structural instability is as follows: During the incremental loading process, when the finite element solver still cannot meet the preset residual capacity or displacement correction tolerance after the maximum allowable number of iterations, it is determined that the calculation will no longer converge. At this time, the load value corresponding to the last converged incremental step is determined as the real-time ultimate bearing capacity under the current damage state. That is, the product of the load scaling factor of the previous incremental step and the resultant force of the reference load vector when non-convergence occurs for the first time is the real-time ultimate bearing capacity under the current damage state.

[0046] Furthermore, the specific logic for calculating the bearing capacity degradation rate is as follows:

[0047] The ratio of the real-time ultimate bearing capacity under the current damage state to the design reference bearing capacity of the gate pier is used to characterize the current structural integrity of the gate pier. The percentage of the difference between 1 and this ratio is the bearing capacity degradation rate of the gate pier under the current damage state.

[0048] When simulating historical extreme load events, after each historical extreme load event simulation is completed, the same potential ultimate load is applied to the stage damage model obtained at that time point. The stage ultimate bearing capacity of the gate pier after the occurrence of the historical event is obtained by incremental loading method, and the corresponding stage bearing capacity degradation rate is calculated. The bearing capacity degradation rates of all historical nodes are connected in chronological order to construct the historical bearing capacity degradation trajectory of the gate pier.

[0049] Based on the historical bearing capacity degradation trajectory, a nonlinear regression method is used to fit the functional relationship between the degradation rate and time; using the fitted prediction function, the predicted bearing capacity degradation rate of the gate pier is predicted within the preset service period.

[0050] The preset safety thresholds include a first safety threshold and a second safety threshold. Both the first and second safety thresholds fall within the range of (0,1), and the second safety threshold is greater than the first safety threshold. The calculated bearing capacity degradation rate under the current damage state and the predicted bearing capacity degradation rate are compared with the safety thresholds to complete the safety status assessment and output an early warning signal. Specifically, this includes:

[0051] Based on the bearing capacity degradation rate under the current damage state of the gate pier, a preliminary warning signal is determined. The warning signals are classified into green warning, yellow warning and red warning according to the level from low to high. The gate pier status corresponding to each warning signal is good status, damaged status and unsafe status, respectively.

[0052] If the load-bearing capacity degradation rate under the current damage state is less than the first safety threshold, a green warning signal will be issued.

[0053] If the bearing capacity degradation rate under the current damage state is not less than the first safety threshold but less than the second safety threshold, a yellow warning signal will be issued.

[0054] If the load-bearing capacity degradation rate under the current damage state is not less than the second safety threshold, a red warning signal will be issued.

[0055] If the initially determined warning signal is not a red warning, the initially determined warning signal will be reviewed and corrected based on the predicted bearing capacity degradation rate to form the final warning signal:

[0056] If the predicted load-bearing capacity degradation rate is always less than the first safety threshold within the preset service period, the warning signal will not be modified.

[0057] If, within the preset service life, the predicted load-bearing capacity degradation rate is not less than the first safety threshold but less than the second safety threshold, the warning signal will be upgraded.

[0058] If the predicted load-bearing capacity degradation rate exceeds the second safety threshold within the preset service period, the warning signal will be directly upgraded to a red warning.

[0059] This invention also provides a system for determining the ultimate bearing capacity of gate piers based on finite element analysis. This system is used to implement the aforementioned method for determining the ultimate bearing capacity of gate piers based on finite element analysis, and includes:

[0060] The data acquisition and initial modeling module is used to establish a three-dimensional finite element model of the gate pier based on its structural drawings, and to define the material constitutive model and boundary conditions.

[0061] The cumulative damage simulation module is used to obtain the sequence of historical extreme load events experienced by the gate pier during the target time period; in chronological order, each historical extreme load event is applied to the three-dimensional finite element model, and the state field variables of the three-dimensional finite element model are iteratively updated through nonlinear finite element analysis.

[0062] The damage state solidification module is used to lock all state field variables in the finite element model after simulating all historical extreme load event sequences, so as to obtain a damaged finite element model that reflects the current damage state of the gate pier.

[0063] The real-time bearing capacity determination module is used to apply the load of the potential ultimate condition to the damaged finite element model and perform nonlinear finite element analysis using the incremental loading method until it no longer converges due to structural instability. The load value corresponding to the previous incremental step is then determined as the real-time ultimate bearing capacity of the gate pier under the current damage state.

[0064] The safety assessment and decision-making module is used to compare the real-time ultimate bearing capacity with the design reference bearing capacity of the gate pier to obtain the current bearing capacity degradation rate of the gate pier; calculate the bearing capacity degradation rate of the gate pier after each historical extreme load event simulation, form a historical bearing capacity degradation trajectory in chronological order, and perform fitting analysis on the relationship between the bearing capacity degradation rate and time, so as to conduct a safety assessment of the gate pier based on the current and predicted bearing capacity degradation rates.

[0065] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0066] This scheme employs nonlinear finite element simulation of historical extreme load events experienced by the gate pier during its service life, arranged in a time series. By utilizing the locking and transfer mechanism of state field variables, it numerically and accurately quantifies the cumulative damage and stiffness degradation of concrete materials, thus constructing a damaged finite element model that truly reflects the current health condition of the structure. This innovation transforms the assessment of ultimate bearing capacity from a traditional, idealized design state to a real-time state based on actual damage, fundamentally solving the technical bottleneck of traditional methods that neglect the influence of historical loads, leading to distorted assessment results. Based on this, by combining the arc-length controlled incremental loading method with static elastoplastic analysis of the damaged model, the scheme effectively overcomes the computational convergence problem near the ultimate state, successfully capturing the instability critical point and thus determining the true ultimate bearing capacity of the structure under its current damage state. Finally, by calculating the bearing capacity degradation rate of the gate pier, a quantitative early warning of structural performance degradation is achieved, providing crucial technical support for making accurate maintenance and reinforcement decisions and ensuring the long-term operational safety of hydraulic structures. Attached Figure Description

[0067] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0068] Figure 2 This is a schematic diagram of the historical and predicted bearing capacity degradation rate curves of this invention;

[0069] Figure 3 This is a schematic diagram of the system structure of the present invention. Detailed Implementation

[0070] 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.

[0071] 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.

[0072] Example:

[0073] Please see Figures 1 to 2 The present invention provides a technical solution:

[0074] A method for determining the ultimate bearing capacity of a gate pier based on finite element analysis, comprising the following steps:

[0075] Step 1: Based on the structural drawings of the gate pier, establish its three-dimensional finite element model and define the material constitutive model and boundary conditions.

[0076] In this embodiment, the definition of the material constitutive model and boundary conditions specifically includes:

[0077] The initial 3D finite element model of the gate is established as follows: Based on the structural drawings of the gate pier, key geometric parameters are extracted, including but not limited to the overall dimensions and outline shape of the gate pier, the detailed dimensions and location of the gate slot, and the connection structure between the gate pier and the base plate, to establish a 3D geometric model. 3D modeling software such as CATIA and SolidWorks are used here. During the modeling process, attention must be paid to the accurate reproduction of structural details, including but not limited to the pier outline, holes, chamfers, and embedded parts, to ensure that the model is consistent with the actual structure. Subsequently, the geometric model is imported into the finite element analysis software for mesh generation. To ensure computational accuracy and efficiency, hexahedral elements or higher-order tetrahedral elements are preferred for mesh generation. For stress concentration areas, such as the edges of the gate slot, the periphery of holes, and the connection with the base plate, local mesh refinement is required, with the mesh size preferably controlled within one-tenth to one-fifth of the minimum feature size of the area structure. This modeling strategy ensures that the model reflects the true geometry and captures the stress gradient changes in key areas.

[0078] In this embodiment, in establishing the initial three-dimensional finite element model of the gate pier based on the structural drawings of the gate pier, the concrete material adopts a plastic damage model to describe its nonlinear mechanical behavior. This model can simultaneously consider the stiffness degradation and damage evolution of concrete under compression and tension.

[0079] The uniaxial stress-strain relationship under compression and tension is analyzed separately, including:

[0080] When the compressive strain of concrete is not greater than the ultimate compressive strain of concrete, the specific logic for obtaining the compressive stress of concrete under compression is as follows:

[0081] Based on a preset compressive damage factor, the difference between 1 and the compressive damage factor is used as the compressive influence coefficient to characterize the remaining effective integrity of the material. The product of the initial elastic modulus of concrete and the compressive strain of concrete is used as the theoretical parameter of compressive stress to characterize the theoretical elastic stress of concrete in an ideal linear elastic state; the product of the compressive influence coefficient and the theoretical parameter of compressive stress is used as the numerator, which characterizes the effective stress of concrete after compressive damage.

[0082] The ratio of the theoretical compressive stress parameter to the standard value of the uniaxial compressive strength of concrete is taken as the first influencing parameter. This first influencing parameter is a dimensionless ratio. The square term of the difference between it and 1 is analyzed to reflect the degree to which the material response deviates from the linear elastic behavior. The sum of 1 and this square term is used for normalization adjustment and as the denominator term to reflect the degree of nonlinear response of the material.

[0083] The ratio of the numerator to the denominator is the compressive stress of the concrete.

[0084] The behavior under pressure can be expressed by the formula:

[0085] ;

[0086] in, This refers to the compressive stress in the concrete. is the compressive damage factor of concrete, with a value range of [0,1), where 0 represents no damage and close to 1 represents complete damage. It is an internal variable function of plastic strain and is used to characterize the irreversible degradation of material stiffness. This refers to the initial elastic modulus of concrete. The initial elastic modulus parameter is obtained through uniaxial compression tests on standard concrete cube or cylindrical specimens. If the test data exhibits dispersion, the least squares method can be used to fit the test data to obtain a fitted curve, thereby determining the representative value. This represents the compressive strain of the concrete. This refers to the standard value of the uniaxial compressive strength of concrete. The standard value of the uniaxial compressive strength is determined according to the "Code for Design of Concrete Structures" or similar standards, and is usually taken as the standard value corresponding to the design strength grade. This represents the ultimate compressive strain of concrete. Its specific value can be determined by referring to the recommended values ​​in the code or by obtaining it through regression analysis of experimental data. For example, the ultimate compressive strain is generally taken as 0.0033 in the code recommendations.

[0087] This formula, by introducing a damage factor and a stress level correction term, can more realistically simulate the stiffness degradation and nonlinear softening behavior of concrete during compression.

[0088] When the tensile strain of concrete is not greater than the ultimate tensile strain of concrete, the specific logic for obtaining the tensile stress of concrete during tensile behavior is as follows:

[0089] Based on the preset tensile damage factor, the difference between 1 and the tensile damage factor is used as the tensile influence coefficient to characterize the degradation of the material's effective stiffness due to tensile damage; and the product of the initial elastic modulus of concrete and tensile strain is used as the theoretical parameter of tensile stress to characterize the theoretical elastic stress of concrete in the tensile direction.

[0090] The tensile stress of concrete is the product of the tensile influence coefficient and the theoretical parameter of tensile stress.

[0091] The behavior under tension can be expressed by the formula:

[0092] ;

[0093] in, This refers to the tensile stress in the concrete. is the tensile damage factor of concrete, with a value range of [0,1), where 0 represents no damage and close to 1 represents complete damage. It is also an internal variable function of plastic strain, used to characterize the irreversible degradation of material stiffness. This is the initial elastic modulus of concrete; This represents the tensile strain of the concrete. This refers to the standard value of the uniaxial compressive strength of concrete. This refers to the ultimate tensile stress of concrete. Its specific value can be determined by referring to the recommended values ​​in the code or by obtaining it through regression analysis of experimental data. For example, the recommended value for ultimate tensile stress in the code is generally in the range of 0.0001-0.00015.

[0094] This model is suitable for simulating the brittle cracking behavior of concrete under tension. The tensile damage factor increases with the increase of plastic strain, reflecting the irreversible degradation of material stiffness.

[0095] The compressive and tensile damage factors are typically determined based on the relationship between concrete plastic strain and damage evolution curves. These curves can be obtained through cyclic loading tests or by validated damage models (such as the Mazars model or Lubliner model) found in the literature. In practical applications, if experimental data is lacking, recommended curves from existing research or code appendices can be referenced. In this embodiment, the curves are obtained based on a validated damage model.

[0096] The parameters mentioned above need to be normalized or standardized before being input into the model to ensure numerical stability and computational convergence. Specifically, for compressive strain... With tensile strain Normalization is performed, i.e., compressive strain. With ultimate compressive strain The ratio is the normalized value of compressive strain, and the tensile strain... With ultimate tensile strain The ratio is used as the normalized value of the tensile strain. The purpose of this normalization is to scale the strain value to the range of [0,1] or nearby, so as to avoid ill-conditioned stiffness matrix due to excessively small strain values; it also facilitates a uniform comparison of strain levels under different stress states.

[0097] Stress data has dimensions. To make it consistent with strain data and improve model convergence, it is also normalized, i.e., compressive stress. Standard value of uniaxial compressive strength of concrete The ratio is used as the normalized value of compressive stress; tensile stress Standard value of uniaxial tensile strength of concrete The ratio is used as the normalized value of tensile stress. The standard value of uniaxial tensile strength here is determined by testing concrete specimens, such as axial tensile tests and splitting tensile tests. This normalization process converts the stress into a dimensionless quantity, which is convenient for use with dimensionless parameters in the constitutive model; it also avoids rounding errors in numerical calculations caused by large differences in the magnitudes of stress and modulus values.

[0098] Damage factors The value range of is [0,1). In actual calculations, attention should be paid to the numerical stability of its evolution process: if the damage factor has abrupt changes or noise in the experimental data, the moving average method or exponential smoothing method can be used to smooth it to avoid oscillations in the finite element iteration. For example, ,in, This represents the smoothed compressive damage factor value for the i-th data point. This represents the original compressive damage factor value of the i-th data point. This represents the smoothed compressive damage factor value of the (i-1)th data point (the previous data point). is the smoothing coefficient, with a value range of [0.6, 0.8], and i represents the index of the data point. For the first data point, since there is no previous smoothing value, the smoothing value of the first point is directly taken as the original value. Starting from the second data point, the calculation is performed according to the above recursive formula.

[0099] Similarly, ,in, This represents the smoothed tensile damage factor value for the i-th data point. This represents the original tensile damage factor value of the i-th data point. This represents the smoothed tensile damage factor value for the (i-1)th data point (the previous data point). For the first data point, since there is no previous smoothed value, the smoothed value for the first point is directly taken as the original value. Starting from the second data point, the calculation is performed according to the above recursive formula. This processing of the damage factor avoids abrupt changes in the damage factor that could lead to drastic changes in the tangent stiffness matrix, affecting convergence, and improves the numerical continuity of the damage evolution process.

[0100] The setting of boundary conditions directly affects the realism of the structural stress behavior. In this embodiment, when defining boundary conditions, the connection section between the gate pier and the base plate is set to be completely fixed to simulate the embedment effect of the foundation. In actual engineering, if the foundation is an elastic foundation, spring units or elastic supports can be used to simulate the foundation stiffness. The stiffness coefficient can be obtained through foundation bearing capacity tests or geological survey reports.

[0101] Simultaneously, a coupling point is established downstream of the gate pier for subsequent application of concentrated forces transmitted by the gate. The coupling point should be consistent with the actual stress point of the gate support and be associated with the pier surface nodes through rigid connection or distributed coupling to ensure the rationality of force transmission.

[0102] The magnitude of the concentrated force is determined by inputting characteristic water levels (such as upstream and downstream water levels) into the gate's force calculation model. This model can be a static equilibrium model or a fluid-structure coupling model, and must consider factors such as water pressure, gate weight, and opening / closing force. If the water level data fluctuates, it is recommended to use extreme value statistical methods (such as P-III type distribution) to determine the design water level, or to take the historical maximum value as input.

[0103] Step 2: Obtain the sequence of historical extreme load events experienced by the gate pier during the target time period; apply each historical extreme load event to the three-dimensional finite element model in chronological order, and iteratively update the state field variables of the three-dimensional finite element model through nonlinear finite element analysis.

[0104] In this embodiment, obtaining the historical extreme load event sequence specifically includes:

[0105] The target time period is defined as the time interval from the moment the gate pier was put into operation to the present moment. The determination of this time period should be based on the actual operation records or design documents of the gate pier, ensuring that all load events that may have a significant impact on the structure are covered.

[0106] Data on all load events experienced by the gate piers within the target time period will be collected. These load events will include at least typical conditions such as flood discharge and water retention. The relevant data will include at least characteristic water level data (upstream and downstream water level hydrographs), gate opening, and support reaction forces. To ensure data accuracy and consistency, the collected raw data will be preprocessed, specifically including: data cleaning, interpolation, smoothing, and unit unification. Data cleaning includes removing obviously abnormal or erroneous records, such as data from periods of water level fluctuations exceeding reasonable ranges or data from periods of sensor failure. Interpolation involves using linear interpolation or historical trend-based fitting methods to complete missing data points. Smoothing includes applying a moving average filter to water level hydrographs with large fluctuations to eliminate the impact of short-term fluctuations on load calculations. Unit unification specifically refers to unifying all data to the International System of Units (SI) (e.g., water level in meters (m) and force in kilometres (N)) for easier subsequent calculations.

[0107] Extract characteristic water level data of the gate pier for each load event within the target time period, including at least the upstream water level process line, the downstream water level process line, and the gate opening and support reaction force determined therefrom.

[0108] Based on the preprocessed data, and according to a preset screening criterion, load events that are identified as historical extreme load events are selected from all load events. The screening criterion is: if the equivalent hydrostatic pressure load borne by the gate pier in a load event reaches or exceeds a preset threshold, then this load event is identified as a historical extreme load event.

[0109] The method for determining the preset threshold is as follows: the threshold value is based on the design reference bearing capacity of the gate pier or the statistical value of the historical maximum load. Specifically, a certain percentage of the design reference bearing capacity can be taken as the threshold, for example, a percentage within the range of 60%-80%; or the top 10%-20% of the maximum load events in historical operating data can be used as a sample of historical extreme load events. This is because the design reference bearing capacity reflects the theoretical bearing capacity of the structure, and exceeding a certain percentage may cause irreversible damage; while the method based on historical statistics can reflect the load level that truly threatens the structure in actual operation. Either method can be chosen to determine the preset threshold, or the two can be combined for two screenings to ensure that the selected load events are representative of the project.

[0110] The selected historical extreme load events are sorted in chronological order of occurrence to form a sequence of historical extreme load events.

[0111] For each historical extreme load event in the sequence, the hydrostatic pressure load intensity acting on the gate pier during that historical extreme load event is calculated based on its corresponding characteristic water level data. The specific logic is as follows:

[0112] The net head at point z is calculated by the difference between the upstream head and the downstream water level at height z; the product of the water density, gravitational acceleration and net head is the hydrostatic pressure load intensity at height z; z represents the coordinate value along the height of the gate pier.

[0113] The formula is expressed as follows:

[0114] ;

[0115] in, Let z be the hydrostatic pressure load intensity at height z. The density of water, It is the acceleration due to gravity. This represents the upstream head at height z. The downstream water level is used when the downstream water level is ignored. .

[0116] Simultaneously, the uplift pressure distribution and gate support reaction corresponding to this historical extreme load event are determined. The uplift pressure distribution can be determined based on seepage analysis or empirical formulas; the gate support reaction can be calculated using a gate force balance model.

[0117] The relevant data for each historical extreme load event should include at least its characteristic water level, the calculated hydrostatic pressure load intensity, the uplift pressure distribution, and the gate support reaction force.

[0118] In this embodiment, applying loads to the initial three-dimensional finite element model specifically includes:

[0119] The relevant data of historical extreme load events are applied sequentially to the initial three-dimensional finite element model in chronological order, specifically including:

[0120] For the first historical extreme load event in the sequence, its corresponding hydrostatic load intensity distribution, uplift pressure distribution and gate support reaction force are applied to the initial three-dimensional finite element model to perform the first nonlinear static analysis.

[0121] After completing the nonlinear static analysis of the first historical extreme load event, the finite element model is updated to generate an updated finite element model.

[0122] Furthermore, after each update, all external loads and constraints in the updated finite element model are reset to their initial state to ensure that each analysis reflects only the independent impact of that load event on the structural state.

[0123] This update is achieved by modifying the state field variables of all integration points in the initial three-dimensional finite element model to the results at the end of the analysis of the first historical extreme load event. The state field variables include at least the compressive damage factor and tensile damage factor of concrete, the plastic strain field of the material, and the stress field of the structure.

[0124] The next historical extreme load event is applied to the updated finite element model for a new round of nonlinear static analysis.

[0125] Repeat the above steps until all historical extreme load events in the historical extreme load event sequence have been simulated.

[0126] When performing nonlinear static analysis, it is necessary to set reasonable convergence criteria and iteration parameters, including residual tolerance, displacement correction tolerance, and maximum number of iterations. Preferably, the residual tolerance is set to... The displacement correction tolerance is set as follows: The maximum number of iterations is set to 20-40 to ensure that the analysis results converge stably within an acceptable range of accuracy.

[0127] Step 3: After simulating all historical extreme load event sequences, lock all state field variables in the finite element model to obtain a damaged finite element model that reflects the current damage state of the gate pier.

[0128] After simulating all historical extreme load events, the state field variables in the finite element model (including but not limited to the compressive damage factor, tensile damage factor, plastic strain field, and stress field of concrete) are locked, forming a damaged finite element model. This model is no longer an ideal, undamaged initial model, but a real structural model that includes irreversible damage effects such as material stiffness degradation and cumulative plastic deformation, and can more accurately reflect the mechanical performance of the gate pier under its current service condition.

[0129] The locking of the state field variables is achieved by updating the state field variables of all integration points in the model to the values ​​at the end of the current analysis after each historical extreme load event simulation, and not resetting them after all event simulations are completed, thereby preserving the cumulative damage effects caused by all historical loads.

[0130] Step 4: Apply the potential limit load to the damaged finite element model and perform nonlinear finite element analysis using the incremental loading method until the model no longer converges due to structural instability. Then, determine the load value corresponding to the previous incremental step as the real-time ultimate bearing capacity of the gate pier under the current damage state.

[0131] In this embodiment, the load applied under the potential limit condition specifically includes: applying a monotonically increasing hydrostatic pressure load on the upstream face of the gate pier in the damaged finite element model. This load is controlled by a load scaling factor, and the magnitude of the hydrostatic pressure load intensity at this time is the product of the hydrostatic pressure load intensity at the corresponding height and the load scaling factor.

[0132] Expressed as a formula:

[0133] ;

[0134] in, This indicates that the applied load scaling factor is... At that time, the hydrostatic pressure load intensity at height z is... The load scaling factor represents a control parameter that monotonically increases from an initial value (usually set to 0). This represents the upstream head at height z. The downstream water level is used when the downstream water level is ignored. .

[0135] The initial value of the load scaling factor is usually set to 0, indicating that no additional load is applied; its increment step is automatically controlled by the arc length method to ensure stable convergence in the region of structural stiffness degradation.

[0136] In this embodiment, the reference load vector needs to be normalized before applying the load to balance the magnitudes of the displacement increment and load factor increment in the arc length constraint equation. This avoids difficulties in solving the problem due to differences in numerical dimensions, thereby improving the numerical stability and convergence efficiency of the arc length method. The specific preprocessing operation is as follows: the reference load vector is divided by its L2 norm to obtain a dimensionless or unit norm normalized reference load vector. After this processing, the reference load vector used in subsequent incremental step analyses is the normalized reference load vector, and its contribution to the arc length constraint equation is standardized, thus ensuring that the displacement and load increments are considered in a balanced manner during the solution process.

[0137] In this embodiment, the incremental loading method for nonlinear finite element analysis specifically includes:

[0138] The arc-length method, used for control, is suitable for solving highly nonlinear and instability problems. By simultaneously controlling the load and displacement increments, the arc-length method ensures that the load-displacement path can still be tracked before and after structural instability.

[0139] The key parameters of the arc-length method are determined based on the current state of the damaged finite element model, including the initial arc-length radius, scaling factor, and maximum allowable number of iterations. The initial arc-length radius is determined by the ratio of the norm of the model's tangent stiffness matrix to the norm of the reference load vector before the first incremental step, expressed by the formula:

[0140] ;

[0141] in, Indicates the initial arc length and radius; Represents the tangent stiffness matrix of the model; Represents the reference load vector, by hydrostatic pressure load intensity at time Sure; This is an empirical coefficient, typically ranging from [0.1, 1], used to adjust the initial arc length to accommodate different structural stiffness characteristics.

[0142] The scaling factor is used to balance the dimensions of displacement and load, and is usually set to 1; the maximum allowable number of iterations is in the range of [20, 40] to ensure convergence accuracy within a reasonable computational cost.

[0143] When using the arc-length method for incremental loading, the equilibrium equations and constraint equations must be solved simultaneously in each incremental step. The solution logic for the equilibrium equations is that the internal force vector of the damaged finite element model is equal to the currently applied external load vector; the internal force vector is a function of the displacement vector, representing the total resultant force generated inside the gate pier resisting the external force after the displacement deformation of the k-th incremental step; the external load vector applied in the k-th incremental step is the product of the preset reference load vector and the load scaling factor of the k-th incremental step, where k is the index of the incremental step.

[0144] The equilibrium equation is expressed by the following formula:

[0145] ;

[0146] in, The internal force vector of the model is represented by the displacement vector. The function; Let be the displacement vector for the k-th increment step; is the load scaling factor for the k-th increment step.

[0147] The arc length constraint equation defines the geometric constraint relationship between the displacement increment and the load factor increment within the increment step, i.e., the square of the displacement vector L2 norm. The first term is the sum of the squares of the displacement increments in the k-th increment step, the second term is the scalarized measure of the load increment in the k-th increment step, and the third term is the square of the dynamic arc length radius in the k-th increment step. The sum of the first and second terms equals the third term, which is the geometric constraint relationship.

[0148] The second term is characterized by the product of three influencing parameters, which are the square of the load factor increment at the kth increment step, the square of the preset scaling factor, and the sum of the squares of the reference load vector, i.e., the square of the L2 norm of the reference load vector.

[0149] It is important to note that the arc length radius is a dynamically changing parameter during the calculation. The arc length radius in the first increment step (k=1) is the initial arc length radius mentioned above. Starting from the second increment step, the arc length radius is automatically scaled and adjusted based on the convergence of the previous increment step (e.g., the number of iterations) to adapt to the development of the nonlinear response of the structure. This dynamic adjustment mechanism is key to the arc length method's ability to effectively track the path after structural instability.

[0150] The arc length constraint equation is expressed by the following formula:

[0151] ;

[0152] in, This is the scaling factor; Let the dynamic arc length radius be the value at the k-th increment step. , These are the displacement increment and load factor increment for the k-th increment step, respectively.

[0153] This equation defines the geometric constraint relationship between the displacement increment and the load increment, ensuring that the solution path advances along the arc length in the load-displacement space.

[0154] In this embodiment, determining the current real-time ultimate bearing capacity specifically includes:

[0155] The criterion for determining whether the finite element solver will cease to converge due to structural instability is as follows: During incremental loading, if the finite element solver still cannot meet the preset residual capacity (e.g., after the maximum allowable number of iterations, such as 20 to 40) during the incremental loading process. ) or displacement correction tolerance (e.g. When the condition reaches a certain threshold, the calculation is considered to have ceased to converge. At this point, the structure is considered to have become unstable.

[0156] The residual capacity and displacement correction tolerance are preset convergence limits, and their values ​​are determined based on the required computational accuracy and model size. Typically, the residual capacity ranges from [...]. The displacement correction tolerance range is []. ].

[0157] When non-convergence occurs for the first time, the load value corresponding to the last converged increment step is determined as the real-time ultimate bearing capacity under the current damage state. That is, when non-convergence occurs for the first time, the product of the load scaling factor of the previous increment step and the resultant force of the reference load vector is the real-time ultimate bearing capacity under the current damage state.

[0158] Expressed as a formula:

[0159] ;

[0160] in, This represents the real-time ultimate bearing capacity under the current damage state. Let K be the load scaling factor corresponding to the Kth increment step, where K represents the index of the previous increment step when non-convergence first occurs. The resultant force of the reference load vector, i.e. The total hydrostatic pressure applied at that time.

[0161] Step 5: Compare the real-time ultimate bearing capacity with the design reference bearing capacity of the gate pier to obtain the current bearing capacity degradation rate of the gate pier; calculate the bearing capacity degradation rate of the gate pier after each historical extreme load event simulation, form a historical bearing capacity degradation trajectory in chronological order, and perform fitting analysis on the relationship between the bearing capacity degradation rate and time, so as to conduct a safety assessment of the gate pier based on the current and predicted bearing capacity degradation rates.

[0162] In this embodiment, the specific logic for calculating the bearing capacity degradation rate is as follows:

[0163] The ratio of the real-time ultimate bearing capacity under the current damage state to the design reference bearing capacity of the gate pier is used to characterize the current structural integrity of the gate pier. The percentage of the difference between 1 and this ratio is the bearing capacity degradation rate of the gate pier under the current damage state.

[0164] The formula for calculating the bearing capacity degradation rate of the gate pier is as follows:

[0165] ;

[0166] in, This represents the bearing capacity degradation rate of the gate pier under its current damaged state. The design reference bearing capacity of the gate pier is obtained by applying the same ultimate load to the initial three-dimensional finite element model and using the same nonlinear finite element incremental loading method until the calculation fails to converge.

[0167] The design reference bearing capacity is obtained as follows: On the initial three-dimensional finite element model (i.e., a complete model that has not experienced any historical loads), the same potential ultimate condition load as in step 4 is applied, and the same nonlinear finite element incremental loading method (such as the arc-length method) is used for analysis until the calculation fails to converge. The load value corresponding to the last convergent incremental step is then the design reference bearing capacity.

[0168] The rationale behind this method is that by comparing and analyzing under the same model and loading path, the impact of differences in modeling and algorithms on the results is eliminated, ensuring the scientific rigor and comparability of the degradation rate calculation.

[0169] To comprehensively reflect the structural performance evolution of the gate pier throughout its service life, it is necessary to construct its historical bearing capacity degradation trajectory. This specifically includes:

[0170] When simulating historical extreme load events, after each historical extreme load event simulation is completed, the same potential limit condition load is applied to the staged damage model obtained at that time point.

[0171] The phased ultimate bearing capacity of the gate pier after the historical event was obtained by analyzing the incremental loading method.

[0172] Calculate the corresponding stage bearing capacity degradation rate;

[0173] By connecting the bearing capacity degradation rates of all historical nodes in chronological order, the historical bearing capacity degradation trajectory of the gate pier is constructed.

[0174] Based on the constructed historical bearing capacity degradation trajectory, nonlinear regression methods (such as polynomial fitting, exponential models, power function models, etc.) are used to fit the relationship between degradation rate and time, obtaining a prediction function for the degradation rate changing over time. Using the fitted prediction function, the predicted bearing capacity degradation rate of the gate pier is predicted within a preset service period.

[0175] During the fitting process, the data on the staged bearing capacity degradation rate should be preprocessed, including:

[0176] Outlier detection and correction: Identify degradation rate data points that deviate significantly from the trend, and if necessary, combine them with engineering records to determine whether they are measurement or simulation errors, and then correct or remove them.

[0177] Outlier identification employs a residual-based statistical discriminant method. First, an initial nonlinear regression model (e.g., a second-order polynomial) is used to preliminarily fit the original historical bearing capacity degradation rate data. Then, the residual for each data point is calculated (i.e., the actual bearing capacity degradation rate minus the model's predicted value). When the absolute value of the residual for a data point exceeds twice the standard deviation of the residuals, that point is preliminarily identified as a candidate outlier. For example, suppose that in the 10th year of service, the simulated stage bearing capacity degradation rate of the gate pier is 8.5%, while the preliminarily fitted curve predicts a value of 6.2% at that point, resulting in a residual of 2.3%. If the standard deviation of the residuals for the entire dataset is 0.7%, then 2.3% > 2 * 0.7% = 1.4%, therefore, the data point from the 10th year is identified as a candidate outlier.

[0178] After identifying candidate outlier points, it is essential to backtrack the engineering records of the corresponding historical extreme load events. For example, check whether a massive flood far exceeding design standards occurred in year 10, whether it was accompanied by coupled disasters such as earthquakes not fully considered by the model, or whether there were any abnormalities in gate operation at that time (such as emergency water flow opening and closing). If there is a clear, historically significant extreme external cause, the outlier may reflect actual step damage and should be retained. If there is no clear extreme external cause, simulation error is suspected. For example, in nonlinear finite element analysis, this incremental step may lead to unreliable calculation results due to mesh distortion, iterative algorithms getting trapped in local solutions, etc.

[0179] For outliers identified as simulation errors, nearest neighbor interpolation is used for correction. Specifically, the carrying capacity degradation rate of the 9th and 11th years (two adjacent normal nodes before and after the outlier) is used to calculate a reasonable estimate for the 10th year through linear interpolation, and this estimate replaces the original outlier. If the simulation of a historical node completely fails, resulting in missing data, the same nearest neighbor interpolation method is used to fill in the missing data to ensure the continuity of the time series. If there are at least two consecutive missing values, these consecutive missing values ​​are treated as a missing value segment. The carrying capacity degradation rate of the node preceding and following this segment is selected. Based on the difference between the two carrying capacity degradation rates before and after the missing value segment, and combined with the number of bits in the missing value, the gradient change rate is calculated. The gradient is then adjusted based on the carrying capacity degradation rate of the previous data point according to the gradient change rate.

[0180] For example, suppose the bearing capacity degradation rate sequence segment of a certain segment is: ..., 8.1%, , , 8.9%, ..., among which, , , Three consecutive missing values ​​constitute a missing value segment. The carrying capacity degradation rate of the node preceding the missing value segment is 8.1%, and the carrying capacity degradation rate of the node following the missing value segment is 8.9%. Therefore, the difference in carrying capacity degradation rate between the two nodes before and after the missing value segment is 0.8%. With three missing values, there will be four gradients, resulting in a gradient of 0.2%. , , .

[0181] Data smoothing: If the data fluctuates significantly, moving average or local weighted regression methods can be used to smooth it and highlight the long-term trend.

[0182] The carrying capacity degradation rates of all historical nodes are connected in chronological order to form a historical carrying capacity degradation rate sequence. The local volatility of the entire historical carrying capacity degradation rate sequence is calculated. Specifically, the absolute value of the difference in carrying capacity degradation rate between adjacent nodes in the sequence is calculated, and its mean and standard deviation are obtained. If the average volatility is greater than 1% of the overall carrying capacity degradation rate average, or the standard deviation is greater than 50% of the average volatility, it indicates that the data fluctuates sharply in the short term, which may mask the long-term degradation trend. In this case, smoothing is required.

[0183] For example, suppose the bearing capacity degradation rate sequence is [1.0%, 1.1%, 1.8%, 1.2%, 1.3%, 2.0%, 1.4%], with adjacent differences of [0.1%, 0.7%, 0.6%, 0.1%, 0.7%, -0.6%], the average volatility is approximately 0.47%, and the standard deviation of volatility is approximately 0.52%. If the overall average bearing capacity degradation rate is 1.4%, then this is greater than 1% of the overall average bearing capacity degradation rate, and the standard deviation of volatility is also large, indicating significant volatility, making smoothing necessary.

[0184] The moving average method is recommended. Select a moving window of length N (N is usually 3 or 5, determined reasonably based on the total number of data points), and use the average carrying capacity degradation rate of the data points within the window as the smoothing value of the window's center point. For points at the ends of the sequence that cannot form a complete window, the window can be appropriately reduced or the original value can be retained. For example, assuming N=3, smooth the above sequence. The first point (1.0%) is retained, the second point becomes (1.0%+1.1%+1.8%) / 3≈1.3%, the third point becomes (1.1%+1.8%+1.2%) / 3≈1.37%, and so on. The smoothed sequence will more clearly show the overall upward trend, rather than frequent ups and downs.

[0185] Time normalization: The time axis is standardized to dimensionless parameters such as service life or cumulative load cycles to facilitate model generalization. Specifically, the actual service time is divided by the design reference service life of the gate pier to achieve normalization. The design reference service life of the gate pier can be obtained from the gate pier design manual.

[0186] The selection of a fitting model should be based on data characteristics and engineering experience. Common models include exponential models, power function models, and polynomial models. Model parameters are determined using optimization algorithms such as the least squares method, and the goodness of fit is evaluated using indicators such as the coefficient of determination.

[0187] The preset security thresholds include a first security threshold and a second security threshold, and ,in The first safety threshold, The first safety threshold, typically ranging from 5% to 10%, indicates that the structure has begun to show slight but acceptable performance degradation, requiring attention. The second safety threshold, typically ranging from 15% to 20%, indicates that the structure has entered a significant degradation stage, posing a safety hazard and requiring intervention. The thresholds were set with reference to the requirements for structural durability and safety factors in relevant standards such as the "Code for Design of Hydraulic Concrete Structures"; engineering practice experience was also considered, taking into account structural redundancy and the possibility of sudden loads. The thresholds need to be verified through numerical simulation and comparison with measured data to ensure their engineering applicability.

[0188] The gate pier safety assessment and early warning logic designed in this invention adopts a phased, dynamically corrective strategy. Its core lies in combining static assessment based on the current state with dynamic prediction based on future trends. It compares the calculated bearing capacity degradation rate under the current damage state and the predicted bearing capacity degradation rate with a safety threshold to complete the safety status assessment and output an early warning signal. Specifically, it includes:

[0189] Based on the bearing capacity degradation rate under the current damage state of the gate pier, a preliminary warning signal is determined. The warning signals are classified into green warning, yellow warning and red warning according to the level from low to high. The gate pier status corresponding to each warning signal is good status, damaged status and unsafe status, respectively.

[0190] If the load-bearing capacity degradation rate under the current damage state is less than the first safety threshold, a green warning signal will be issued. The assessment conclusion will be that the structure is in good safety condition with a stable degradation trend, and the decision recommendation will be normal use with regular periodic inspections.

[0191] If the load-bearing capacity degradation rate under the current damage state is not less than the first safety threshold but less than the second safety threshold, a yellow warning signal will be issued. The assessment conclusion will be that the structure is damaged and the degradation is progressing, indicating low safety. The recommended course of action is to focus on this area and shorten the monitoring cycle.

[0192] Phase 1: Preliminary Assessment Based on Current Status. This phase relies entirely on the current and existing damage data of the gate pier (i.e., the current rate of bearing capacity degradation). By setting three clear warning levels—green, yellow, and red—and corresponding them to three structural states—good condition, damaged condition, and unsafe condition—a rapid, intuitive, and unambiguous diagnosis of the gate pier's current safety status is achieved. This phase ensures that any existing risks can be immediately identified and an alarm of the appropriate level can be issued.

[0193] If the load-bearing capacity degradation rate under the current damage state is not less than the second safety threshold, a red warning signal will be issued. The assessment conclusion will be "structural insecurity," and the decision recommendation will be "immediate engineering measures."

[0194] If the initially determined warning signal is not a red warning, the initially determined warning signal will be reviewed and corrected based on the predicted bearing capacity degradation rate to form the final warning signal:

[0195] If the predicted load-bearing capacity degradation rate remains below the first safety threshold throughout the preset service life, the warning signal will not be modified. In other words, if the future is predicted to remain safe (always below the first safety threshold), it proves that the current good or damaged state is stable, and maintenance can proceed as planned.

[0196] If, within the preset service life, the predicted load-bearing capacity degradation rate is not less than the first safety threshold but less than the second safety threshold, the warning signal is upgraded. In other words, if it is predicted that the system will enter a higher risk zone (e.g., transitioning from a good to a damaged zone, i.e., not less than the first safety threshold), it means that the currently seemingly safe situation hides a trend of accelerated deterioration, necessitating an earlier, higher-level warning to prompt management to be more vigilant. For example, if the initially determined warning signal is a green warning, it is upgraded to a yellow warning. If the initially determined warning signal is a yellow warning, it is upgraded to a red warning.

[0197] If the predicted load-bearing capacity degradation rate exceeds the second safety threshold within the preset service life, the warning signal is directly upgraded to a red warning. Once the prediction indicates that the danger boundary (not less than the second safety threshold) will be reached at any time in the future, regardless of whether the current warning is green or yellow, it is directly determined to be the highest risk. This achieves a fundamental shift from post-event remediation to pre-event warning, providing a crucial decision-making window for taking preventive reinforcement measures.

[0198] Phase Two: Early Warning Correction Based on Future Predictions. It is stipulated that predictive data will only be used for verification when the initial warning is not the highest level (red). This is because a red warning indicates that the structure is currently in a dangerous state, the situation is urgent, and engineering measures must be taken immediately without waiting for future prediction results, thus avoiding delays in emergency response due to complex predictive analysis. For green and yellow warnings, risk reassessment is conducted by predicting the degradation trajectory over the entire preset service life. The first and second safety thresholds constitute clear decision boundaries. Each warning signal not only corresponds to a state conclusion but also directly relates to specific, actionable decision recommendations (such as regular inspections, shortening cycles, and immediate measures). This allows field engineers and managers to take corresponding actions directly based on the warning signals output by the system without secondary interpretation, greatly improving the practicality and efficiency of the method. Predictive verification is also introduced, extending the assessment dimension from the present to the future, effectively preventing catastrophic accidents and shifting the operation and maintenance model from repairing after failure to prevention.

[0199] For example, assuming a gate pier has been in service for 15 years, the bearing capacity degradation rate of its historical nodes is obtained, and an exponential function is used to fit the relationship between the degradation rate and time. Based on this functional relationship, the degradation trend for the next 15 years is predicted. The resulting prediction function is: Where t is the service life, This represents the bearing capacity degradation rate in year t. Details are as follows:

[0200] Table 1: Schematic diagram of bearing capacity degradation rate of gate piers at different service years

[0201]

[0202] As shown in Table 1 above and Figure 2 As shown, the design benchmark bearing capacity is set at 10000kN, the first safety threshold is 8%, the second safety threshold is 18%, the preset service life is 30 years, and the initial degradation rate is 0%.

[0203] During the historical phase (0-15 years), the curve shows a slow but accelerating upward trend. In the first 10 years, the degradation rate is below 5%, and the structural performance deteriorates slowly. Starting from the 12th year, the slope of the curve increases significantly, and the degradation rate accelerates, reaching 7.9% in the 12th year, close to the first safety threshold.

[0204] The current state (year 15) shows a degradation rate of 11.5%, which clearly exceeds the first safety threshold, indicating that the structure has suffered significant damage and is showing a progressive trend. At this point, a preliminary assessment issues a yellow warning signal.

[0205] During the forecast phase (15-30 years), the prediction curve based on the exponential model shows that the degradation rate will continue to increase rapidly. It is projected that around year 20, the degradation rate (19.5%) will exceed the second safety threshold, marking the structure's entry into an unsafe state. By the end of service in year 30, the predicted degradation rate will reach as high as 53%, indicating a severe deficiency in the structure's load-bearing capacity. At this point, the initial yellow warning signal will be upgraded to a red warning signal.

[0206] based on Figure 2 Based on the curve and the data in the table above, the following assessment can be made: The current bearing capacity degradation rate of the gate pier is 11.5%, which is greater than the first safety threshold but less than the second safety threshold. The assessment concludes that the structure is damaged and the degradation is progressing, resulting in low safety. The decision recommendation is to focus on this area, shorten the monitoring cycle (e.g., from once a year to once a quarter), and prepare a repair and reinforcement plan. However, predictions show that within the preset service life, the predicted degradation rate will exceed the second safety threshold in the 20th year. The assessment concludes that the structure will be in an unsafe state in the future. The decision recommendation is to take immediate engineering measures.

[0207] This assessment system comprehensively considers the current situation and future trends, realizing the transformation from post-event judgment to pre-event early warning, and has strong engineering guidance significance.

[0208] Please see Figure 3 The present invention also provides a system for determining the ultimate bearing capacity of a gate pier based on finite element analysis. This system is used to implement the aforementioned method for determining the ultimate bearing capacity of a gate pier based on finite element analysis, and includes:

[0209] The data acquisition and initial modeling module is used to establish a three-dimensional finite element model of the gate pier based on its structural drawings, and to define the material constitutive model and boundary conditions.

[0210] The cumulative damage simulation module is used to obtain the sequence of historical extreme load events experienced by the gate pier during the target time period; in chronological order, each historical extreme load event is applied to the three-dimensional finite element model, and the state field variables of the three-dimensional finite element model are iteratively updated through nonlinear finite element analysis.

[0211] The damage state solidification module is used to lock all state field variables in the finite element model after simulating all historical extreme load event sequences, so as to obtain a damaged finite element model that reflects the current damage state of the gate pier.

[0212] The real-time bearing capacity determination module is used to apply the load of the potential ultimate condition to the damaged finite element model and perform nonlinear finite element analysis using the incremental loading method until it no longer converges due to structural instability. The load value corresponding to the previous incremental step is then determined as the real-time ultimate bearing capacity of the gate pier under the current damage state.

[0213] The safety assessment and decision-making module is used to compare the real-time ultimate bearing capacity with the design reference bearing capacity of the gate pier to obtain the current bearing capacity degradation rate of the gate pier; calculate the bearing capacity degradation rate of the gate pier after each historical extreme load event simulation, form a historical bearing capacity degradation trajectory in chronological order, and perform fitting analysis on the relationship between the bearing capacity degradation rate and time, so as to conduct a safety assessment of the gate pier based on the current and predicted bearing capacity degradation rates.

[0214] 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.

[0215] 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.

[0216] 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 according to actual needs.

[0217] 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 determining the ultimate bearing capacity of a gate pier based on finite element analysis, characterized in that, The specific steps include: Step 1: Based on the structural drawings of the gate pier, establish its three-dimensional finite element model and define the material constitutive model and boundary conditions; Step 2: Obtain the sequence of historical extreme load events experienced by the gate pier during the target time period; apply each historical extreme load event to the three-dimensional finite element model in chronological order, and iteratively update the state field variables of the three-dimensional finite element model through nonlinear finite element analysis. Step 3: After simulating all historical extreme load event sequences, lock all state field variables in the finite element model to obtain a damaged finite element model that reflects the current damage state of the gate pier. Step 4: Apply the load of the potential ultimate condition to the damaged finite element model and perform nonlinear finite element analysis using the incremental loading method until the model no longer converges due to structural instability. Then, determine the load value corresponding to the previous incremental step as the real-time ultimate bearing capacity of the gate pier under the current damage state. Step 5: Compare the real-time ultimate bearing capacity with the design reference bearing capacity of the gate pier to obtain the current bearing capacity degradation rate of the gate pier; calculate the bearing capacity degradation rate of the gate pier after each historical extreme load event simulation, form a historical bearing capacity degradation trajectory in chronological order, and fit and analyze the relationship between the bearing capacity degradation rate and time, so as to conduct a safety assessment of the gate pier based on the current and predicted bearing capacity degradation rates.

2. The method for determining the ultimate bearing capacity of a gate pier based on finite element analysis according to claim 1, characterized in that, The defined material constitutive model and boundary conditions specifically include: In establishing the initial three-dimensional finite element model of the gate pier based on the structural drawings, a plastic damage model is used to define the nonlinear mechanical behavior of concrete material. The uniaxial stress-strain relationship under compressive and tensile conditions is analyzed, specifically including: When the compressive strain of concrete is not greater than the ultimate compressive strain of concrete, the specific logic for obtaining the compressive stress of concrete under compression is as follows: Based on the preset compressive damage factor, the difference between 1 and the compressive damage factor is used as the compressive influence coefficient to characterize the remaining effective integrity of the material; the product of the initial elastic modulus of concrete and the compressive strain of concrete is used as the theoretical parameter of compressive stress to characterize the theoretical elastic stress of concrete in the ideal linear elastic state; the product of the compressive influence coefficient and the theoretical parameter of compressive stress is used as the numerator, which characterizes the effective stress of concrete after compressive damage. The ratio of the theoretical compressive stress parameter to the standard value of the uniaxial compressive strength of concrete is taken as the first influencing parameter. This first influencing parameter is a dimensionless ratio. The square term of the difference between it and 1 is analyzed to reflect the degree to which the material response deviates from the linear elastic behavior. The sum of 1 and this square term is used for normalization adjustment and is used as the denominator term. The ratio of the numerator to the denominator is the compressive stress of the concrete. When the tensile strain of concrete is not greater than the ultimate tensile strain of concrete, the specific logic for obtaining the tensile stress of concrete during tensile behavior is as follows: Based on the preset tensile damage factor, the difference between 1 and the tensile damage factor is used as the tensile influence coefficient to characterize the degradation of the material's effective stiffness due to tensile damage; and the product of the initial elastic modulus of concrete and tensile strain is used as the theoretical parameter of tensile stress to characterize the theoretical elastic stress of concrete in the tensile direction. The product of the tensile influence coefficient and the theoretical parameter of tensile stress is the tensile stress of concrete. When defining boundary conditions, the connection section between the gate pier and the bottom plate is set as a fixed constraint to simulate the embedment effect of the foundation. At the same time, a coupling point is established downstream of the gate pier for subsequent application of concentrated force transmitted by the gate. The magnitude of the concentrated force is determined by inputting the characteristic water level into the gate stress calculation model.

3. The method for determining the ultimate bearing capacity of a gate pier based on finite element analysis according to claim 1, characterized in that, Obtaining the historical extreme load event sequence specifically includes: The time interval from the time the gate pier was put into operation to the present time is defined as the target time period; relevant data of all load events experienced by the gate pier within the target time period are collected, and the load events include at least flood discharge and water blocking; The relevant data includes at least characteristic water level data; characteristic water level data of the gate pier for each load event within the target time period is extracted, including at least the upstream water level process line, the downstream water level process line, and the gate opening and support reaction force determined therefrom; based on the relevant data, load events judged as historical extreme load events are selected from all load events according to the preset screening criteria; the screening criteria are: if the equivalent hydrostatic pressure load borne by the gate pier in a load event reaches or exceeds the preset threshold, then this load event is judged as a historical extreme load event; The selected historical extreme load events are sorted in chronological order of occurrence to form a sequence of historical extreme load events. For each historical extreme load event in the sequence, the hydrostatic pressure load intensity acting on the gate pier during that historical extreme load event is calculated based on its corresponding characteristic water level data. The specific logic is as follows: The net head at point z is calculated by the difference between the upstream head and the downstream water level at height z; the product of the water density, gravitational acceleration and net head is the hydrostatic pressure load intensity at height z; z represents the coordinate value along the height of the gate pier. At the same time, the distribution of uplift pressure and gate support reaction force corresponding to this historical extreme load event were determined; The relevant data for each historical extreme load event should include at least its characteristic water level, the calculated hydrostatic pressure load intensity, the uplift pressure distribution, and the gate support reaction force.

4. The method for determining the ultimate bearing capacity of a gate pier based on finite element analysis according to claim 1, characterized in that, Applying loads to the initial three-dimensional finite element model specifically includes: The relevant data of historical extreme load events are applied sequentially to the initial three-dimensional finite element model in chronological order, specifically including: For the first historical extreme load event in the sequence, its corresponding hydrostatic load intensity distribution, uplift pressure distribution and gate support reaction force are applied to the initial three-dimensional finite element model to perform the first nonlinear static analysis. After completing the nonlinear static analysis of the first historical extreme load event, the finite element model is updated to generate an updated finite element model. After each update, all external loads and constraints in the updated finite element model are reset to the initial state. This update is achieved by modifying the state field variables of all integration points in the initial three-dimensional finite element model to the results at the end of the analysis of the first historical extreme load event. The state field variables include at least the compressive damage factor and tensile damage factor of concrete, the plastic strain field of the material, and the stress field of the structure. The next historical extreme load event is applied to the updated finite element model for a new round of nonlinear static analysis. Repeat the above steps until all historical extreme load events in the historical extreme load event sequence have been simulated. After simulating all historical extreme load events, the final updated finite element model state is defined as the damaged finite element model.

5. The method for determining the ultimate bearing capacity of a gate pier based on finite element analysis according to claim 1, characterized in that, The incremental loading method specifically includes: The load applied under the potential limit condition is as follows: On the upstream face of the gate pier with the damaged finite element model, a monotonically increasing hydrostatic pressure load is applied. This load is controlled by a load scaling factor. The magnitude of the hydrostatic pressure load intensity at this time is the product of the hydrostatic pressure load intensity at the corresponding height and the load scaling factor. The nonlinear finite element analysis using the incremental loading method employs the arc length method for control. The key parameters are determined based on the current state of the damaged finite element model, including the initial arc length radius, scaling factor, and maximum allowable number of iterations. When using the arc-length method for incremental loading, the equilibrium equation and constraint equation are solved simultaneously in each incremental step. The specific logic of the equilibrium equation is that the internal force vector of the damaged finite element model is equal to the currently applied external load vector. The internal force vector is a function of the displacement vector, representing the total resultant force generated inside the gate pier to resist the external force after the displacement deformation of the k-th incremental step. The external load vector applied in the k-th incremental step is the product of the preset reference load vector and the load scaling factor of the k-th incremental step, where k is the index of the incremental step. The arc length constraint equation defines the geometric constraint relationship between the displacement increment and the load factor increment within the increment step. The first term is the sum of squares of the displacement increments in the k-th increment step, i.e., the square of the L2 norm of the displacement vector. The second term is a scalarized measure of the load increment in the k-th increment step. The third term is the square of the dynamic arc length radius in the k-th increment step. The sum of the first and second terms equals the third term, which is the geometric constraint relationship. The second term is characterized by the product of three influencing parameters, which are the square of the load factor increment at the kth increment step, the square of the preset scaling factor, and the sum of the squares of the reference load vector, i.e., the square of the L2 norm of the reference load vector.

6. The method for determining the ultimate bearing capacity of a gate pier based on finite element analysis according to claim 5, characterized in that, Determining the current real-time ultimate bearing capacity specifically includes: The criterion for determining whether the calculation will no longer converge due to structural instability is as follows: During the incremental loading process, when the finite element solver still cannot meet the preset residual capacity or displacement correction tolerance after the maximum allowable number of iterations, it is determined that the calculation will no longer converge. At this time, the load value corresponding to the last converged incremental step is determined as the real-time ultimate bearing capacity under the current damage state. That is, the product of the load scaling factor of the previous incremental step and the resultant force of the reference load vector when non-convergence occurs for the first time is the real-time ultimate bearing capacity under the current damage state.

7. The method for determining the ultimate bearing capacity of a gate pier based on finite element analysis according to claim 6, characterized in that, The specific logic for calculating the bearing capacity degradation rate is as follows: The ratio of the real-time ultimate bearing capacity under the current damage state to the design reference bearing capacity of the gate pier is used to characterize the current structural integrity of the gate pier. The percentage of the difference between 1 and this ratio is the bearing capacity degradation rate of the gate pier under the current damage state. When simulating historical extreme load events, after each historical extreme load event simulation is completed, the same potential ultimate load is applied to the stage damage model obtained at that time point. The stage ultimate bearing capacity of the gate pier after the occurrence of the historical event is obtained by incremental loading method, and the corresponding stage bearing capacity degradation rate is calculated. The bearing capacity degradation rates of all historical nodes are connected in chronological order to construct the historical bearing capacity degradation trajectory of the gate pier. Based on the historical carrying capacity degradation trajectory, a nonlinear regression method is used to fit the functional relationship between the degradation rate and time. Using the fitted prediction function, the predicted bearing capacity degradation rate of the gate pier is predicted within the preset service period. The preset security thresholds include a first security threshold and a second security threshold; Both the first safety threshold and the second safety threshold are within the range of (0,1), and the second safety threshold is greater than the first safety threshold; The calculated bearing capacity degradation rate under the current damage state and the predicted bearing capacity degradation rate are compared with a safety threshold to complete the safety status assessment and output an early warning signal, specifically including: Based on the bearing capacity degradation rate under the current damage state of the gate pier, a preliminary warning signal is determined. The warning signals are classified into green warning, yellow warning and red warning according to the level from low to high. The gate pier status corresponding to each warning signal is good status, damaged status and unsafe status, respectively. If the load-bearing capacity degradation rate under the current damage state is less than the first safety threshold, a green warning signal will be issued. If the bearing capacity degradation rate under the current damage state is not less than the first safety threshold but less than the second safety threshold, a yellow warning signal will be issued. If the load-bearing capacity degradation rate under the current damage state is not less than the second safety threshold, a red warning signal will be issued. If the initially determined warning signal is not a red warning, the initially determined warning signal will be reviewed and corrected based on the predicted bearing capacity degradation rate to form the final warning signal: If the predicted load-bearing capacity degradation rate is always less than the first safety threshold within the preset service period, the warning signal will not be modified. If, within the preset service life, the predicted load-bearing capacity degradation rate is not less than the first safety threshold but less than the second safety threshold, the warning signal will be upgraded. If the predicted load-bearing capacity degradation rate exceeds the second safety threshold within the preset service period, the warning signal will be directly upgraded to a red warning.

8. A system for determining the ultimate bearing capacity of a gate pier based on finite element analysis, characterized in that, The system for determining the ultimate bearing capacity of a gate pier based on finite element analysis is used to implement the method for determining the ultimate bearing capacity of a gate pier based on finite element analysis as described in any one of claims 1-7, including: The data acquisition and initial modeling module is used to establish a three-dimensional finite element model of the gate pier based on its structural drawings, and to define the material constitutive model and boundary conditions. The cumulative damage simulation module is used to obtain the sequence of historical extreme load events experienced by the gate pier during the target time period; in chronological order, each historical extreme load event is applied to the three-dimensional finite element model, and the state field variables of the three-dimensional finite element model are iteratively updated through nonlinear finite element analysis. The damage state solidification module is used to lock all state field variables in the finite element model after simulating all historical extreme load event sequences, so as to obtain a damaged finite element model that reflects the current damage state of the gate pier. The real-time bearing capacity determination module is used to apply the load of the potential ultimate condition to the damaged finite element model and perform nonlinear finite element analysis using the incremental loading method until it no longer converges due to structural instability. The load value corresponding to the previous incremental step is then determined as the real-time ultimate bearing capacity of the gate pier under the current damage state. The safety assessment and decision-making module is used to compare the real-time ultimate bearing capacity with the design reference bearing capacity of the gate pier to obtain the current bearing capacity degradation rate of the gate pier; calculate the bearing capacity degradation rate of the gate pier after each historical extreme load event simulation, form a historical bearing capacity degradation trajectory in chronological order, and perform fitting analysis on the relationship between the bearing capacity degradation rate and time, so as to conduct a safety assessment of the gate pier based on the current and predicted bearing capacity degradation rates.

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