Anti-seismic reliability analysis method, device and system for self-resetting assembled bridge pier and storage medium

Abstract

The invention discloses an anti-seismic reliability analysis method, device and system for a self-resetting assembled pier, and a storage medium. The method comprises the following steps: step 1, determining a basic random variable of a structure; 2, selecting a representative sample, and calculating an assignment probability of a probability subspace; step 3, structural random response analysis; 4, carrying out structure hysteresis analysis; 5, calculating a damage index and an evolution speed of each sample; step 6, defining a damage criterion of the self-resetting segment prefabricated assembled pier; 7, solving a generalized probability density evolution equation with an absorption boundary; step 8, obtaining a'residual 'probability density function; and step 9, evaluating the time-varying anti-seismic reliability of the self-resetting segment prefabricated assembled pier. By adopting the technical scheme of the invention, scientific evaluation of the anti-seismic safety performance of the self-resetting segment prefabricated assembled pier under the consideration of the influence of material randomness is realized.

Description

Technical Field

[0001] This invention belongs to the field of structural engineering technology, specifically relating to a method, device, system, and storage medium for analyzing the seismic reliability of self-resetting assembled bridge piers. Background Technology

[0002] With the deepening of my country's strategy to build a strong transportation network, modern bridge engineering is developing towards high efficiency, greenness, and resilience. Prestressed segmental precast self-resetting bridge piers (SC-PSBCs), as a representative new type of structure, possess the structural characteristics of post-tensioned unbonded prestressed tendons connected in series with precast segments and supplemented by local energy-dissipating reinforcement. During strong earthquakes, they achieve significant self-resetting functionality through the opening-closing mechanism of the segmental joints and the elastic restoring force of the prestressed tendons. This effectively controls residual displacement after earthquakes, combining industrialized construction quality with superior seismic toughness, and has shown broad application prospects in major projects both domestically and internationally.

[0003] However, the mechanical behavior of SC-PSBCs differs fundamentally from that of traditional cast-in-place piers. Their damage process is highly concentrated at the segmental joint interface, manifesting as a complex coupling of multiple mechanisms, including localized concrete crushing, yielding of energy-dissipating steel reinforcement, and stress changes in prestressing tendons. This makes it difficult to scientifically characterize their true damage state using traditional damage assessment methods based on overall deformation or cumulative energy dissipation. Current research largely focuses on the deterministic hysteretic behavior and damage mechanisms of this system. However, systematic and reliable analytical methods are lacking for nonlinear seismic response analysis under the stochastic influence of key parameters such as the strength of concrete and steel reinforcement, as well as for quantitative assessment of performance-based seismic reliability. This severely restricts the refined design and safety evaluation of this advanced structural system.

[0004] As a highly nonlinear, multi-stage stochastic dynamic system, SC-PSBCs face a dual challenge in seismic reliability analysis. On the one hand, the structural response exhibits high path dependence and state-switching characteristics, and classical reliability methods (such as the first-order second-moment method and Monte Carlo simulation) often suffer from low computational efficiency or insufficient accuracy when dealing with such complex nonlinear functional functions. On the other hand, the randomness of seismic input and material properties profoundly influences and intertwines with the entire response evolution of the structure, from linear elasticity, joint opening, energy-dissipating reinforcement yielding, to final failure. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method, device, system, and storage medium for analyzing the seismic reliability of self-resetting prefabricated bridge piers. Based on the probability density evolution theory, it realizes the seismic reliability analysis of self-resetting segmental prefabricated bridge piers. By coupling the randomness of materials with the seismic dynamic response, it provides a scientific and effective analytical approach for evaluating the seismic reliability of this type of structure.

[0006] To achieve the above objectives, the present invention provides the following solution: A method for seismic reliability analysis of self-resetting assembled bridge piers includes: Step 1: Determine the basic random variables of the structure; Step 2: Select representative samples and calculate the assigned probabilities of the probability subspace; Step 3: Analyze the structural random response; Step 4: Analyze structural hysteresis; Step 5: Calculate the damage index and its evolution rate for each sample; Step 6: Define the failure criteria for self-resetting segmental prefabricated bridge piers; Step 7: Solve the generalized probability density evolution equation with absorbing boundary; Step 8: Obtain the residual probability density function; Step 9: Evaluate the time-varying seismic reliability of self-resetting segmental precast piers.

[0007] The preferred generalized probability density evolution equation is: , in, Damage indicators With random variables The joint probability density function reflects the probability distribution characteristics of the structural damage index D and the random variable taking a certain combination value under a given generalized time. Given a random variable taking the value At that time, structural damage The instantaneous evolution speed as the loading process progresses; For time in a general sense.

[0008] Its boundary and initial conditions are as follows: , in, It is the joint probability density function of the damage index D and the random variable. It describes the deterministic initial value of the damage state, in At infinity, and elsewhere The value is zero at the point, and it is zero throughout the entire... d The spatial integral is 1; Characterizing the inherent uncertainty of random variables, the basic random variables The probability distribution at the initial time; at the initial time The structural damage index D of all samples is definitively equal to the same initial value with 100% probability. , , in, The failure domain, i.e., the damage index D Areas that have reached or exceeded the damage threshold It is the damage index D and the random variable The joint probability density function; if the damage enters the failure domain. Its probability density immediately becomes zero.

[0009] Preferably, the generalized probability density evolution equation is solved, and the integral is performed in the space of random variables to obtain the remaining probability density function in the safe region: , in, For the space of random variables, It is the joint probability density function of the damage index D and the random variable, and its expression in the random variable... Throughout the space By integrating the above, the total probability distribution of the damage index within the safety region can be obtained. , Therefore, the reliability can be calculated as follows: , in, The structure represents the generalized time. The reliability of the changes; This indicates the safe range of damage indicators. Integrate over the above; calculate the "residual" probability density function of the damage index. In the security domain The time-varying reliability of the structure can be obtained by integrating within the time limit.

[0010] This invention also provides a seismic reliability analysis device for self-resetting assembled bridge piers, comprising: The first processing module is used to determine the basic random variables of the structure; The second processing module is used to select representative samples and calculate the assigned probabilities of the probability subspace. The third processing module is used to analyze the structural random response; The fourth processing module is used to analyze structural hysteresis; The fifth processing module is used to calculate the damage index and its evolution rate for each sample; The sixth processing module is used to define the failure criteria for self-resetting segmental prefabricated bridge piers; The seventh processing module is used to solve the generalized probability density evolution equation with absorbing boundaries; The eighth processing module is used to obtain the residual probability density function; The ninth processing module is used to evaluate the time-varying seismic reliability of self-resetting segmental prefabricated piers.

[0011] The preferred generalized probability density evolution equation is: in, Damage indicators With random variables The joint probability density function, In the given hour The rate of change; Its boundary and initial conditions are as follows: , .

[0012] Preferably, the eighth processing module solves the generalized probability density evolution equation, integrates it in the random variable space, and obtains the remaining probability density function in the safe region as follows: , The time-varying seismic reliability obtained from the eighth processing module is: .

[0013] The present invention also provides a seismic reliability analysis system for self-resetting assembled bridge piers, comprising: a memory and a processor, wherein the memory stores a computer program executed by the processor, and the computer program, when executed by the processor, performs the seismic reliability analysis method for self-resetting assembled bridge piers as described in any one of claims 1-3.

[0014] The present invention also provides a storage medium storing a computer program, which, when running, executes the seismic reliability analysis method for self-resetting assembled bridge piers as described in any one of claims 1-3.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: To address the unique mechanical behavior and self-resetting mechanism of this type of bridge pier, characterized by joint opening, low residual deformation, and localized damage, this invention constructs a dedicated seismic reliability assessment framework. By introducing a Burr distribution model that better reflects the stochastic characteristics of concrete material properties, the scientific rigor and accuracy of material uncertainty characterization are significantly improved. Simultaneously, a damage quantification method and limit state determination criterion, strictly matched to the failure mechanism, are established using damage indicators specifically developed for this type of bridge pier. Ultimately, a complete and accurate reliability analysis method is formed, enabling a scientific assessment of the seismic safety performance of self-resetting segmental precast bridge piers considering the influence of material stochasticity. This provides crucial theoretical and technical support for the seismic design, safety evaluation, and maintenance decisions of this type of high-performance bridge pier. Attached Figure Description

[0016] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart of the seismic reliability analysis method for self-resetting assembled bridge piers according to an embodiment of the present invention; Figure 2 Here is a schematic diagram of the SC-PSBCs structure; (a) is the overall layout diagram; (b) is the cross-sectional reinforcement diagram. Figure 3 Let be the probability density function curve of the representative point set; where (a) is the strength of C40 concrete; and (b) is the yield strength of HRB400E steel reinforcement. Figure 4 This is a schematic diagram of the loading system; Figure 5 Hysteresis curves for a portion of the samples; Figure 6 A schematic diagram defining the residual displacement; Figure 7 The residual displacement curves represent the point set; Figure 8 The representative point set damage index curve; Figure 9 The results show the evolution of the probability density of bridge pier damage index under cyclic loading; (a) the evolution surface of the probability density of damage index; (b) the contour lines of the probability density of damage index; and (c) the probability density curve of the damage index at a specific moment. Figure 10 This is the seismic reliability curve of the bridge pier under cyclic loading. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] Example 1 like Figure 1As shown, this invention provides a seismic reliability analysis method for self-resetting assembled bridge piers. Its core theoretical basis consists of two parts: First, establishing a physical model and limit state determination criteria that can accurately quantify the seismic damage unique to SC-PSBCs; Second, based on this physical model, developing a probability density evolution reliability analysis method that can strictly consider the randomness of material parameters.

[0021] ① Damage quantification methods and limit state determination criteria for SC-PSBCs To conduct performance-based seismic reliability analysis, two fundamental issues must first be addressed: how to scientifically quantify the degree of structural damage under seismic loading, and how to define its failure (limit) state. The failure mechanism of SC-PSBCs differs fundamentally from that of traditional cast-in-place bridge piers. Its damage is concentrated at the segmental joint interface, manifesting as a complex coupling of localized concrete crushing, yielding of energy-dissipating steel bars, and stress changes in prestressing tendons, exhibiting significant self-resetting characteristics and a clear damage evolution path.

[0022] To accurately characterize this feature, this invention employs an improved two-parameter seismic damage model. Based on the classic Park-Ang framework, this model incorporates three key improvements to address the small residual displacement and complex damage mechanism of SC-PSBCs: (1) a new combination of deformation and energy terms; (2) the introduction of an "effective energy dissipation factor" related to displacement amplitude to reflect the differences in the contribution of energy dissipation to cumulative damage at different deformation stages; and (3) the introduction of yield displacement to correct for ultimate energy dissipation. Damage Indicators D The expression is as follows: In the formula: The combination coefficient for segmental precast hollow piers is related to the structural design parameters. This represents the ratio of residual displacement after the earthquake. The ultimate residual displacement ratio; This is the structural yield load; and These are the yield displacement and ultimate displacement of the structure, respectively. is the effective energy dissipation factor for the i-th loading cycle, which is related to the self-resetting performance of the structure; Let be the energy dissipation during the i-th loading cycle.

[0023] Specifically, the combination coefficient It can be represented as a linear combination of various key parameters.

[0024] In the formula, For shear span ratio; It is the axial compression ratio; This refers to the longitudinal reinforcement ratio; This refers to the prestressed tendon reinforcement ratio; The energy-consuming steel reinforcement ratio; This refers to the stirrup reinforcement ratio; This refers to the concrete strength.

[0025] The effective energy consumption factor is expressed as follows: In the formula, This represents the effective energy consumption factor corresponding to the i-th cycle; Let be the displacement amplitude under the i-th cycle of loading; This represents the yield displacement of the component. This represents the ultimate displacement of the component. In this factor, it is assumed that the effective energy dissipation of the structure is very small before reaching the yield displacement, but will rapidly increase after exceeding the yield displacement.

[0026] A clearly defined limit state is the cornerstone of reliability calculation. Based on extensive experimental and numerical analysis results, the damage state of SC-PSBCs can be classified into multiple performance levels according to the damage index D. Among them, the "collapse failure" state corresponds to the complete loss of structural function, and its macroscopic manifestations include unacceptable failure forms such as large-scale spalling of the concrete cover, excessive pier tilt angle, significant decrease in bearing capacity, or yielding of prestressing tendons. Therefore, this invention precisely defines the limit state (i.e., failure) criterion of SC-PSBCs as: when the seismic load is sustained, the structure's damage index first reaches or exceeds the critical threshold corresponding to "collapse failure". in, For the duration of seismic load; A random vector characterizing the randomness of material parameters; The threshold for structural damage indicators to reach the point of collapse and failure.

[0027] ② Probability density evolution reliability analysis method considering material randomness Once the physical damage model and failure criteria are defined, a corresponding probabilistic analysis framework can be established. Since the material parameters of SC-PSBCs (such as concrete and steel reinforcement strength) have inherent randomness, they can be characterized as a random vector. The nonlinear stochastic response of a structure under seismic loading, and the damage index calculated therefrom. All of these become stochastic processes that depend on random variables and time.

[0028] To accurately solve damage indices Probability evolution and its transcendence threshold The probability of failure (i.e., the probability of randomness) is determined by probability density evolution theory based on the principle of probability conservation. The core of this theory is that for randomness entirely derived from basic variables… The system, augmentation system This constitutes a probabilistically conservative system. The generalized probability density evolution equation derived from this describes the propagation law of the system's randomness: in, Damage indicators With random variables The joint probability density function, In the given hour The rate of change.

[0029] Its boundary and initial conditions are respectively in The failure domain of the structure is defined by the limit state determination criteria of SC-PSBCs mentioned above.

[0030] Solve the above equation, then integrate in the space of random variables to obtain the probability density function of the "residual" within the safe region. The reliability can then be calculated as follows: The recently developed probability density evolution theory profoundly reveals the propagation law of probabilistic information in stochastic dynamic systems. By decoupling physical states, it achieves a precise description of the stochastic response of complex systems, providing an innovative approach to structural reliability research. Based on this, this invention focuses on self-resetting segmental precast bridge piers (SC-PSBCs), a structural system with unique damage and reset mechanisms. It introduces an improved two-parameter damage model specifically designed for SC-PSBCs, considering their joint opening, low residual deformation, and localized energy dissipation characteristics, thereby scientifically quantifying their unique damage evolution process. Secondly, it uses key parameters describing the properties of concrete and steel reinforcement as basic random variables, and combines them with the physical failure criteria defined by the aforementioned dedicated damage model to precisely introduce absorbing boundary conditions into the probability density evolution equation. Thus, this invention establishes a reliability assessment method that fully couples dedicated physical damage criteria to stochastic probability analysis, achieving an accurate grasp of the seismic reliability evolution law and overall safety performance of SC-PSBCs under seismic loading, considering material randomness. This provides a precise and reliable analytical tool for the performance-based design and safety assessment of this type of high-performance bridge pier.

[0031] This invention, based on the damage evolution law of self-resetting segmental prefabricated bridge piers and a dedicated damage model for this type of pier, establishes structural failure criteria and evaluates the seismic reliability of self-resetting segmental prefabricated bridge piers under cyclic loading. A scaled-down model of a self-resetting segmental prefabricated bridge pier with energy-dissipating reinforcement is used as an example to illustrate the seismic reliability evaluation method of this invention.

[0032] The overall structural layout of the bridge piers is as follows Figure 2 As shown in (a). This invention takes this bridge pier as the analysis object, which mainly consists of three parts: the pier cap, the pier body, and the pier crown. The specific geometric structure is as follows: the pier cap has dimensions of 900mm × 900mm × 500mm; the pier body has a rectangular hollow cross-section with outer dimensions of 400mm × 300mm, inner cavity dimensions of 200mm × 100mm, and a wall thickness of 100mm. The pier body is divided into four segments of equal height along the height direction, each segment being 300mm high, and numbered sequentially from bottom to top as the first to the fourth segment.

[0033] For details on the overall layout and cross-sectional reinforcement of the bridge piers, please refer to Figure 2 (b) Reinforcing bars are configured according to different locations, with diameters of 14mm, 12mm, and 8mm respectively. Specifically, 14mm diameter bars are used only for longitudinal reinforcement at the top of the pier cap; 12mm diameter bars are used for longitudinal reinforcement at the bottom of the pier cap, longitudinal reinforcement in the pier cap, and energy-dissipating reinforcement in the pier body; 8mm diameter bars are used for stirrups in the pier cap and pier cap, and for longitudinal and stirrup configuration in the pier body section. A total of 32 longitudinal reinforcing bars are arranged in the pier body section; the stirrups are evenly distributed longitudinally, with a stirrup spacing of 62mm in the second to fourth segments; considering that seismic damage is mainly concentrated at the bottom of the pier body, the stirrups in the first segment are densified, with a spacing of 50mm. The concrete cover thickness for all stirrups is 20mm. In addition, high-strength, low-relaxation steel strands with a diameter of 15.2mm are used for prestressing tendons.

[0034] like Figure 1 As shown in the embodiment, the seismic reliability analysis method for self-resetting assembled bridge piers is applicable to scenarios where the external load is a reciprocating seismic load, enabling accurate and efficient analysis of the seismic reliability of SC-PSBCs; including: Step 1: Determine the basic random variables of the structure. This invention considers the compressive strength of the structural concrete. With the yield strength of steel bars Let be the basic random variable, represented as Among them, concrete compressive strength Follows Burr distribution; yield strength of steel reinforcement It follows a log-normal distribution. The joint probability density function of the two... Constitutes the overall probability space The strength of C40 concrete follows a Burr distribution, and its dimensional parameters... The shape parameters are respectively , The yield strength of HRB400E follows a log-normal distribution. According to the Code for Design of Concrete Structures (GB50010-2010), its average yield strength and coefficient of variation are 431.98 MPa and 0.036, respectively.

[0035] Step 2: Select representative samples. Using the Voronoi region probability space partitioning method, the overall probability space spanned by the probability spaces of all basic random variables is partitioned, resulting in 251 probability subspaces. Representative points are selected using the GF bias point selection strategy to obtain the corresponding representative points for each probability subspace. ,in The total number of representative samples; and the corresponding assigned probabilities are calculated. Appendix Figure 3 The probability density distribution scatter plots of the strength of C40 concrete and HRB400E steel bars corresponding to 251 representative points selected in the example are shown, where (a) is the strength of C40 concrete and (b) is the yield strength of HRB400E steel bars, which intuitively reflects the statistical distribution characteristics of the sampling points under the given probability model.

[0036] Step 3: Structural stochastic response analysis. For each representative point... Deterministic mechanical response analysis was performed to solve the response of SC-PSBCs under cyclic loading. During loading, the displacement ratio increased progressively in the following sequence: 0.1%, 0.2%, 0.3%, 0.5%, 0.75%, 1%, 1.5%, 2%, 2.5%, 3%, 3.5%, 4%, 4.5%, 5%, 6%. Within the displacement ratio range of 0.1% to 1%, each displacement amplitude was applied once; when the displacement ratio reached 1% or higher, each displacement amplitude was applied twice. This loading regime aims to simulate the progressive nonlinear response of the structure under seismic loading and effectively capture its entire behavior from yielding and strengthening to failure. The corresponding loading amplitude history curves are shown below. Figure 4 As shown. The finite element method was used for numerical solution, and the calculations were performed using ABAQUS software. The displacement response at the top of the bridge pier was ultimately obtained. Force response .

[0037] Step 4: Structural Hysteresis Analysis. The pier top force and displacement data obtained in Step 3 are processed to plot hysteresis curves. Using the displacement response at the pier top as the x-axis and the force response as the y-axis, the preprocessed displacement-force data sets are used to plot the complete hysteresis curve for each representative sample. Some sample hysteresis curves are shown below. Figure 5 As shown.

[0038] (1) Extracting residual displacement For each loading amplitude level, the corresponding hysteresis loop is extracted from the hysteresis curve. The horizontal displacement value at the pier top corresponding to the moment of unloading from the last load cycle to zero under that level is then extracted; this is the residual displacement under that loading amplitude. Figure 6 This is a schematic diagram for extracting residual displacement. Specifically, when the load is completely unloaded to zero horizontal restoring force, if there is still unrecovered permanent displacement at the pier top, this displacement value is the residual displacement, and its magnitude reflects the pier's self-restoring ability under that load intensity. (See attached diagram) Figure 7 The residual displacement curve represents the point set.

[0039] (2) Extracting energy consumption per cycle The hysteresis curve of each representative sample is quantitatively calculated using the "hysteresis loop area integration method": for each loading amplitude level, the area of ​​the hysteresis loops corresponding to all load cycles under that level is integrated, and the integration result is the energy consumption of a single cycle under that loading amplitude.

[0040] (3) Extracting the yield displacement Yield load Limit displacement Extracting the skeleton curve from the hysteresis curve: Select the peak point of the last load cycle under each loading amplitude level, and connect all peak points in ascending order of loading amplitude to form the skeleton curve. The ultimate displacement is the displacement corresponding to the maximum horizontal restoring force of the skeleton curve. If the curve has a significant downward segment, the displacement corresponding to the restoring force dropping to 85% of the peak value is taken. Extracting the yield parameter using the energy equivalence method: First, determine the elastic stiffness of the skeleton curve through linear fitting. Draw an elastic straight line with this stiffness through the origin, and then draw a horizontal line from the endpoint corresponding to the ultimate displacement to obtain the equivalent elastic ultimate load. Calculate the energy dissipation area enclosed by the skeleton curve and the equivalent elastic polygonal line, and make it equal to the area of ​​the triangle formed by the skeleton curve and the equivalent elastic polygonal line. The intersection point is the yield point, the corresponding displacement is the yield displacement, and the corresponding restoring force is the yield load.

[0041] Step 5: Calculate the damage index and its evolution rate for each sample. First, based on the improved seismic damage model of precast segmental piers, substitute the response data obtained in Step 4 to calculate the damage index of SC-PSBCs under seismic load. in, For sample number, ; In this invention, time refers to the displacement amplitude during reciprocating cyclic loading; These are the combination coefficients for each sample, which are related to the structural design parameters; This represents the evolution process of the residual displacement ratio; The ratio of the structural ultimate residual displacement; is the effective energy dissipation factor for the i-th loading cycle, which is related to the self-resetting performance of the structure; The energy dissipation of the i-th loading loop; This is the structural yield load; , These are the yield displacement and the ultimate displacement, respectively.

[0042] Finally, the curves showing the change of damage indices of each sample with the loading amplitude can be obtained as follows: Figure 8 As shown.

[0043] Furthermore, obtain damage indicators Regarding generalized time derivative .

[0044] Step 6: Define the failure criterion for self-resetting segmental precast bridge piers. Under the first exceedance failure criterion, the structure is considered to be in a state of cyclic loading. In, its damage index First time reaching or exceeding the collapse damage threshold At that time, the structure fails. Its mathematical expression is: in, In this embodiment, time is defined as the loading amplitude; A random vector characterizing the randomness of material parameters; The threshold for structural damage indicators to reach the point of collapse and failure.

[0045] For self-resetting segmental precast bridge piers, based on existing damage models and damage state grading mechanisms for this type of pier, failure is defined as a structural damage index exceeding 1.029. Therefore, the failure criterion can be expressed as: Step 7: Solve the generalized probability density evolution equation with absorbing boundaries. Its mathematical expression is: Its initial conditions are The damage index obtained in step 5 And its concept of generalized time derivative Substituting the generalized probability density evolution equation, the probability density distribution of bridge pier damage indicators can be obtained through numerical methods. .

[0046] Step 8: Obtain the "residual" probability density function. This involves applying the probability density distribution of the pier damage index obtained in Step 7. Integrating in the space of random variables yields the probability density function of the "residual" region. The final probability density evolution results of the damage index of the self-resetting segmental precast bridge pier under low-cycle cyclic loading are as follows: Figure 9 As shown.

[0047] Step 9: Evaluate the time-varying reliability of SC-PSBCs. The time-varying reliability of the structure is obtained by integrating the "residual" probability density over the safety region. The final reliability curve of the self-resetting segmental precast bridge pier under low-cycle cyclic loading is shown in the figure. Figure 10 As shown.

[0048] The innovation of this invention lies first in the organic integration of probability density evolution theory with a two-parameter damage model for SC-PSBCs, forming an evaluation framework that combines theoretical rigor with engineering applicability. Probability density evolution theory, as the probabilistic analysis basis of the method in this invention, can rigorously characterize the entire process of material randomness propagation in nonlinear systems; while the introduced two-parameter damage model for SC-PSBCs accurately reflects its joint opening, damage localization, and self-resetting characteristics, overcoming the limitations of traditional models in applicability to such structures. By transforming the dedicated damage criterion into an absorbing boundary in probability space, a deep integration of physical damage mechanisms and probabilistic reliability analysis is achieved for the first time in the seismic reliability assessment of SC-PSBCs.

[0049] Example 2 This invention also provides a seismic reliability analysis device for self-resetting assembled bridge piers, comprising: The first processing module is used to determine the basic random variables of the structure; The second processing module is used to select representative samples and calculate the assigned probabilities of the probability subspace. The third processing module is used to analyze the structural random response; The fourth processing module is used to analyze structural hysteresis; The fifth processing module is used to calculate the damage index and its evolution rate for each sample; The sixth processing module is used to define the failure criteria for self-resetting segmental prefabricated bridge piers; The seventh processing module is used to solve the generalized probability density evolution equation with absorbing boundaries; The eighth processing module is used to obtain the residual probability density function; The ninth processing module is used to evaluate the time-varying seismic reliability of self-resetting segmental prefabricated piers.

[0050] Example 3 The present invention also provides a seismic reliability analysis system for self-resetting assembled bridge piers, comprising: a memory and a processor, wherein the memory stores a computer program executed by the processor, and the computer program executes a seismic reliability analysis method for self-resetting assembled bridge piers when executed by the processor.

[0051] Example 4 The present invention also provides a storage medium storing a computer program, which executes a method for analyzing the seismic reliability of self-resetting assembled bridge piers during operation.

[0052] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for seismic reliability analysis of self-resetting assembled bridge piers, characterized in that, include: Step 1: Determine the basic random variables of the structure; Step 2: Select representative samples and calculate the assigned probabilities of the probability subspace; Step 3: Analyze the structural random response; Step 4: Analyze structural hysteresis; Step 5: Calculate the damage index and its evolution rate for each sample; Step 6: Define the failure criteria for self-resetting segmental prefabricated bridge piers; Step 7: Solve the generalized probability density evolution equation with absorbing boundary; Step 8: Obtain the residual probability density function; Step 9: Evaluate the time-varying seismic reliability of self-resetting segmental precast piers.

2. The seismic reliability analysis method for self-resetting assembled bridge piers as described in claim 1, characterized in that, The generalized probability density evolution equation is: ， in, Damage indicators With random variables The joint probability density function reflects the probability distribution characteristics of the structural damage index D and the random variable taking a certain combination value under a given generalized time. Given a random variable taking the value At that time, structural damage The instantaneous evolution speed as the loading process progresses; For time in a general sense. Its boundary and initial conditions are as follows: ， in, It is the joint probability density function of the damage index D and the random variable. It describes the deterministic initial value of the damage state, in At infinity, and elsewhere The value is zero at the point, and it is zero throughout the entire... d The spatial integral is 1; Characterizing the inherent uncertainty of random variables, the basic random variables The probability distribution at the initial time; at the initial time The structural damage index D of all samples is definitively equal to the same initial value with 100% probability. , ， in, The failure domain, i.e., the damage index D Areas that have reached or exceeded the damage threshold It is the damage index D and the random variable The joint probability density function; if the damage enters the failure domain. Its probability density immediately becomes zero.

3. The seismic reliability analysis method for self-resetting assembled bridge piers as described in claim 2, characterized in that, Solving the generalized probability density evolution equation and integrating it in the space of random variables yields the remaining probability density function within the safe region: ， in, For the space of random variables, It is the joint probability density function of the damage index D and the random variable, and its expression in the random variable... Throughout the space By integrating the above, the total probability distribution of the damage index within the safety region can be obtained. , Therefore, the reliability can be calculated as follows: ， in, The structure represents the generalized time. The reliability of the changes; Indicates the safe range of damage indicators Integrate over the above; calculate the "residual" probability density function of the damage index. In the security domain The time-varying reliability of the structure can be obtained by integrating within the time limit.

4. A seismic reliability analysis device for self-resetting assembled bridge piers, characterized in that, include: The first processing module is used to determine the basic random variables of the structure; The second processing module is used to select representative samples and calculate the assigned probabilities of the probability subspace. The third processing module is used to analyze the structural random response; The fourth processing module is used to analyze structural hysteresis; The fifth processing module is used to calculate the damage index and its evolution rate for each sample; The sixth processing module is used to define the failure criteria for self-resetting segmental prefabricated bridge piers; The seventh processing module is used to solve the generalized probability density evolution equation with absorbing boundaries; The eighth processing module is used to obtain the residual probability density function; The ninth processing module is used to evaluate the time-varying seismic reliability of self-resetting segmental prefabricated piers.

5. The self-resetting assembled bridge pier seismic reliability analysis device as described in claim 4, characterized in that, The generalized probability density evolution equation is: in, Damage indicators With random variables The joint probability density function, In the given hour The rate of change; Its boundary and initial conditions are as follows: ， 。 6. The self-resetting assembled bridge pier seismic reliability analysis device as described in claim 5, characterized in that, The eighth processing module solves the generalized probability density evolution equation, integrates it in the space of random variables, and obtains the remaining probability density function in the safe region as follows: ， The time-varying seismic reliability obtained from the eighth processing module is: 。 7. A seismic reliability analysis system for self-resetting assembled bridge piers, characterized in that, include: The system includes a memory and a processor, wherein the memory stores a computer program that is executed by the processor, and the computer program, when executed by the processor, performs the seismic reliability analysis method for self-resetting assembled bridge piers as described in any one of claims 1-3.

8. A storage medium, characterized in that, The storage medium stores a computer program, which executes the seismic reliability analysis method for self-resetting assembled bridge piers as described in any one of claims 1-3 when the computer program is running.

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