Bridge pile foundation reliability assessment method and system

Abstract

The invention discloses a bridge pile foundation reliability assessment method and system, and belongs to the technical field of safety assessment. Historical sample flow data of scouring a bridge pile foundation is obtained, and the value range and distribution condition of flow are determined; on the basis of the value range of the flow, selecting representative points to generate a representative point set, and determining the probability weight of each representative point according to the distribution condition of the flow; according to the representative point set, the scouring depth of the pile foundation corresponding to each flow is determined; the time and the scouring depth are discretized in the time dimension and the space dimension respectively, a probability density evolution equation is introduced and solved, and the probability density evolution result of the scouring depth of the pile foundation corresponding to each historical sample flow at different moments is obtained; the critical scouring depth of the pile foundation is determined according to the probability weight, and a limit state equation is constructed; and determining the failure probability of the pile foundation at any moment according to the limit state equation and the probability density evolution result. According to the method, the pile foundation reliability evaluation precision and efficiency can be remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of safety assessment technology, and more specifically to a method and system for assessing the reliability of bridge pile foundations. Background Technology

[0002] In the field of bridge engineering safety assessment, the reliability assessment of bridge pile foundations under scour is crucial. Scour is one of the key factors affecting the stability and reliability of bridge pile foundations, especially in random scour scenarios such as floods, where its uncertainty poses a significant challenge to the safe service of bridges.

[0003] While current research has made some progress, many shortcomings remain. Existing studies have included analyses of the damage caused by scour to bridges or structures, but most are limited to deterministic analysis methods. However, in actual scour processes, the scouring behavior of rivers or floods exhibits significant randomness and uncertainty. Such deterministic analysis methods cannot accurately reflect the actual situation and are insufficient to effectively assess the impact of random scour on the reliability of bridges during service, leading to significant discrepancies between assessment results and actual conditions.

[0004] Currently, some scholars have attempted to study the impact of uncertainty using the Monte Carlo simulation method. However, this method is a traditional simulation technique with significant drawbacks. It requires extensive sampling based on a large amount of sample data, which not only leads to excessively long calculation cycles and affects evaluation efficiency, but also, due to the limitations of sampling, its accuracy is often difficult to guarantee, failing to meet the needs of rapid and accurate reliability assessment of bridge pile foundations in practical engineering. Summary of the Invention

[0005] To address the problems existing in the above-mentioned fields, this invention proposes a reliability assessment method and system for bridge pile foundations. It comprehensively considers factors such as flow distribution, scour depth variation, and critical scour depth. The introduced probability density evolution equation can capture the randomness (uncertainty) of the scour depth variation of the pile foundation. By calculating the failure probability of the pile foundation, the reliability of the bridge pile foundation is comprehensively assessed, which can more accurately reflect the reliability risks faced by the bridge pile foundation in actual operation.

[0006] To address the aforementioned technical problems, this invention discloses a method for evaluating the reliability of bridge pile foundations, comprising the following steps: Historical sample flow data of scour of bridge pile foundations is obtained, and parameter fitting is performed on the distribution type of historical sample flow data to predict future flow and determine the range and distribution of flow values. Based on the range of traffic values, representative points are selected to generate a representative point set, and the probability weight of each representative point is determined according to the traffic distribution. Based on the representative point set, the scour depth of the pile foundation corresponding to each flow rate is determined by establishing a conversion formula of flow rate-velocity-scour depth. Time and scour depth are discretized in the time and space dimensions, respectively. A probability density evolution equation is introduced and the TVD difference method is used to solve the probability density evolution equation to obtain the probability density evolution results of the scour depth of the pile foundation corresponding to each historical sample flow at different times. The critical scour depth of the pile foundation is determined based on the probability weights, and the limit state equation is constructed. Based on the limit state equation and the probability density evolution results, the failure probability of the pile foundation at any time is determined.

[0007] Preferably, the step of acquiring historical sample flow data of bridge pile foundation scour and performing parameter fitting on the distribution type of the historical sample flow data to predict future flow, and determining the range and distribution of flow values, specifically includes: Determine that the historical sample flow data are independent random variables and follow a log-normal distribution, and obtain the mean and standard deviation of the historical sample flow data; Based on the mean and standard deviation, the future flow rate is predicted through parameter fitting, and the range of flow rate values ​​is defined.

[0008] Preferably, the step of selecting representative points to generate a representative point set based on the flow range and determining the probability weight of each representative point according to the flow distribution specifically includes: Based on the range of flow values, a one-dimensional uniform point selection method is used to select several representative points from the range of flow values ​​to generate a representative point set. Based on the distribution of traffic, the probability weight of each representative point in the representative point set is determined by the Voronoi partitioning method.

[0009] Preferably, the step of determining the scour depth of the pile foundation corresponding to each flow rate by establishing a conversion formula of flow rate-velocity-scour depth based on a representative point set specifically includes: Based on the representative point set, the conversion formula of flow rate-velocity-scour depth is established using the SRICOS formula and Manning formula to determine the scour depth of the pile foundation corresponding to each flow rate. The SRICOS formula is: In the formula: Let t be the scour depth of the pile foundation at time t; Z represents the initial erosion rate of the pile foundation; max This represents the maximum scour depth of the pile foundation. Maximum scour depth of pile foundation z max for: In the formula: K sh The shape influence factor of the pile foundation; K w Water depth influencing factors; K sp The spacing of the pile foundation is an influencing factor. D ' is the projected width of the pile foundation perpendicular to the water flow; v The viscosity of water; The viscosity of water is obtained using Manning's formula. v for: In the formula: Q 0 represents the river flow rate; W The width of the river is expressed in meters (m). y 0 represents the depth of the upstream water flow, in meters (m). This is the Manning coefficient; s This refers to the longitudinal slope of the river channel.

[0010] Preferably, the step of discretizing time and scour depth in the time and spatial dimensions respectively, introducing a probability density evolution equation, and solving the probability density evolution equation using the TVD difference method to obtain the probability density evolution result of the scour depth of the pile foundation corresponding to each historical sample flow at different times specifically includes: Get time variables t scour depth X and traffic ; Time discretization The service life of the bridge is determined as follows T ,Will T The corresponding time domain [0, T Discretized into several discrete time steps Obtain time grid points t n = n Δ t ,in, n =0, 1, 2, ... N , N The number of grid cells corresponding to discrete time; Scouring depth discretization The scour depth range of the pile foundation is determined as [ X min , X max ],Will[ X min , X maxDivided into several discrete scour depth steps Δ X , obtain the scour depth grid points X i = i Δ h ,in i =0, 1, 2, ... m , m The number of grid cells corresponding to discrete scour depths; Define the scour depth of the pile foundation X The state equation is: Where M and C are the flow rates, respectively. The mass matrix and damping matrix; and Corresponding to traffic The response vector of nth-order displacement and velocity; It's traffic. The restoring force vector; For traffic The excitation vector received; Define to add traffic scour depth X The corresponding state equation becomes: Assuming the solution involves adding flow scour depth X The analytical expression obtained from the corresponding state equation is: Its derivative is ; In the formula, , for The j One portion, J Indicates the total number of components; Define traffic and scour depth X The extended state vector is: The state equation for obtaining the extended state vector is: in, ; Based on the principle of probability conservation, the extended state vector... joint probability density function satisfy: in, , For traffic The corresponding real-valued variable; get joint probability density The corresponding evolution equation is: The initial conditions for the evolution equation are: in, yes The initial value is known; It's traffic. The joint probability density; The ratio of the discrete time step to the scour depth step is obtained as follows: r L , ; Will CFL condition as a difference in TVD; Using the difference method of TVD, the joint probability density is analyzed with respect to flow rate. Integrate and solve the evolution equation corresponding to the probability density; Get each traffic The probability density evolution results at any time and any scour depth .

[0011] Preferably, the step of determining the critical scour depth of the pile foundation based on probability weights and constructing the limit state equation specifically includes: Obtain the scour depth of the pile foundation corresponding to the historical sample flow at different times; Based on the scour depth of the pile foundation corresponding to the historical sample flow at different times, the probability weight of its occurrence is determined by statistically analyzing the frequency of occurrence of the scour depth among all the obtained scour depths. Based on probability weights, and taking into account engineering experience and safety standards, a critical scour depth is determined. The limit state equations are established as follows: in, x critical This indicates the critical scour depth of the pile foundation. x i It is any time t The corresponding scour depth of the pile foundation.

[0012] Preferably, determining the failure probability of the pile foundation at any given time based on the limit state equation and the probability density evolution results specifically includes: The scour depth of the pile foundation is obtained from the probability density evolution results obtained by the TVD finite difference method. z ( t The corresponding probability density function is ; Define the failure probability of pile foundations The probability that R ≤ 0, i.e. ; For probability density function exist Integrate over the interval to obtain... .

[0013] Preferably, it also includes a bridge pile foundation reliability assessment system, comprising: The data acquisition module is used to acquire historical sample flow data of bridge pile foundation scour, and to perform parameter fitting on the distribution type of the historical sample flow data to predict future flow, and determine the range and distribution of flow values. The pile foundation scour depth determination module is used to select representative points to generate a representative point set based on the range of flow rate values, and determine the probability weight of each representative point according to the flow rate distribution; based on the representative point set, the scour depth of the pile foundation corresponding to each flow rate is determined by establishing a conversion formula of flow rate-velocity-scour depth. The scour depth probability density evolution module is used to discretize time and scour depth in the time and space dimensions, respectively, introduce the probability density evolution equation, and use the TVD difference method to solve the probability density evolution equation to obtain the probability density evolution result of the scour depth of the pile foundation corresponding to each historical sample flow at different times. The reliability assessment module is used to determine the critical scour depth of the pile foundation based on probability weights and to construct the limit state equation. Based on the limit state equation and the probability density evolution results, the failure probability of the pile foundation at any time is determined.

[0014] Compared with the prior art, the present invention has the following beneficial effects: The bridge pile foundation reliability assessment method proposed in this invention recognizes that flow rate is a crucial factor influencing the reliability of bridge pile foundations. Since water flow exerts a scouring effect on bridge pile foundations, different flow rates and their distributions determine the intensity and frequency of this scouring, thus affecting the stability and reliability of the pile foundations. Accurately predicting the flow rate and determining its range and distribution provides fundamental data for subsequent assessments of pile foundation reliability under various flow conditions. Determining representative points and their probability weights based on the flow rate range and distribution reflects different flow conditions and their likelihood of occurrence. Since different flow rates have varying scouring effects on bridge pile foundations, this method comprehensively considers the impact of various possible flow conditions on pile foundation reliability, making the assessment results more representative. Scouring depth is a key indicator for measuring the scouring effect of water flow on bridge pile foundations, directly related to the pile foundation's burial depth and stability. Excessive scouring depth reduces the pile foundation's bearing capacity, potentially leading to bridge structural instability. Therefore, accurately determining the scouring depth is crucial for assessing the reliability of bridge pile foundations. The obtained probability density evolution results fully consider the changes in scour depth over time and its probability distribution, comprehensively reflecting the dynamic process and uncertainty of bridge pile foundations under the scour effect of water flow at different times, providing dynamic information for accurately assessing pile foundation reliability. Failure probability is an important indicator for measuring the reliability of bridge pile foundations. When the scour depth reaches or exceeds a critical value, the pile foundation may fail, threatening the safety of the bridge structure. By determining the failure probability, the reliability of bridge pile foundations under various water flow conditions can be intuitively assessed, providing a scientific basis for bridge maintenance, reinforcement, and safety management. Attached Figure Description

[0015] Figure 1 This is a flowchart of the bridge pile foundation reliability assessment method proposed in this invention. Detailed Implementation

[0016] The following will refer to the appendices in the embodiments of the present invention. Figure 1 The technical solutions in the embodiments of the present invention will be clearly and completely described. It should be understood that the terminology used in the present invention is only for describing particular implementation methods and is not intended to limit the present invention.

[0017] Example like Figure 1 As shown, this invention proposes a method for assessing the reliability of bridge pile foundations, comprising the following steps: S1: Obtain historical sample flow data of scouring bridge pile foundations, and perform parameter fitting on the distribution type of historical sample flow data to predict future flow, and determine the range and distribution of flow values; S2: Based on the range of traffic values, select representative points to generate a representative point set, and determine the probability weight of each representative point according to the distribution of traffic. S3: Based on the representative point set, the scour depth of the pile foundation corresponding to each flow rate is determined by establishing a conversion formula of flow rate-velocity-scour depth. S4: Discretize time and scour depth in the time and space dimensions respectively, introduce a probability density evolution equation, and use the TVD difference method to solve the probability density evolution equation to obtain the probability density evolution results of the scour depth of the pile foundation corresponding to each historical sample flow at different times. S5: Determine the critical scour depth of the pile foundation based on the probability weights and construct the limit state equation; determine the failure probability of the pile foundation at any time based on the limit state equation and the probability density evolution results.

[0018] In step S1, historical sample flow data of scour of bridge pile foundations are determined. Q Independent random variables y And it follows a log-normal distribution: In the formula, μ Q and σ Q These are known historical sample traffic data. Q The mean and standard deviation.

[0019] Based on the mean and standard deviation, the future flow rate is predicted through parameter fitting, thus obtaining the range of flow rate values.

[0020] By obtaining historical sample flow data of the bridge pile foundation, a basic information foundation is provided for subsequent analysis and calculation. These data reflect the historical flow changes of the hydrological environment in which the bridge is located and are an important basis for assessing the reliability of the pile foundation.

[0021] Predicting future flow rates by fitting parameters to the distribution types of historical sample flow data allows for an understanding of the potential flow range and distribution characteristics in advance. This helps in preparing for contingencies, assessing the reliability of bridge pile foundations under different flow scenarios, and providing forward-looking guidance for bridge design, maintenance, and management.

[0022] Determining the range and distribution of flow rates allows for a more accurate and comprehensive description of the flow. Understanding the range of flow rates reveals the maximum and minimum possible flow values, while the distribution reflects the probability of different flow values ​​occurring, providing essential information for subsequent selection of representative points and calculation of probability weights.

[0023] In step S2, based on the range of flow values, a number of representative points are selected from the range of flow values ​​using a one-dimensional uniform point selection method to generate a representative point set; based on the distribution of flow, the probability weight of each representative point in the representative point set is determined using the Voronoi partitioning method.

[0024] The relevant theory for the one-dimensional Voronoi partitioning method is as follows: Let a one-dimensional random vector (flow) be denoted as The range space of the set Θ(s) is ΩΘ⊆Rs. ΩΘ is partitioned into a set of mutually exclusive subdomains. Voronoi decomposition is widely used due to its clear geometric meaning and computational convenience.

[0025] Voronoi subfield with θq as its core The definition is: for any q = 1, 2, ..., a, we have: In the formula, denoted as a point in the distribution space ΩΘ, i.e., a representative point, and s represents the number of that point in the distribution space ΩΘ; This represents the Euclid distance.

[0026] Based on the range of flow values, a one-dimensional uniform point sampling method is used to analyze the flow. By selecting several representative points within the range of values ​​to generate a representative point set, the continuous flow range is discretized into a finite number of representative points, which greatly simplifies the subsequent calculation process. Instead of calculating every possible flow value, the representative points are used to approximate the entire flow range, thus improving computational efficiency.

[0027] Based on the distribution of traffic flow, the probability weight of each representative point in the representative point set is determined by the Voronoi partitioning method. This fully considers the probability differences of different traffic flow values, so that each representative point can be assigned a corresponding weight according to its probability of occurrence in subsequent calculations. This results in a more accurate reflection of the actual situation and improves the accuracy of the assessment.

[0028] In step S3, based on the representative point set, the scour depth of the pile foundation corresponding to each flow rate is determined by establishing a conversion formula of flow rate-velocity-scour depth using the Manning formula and the SRICOS formula.

[0029] SRICOS formula: In the formula: The depth of scour at time t is the depth of the pile foundation in meters. The initial erosion rate of the pile foundation is expressed in m³ / s; zmax This represents the maximum scour depth of the pile foundation, expressed in meters (m).

[0030] The initial erosion rate can be obtained by testing the shear stress-erosion rate curve of the pile foundation and by consulting the shear stress-erosion rate curve to obtain the erosion rate value of the pile foundation under different flow velocities. In particular, if the erosion rate value of the pile foundation cannot be obtained by testing, the initial erosion rate of the pile foundation under different flow velocities can be obtained directly by consulting relevant literature.

[0031] The maximum scour depth z of the pile foundation in the above formula max It can be represented as: In the formula: K sh The shape influence factor of the pile foundation; K w Water depth influencing factors; K sp The spacing of the pile foundation is an influencing factor. D ' is the projected width of the pile foundation perpendicular to the water flow, in meters; v Viscosity of water, measured in meters (m). 2 / s.

[0032] If the cross-section of a river is rectangular, the viscosity of the water... v This can be expressed using Manning's formula as follows: In the formula: Q 0 represents the river flow rate, in cubic meters per second (m³). 3 / s; W The width of the river is expressed in meters (m). y 0 represents the depth of the upstream water flow, in meters (m). This is the Manning coefficient, which is typically taken as 0.035. s This refers to the longitudinal slope of the river channel.

[0033] By establishing a conversion formula between flow rate, velocity, and scour depth, the scour depth of the pile foundation corresponding to each flow rate is determined, establishing a direct relationship between flow rate and scour depth of the pile foundation. This allows flow rate information to be converted into scour depth information that is closely related to the reliability of the pile foundation, providing key intermediate parameters for subsequent reliability assessment.

[0034] By specifying the scour depth corresponding to each flow rate, the scour effect on bridge pile foundations under different flow conditions can be quantified. This helps to understand the degree of scour that pile foundations may experience under different flow scenarios, and provides specific numerical basis for assessing the stability and safety of pile foundations.

[0035] In step S4, time and scour depth are discretized in the time and spatial dimensions, respectively. A probability density evolution equation is introduced, and the TVD finite difference method is used to solve the probability density evolution equation to obtain the probability density evolution results of the scour depth of the pile foundation corresponding to each historical sample flow at different times. Specifically, this includes: Get time variables t scour depth X and traffic ; Time discretization The service life of the bridge is determined as follows T ,Will T The corresponding time domain [0, T Discretized into several discrete time steps Obtain time grid points t n = n Δ t ,in, n =0, 1, 2, ... N , N The number of grid cells corresponding to discrete time; Scouring depth discretization The scour depth range of the bridge is determined as [ X min , X max ],Will[ X min , X max Divided into several discrete scour depth steps Δ X , obtain the scour depth grid points X i = i Δ h ,in i =0, 1, 2, ... m , m The number of grid cells corresponding to discrete scour depths; Consider a general stochastic dynamical system, whose dynamic response equation can be expressed as: Where M and C are the flow rates, respectively. The mass matrix and damping matrix; , and Corresponding to traffic The response vector of nth-order displacement, velocity, and acceleration; It's traffic. The restoring force vector; For traffic The excitation vector received, This represents a parameter vector that reflects the physical characteristics of a stochastic dynamic system, i.e., the flow rate.

[0036] Subsequently, the scour depth was introduced into the dynamic response equation. X state vector Its state equation can be obtained as follows: When considering traffic At that time, the scouring depth X The corresponding state equation is transformed into: Assuming the scouring depth of the conversion X The analytical expression obtained from the corresponding state equation is: Its derivative is ; In the formula, , for The j One portion, J Indicates the total number of components; Define traffic and scour depth X The extended state vector is: The state equation for the extended state vector is: in, ; Based on the principle of probability conservation, the extended state vector... joint probability density function Must meet: in, , for The corresponding real-valued variable.

[0037] If we are only interested in a component of a particular response, we can obtain information about... joint probability density The corresponding evolution equation is: The initial conditions for the evolution equation are: in, yes The initial value is known. It is a random parameter The joint probability density.

[0038] The probability density evolution equation is solved using the difference method of TVD: in, g n Indicates two adjacent time steps t n-1 and t n The average scour depth of the corresponding pile foundation. p The superscript indicates the index of the discrete time step, and the subscript indicates the index of the discrete scour depth step. p Parameters with subscripts and superscripts are represented at discrete grid points ( x j , t n Approximate values ​​on ) It is the grid ratio of the difference method in TVD; For the flux limiter of the differential method of TVD, ; The CFL condition for TVD difference is ,in, It is the ratio of the discrete time step to the scour depth step.

[0039] For joint probability density with respect to flow Integrate points: Get each traffic The probability density evolution results at any time and any scour depth .

[0040] This invention describes the variation of scour depth over time from a probabilistic perspective. It not only tells us the possible values ​​of the scour depth of the pile foundation at different times, but also how the probability density of each value evolves over time.

[0041] Considering the uncertainties in the scour process of the pile foundation, the randomness (uncertainty) of the scour depth variation can be captured by the probability density evolution equation. This is crucial for accurately assessing the reliability of bridge pile foundations in complex hydrological environments, because the actual scour process is affected by a variety of uncertainties, such as fluctuations in water flow velocity and the heterogeneity of riverbed geological conditions.

[0042] In step S5, the scour depth of the pile foundation corresponding to the historical sample flow at different times is obtained; based on the obtained scour depth of the pile foundation corresponding to the historical sample flow at different times, the probability weight of its occurrence is determined by statistically analyzing the frequency of occurrence of the scour depth of the pile foundation among all the obtained scour depths.

[0043] According to relevant reliability theories, limit state equations (performance functions) are generally used to describe the working state of a structure. The equations include two main indices: load effect and resistance. For the scour problem of bridge pile foundations, the "load effect" is the scour depth around the bridge pile foundation, and the "resistance" is the critical scour depth around the bridge pile foundation.

[0044] Based on probability weights, engineering experience, and safety standards, the critical scour depth of a pile foundation is determined, and the limit state equation is established as follows: The limiting scour depth defined in this invention is... x critical A bridge pile diameter of 1.5 times the empirical value is used as a reference.

[0045] when At that time, the bridge pile foundation is in a reliable state; when At that time, the bridge pile foundation was in a state of failure; when R When = 0, the bridge pile foundation is in a limit state.

[0046] In the formula: R This represents the critical scour depth around the bridge pile foundation. x i This represents the actual scour depth around the bridge pile foundation.

[0047] When the limit state equation At that time, the probability of the pile foundation being in a failure state is calculated, and the failure probability is... : in, This represents the probability that the actual scour depth of a bridge pile foundation exceeds its critical scour depth. The probability of that time.

[0048] Failure probability is an important indicator for evaluating the reliability of bridge pile foundations. It directly reflects the likelihood of bridge pile foundations failing under specific conditions.

[0049] Based on the probability density evolution results obtained earlier, i.e., the probability density curve of the scour depth at any given time, where the horizontal axis represents the scour depth and the vertical axis represents the normalized probability density, this curve is characterized by the area enclosed by the curve and the coordinate axes being 1. A limiting scour depth is defined, which is the bridge pile diameter D, previously used as an empirical value of 1.5 times, as a reference. x critical ,Right now x critical =1.5D, and then integrate this probability density curve over the interval from 1.5D to positive infinity to obtain the failure probability of the bridge pile foundation at this moment. By clearly defining the failure probability, a clear decision-making basis can be provided for the design, maintenance and reinforcement of bridges.

[0050] This invention also proposes a bridge pile foundation reliability assessment system, comprising: The data acquisition module is used to acquire historical sample flow data of bridge pile foundation scour, and to perform parameter fitting on the distribution type of the historical sample flow data to predict future flow, and determine the range and distribution of flow values. The pile foundation scour depth determination module is used to select representative points to generate a representative point set based on the range of flow rate values, and determine the probability weight of each representative point according to the flow rate distribution; based on the representative point set, the scour depth of the pile foundation corresponding to each flow rate is determined by establishing a conversion formula of flow rate-velocity-scour depth. The scour depth probability density evolution module is used to discretize time and scour depth in the time and space dimensions, respectively, introduce the probability density evolution equation, and use the TVD difference method to solve the probability density evolution equation to obtain the probability density evolution result of the scour depth of the pile foundation corresponding to each historical sample flow at different times. The reliability assessment module is used to determine the critical scour depth of the pile foundation based on probability weights and to construct the limit state equation. Based on the limit state equation and the probability density evolution results, the failure probability of the pile foundation at any time is determined.

[0051] This invention comprehensively considers factors such as flow distribution, scour depth variation, and critical scour depth, and comprehensively evaluates the reliability of bridge pile foundations by calculating the failure probability. This method can more accurately reflect the reliability risks faced by bridge pile foundations during actual operation, providing strong technical support for ensuring the safe operation of bridges.

[0052] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

[0053] Furthermore, unless otherwise stated, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. All references to this specification are incorporated by way of citation to disclose and describe methods relating to those references. In the event of any conflict with any incorporated reference, the content of this specification shall prevail.

Claims

1. A method for assessing the reliability of bridge pile foundations, characterized in that, Includes the following steps: Historical sample flow data of scour of bridge pile foundations is obtained, and parameter fitting is performed on the distribution type of historical sample flow data to predict future flow and determine the range and distribution of flow values. Based on the range of traffic values, representative points are selected to generate a representative point set, and the probability weight of each representative point is determined according to the distribution of traffic. Based on the representative point set, the scour depth of the pile foundation corresponding to each flow rate is determined by establishing a conversion formula of flow rate-velocity-scour depth. Time and scour depth are discretized in the time and space dimensions, respectively. A probability density evolution equation is introduced and the TVD difference method is used to solve the probability density evolution equation to obtain the probability density evolution results of the scour depth of the pile foundation corresponding to each historical sample flow at different times. The critical scour depth of the pile foundation is determined based on the probability weights, and the limit state equation is constructed. Based on the limit state equation and the probability density evolution results, the failure probability of the pile foundation at any time is determined.

2. The bridge pile foundation reliability assessment method according to claim 1, characterized in that, The process of acquiring historical sample flow data of bridge pile foundation scour and performing parameter fitting on the distribution type of the historical sample flow data to predict future flow, determining the range and distribution of flow values, specifically includes: Determine that the historical sample flow data are independent random variables and follow a log-normal distribution, and obtain the mean and standard deviation of the historical sample flow data; Based on the mean and standard deviation, the future flow rate is predicted through parameter fitting, and the range of flow rate values ​​is defined.

3. The bridge pile foundation reliability assessment method according to claim 2, characterized in that, The process of selecting representative points based on the range of traffic values ​​to generate a representative point set, and determining the probability weight of each representative point according to the traffic distribution, specifically includes: Based on the range of flow values, a one-dimensional uniform point selection method is used to select several representative points from the range of flow values ​​to generate a representative point set. Based on the distribution of traffic, the probability weight of each representative point in the representative point set is determined by the Voronoi partitioning method.

4. The bridge pile foundation reliability assessment method according to claim 3, characterized in that, The process involves determining the scour depth of a pile foundation for each flow rate by establishing a conversion formula between flow rate, velocity, and scour depth based on a representative point set. Specifically, this includes: Based on the representative point set, the conversion formula of flow rate-velocity-scour depth is established using the SRICOS formula and Manning formula to determine the scour depth of the pile foundation corresponding to each flow rate. The SRICOS formula is: In the formula: Let t be the scour depth of the pile foundation at time t; Z represents the initial erosion rate of the pile foundation; max This represents the maximum scour depth of the pile foundation. Maximum scour depth of pile foundation z max for: In the formula: K sh The shape influence factor of the pile foundation; K w Water depth influencing factors; K sp The spacing of the pile foundation is an influencing factor. D ' is the projected width of the pile foundation perpendicular to the water flow; v The viscosity of water; The viscosity of water is obtained using Manning's formula. v for: In the formula: Q 0 represents the river flow rate; W The width of the river is expressed in meters (m). y 0 represents the depth of the upstream water flow, in meters (m). This is the Manning coefficient; s This refers to the longitudinal slope of the river channel.

5. The bridge pile foundation reliability assessment method according to claim 4, characterized in that, The process involves discretizing time and scour depth in both time and spatial dimensions, introducing a probability density evolution equation, and solving the equation using the TVD finite difference method. This yields the probability density evolution results of the scour depth of the pile foundation corresponding to each historical sample flow at different times. Specifically, this includes: Get time variables t scour depth X and traffic ; Time discretization The service life of the bridge is determined as follows T ,Will T The corresponding time domain [0, T Discretized into several discrete time steps Obtain time grid points t n = n Δ t ,in, n =0, 1, 2, ... N , N The number of grid cells corresponding to discrete time; Scouring depth discretization The scour depth range of the pile foundation is determined as [ X min , X max ],Will[ X min , X max Divided into several discrete scour depth steps Δ X , obtain the scour depth grid points X i = i Δ h ,in i =0, 1, 2, ... m , m The number of grid cells corresponding to discrete scour depths; Define the scour depth of the pile foundation X The state equation is: Where M and C are the flow rates, respectively. The mass matrix and damping matrix; and Corresponding to traffic The response vector of nth-order displacement and velocity; It's traffic. The restoring force vector; For traffic The excitation vector received; Define to add traffic scour depth X The corresponding state equation becomes: Assuming the solution involves adding flow scour depth X The analytical expression obtained from the corresponding state equation is: Its derivative is ; In the formula, , for The j One portion, J Indicates the total number of components; Define traffic and scour depth X The extended state vector is: The state equation for obtaining the extended state vector is: in, ; Based on the principle of probability conservation, the extended state vector... joint probability density function satisfy: in, , For traffic The corresponding real-valued variable; get joint probability density The corresponding evolution equation is: The initial conditions for the evolution equation are: in, yes The initial value is known; It's traffic. The joint probability density; The ratio of the discrete time step to the scour depth step is obtained as follows: r L , ; Will CFL condition as a difference in TVD; Using the difference method of TVD, the joint probability density is analyzed with respect to flow rate. Integrate and solve the evolution equation corresponding to the probability density; Get each traffic The probability density evolution results at any time and any scour depth .

6. The bridge pile foundation reliability assessment method according to claim 3, characterized in that, The determination of the critical scour depth of the pile foundation based on probability weights and the construction of the limit state equations specifically include: Obtain the scour depth of the pile foundation corresponding to the historical sample flow at different times; Based on the scour depth of the pile foundation corresponding to the historical sample flow at different times, the probability weight of its occurrence is determined by statistically analyzing the frequency of occurrence of the scour depth among all the obtained scour depths. Based on probability weights, and taking into account engineering experience and safety standards, a critical scour depth is determined. The limit state equations are established as follows: in, x critical This indicates the critical scour depth of the pile foundation. x i It is any time t The corresponding scour depth of the pile foundation.

7. The bridge pile foundation reliability assessment method according to claim 6, characterized in that, The determination of the failure probability of the pile foundation at any given time based on the limit state equation and the probability density evolution results specifically includes: The scour depth of the pile foundation is obtained from the probability density evolution results obtained by the TVD finite difference method. z ( t The corresponding probability density function is ; Define the failure probability of pile foundations The probability that R ≤ 0, i.e. ; For probability density function exist Integrate over the interval to obtain... .

8. A bridge pile foundation reliability assessment system, characterized in that, include: The data acquisition module is used to acquire historical sample flow data of bridge pile foundation scour, and to perform parameter fitting on the distribution type of the historical sample flow data to predict future flow, and determine the range and distribution of flow values. The scour depth determination module for pile foundations is used to select representative points to generate a representative point set based on the range of flow rates, and to determine the probability weight of each representative point according to the flow distribution. Based on the representative point set, the scour depth of the pile foundation corresponding to each flow rate is determined by establishing a conversion formula of flow rate-velocity-scour depth. The scour depth probability density evolution module is used to discretize time and scour depth in the time and space dimensions, respectively, introduce the probability density evolution equation, and use the TVD difference method to solve the probability density evolution equation to obtain the probability density evolution result of the scour depth of the pile foundation corresponding to each historical sample flow at different times. The reliability assessment module is used to determine the critical scour depth of the pile foundation based on probability weights and to construct the limit state equation. Based on the limit state equation and the probability density evolution results, the failure probability of the pile foundation at any time is determined.

Images