Bridge pile foundation scouring toughness analysis method and system

Abstract

The invention discloses a method and a system for analyzing scouring toughness of a bridge pile foundation. The method comprises the following steps: constructing a simplified finite element model of the bridge pile foundation; constructing a soil spring model, and coupling the soil spring model with the bridge pile foundation simplified finite element model to form a bridge pile-soil system finite element model; establishing a cylindrical streaming model based on Fluent to obtain a water flow load of the lower structure of the bridge; calculating a scouring load; removing insensitive parameters; loading a water flow load and a scouring load into the bridge pile-soil system finite element model, taking sensitive parameters as input variable parameters, performing finite element analysis, outputting a response result, and forming a sample working condition combination; constructing a BP neural network agent model through sample working condition combination; establishing a vulnerability curve, and constructing pile foundation performance functions in different damage states; performing weighted summation on the pile foundation performance functions to obtain a comprehensive performance function; and calculating the comprehensive performance function to obtain a bridge pile foundation scouring toughness index. According to the invention, toughness-based bridge scouring performance evaluation is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge pile foundation scour, and in particular relates to a bridge pile foundation scour toughness analysis method and system. Background Art

[0002] With the increasing frequency of extreme climate events, flood scour has become a key threat to bridge foundation safety. Bridge pile foundations, located in areas subject to intense hydrodynamic forces, are highly susceptible to localized scour erosion, leading to structural instability and even bridge collapse. Traditional scour analysis focuses on scour depth prediction and localized protection, while neglecting the dynamic performance evolution of structures under scour disturbances. This makes it difficult to comprehensively assess the safety of structures under extreme conditions.

[0003] In recent years, resilience theory has gradually become an important guide for infrastructure disaster resilience research. Resilience refers to the ability of a structure to maintain functionality, recover quickly, and adapt to changes after encountering external disturbances. In the case of bridge scour, resilience assessment focuses not only on whether the structure is damaged, but also on the extent of damage and the speed of recovery, emphasizing multi-stage, full-process system response modeling. There is an urgent need to incorporate resilience concepts into bridge scour analysis and establish assessment methods that integrate multiple sources of uncertainty and can describe the evolution of damage and the recovery process. Summary of the Invention

[0004] Purpose of the invention: The first purpose of the present invention is to provide a bridge pile foundation scour toughness analysis method to realize the bridge scour performance evaluation based on toughness.

[0005] The second object of the present invention is to provide a bridge pile foundation scour toughness analysis system.

[0006] Technical solution: To achieve the above objectives, the present invention provides a bridge pile foundation scour toughness analysis method, comprising the following steps:

[0007] S1. Use the concrete constitutive model and the steel constitutive model to construct a simplified finite element model of the bridge pile foundation;

[0008] S2. Use the py curve to simplify the soil into a nonlinear spring and construct a soil spring model. Then, couple the simplified finite element model of the bridge pile foundation and the soil spring model to form a finite element model of the bridge pile-soil system.

[0009] S3. Build a flow model around a cylinder based on Fluent to determine the average pressure on the water-facing and water-repelling surfaces of the pile foundation. The total pressure on the cylinder surface obtained is the water flow load on the bridge substructure.

[0010] S4. Introduce a correction factor for floating objects to calculate the equivalent width of the pile foundation and the local scour depth. In the finite element model of the bridge pile-soil system, passivate the soil spring at the corresponding depth according to the local scour depth, which is equivalent to the scour load.

[0011] S5. Screen the parameters other than the basic hydraulic parameters in the finite element model of the bridge pile-soil system through parameter sensitivity analysis and eliminate insensitive parameters;

[0012] S6. Loading the water flow load and scour load of the bridge substructure into the finite element model of the bridge pile-soil system, using the sensitive parameters as input variable parameters of the finite element model of the bridge pile-soil system, performing finite element analysis based on different values ​​of the input variable parameters to obtain the corresponding pile top displacement as the finite element response, and forming a sample working condition combination; constructing a BP neural network proxy model based on the sample working condition combination, and establishing a mapping relationship between the input variable parameters and the response index in the BP neural network proxy model;

[0013] S7. Based on the BP neural network proxy model and the damage states of the pile foundation, a vulnerability curve is established. The functional function of the pile foundation under different damage states is constructed by coupling the scour repair idle time and the functional recovery process through the Heaviside function and the repair function. Considering the uncertainty of the scour response time and combining the probability of occurrence of each damage state, the weighted summation of the pile foundation functional function under each damage state is performed to obtain the comprehensive functional function at any time. The scour toughness index of the bridge pile foundation is obtained by integrating and normalizing the comprehensive functional function of the pile foundation within the scour repair idle and recovery time intervals.

[0014] Optionally, step S2 specifically includes the following steps:

[0015] The py curve is a nonlinear model used to simulate the lateral reaction force provided by the soil to the pile body under the action of the pile lateral load. p represents the soil reaction force corresponding to the unit pile length; y represents the lateral compression displacement of the soil spring; the py curve uses a modified semi-empirical curve, namely the API curve; the horizontal axis in the py curve is the normalized displacement y / Y c , that is, the spring lateral compression displacement y and characteristic displacement Y c The ordinate in the py curve is the normalized soil reaction force p / P u , that is, the soil reaction force p on the pile per unit length and its ultimate reaction force P u The ratio of

[0016] The ultimate reaction force P in the API curve u and characteristic displacement Y c , the calculation formula for clay soil and sandy soil is:

[0017]

[0018] Yc =2.5ε 50 D

[0019] Among them, P u is the lateral limit reaction force, C u is the undrained shear strength of the soil at the corresponding soil layer, D is the pile diameter, γ′ is the effective density of the soil, J is a dimensionless empirical constant ranging from 0.25 to 0.5, z is the depth of the soil, and R is the depth from the natural soil surface to the surface of the bearing capacity stable area. In the area greater than this depth, the lateral ultimate reaction force will remain constant; C1, C2, C3 are coefficients related to the internal friction angle of sandy soil, ε 50 Y represents the strain value at 0.5 times the maximum deviatoric stress in the undrained compression test of undisturbed soil. c is the characteristic displacement of the pile foundation under lateral load, and the API curve is a deterministic model of the soil spring model;

[0020] The soil spring model is constructed, the spring spacing is set, the simplified finite element model of the bridge pile foundation and the soil spring model are meshed, and mesh convergence analysis is performed. After meshing, constant stiffness is assigned to the nodes where springs need to be added in batches based on Python scripts; then the spring material is set to nonlinear, and the spring stiffness is assigned according to the py curve. The characteristics of the soil spring are indirectly determined by the lateral limit reaction force P. u Determined, take P u (z i ) is a lognormal random variable with vertical spatial correlation, whose mean is the calculated value that increases linearly with depth in the soil spring deterministic model, and the coefficient of variation is Take 10% and do not change with depth, and establish P u (z i ) random field in the depth direction;

[0021] Build P u (z i )The formula of the random field in the depth direction is:

[0022]

[0023] Where G i (z i ) is a normally distributed random field with zero mean and unit variance, and It is calculated by the transformation of lognormal mean and variance, and the calculation formula is:

[0024]

[0025] For spatially random distribution of soil, G i (z i)The random field is chosen as the correlation function based on exponential decay:

[0026]

[0027] where τ = |z1-z2| represents the distance between two points, δ z is the spatial correlation distance, which is selected according to the spring setting spacing; the correlation matrix is ​​established based on the correlation coefficient Use Choleskey decomposition to decompose it into a lower triangular matrix L and an upper triangular matrix L T The product of the matrix L and the randomly generated standard normal distribution sample Z j Generate P u (z i ) random field, the formula is:

[0028]

[0029] Define boundary conditions and loads, create a finite element analysis calculation task, and export the .inp calculation file. Then, use a Python script to batch modify the spring type after each *Spring keyword in the calculation file to NONLINEAR, and specify a table showing how the spring reaction force changes with compression. When simulating the nonlinear spring of the soil, the change in the reaction force during compression is set according to the py curve. When the soil is under tension, the reaction force is set to 0 to indicate that the soil can only withstand pressure but not tension, thus forming a finite element model of the bridge pile-soil system.

[0030] Optionally, step S3 specifically includes the following steps:

[0031] The computational domain of the cylindrical flow model is set to 30D×20D×H, where H is the height of the pile foundation between the water surface and the riverbed. The cylindrical flow model is meshed using an O-block method, with hexahedral elements used. Local density is applied within the 2D range of the cylindrical wall of the cylindrical flow model. The inlet boundary adopts a velocity inlet, and the distribution along the depth direction is an exponential velocity profile, expressed as follows:

[0032]

[0033] z is the depth, u is m is the liquid surface velocity, is the average inlet flow velocity, and the water flow direction is perpendicular to the inlet surface; the outlet boundary uses a pressure outlet with a gauge pressure of 0; fixed rough walls are set on the cylindrical surface and the bottom of the model, and symmetric boundary conditions are set on the side and top surfaces of the model. The SIMPLE algorithm is used to solve the cylinder flow model to obtain the total pressure on the cylindrical surface, that is, the water flow load on the bridge substructure.

[0034] Optionally, in step S4, the equivalent width of the pile foundation is calculated based on the accumulation of floating objects in a rectangular form in front of the structure.

[0035]

[0036] in, is the equivalent width of the pile foundation, a is the actual width of the pile foundation, K4 is the floating debris accumulation shape correction coefficient, H f is the height of floating debris accumulation, W is the width of floating debris accumulation, y is the water flow depth, and K1 is the correction coefficient of the pile cross-section shape.

[0037] Optionally, in step S4, for non-cohesive soil, the scour depth is calculated using the modified CSU equation, which is:

[0038]

[0039] Among them, y ls is the local scouring depth of non-cohesive soil; y1 is the average water flow depth in front of the pile; K1 is the correction factor for the cross-sectional shape of the pile; K2 is the correction factor for the water flow angle; K3 is the correction factor related to the riverbed conditions; is the equivalent width of the pile foundation; Fr is the Froude number of the water flow in front of the pile, which is given by V / (gy1) 0.5 Calculation: V is the average velocity of the water flow in front of the pile, g is the acceleration of gravity, θ is the slope angle of the riverbed, and L is the length of the water-facing surface in front of the pier along the direction of water flow;

[0040] In step S4, for clay soil, the scour depth is calculated using the Briaud shrinkage scour formula:

[0041]

[0042] Among them, y ls-ult is the local scouring depth of clay soil, V c is the critical starting average flow velocity, is the initial scouring rate of clay soil, V1 is the average velocity of water flow in the scouring area, y s (t) is the basic time-varying scour depth.

[0043] Optionally, in step S5, the parameter to be screened is subjected to a three-fold fluctuation range. When the damage indicator pile top displacement does not vary by more than 20% with the parameter fluctuation, the parameter is considered to be insensitive.

[0044] Optionally, in step S7, flood intensity is graded. Based on the hydrological records of the bridge site, floods with a recurrence period of less than 50 years are classified as Level III, floods with a recurrence period of 50-100 years are classified as Level II, and floods with a recurrence period of more than 100 years are defined as Level I.

[0045] Optionally, in step S7, the damage state is defined according to the size of the damage index, and a pile top displacement of 0 to 15 mm is defined as slight damage, a pile top displacement of 15 to 30 mm is defined as moderate damage, a pile top displacement of 30 mm to 50 mm is defined as severe damage, and a pile top displacement greater than 50 mm is defined as complete destruction.

[0046] Optionally, the formula of the performance function at each flood level in step S7 is:

[0047] Z y,i =R y,i -λ·S y (f c ,d,s d ,h0,v0)

[0048] Where Z y,i is the limit state performance function value based on the pile top displacement index; R y,i is the critical displacement value corresponding to the i-th damage state; λ is the uncertainty factor affecting the soil spatial distribution; S y is the displacement response of the pile top under the water flow load of water depth and flow velocity, h0 and s d are the water depth and the scour depth corresponding to the flow velocity v0, d is the pile diameter, f c is the compressive strength of concrete cube; R in the pile foundation function under each flood level y,i ,d,f c ,λ is considered as a normal distribution to take into account the uncertainty of the variable, where the critical displacement value R under the slight damage state is y,1 , which obeys the normal distribution with mean and standard deviation of 10 and 2 respectively; for the critical displacement value R under moderate damage state y,2 , which obeys a normal distribution with a mean and standard deviation of 18 and 2.8 respectively; for the critical displacement value R under severe damage state y,3 , which obeys the normal distribution with mean and standard deviation of 26 and 3.4 respectively; for the critical displacement value R under the complete damage state y,4 , which obeys a normal distribution with a mean and standard deviation of 36 and 6 respectively; the pile diameter d obeys a normal distribution with a mean and standard deviation of 1 and 0.04 respectively; the concrete cube compressive strength f c The mean and standard deviation are 1.25f cu,k and 0.15f cu,k Normal distribution, where f cu,kis the standard value of concrete cube compressive strength obtained from experimental tests; the soil spatial distribution uncertainty factor λ follows a normal distribution with a mean and standard deviation of 1 and 0.05, respectively, when the flow velocity v0 ≤ 5 m / s, and a normal distribution with a mean and standard deviation of 1 and 0.15, respectively, when the flow velocity v0 > 5 m / s;

[0049] After obtaining the distribution of variables in the functional function, for each flood level, the flood recurrence period is used as a variable to obtain the water depth h0 and flow velocity v0 under the flood recurrence period, and then the scour depth s is obtained. d Then, the Monte Carlo method is used to simulate several groups of different d,f c ,λ value, the displacement response S of the pile top is calculated by BP neural network agent model y (f c ,d,s d ,h0,v0); determine the damage state of several groups of samples according to the defined damage index range, and divide the number of samples of each damage state by the total number of samples to obtain the probability P of each damage state under a given flood intensity. i (IM), also known as the vulnerability curve;

[0050] The structural toughness curve is derived based on the fragility curve. For different pile damage states obtained by several groups of samples, the R corresponding to each sample is y,i Take as the critical displacement value under the damage state, and then calculate several groups of extreme pile foundation state function values ​​Z considering different damage states y,i ; The functional function of the pile foundation under different damage states is introduced as follows:

[0051]

[0052] Where Q i (t,IM) is the functional function of the pile foundation under different damage states; t0 is the time point when the scour occurs; δ x,i is the idle time after the flush occurs; H(·) is the Heaviside function, which outputs 0 when the input value is negative and 1 when it is positive, and is used to activate the recovery function f after the idle time. i (·); δ r,i is the repair time after the scour occurs;

[0053] The distribution of each variable is as follows:

[0054] δ x,1 ~U(3.8,15.8);δ x,2 ~U(5.0,20.6);δ x,3 ~U(10.4,25.6);δ x,4 ~U(18.4,37.6)

[0055] δ r,1 ~N(10.29,9.45);δ r,2 ~N(15.9,10.8);δ r,3 ~N(32.1,15.4);δ r,4 ~N(62.3,22.6)

[0056] f1(τ)=1-e -0.2τ ; f4(τ)=e -0.2(1-τ)

[0057] Among them U(a LL ,b UL ) represents the lower limit of a LL , the upper limit is b UL uniform distribution, N(a M ,b SD ) represents the mean value a M , with a standard deviation of b SD Normal distribution; thus, the functional functions of several groups of samples under various damage states can be obtained; the functional functions of several groups of samples under various damage states are compared with the corresponding probability of occurrence of each damage state P i Multiply and add to get the comprehensive functional expression of pile foundation:

[0058]

[0059] The pile foundation scour toughness is defined as follows:

[0060]

[0061] Where δ x and δ r are the idle time and repair time of the comprehensive functional function Q(t,IM) of the pile foundation respectively. The average toughness value under the corresponding flood intensity can be obtained by taking the average value of the toughness of several groups of samples obtained at last.

[0062] Based on the same inventive concept, the bridge pile foundation scour toughness analysis system of the present invention includes:

[0063] The pre-processing module is used to construct a simplified finite element model of the bridge pile foundation using the concrete constitutive model and the steel bar constitutive model; the py curve is used to simplify the soil into a nonlinear spring, and a soil spring model is constructed. The simplified finite element model of the bridge pile foundation and the soil spring model are then coupled to form a finite element model of the bridge pile-soil system; a cylindrical flow model is established based on Fluent to determine the average pressure on the water-facing and water-removing surfaces of the pile foundation, and the total pressure on the cylindrical surface obtained is the water flow load of the bridge substructure; a correction coefficient considering floating objects is introduced to calculate the equivalent width and local scour depth of the pile foundation, and the soil spring of the corresponding depth is passivated according to the local scour depth in the finite element model of the bridge pile-soil system, which is equivalent to the scour load; parameters other than the basic hydraulic parameters in the finite element model of the bridge pile-soil system are screened through parameter sensitivity analysis to eliminate insensitive parameters;

[0064] The BP neural network proxy module is used to load the water flow load and scour load of the bridge substructure into the finite element model of the bridge pile-soil system. The sensitive parameters are used as input variable parameters of the finite element model of the bridge pile-soil system. Finite element analysis is performed based on different values ​​of the input variable parameters to obtain the corresponding pile top displacement as the finite element response, forming a sample working condition combination. The BP neural network proxy model is constructed based on the sample working condition combination, and a mapping relationship between the input variable parameters and the response index is established in the BP neural network proxy model.

[0065] The toughness calculation module is used to establish a vulnerability curve based on the BP neural network proxy model and various damage states of the pile foundation. The pile foundation function function under different damage states is constructed by coupling the scour repair idle time and the functional recovery process through the Heaviside function and the repair function. The weighted summation of the pile foundation function function under each damage state is taken into account, considering the uncertainty of the scour response time and the probability of occurrence of each damage state, to obtain the comprehensive function function at any time. The scour toughness index of the bridge pile foundation is obtained by integrating and normalizing the comprehensive function function of the pile foundation within the scour repair idle and recovery time intervals.

[0066] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0067] (1) This paper implements a quantitative assessment method for the scour resilience of bridge pile foundations based on multi-source uncertainty parameters. It can accurately simulate the functional degradation and recovery process of bridges under different scour scenarios and soil property fluctuations, and improves the assessment level of the structural retention capacity of bridge foundation systems under extreme floods.

[0068] (2) This invention constructs a full-process pile foundation function evolution curve and integrates a toughness calculation expression that considers the recovery process, supporting multi-level damage state assessment and recovery capacity analysis of bridge foundation systems, providing a scientific basis and technical support for risk-oriented bridge design optimization and post-disaster resource allocation;

[0069] (3) The present invention converts inputs such as scour depth and water flow load into pile top displacement, an indicator reflecting structural response, and captures the complex input-output relationship through machine learning methods. It then constructs a time-evolving functional curve to quantify the functional degradation and recovery capacity of the structure under different damage states, thereby realizing toughness-based bridge scour performance evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 Schematic diagram of the system flow in the present invention;

[0071] Figure 2 A diagram for calculating the water flow load on the bridge substructure under the action of floods of different water depths and flow velocities is defined for the present invention;

[0072] Figure 3 The diagram shows the boundary conditions, water flow load, pile-soil interaction and scour load of the bridge pile foundation simulated by the present invention;

[0073] Figure 4 A diagram illustrating the conversion of the effects of different forms of floating debris distribution on scour depth considered in the present invention;

[0074] Figure 5 This is a recovery curve diagram of the pile foundation under different damage states in the present invention. DETAILED DESCRIPTION

[0075] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0076] Example 1: Figure 1 As shown, a bridge pile foundation scour toughness analysis method includes the following steps:

[0077] S1. In ABAQUS, a simplified finite element model of the bridge pile foundation is constructed using the concrete constitutive model and the steel constitutive model. The concrete constitutive model uses the concrete plastic damage model (CDP) built into ABAQUS, and the steel constitutive model uses the bilinear stress-strain constitutive model.

[0078] S2. Use the py curve to simplify the soil into a series of nonlinear springs whose stiffness varies with soil depth and soil layer type, and construct a soil spring model. Then, couple the simplified finite element model of the bridge pile foundation and the soil spring model to form a finite element model of the bridge pile-soil system.

[0079] Step S2 specifically includes the following steps:

[0080] The py curve is a nonlinear model used to simulate the lateral reaction force provided by the soil to the pile body under the action of the pile lateral load. p represents the soil reaction force corresponding to the unit pile length, in kPa; y represents the lateral compression displacement of the soil spring, in mm. The py curve uses the modified semi-empirical curve recommended in the 2014 API Guide, namely the API curve. The horizontal axis of the py curve is the normalized displacement y / Y c , that is, the spring lateral compression displacement y and characteristic displacement Y c The ordinate in the py curve is the normalized soil reaction force p / P u , that is, the soil reaction force p on the pile per unit length and its ultimate reaction force P u The ratio of the ultimate reaction force P in the API curve u and characteristic displacement Y c , the calculation formula for clay soil and sandy soil is:

[0081]

[0082] Y c =2.5ε 50 D

[0083] Among them, P u is the lateral limit reaction force, in kPa, C u is the undrained shear strength of the soil at the corresponding soil layer, in kPa, D is the pile diameter, in m, and γ′ is the effective density of the soil, in kN / m 3 , J is a dimensionless empirical constant, usually between 0.25 and 0.5, z is the depth of the soil, in meters, z R is the depth from the natural soil surface to the surface of the bearing capacity stable area, in meters. In areas greater than this depth, the lateral ultimate reaction will remain constant. C1, C2, and C3 are coefficients related to the internal friction angle of sandy soil, calculated using the formula given in Section 8.5.6 of the API Manual. ε 50 Y represents the strain value at 0.5 times the maximum deviatoric stress in the undrained compression test of undisturbed soil. c is the characteristic displacement of the pile foundation under lateral load, and the API curve is a deterministic model of the soil spring model;

[0084] A soil spring model was constructed with the spring spacing set to 0.1m. The simplified finite element model of the bridge pile foundation and the soil spring model were meshed and mesh convergence analysis was performed. After meshing, constant stiffness was assigned to the nodes where springs needed to be added in batches based on Python scripts. The spring material was then set to nonlinear and the spring stiffness was assigned according to the py curve. The uncertainty of the vertical distribution of soil parameters was considered in particular. The characteristics of the soil spring were indirectly determined by the lateral limit reaction force P. u Determined, take Pu (z i ) is a lognormal random variable with vertical spatial correlation, whose mean is the calculated value that increases linearly with depth in the soil spring deterministic model, and the coefficient of variation is Take 10% and do not change with depth, thus establishing P u (z i ) random field in the depth direction;

[0085] Build P u (z i )The formula of the random field in the depth direction is:

[0086]

[0087] Where G i (z i ) is a normally distributed random field with zero mean and unit variance, and It is calculated by the transformation of lognormal mean and variance, and the calculation formula is:

[0088]

[0089] For spatially random distribution of soil, G i (z i )The random field is chosen as the correlation function based on exponential decay:

[0090]

[0091] where τ = |z1-z2| represents the distance between two points, δ z is the spatial correlation distance, which is selected according to the spring setting spacing in step S2; the correlation matrix is ​​established based on the correlation coefficient Use Choleskey decomposition to decompose it into a lower triangular matrix L and an upper triangular matrix L T The product of the matrix L and the randomly generated standard normal distribution sample Z j Generate P u (z i ) random field, the formula is:

[0092]

[0093] Define boundary conditions and loads. Specifically, the boundary conditions set the bottom of the pile foundation to a fixed connection, and the loads are the constant load and live load determined according to the specifications. Create a finite element analysis calculation task and export the .inp calculation file. Then, use a Python script to batch modify the spring type after the *Spring keyword in the calculation file to NONLINEAR, and specify a table showing how the spring reaction force changes with compression. When simulating the nonlinear spring of the soil, set the change in the reaction force during compression according to the py curve. When the soil is in tension, set its reaction force to 0 to indicate that the soil can only withstand pressure but not tension, thus forming a finite element model of the bridge pile-soil system.

[0094] S3. A cylinder flow model is established based on Fluent to determine the average pressure on the water-facing and water-repelling surfaces of the pile foundation. The cylinder size in the cylinder flow model is consistent with the actual bridge pile foundation. The total pressure on the cylinder surface is the water flow load on the bridge substructure.

[0095] Step S3 specifically includes the following steps:

[0096] Considering that when the distance between the structure and the computational domain boundary is greater than 8D, D is the pile foundation diameter, and the influence of the boundary effects on both sides can be ignored; therefore, the computational domain of the cylindrical flow model is set to 30D × 20D × H, where H is the height of the pile foundation between the water surface and the riverbed; the cylindrical flow model is meshed based on the O-block method, and all meshes use hexahedral elements; the cylindrical wall of the cylindrical flow model is locally encrypted within the 2D range, with a transition from 0.01mm spacing at the cylindrical wall to 0.4mm at the edge of the encrypted area according to an exponential coefficient of 1.1; the inlet boundary uses a velocity inlet, and the distribution along the depth direction is an exponential velocity profile, expressed as:

[0097]

[0098] z is the depth, u is m is the liquid surface velocity, is the average inlet velocity, and the water flow direction is perpendicular to the inlet surface; the outlet boundary adopts a pressure outlet with a gauge pressure of 0; a fixed rough wall is set on the cylindrical surface and the bottom surface of the model, and the roughness height K s Take 0.3mm and 1mm respectively, the roughness constant C S Taking 0.5, the side and top surfaces of the model are set to symmetric boundary conditions, and the SIMPLE algorithm is used to solve the cylinder flow model to obtain the total pressure on the cylinder surface, that is, the water flow load on the bridge substructure;

[0099] S4. Considering that the accumulation of floating objects in front of the structure will increase the impact strength of the horseshoe vortex on the riverbed, thereby increasing the local scouring depth of the foundation, a correction factor considering floating objects is introduced to calculate the equivalent width of the pile foundation. For non-cohesive soils, the modified CSU equation is used to calculate the local scour depth; for cohesive soils, the Briaud shrinkage scour formula is used to calculate the local scour depth. In the finite element model of the bridge pile-soil system, the soil spring at the corresponding depth is passivated according to the calculated local scour depth, which is equivalent to the scour load.

[0100] Step S4 specifically includes the following steps:

[0101] Calculate the equivalent width of the pile foundation based on the rectangular accumulation of floating objects in front of the structure

[0102]

[0103] in, is the equivalent width of the pile foundation, in m, a is the actual width of the pile foundation, in m, K4 is the correction coefficient for the shape of floating debris accumulation, which is 0.79 for a rectangle, and H f is the height of floating debris accumulation, in m, W is the width of floating debris accumulation, in m, y is the water flow depth, in m, K1 is the pile cross-section shape correction coefficient;

[0104] For non-cohesive soil, the modified CSU equation is used to calculate the scour depth, which is:

[0105]

[0106] Among them, y ls is the local scouring depth of non-cohesive soil, in meters; y1 is the average water flow depth in front of the pile, in meters; K1 is the correction factor for the cross-sectional shape of the pile; K2 is the correction factor for the water flow angle; K3 is the correction factor related to the riverbed conditions; is the equivalent width of the pile foundation; Fr is the Froude number of the water flow in front of the pile, which is given by V / (gy1) 0.5 Calculation: V is the average velocity of the water flow in front of the pile, g is the acceleration of gravity, θ is the slope angle of the riverbed, and L is the length of the water-facing surface in front of the pier along the direction of water flow;

[0107] For clay soil, the scour depth is calculated using the Briaud shrinkage scour formula:

[0108]

[0109] Among them, y ls-ult is the local scouring depth of clay soil, in m, V c is the critical starting average flow velocity, in m / s, is the initial scouring rate of clay soil, in mm / h, V1 is the average velocity of water flow in the scouring area, y s (t) Time-varying scour depth of the foundation; considering that the accumulation floating in front of the structure will increase the impact intensity of the horseshoe vortex on the riverbed, thereby increasing the local scour depth of the foundation;

[0110] S5. The response of bridge pile foundations to floods will be affected by the strength of concrete and steel, the lateral stiffness of each soil layer, water depth, flow velocity, and scour depth. Water depth and flow velocity are the basic hydraulic parameters of flood loads, and the remaining parameters need to be screened through parameter sensitivity analysis.

[0111] The pile top displacement was selected as the damage index. The magnitude of the damage index determined the damage state of the bridge structure. The damage state was also defined based on the magnitude of the damage index. Four different pile foundation damage states were defined as follows: a pile top displacement of 0 to 15 mm was defined as slight damage, a pile top displacement of 15 to 30 mm was defined as moderate damage, a pile top displacement of 30 to 50 mm was defined as severe damage, and a pile top displacement greater than 50 mm was defined as complete destruction. Parameters other than the basic hydraulic parameters in the finite element model of the bridge pile-soil system were subjected to a three-fold fluctuation range. When the damage index did not vary by more than 20% with the parameter fluctuation, the parameter was identified as insensitive. Specifically, the insensitive parameters included the elastic modulus of the steel bars and soil-related parameters. Sensitive parameters included water depth, flow velocity, scour depth, concrete strength, and pile foundation diameter.

[0112] S6. Load the water flow load and scour load of the bridge substructure into the finite element model of the bridge pile-soil system, exclude insensitive parameters, and use sensitive parameters as input variable parameters of the finite element model of the bridge pile-soil system. According to different values ​​of the input variable parameters, perform finite element analysis to obtain the corresponding pile top displacement as the finite element response to form the sample working condition combination LC. i ; Sample working condition combination LC i The variables controlled in step S5 are the sensitive parameters, including water depth H, flow velocity V, scour depth S d , concrete strength f c , pile foundation diameter D;

[0113] Combine LC by sample case i Constructing a BP neural network agent model, in which a mapping relationship between input variable parameters and response indicators is established;

[0114] The specific approach is to select the pile top displacement as the response indicator, and then start training by removing extreme values ​​from the calculation samples under different working condition combinations based on the BP neural network toolbox provided by MATLAB software. When the response value under some extreme working conditions exceeds twice the critical value of complete structural damage, the critical value of complete structural damage is 50mm, which should be discarded during training to avoid affecting the training accuracy.

[0115] The input layer of the BP neural network is d attribute variables, which are sensitive parameters. The output layer is l output neurons, and the middle layer is q hidden neurons. The threshold of the jth neuron in the output layer is θ j Indicates that the threshold of the hth neuron in the hidden layer is γ h Indicates that the connection weight between the i-th neuron in the input layer and the h-th neuron in the hidden layer is v hi , the connection weight between the hth neuron in the hidden layer and the jth neuron in the output layer is ω hj ; It is usually assumed that the nonlinear function selected is the Sigmoid function, then the output obtained from the neural network training is:

[0116]

[0117] in is the result of the j-th output neuron in the k-th group output, then the mean square error can be expressed as:

[0118]

[0119] The BP neural network algorithm adjusts the parameters in the negative gradient direction of the target by applying a gradient descent strategy to the error. For a specified error learning rate η,

[0120]

[0121] And because the Sigmoid function has the following properties:

[0122] f′(x)=f(x)(1-f(x))

[0123] According to the chain derivation method, we can get the value of Δω in the BP algorithm. hj Updated formula:

[0124] Δω hj =ηg j b h

[0125]

[0126] The error between the threshold and weight at each node of the neural network is obtained, and the standard BP neural network is used for classification and regression calculation. By regularizing the objective function, the connection weight and the sum of squares of the threshold are added to obtain the following error calculation method:

[0127]

[0128] S7. Based on the BP neural network agent model and the damage states of the pile foundation, a vulnerability curve is established. The functional function of the pile foundation under different damage states is constructed by coupling the scour repair idle time and the functional recovery process through the Heaviside function and the repair function. Considering the uncertainty of the scour response time and combining the probability of occurrence of each damage state, the weighted summation of the pile foundation functional function under each damage state is performed to obtain the comprehensive functional function at any time. The scour resilience index of the bridge pile foundation is obtained by integrating and normalizing the comprehensive functional function of the pile foundation within the scour repair idle and recovery time intervals. Among them, the flood intensity is graded. According to the hydrological records of the bridge site, the flood recurrence period is less than 50 years as Class III, the flood recurrence period is 50-100 years as Class II, and the flood recurrence period is more than 100 years as Class I.

[0129] In step S7, the formula of the pile foundation performance function under each flood level is:

[0130] Z y,i =R y,i -λ·S y (f c ,d,s d ,h0,v0)

[0131] where Z y,i is the limit state performance function value based on the pile top displacement index, in mm; R y,i is the critical displacement value corresponding to the i-th damage state, in mm; λ is the uncertainty factor affecting the soil spatial distribution; S y is the displacement response of the pile top under the water flow load of water depth and flow velocity, in mm, s d is the scour depth corresponding to the water depth h0 and flow velocity v0, in mm, d is the pile diameter, f c is the compressive strength of concrete cube, in MPa;

[0132] In step S7, the pile foundation function R under each flood level y,i ,d,f c ,λ is considered as a normal distribution to take into account the uncertainty of the variable, where the critical displacement value R under the slight damage state is y,1 , which obeys the normal distribution with mean and standard deviation of 10 and 2 respectively; for the critical displacement value R under moderate damage state y,2, which obeys a normal distribution with a mean and standard deviation of 18 and 2.8 respectively; for the critical displacement value R under severe damage state y,3 , which obeys the normal distribution with mean and standard deviation of 26 and 3.4 respectively; for the critical displacement value R under the complete damage state y,4 , which obeys a normal distribution with a mean and standard deviation of 36 and 6 respectively; the pile diameter d obeys a normal distribution with a mean and standard deviation of 1 and 0.04 respectively; the concrete cube compressive strength f c The mean and standard deviation are 1.25f cu,k and 0.15f cu,k Normal distribution, where f cu,k is the standard value of the compressive strength of concrete cube obtained from experimental tests; the uncertainty influencing factor λ of the soil spatial distribution obeys a normal distribution with a mean and standard deviation of 1 and 0.05 respectively when the flow velocity v0 ≤ 5 m / s, and obeys a normal distribution with a mean and standard deviation of 1 and 0.15 respectively when the flow velocity v0 > 5 m / s.

[0133] After obtaining the distribution of variables in the functional function, for each flood level, the flood recurrence period is used as a variable to obtain the water depth h0 and flow velocity v0 under the flood recurrence period, and then the scour depth s is obtained. d Then, the Monte Carlo method was used to simulate 10,000 sets of different d,f c ,λ value, the displacement response S of the pile top is calculated by BP neural network agent model y (f c ,d,s d ,h0,v0); determine the damage state of 10,000 groups of samples according to the defined damage index range, and divide the number of samples of each damage state by the total number of samples to obtain the probability P of each damage state under a given flood intensity. i (IM), also known as the vulnerability curve.

[0134] The structural toughness curve is further derived based on the fragility curve. For different pile foundation damage states obtained by 10,000 groups of samples, the R y,i Take it as the critical displacement value under the damage state, and then calculate 10,000 sets of extreme pile foundation state function values ​​Z considering different damage states y,i ; The functional function of the pile foundation under different damage states is introduced as follows:

[0135]

[0136] where Q i (t,IM) is the functional function of the pile foundation under different damage states; t0 is the time point when the scour occurs; δ x,iis the idle time after the flush occurs; H(·) is the Heaviside function, which outputs 0 when the input value is negative and 1 when it is positive, and is used to activate the recovery function f after the idle time. i (·); δ r,i is the repair time after the scour occurs;

[0137] The distribution of each variable is as follows:

[0138] δ x,1 ~U(3.8,15.8);δ x,2 ~U(5.0,20.6);δ x,3 ~U(10.4,25.6);δ x,4 ~U(18.4,37.6)

[0139] δ r,1 ~N(10.29,9.45);δ r,2 ~N(15.9,10.8);δ r,3 ~N(32.1,15.4);δ r,4 ~N(62.3,22.6)

[0140] f1(τ)=1-e -0.2τ ; f 3,4 (τ) = e -0.2(1-τ)

[0141] Among them U(a LL ,b UL ) represents the lower limit of a LL , the upper limit is b UL uniform distribution, N(a M ,b SD ) represents the mean value a M , with a standard deviation of b SD Normal distribution; thus, the functional function of 10,000 groups of samples under various damage states can be obtained; the functional function of 10,000 groups of samples under various damage states can be compared with the corresponding probability of occurrence of each damage state P i Multiply and add to get the comprehensive functional expression of pile foundation:

[0142]

[0143] The pile foundation scour toughness is defined as follows:

[0144]

[0145] where δ x and δ rare the idle time and repair time of the comprehensive functional function Q(t,IM) of the pile foundation, respectively. The average toughness value under the corresponding flood intensity can be obtained by taking the average value of the toughness of the last 10,000 groups of samples.

[0146] Example 1 uses two bridge pile foundations as a specific example for illustration, wherein the constructed cylinder flow geometric model is as follows: Figure 2 As shown, the flood inlet 2 is located on the left, the bridge pile foundation 1 is located near the flood inlet, the flood inundation depth 3 is the height of the model domain, the inlet and outlet boundary distance 4 is set to L, and the inlet and outlet boundary conditions are 5. In the present invention, the bridge pile foundation boundary conditions, water flow load, pile-soil interaction, and scour load are as follows: Figure 3 As shown, the spring 6 set according to the py curve is connected to the pile foundation, the constraint boundary condition at the bottom of the pile foundation is 7, the water flow load 8 acts on the water-facing side of the bridge pile foundation, and the maximum depth of the scour pit is 9; the influence of different forms of floating object distribution on the scour depth of the present invention is as follows Figure 4 As shown, the full accumulation form 10 and the semi-accumulation form 11 of floating objects will cause different effects on the scouring depth, and the soil layer thickness 12 covers the bottom of the pile foundation. The recovery curves of the pile foundation under different damage states in the present invention are as follows Figure 5 shown.

[0147] Example 2:

[0148] The present invention provides a bridge pile foundation scour toughness analysis system, which comprises a pre-processing module, a BP neural network agent module and a toughness calculation module.

[0149] In the pre-processing module, in ABAQUS, the concrete constitutive model and the steel constitutive model are used to construct a simplified finite element model of the bridge pile foundation. The concrete constitutive model adopts the concrete plastic damage model CDP built into ABAQUS, and the steel constitutive model adopts the bilinear stress-strain constitutive model.

[0150] In the pre-processing module, the py curve is used to simplify the soil into a series of nonlinear springs whose stiffness varies with soil depth and soil layer type, and a soil spring model is constructed. The simplified finite element model of the bridge pile foundation and the soil spring model are then coupled to form a finite element model of the bridge pile-soil system.

[0151] The py curve is a nonlinear model used to simulate the lateral reaction force provided by the soil to the pile body under the action of the pile lateral load. p represents the soil reaction force corresponding to the unit pile length, in kPa; y represents the lateral compression displacement of the soil spring, in mm. The py curve uses the modified semi-empirical curve recommended in the 2014 API Guide, namely the API curve. The horizontal axis of the py curve is the normalized displacement y / Y c , that is, the spring lateral compression displacement y and characteristic displacement Y c The ordinate in the py curve is the normalized soil reaction force p / Pu , that is, the soil reaction force p on the pile per unit length and its ultimate reaction force P u The ratio of the ultimate reaction force P in the API curve u and characteristic displacement Y c , the calculation formula for clay soil and sandy soil is:

[0152]

[0153] Y c =2.5ε 50 D

[0154] Among them, P u is the lateral limit reaction force, in kPa, C u is the undrained shear strength of the soil at the corresponding soil layer, in kPa, D is the pile diameter, in m, and γ′ is the effective density of the soil, in kN / m 3 , J is a dimensionless empirical constant, usually between 0.25 and 0.5, z is the depth of the soil, in meters, z R is the depth from the natural soil surface to the surface of the bearing capacity stable area, in meters. In areas greater than this depth, the lateral ultimate reaction will remain constant. C1, C2, and C3 are coefficients related to the internal friction angle of sandy soil, calculated using the formula given in Section 8.5.6 of the API Manual. ε 50 Y represents the strain value at 0.5 times the maximum deviatoric stress in the undrained compression test of undisturbed soil. c is the characteristic displacement of the pile foundation under lateral load, and the API curve is a deterministic model of the soil spring model.

[0155] A soil spring model was constructed with the spring spacing set to 0.1m. The simplified finite element model of the bridge pile foundation and the soil spring model were meshed and mesh convergence analysis was performed. After meshing, constant stiffness was assigned to the nodes where springs needed to be added in batches based on Python scripts. The spring material was then set to nonlinear and the spring stiffness was assigned according to the py curve. The uncertainty of the vertical distribution of soil parameters was considered in particular. The characteristics of the soil spring were indirectly determined by the lateral limit reaction force P. u Determined, take P u (z i ) is a lognormal random variable with vertical spatial correlation, whose mean is the calculated value that increases linearly with depth in the soil spring deterministic model, and the coefficient of variation is Take 10% and do not change with depth, thus establishing P u (z i ) is a random field in the depth direction.

[0156] Build P u (z i)The formula of the random field in the depth direction is:

[0157]

[0158] Where G i (z i ) is a normally distributed random field with zero mean and unit variance, and It is calculated by the transformation of lognormal mean and variance, and the calculation formula is:

[0159]

[0160] For spatially random distribution of soil, G i (z i )The random field is chosen as the correlation function based on exponential decay:

[0161]

[0162] where τ = |z1-z2| represents the distance between two points, δ z is the spatial correlation distance, which is selected according to the spring setting spacing in step S2; the correlation matrix is ​​established based on the correlation coefficient Use Choleskey decomposition to decompose it into a lower triangular matrix L and an upper triangular matrix L T The product of the matrix L and the randomly generated standard normal distribution sample Z j Generate P u (z i ) random field, the formula is:

[0163]

[0164] Define boundary conditions and loads. Specifically, the boundary conditions are to set the bottom of the pile foundation to fixed connection, and the loads are to set the constant load and live load according to the specifications. Create a finite element analysis calculation task and export the .inp calculation file. Then, use Python scripts to batch modify the spring type after each *Spring keyword in the calculation file to NONLINEAR, and specify a table showing how the spring reaction force changes with the compression amount. When simulating the nonlinear spring of the soil, the change in the reaction force during compression is set according to the py curve. When the soil is under tension, the reaction force is set to 0 to indicate that the soil can only withstand pressure but not tension, thus forming a finite element model of the bridge pile-soil system.

[0165] In the pre-processing module, a cylindrical flow model is established based on Fluent to determine the average pressure on the water-facing and water-repelling surfaces of the pile foundation. The cylinder size in the cylindrical flow model is consistent with the actual bridge pile foundation. The total pressure on the cylindrical surface is the water flow load on the bridge substructure.

[0166] Considering that when the distance between the structure and the computational domain boundary is greater than 8D, D is the pile foundation diameter, and the influence of the boundary effects on both sides can be ignored; therefore, the computational domain of the cylindrical flow model is set to 30D × 20D × H, where H is the height of the pile foundation between the water surface and the riverbed; the cylindrical flow model is meshed based on the O-block method, and all meshes use hexahedral elements; the cylindrical wall of the cylindrical flow model is locally encrypted within the 2D range, with a transition from 0.01mm spacing at the cylindrical wall to 0.4mm at the edge of the encrypted area according to an exponential coefficient of 1.1; the inlet boundary uses a velocity inlet, and the distribution along the depth direction is an exponential velocity profile, expressed as:

[0167]

[0168] z is the depth, u is m is the liquid surface velocity, is the average inlet velocity, and the water flow direction is perpendicular to the inlet surface; the outlet boundary adopts a pressure outlet with a gauge pressure of 0; a fixed rough wall is set on the cylindrical surface and the bottom surface of the model, and the roughness height K s Take 0.3mm and 1mm respectively, the roughness constant C S The value is set to 0.5, and the side and top surfaces of the model are set to symmetric boundary conditions. The SIMPLE algorithm is used to solve the cylinder flow model to obtain the total pressure on the cylinder surface, that is, the water flow load on the bridge substructure.

[0169] At the same time, considering that the accumulation of floating objects in front of the structure will increase the impact intensity of the horseshoe vortex on the riverbed, thereby increasing the local scouring depth of the foundation; therefore, a correction factor considering floating objects is introduced to calculate the equivalent width of the pile foundation. For non-cohesive soils, the modified CSU equation is used to calculate the local scour depth; for cohesive soils, the Briaud shrinkage scour formula is used to calculate the local scour depth. In the finite element model of the bridge pile-soil system, the soil spring at the corresponding depth is passivated according to the calculated local scour depth, which is equivalent to the scour load.

[0170] Calculate the equivalent width of the pile foundation based on the rectangular accumulation of floating objects in front of the structure

[0171]

[0172] in, is the equivalent width of the pile foundation, in m, a is the actual width of the pile foundation, in m, K4 is the correction coefficient for the shape of floating debris accumulation, which is 0.79 for a rectangle, and H fis the height of floating objects accumulation, in m, W is the width of floating objects accumulation, in m, y is the water flow depth, in m, and K1 is the correction coefficient of the pile cross-section shape.

[0173] For non-cohesive soil, the modified CSU equation is used to calculate the scour depth, which is:

[0174]

[0175] Among them, y ls is the local scouring depth of non-cohesive soil, in meters; y1 is the average water flow depth in front of the pile, in meters; K1 is the correction factor for the cross-sectional shape of the pile; K2 is the correction factor for the water flow angle; K3 is the correction factor related to the riverbed conditions; is the equivalent width of the pile foundation; Fr is the Froude number of the water flow in front of the pile, which is given by V / (gy1) 0.5 Calculation: V is the average velocity of the water flow in front of the pile, g is the acceleration of gravity, θ is the slope angle of the riverbed, and L is the length of the water-facing surface in front of the pier along the direction of water flow.

[0176] For clay soil, the scour depth is calculated using the Briaud shrinkage scour formula:

[0177]

[0178] Among them, y ls-ult is the local scouring depth of clay soil, in m, V c is the critical starting average flow velocity, in m / s, is the initial scouring rate of clay soil, in mm / h, V1 is the average velocity of water flow in the scouring area, y s (t) is the time-varying scour depth of the foundation; it is considered that the accumulation floating in front of the structure will increase the impact intensity of the horseshoe vortex on the riverbed, thereby increasing the local scour depth of the foundation.

[0179] The response of bridge pile foundations to floods will be affected by the strength of concrete and steel materials, the lateral stiffness of each soil layer, water depth, flow velocity, and scour depth parameters. Water depth and flow velocity are the basic hydraulic parameters of flood loads, and the remaining parameters need to be screened through parameter sensitivity analysis.

[0180] The pile top displacement was selected as the damage index. The magnitude of the damage index determined the damage state of the bridge structure. The damage state was also defined based on the magnitude of the damage index. Four different pile foundation damage states were defined as follows: a pile top displacement of 0 to 15 mm was defined as slight damage, a pile top displacement of 15 to 30 mm was defined as moderate damage, a pile top displacement of 30 to 50 mm was defined as severe damage, and a pile top displacement greater than 50 mm was defined as complete destruction. Parameters other than the basic hydraulic parameters in the finite element model of the bridge pile-soil system were subjected to a three-fold fluctuation range. When the damage index did not vary by more than 20% with the parameter fluctuation, the parameter was identified as insensitive. Specifically, the insensitive parameters included the elastic modulus of the steel bars and soil-related parameters. Sensitive parameters included water depth, flow velocity, scour depth, concrete strength, and pile foundation diameter.

[0181] The BP neural network proxy module is used to load the water flow load and scouring load of the bridge substructure into the finite element model of the bridge pile-soil system, and use the sensitive parameters as the input variable parameters of the bridge pile-soil system finite element model. According to the different values ​​of the input variable parameters, the finite element analysis is performed to obtain the corresponding pile top displacement as the finite element response to form a sample working condition combination; the BP neural network proxy model is constructed through the sample working condition combination, and the mapping relationship between the input variable parameters and the response index is established in the BP neural network proxy model; the sample working condition combination LC i The variables controlled in the experiment are sensitive parameters, including water depth H, flow velocity V, scour depth S d , concrete strength f c , pile foundation diameter D.

[0182] Combine LC by sample case i A BP neural network agent model is constructed, and a mapping relationship between input variable parameters and response indicators is established in the BP neural network agent model.

[0183] The specific approach is to select the pile top displacement as the response indicator, and start training after removing extreme values ​​of the calculation samples under different working condition combinations based on the BP neural network toolbox provided in the MATLAB software. When the response value under some extreme working conditions exceeds 2 times the critical value of complete structural destruction, the critical value of complete structural destruction refers to the pile top displacement of 50mm, which should be discarded during training to avoid it from affecting the training accuracy.

[0184] The input layer of the BP neural network is d attribute variables, which are sensitive parameters. The output layer is l output neurons, and the middle layer is q hidden neurons. The threshold of the jth neuron in the output layer is θ j Indicates that the threshold of the hth neuron in the hidden layer is γ h Indicates that the connection weight between the i-th neuron in the input layer and the h-th neuron in the hidden layer is v hi, the connection weight between the hth neuron in the hidden layer and the jth neuron in the output layer is ω hj ; It is usually assumed that the nonlinear function selected is the Sigmoid function, then the output obtained from the neural network training is:

[0185]

[0186] in is the result of the j-th output neuron in the k-th group output, then the mean square error can be expressed as:

[0187]

[0188] The BP neural network algorithm adjusts the parameters in the negative gradient direction of the target by applying a gradient descent strategy to the error. For a specified error learning rate η,

[0189]

[0190] And because the Sigmoid function has the following properties:

[0191] f′(x)=f(x)(1-f(x))

[0192] According to the chain derivation method, we can get the value of Δω in the BP algorithm. hj Updated formula:

[0193] Δω hj =ηg j b h

[0194]

[0195] The error between the threshold and weight at each node of the neural network is obtained, and the standard BP neural network is used for classification and regression calculation. By regularizing the objective function, the connection weight and the sum of squares of the threshold are added to obtain the following error calculation method:

[0196]

[0197] The toughness calculation module is used to establish a vulnerability curve based on the BP neural network agent model and various damage states of the pile foundation, and to construct the pile foundation function function under different damage states by coupling the scour repair idle time and functional recovery process through the Heaviside function and the repair function. The weighted summation of the pile foundation function function under each damage state is performed considering the uncertainty of the scour response time and the probability of occurrence of each damage state to obtain the comprehensive function function at any time. The scour resilience index of the bridge pile foundation is obtained by integrating and normalizing the comprehensive function function of the pile foundation within the scour repair idle and recovery time intervals. The flood intensity is graded. According to the hydrological records of the bridge site, floods with a recurrence period of less than 50 years are defined as Class III, those with a recurrence period of 50-100 years are defined as Class II, and those with a recurrence period of more than 100 years are defined as Class I.

[0198] The formula for the pile foundation performance function under each flood level is:

[0199] Z y,i =R y,i -λ·S y (f c ,d,s d ,h0,v0)

[0200] where Z y,i is the limit state performance function value based on the pile top displacement index, in mm; R y,i is the critical displacement value corresponding to the i-th damage state, in mm; λ is the uncertainty factor affecting the soil spatial distribution; S y is the displacement response of the pile top under the water flow load of water depth and flow velocity, in mm, s d is the scour depth corresponding to the water depth h0 and flow velocity v0, in mm, d is the pile diameter, f c is the compressive strength of concrete cube, in MPa;

[0201] R in the pile foundation function under each flood level y,i ,d,f c ,λ is considered as a normal distribution to take into account the uncertainty of the variable, where the critical displacement value R under the slight damage state is y,1 , which obeys the normal distribution with mean and standard deviation of 10 and 2 respectively; for the critical displacement value R under moderate damage state y,2 , which obeys a normal distribution with a mean and standard deviation of 18 and 2.8 respectively; for the critical displacement value R under severe damage state y,3 , which obeys the normal distribution with mean and standard deviation of 26 and 3.4 respectively; for the critical displacement value R under the complete damage state y,4, which obeys a normal distribution with a mean and standard deviation of 36 and 6 respectively; the pile diameter d obeys a normal distribution with a mean and standard deviation of 1 and 0.04 respectively; the concrete cube compressive strength f c The mean and standard deviation are 1.25f cu,k and 0.15f cu,k Normal distribution, where f cu,k is the standard value of the compressive strength of concrete cube obtained from experimental tests; the uncertainty influencing factor λ of the soil spatial distribution obeys a normal distribution with a mean and standard deviation of 1 and 0.05 respectively when the flow velocity v0 ≤ 5 m / s, and obeys a normal distribution with a mean and standard deviation of 1 and 0.15 respectively when the flow velocity v0 > 5 m / s.

[0202] After obtaining the distribution of variables in the functional function, for each flood level, the flood recurrence period is used as a variable to obtain the water depth h0 and flow velocity v0 under the flood recurrence period, and then the scour depth s is obtained. d Then, the Monte Carlo method was used to simulate 10,000 sets of different d,f c ,λ value, the displacement response S of the pile top is calculated by BP neural network agent model y (f c ,d,s d ,h0,v0); determine the damage state of 10,000 groups of samples according to the defined damage index range, and divide the number of samples of each damage state by the total number of samples to obtain the probability P of each damage state under a given flood intensity. i (IM), also known as the vulnerability curve.

[0203] The structural toughness curve is further derived based on the fragility curve. For different pile foundation damage states obtained by 10,000 groups of samples, the R y,i Take it as the critical displacement value under the damage state, and then calculate 10,000 sets of extreme pile foundation state function values ​​Z considering different damage states y,i ; The functional function of the pile foundation under different damage states is introduced as follows:

[0204]

[0205] where Q i (t,IM) is the functional function of the pile foundation under different damage states; t0 is the time point when the scour occurs; δ x,i is the idle time after the flush occurs; H(·) is the Heaviside function, which outputs 0 when the input value is negative and 1 when it is positive, and is used to activate the recovery function f after the idle time. i (·); δ r,i is the repair time after the scour occurs;

[0206] The distribution of each variable is as follows:

[0207] δ x,1 ~U(3.8,15.8);δ x,2 ~U(5.0,20.6);δ x,3 ~U(10.4,25.6);δ x,4 ~U(18.4,37.6)

[0208] δ r,1 ~N(10.29,9.45);δ r,2 ~N(15.9,10.8);δ r,3 ~N(32.1,15.4);δ r,4 ~N(62.3,22.6)

[0209] f1(τ)=1-e -0.2τ ; f 3,4 (τ) = e -0.2(1-τ)

[0210] Among them U(a LL ,b UL ) represents the lower limit of a LL , the upper limit is b UL uniform distribution, N(a M ,b SD ) represents the mean value a M , with a standard deviation of b SD Normal distribution; thus, the functional function of 10,000 groups of samples under various damage states can be obtained; the functional function of 10,000 groups of samples under various damage states can be compared with the corresponding probability of occurrence of each damage state P i Multiply and add to get the comprehensive functional expression of pile foundation:

[0211]

[0212] The pile foundation scour toughness is defined as follows:

[0213]

[0214] where δ x and δ r are the idle time and repair time of the comprehensive functional function Q(t,IM) of the pile foundation, respectively. The average toughness value under the corresponding flood intensity can be obtained by taking the average value of the toughness of the last 10,000 groups of samples.

Claims

1. A bridge pile foundation scour toughness analysis method, characterized in that: The steps include: S1. Use the concrete constitutive model and the steel constitutive model to construct a simplified finite element model of the bridge pile foundation; S2. Use the py curve to simplify the soil into a nonlinear spring and construct a soil spring model. Then, couple the simplified finite element model of the bridge pile foundation and the soil spring model to form a finite element model of the bridge pile-soil system. S3. Build a flow model around a cylinder based on Fluent to determine the average pressure on the water-facing and water-repelling surfaces of the pile foundation. The total pressure on the cylinder surface obtained is the water flow load on the bridge substructure. S4. Introduce a correction factor for floating objects to calculate the equivalent width of the pile foundation and the local scour depth. In the finite element model of the bridge pile-soil system, passivate the soil spring at the corresponding depth according to the local scour depth, which is equivalent to the scour load. S5. Screen the parameters other than the basic hydraulic parameters in the finite element model of the bridge pile-soil system through parameter sensitivity analysis and eliminate insensitive parameters; S6. Loading the water flow load and scour load of the bridge substructure into the finite element model of the bridge pile-soil system, using the sensitive parameters as input variable parameters of the finite element model of the bridge pile-soil system, performing finite element analysis based on different values ​​of the input variable parameters to obtain the corresponding pile top displacement as the finite element response, and forming a sample working condition combination; constructing a BP neural network proxy model based on the sample working condition combination, and establishing a mapping relationship between the input variable parameters and the response index in the BP neural network proxy model; S7. Based on the BP neural network proxy model and the damage states of the pile foundation, a vulnerability curve is established. The functional function of the pile foundation under different damage states is constructed by coupling the scour repair idle time and the functional recovery process through the Heaviside function and the repair function. Considering the uncertainty of the scour response time and combining the probability of occurrence of each damage state, the weighted summation of the pile foundation functional function under each damage state is performed to obtain the comprehensive functional function at any time. The scour toughness index of the bridge pile foundation is obtained by integrating and normalizing the comprehensive functional function of the pile foundation within the scour repair idle and recovery time intervals.

2. A bridge pile foundation scour toughness analysis method according to claim 1, characterized in that: The step S2 specifically includes the following steps: The py curve is a nonlinear model used to simulate the lateral reaction force provided by the soil to the pile body under the action of the pile lateral load. p represents the soil reaction force corresponding to the unit pile length, and y represents the lateral compression displacement of the soil spring. The py curve uses a modified semi-empirical curve, namely the API curve; the horizontal axis in the py curve is the normalized displacement y / Y c , that is, the spring lateral compression displacement y and characteristic displacement Y c The ordinate in the py curve is the normalized soil reaction force p / P u , that is, the soil reaction force p on the pile per unit length and its ultimate reaction force P u The ratio of The ultimate reaction force P in the API curve u and characteristic displacement Y c , the calculation formula for clay soil and sandy soil is: Y c =2.5ε 50 D Among them, P u is the lateral limit reaction force, C u is the undrained shear strength of the soil at the corresponding soil layer, D is the pile diameter, γ′ is the effective density of the soil, J is a dimensionless empirical constant ranging from 0.25 to 0.5, z is the depth of the soil, and R is the depth from the natural soil surface to the surface of the bearing capacity stable area; C1, C2, C3 are coefficients related to the internal friction angle of sandy soil, ε 50 Y represents the strain value at 0.5 times the maximum deviatoric stress in the undrained compression test of undisturbed soil. c is the characteristic displacement of the pile foundation under lateral load, and the API curve is a deterministic model of the soil spring model; The soil spring model is constructed, the spring spacing is set, the simplified finite element model of the bridge pile foundation and the soil spring model are meshed, and mesh convergence analysis is performed. After meshing, constant stiffness is assigned to the nodes where springs need to be added in batches based on Python scripts; then the spring material is set to nonlinear, and the spring stiffness is assigned according to the py curve. The characteristics of the soil spring are indirectly determined by the lateral limit reaction force P. u Determined, take P u (z i ) is a lognormal random variable with vertical spatial correlation, whose mean is the calculated value that increases linearly with depth in the soil spring deterministic model, and the coefficient of variation is Take 10% and do not change with depth, and establish P u (z i ) random field in the depth direction; Build P u (z i )The formula of the random field in the depth direction is: Where G i (z i ) is a normally distributed random field with zero mean and unit variance, and It is calculated by the transformation of lognormal mean and variance, and the calculation formula is: For spatially random distribution of soil, G i (z i )The random field is chosen as the correlation function based on exponential decay: where τ = |z1-z2| represents the distance between two points, δ z is the spatial correlation distance, which is selected according to the spring setting spacing; the correlation matrix is ​​established based on the correlation coefficient Use Choleskey decomposition to decompose it into a lower triangular matrix L and an upper triangular matrix L T The product of the matrix L and the randomly generated standard normal distribution sample Z j Generate P u (z i ) random field, the formula is: Define boundary conditions and loads, create a finite element analysis calculation task, and export the .inp calculation file. Then, use a Python script to batch modify the spring type after each *Spring keyword in the calculation file to NONLINEAR, and specify a table showing how the spring reaction force changes with compression. When simulating the nonlinear spring of the soil, the change in the reaction force during compression is set according to the py curve. When the soil is under tension, the reaction force is set to 0 to indicate that the soil can only withstand pressure but not tension, thus forming a finite element model of the bridge pile-soil system.

3. The bridge pile foundation scour toughness analysis method according to claim 1 is characterized in that: The step S3 specifically includes the following steps: The computational domain of the cylindrical flow model is set to 30D×20D×H, where H is the height of the pile foundation between the water surface and the riverbed. The cylindrical flow model is meshed using an O-block method, with hexahedral elements used. Local density is applied within the 2D range of the cylindrical wall of the cylindrical flow model. The inlet boundary adopts a velocity inlet, and the distribution along the depth direction is an exponential velocity profile, expressed as follows: z is the depth, u is m is the liquid surface velocity, is the average inlet flow velocity, and the water flow direction is perpendicular to the inlet surface; the outlet boundary uses a pressure outlet with a gauge pressure of 0; fixed rough walls are set on the cylindrical surface and the bottom of the model, and symmetric boundary conditions are set on the side and top surfaces of the model. The SIMPLE algorithm is used to solve the cylinder flow model to obtain the total pressure on the cylindrical surface, that is, the water flow load on the bridge substructure.

4. A bridge pile foundation scour toughness analysis method according to claim 1, characterized in that: In step S4, the equivalent width of the pile foundation is calculated based on the accumulation of floating objects in a rectangular form in front of the structure. in is the equivalent width of the pile foundation, a is the actual width of the pile foundation, K4 is the floating debris accumulation shape correction coefficient, H f is the height of floating debris accumulation, W is the width of floating debris accumulation, y is the water flow depth, and K1 is the correction coefficient of the pile cross-section shape.

5. The bridge pile foundation scour toughness analysis method according to claim 1, characterized in that: In step S4, for non-cohesive soil, the scour depth is calculated using the modified CSU equation, which is: where y ls is the local scouring depth of non-cohesive soil; y1 is the average water flow depth in front of the pile; K1 is the correction factor for the cross-sectional shape of the pile; K2 is the correction factor for the water flow angle; K3 is the correction factor related to the riverbed conditions; is the equivalent width of the pile foundation; Fr is the Froude number of the water flow in front of the pile, which is given by V / (gy1) 0.5 Calculation: V is the average velocity of the water flow in front of the pile, g is the acceleration of gravity, θ is the slope angle of the riverbed, and L is the length of the water-facing surface in front of the pier along the direction of water flow; In step S4, for clay soil, the scour depth is calculated using the Briaud shrinkage scour formula: where y ls-ult is the local scouring depth of clay soil, V c is the critical starting average flow velocity, is the initial scouring rate of clay soil, V1 is the average velocity of water flow in the scouring area, y s (t) is the basic time-varying scour depth.

6. A bridge pile foundation scour toughness analysis method according to claim 1, characterized in that: In step S5, the parameter to be screened is subjected to a three-fold fluctuation range. When the damage indicator pile top displacement does not vary by more than 20% with the parameter fluctuation, it is considered an insensitive parameter.

7. The bridge pile foundation scour toughness analysis method according to claim 1, characterized in that: In step S7, flood intensity is graded. Based on the hydrological records of the bridge site, floods with a return period of less than 50 years are classified as Level III, floods with a return period of 50-100 years are classified as Level II, and floods with a return period of more than 100 years are defined as Level I.

8. A bridge pile foundation scour toughness analysis method according to claim 7, characterized in that: In step S7, the damage state is defined according to the size of the damage index. A total of four different pile foundation damage states are defined as follows: a pile top displacement of 0 to 15 mm is defined as slight damage, a pile top displacement of 15 to 30 mm is defined as moderate damage, a pile top displacement of 30 to 50 mm is defined as severe damage, and a pile top displacement greater than 50 mm is defined as complete destruction.

9. A bridge pile foundation scour toughness analysis method according to claim 8, characterized in that: The formula of the performance function under each flood level in step S7 is: Z y,i =R y,i -λ·S y (f c ,d,s d ,h0,v0) Where Z y,i is the limit state performance function value based on the pile top displacement index; R y,i is the critical displacement value corresponding to the i-th damage state; λ is the uncertainty factor affecting the soil spatial distribution; S y is the displacement response of the pile top under the water flow load of water depth and flow velocity, h0 and s d are the water depth and the scour depth corresponding to the flow velocity v0, d is the pile diameter, f c is the compressive strength of concrete cube; R in the pile foundation function under each flood level y,i ,d,f c ,λ is considered as a normal distribution to take into account the uncertainty of the variable, where the critical displacement value R under the slight damage state is y,1 , which obeys the normal distribution with mean and standard deviation of 10 and 2 respectively; for the critical displacement value R under moderate damage state y,2 , which obeys a normal distribution with a mean and standard deviation of 18 and 2.8 respectively; for the critical displacement value R under severe damage state y,3 , which obeys the normal distribution with mean and standard deviation of 26 and 3.4 respectively; for the critical displacement value R under the complete damage state y,4 , which obeys a normal distribution with a mean and standard deviation of 36 and 6 respectively; the pile diameter d obeys a normal distribution with a mean and standard deviation of 1 and 0.04 respectively; the concrete cube compressive strength f c The mean and standard deviation are 1.25f cu,k and 0.15f cu,k Normal distribution, where f cu,k is the standard value of concrete cube compressive strength obtained from experimental tests; the soil spatial distribution uncertainty factor λ follows a normal distribution with a mean and standard deviation of 1 and 0.05, respectively, when the flow velocity v0 ≤ 5 m / s, and a normal distribution with a mean and standard deviation of 1 and 0.15, respectively, when the flow velocity v0 > 5 m / s; After obtaining the distribution of variables in the functional function, for each flood level, the flood recurrence period is used as a variable to obtain the water depth h0 and flow velocity v0 under the flood recurrence period, and then the scour depth s is obtained. d Then, the Monte Carlo method is used to simulate several groups of different d,f c ,λ value, the displacement response S of the pile top is calculated by BP neural network agent model y (f c ,d,s d ,h0,v0); determine the damage state of several groups of samples according to the defined damage index range, and divide the number of samples of each damage state by the total number of samples to obtain the probability P of each damage state under a given flood intensity. i (IM), also known as the vulnerability curve; The structural toughness curve is derived based on the fragility curve. For different pile damage states obtained by several groups of samples, the R corresponding to each sample is y,i Take as the critical displacement value under the damage state, and then calculate several groups of extreme pile foundation state function values ​​Z considering different damage states y,i , the functional function of the pile foundation under different damage states is introduced as follows: where Q i (t,IM) is the functional function of the pile foundation under different damage states; t0 is the time point when the scour occurs; δ x,i is the idle time after the flush occurs; H(·) is the Heaviside function, which outputs 0 when the input value is negative and 1 when it is positive, and is used to activate the recovery function f after the idle time. i (·); δ r,i is the repair time after the scour occurs; The distribution of each variable is as follows: d x,1 ~U(3.8,15.8);δv x,2 ~U(5.0,20.6);δ x,3 ~U(10.4,25.6);d x,4 ~U(18.4,37.6) d r,1 ~N(10.29,9.45);d r,2 ~N(15.9,10.8);d r,3 ~N(32.1,15.4);d r,4 ~N(62.3,22.6) Among them U(a LL ,b UL ) represents the lower limit of a LL , the upper limit is b UL uniform distribution, N(a M ,b SD ) represents the mean value a M , with a standard deviation of b SD Normal distribution; thus, the functional functions of several groups of samples under various damage states can be obtained; the functional functions of several groups of samples under various damage states are compared with the corresponding probability of occurrence of each damage state P i Multiply and add to get the comprehensive functional expression of pile foundation: The pile foundation scour toughness is defined as follows: Where δ x and δ r are the idle time and repair time of the comprehensive functional function Q(t,IM) of the pile foundation respectively. The average toughness value under the corresponding flood intensity can be obtained by taking the average value of the toughness of several groups of samples obtained at last.

10. A bridge pile foundation scour toughness analysis system, characterized in that: include: The pre-processing module is used to construct a simplified finite element model of the bridge pile foundation using the concrete constitutive model and the steel bar constitutive model; the py curve is used to simplify the soil into a nonlinear spring, and a soil spring model is constructed. The simplified finite element model of the bridge pile foundation and the soil spring model are then coupled to form a finite element model of the bridge pile-soil system; a cylindrical flow model is established based on Fluent to determine the average pressure on the water-facing and water-removing surfaces of the pile foundation, and the total pressure on the cylindrical surface obtained is the water flow load of the bridge substructure; a correction coefficient considering floating objects is introduced to calculate the equivalent width and local scour depth of the pile foundation, and the soil spring of the corresponding depth is passivated according to the local scour depth in the finite element model of the bridge pile-soil system, which is equivalent to the scour load; parameters other than the basic hydraulic parameters in the finite element model of the bridge pile-soil system are screened through parameter sensitivity analysis to eliminate insensitive parameters; The BP neural network proxy module is used to load the water flow load and scour load of the bridge substructure into the finite element model of the bridge pile-soil system. The sensitive parameters are used as input variable parameters of the finite element model of the bridge pile-soil system. Finite element analysis is performed based on different values ​​of the input variable parameters to obtain the corresponding pile top displacement as the finite element response, forming a sample working condition combination. The BP neural network proxy model is constructed based on the sample working condition combination, and a mapping relationship between the input variable parameters and the response index is established in the BP neural network proxy model. The toughness calculation module is used to establish a vulnerability curve based on the BP neural network proxy model and various damage states of the pile foundation. The pile foundation function function under different damage states is constructed by coupling the scour repair idle time and the functional recovery process through the Heaviside function and the repair function. The weighted summation of the pile foundation function function under each damage state is taken into account, considering the uncertainty of the scour response time and the probability of occurrence of each damage state, to obtain the comprehensive function function at any time. The scour toughness index of the bridge pile foundation is obtained by integrating and normalizing the comprehensive function function of the pile foundation within the scour repair idle and recovery time intervals.

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