A bridge pile foundation local scour evaluation system and method based on flow velocity strain rate

Abstract

The application belongs to the technical field of bridge safety evaluation, and specifically discloses a bridge pile foundation local scour evaluation method and system based on flow velocity strain rate, establishes a calculation model for the local scour pit shape and maximum scour depth of a river-crossing sea bridge pile foundation, converts the Reynolds stress tensor into a flow velocity strain rate scalar, proposes an erosion-deposition model, analyzes the erosion and deposition rates, establishes a scour depth relationship, uses a sediment transport model for storing parameters of a grid unit, simulates the dynamic response of a water-sediment mixture, triggers the sediment sliding with the aid of a sliding model when the scour pit inclination angle exceeds the critical slope, updates the riverbed topography, and realizes efficient simulation of the local scour of the pile foundation through cooperation of the models. The application can efficiently and accurately calculate the local scour pit shape evolution and maximum scour depth of a single pile and a group of piles, and provides support for the design of a bridge pile foundation and the optimization of an anti-scour structure.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge safety evaluation, and particularly relates to a bridge pile foundation local scour evaluation system and method based on flow velocity strain rate. BACKGROUND

[0002] Local scour is one of the main reasons for the collapse of bridges across valleys, rivers and seas. From 1960 to 1986, 108 bridges collapsed in New Zealand, of which 29 were destroyed by local scour. From 1989 to 2000, there were 490 cases of bridge damage in the United States, of which 243 bridges were destroyed by local scour; from 2000 to 2014, there were 106 bridges destroyed in China, of which 35 were destroyed by local scour. Bridges destroyed by local scour account for 1 / 3 of the total number of collapsed bridges, 6 times the number of bridges destroyed by overloading, and 20 times the number of bridges destroyed by earthquakes. Therefore, the stability of bridge pile foundations under local scour conditions has been widely concerned.

[0003] There are many models for analyzing local scour of pile foundations, including empirical models, analytical and numerical models, etc. Among them, the empirical model is mostly based on physical experiments, and the model has statistical characteristics but weak physical properties, and cannot well reveal the local scour process; the analytical model is often based on complex theories such as fluid dynamics and sediment particle kinematics, and is difficult to solve; the numerical model is mostly based on analytical models, and integrates Reynolds averaging theory to consider the average characteristics and turbulent characteristics of the fluid separately, but still has problems such as low calculation accuracy and efficiency, insufficient estimation of scour pit shape and depth, etc. due to various theoretical generalizations. Therefore, there is an urgent need to establish a high-efficiency and accurate bridge pile foundation local scour evaluation system and method. SUMMARY

[0004] The purpose of the present application is to overcome the defects in the prior art and provide a bridge pile foundation local scour evaluation method based on flow velocity strain rate.

[0005] In a first aspect, the present application provides a bridge pile foundation local scour evaluation method based on flow velocity strain rate, comprising the following steps:

[0006] S1, obtaining a flow velocity strain rate of a water flow, expressing the flow velocity strain rate of the water flow with a flow velocity strain rate DEV, the flow velocity strain rate DEV being used to characterize the flow dynamic characteristics around the pile foundation;

[0007] S2, based on the flow velocity strain rate DEV, deducing and establishing an erosion-deposition model of riverbed sediment in the local scour process of the pile foundation;

[0008] S3, performing parameter calculation and analysis on the riverbed sediment erosion-deposition model;

[0009] S4, the iSquares numerical grid is used to store the water and sediment dynamics parameters, the inter-particle force is regarded as the grid internal force, a water and sediment transport force model is established, and the dynamic response law of the sediment and water body moving at the same speed but accompanied by sedimentation / suspension is revealed; the critical slope of the riverbed is set by combining the sliding model c When the inclination of the scour pit exceeds the critical value, the sediment sliding mechanism is triggered, and the scour pit topography is dynamically updated;

[0010] S5, the erosion-deposition model and the water and sediment transport force model are coupled to simulate the interaction of water flow-sediment-riverbed around the pile, and the high-precision dynamic analysis of the local scour characteristics of the pile foundation is realized.

[0011] Further, in the S1, the Reynolds stress tensor is converted into a flow velocity strain rate scalar form in a two-dimensional flow case, and the Reynolds stress tensor is expressed as:

[0012]

[0013] The eigenvalue is:

[0014]

[0015] In the formula, represents the flow velocity strain rate of the grid at r at t, e xx (r,t) and e xy (r,t) are both flow velocity strain rate scalar expressions, e xx (r,t) represents the shear stress in the x direction caused by the turbulent fluctuation in the x direction of the grid at position r at time t, e xy (r,t) represents the shear stress in the y direction caused by the turbulent fluctuation in the x direction of the grid at position r at time t.

[0016] The calculation formula of the flow velocity strain rate DEV around the pile foundation is:

[0017]

[0018] In the formula, e ij is the strain rate tensor, i and j represent two mutually perpendicular directions in the Cartesian coordinate system, which represent the x and y directions here; u i is the velocity of the fluid in the i direction, u j is the velocity of the fluid in the j direction, and the meanings of the remaining parameters are the same as above.

[0019] The maximum shear strain rate is calculated as 1 / 2 of the difference between the principal strain rates:

[0020]

[0021] The Reynolds stress is expressed by DEV as:

[0022] τ(r, t) = μDEV(r, t) (6)

[0023] τ(r, t) represents the shear stress at r position at t time, μ represents the dynamic viscosity of fluid, μ = ρv, ρ is the density of fluid, v is the kinematic viscosity of fluid, and DEV(r, t) represents the flow velocity strain rate at r position at t time.

[0024] Further, the formula for calculating the flow velocity near the pile foundation is:

[0025] v x = v in (1 - e a / kD ) (7)

[0026] wherein the pile foundation flow face is set as 0°, the back flow face is set as 180°, other directions are set according to clockwise angle, v x represents the average flow velocity in the plane near the pile foundation, v in represents the average flow velocity in the plane near the pile foundation, a represents the position of the flow velocity calculation point, a > 0 represents that the calculation point is located downstream of the pile foundation, a < 0 represents that the calculation point is located upstream of the pile foundation, |a| is the distance between the calculation point and the center of the pile foundation, k is a parameter related to the angle of the calculation point, k takes different values at different angles, and D is the equivalent pile foundation diameter.

[0027] Further, S2 is specifically:

[0028] Riverbed sediment erosion model:

[0029]

[0030] Riverbed sediment deposition model:

[0031]

[0032] wherein T(r, t) represents the scouring depth at r position at t time, respectively represent the erosion and deposition coefficients, DEV(r, t) represents the flow velocity strain rate at r position at t time, and DEV c represents the critical DEV value for riverbed sediment transport, T max (r, t) represents the maximum scouring depth of the riverbed (r, t) position, which is used as a discrimination condition for scouring balance, and T0(r) represents the initial depth of the riverbed before local scouring;

[0033] According to the relationship between the flow velocity strain rate DEV(r, t) near the pile foundation and the critical flow velocity strain rate DEV c , the erosion or deposition model is selected to update the riverbed depth at a certain time;

[0034] If DEV(r, t) > DEVc , T(r, t) < T max (r, t), the flow carrying capacity of sediment is greater than the critical tractive force of riverbed sediment, and the scour pit has not reached the maximum scour depth, the riverbed sediment is eroded, at this moment the scour pit depth at this position increases, and the scour pit depth increases at a rate of dT(r, t) / dt;

[0035] If DEV(r, t) > DEV c , T(r, t) > T max (r, t), the flow carrying capacity of sediment is greater than the critical tractive force of riverbed sediment, but the scour pit depth is greater than the maximum scour depth, at this moment the riverbed is no longer eroded, and the scour pit depth increases at a rate of 0;

[0036] If DEV(r, t) < DEV c , the flow carrying capacity of sediment is less than the critical tractive force of riverbed sediment, the riverbed sediment is deposited, at this moment the scour pit depth at this position decreases, and the scour pit depth decreases at a rate of dT(r, t) / dt.

[0037] Further, the calculation and analysis process in S3 is:

[0038] (1) The critical flow velocity strain rate DEV c The calculation formula is:

[0039]

[0040] DEV c = C -1 v dc d b , where DEV c is the critical flow velocity strain rate, with the unit of s -1 ; C dc is a dimensionless parameter; v b represents the sediment incipient velocity; d 50 represents the median particle size of sediment;

[0041] When the riverbed flow velocity ,

[0042]

[0043] v b d is the bed flow velocity when the sediment starts; g is the acceleration of gravity; s is the ratio of the density of sediment and the density of water; C dc = -0.317Fr 2 + 0.392Fr - 0.077;

[0044] (2) For the scour depth at any position of the riverbed at time t, the formula is satisfied:

[0045]

[0046] T max(r, t) represents the maximum scour depth of the riverbed (r, t) position, T max represents the maximum scour of the riverbed in the local scour range;

[0047] wherein the maximum scour depth of the riverbed T max satisfies formula (13) or (14) or (15):

[0048] Formula (13)

[0049]

[0050] In the formula, V in is the incoming flow, and DEV is the flow velocity strain rate. In the formula, it is assumed that the flow field is uniform, and the flow velocity is the only factor determining the scour depth;

[0051] Formula (14)

[0052]

[0053] In the formula, DEV c is the critical flow velocity strain rate;

[0054] Formula (15)

[0055]

[0056] In the formula, h is the water depth, D is the pile diameter, and by introducing to adjust the erosion depth, the scour depth near the critical value can be more finely simulated;

[0057] (3) Erosion rate coefficient

[0058]

[0059] When DEV is greater than DEV c , erosion occurs, and the greater the DEV or the smaller the DEV c , the faster the erosion rate; if DEV is much greater than DEV c , the erosion rate approaches the limit;

[0060] (4) Deposition coefficient

[0061]

[0062] In the formula, is the deposition rate coefficient, with the unit of m / s; a1 is an empirical coefficient; ω s is the sediment settling velocity, which is determined by the particle size, shape, and fluid viscosity of the sediment; d 50is the representative particle size; h is the water depth; s is the relative density of sediment and water; g is the acceleration of gravity; C d is the drag coefficient, reflecting the size of the fluid resistance to sediment particles.

[0063] Further, the force of the sediment transport or collapse in S4 includes:

[0064]

[0065] wherein Mg is the bulk density of the block, r i is the position of the ith block, t represents time, is the elevation of the upper surface of the block;

[0066] x-direction viscous resistance

[0067] y-direction viscous resistance

[0068] F vx and F vy represent the x-direction and y-direction viscous resistance respectively, v is the kinematic viscosity of the fluid, M is the mass of the block, ν x (n+1, m) and ν x (n-1, m) represent the grid (n+1, m) and grid (n-1, m) in the x-direction flow velocity respectively, ν y (n+1, m) and ν y (n-1, m) represent the grid (n+1, m) and grid (n-1, m) in the y-direction flow velocity respectively, dxspace and dyspace are the x-direction and y-direction grid size respectively. The meanings of the remaining parameters are the same as above;

[0069] base friction

[0070] wherein F b (r i ,t) is the base friction of the ith block at time t, H w (r i ,t) is the water depth of the ith block at time t, H s (r i ,t) is the sediment thickness carried by the ith block at time t, fract(r i ,t) is the sediment volume fraction of the ith block at time t, fract(r i ,t) = H s (r i ,t) / (H s (r i ,t) + H w (r i, μ1 is the base friction coefficient between the water body and the riverbed, μ2 represents the base friction coefficient of the sediment and the riverbed, is the unit velocity vector, which represents the tendency of the block to decelerate due to the base friction.

[0071] Further, the riverbed scouring depth dynamic balance is controlled by using a sliding collapse model based on the iSquares theory, and the specific action process of the sliding collapse model is as follows: there is a critical slope for each type of riverbed, when the inclination of the riverbed scouring pit is greater than the critical slope, the sediment attached to the upper edge of the scouring pit will slide into the scouring pit, so that the depth and slope of the scouring pit are both reduced, and then the riverbed terrain around the scouring pit is updated again.

[0072] Further, the riverbed critical slope α c is 25°-30°.

[0073] In the second aspect of the present application, a bridge pile foundation local scouring evaluation system based on flow velocity strain rate is provided, which comprises:

[0074] A flow velocity strain rate construction module, which converts the Reynolds stress tensor into a flow velocity strain rate scalar form based on the Reynolds stress theory, so as to propose a flow velocity strain rate DEV representing the dynamic characteristics of the water flow around the pile foundation;

[0075] An erosion-deposition model establishment module, which deduces and establishes an erosion-deposition model of the riverbed sediment in the pile foundation local scouring process based on the flow velocity strain rate DEV;

[0076] A model parameter analysis module, which is used for calculating and analyzing the parameters of the erosion-deposition model;

[0077] A water and sediment transport and sliding collapse simulation module, which stores the water and sediment dynamics parameters by using an iSquares numerical grid, converts the inter-particle force into an internal force in the grid, establishes a water and sediment transport force model, so as to reveal the dynamic response law of the sediment settlement / suspension; in combination with the sliding collapse model, the riverbed critical slope is set, the sediment sliding mechanism is triggered when the inclination of the scouring pit exceeds the critical value, and the scouring pit terrain is dynamically updated;

[0078] A dynamic scouring analysis module, which is used for coupling the erosion-deposition model and the water and sediment transport model, simulating the water flow-sediment-riverbed interaction around the pile, and realizing high-precision dynamic analysis of the pile foundation local scouring characteristics.

[0079] Compared with the prior art, the present application has the following beneficial effects:

[0080] This invention discloses a system and method for assessing local scour of bridge pile foundations based on velocity-strain rate. A computational model is established for the morphology and maximum scour depth of local scour pits in cross-river and sea bridge pile foundations. This method is based on the derivation of the Reynolds stress tensor into a scalar form of velocity-strain rate, proposing an erosion-deposition model based on velocity-strain rate. By determining the relationship between velocity-strain rate and critical velocity-strain rate, and analyzing the erosion-deposition rate based on a given erosion-deposition coefficient, the relationship between the scour depth at any point in the riverbed and the maximum scour depth is established. Furthermore, a sediment transport model stores hydrodynamic parameters through grid cells, converting interparticle forces into grid internal forces to accurately simulate the transport of water-sediment mixtures and the dynamic response of sediment settling / suspension. When the dip angle of the scour pit exceeds the critical slope, a sediment slippage mechanism is triggered through a slump model, dynamically adjusting the scour pit depth and slope to achieve adaptive updating and balancing of the riverbed topography. The synergistic effect of various models achieves efficient simulation of local scour characteristics of the pile foundation. The bridge pile foundation local scour assessment system and method based on flow velocity and strain rate established by this invention can efficiently and accurately calculate the morphological evolution and maximum scour depth of local scour pits in single piles and pile groups. This invention provides a scientific basis for bridge pile foundation design under special structural and topographical conditions, and also provides strong technical support for the optimized design of scour-resistant structures. It also supplements and improves existing bridge scour calculation and numerical simulation techniques, providing engineers with more tools and methods to address complex scour problems. While improving simulation accuracy, it also increases simulation speed, greatly expanding our ability to predict more complex scour scenarios. Attached Figure Description

[0081] The following figures are for illustrative purposes only and are not intended to limit the scope of the invention, wherein:

[0082] Figure 1 This is an overall framework diagram of a bridge pile foundation local scour assessment system and method based on flow velocity and strain rate according to the present invention.

[0083] Figure 2 It is a graph showing the flow velocity and velocity-strain rate of water near the pile foundation;

[0084] Figure 3 It is the DEV(r,t)-DEV near the pile foundation c Relationship between the shape and size of the scour pit;

[0085] Figure 4 This is a graph showing the change in the depth of the flushing pit over time between water flushing and moving bed flushing;

[0086] Figure 5 This is a schematic diagram of the critical slope of the riverbed. Detailed Implementation

[0087] In order to make the purpose, technical scheme, design method and advantages of the present application more clear, the present application is further described in detail below with specific examples in combination with the drawings. It should be understood that the specific examples described herein are only used to explain the present application and not to limit the present application.

[0088] As shown in Figure 1 The present application provides a bridge pile local scouring evaluation system based on flow velocity strain rate, which comprises: a flow velocity strain rate construction module, which converts the Reynolds stress tensor into a flow velocity strain rate scalar form based on the Reynolds stress theory to propose a flow velocity strain rate DEV representing the dynamic characteristics of the water flow around the pile foundation; an erosion-deposition model establishment module, which establishes an erosion-deposition model of the riverbed sediment in the process of the local scouring of the pile foundation based on the flow velocity strain rate DEV; a model parameter analysis module, which is used for calculating and analyzing the parameters of the erosion-deposition model; a water-sediment transport and sliding simulation module, which stores the water-sediment dynamics parameters in the iSquares numerical grid, converts the inter-particle force into the internal force in the grid, establishes a water-sediment transport force model to reveal the dynamic response law of the sediment settlement / suspension, and sets the critical slope of the riverbed in combination with the sliding model, triggers the sediment sliding mechanism when the scour pit inclination exceeds the critical value, and dynamically updates the scour pit topography; and a dynamic scouring analysis module, which is used for coupling the erosion-deposition model and the water-sediment transport model, simulating the water flow-sediment-riverbed interaction around the pile, and realizing the high-precision dynamic analysis of the local scouring characteristics of the pile foundation.

[0089] Specifically, continuing to refer to Figure 1 The system realizes the following steps:

[0090] 1) Tensor expression of the Reynolds stress, and proposal of the flow velocity strain rate DEV

[0091] Based on the theoretical basis that the Reynolds stress is the additional stress generated by the turbulent flow of water and reflects the influence of the turbulent flow on the sediment movement, the flow velocity strain rate (DEV) is proposed by converting the Reynolds stress tensor into a flow velocity strain rate scalar form:

[0092] In the case of two-dimensional flow, the Reynolds stress tensor is expressed as:

[0093]

[0094] The eigenvalue is:

[0095]

[0096] In the formula, r represents the grid, t represents the time, e (r,t) represents the flow velocity strain rate of the grid at r and t, e xx (r,t) represents the flow velocity strain rate of the grid at r and t, and e xy (r,t) represents the flow velocity strain rate of the grid at r and t, and e xy (r,t) represents the flow velocity strain rate of the grid at r and t, and exx (r,t) represents the shear stress in the x-direction caused by turbulent fluctuations in the r-direction grid at time t. The meanings of the other parameters are deduced similarly.

[0097] DEV represents the flow velocity strain rate, a parameter describing the flow state, and is related to the flow velocity, water depth, pile foundation geometry, and riverbed elevation. The following formula is used to calculate the flow velocity strain rate (DEV) around the pile foundation:

[0098]

[0099] Among them, e ij Let i and j be the strain rate tensor, representing two mutually perpendicular directions in the Cartesian coordinate system, here representing the x and y directions; u i Let u be the velocity of the fluid in the i-direction. j The velocity of the fluid in the j-direction is given by the above parameter; the meanings of the other parameters are the same as above.

[0100] Calculate the maximum shear strain rate as half of the difference between the principal strain rates:

[0101]

[0102] Reynolds stress can be further expressed using DEV:

[0103] τ(r,t)=μDEV(r,t) (27)

[0104] τ(r,t) represents the shear stress at position r at time t, μ represents the fluid dynamic viscosity, μ=ρv, ρ is the fluid density, v is the fluid kinematic viscosity, and DEV(r,t) represents the flow velocity strain rate at position r at time t.

[0105] Assuming the upstream face of the pile foundation is 0°, the downstream face is 180°, and other directions follow a clockwise rotation angle, the flow velocity near the pile foundation can be calculated using the following formula:

[0106] v x =v in (1-e a / kD (28)

[0107] Among them, v x The average flow velocity at a depth near the pile foundation in the plane, v inV (r, t) = V (r, t) + aDkcos (a), where V (r, t) represents the average flow velocity at the r position at t time, a represents the position of the flow velocity calculation point, where a > 0 represents that the calculation point is located downstream of the pile foundation, a < 0 represents that the calculation point is located upstream of the pile foundation, |a| is the distance between the calculation point and the centroid of the pile foundation, k is a parameter related to the angle of the calculation point, k takes different values at different angles, and D is the equivalent pile foundation diameter. For a cylindrical pile foundation, the equivalent pile foundation diameter is the diameter thereof; for a round-end-shaped, rectangular or other special-shaped pile foundation, the equivalent pile foundation diameter is the structural coefficient multiplied by the pile foundation diameter.

[0108] 2) Based on the parameter flow velocity strain rate (DEV), a riverbed sediment erosion-deposition model in pile local scour is derived and established

[0109] 2.1) Riverbed sediment erosion-deposition model based on DEV

[0110] Riverbed sediment erosion model:

[0111]

[0112] Riverbed sediment deposition model:

[0113]

[0114] where T (r, t) represents the scour depth at the r position at t time, respectively represent the erosion and deposition coefficients, DEV (r, t) represents the flow velocity strain rate at the r position at t time, and DEV c represents the critical DEV value for riverbed sediment transport, T max (r, t) represents the maximum scour depth of the riverbed (r, t) position, which is used as a discrimination condition for scour balance, and T0 (r) represents the initial depth of the riverbed before local scour.

[0115] According to the relationship between the flow velocity strain rate DEV (r, t) value near the pile foundation and the critical flow velocity strain rate DEV c , the erosion or deposition model is selected to update the riverbed depth at a certain time;

[0116] If DEV (r, t) > DEV c , T (r, t) < T max (r, t), the flow sediment carrying capacity is greater than the critical transport value of the riverbed sediment, and the scour pit does not reach the maximum scour depth, the riverbed sediment is eroded, and the scour pit depth increases at this time, and the scour pit depth increase rate is d T (r, t) / dt;

[0117] If DEV (r, t) > DEV c , T (r, t) > T max(r, t), the flow capacity is greater than the critical value of the river bed sediment transport, but the scour pit depth is greater than the maximum scour depth, at this time the river bed is no longer eroded, and the scour pit depth increases at a rate of 0;

[0118] If DEV(r, t) < DEV c , the flow capacity is less than the critical value of the river bed sediment transport, and the river bed sediment is deposited at this moment, at this moment the scour pit depth decreases, and the scour pit depth decreases at a rate of dT(r, t) / dt.

[0119] 2.2) Model parameter analysis and calculation

[0120] Critical flow velocity strain rate (DEV c ):

[0121]

[0122] DEV c (r, t) = C -1 v dc d b Fr 50 , where DEV -1 (r, t) is the critical flow velocity strain rate, with the unit of s -1 ; C dc is a dimensionless parameter; v b represents the sediment starting flow velocity; d 50 represents the median diameter of the sediment; and Fr is the Froude number.

[0123] When the river bed flow velocity is less than the critical flow velocity strain rate, the river bed is in a state of deposition, and the scour pit depth decreases at a rate of dT(r, t) / dt.

[0124]

[0125] where v b is the bed flow velocity when the sediment starts; g is the acceleration of gravity; s is the ratio of the sediment density to the water density; d 50 is the median diameter of the sediment; C dc = -0.317Fr 2 + 0.392Fr - 0.077; and the remaining parameters are the same as above.

[0126] For the scour depth of the river bed at any position at time t, the formula is satisfied:

[0127]

[0128] where T max (r, t) represents the maximum scour depth of the river bed (r, t), and T max represents the maximum scour of the river bed within the local scour range.

[0129] The maximum scour depth of the river bed (T max ): The maximum scour depth of the river bed is related to the equivalent diameter of the pile foundation, the water depth, the flow velocity, the sediment particle size, etc. It can be considered that the maximum scour depth of the river bed satisfies formula (13) or (14) or (15):

[0130] Formula (13)

[0131]

[0132] In the formula: V in Let DEV be the inflow velocity and DEV be the strain rate. This formula assumes simple flow conditions and small changes in strain rate. It also assumes a relatively uniform flow field and that the flow velocity is the sole factor determining the scour depth.

[0133] Formula (14)

[0134]

[0135] In the formula, DEV c This represents the critical velocity-strain rate; the remaining footnotes have the same meaning as above. The flow velocity and strain rate of water vary significantly in different regions (such as before and after the pile, and on both sides). When the water flow's DEV exceeds the critical velocity-strain rate... c Only when sediment particles are eroded, leading to an increase in scour depth, will this process occur. This formula incorporates DEV (Depth Erosion Value). c This better simulates this nonlinear relationship.

[0136] Formula (15)

[0137]

[0138] In the formula, h is the water depth, D is the pile diameter, and the remaining annotations have the same meaning as above, based on the nonlinear characteristics of the sediment erosion process. The correction factor takes into account the DEV. c The impact, by introducing This allows for adjustment of the erosion depth, enabling more precise simulation of the scour depth near the critical value.

[0139] Erosion rate coefficient

[0140]

[0141] When DEV is greater than DEV c At that time, erosion occurs, and the larger the DEV or the higher the DEV, the more likely erosion will occur. c The smaller the value, the faster the erosion rate; if the DEV is much larger than the DEV... c The erosion rate is approaching its limit.

[0142] Sedimentation coefficient

[0143]

[0144] In the formula, ω is the deposition rate coefficient, in m / s; a1 is an empirical coefficient; sThe settling velocity of sediment is determined by factors such as sediment particle size, morphology, and fluid viscosity; d 50 ρ is the representative particle size; h is the water depth; s is the relative density of sediment and water; g is the acceleration due to gravity; C d The drag coefficient reflects the magnitude of the resistance of the fluid to the sediment particles.

[0145] 3) Sediment transport and landslide model based on iSquares

[0146] 3.1) Using the iSquares grid as the basic unit to store hydrodynamic parameters, the interparticle forces are considered as internal forces within the grid. The dynamic response of particles moving at the same velocity as the water body but accompanied by sedimentation / suspension is revealed through key force components. Specific calculations include:

[0147] gravity

[0148] In the formula, Mg is the bulk density, and r i Let t represent the position of the i-th block and t represent time. This represents the elevation of the upper surface of the block.

[0149] Viscous resistance in the x direction

[0150] Viscous resistance in the y direction

[0151] F vx With F vy Let ν represent the viscous drag in the x and y directions, respectively; v be the kinematic viscosity of the fluid; M be the mass of the block; and ν be the viscosity of the fluid. x (n+1,m), ν x (n-1, m) represent the water flow velocities in the x-direction of grids (n+1, m) and (n-1, m), respectively, ν y (n+1,m), ν y (n-1, m) represent the water flow velocities in the y-direction for grids (n+1, m) and (n-1, m), respectively, while dxspace and dyspace represent the grid dimensions in the x and y directions, respectively. The meanings of the remaining parameters are the same as above.

[0152] Basic friction

[0153] In the formula, F b (r i H(t) represents the base friction force of the i-th block at time t. w (r i H(t) represents the water thickness of the i-th block at time t. s (r i fract(r) represents the thickness of the sediment carried by the i-th block at time t. ifract(r) represents the volume percentage of sediment in block i at time t. i ,t)=H s (r i ,t) / (H s (r i ,t)+H w (r i ,t)), where μ1 is the base friction coefficient between the water body and the riverbed, and μ2 represents the base friction coefficient between the sediment and the riverbed. The vector represents the unit velocity, indicating that the frictional force at the base causes the block to decelerate.

[0154] 3.2) A landslide model based on iSquares theory is used to control the dynamic equilibrium of riverbed scour depth. Each riverbed type has a critical slope α. c When the inclination angle α of the riverbed scour pit is greater than the critical slope α c The sediment adhering to the upper edge of the scour pit will slide into the pit, reducing its depth and slope, thus renewing the riverbed topography around the scour pit. The commonly used critical riverbed slope α... c The angle is 25° to 30°.

[0155] 4) Assessment of local scour of bridge pile foundations

[0156] like Figure 2 As shown, the water flow velocity and velocity strain rate near the pile foundation include:

[0157] As water flows near the pile foundation, the average flow velocity decreases exponentially, while the flow velocity strain rate increases exponentially. Similarly, as water flows away from the pile foundation, the average flow velocity increases exponentially, while the flow velocity strain rate decreases exponentially. The difference lies in the rate and magnitude of change of the average flow velocity and flow velocity strain rate at different locations within the pile foundation.

[0158] like Figure 3 As shown, DEV(r,t)-DEV near the pile foundation c A diagram showing the relationship between the shape and size of the scour pit, where the scour pit shape is presented as a top view. This includes: calculating DEV(r,t)-DEV. c The value is used to determine if it is greater than 0:

[0159] If so, at time t and position r, the sediment particles on the riverbed surface are eroded and enter the water flow;

[0160] If not, the sediment particles in the water flow at position r at time t will settle, and the concentration of sediment particles in the water flow at this point will decrease.

[0161] The rate at which sediment particles are eroded or settled depends on |DEV(r,t)-DEV c | / DEVc Erosion deposition coefficient and riverbed erosion depth. When |DEV(r,t)-DEV c | / DEV c The higher the value, the greater the erosion-deposition coefficient, and the faster the erosion or deposition rate; the greater the riverbed erosion depth, the slower the erosion rate.

[0162] DEV c The reasonableness of the numbers is crucial. When DEV c Value too small (e.g.) Figure 3 (Top left), DEV(r,t)-DEV appearing before and after the pile foundation c The areas >0, i.e., the extent of erosion, are almost uniform, resulting in scour pits that are nearly circular in shape (e.g. Figure 3 (Lower left), which contradicts actual scour characteristics; in reality, scour pits are not shaped in such a regular way. When DEV c When the value is too large (e.g.) Figure 3 (top right), DEV(r,t)-DEV c The erosion range >0 exists only in front of the pile foundation, meaning that the scour pit only appears in front of the pile. Figure 3 (Lower right), this also does not conform to the true characteristics of scouring. Therefore, DEV must be avoided. c The value is too large or too small to ensure that the analysis of pile foundation scour is more realistic.

[0163] like Figure 4 As shown, the local scour depth near the pile foundation varies with time, including:

[0164] When the upstream flow velocity is low, clear water scouring occurs near the pile foundation, and the scouring depth increases exponentially.

[0165] When the upstream flow velocity is high, dynamic bed scouring occurs near the pile foundation. The scouring depth increases exponentially in a dynamic manner, eventually reaching the equilibrium scouring depth.

[0166] like Figure 5 The diagram shown illustrates the critical slope of the riverbed, including:

[0167] a1 is the riverbed slope at time t, and a2 is the riverbed slope at time t+Δt, which is also the critical riverbed slope. When the riverbed slope exceeds the critical riverbed slope at a certain time, the sediment attached to the upper edge of the scour pit will slide into the scour pit, causing the depth and slope of the scour pit to decrease, and the area of ​​the scour pit to increase.

[0168] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for assessing local scour of bridge pile foundations based on flow velocity-strain rate, characterized in that, Includes the following steps: S1. Obtain the water flow velocity strain rate and express the water flow velocity strain rate as DEV. The water flow velocity strain rate DEV is used to characterize the dynamic characteristics of the water flow around the pile foundation. S2. Based on the flow velocity-strain rate (DEV), an erosion-deposition model of riverbed sediment during local scour of the pile foundation is established. S3. Perform parameter calculation and analysis on the riverbed sediment erosion-deposition model; S4. Using the iSquares numerical grid to store water and sediment dynamic parameters, and treating interparticle forces as internal grid forces, a water and sediment transport force model was established to reveal the dynamic response law of sediment moving at the same velocity as water but accompanied by sedimentation / suspension; combined with the landslide model, the critical slope α of the riverbed was set. c When the inclination angle of the scour pit exceeds the critical value, the sediment sliding mechanism is triggered, and the topography of the scour pit is dynamically updated. S5. Couple the erosion-deposition model with the water and sediment transport stress model to simulate the interaction between water flow, sediment and riverbed around the pile, and realize the dynamic analysis of local scour characteristics of the pile foundation.

2. The method for assessing local scour of bridge pile foundations based on flow velocity-strain rate according to claim 1, characterized in that, In S1, the Reynolds stress tensor is transformed into a scalar form of velocity-strain rate in the two-dimensional flow case. The Reynolds stress tensor is expressed as: Its characteristic values ​​are: In the formula, E represents the strain rate of the water flow velocity at time t for the grid at position r. xx (r,t), e xy (r,t) and e yy (r,t) are both scalar expressions for flow velocity and strain rate, e xx (r,t) represents the shear stress in the x-direction caused by turbulent fluctuations in the r-direction grid at time t, e xy (r,t) represents the shear stress in the y direction caused by turbulent fluctuations in the x direction of the grid at position r at time t; e yy (r,t) represents the shear stress in the x direction caused by the turbulent fluctuations in the y direction of the grid at position r at time t; The formula for calculating the flow velocity-strain rate (DEV) of the water flow around the pile foundation is as follows: Among them, e ij Let i and j be the strain rate tensor, representing two mutually perpendicular directions in the Cartesian coordinate system, here representing the x and y directions; u i Let u be the velocity of the fluid in the i-direction. j This represents the velocity of the fluid in the j-direction; the other parameters have the same meaning as above. Calculate the maximum shear strain rate as half of the difference between the principal strain rates: Reynolds stress is expressed by DEV as: τ(r,t)=μDEV(r,t) (6) τ(r,t) represents the shear stress at position r at time t, μ represents the fluid dynamic viscosity, μ=ρv, ρ is the fluid density, v is the fluid kinematic viscosity, and DEV(r,t) represents the flow velocity strain rate at position r at time t.

3. The method for assessing local scour of bridge pile foundations based on flow velocity-strain rate according to claim 1, characterized in that, The formula for calculating the flow velocity of water near the pile foundation is: v x =v in (1-e a / kD ) (7) Specifically, the upstream face of the pile foundation is set to 0°, the downstream face to 180°, and other directions are set at clockwise angles. x The average flow velocity at a depth near the pile foundation in the plane, v in The value represents the average velocity at depth of the upstream flow, a represents the location of the velocity calculation point, a>0 indicates that the calculation point is located downstream of the pile foundation, a<0 ​​indicates that the calculation point is located upstream of the pile foundation, |a| is the distance between the calculation point and the centroid of the pile foundation, k is a parameter related to the angle of the calculation point, and k takes different values ​​at different angles, and D is the equivalent pile foundation diameter.

4. The method for assessing local scour of bridge pile foundations based on flow velocity-strain rate according to claim 1, characterized in that, S2 specifically refers to: Riverbed sediment erosion model: Riverbed sediment deposition model: Where T(r,t) represents the scour depth at position r at time t. Let DEV(r,t) represent the erosion and deposition coefficients, respectively, and let DEV(r,t) represent the water flow velocity strain rate at position r at time t. c T represents the critical DEV value for sediment transport in riverbeds. max (r,t) represents the maximum scour depth at the riverbed position (r,t), which serves as a criterion for scour equilibrium. T0(r) represents the initial depth of the riverbed before local scour. Based on the water flow velocity strain rate DEV(r,t) near the pile foundation and the critical flow velocity strain rate DEV c The relationship between the two factors determines whether to select an erosion or deposition model to update the riverbed depth change at a given time. If DEV(r,t)>DEV c , T(r,t) <T max (r,t), the sediment carrying capacity of the water flow is greater than the critical displacement value of the riverbed sediment and the scour pit has not reached the maximum scour depth, the riverbed sediment is eroded, and at this moment the depth of the scour pit increases, and the rate of increase of the scour pit depth is d T(r,t) / dt. If DEV(r,t)>DEV c T(r,t)>T max (r,t) indicates that the sediment-carrying capacity of the water flow is greater than the critical shift value of sediment in the riverbed, but the depth of the scour pit is greater than the maximum scour depth. At this point, the riverbed no longer erodes, and the rate of increase in the depth of the scour pit is 0. If DEV(r,t) <DEV c When the sediment-carrying capacity of the water flow is less than the critical displacement value of the riverbed sediment, sediment is deposited in the riverbed. At this moment, the depth of the scour pit decreases, and the rate of decrease in the depth of the scour pit is dT(r,t) / dt.

5. The method for assessing local scour of bridge pile foundations based on flow velocity-strain rate according to claim 4, characterized in that, The calculation and analysis process in S3 is as follows: (1) Critical flow velocity strain rate (DEV) c The calculation formula is: In the formula, DEV c Critical flow velocity strain rate, in seconds (s). -1 C dc v is a dimensionless parameter; b Indicates the initial flow velocity of sediment; d 50 Indicates the median particle size of sediment; When the riverbed flow velocity hour, In the formula, v b d is the surface water velocity when sediment is initiated; g is the acceleration due to gravity; s is the ratio of sediment density to water density; C dc = -0.317Fr 2 +0.392Fr-0.077; (2) For the scour depth at any location on the riverbed at time t, the following formula is satisfied: In the formula, T max (r,t) represents the maximum scour depth at the location (r,t) in the riverbed, where T max This indicates the maximum scour of the riverbed within the localized scour area; The maximum scour depth of the riverbed, T max Satisfying formula (13) or (14) or (15): In the formula: V in For the incoming flow, DEV is the flow velocity strain rate. In this formula, it is assumed that the flow field is uniform and the water velocity is the only factor that determines the scour depth. In the formula, DEV c The critical flow velocity strain rate; In the formula, h is the water depth, and D is the pile diameter. This is achieved by introducing... This allows for adjustment of the erosion depth, enabling more precise simulation of the scour depth near the critical value. (3) Erosion rate coefficient When DEV is greater than DEV c At that time, erosion occurs, and the larger the DEV or the higher the DEV, the more likely erosion will occur. c The smaller the value, the faster the erosion rate; if the DEV is much larger than the DEV... c The erosion rate is approaching its limit; (4) Sedimentation coefficient In the formula, ω is the deposition rate coefficient, in m / s; a1 is an empirical coefficient; s The sediment settling velocity is determined by the sediment particle size, shape, and fluid viscosity; d 50 ρ is the representative particle size; h is the water depth; s is the relative density of sediment and water; g is the acceleration due to gravity; C d The drag coefficient reflects the magnitude of the resistance of the fluid to the sediment particles.

6. The method for assessing local scour of bridge pile foundations based on flow velocity-strain rate according to claim 1, characterized in that, In S4, the forces involved in sediment transport or landslides include: In the formula, Mg is the bulk density, and r i Let ζ(r) represent the position of the i-th block, t represent time, and ζ(r) represent the position of the i-th block. i ,t) represents the elevation of the upper surface of the block; F vx With F vy Let ν represent the viscous drag in the x and y directions, respectively; v be the kinematic viscosity of the fluid; M be the mass of the block; and ν be the viscosity of the fluid. x (n+1,m), ν x (n-1, m) represent the water flow velocities in the x-direction of grids (n+1, m) and (n-1, m), respectively, ν y (n+1,m), ν y (n-1,m) represent the water flow velocities in the y direction of grids (n+1,m) and (n-1,m), respectively; dxspace and dyspace are the grid sizes in the x and y directions, respectively; the meanings of the other parameters are the same as above. In the formula, F b (r i fract(r) represents the base friction force of the i-th block at time t. i fract(r) represents the volume percentage of sediment in block i at time t. i ,t)=H s (r i ,t) / (H s (r i ,t)+H w (r i ,t)), where μ1 is the base friction coefficient between the water body and the riverbed, and μ2 represents the base friction coefficient between the sediment and the riverbed. H is a unit velocity vector, representing the tendency of the block to decelerate due to the base friction. w (r i H(t) represents the water thickness of the i-th block at time t. s (r i ,t) represents the thickness of the mud and sand carried by the i-th block at time t.

7. The method for assessing local scour of bridge pile foundations based on flow velocity-strain rate according to claim 1, characterized in that, A landslide model based on iSquares theory is used to control the dynamic balance of riverbed scour depth. The specific working process of the landslide model is as follows: each type of riverbed has a critical slope. When the inclination angle of the scour pit is greater than the critical slope, the sediment attached to the upper edge of the scour pit will slide into the scour pit, making the depth and slope of the scour pit smaller, thereby realizing the regeneration of the riverbed topography around the scour pit.

8. The method for assessing local scour of bridge pile foundations based on flow velocity-strain rate according to claim 7, characterized in that, The critical slope α of the riverbed c The angle is 25° to 30°.

9. A bridge pile foundation local scour assessment system based on flow velocity-strain rate, characterized in that, include: The velocity-strain rate construction module transforms the Reynolds stress tensor into a scalar form of velocity-strain rate based on Reynolds stress theory, in order to propose a velocity-strain rate (DEV) that characterizes the hydrodynamic features around the pile foundation. The erosion-deposition model building module, based on the flow velocity-strain rate (DEV), derives and builds an erosion-deposition model of riverbed sediment during local scouring of the pile foundation. The model parameter analysis module is used to calculate and analyze the parameters of the erosion-deposition model. The water and sediment transport and landslide simulation module uses the iSquares numerical grid to store water and sediment dynamic parameters, transforms interparticle forces into grid internal forces, and establishes a water and sediment transport force model to reveal the dynamic response law of sediment settling / suspension; combined with the landslide model, it sets the critical slope of the riverbed, and triggers the sediment sliding mechanism when the dip angle of the scour pit exceeds the critical value, dynamically updating the topography of the scour pit. The dynamic scour analysis module is used to couple the erosion-deposition model with the water and sediment transport model to simulate the interaction between water flow, sediment and riverbed around the pile, and realize high-precision dynamic analysis of local scour characteristics of the pile foundation.

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