Bridge pile foundation local scouring evaluation system and method based on flow velocity strain rate

Abstract

The invention belongs to the technical field of bridge safety evaluation, and particularly discloses a method and a system for evaluating local scouring of a bridge pile foundation based on a flow velocity strain rate. A calculation model of a local scouring pit form and a maximum scouring depth of a river-sea crossing bridge pile foundation is established, and a Reynolds stress tensor is converted into a flow velocity strain rate scalar; the method comprises the following steps: providing an erosion-deposition model, analyzing an erosion-deposition rate, establishing a scouring depth relationship, utilizing a sediment transportation model of grid unit storage parameters, simulating dynamic response of a water-sediment mixture, and triggering sediment sliding and updating a riverbed terrain when the dip angle of a scouring pit is at a supercritical slope by virtue of a slump model. All the models cooperate to achieve efficient simulation of local scouring of the pile foundation. According to the method, the form evolution and the maximum scouring depth of the local scouring pit of the single pile and the pile group can be efficiently and accurately calculated, and support is provided for bridge pile foundation design and anti-scouring structure optimization.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge safety assessment, and particularly relates to a bridge pile foundation local scour assessment system and method based on flow velocity strain rate. Background Art

[0002] Local scour is one of the main reasons for the collapse of bridges across valleys, rivers, and seas. Among the 108 bridges that collapsed in New Zealand between 1960 and 1986, 29 were damaged by local scour. Among the 490 bridge damage cases that occurred in the United States between 1989 and 2000, 243 bridges were damaged due to local scour; among the 106 bridges that were destroyed in China between 2000 and 2014, 35 bridges were destroyed due to local scour. Bridges damaged by local scour account for 1 / 3 of the total number of collapsed bridges, 6 times that of bridges damaged by overloading, and 20 times that of bridges damaged by earthquakes. Therefore, the research on the stability of bridge pile foundations under local scour conditions has received extensive attention.

[0003] There are many analysis models for local scour of pile foundations, including empirical models, analytical and numerical models, etc. Among them, empirical models are mostly obtained based on physical experiments. The models have statistical characteristics but weak physical properties and cannot well reveal the local scour process; analytical models are often based on complex theories such as hydrodynamics and sediment particle kinematics, and are difficult to solve; numerical models are mostly based on analytical models, integrating the Reynolds-averaged theory, and considering the average characteristics and turbulent characteristics of fluids separately. However, due to various theoretical generalizations, there are still problems such as low calculation accuracy and efficiency, and insufficient estimation of the shape and depth of the scour pit. Therefore, there is an urgent need to establish an efficient and accurate bridge pile foundation local scour assessment system and method. Summary of the Invention

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

[0005] In the first aspect of the present invention, a bridge pile foundation local scour assessment method based on flow velocity strain rate is provided, including the following steps:

[0006] S1. Obtain the flow velocity strain rate of the water flow, express the flow velocity strain rate of the water flow as DEV of the flow velocity strain rate, and the flow velocity strain rate DEV is used to characterize the hydrodynamic characteristics of the water flow around the pile foundation;

[0007] S2. Based on the flow velocity strain rate DEV, derive and establish an erosion-deposition model of the riverbed sediment during the local scour of the pile foundation;

[0008] S3. Conduct parameter calculation and analysis on the erosion-deposition model of the riverbed sediment;

[0009] S4. Use iSquares numerical grids to store the hydrodynamic and sediment transport parameters, consider the inter-particle forces as internal grid forces, establish a hydrodynamic and sediment transport force model, and reveal the dynamic response law of the co-movement of sediment and water body with sediment settlement / suspension; combine with the slump model to set the critical slope α of the riverbed c , when the inclination angle of the scouring pit exceeds the critical value, trigger the sediment slumping mechanism and dynamically update the topography of the scouring pit;

[0010] S5. Couple the erosion-deposition model with the hydrodynamic and sediment transport force model to simulate the interaction of the flow-sediment-riverbed around the pile foundation, and achieve high-precision dynamic analysis of the local scouring characteristics of the pile foundation.

[0011] In a further solution, in the two-dimensional flow case where the Reynolds stress tensor is transformed into the form of the velocity strain rate scalar, the Reynolds stress tensor is expressed as:

[0012]

[0013] Its eigenvalues are:

[0014]

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

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

[0017]

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

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

[0020]

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

[0022] τ(r,t) = μDEV(r,t) (6)

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

[0024] A further solution is that the calculation formula for the water flow velocity near the pile foundation is as follows:

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

[0026] Where, it is set that the upstream face of the pile foundation is 0°, the downstream face is 180°, and other directions are specified by angles in the clockwise direction. v x represents the depth-averaged flow velocity near the pile foundation in the plane, v in represents the depth-averaged flow velocity of the upstream incoming flow, a represents the position of the flow 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 the value of k is different at different angles, and D is the equivalent pile foundation diameter.

[0027] A further solution is that S2 is specifically as follows:

[0028] Riverbed sediment erosion model:

[0029]

[0030] Riverbed sediment deposition model:

[0031]

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

[0033] According to the relationship between the value of the flow velocity strain rate DEV(r,t) near the pile foundation and the critical flow velocity strain rate DEV c select the erosion or deposition model to update the change in the riverbed depth at a certain moment;

[0034] If DEV(r,t) > DEVc , T(r, t) < T max (r, t), the sediment-carrying capacity of the water flow is greater than the critical entrainment value of the riverbed sediment and the scour pit has not reached the maximum scour depth, and the riverbed sediment is eroded. At this moment, the depth of the scour pit here increases, and the increasing rate of the scour pit depth is dT(r, t) / dt;

[0035] 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 entrainment value of the riverbed sediment but the depth of the scour pit is greater than the maximum scour depth. At this time, the riverbed is no longer eroded, and the increasing rate of the scour pit depth is 0;

[0036] If DEV(r, t) < DEV c , the sediment-carrying capacity of the water flow is less than the critical entrainment value of the riverbed sediment, and the riverbed sediment is deposited. At this moment, the depth of the scour pit here decreases, and the decreasing rate of the scour pit depth is dT(r, t) / dt.

[0037] A further solution is that the calculation and analysis process in S3 is as follows:

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

[0039]

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

[0041] When the riverbed velocity ,

[0042]

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

[0044] (2) For the scour depth at any position on the riverbed at time t, it satisfies the formula:

[0045]

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

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

[0048] Formula (13)

[0049]

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

[0051] Formula (14)

[0052]

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

[0054] Formula (15)

[0055]

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

[0057] (3) Erosion rate coefficient

[0058]

[0059] When DEV is greater than DEV c , erosion occurs, and the greater DEV is or the smaller DEV c is, 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 the empirical coefficient; ω s is the sediment settling velocity, which is determined by the sediment particle size, shape, and fluid viscosity; d 50is the representative particle size; h is the water depth; s is the relative density of sediment to water; g is the acceleration due to gravity; C d is the drag coefficient, reflecting the magnitude of the fluid's resistance to sediment particles.

[0063] A further solution is characterized in that in S4, the forces acting on sediment transport or slumping include:

[0064]

[0065] In the formula, Mg is the unit weight of the block, r i is the position of the i-th block, t represents time, is the elevation of the upper surface of the block;

[0066] Viscous resistance in the x direction

[0067] Viscous resistance in the y direction

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

[0069] Base friction

[0070] In the formula, F b (r i , t) is the basal friction of the i-th block at time t, H w (r i , t) is the water thickness of the i-th block at time t, H s (r i , t) is the sediment thickness carried by the i-th block at time t, fract(r i , t) is the sediment volume ratio of the i-th block at time t, fract(r i , t) = H s (r i , t) / (H s (r i , t) + H w (r i, t)), where μ1 is the basal friction coefficient between the water body and the riverbed, and μ2 represents the friction coefficient between the sediment and the riverbed base is the unit velocity vector, indicating that the basal friction force tends to decelerate the block.

[0071] A further solution is to adopt a slump model based on the iSquares theory to control the dynamic balance of the riverbed scouring depth. The specific action process of the slump model is as follows: Each riverbed type has a critical slope. When the inclination angle 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, making the depth and slope of the scouring pit smaller, and then realizing the re-update of the riverbed topography around the scouring pit.

[0072] A further solution is that the critical slope α of the riverbed c is 25° - 30°.

[0073] In the second aspect of the present invention, a local scour assessment system for bridge pile foundations based on flow velocity strain rate is provided, including:

[0074] A flow velocity strain rate construction module that 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 characterizing the hydrodynamic characteristics of the flow around the pile foundation;

[0075] An erosion - deposition model establishment module that derives and establishes an erosion - deposition model of the riverbed sediment during the local scour process of the pile foundation based on the flow velocity strain rate DEV;

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

[0077] A water - sediment transport and slump simulation module that stores water - sediment dynamics parameters using iSquares numerical grids, converts the inter - particle forces into grid internal forces, establishes a water - sediment transport force model to reveal the dynamic response law of sediment settlement / suspension; combines the slump model to set the critical slope of the riverbed, and triggers the sediment sliding mechanism when the inclination angle of the scouring pit exceeds the critical value to dynamically update the scouring pit topography;

[0078] A dynamic scour analysis module for coupling the erosion - deposition model and the water - sediment transport model to simulate the interaction of the flow - sediment - riverbed around the pile and achieve high - precision dynamic analysis of the local scour characteristics of the pile foundation.

[0079] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0080] The present invention discloses a local scour assessment system and method for bridge pile foundation based on velocity strain rate, and establishes a calculation model for the local scour pit morphology and maximum scour depth of the pile foundation of a cross-river-sea bridge. The method is based on the derivation of the Reynolds stress tensor into the velocity strain rate scalar form, and proposes an erosion-deposition model based on the velocity strain rate; by determining the relationship between the velocity strain rate and the critical velocity strain rate, the erosion deposition rate is analyzed based on a given erosion deposition coefficient, and the relationship between the scour depth and the maximum scour depth at any position of the riverbed at any time is established; in addition, the sediment transport model stores water-sediment dynamic parameters through grid units, converts the inter-particle force into grid internal force, and accurately simulates the transport of water-sediment mixtures and the dynamic response of sediment sedimentation / suspension. When the scour pit inclination exceeds the critical slope, the sediment sliding mechanism is triggered by the landslide model, and the depth and slope of the scour pit are dynamically adjusted to achieve adaptive updating and balance of the riverbed terrain. The synergistic effect of each model realizes efficient simulation of the local scour characteristics of the pile foundation. The local scour assessment system and method for bridge pile foundations based on flow velocity strain rate established by the present invention can efficiently and accurately calculate the morphological evolution and maximum scour depth of local scour pits of single piles and pile groups. The present invention provides a scientific basis for the design of bridge pile foundations under special structural and terrain conditions, and can also provide strong technical support for the optimization design of anti-scour structures. It is also a supplement and improvement to the current field of bridge scour calculation and numerical simulation, and it provides engineers with more tools and methods when facing complex scour problems. While improving the simulation accuracy, it also improves the simulation speed, greatly expanding our ability to predict more complex scour scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] The following drawings are only used to illustrate and explain the present invention, and are not used to limit the scope of the present invention, wherein:

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

[0083] Figure 2 It is the water flow velocity and flow velocity strain rate curve near the pile foundation;

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

[0085] Figure 4 It is a graph showing the variation of scour pit depth with time for clean water scouring and moving bed scouring;

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

[0087] In order to make the objectives, technical solutions, design methods, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below through specific embodiments in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0088] As Figure 1 shown, the present invention provides a local scour assessment system for bridge pile foundations based on flow velocity strain rate, including: a flow velocity strain rate construction module that converts the Reynolds stress tensor into a scalar form of flow velocity strain rate based on the Reynolds stress theory to propose a flow velocity strain rate DEV characterizing the hydrodynamic characteristics of the water flow around the pile foundation; an erosion-deposition model establishment module that, based on the flow velocity strain rate DEV, derives and establishes an erosion-deposition model for the riverbed sediment during the local scour process of the pile foundation; a model parameter analysis module for calculating and analyzing the parameters of the erosion-deposition model; a water-sediment transport and slump simulation module that stores water-sediment dynamics parameters using iSquares numerical grids, converts the inter-particle forces into internal grid forces, and establishes a water-sediment transport force model to reveal the dynamic response law of sediment settlement / suspension; sets the critical slope of the riverbed in combination with the slump model, triggers the sediment slump mechanism when the inclination angle of the scour pit exceeds the critical value, and dynamically updates the topography of the scour pit; a dynamic scour analysis module for coupling the erosion-deposition model and the water-sediment transport model to simulate the interaction of the water flow-sediment-riverbed around the pile, and realizing high-precision dynamic analysis of the local scour characteristics of the pile foundation.

[0089] Specifically, continuing to refer to Figure 1 , this system is implemented through the following steps:

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

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

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

[0093]

[0094] Its eigenvalues are:

[0095]

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

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

[0098]

[0099] where e ij is the strain rate tensor, i and j represent two mutually perpendicular directions in the Cartesian coordinate system, representing 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. The meanings of the other parameters are the same as above.

[0100] The maximum shear strain rate is calculated as 1 / 2 of the difference between the principal strain rates:

[0101]

[0102] The Reynolds stress can be further expressed through 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 dynamic viscosity of the fluid, μ = ρv, ρ is the density of the fluid, v is the kinematic viscosity of the fluid, and DEV(r, t) represents the strain rate of the flow velocity at position r at time t.

[0105] Assume that the upstream face of the pile foundation is 0°, the downstream face is 180°, and the angles in other directions are specified clockwise. Then the water flow velocity near the pile foundation is calculated using the following formula:

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

[0107] where v x represents the depth - averaged flow velocity near the pile foundation in the plane, v in$U$ represents the depth-averaged velocity of the upstream incoming flow, $a$ represents the position of the velocity calculation point, where $a > 0$ indicates that the calculation point is downstream of the pile foundation, $a < 0$ indicates that the calculation point is 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 the value of $k$ is different at different angles. $D$ is the equivalent pile foundation diameter. For a cylindrical pile foundation, its equivalent pile foundation diameter is its diameter; for special-shaped pile foundations such as round-ended and rectangular ones, its equivalent pile foundation diameter is the structural coefficient multiplied by the pile foundation diameter.

[0108] 2) Based on the parameter velocity strain rate (DEV), a riverbed sediment erosion - deposition model in local scour of pile columns 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] Among them, $T(r, t)$ represents the scour depth at position $r$ at time $t$. $\alpha$ and $\beta$ respectively represent the erosion and deposition coefficients, $DEV(r, t)$ represents the water flow velocity strain rate at position $r$ at time $t$, and $DEV$ c represents the critical DEV value for the movement of riverbed sediment, and $T$ max (r, t) represents the maximum scour depth at the position $(r, t)$ of the riverbed, which is used as the discriminant condition for scour equilibrium, and $T_0(r)$ represents the initial depth of the riverbed before local scour.

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

[0116] 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 bed load value of the riverbed sediment and the scour pit has not reached the maximum scour depth, so the riverbed sediment is eroded. At this moment, the depth of the scour pit here increases, and the increasing rate of the scour pit depth is $dT(r, t) / dt$;

[0117] 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 bed-load value of the riverbed sediment, but the scour depth is greater than the maximum scour depth. At this time, the riverbed is no longer eroded, and the increasing rate of the scour depth is 0;

[0118] If DEV(r, t) < DEV c , the sediment-carrying capacity of the water flow is less than the critical bed-load value of the riverbed sediment, and the riverbed sediment is deposited. At this moment, the scour depth here decreases, and the decreasing rate of the scour depth is dT(r, t) / dt.

[0119] 2.2) Analysis and calculation of model parameters

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

[0121]

[0122] In the formula, 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 motion velocity; d 50 represents the median sediment diameter; Fr is the Froude number.

[0123] When the riverbed flow velocity ,

[0124]

[0125] In the formula, v b is the bed surface water flow velocity at sediment incipient motion; g is the acceleration due to gravity; s is the ratio of sediment density to water density; d 50 is the median sediment diameter; C dc =-0.317Fr 2 +0.392Fr - 0.077; the other parameters are the same as above.

[0126] For the scour depth at any position of the riverbed at time t, it satisfies the formula:

[0127]

[0128] In the formula, T max (r, t) represents the maximum scour depth at the position (r, t) of the riverbed, and T max represents the maximum scour of the riverbed within the local scour range.

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

[0130] Formula (13)

[0131]

[0132] Where: V in is the incoming flow, and DEV is the flow velocity strain rate. Under the condition of simple water flow and small change in strain rate, this formula assumes that the flow field is relatively uniform and the water flow velocity is the only factor determining the scour depth.

[0133] Formula (14)

[0134]

[0135] Wherein, DEV c is the critical flow velocity strain rate, and the meanings of the remaining footnotes are the same as above. There are significant differences in the flow velocity and strain rate of water flow in different regions (such as in front of and behind the pile column, on both sides, etc.). When the DEV of the water flow exceeds DEV c , the sediment particles will be eroded, resulting in an increase in the scour depth. By introducing DEV c , this formula better simulates this non-linear relationship.

[0136] Formula (15)

[0137]

[0138] Wherein, h is the water depth, D is the pile diameter, and the meanings of the remaining footnotes are the same as above. Based on the non-linear characteristics of the sediment scour process, the correction coefficient takes into account the influence of DEV c , and adjusts the erosion depth by introducing to enable a more refined simulation of the scour depth near the critical value.

[0139] Erosion rate coefficient

[0140]

[0141] 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.

[0142] Deposition coefficient

[0143]

[0144] Wherein, is the deposition rate coefficient, with the unit of m / s; a1 is an empirical coefficient; ω sis the sediment settling velocity, which is determined by factors such as sediment particle size, shape, and fluid viscosity; d 50 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 is the drag coefficient, which reflects the magnitude of the resistance of the fluid to sediment particles.

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

[0146] 3.1) Use iSquares grids as the basic units to store the hydrodynamic parameters of water and sediment. Regard the inter-particle forces as internal grid forces, and reveal the dynamic response law of co-moving with the water body but accompanied by sedimentation / suspension through the key force components. The specific calculations are as follows:

[0147] Gravity

[0148] In the formula, Mg is the bulk specific weight, r i is the position of the i-th block, t represents time, is 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 and F vy represent the viscous resistances in the x and y directions 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 water flow velocities in the x direction of grids (n + 1, m) and (n - 1, m) respectively. ν y (n + 1, m) and 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;

[0152] Base friction

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

[0154] 3.2) Adopt a slump model based on the iSquares theory to control the dynamic balance of the riverbed scouring depth. There will be a critical slope α for each riverbed type. c , when the inclination angle α of the riverbed scouring pit is greater than the critical slope α c , the sediment attached to the upper edge of the scouring pit will slide into the scouring pit, resulting in a decrease in both the depth and slope of the scouring pit, thereby realizing the re-update of the riverbed topography around the scouring pit. The commonly used critical slope α of the riverbed c is 25° - 30°.

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

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

[0157] When the water flow approaches the pile foundation, the average water flow velocity decreases exponentially, while the water flow velocity strain rate increases exponentially. Similarly, when the water flow leaves the pile foundation, the average water flow velocity increases exponentially, while the water flow velocity strain rate decreases exponentially. The difference is that the change speed and amplitude of the average water flow velocity and velocity strain rate are different in different directions of the pile foundation.

[0158] As Figure 3 shown, the relationship diagram between DEV(r, t) - DEV c and the shape and size of the scouring pit, where the shape of the scouring pit is a top view. It includes: calculating the value of DEV(r, t) - DEV c and judging whether it is greater than 0:

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

[0160] If not, the sediment particles in the water flow at the r position at time t settle, and the sediment particle concentration in the water flow here decreases;

[0161] The erosion or settlement rate of sediment particles depends on |DEV(r, t) - DEV c | / DEVc Erosion and deposition coefficient and riverbed erosion depth. When |DEV(r,t) - DEV| / DEV c is larger, the erosion and deposition coefficient is larger, and the erosion or deposition rate is faster; when the riverbed erosion depth is larger, the erosion rate slows down. c The rationality of the DEV value is crucial. When the DEV value is too small (e.g., in the upper left), the DEV(r,t) - DEV > 0 regions that appear before and after the pile foundation, i.e., the erosion range, are nearly the same, resulting in the scour pit morphology being approximately circular (e.g., in the lower left), which is contrary to the actual scour characteristics. In reality, the scour pit morphology is not so regular. When the DEV value is too large (e.g., in the upper right), the erosion range where DEV(r,t) - DEV > 0 only exists in front of the pile foundation, meaning the scour pit only appears in front of the pile (in the lower right), which also does not conform to the real scour characteristics. Therefore, it is necessary to avoid the situation where the DEV value is too large or too small to ensure that the analysis of the scour situation of the pile foundation is more in line with the actual situation.

[0162] DEV c As shown in, the local scour depth near the pile foundation changes with time, including: c When the upstream flow velocity is small, clear-water scour occurs near the pile foundation, and the scour depth increases exponentially; Figure 3 When the upstream flow velocity is large, movable-bed scour occurs near the pile foundation, and the scour depth increases exponentially during the dynamic process and finally reaches the equilibrium scour depth. c As shown in, the schematic diagram of the critical riverbed slope, including: Figure 3 a1 is the riverbed slope at time t, and a1 is also the riverbed slope at time t + Δt, which is the critical riverbed slope. When the slope of the riverbed at a certain moment exceeds the critical riverbed slope, the sediment attached to the upper edge of the scour pit will slide into the scour pit, resulting in a decrease in both the depth and slope of the scour pit and an increase in the scour pit range. c When the upstream flow velocity is small, clear-water scour occurs near the pile foundation, and the scour depth increases exponentially; Figure 3 When the upstream flow velocity is large, movable-bed scour occurs near the pile foundation, and the scour depth increases exponentially during the dynamic process and finally reaches the equilibrium scour depth. c As shown in, the schematic diagram of the critical riverbed slope, including: Figure 3 a1 is the riverbed slope at time t, and a1 is also the riverbed slope at time t + Δt, which is the critical riverbed slope. When the slope of the riverbed at a certain moment exceeds the critical riverbed slope, the sediment attached to the upper edge of the scour pit will slide into the scour pit, resulting in a decrease in both the depth and slope of the scour pit and an increase in the scour pit range. c Therefore, it is necessary to avoid the situation where the DEV value is too large or too small to ensure that the analysis of the scour situation of the pile foundation is more in line with the actual situation.

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

[0164] When the upstream flow velocity is small, clear-water scour occurs near the pile foundation, and the scour depth increases exponentially;

[0165] When the upstream flow velocity is large, movable-bed scour occurs near the pile foundation, and the scour depth increases exponentially during the dynamic process and finally reaches the equilibrium scour depth.

[0166] As Figure 5 shown, the schematic diagram of the critical riverbed slope, including:

[0167] a1 is the riverbed slope at time t, and a1 is also the riverbed slope at time t + Δt, which is the critical riverbed slope. When the slope of the riverbed at a certain moment exceeds the critical riverbed slope, the sediment attached to the upper edge of the scour pit will slide into the scour pit, resulting in a decrease in both the depth and slope of the scour pit and an increase in the scour pit range.

[0168] The embodiments of the present invention have been described above. The above description is exemplary and not exhaustive, and is also not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The choice of terms used herein is intended to best explain the principles of the embodiments, the practical application, or the improvement of technology in the market, or to enable other ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A method for evaluating local scour of bridge pile foundation based on flow velocity strain rate, characterized in that It includes the following steps: S1. Obtain the water flow velocity strain rate, and express the water flow velocity strain rate by the water flow velocity strain rate DEV, where the water flow velocity strain rate DEV is used to characterize the hydrodynamic characteristics of the water flow around the pile foundation; S2. Based on the velocity strain rate DEV, establish an erosion-deposition model of the riverbed sediment during the local scour process of the pile foundation; S3. Conduct parameter calculation and analysis on the riverbed sediment erosion-deposition model; S4. Use the iSquares numerical grid to store the hydrodynamic and sediment transport parameters, consider the inter-particle forces as internal grid forces, establish a hydrodynamic and sediment transport force model, and reveal the dynamic response law of the synchronous movement of sediment and water body with sedimentation / suspension; combined with the slump model, set the critical slope α of the riverbed c , when the inclination angle of the scouring pit exceeds the critical value, trigger the sediment slumping mechanism and dynamically update the topography of the scouring pit; S5. Couple the erosion-deposition model with the water-sediment transport force model to simulate the interaction of water flow-sediment-riverbed around the pile, and realize the dynamic analysis of the local scour characteristics of the pile foundation.

2. The local scour evaluation method for bridge pile foundations based on flow velocity strain rate according to claim 1, characterized in that, In the above S1, in the case of two-dimensional flow, the Reynolds stress tensor is transformed into the form of a velocity strain rate scalar, and the Reynolds stress tensor is expressed as: Its eigenvalues are: In the formula, represents the strain rate of the water flow velocity at the grid at r at time t, e xx (r,t), e xy (r,t) and e yy (r,t) are all scalar expressions of the strain rate of the flow velocity, e xx (r,t) represents the shear stress in the x direction caused by the turbulent pulsation 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 pulsation 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 pulsation in the y direction of the grid at position r at time t; The calculation formula for the water flow velocity strain rate DEV around the pile foundation is: where e ij is the strain rate tensor, i and j represent two mutually perpendicular directions in the Cartesian coordinate system, representing 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; Calculate the maximum shear strain rate as 1 / 2 of the difference between the principal strain rates: The Reynolds stress is expressed by DEV as: τ(r,t)=μDEV(r,t) (6) τ(r,t) represents the shear stress at the position r at time t, μ represents the dynamic viscosity of the fluid, μ = ρv, ρ is the density of the fluid, v is the kinematic viscosity of the fluid, and DEV(r,t) represents the velocity strain rate at the position r at time t.

3. The local scour evaluation method for bridge pile foundations based on flow velocity strain rate according to claim 1, wherein The calculation formula for the water flow velocity near the pile foundation is: v x = v in (1 - e a / kD ) (7) Among them, the upstream face of the pile foundation is set as 0°, the downstream face is 180°, and the angles in other directions are specified clockwise. v x represents the depth-averaged velocity near the pile foundation in the plane. v in represents the depth-averaged velocity of the upstream incoming flow. a represents the position 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 the value of k is different at different angles. D is the equivalent pile foundation diameter.

4. A method for evaluating local scour of bridge pile foundation based on flow velocity strain rate according to claim 1, characterized in that, S2 is specifically: Riverbed sediment erosion model: Riverbed sediment deposition model: Among them, T(r,t) represents the scouring depth at position r at time t. respectively represent the erosion and deposition coefficients, DEV(r,t) represents the strain rate of the water flow velocity at position r at time t, DEV c represents the critical DEV value for sediment transport on the riverbed, T max (r,t) represents the maximum scouring depth at the position (r,t) of the riverbed, which is used as the discrimination condition for scouring equilibrium, and T0(r) represents the initial depth of the riverbed before local scouring; According to the relationship between the value of the water flow velocity strain rate DEV(r,t) near the pile foundation and the critical flow velocity strain rate DEV c select an erosion or deposition model to update the change in the riverbed depth at a certain moment; 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 bed-load value of the riverbed sediment and the scouring pit has not reached the maximum scouring depth. The riverbed sediment is eroded. At this moment, the depth of the scouring pit here increases, and the increasing rate of the scouring pit depth is dT(r, t) / dt; 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 bedload threshold of the riverbed, but the scour depth is greater than the maximum scour depth. At this time, the riverbed no longer erodes, and the increasing rate of the scour depth is 0; If DEV(r, t) < DEV c , the sediment-carrying capacity of the water flow is less than the critical bedload value of the riverbed sediment, and the riverbed sediment is deposited. At this moment, the depth of the scouring pit here decreases, and the decreasing rate of the scouring pit depth is dT(r, t) / dt.

5. The local scour evaluation method for bridge pile foundations based on flow velocity strain rate according to claim 4, characterized in that The calculation and analysis process in the above S3 is: (1) Critical flow velocity strain rate DEV c The calculation formula is as follows: 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 motion velocity; d 50 represents the median grain size of sediment; When the riverbed flow velocity is where, v b d is the bed surface water flow velocity at sediment incipient motion; g is the acceleration of 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 position of the riverbed at time t, it satisfies the formula: where, T max (r, t) represents the maximum scour depth at the position of the riverbed (r, t), and T max represents the maximum scour of the riverbed within the local scour range; Among them, the maximum scouring depth T of the riverbed max satisfies formula (13) or (14) or (15): Where: V in is the incoming flow, and DEV is the flow velocity strain rate. In this formula, it is assumed that the flow field is uniform and the water flow velocity is the only factor determining the scour depth; where DEV c is the critical flow velocity strain rate; where h is the water depth and D is the pile diameter. By introducing to adjust the erosion depth, the scour depth can be more finely simulated near the critical value; (3) Erosion rate coefficient When DEV is greater than DEV c erosion occurs, and the greater DEV is or the smaller DEV c is, the faster the erosion rate; if DEV is much greater than DEV c , the erosion rate approaches the limit; (4) Deposition coefficient In the formula, is the deposition rate coefficient with the unit of m / s; a1 is the empirical coefficient; ω s is the sediment settling velocity, which is determined by the sediment particle size, shape, and fluid viscosity; d 50 is the representative particle size; h is the water depth; s is the relative density of sediment to water; g is the acceleration due to gravity; C d is the drag coefficient, which reflects the magnitude of the resistance of the fluid to sediment particles.

6. The local scour evaluation method for bridge pile foundations based on flow velocity strain rate according to claim 1, wherein, In S4, the forces on sediment transport or landslide include: where Mg is the unit weight of the block, r i is the position of the i-th block, t represents time, ζ(r i , t) is the elevation of the upper surface of the block; F vx and F vy respectively represent the viscous resistance in the x and y directions, 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) respectively represent the water flow velocities in the x direction of the grids (n + 1, m) and (n - 1, m), ν y (n + 1, m) and ν y (n - 1, m) respectively represent the water flow velocities in the y direction of the grids (n + 1, m) and (n - 1, m), dxspace and dyspace are the grid sizes in the x and y directions respectively; the meanings of the remaining parameters are the same as above; Where F b (r i , t) is the basal friction force of the i-th block at time t, fract(r i , t) is the proportion of sediment volume of the i-th block at time t, fract(r i , t) = H s (r i , t) / (H s (r i , t) + H w (r i , t)), μ1 is the basal friction coefficient between the water body and the river bed, μ2 represents the sediment and river bed basal friction coefficient, is the unit velocity vector, indicating that the basal friction force tends to decelerate the block, H w (r i , t) is the water body thickness of the i-th block at time t, H s (r i , t) is the sediment thickness carried by the i-th block at time t.

7. A method for evaluating local scour of bridge pile foundation based on flow velocity strain rate according to claim 1, characterized in that Adopt a landslide model based on the iSquares theory to control the dynamic balance of the riverbed scour depth. The specific action process of the landslide model is: there is a critical slope for each riverbed type. When the inclination angle of the riverbed 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, and then realizing the re-update of the riverbed topography around the scour pit.

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

9. A local scour assessment system for bridge pile foundations based on flow velocity strain rate, characterized in that, It includes: A velocity strain rate construction module, which transforms the Reynolds stress tensor into the form of a velocity strain rate scalar based on the Reynolds stress theory to propose the velocity strain rate DEV characterizing the hydrodynamic characteristics of the water flow around the pile foundation; An erosion-deposition model establishment module, which derives and establishes an erosion-deposition model of the riverbed sediment during the local scour process of the pile foundation based on the velocity strain rate DEV; A model parameter analysis module, which is used to calculate and analyze the parameters of the erosion-deposition model; A water-sediment transport and landslide simulation module, which stores the water-sediment dynamics parameters using the iSquares numerical grid, converts the inter-particle forces into internal grid forces, and establishes a water-sediment transport force model to reveal the dynamic response law of sediment settlement / suspension; combines the landslide model to set the critical slope of the riverbed. When the inclination angle of the scour pit exceeds the critical value, trigger the sediment sliding mechanism and dynamically update the topography of the scour pit; A dynamic scour analysis module, which is used to couple the erosion-deposition model with the water-sediment transport model to simulate the interaction of water flow-sediment-riverbed around the pile, and realize the high-precision dynamic analysis of the local scour characteristics of the pile foundation.

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