Flood scouring damage simulation method for shallow foundation bridge

Abstract

The invention provides a flood scouring damage simulation method for a shallow foundation bridge, which comprises the following steps: S1, riverbed scouring characteristics are analyzed, and data needing to be extracted comprise scouring depth, a pier peripheral flow field and a scouring pit form; s2, establishing a structure model; s3, adopting a point cloud reverse engineering technology and a fluid-solid coupling technology to transmit foundation soil contact and water flow load into the structure model; s4, structural damage analysis under the combined action of the flood and the loaded vehicle; and S5, obtaining a structural safety evaluation conclusion of the bridge under the combined action of flood scouring and heavy vehicle load through simulation and data analysis. The device has the advantages that the scouring effect of flood on the shallow foundation is accurately simulated, the combined action of foundation void and vehicle eccentric load is accurately simulated, multi-physical field coupling among water flow, soil, heavy vehicles and a bridge structure is achieved, simulation is convenient, accurate and rapid, and the cost benefit is high.

Description

Technical Field

[0001] The invention relates to the technical field of disaster prevention and reduction engineering, and in particular to a flood scour damage simulation method for a shallow-buried foundation bridge. Background Art

[0002] In recent years, bridge collapses caused by floods have occurred frequently, showing that climate change poses a serious threat to the safety of transportation infrastructure. Shallow foundation bridges are particularly susceptible to scouring and structural damage due to their shallow burial depth and small contact area between the soil and the foundation. However, there is insufficient research on this phenomenon at home and abroad, and the level of attention paid to disaster prevention and control needs to be improved. This situation reveals a practical need: to strengthen the research on the damage behavior of shallow foundation bridges in flood environments, so as to provide more effective strategies and measures for their safety assessment and maintenance.

[0003] Shallow foundation bridges are extremely sudden due to water damage, a feature that stems from the strong concealment of their internal damage. Usually, these internal damages are not easy to be discovered in time. In the bridge structure that appears intact, hidden damages such as concrete plastic damage, partial foundation voiding, or component displacement response may quietly accumulate. Especially when heavy vehicles pass through these partially damaged shallow foundation bridges, these invisible damages will deteriorate instantly, causing key components to exceed their bearing capacity and fail in a short period of time, which will then trigger a chain reaction, leading to the rapid collapse and overall collapse of the bridge structure.

[0004] Previous studies have mainly focused on the mechanism of bridge flood scour, scour depth prediction, on-site monitoring methods, and scour protection measures, and have also considered the relevant conditions of pile-foundation bridges. However, compared with deep-foundation bridges, shallow-foundation bridges have received relatively little attention due to their susceptibility to scour and damage. This situation suggests that more research and discussion is needed on the scour problem of shallow-foundation bridges.

[0005] The prior art has the following deficiencies:

[0006] (1) Currently, most of the research work on bridge structure damage analysis focuses on earthquake, fire, corrosion, low temperature, natural fatigue and other research directions. In contrast, there is little research on structural flood damage. Therefore, this paper systematically discusses the impact of flood erosion on shallow foundation bridge structure damage to make up for the existing deficiencies.

[0007] (2) The damage mechanism of shallow-buried bridge structures in flood environments is cumbersome and complex. Early research methods regarded the process as two independent processes: flood scour and damage analysis, without considering the multi-field coupling problem of flood-soil-structure. In addition, the simulation of scour morphology did not restore the actual situation, so it was still insufficient in accurately representing complex scour morphology (such as irregular scour pits).

[0008] (3) The bearing capacity of shallow-buried bridges in flood environments may be reduced due to a variety of factors, especially when heavy vehicles pass by, which makes them more likely to reach or approach their limit state. No analysis or research on the bearing capacity of bridge structures under the combined effects of heavy vehicles and floods has been found in the existing literature, which needs to be further improved. Summary of the invention

[0009] 1. Technical Problems Solved

[0010] The technical problem to be solved by the present invention is to provide a convenient, fast and cost-effective method for simulating flood scour damage of shallow-buried foundation bridges in view of the above problems.

[0011] 2. Technical Solution

[0012] In order to solve the above technical problems, the present invention provides the following technical solutions: a flood scour damage simulation method for shallow buried foundation bridges, comprising the following steps:

[0013] S1. Analysis of riverbed scour characteristics, the data to be extracted include scour depth, flow field around piers and scour pit morphology;

[0014] S2. Establish the structural model, including material definition, loading method of heavy vehicle load, definition of nonlinear reinforcement, boundary condition setting and meshing;

[0015] S3, using point cloud reverse engineering technology and fluid-solid coupling technology to transfer foundation soil contact and water flow loads to the structural model;

[0016] S4. Structural damage analysis under the combined effects of flood and heavy vehicles, including concrete working state, steel bar working state, support contact state, pier body vertical stress distribution, foundation vertical displacement and pier top lateral displacement;

[0017] S5. Through simulation and data analysis, the structural safety assessment conclusion of the bridge under the combined effects of flood scouring and heavy vehicle loads was obtained.

[0018] Furthermore, when conducting scour characteristics analysis, the scour model is first constructed. The scour model evaluates sediment behavior by predicting the erosion, transfer and sinking processes of sediment, covering four main aspects: sediment deposition under the influence of gravity, sediment agitation caused by bottom shear force and water flow disturbance, suspended sediment transport, and bedload transport.

[0019] Furthermore, in the scour model, the deposition and entrainment of sediment particles are two simultaneous and opposing behaviors, which together affect the conversion efficiency between suspended load and bedload.

[0020] (1) The sinking rate of sediment particles can be expressed by the following formula:

[0021]

[0022] Where: v is the fluid kinematic viscosity; u settling The direction of is consistent with the direction of gravity acceleration.

[0023] (2) The rate at which sediment particles are carried by water flow can be expressed by the following formula:

[0024]

[0025] Where: α is the entrainment coefficient, the initial value is set to 0.018, ns refers to the normal vector perpendicular to the bed surface,

[0026] (3) The transport of sediment particles is divided into suspended load transport and bedload transport. The former refers to the phenomenon that when sediment particles are above a certain height of the riverbed, they are carried by the water flow. The latter refers to the behavior of sediment particles on the riverbed sliding, rolling, and jumping along the direction of fluid movement. The suspended sediment convection diffusion equation is as follows:

[0027]

[0028] Where: C s,i is the mass of sediment contained in a unit volume of water-sand mixture, that is, the mass concentration of suspended sediment, D is the sediment diffusion rate, u s,i is the velocity of the suspended particle,

[0029] (4) The single-width sediment transport rate of bed load is calculated according to the relevant equation proposed by Van Rijn.

[0030]

[0031] Where: Φ is the dimensionless bed load transport rate, ||g|| is the norm of gravitational acceleration, i p is the density of the i-th type of sediment, p is the density of the fluid, i d It is the median particle of sediment.

[0032] Furthermore, the riverbed scour data around the bridge piers after logical correction is imported into the structural model through three-dimensional surface fitting through point cloud reverse engineering technology to realize real-time transmission of boundary conditions. The process of describing the logical correction is as follows: First, the sediment three-dimensional coordinate matrix data is imported into MATLAB for processing. In MATLAB, multiple data points existing on the same grid node are identified, and these data points are packaged uniformly for logical correction. MATLAB groups the data according to the node ID, and each group contains all data points with the same node ID. Then, the logical corrector executes the command in MATLAB to filter out the points with the smallest vertical coordinate value in each group of data as valid data points. The remaining data points with larger vertical coordinate values ​​are excluded and filtered. After the processing is completed, the valid data points will be integrated and summarized to complete the logical correction.

[0033] Furthermore, the calculated hydraulic effect is transferred to the pier wall in the structural model using fluid-solid coupling technology. The fluid part is described by pressure, while the solid part is characterized by displacement, forming a set of classic fluid-solid coupling finite element equations (see Equation 2-13).

[0034]

[0035] Where: M s and M f are the mass matrices of the solid and fluid, respectively, K s and K f are the stiffness matrices of the solid and fluid, respectively, P is the pressure vector of the fluid node, and Z is the displacement vector of the solid node. Q is the fluid-solid coupling matrix, F s is the load vector acting on the structure, p f is the fluid density.

[0036] Furthermore, the Menetrey-Willam constitutive model is used to describe the yield and failure of concrete in the structural model under complex stress states, including compression, tension and shear behavior under three-dimensional stress conditions. The Menetrey-Willam model simulates this behavior by introducing a softening parameter. The relevant yield criterion describing the model is as follows:

[0037] (1) Yield surface and flow potential,

[0038] (2) Linear softening.

[0039] Furthermore, the material parameters defining the yield function are the uniaxial tensile yield strength ft, the uniaxial compressive yield strength fc and the biaxial compressive yield strength fcc,

[0040] The concrete matrix hardening and softening parameters are defined as follows:

[0041]

[0042] Where: Ω c and Ω t denote the hardening / softening functions of the concrete matrix under compression and tension, respectively, depending on the compression and tension hardening variables f t 、f c and f cc ;k cm is the material parameter; k c and k t denote the compression hardening and tension hardening variables of the concrete matrix,

[0043] The yield surface in Haigh-Westergaard stress coordinates is given by:

[0044]

[0045] I1=σ +σ 22 +σ 33 (2-28)

[0046]

[0047] J3=det(σ-Iσ 22 ) (2-30)

[0048]

[0049]

[0050] Where I1 is the first principal invariant of the stress tensor, J2 and J3 are the second and third principal invariants of the deviatoric stress tensor, and ω is the expansion angle.

[0051] Furthermore, the compressive yield function Ω c Given by a nonlinear hardening function and a linear softening function, the relative stress value at the beginning of nonlinear hardening is Ω ci , the hardening yield function is:

[0052]

[0053] When k cm = k, it reaches the peak compressive strength and begins to soften

[0054]

[0055] When k cm When >k, the relative stress residual value is Ω cr , tension yield function Ω t Given by the linear softening function, the relative yield stress at initial yield is 1, and when the effective plastic strain is ktr When the relative yield stress is reduced to the relative residual stress Ω tr , when k tr >k, the relative yield stress remains unchanged, k cm is the plastic strain under uniaxial compressive strength, k cr is the limiting effective plastic strain in compression, Ω ci is the relative stress at the onset of nonlinear hardening, Ω cr is the residual compressive relative stress, k tr is the plastic strain limit during tension, Ω tr is the residual tensile relative stress.

[0056] 3. Beneficial Effects

[0057] The advantages of the present invention compared with the prior art are:

[0058] (1) An in-depth analysis of the theory of flood scour and structural damage simulation was conducted. Through turbulence models, basic control equations, and scour models, a scientific basis was provided for the subsequent understanding and simulation of the dynamic scour of water flow on shallow-buried foundation bridges. The importance and effectiveness of numerical simulation in the study of bridge flood damage were emphasized.

[0059] (2) Point cloud reverse engineering technology was used to solve the problem of the difficulty in converting the complex scouring pattern of the riverbed around the bridge foundation under flood scouring into the structural model. The multi-hazard damage behavior of the bridge was studied by coupling the extreme hydraulic effects on the pier wall and arranging the most unfavorable heavy vehicle loads on the bridge deck.

[0060] (3) The relevant principles of nonlinear finite element analysis are covered, and the relevant theories and analysis methods of material nonlinearity, geometric nonlinearity and contact nonlinearity are discussed. Through these advanced analysis techniques, the understanding and simulation capabilities of complex structural responses are further improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a flow chart of the present invention.

[0062] Figure 2 Linear softening of the concrete of the present invention in compression (left) and tension (right).

[0063] Figure 3 This is a table of parameter values ​​of the Menetrey-Willam constitutive model of the present invention.

[0064] Figure 4 Dimensional drawing of the bridge of the present invention.

[0065] Figure 5 The material parameters of the present invention are shown in the table.

[0066] Figure 6It is the size of a single square grid in different areas of the present invention.

[0067] Figure 7 Schematic diagram of the triangulation algorithm in reverse engineering of the present invention.

[0068] Figure 8 This is a graph of the surface fitting results after triangulation of the present invention.

[0069] Fig. 9 This is a diagram showing the variation of the scouring depth at the first emptying point of the riverbed around the foundation under different working conditions of the present invention.

[0070] Fig.10 It is a schematic diagram of the riverbed height under different scouring depths of the present invention.

[0071] Fig.11 It is the velocity magnitude and direction on the XY plane at T=2940s and Z=+2.5 in the mesh encryption area of ​​the present invention.

[0072] Fig.12 It is the velocity magnitude and direction diagram on the XZ plane at T=2940s and y=+14.5 in the mesh encryption area of ​​the present invention.

[0073] Fig.13 It is the velocity magnitude and direction diagram on the XZ plane at T=3060s and y=+14.5 in the mesh encryption area of ​​the present invention.

[0074] Fig.14 It is the velocity magnitude and direction on the XZ plane at T=3180s and y=+14.5 in the mesh encryption area of ​​the present invention.

[0075] Fig.15 It is a progressive development diagram of the scour pit morphology under extreme hydrological conditions of the present invention.

[0076] Fig.16 This is the relationship between the substrate de-hollowing area and time under the extreme hydrological conditions of the present invention.

[0077] Fig.17 From left to right, depth contours of the riverbed scour around the foundation at T = 2940, 3060, and 3180s.

[0078] Fig.18 Maximum principal stress cloud map at 2940s under flood scouring and heavy vehicle loading conditions.

[0079] Fig.19 Maximum principal stress cloud map at 3060s under flood scouring and heavy vehicle loading conditions.

[0080] Fig. 20 Maximum principal stress cloud map at 3180s under flood scouring and heavy vehicle loading conditions.

[0081] Fig.21 Maximum principal stress cloud map at 2940s under flood scouring and no vehicle loading conditions.

[0082] Fig. 22 Maximum principal stress cloud map at 3060s under flood scouring and no vehicle loading conditions.

[0083] Fig.23 Maximum principal stress cloud map at 3180s under flood scouring and no vehicle loading conditions.

[0084] Fig.24 Cloud diagram of minimum composite stress of steel bars in Pier 3 at time 3180s under flood scouring and heavy vehicle loading conditions.

[0085] Fig.25 The maximum composite stress cloud of the steel bars of Pier 3 at 3180s under the conditions of flood scouring and heavy vehicle loading.

[0086] Fig.26 Cloud diagram of minimum composite stress of reinforcement of Pier 3 at time 3180s under flood scouring and no vehicle loading conditions.

[0087] Fig. 27 Cloud diagram of the maximum composite stress of the reinforcement of Pier 3 at time 3180s under flood scouring and no vehicle loading conditions.

[0088] Fig.28 Cloud diagram of minimum composite stress of steel bars in Pier 3 at 3060s under flood scouring and heavy vehicle loading conditions.

[0089] Fig.29 Cloud diagram of the maximum composite stress of the steel bars in Pier 3 at time 3060s under flood scouring and heavy vehicle loading conditions.

[0090] Fig.30 Contact stress cloud diagram of the bearing surface of Pier 3 at 3180s under flood scouring and heavy vehicle loading conditions.

[0091] Fig.31 Selection of path and direction for monitoring point No. 3.

[0092] Fig.32 Vertical stress values ​​at various points on the column of Pier 3 at 2940s under flood scouring and heavy vehicle loading conditions.

[0093] Fig.33 Vertical stress values ​​at various points on the column of Pier 3 at 2940s under flood scouring and no vehicle loading conditions.

[0094] Fig.34 Vertical stress values ​​at various points on the column of Pier 3 at 3060s under flood scouring and heavy vehicle loading conditions.

[0095] Fig.35 Vertical stress values ​​at various points on the column of Pier 3 at 3060s under flood scouring and no vehicle loading conditions.

[0096] Fig.36 Vertical stress values ​​at various points on the column of Pier 3 at time 3180s under flood scouring and heavy vehicle loading conditions.

[0097] Fig.37 Vertical stress values ​​at various points on the column of Pier 3 at 3180s under flood scouring and no vehicle loading conditions.

[0098] Fig.38 The paths and directions of the monitoring points at Piers No. 2 and No. 3.

[0099] Fig.39 Vertical displacement values ​​of the paths of Piers No. 2 and No. 3 at time 2940s under flood scouring and heavy vehicle loading conditions.

[0100] Fig.40 Vertical displacement of the paths of Piers 2 and 3 at 2940s under flood scouring and no vehicle loading conditions.

[0101] Fig.41 Vertical position of the paths of Piers No. 2 and No. 3 at time 3060s under flood scouring and heavy vehicle loading conditions.

[0102] Fig.42 Vertical displacement of the paths of Piers 2 and 3 at 3060s under flood scouring and no vehicle loading conditions.

[0103] Fig.43 Vertical positions of the paths of Piers No. 2 and No. 3 at time 3180s under flood scouring and vehicle loading conditions.

[0104] Fig.44 Vertical positions of the paths of Piers No. 2 and No. 3 at time 3180s under flood scouring and no vehicle loading conditions.

[0105] Fig.45 Table of maximum horizontal displacement of the top of Pier No. 2 and Pier No. 3.

[0106] Fig.46 This is the diagram of the vehicle load layout. DETAILED DESCRIPTION

[0107] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0108] It should be noted that all directional indications such as up, down, left, right, front, back, etc. in the embodiments of the present invention are only used to explain the relative position relationship, movement status, etc. between the components in a certain specific posture as shown in the accompanying drawings. If the specific posture changes, the directional indication will also change accordingly.

[0109] In addition, in the present invention, descriptions such as "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of the present invention, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0110] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. 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 invention.

[0111] The present invention will now be further described with reference to embodiments.

[0112] Example

[0113] The project is based on a steel-concrete composite beam main bridge in a certain city. The bridge is designed with a shallow foundation and is 36 meters long, with a span of 12 meters and three spans. The total width of the bridge deck is 9 meters, and the horizontal layout is: 0.5m (anti-collision guardrail) + 8m (driving lane) + 0.5m (anti-collision guardrail). The bridge deck material is C40 concrete, and the bridge deck pavement includes a 10mm asphalt surface treatment layer and a 50mm asphalt concrete layer. The bridge pier is a double-column type with a diameter of 1.2m, a pier height of 3m, and a concrete strength of C30. Piers 2 and 3 are reinforced concrete columns and double-layer expanded foundations. The foundation size is 9.332m long and 5m wide, and the top surface of the foundation is buried 0.5 meters below the riverbed scour line on average. The lowest riverbed elevation is 1633.72 meters, and the foundation bottom elevation is 1631.43 meters. The surrounding soil from top to bottom is generally silty silty clay, silty clay, and silty clay mixed with silt. Under the foundation is artificially replaced with gravel, sand, and siltstone. The foundation has been reinforced to meet the foundation bearing capacity of more than 160kPa.

[0114] Taking the location of a steel-concrete composite beam main bridge in a certain city as the engineering background, based on its river characteristics and geological conditions, a local scour model of the flow field around the shallow buried foundation bridge was constructed in the CFD software with a 1:1 restoration. The aim is to analyze the scour pattern of sediment around the foundation, explore the influence of water flow depth and flow velocity on the erosion and hollowing evolution of sediment at the bottom of the pier foundation, and finally output the three-dimensional coordinate matrix of the scattered sediment points in the grid encryption area, which is introduced into the numerical analysis module for the next step.

[0115] The model size is consistent with the actual bridge landform size. The entire geometric model is symmetrical along the horizontal and vertical center lines. Since the calculation of the model will consume a lot of computing resources, the idea of ​​determining the calculation domain follows the principle of selecting the smallest possible calculation area without affecting the calculation results. The total length in the X direction is 109.332m, the width in the Y direction is 31m, and the height in the Z direction is 15m. Hidden water blocks with a thickness of 5m, a width of 31m, and a height of 7.5m are set at the upstream entrance and the downstream exit. Silty clay is covered at 0-2.5m below the riverbed scour line, and gravel and sand are laid at 2.5-7.5m. The material parameters related to sediment particles are shown in Figure 5 .

[0116] When constructing the numerical simulation of sediment scour module, setting appropriate boundary conditions is the key to ensure the accuracy of the calculation results. CFD software supports a variety of boundary conditions, including continuous boundary (Continuative), grid overlay boundary, free outflow boundary (Outflow), periodic boundary (Periodic), pressure boundary (Specifiedpressure), velocity boundary (Specified velocity), symmetry boundary (Symmetry), flow boundary (Volumeflow rate), wall boundary (Wall), wave boundary (Wave) and other 10 different boundary conditions. For the scour numerical model in this study, the selected boundary conditions are as follows:

[0117] (1) Inlet boundary: The upstream water inlet of the simulated actual river channel is set as the flow boundary. The velocity boundary condition (specified velocity) is used to introduce uniform inflow fluid velocities of 2 m / s, 4 m / s, and 8 m / s, and the inflow water depths are 3 m and 5 m. The required flow field is formed through the development of appropriate areas.

[0118] (2) Outlet boundary: The downstream outlet of the simulated actual river channel is set as the outflow boundary, and the pressure outlet boundary condition (Specified pressure) is selected. This boundary can set the outlet fluid elevation to be consistent with the inlet fluid elevation to explore the effect of different fluid heights on the sediment flushing efficiency of the river channel.

[0119] (3) Boundary between mesh encryption area and non-encrypted area: In order to save computing resources, there are mesh encryption areas and non-encrypted areas in the entire flow field area, and the boundary between the areas adopts continuous boundary conditions. This type of boundary allows the fluid to maintain the continuity of its velocity and pressure when entering and leaving the computational domain, thereby simulating an open flow scenario without artificially affecting the natural behavior of the fluid.

[0120] (4) Bottom boundary: In actual riverbeds, the sediments usually include sand, gravel, pebbles, and rocks as you go deeper. In this case, the bottom surface of the numerical model uses the wall boundary condition (Wall) to ensure that the vertical velocity of the fluid on the wall is zero, and the slip boundary condition is applied to deal with the wall shear effect.

[0121] (5) Top boundary and side boundaries: In this study, the water flow is unidirectional and the Froude number Fr is small, so a symmetric boundary is used to achieve the effect of the steel cover assumption and retain a certain height to allow the free liquid surface to develop fully. The left and right sides of the computational domain are also symmetric boundaries to reduce the influence of wall reflection.

[0122] The CFD software provides a structured grid generation function, using simple rectangular units to make grid construction simple and accurate. By applying FAVOR technology, unique and complex shapes can be easily defined. The software supports local mesh encryption, splicing and nesting functions, allowing local encryption of specific areas through mesh nesting and boundary continuity, which not only ensures accuracy requirements, but also reduces the total number of required meshes, thereby improving calculation efficiency.

[0123] Select the smallest possible calculation area. The total length in the X direction is 109.332m, the width in the Y direction is 31m, and the height in the Z direction is 15m. After the geometric model is established, the FAVOR meshing technology is used to process the mesh, and local mesh encryption is performed near the shallow foundation piers. The mesh is divided into square meshes. The unit sizes between different regions are 2m and 0.5m, and the size ratio is 4:1.

[0124] In the sediment scour model, due to the effect of water flow entrainment, some sediment particles will be retained on the surface of the structure, resulting in a single grid node extracted near the structure corresponding to multiple sediment scour elevations. At this time, the output data matrix needs to be logically corrected in the conversion interface. Specifically, multiple data appearing in the same grid node are first identified, and then the data groups are uniformly packaged and inserted into the logic corrector for processing. The logic corrector starts to execute the command, and the data with the smallest vertical coordinate of the same node is considered valid, and the others are excluded and filtered. After processing, the data output is integrated and summarized, and the logic correction is completed.

[0125] Based on this data set, the linear interpolation function of the point cloud can be fitted to obtain the nonlinear surface of the foundation-soil interface contact in the structural model, and realize the cross-module transmission of the basic boundary conditions. Using Delaunay triangulation to optimize the mesh of the point cloud data is an important part of reverse engineering. Ensure that there are no other scattered points on the circumscribed circle / circumscribed sphere formed by any triangle / tetrahedron vertices.

[0126] After the scour data is processed by the triangulation algorithm, each grid node in the structural model can be assigned to the corresponding triangle. Among them, P1 (x1, y1, z1), P2 (x2, y2, z2), P3 (x3, y3, z3) are the sand bed grid points from the sediment scour model, P (x, y, z) is the grid point from the structural model, S1, S2, S3, S represent the area of ​​▲PP2P3, ▲PP1P3, ▲PP1P2, ▲P1P2P3 respectively, and the sediment scour elevation z corresponding to any grid node in the structural model satisfies the following relationship:

[0127]

[0128] The surface after triangulation is as follows Figure 8 As shown in the figure, since the contact area between the bottom surface of the foundation and the curved surface of the riverbed is the primary factor that directly affects the safety and stability of the overall bridge structure, there is no need for detailed simulation of the area outside the critical surface of the curved body in the coupling calculation. When reconstructing the curved body, it is roughly assumed that the upper and lower surfaces are consistent.

[0129] When performing fluid-solid coupling operations, the flow field domain needs to be reconstructed in order to synchronize the calculation results and improve work efficiency. The editable features in SpaceClaim are used to model the model in proportion based on the sediment scour model. The hydrological conditions follow the parameters selected under extreme hydraulic conditions, with a water depth of 5 meters and a flow velocity of 8 meters per second. The RNGk-ε turbulence model is used to describe the phenomenon that after the fluid passes through the bridge pier, the fluid particles move extremely irregularly and the flow direction changes greatly. Unlike the 15-meter-high flow field in the riverbed scour model, the height of the flow field domain constructed in this section is reduced to 5 meters (consistent with the extreme working conditions), covering the entire double-layer foundation and double-row column area of ​​the bridge pier, but excluding the cap beam. Therefore, the size of the fluid domain is set to a hexahedron with a length of 109.332 meters, a width of 31 meters, and a height of 5 meters. The quality of the mesh directly affects the accuracy and reliability of the simulation results, especially when performing fluid-solid coupling analysis, the requirements for mesh quality are more stringent. This study uses the software's built-in meshing module Mesh for meshing, selects structured hexahedral meshes to ensure the accuracy and convergence of the calculation, and performs encryption around the wall at the junction of the pier model, and finally obtains the fluid domain mesh model and the local mesh refinement of the pier. After the settings are completed, enter the Static Structural module to set the solid material, constraints and some corresponding outputs. Define the fluid-solid coupling surface, set the coupling time term in System Coupling, create the data transfer of the coupling surface, and the solution order of the flow field and solid, and finally set the frequency of saving the results before starting the solution.

[0130] Scientific planning of the vehicle load layout strategy is particularly important to ensure the safety and stability of the overall structure. According to the recommendations of the General Specification for Highway Bridge and Culvert Design JTGD60-2015 (Ministry of Transport of the People's Republic of China, 2015), a 45-ton vehicle load is applied to the bridge in an eccentric arrangement, and the load is set 0.6 meters away from the crash barrier. This loading strategy is to simulate the maximum impact that the vehicle load may have on the bridge in actual situations. Furthermore, considering the extreme impact of flood scouring and vehicle load, the center wheel axle of the vehicle is aligned with the center line position of the pier support. This arrangement can induce the maximum adverse structural response when the bridge is loaded, thereby simulating the response of the entire bridge under extreme load conditions. The vehicle load is finally implemented by applying a uniformly distributed load to the vehicle steel sheet. The specific parameters are shown in the table below, and the vehicle load layout is shown in the figure below.

[0131] Table Specific parameters of vehicle load

[0132] Heavy vehicle (45t) Front wheel (45KN) Middle wheel (90KN) Rear wheel (90KN) Uniform load 0.3Mpa 0.6Mpa 0.6Mpa

[0133] Frictional contact is set up between the wheel steel sheet and the bridge deck pavement. This contact can simulate the vertical load applied by the wheel to the bridge deck and the lateral force caused by wheel rolling or braking, which are crucial to the structural response and overall performance evaluation of the bridge. There will be no normal separation or tangential friction between the bridge deck pavement and the bridge deck, and between the bridge deck and the main beam, so it is more in line with the actual situation to define the contact between the two as binding. For the main beam and the support, because the foundation may cause the pier to tilt and displace, when the pier is displaced, there will be slight sliding and displacement between the two, so it is more appropriate to define it as frictional contact. The support and the pier are not the focus of this study. In order to improve the convergence of the model calculation, it is assumed that there is perfect bonding between the two, and binding contact is adopted.

[0134] In the analysis of the internal forces of bridge structures, it is very important to select the appropriate control section, which can ensure the accurate capture and calculation of the structural forces. By focusing on the key areas of the structure, stress concentration areas or potential weak points can be analyzed more finely, thereby improving the accuracy of the entire analysis process.

[0135] Based on the Willam-Warnke five-parameter strength model, the yield surface is improved and combined with the hardening / softening curve to consider the change of the mechanical properties of concrete materials under external loads. The Young's modulus of concrete is 30Gpa, the Poisson's ratio is 0.2, and the density is 2400kg / m 3, the expansion angle is 30°, the uniaxial compressive strength is 20.1Mpa, the uniaxial tensile strength is 2.01Mpa, and the biaxial compressive strength is 1.2 times the uniaxial compressive strength, which is 24.12Mpa. The nonlinear steel bars in the steel-concrete composite beams, wheel steel sheets and pier columns are all made of Q235 steel, with a Young's modulus of 206Gpa, a Poisson's ratio of 0.3, and a density of 7850kg / m 3 , the yield strength is 235Mpa and the ultimate strength is 375Mpa.

[0136] When performing finite element analysis of reinforced concrete structures, the software provides an efficient method to simulate the coupled behavior of concrete and steel. Concrete materials are usually defined using Solid186 three-dimensional solid elements, which are suitable for simulating structures with complex geometries and nonlinear material behavior. The Solid186 element has high-order displacement capabilities, enabling it to capture the micro-cracks and plastic deformation behavior of concrete. The modeling of tensile steel bars uses a special steel bar element REINF264, which is designed specifically for simulating steel bars embedded in concrete. It can simulate the linear elastic-plastic behavior of steel bars while taking into account the axial tensile properties of steel bars. Stirrups and upper longitudinal reinforcement also use REINF264 units to ensure the accuracy of the steel bars in the model and the consistency of the simulation.

[0137] The coupling of concrete and steel bars is achieved by simulating the contact friction behavior of the bonded parts. The contact interface is set as a nonlinear contact problem with a certain friction coefficient, allowing the shear force to be transmitted between the steel bars and the concrete. Regarding the selection of the friction coefficient, a comprehensive analysis of historical data was conducted by combining the discrete element method and the neural network method, and the optimal range of the friction coefficient between the steel bar and concrete interface was found to be 0.612 to 0.643. This range can reflect the behavioral characteristics of the contact interface under different load conditions.

[0138] The fluid elevation is 3m and 5m, and the flow velocity is 2m / s, 4m / s, and 8m / s. Fig. 9The relationship curves of the scouring depth of the void point with time under six conditions with calculation time ranging from 3600s to 54000s are given. It can be seen that when the hydraulic factor is small, the rate of sediment entrainment and loss is at a low level, and the scouring depth is difficult to break through the surface cover of the shallow buried foundation within the limited calculation time. The maximum scouring depth is ≥-0.5m. This situation includes four conditions of H=3m, V=2, 4, 8m / s and H=5m, V=2m / s. However, the step-by-step increase in water depth and flow rate has a significant impact on the development of scouring, which will bring the model scouring equilibrium state to an early stage. The two conditions of H=5m, V=4, 8m / s first appeared voiding at 21000s and 2580s respectively due to the loss of sediment at the bottom of the foundation, and sediment erosion continued to progress. Under the condition of relatively slow water flow (V = 4m / s), when the scouring depth reaches about -1.5m, the riverbed's ability to resist scouring and the blocked water flow's ability to erode the bed surface sediment reach a relative balance, and there is a long period of scouring stagnation until tiny scouring holes form and expand around the second step of the shallow foundation, causing a sharp change in the flow field environment and accelerating the scouring speed again. Comparison of bridge pier foundation and riverbed height at different scouring depths is shown in Figure 2. Fig.10 .

[0139] In extreme hydrological environments, bridge structures are particularly vulnerable to damage, which may cause severe scour.

[0140] Fig.11 The velocity magnitude and direction on the XY plane at Z = +2.5 under the extreme working condition of the mesh densification area (H = 5m, V = 8m / s) are shown. When the water flow encounters the double-row columns of the bridge pier, a circumferential flow phenomenon occurs, and a region with lower velocity is formed on the front side (flow direction side) of the incoming column, which is called the "incoming surface". The increase in velocity on both sides leads to the generation of vortices, which may induce erosion on a long time scale and pose a potential risk to the structural stability of the bridge pier. After the vorticity accumulates to a critical threshold, the vortex will break away from the wall of the column. Part of the vortex in this process will migrate to the area between the two columns, where the velocity is reduced to the minimum and the turbulent behavior is extremely complex. In addition, the remaining vortices continue to flow downstream, forming a wake area on the back side of the wake column, which is characterized by low velocity and variable flow direction.

[0141] Figure 12-14The flow velocity magnitude and direction on the XZ plane (y = +14.5) at T = 2940s, 3060s, and 3180s under the extreme working conditions of the mesh densification area (H = 5m, V = 8m / s) are shown. It can be seen from the figure that the fluid area on the water-facing and wake surfaces of the piers is green in color. Due to the lack of obstruction from the piers, the water flow develops freely and the fluid velocity in this area is relatively high. A blue low-speed area is formed between the two columns. This is because after the water flow bypasses the first column, a more complex flow pattern is formed between the two columns, including vortices and backflows. The density and color changes of the flow velocity vectors also show this. At T = 2940s, due to the influence of the water blocking in front of the pier, the descending water flow forms a special flow pattern called a horseshoe vortex at the bottom of the front end of the pier. This vortex will form strong local erosion at the bottom around the foundation, constantly entraining and entraining the mud and sand bordering it, resulting in irregular and missing corners at the edge of the soil, and erosion begins to appear. At T = 3060s, the soil at the bottom of the vertical pier has obvious de-hollowing phenomenon, which can be judged by the reduction of soil area. The formation of de-hollowing area indicates that the flow velocity has become very large in this narrow area, and the local acceleration has increased the shear force of the water flow on the bottom sediment, making the sediment in these areas easier to be washed away.

[0142] When T = 3180s, the velocity vector distribution at the bottom of the pier becomes more scattered, the water flow behavior becomes more complex and chaotic, and the soil loss becomes more serious. Scour may have caused the formation of local scour pits around the piers, posing a serious threat to the stability of the piers.

[0143] Flood scour can cause large local deformation of the riverbed around the foundation. When the sediment particles move according to the transport equation, the slope of the bed unit on the scour side will continue to increase. As the local scour increases, once the bed slope is greater than the angle of repose, the sediment will collapse and automatically adjust the bed slope, thereby achieving a gradual development of the scour pit morphology until the final balance is reached. Fig.15 The process of progressive scouring of the riverbed around shallow buried foundation piers under the working conditions of H=5m, V=8m / s is further demonstrated. It can be observed that as the scouring progresses, the two sides of the water-facing surface of the pier foundation become weak points of the riverbed, forming a deeper horseshoe-shaped scouring pit. The scouring range on the front and back sides of the foundation is smaller than that on the left and right sides, and there is silt deposition. The maximum scouring depth occurs near the first hollowing point of the foundation.

[0144] Relevant flume tests have shown that the slope of the riverbed is the largest near the maximum scour depth, which is roughly the same as the angle of repose. After reaching a state of equilibrium, the soil layer with a slope less than the angle of repose near the local scour hole will be carried away by the water flowing into the scour hole, and soil erosion will progress. Especially at the bottom of the foundation, when a local scour hole is formed, the movement of the underwater current is hindered due to the narrow water flow area at this location, and vortices will be generated inside and near the hole. This complex turbulence phenomenon will further promote and accelerate the process of erosion and hollowing out of the bottom of the foundation. The relationship between the maximum scour depth of the model and the hollowing out area of ​​the bottom of the foundation over time can be seen in Fig.16 The first 540s of the scouring process is the sediment initiation stage, the hydrological conditions are not stable, and the initial scouring depth develops rapidly. Then, in the two 17-minute time periods from 540s to 1560s and from 1560s to 2580s, the scouring speed tends to be gentle, and the maximum scouring depth decreases from -1.65m to -1.91m, and then from -1.91m to -2.51m. No local scouring holes are formed in this stage, and the sediment loss rate is relatively stable. Since T=2580s, local scouring holes in the riverbed near the foundation gradually form, and the basement void appears for the first time. At this time, the maximum scouring depth is -2.51m. In the last 17 minutes from 2580s to 3600s, the scouring speed of the riverbed around the foundation accelerates, and the maximum scouring depth decreases rapidly from -2.51m to -3.50m. The basement sediment loss is serious, and the voiding area in a short time reaches 79.09%.

[0145] Fig.17 The isobath distribution maps of the sediment erosion characteristics at the bottom of the shallow buried foundation and the scouring morphology of the surrounding riverbed at T=2940s, 3060s and 3180s are given. Figure 18-Figure 21 The maximum principal stress cloud diagrams of shallow buried foundation bridge structures under flood scouring and heavy vehicle loading conditions are shown at T = 2940s, 3060s, and 3180s. Figure 17-Figure 21 It can be seen that when the void area is 7.27%, the foundation of the control section of Pier 3 is completely in contact with the riverbed line. The area between the two supports on the left side of the cap beam is transmitted to the left pier column through the supports due to the heavy vehicle load on the bridge. The top area unit of the cap beam mapped by the left pier column has a tendency to buckle, and the stress will be slightly greater than that in other areas. Even so, the maximum principal stress limit value is still far less than the standard value of concrete tensile strength. At T = 2940s, the concrete material of the entire bridge is in normal working condition. After the scouring develops for a time step, at T = 3060s, the void area at the bottom of the foundation reaches 24.09%, and the scope of the scouring pit on both sides of the foundation facing the water becomes larger. There is a small area on the left side of the foundation of the control section of Pier 3 that is separated from the riverbed line. The maximum principal stress of some nodes of the concrete at the bottom of the foundation mapped by the left pier column is slightly greater than f tkSince concrete is a brittle material, the maximum tensile stress (first strength) theory shows that the concrete at the above position may have cracked, and micro cracks began to appear at the stress concentration point at the bottom of the foundation. At this time, the concrete of Pier 3 is in the cracked working stage.

[0146] At T = 3180s, the scouring phenomenon on the left side of Pier 3 became more obvious under continuous scouring, the bottom of the foundation was emptied to 42.73%, and the scouring pits on both sides of the foundation facing the water surface had been connected in a large range. The control section of the pier did not fit the riverbed line in a large range. The upper structure load of the bridge was transmitted through the cap beam of the Pier 3 support and spread to the bottom of the double column piers. Since the foundation in the vacant area was suspended and not stressed, the concrete in the transition to the non-vacant area had large-scale vertical penetration damage, and the maximum principal stress was 2.17Mpa. At the same time, due to the reduction of the stress area of ​​the bottom surface of the foundation, the pressure in the connection area between the right pier column and the foundation surged. The concrete shear fracture around the pier column may have occurred here, and there was a risk of separation between the column bottom and the foundation. At the next time step, T = 3300, the bottom of the foundation was emptied to 57.27%, and the coupling solver prompted that the structural deformation was too large and the calculation could not converge. It was judged that the bridge might overturn and the structure would fail completely.

[0147] Figure 18-Figure 20 The maximum principal stress cloud diagrams of the shallow buried foundation bridge structure under flood scouring and no vehicle loading conditions at T=2940s, 3060s, and 3180s respectively.

[0148] When T = 2940s, the void area reached 7.27%. At this time, the overall stress distribution of the bridge pier under no-vehicle relative to heavy vehicle loading showed the characteristics of axis symmetry along the center line of the bridge pier. The whole bridge was evenly stressed and in normal working condition. When T = 3060s, the void area increased to 24.09%. There was stress concentration in some areas at the bottom of the foundation mapped by the left pier column under no-vehicle relative to heavy vehicle loading. Although the maximum principal stress value in this area is less than f tk , the concrete has not cracked yet, but the stress changes in this area should be closely monitored and early warning measures should be taken. When T = 3180s, the void area increased to 42.73%. The continuous scouring caused the void area at the bottom of the foundation to be close to the limit that the bridge structure can withstand. Compared with the heavy vehicle loading, most of the concrete still failed and cracked under the no-vehicle loading. However, the difference from the latter is that the eccentric load applied to the cap beam by the heavy vehicle is missing, and the cracking range of the foundation concrete in the void area is slightly smaller. There is only a slight stress concentration phenomenon in the connection area between the right pier and the foundation, and the maximum principal stress has not exceeded the standard value of the tensile strength of C30 concrete.

[0149] Figure 21-23The maximum principal stress cloud diagrams of shallow buried foundation bridge structures at T=2940s, 3060s, and 3180s under flood scouring and vehicle-free loading conditions, respectively. When T=2940s, the void area reached 7.27%. At this time, the overall stress distribution of the bridge pier under vehicle-free relative to heavy vehicle loading showed the characteristics of axis symmetry along the center line of the bridge pier. The whole bridge was evenly stressed and was in normal working condition. When T=3060s, the void area increased to 24.09%. There was stress concentration in some areas at the bottom of the foundation mapped by the left pier under vehicle-free relative to heavy vehicle loading. Although the maximum principal stress value in this area is less than f tk , the concrete has not cracked yet, but the stress changes in this area should be closely monitored and early warning measures should be taken. When T = 3180s, the void area increased to 42.73%. The continuous scouring caused the void area at the bottom of the foundation to be close to the limit that the bridge structure can withstand. Compared with the heavy vehicle loading, most of the concrete still failed and cracked under the no-vehicle loading. However, the difference from the latter is that the eccentric load applied to the cap beam by the heavy vehicle is missing, and the cracking range of the foundation concrete in the void area is slightly smaller. There is only a slight stress concentration phenomenon in the connection area between the right pier and the foundation, and the maximum principal stress has not exceeded the standard value of the tensile strength of C30 concrete.

[0150] Fig.24 and Fig.25 The minimum and maximum composite stress distribution of the internal steel bars under the impact of flood and heavy load at T = 3180s, when the foundation void area of ​​pier 3 reached 42.73%. The analysis shows that due to the erosion and voiding of the bottom sediment, pier 3 as a whole has settled and tilted to the left. This caused the steel bars at the tearing of the concrete inside the double-layer expanded foundation near the water surface to undergo compressive yielding, with a maximum composite compressive stress value of -279.98Mpa, which is lower than the ultimate compressive strength of Q235 carbon structural steel (375Mpa), but higher than its compressive yield strength (235Mpa). At the same time, the right column was affected by the eccentric bending moment on the left, and the bottom steel bars underwent tensile yielding, with a maximum composite tensile stress value of 260.35Mpa, which is also lower than the ultimate tensile strength of Q235 carbon structural steel (375Mpa), but higher than the tensile yield strength (235Mpa). The composite stress distribution of the steel bars inside the pier revealed that under extreme hydraulic conditions, some areas of the steel bars at the bottom of the column underwent compressive and tensile yielding, indicating that the reinforced concrete structure was at its ultimate bearing capacity.

[0151] Fig.26 and Fig. 27 The distribution of composite stress of the internal reinforcement of the No. 3 pier column under flood impact and vehicle-free loading at T = 3180s is shown. Compared with the vehicle-free loading, the yield area at the bottom of the reinforcement of the left column of the pier is significantly reduced, and the maximum composite compressive stress reaches -259.61Mpa. Figure 7 The data confirms that the steel bar yielding and concrete cracking have occurred, indicating that the structure is in a cracked working state. The maximum composite compressive stress and tensile stress of the steel bar in the right column are both less than the yield strength of Q235 carbon structural steel (235Mpa), indicating that the bearing capacity of the right column is still good.

[0152] Fig.28 and Fig.29 The distribution of composite stress of the internal reinforcement of the No. 3 bridge pier column under flood impact and heavy vehicle loading conditions is shown when T=3060s and the base void area is 24.09%. It is obvious that the degree of foundation voiding has a significant impact on the overall stability of the pier and its stress state. In this case, the maximum composite compressive stress and tensile stress of the internal reinforcement are -136.06Mpa and 127.87Mpa, respectively. Both values ​​are significantly lower than the yield strength of 235Mpa specified by Q235 carbon structural steel, indicating that although the pier has suffered a certain degree of structural pressure, the bearing capacity of its internal reinforcement has not been seriously affected and is still within the safe range. It is worth noting that although some cracks have occurred in the edge of the pier bottom near the voiding area due to stress concentration, this has not caused problems with the working state of the internal reinforcement or yielding.

[0153] Fig.30 The contact stress cloud diagram of the top support of the scour No. 3 pier and the main beam end at T = 3180s under the conditions of flood scouring and heavy vehicle loading is given. Due to the influence of local sediment hollowing out of the base, the bridge pier as a whole settles and tilts to the left, resulting in a reduction in the contact area between the main beam end and the support, and the compressive stress on the support surface is concentrated from the outside to the inside. Due to the resistance of the stiffness of the support material, the support buckles at the junction of the gray extremely compressed area and the green suspended separation area of ​​the cloud diagram, and stress concentration occurs. At the same time, the main beam attached to it has a "V"-shaped deflection inward and tends to overturn toward the hollow area at the bottom of the column.

[0154] The path and direction of the measuring points of the double-row columns of Pier 3 (empty) are as follows: Fig.31 shown. Figure 32-Figure 37 The vertical stresses at each measuring point of the double-row columns of Pier 3 under flood scouring at T=2940s, 3060s and 3180s with and without vehicle loading are given.

[0155] At T = 2940 seconds, see Fig.32 and Fig.33It was observed that the vertical stress value curves of each measuring point on the four paths (1-4) of Pier 3 in the no-vehicle state were basically consistent. This phenomenon shows that under the condition of 7.27% of the foundation void area, the left and right columns of the pier evenly shared half of the pressure of the bridge superstructure, and the force distribution was uniform. The vertical stress distribution in the no-vehicle state and the vehicle-loaded state has a common feature: in the area where the cap beam is connected to the column, the stress concentration effect is generated due to the sudden change of the cross section. Within a range of 0.5 meters below the top of the double column, the axial stress changes from large to small and then tends to be stable. However, unlike the no-vehicle state, in the vehicle-loaded state, the stress curves begin to not overlap, especially the stress values ​​of the middle and lower measuring points of path 1 generally increase, which indicates that the load generated by the vehicle is mainly borne by this part of the area.

[0156] When T=3060s, see Fig.34 and Fig.35 , whether in the state with or without vehicles, the vertical stress curve begins to disperse, which shows that when the foundation void area reaches 24.09%, the stress condition of the pier column has begun to become uneven and unstable. In both states, the maximum vertical stress value appears on path 3, which indicates that the load of the bridge superstructure is mainly transmitted to the foundation through path 3. In addition, under the influence of heavy vehicle loading, the maximum vertical stress values ​​of path 1 and path 2 increase significantly, while the stress curves of path 3 and path 4 do not change much in the comparison before and after loading. This shows that in the case of foundation voiding, the columns close to the voiding area (path 1 and path 2) mainly bear the load of heavy vehicles.

[0157] When T = 3180s, see Fig.36 and Fig.37 , the foundation void area expanded to 42.73%. Compared with the previous two moments (2940s and 3060s), it can be observed that the dispersion of the vertical stress curves on each path has significantly increased. The stress sudden change phenomenon at the top and bottom of the double-row columns (paths 1 to 4) is more prominent, and the stress distribution has become extremely uneven. Even tensile stress appeared on the left side of the double column bottom (path 1 and path 3), which is an obvious signal of unstable structural stress state. This change shows that the foundation void has a huge impact on the stress performance of the bridge pier and even the entire bridge. Moreover, under the action of heavy vehicles, the maximum vertical stress value of the double columns showed a continuous increase, reaching a peak value of -3.66MPa. The increase in this data further aggravated the structural instability caused by the foundation void and increased the risk of damage and failure of the bridge pier.

[0158] Analysis of vertical displacement of bridge pier foundation

[0159] The selection of the measurement path and direction of the No. 2 and No. 3 (empty) piers is as follows: Fig.38 shown. Figure 39-Figure 43The maximum normal displacement values ​​(positive for upward direction and negative for downward direction) of the measuring points along Path 5 and Path 6 of the No. 2 and No. 3 (empty) piers with and without vehicles under flood scouring conditions are shown.

[0160] By comparison Fig.39 and Fig.40 When the scouring time is 2940s, the vertical displacement value on path 5 shows a trend of gradual decrease, which indicates that the foundation settlement of the backwater side of the pier is more serious than that of the frontwater side. Due to the direct effect of hydraulic force, Pier 2 (not empty) tilted slightly to the right at this time, and under the action of eccentric vehicle load, this tilting effect to the right was weakened. In the absence of vehicles, path 6 is basically horizontal, indicating that the vertical displacement difference caused by the foundation emptying and hydraulic effect of Pier 3 (empty) offset each other, and the pier remained relatively static. When loaded with vehicles, the vertical displacement value of the measuring point on path 6 gradually increased, and the pier began to tilt significantly to the side with vehicles.

[0161] At T = 3060s (see Fig.41 and Fig.42 ), the vertical displacement value of path 5 in the car-free state continued to decrease linearly, but the rate of decrease was slower than that in the previous 2 minutes; while in the car-car state, the vertical displacement value of the measuring point on this path was stable at about -13mm, which shows that the slight right tilt effect of Pier 2 was completely eliminated due to the hollowing of the left foundation of Pier 3 and the eccentric load of the heavy vehicle. On the contrary, at each measuring point on path 6, the maximum vertical displacement difference in the car-free state was 2.99mm, which increased to 4.01mm in the car-car state, and the displacement curve showed a gradual increase trend regardless of whether there was a car or not, revealing that the uneven foundation settlement occurred on the water-facing side of Pier 3 due to the hollowing phenomenon, and this phenomenon was more significant under the action of the car.

[0162] Scour further develops, T = 3180s (see Fig.43 and Fig.44 ), the vertical displacement difference between the measuring points on Path 5 and Path 6 reached the maximum. The foundation settlement of the vacant side of Pier 3 when there was a vehicle exceeded that of the non-vacant side by 8.28mm. At the same time, the maximum difference in normal displacement of the measuring points on the front and rear paths of the foundation of Pier 2 was 1.03mm. This phenomenon shows that Pier 2 also experienced significant displacement and settlement due to the chain effect of the instability of the foundation of Pier 3.

[0163] Analysis of lateral displacement of bridge pier top

[0164] Fig.45 The maximum horizontal displacement values ​​of the tops of Pier 2 and Pier 3 (empty) under flood scouring conditions with and without vehicles are given. At T=2940s, 3060s, and 3180s, there is no foundation emptying phenomenon in Pier 2.

[0165] When T = 2940s, the top of the No. 2 pier showed a slight displacement in the downstream direction in both the case of vehicles and vehicles without vehicles, with the displacement of 0.47mm and 0.80mm respectively. This change can be directly attributed to the hydraulic effect of the flood. In contrast, the top of the No. 3 pier shifted 0.19mm in the upstream direction in the absence of vehicles, indicating that the 7.27% of the void area has caused slight instability of the foundation. However, under the influence of vehicle loads, the displacement increased to 0.98mm, indicating that vehicle loads have a significant amplification effect on the displacement, exacerbating the degree of foundation instability.

[0166] When T = 3060s, the more serious local de-airing phenomenon caused the displacement direction of Pier 2 to change from downstream to upstream in both the no-vehicle and vehicle-car states, with a displacement of 0.52mm and 0.63mm, respectively. At this time, the displacement difference of Pier 2 under the influence of heavy vehicle load was not obvious. However, in contrast, Pier 3 faced different foundation contact conditions from Pier 2, and its foundation bottom was 24.09% de-aired, resulting in the horizontal displacement of the top of Pier 3 significantly increasing from 1.40mm to 2.73mm under the dual effects of foundation de-airing and vehicle eccentric load.

[0167] When T = 3180s, the foundation void area increased to 42.73%. At this time, the horizontal displacement of the top of piers 2 and 3 increased significantly regardless of whether they were subjected to vehicle loads. In particular, under the action of heavy vehicle loads, the maximum horizontal displacement of the top of pier 3 (void) surged to 4.61mm, while that of pier 2 (not void) was 1.68mm. Obviously, the former is nearly three times the value of the latter. In addition, the horizontal displacement of the top of pier 3 increased by 0.72mm under vehicle loads compared with that without vehicle loads. These two sets of data clearly reveal that the horizontal displacement effect caused by foundation voids significantly exceeds the influence of vehicle loads, indicating that foundation voids are the main factor leading to pier column damage and failure. However, it must be pointed out that under the action of heavy vehicles, the probability of extreme situations will be further aggravated. These results emphasize that in bridge design and evaluation, not only the direct impact of loads should be considered, but also the long-term impact of foundation conditions on structural stability should be taken into account.

[0168] The foundation void area increased from 7.27% at T = 2940s to 42.73% at T = 3180s, resulting in a significant increase in the stress of the concrete material and internal steel bars of the shallow foundation bridge, a large number of cracks in the concrete, and yielding of the steel bars. When T = 3180s, the vertical crack penetration of the concrete and the yielding of the steel bars indicate that the structural bearing capacity has reached its limit at this time point.

[0169] The stress analysis of the bearings revealed that under extreme conditions, the reduction in the contact area of ​​the bearings caused the upper main beam to deflect inward in a "V" shape and tilt toward the hollow area at the bottom of the column. This situation is very likely to cause the bridge structure to fall and be damaged.

[0170] The vertical stress analysis at different time points and loading conditions shows that with the increase of the void area, the stress distribution becomes more and more uneven, especially under heavy vehicle load, the maximum vertical stress value increases significantly. This highlights the important influence of eccentric heavy load and erosion on the stability of bridge pier foundation.

[0171] Displacement analysis shows that flood scouring can cause lateral displacement of the pier top in the direction of the water flow and vertical displacement of the foundation on the back side, even if the foundation is not de-sunk. When the foundation is de-sunk and affected by the eccentric load of the vehicle, the structural displacement increases significantly. This extreme situation poses a major risk to the overall stability and safety of the bridge.

[0172] This patent and its implementation methods are described, and this description is not restrictive. What is shown in the embodiment is only one of the implementation methods of this patent, and the actual method is not limited to this. In short, if ordinary technicians in this field are inspired by it and design embodiments similar to the technical solution without creative design without departing from the purpose of the invention of this patent, they should all fall within the scope of protection of this patent.

Claims

1. A flood scour damage simulation method for shallow buried foundation bridges, characterized in that: The following steps are involved: S1. Analysis of riverbed scour characteristics, the data to be extracted include scour depth, flow field around piers and scour pit morphology; S2. Establish the structural model, including material definition, loading method of heavy vehicle load, definition of nonlinear reinforcement, boundary condition setting and meshing; S3, using point cloud reverse engineering technology and fluid-solid coupling technology to transfer foundation soil contact and water flow loads to the structural model; S4. Structural damage analysis under the combined effects of flood and heavy vehicles, including concrete working state, steel bar working state, support contact state, pier body vertical stress distribution, foundation vertical displacement and pier top lateral displacement; S5. Through simulation and data analysis, the structural safety assessment conclusion of the bridge under the combined effects of flood scouring and heavy vehicle loads was obtained.

2. The flood scour damage simulation method for shallow-buried foundation bridges according to claim 1 is characterized in that: When conducting scour characteristics analysis, the scour model is first constructed. The scour model evaluates sediment behavior by predicting the erosion, transfer and sinking processes of sediment, covering four main aspects: sediment deposition under the influence of gravity, sediment agitation caused by bottom shear force and water flow disturbance, suspended sediment transport, and bedload transport.

3. The flood scour damage simulation method for shallow-buried foundation bridges according to claim 1 is characterized in that: In the scour model, the deposition and entrainment of sediment particles are two simultaneous and opposing behaviors, which together affect the conversion efficiency between suspended load and bedload. (1) The sinking rate of sediment particles can be expressed by the following formula: Where: v is the fluid kinematic viscosity; u settling The direction of is consistent with the direction of gravity acceleration. (2) The rate at which sediment particles are carried by water flow can be expressed by the following formula: Where: α is the entrainment coefficient, the initial value is set to 0.018, n s Refers to the normal vector of the bed surface pointing vertically outward. (3) The transport of sediment particles is divided into suspended load transport and bedload transport. The former refers to the phenomenon that when sediment particles are above a certain height of the riverbed, they are carried by the water flow. The latter refers to the behavior of sediment particles on the riverbed sliding, rolling, and jumping along the direction of fluid movement. The suspended sediment convection diffusion equation is as follows: Where: C s,i is the mass of sediment contained in a unit volume of water-sand mixture, that is, the mass concentration of suspended sediment, D is the sediment diffusion rate, u s,i is the velocity of the suspended particle, (4) The single-width sediment transport rate of bed load was calculated according to the relevant equation proposed by Van Rijn. Where: Φ is the dimensionless bed load transport rate, ||g|| is the norm of gravitational acceleration, i p is the density of the i-th type of sediment, p is the density of the fluid, i d It is the median particle of sediment.

4. The flood scour damage simulation method for shallow-buried foundation bridges according to claim 3 is characterized by: The riverbed scour data around the bridge piers after logical correction is imported into the structural model through three-dimensional surface fitting by point cloud reverse engineering technology to realize the real-time transmission of boundary conditions. The process of describing the logical correction is as follows: First, the sediment three-dimensional coordinate matrix data is imported into MATLAB for processing. In MATLAB, multiple data points existing on the same grid node are identified, and these data points are packaged uniformly for logical correction. MATLAB groups the data according to the node ID, and each group contains all data points with the same node ID. Then, the logical corrector executes the command in MATLAB to filter out the points with the smallest vertical coordinate value in each group of data as valid data points. The remaining data points with larger vertical coordinate values ​​are excluded and filtered. After the processing is completed, the valid data points will be integrated and summarized to complete the logical correction.

5. The flood scour damage simulation method for shallow-buried foundation bridges according to claim 3 is characterized by: Fluid-solid coupling technology is used to transfer the calculated hydraulic effects to the pier wall in the structural model. The fluid part is described by pressure, while the solid part is characterized by displacement, forming a set of classic fluid-solid coupling finite element equations (see Equation 2-13). Where: M s and M f are the mass matrices of the solid and fluid, respectively, K s and K f are the stiffness matrices of the solid and fluid, respectively, P is the pressure vector of the fluid node, and Z is the displacement vector of the solid node. Q is the fluid-solid coupling matrix, F s is the load vector acting on the structure, p f is the fluid density.

6. The flood scour damage simulation method for shallow-buried foundation bridges according to claim 2 is characterized by: The Menetrey-Willam constitutive model is used to describe the yield and failure of concrete in the structural model under complex stress states, including compression, tension and shear behavior under three-dimensional stress conditions. The Menetrey-Willam model simulates this behavior by introducing a softening parameter. The relevant yield criteria describing the model are as follows: (1) Yield surface and flow potential, (2) Linear softening.

7. The flood scour damage simulation method for shallow-buried foundation bridges according to claim 2 is characterized by: The material parameters defining the yield function are the uniaxial tensile yield strength ft, the uniaxial compressive yield strength fc, and the biaxial compressive yield strength fcc. The hardening and softening parameters of the concrete matrix are defined as follows: Where: Ωc and Ωt represent the hardening / softening functions of the concrete matrix under compression and tension, respectively, depending on the compression and tension hardening variables f t 、f c and f cc ;k cm is the material parameter; k c and k t denote the compression hardening and tension hardening variables of the concrete matrix, The yield surface in Haigh–Westergaard stress coordinates is given by: I1=σ 11 +s 22 +s 33 (2-28) J3=det(σ-Iσ m ) (2-30) Q WM =θ 2 +B g θ+C g ξ (2-31) Where I1 is the first principal invariant of the stress tensor, J2 and J3 are the second and third principal invariants of the deviatoric stress tensor, and ω is the expansion angle.

8. The flood scour damage simulation method for shallow-buried foundation bridges according to claim 2 is characterized by: Compression yield function Ω c Given by a nonlinear hardening function and a linear softening function, the relative stress value at the onset of nonlinear hardening is Ω ci , the hardening yield function is: When k cm = k, it reaches the peak compressive strength and begins to soften When k cm When >k, the relative stress residual value is Ω cr , tension yield function Ω t Given by the linear softening function, the relative yield stress at initial yield is 1, and when the effective plastic strain is k tr When the relative yield stress is reduced to the relative residual stress Ω tr , when k tr >k, the relative yield stress remains unchanged, k cm is the plastic strain under uniaxial compressive strength, k cr is the limiting effective plastic strain in compression, Ω ci is the relative stress at the onset of nonlinear hardening, Ω cr is the residual compressive relative stress, k tr is the plastic strain limit during tension, Ω tr is the relative residual tensile stress.

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