A numerical simulation method and system for the combined action of multiple disasters on bridges based on triangulation and collaborative interpolation of characteristic points

Abstract

The invention discloses a numerical simulation method and a simulation system for the joint action of multiple disasters of a bridge based on triangulation and feature point collaborative interpolation, comprising the following steps: constructing a CFD numerical model of foundation scour of a mountain highway bridge based on REEF3D, and constructing a FEM numerical model of rockfall impact on a bridge pier based on ABAQUS; acquiring simulation data of REEF3D scour, processing the simulation data using two-dimensional Delaunay triangulation and triangle internal linear interpolation theory to obtain structural domain scour depth data, and screening soil units that should be passivated in the FEM numerical model; when the scour depth data in REEF3D reaches a set value, extracting corresponding scour terrain data, and constructing a numerical model of pile foundation erosion; the invention can simultaneously consider the influence of foundation scour, abrasion and collapse rockfall impact on bridge piers, and can perform numerical simulation on mountain highway bridge piers under the action of multiple disasters.

Description

Technical Field

[0001] The present invention relates to a numerical simulation method and a simulation system for the combined action of multiple disasters on a bridge, and in particular to a numerical simulation method and a simulation system for the combined action of multiple disasters on a bridge based on triangulation and collaborative interpolation of characteristic points. Background Art

[0002] In the mountainous areas of southwest my country, a large number of highway bridges have been built, and the impact of rockfall in mountainous areas has great destructive power on bridge piers. According to relevant surveys and studies, among all kinds of geological disasters in mountainous areas, the damage to bridge piers caused by rockfall accounts for a large proportion; in addition, highway bridges in mountainous areas have been eroded and abraded by mountain streams for a long time. However, in the current numerical simulation of rockfall in mountainous areas impacting bridge piers, the influence of foundation erosion and abrasion is not considered at the same time, which causes serious distortion between the calculated value of bridge pier response and the actual value of bridge pier response, which will lead to cracking of bridge piers in the later stage. In serious cases, the bridge piers may even be damaged and cannot be used normally. Summary of the invention

[0003] Purpose of the invention: The first purpose of the present invention is to provide a numerical simulation method for the combined effects of multiple disasters on bridges based on triangulation and collaborative interpolation of characteristic points, which can simultaneously consider the effects of foundation scour, abrasion and rockfall impact on bridge piers.

[0004] The second object of the present invention is to provide a numerical simulation system for the combined effects of multiple disasters on bridges based on triangulation and collaborative interpolation of characteristic points.

[0005] Technical solution: The present invention discloses a numerical simulation method for the combined action of multiple disasters on bridges based on triangulation and feature point collaborative interpolation, comprising the following steps:

[0006] A CFD numerical model of mountain highway bridge foundation scour was constructed based on REEF3D, and a FEM numerical model of rockfall impact on bridge piers was constructed based on ABAQUS.

[0007] Get the simulation data of REEF3D scour, use two-dimensional Delaunay triangulation and triangle internal linear interpolation theory to process the simulation data, get the structural domain scour depth data, and select the soil units that should be passivated in the FEM numerical model;

[0008] When the scour depth data in REEF3D reaches the set value, the corresponding scour terrain data is extracted and a numerical model of pile foundation erosion is constructed;

[0009] The abrasion rate and wave-current force data obtained from the abrasion simulation are obtained, and the abrasion rate and wave-current force data are processed by using the three-dimensional surface Delaunay triangulation combined with the inner and outer linear interpolation theory of the triangle and the characteristic point collaborative interpolation algorithm, and the pile foundation units that should be passivated at each abrasion stage in the FEM numerical model are selected, and the wave-current force that should be applied to each pile foundation unit is calculated;

[0010] Based on the life and death unit function of ABAQUS, the corresponding soil units and pile foundation units are passivated in the numerical model of rockfall impact on mountain highway bridge piers, and the corresponding wave and flow forces are applied to construct a numerical model of multi-hazard combined action.

[0011] Furthermore, the specific steps for screening the soil elements that should be passivated in the FEM numerical model are as follows:

[0012] Extract the riverbed scour depth data in the local area around the REEF3D foundation and store it as data set Data1;

[0013] The data set Data1 is triangulated using two-dimensional Delaunay triangulation to obtain the surface SU1;

[0014] The center P of the target soil unit for which scour depth data is to be extracted in the FEM model is g (x, y) is mapped to the surface SU1 to obtain the target soil unit center P g The three vertices P1 of the triangular plane where (x,y) is located g (x1,y1), Calculate the target soil unit center P g (x,y) scour depth data;

[0015] Target soil unit center P g The (x,y) scour depth z is estimated by interpolation:

[0016]

[0017] Among them, z1, z2, and z3 are vertex P1 respectively. g (x1,y1), The scouring depth, A is The total area of ​​A1, A2 and A3 are area;

[0018] According to the calculated target soil unit center P g The scour depth data of (x, y) is used to select the soil elements that should be passivated in the FEM model during the foundation scour simulation based on the current scour depth and the distance between the upper and lower soil elements, and store them as the element set ELSet1.

[0019] Furthermore, the specific steps of constructing the Fluent numerical model of pile foundation abrasion are as follows:

[0020] Extract the scour depth up to z in REEF3D i =0.8z max The terrain data at that time was used to construct the Fluent numerical model of pile foundation erosion under the coupling of water and sand in the CFD numerical model; max Refers to the equilibrium scour depth.

[0021] Furthermore, the specific steps for screening the pile foundation units that should be passivated at each abrasion stage in the FEM numerical model are as follows:

[0022] The average abrasion rate data of each node of the Fluent bridge pile foundation wall of the CFD numerical model is extracted and stored as data set Data2;

[0023] The three-dimensional surface Delaunay triangulation is used to triangulate the data set Data2 to obtain the surface SU2. The pile foundation target unit node P(x, y) and the pile foundation target unit center P of the FEM numerical model are searched in the surface SU2. c (x c ,y c ) are located in the respective triangular planes, and the average erosion rate E of the target unit node P(x, y) of the pile foundation is calculated by weight. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C ;

[0024] For the pile-based target unit nodes P(x, y) and pile-based target unit centers P of the triangular plane obtained by Delaunay triangulation of the surface not included in the three-dimensional c (x c ,y c ), search for the triangle ΔP1P2P3 that is coplanar with the triangular plane obtained by the three-dimensional surface Delaunay triangulation, divide the outside of the triangle ΔP1P2P3 into 6 areas: the external area Ω1 of the edge P1P2, the external area Ω3 of the edge P2P3, the external area Ω5 of the edge P1P3, the external area Ω6 of the vertex P1, the external area Ω2 of the vertex P2 and the external area Ω4 of the vertex P3, and determine the pile foundation target unit node P(x, y) and the pile foundation target unit center P c (x c ,y c ) belongs to the external area, and calculate the average erosion rate E of the target unit node P(x,y) of the pile foundation respectively P and the pile foundation target unit center Pc (x c ,y c ) average abrasion rate E C ;

[0025] The average erosion rate E based on the target unit node P(x,y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C Calculate the total average erosion rate E of the target unit in the structural domain avg ;

[0026] The total average wear rate E based on the structural domain target unit avg , calculate the annual average abrasion thickness h of the target unit in the structural domain avg,a ;

[0027] The annual average abrasion thickness h based on the structural domain target unit avg,a , based on the current abrasion thickness and the distance between the centers of each unit, the pile foundation units that should be passivated in the FEM numerical model during the simulated abrasion process are selected and stored as the unit set ELSet2;

[0028] The method for calculating the wave-flow force that should be applied to each pile foundation unit is as follows: the wave-flow force of each node of the target unit in the structural domain is calculated based on the wave-flow force of the pile foundation grid nodes in the fluid domain by using the linear interpolation formula inside and outside the triangle and the characteristic point collaborative interpolation algorithm.

[0029] Furthermore, the average erosion rate E of the target unit node P(x,y) of the pile foundation is calculated by weighted calculation. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The specific steps are as follows:

[0030]

[0031] Where E P,1 、E P,2 、E P,3 are the average abrasion rates of the three vertices of the triangle where the target unit node P(x, y) of the pile foundation is located, A P is the total area of ​​the triangle where the target unit node P(x,y) is located, They are the areas of three small triangles formed by the three vertices of the triangle where the target unit node P(x, y) is located and the line connecting the target unit node P(x, y);

[0032]

[0033] Where E C,1 、E C,2 、E C,3 are the target unit center P of the pile foundation respectively. c (x c ,y c ) is the average abrasion rate of the three vertices of the triangle, A C is the target unit center of pile foundation c (x c ,y c ) is the total area of ​​the triangle where are the target unit center P of the pile foundation respectively. c (x c ,y c ) and the three vertices of the triangle where the pile foundation target unit center P c (x c ,y c )The area of ​​the three small triangles formed by the connecting lines.

[0034] Furthermore, for the pile target unit nodes P(x, y) and pile target unit centers P of the triangular planes obtained by Delaunay triangulation of the three-dimensional surface, c (x c ,y c ), when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the edge of the coplanar triangle ΔP1P2P3, the average erosion rate E of the target unit node P(x,y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The specific steps are as follows:

[0035] Assume the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the outer area Ω1 of the coplanar triangle ΔP1P2P3 side P1P2, and intersects with the side P1P2 at point O. The angle between the straight line PP3 and P1P2 is α. The average erosion rate E of the target unit node P(x, y) of the pile foundation is obtained by linear interpolation theory. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0036]

[0037] in, are the areas of ΔPP2P3, ΔPP1P3, ΔPP1P2, and ΔP1P2P3 respectively, are the average erosion rates of the three vertices of the triangle coplanar with the target unit node P(x,y) of the pile foundation, They are △P c P2P3, △P c P1P3, △P c The area of ​​P1P2, are the target unit center P of the pile foundation respectively. c (x c ,y c ) the average abrasion rate of the three vertices of a coplanar triangle;

[0038] Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the outer area Ω3 of the edge P2P3, the average erosion rate E of the target unit node P(x, y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0039]

[0040] Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the area Ω5 outside P1P3, the average erosion rate E of the target unit node P(x, y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0041]

[0042] When the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertex of the coplanar triangle ΔP1P2P3, the average erosion rate E of the target unit node P(x,y) of the pile foundation P and the pile foundation target unit center P c(x c ,y c ) average abrasion rate E C The specific steps are as follows:

[0043] Assume the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the outer area Ω2 of the vertex P2 of the coplanar triangle ΔP1P2P3. The extended PP2 intersects with P1P3 at point O, and the angle is α. The average erosion rate E of the target unit node P(x, y) of the pile foundation is obtained by linear interpolation theory. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0044]

[0045] in, are the areas of ΔPP1P3, ΔPP1P2, ΔPP2P3 and ΔP1P2P3 respectively, are the average erosion rates of the three vertices of the triangle coplanar with the target unit node P(x,y) of the pile foundation, are the target unit center P of the pile foundation respectively. c (x c ,y c ) the average abrasion rate of the three vertices of a coplanar triangle;

[0046] Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the region Ω4 outside the vertex P3, the average erosion rate E of the target unit node P(x, y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0047]

[0048] Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertex and within the area Ω6 outside P1, the average erosion rate E of the target unit node P(x, y) of the pile foundation Pand the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are

[0049]

[0050] Furthermore, the total average erosion rate E of the target unit in the structure domain is calculated avg The specific steps are as follows:

[0051] The average erosion rate E of the target unit node of the structural domain pile foundation is estimated by using the linear interpolation formula inside and outside the triangle. P and the average erosion rate E of the target unit center of the pile foundation in the structural domain C , calculate the total average erosion rate E of the target unit in the structure domain according to the following feature point collaborative interpolation algorithm: avg :

[0052]

[0053] Among them, E C 、E P 、E i They are the average abrasion rate at the center of the pile foundation target unit, the final average abrasion rate at the nodes of the pile foundation target unit, and the average abrasion rate at each surface node of the target unit, all in kg / (m 2 ·s); γ∈[0,1] is the weight coefficient.

[0054] Calculate the annual average abrasion thickness h of the target unit in the structural domain avg,a The formula group is as follows:

[0055] Among them, Em is the average abrasion mass, in kg / s; R is the radius of the pile foundation before abrasion, in m; T is the total time of the flood period, in s; Et is the total abrasion mass of the pile foundation during the annual flood period, in kg; r is the equivalent radius of the pile foundation after abrasion, in m; V is the total volume of the pile foundation abraded, in m3; ρ is the density of the pile foundation, in kg / m3.

[0056] Furthermore, the specific steps for calculating the wave and flow forces at each node of the target unit in the structure domain are as follows:

[0057] For the target unit node in the structural domain contained in the triangular surface formed by the triangulation of the pile foundation mesh node in the fluid domain, the calculation formula is as follows:

[0058]

[0059] Where F is the wave flow force at the node of the structure domain; A Fis the area of ​​the current fluid domain triangle, A1 F , They are the areas of each triangle after the structure domain node divides the fluid domain triangle; F1, F2, and F3 are the wave and flow force data of each vertex of the fluid domain triangle;

[0060] For the structural domain nodes that are not included in the triangular surface formed by the triangulation of the pile foundation mesh nodes in the fluid domain,

[0061] When the structural domain node is located outside the coplanar triangle edge, the target unit node P(x, y) is located in the area Ω1 outside the coplanar triangle ΔP1P2P3 edge P1P2, and intersects with the edge P1P2 at point O. The angle between the straight line PP3 and P1P2 is α. The wave flow force of the target unit node P(x, y) is obtained by linear interpolation theory:

[0062]

[0063] Among them, F1, F2, and F3 are the wave and flow force data of each vertex of the fluid domain triangle;

[0064] Similarly, when the target unit node P(x, y) is located in the area Ω3 outside the edge P2P3 and in the area Ω5 outside the edge P1P3, the wave flow force calculation formulas are:

[0065]

[0066] When the structural domain node is located outside the vertex of the coplanar triangle, the target unit node P(x, y) is located in the area Ω2 outside the vertex P2 of the coplanar triangle ΔP1P2P3, and PP2 is extended to intersect with P1P3 at point O, with an angle of α. The wave flow force of the target unit node P(x, y) is obtained by linear interpolation theory:

[0067]

[0068] Similarly, when the target unit node P(x, y) is located in the region Ω4 outside the vertex P3 and in the region Ω6 outside P1, the wave flow force calculation formulas are:

[0069]

[0070] Furthermore, the specific steps of constructing a numerical model of multi-hazard combined effects are as follows:

[0071] In the FEM numerical model, a designated scouring analysis step is created for the scouring process, and according to the actual scouring process, the soil elements in the element set ELSet1 are gradually passivated using the birth and death element function;

[0072] In each scour analysis step in the FEM numerical model, the pile foundation elements in the element set ELSet2 are gradually passivated using the birth and death element function according to the actual erosion process;

[0073] In each scour analysis step in the FEM numerical model, wave flow force is applied to the target unit of the pile foundation;

[0074] Based on the FEM numerical model that has considered the scouring and abrasion effects, a specified rockfall impact analysis step is created for rockfall impacting bridge piers, and a numerical model of rockfall impacting mountain highway bridge piers considering the scouring and abrasion effects is constructed.

[0075] Based on the same inventive concept, the present invention discloses a bridge multi-hazard joint action numerical simulation system based on triangulation and feature point collaborative interpolation, including: an initial numerical model construction module, which constructs a CFD numerical model of mountain highway bridge foundation scour based on REEF3D;

[0076] The first processing module is used to obtain the simulation data of REEF3D scour, and use two-dimensional Delaunay triangulation and triangle internal linear interpolation theory to process the simulation data to obtain the structural domain scour depth data and screen the soil units that should be passivated in the FEM numerical model;

[0077] The second disaster numerical construction module, when the scour depth data in REEF3D reaches the set value, extracts the corresponding scour terrain data and constructs a numerical model of pile foundation erosion;

[0078] The second processing module is used to obtain the abrasion rate and wave-current force data obtained by the abrasion simulation, and process the abrasion rate and wave-current force data by using the three-dimensional surface Delaunay triangulation combined with the inner and outer linear interpolation theory of the triangle and the characteristic point collaborative interpolation algorithm, to select the pile foundation units that should be passivated at each abrasion stage in the FEM numerical model, and calculate the wave-current force that should be applied to each pile foundation unit;

[0079] The multi-hazard numerical model construction module, based on the life and death unit function, passivates the corresponding soil units and pile foundation units in the numerical model of rockfall impact on mountain highway bridge piers, applies corresponding wave and flow forces, and constructs a numerical model of the combined action of multiple hazards.

[0080] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention processes the numerical simulation results of the scouring of the foundation of the mountain highway bridge by using the scattered point interpolation theory, and calculates the scouring depth data of the center of the target soil unit in the local range around the pile in the FEM numerical model by combining the internal linear interpolation theory of the triangle, searches for the soil unit to be passivated according to the scouring depth data, and finally passivates the soil unit step by step through the life and death unit function to take into account the scouring effect of the foundation of the mountain highway bridge;

[0081] The present invention calculates the average abrasion rate and wave flow force of the target unit nodes and centers of the pile foundation wall based on the inner and outer linear interpolation theory of the triangle, and estimates the total average abrasion rate and total wave flow force of the target unit by using the characteristic point collaborative interpolation algorithm. Then, the annual average abrasion thickness is converted according to the total average abrasion rate of the target unit, and the pile foundation target unit that needs to be passivated during the abrasion process is searched in combination with the abrasion distribution obtained by simulation. Finally, the pile foundation unit is gradually passivated through the life and death unit function to take into account the abrasion effect of the pile foundation. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a schematic diagram of the process of the present invention;

[0083] Figure 2 It is a schematic diagram of the inner and outer linear interpolation theory of a triangle adopted by the present invention;

[0084] Figure 3 is the pile foundation target unit node P (x, y) and the pile foundation target unit center P c (x c ,y c ) is located outside the side of the coplanar triangle ΔP1P2P3 using the triangle exterior linear interpolation theory;

[0085] Figure 4 is the pile foundation target unit node P (x, y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertices of the coplanar triangle ΔP1P2P3 using the triangle exterior linear interpolation theory;

[0086] Figure 5 is a FEM numerical model considering the scouring effect in Example 1 of the present invention;

[0087] Figure 6 The present invention Figure 5 The REEF3D scour model corresponding to the FEM numerical model considering the scour effect;

[0088] Figure 7 is the FEM numerical model considering the abrasion effect in Example 1 of the present invention;

[0089] Figure 8 The present invention Figure 6 The Fluent numerical model corresponding to the FEM numerical model considering the abrasion effect;

[0090] Fig. 9 This is a numerical simulation result diagram of rockfall impacting a mountain highway bridge taking into account the scouring and abrasion effects in Example 1 of the present invention. DETAILED DESCRIPTION

[0091] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0092] Example 1

[0093] The present invention discloses a numerical simulation method for the combined action of multiple disasters on a bridge based on triangulation and feature point collaborative interpolation, comprising the following steps:

[0094] 1. A CFD numerical model of mountain highway bridge foundation scour is constructed based on REEF3D, and a FEM numerical model of rockfall impact on bridge piers is constructed based on ABAQUS.

[0095] 2. Obtain the simulation data of REEF3D scour, use two-dimensional Delaunay triangulation and triangle internal linear interpolation theory to process the simulation data, obtain the structural domain scour depth data, and screen the soil units that should be passivated in the FEM numerical model.

[0096] The specific steps to obtain the soil elements that should be passivated at each scour stage in the FEM numerical model are as follows:

[0097] 2.1. Extract the riverbed scour depth data in the local area around the REEF3D foundation and store it as data set Data1;

[0098] 2.2. Use two-dimensional Delaunay triangulation to triangulate the data set Data1 and obtain the surface SU1;

[0099] 2.3, such as Figure 1 As shown in the figure, the center P of the target soil unit for which scour depth data is to be extracted in the FEM numerical model is g (x, y) is mapped to the surface SU1, and then the target soil unit center P is obtained g The three vertices P1 of the triangular plane where (x,y) is located g (x1,y1), Then, the center P of the target soil unit is obtained according to the area weight interpolation scheme determined by the following formula: g (x,y) scour depth data:

[0100]

[0101] Among them, γ i is the weighting coefficient (i=1, 2, 3), calculated as follows:

[0102]

[0103] Among them, A is The total area of ​​A1, A2 and A3 are area;

[0104] Based on the linear relationship, it can be seen that the target soil unit center P g The (x,y) scour depth z is estimated by interpolation:

[0105]

[0106] Among them, z1, z2, and z3 are vertex P1 respectively. g (x1,y1), Depth of scouring.

[0107] 2.4. According to the target soil unit center P calculated in step 2.3 above g The scour depth data of (x, y) is used to select the soil units that should be passivated in the FEM numerical model during the foundation scour simulation process based on the current scour depth and the distance between the upper and lower soil units, and store them as the unit set ELSet1. The FEM numerical model considering the scour effect is as follows Figure 5 As shown, REEF3D scour model considering scour effect Figure 6 shown.

[0108] 3. When the scour depth data in REEF3D reaches the set value, the corresponding scour terrain data is extracted and the Fluent numerical model of pile foundation erosion is constructed.

[0109] Specifically, extract the scour depth in REEF3D up to z i =0.8z max The topographic data at that time was used to construct a Fluent numerical model of pile foundation erosion under the coupling of water and sand phases using CFD software, in which the water flow was modeled as a continuous phase and the sediment particles were simulated using the DPM model; the time for the scouring depth to develop to 80% of the equilibrium scouring depth was short, so the erosion of the pile foundation during this period was ignored in this embodiment, and it was assumed that the erosion of the pile foundation mainly developed from 80% of the equilibrium scouring depth to the final equilibrium scouring depth. Therefore, the construction of the subsequent erosion model will be based on the scouring topography at 80% of the equilibrium scouring depth obtained by numerical simulation.

[0110] 4. If Figure 2 As shown in the figure, the abrasion rate and wave-current force data obtained by the abrasion simulation are obtained, and the abrasion rate and wave-current force data are processed by using the three-dimensional surface Delaunay triangulation combined with the inner and outer linear interpolation theory of the triangle and the characteristic point collaborative interpolation algorithm. The pile foundation units that should be passivated in each abrasion stage in the FEM numerical model are screened, and the wave-current force that should be applied to each pile foundation unit is calculated.

[0111] 4.1. Extract the average abrasion rate data of each node on the bridge pile foundation wall of the Fluent numerical model and store it as data set Data2;

[0112] 4.2. Use three-dimensional surface Delaunay triangulation to triangulate the data set Data2 of the average erosion rate data in step S4.1 to obtain the surface SU2; search the pile foundation target unit node P(x, y) and the pile foundation target unit center P of the FEM numerical model from the surface SU2. c (x c ,y c ) and estimate the average erosion rate E of the target unit node P(x,y) of the pile foundation according to the area weight interpolation formula in step 2.3 P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C , the specific calculation steps are as follows:

[0113]

[0114] Where E P,1 、E P,2 、E P,3 are the average abrasion rates of the three vertices of the triangle where the target unit node P(x, y) of the pile foundation is located, A P is the total area of ​​the triangle where the target unit node P(x,y) is located, They are the areas of three small triangles formed by the three vertices of the triangle where the target unit node P(x, y) is located and the line connecting the target unit node P(x, y);

[0115]

[0116] Where E C,1 、E C,2 、E C,3 are the target unit center P of the pile foundation respectively. c (x c ,y c ) is the average abrasion rate of the three vertices of the triangle, A C is the target unit center of pile foundation c (x c ,y c ) is the total area of ​​the triangle where are the target unit center P of the pile foundation respectively. c (x c ,y c ) and the three vertices of the triangle where the pile foundation target unit center P c (x c ,y c )The area of ​​the three small triangles formed by the connecting lines.

[0117] 4.3. For the pile foundation target unit nodes P(x, y) and pile foundation target unit centers P that are not included in the triangular plane obtained by Delaunay triangulation of the three-dimensional surface c (x c ,y c ), search for the triangle ΔP1P2P3 that is coplanar with the triangular plane obtained by the three-dimensional surface Delaunay triangulation, and divide the outside of the triangle ΔP1P2P3 into the following six areas: the outer area Ω1 of the edge P1P2, the outer area Ω3 of the edge P2P3, the outer area Ω5 of the edge P1P3, the outer area Ω6 of the vertex P1, the outer area Ω2 of the vertex P2, and the outer area Ω4 of the vertex P3; determine the pile foundation target unit node P(x, y) and the pile foundation target unit center P c (x c ,y c ) belongs to the external area, and calculate the average erosion rate E of the target unit node P(x,y) of the pile foundation respectively P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C ;

[0118] 4.3.1, such as Figure 3 As shown, the pile foundation target unit node P (x, y) and the pile foundation target unit center P c (x c ,y c ) is outside the side of the coplanar triangle ΔP1P2P3:

[0119] Assume the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the coplanar triangle ΔP1P2P3 side P1P2 (i.e., region Ω1), and intersects with side P1P2 at point O. The angle between straight line PP3 and P1P2 is α. The average erosion rate E of the target unit node P(x, y) of the pile foundation is obtained by linear interpolation theory. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0120]

[0121] in, are the areas of ΔPP2P3, ΔPP1P3, ΔPP1P2, and ΔP1P2P3 respectively, are the average erosion rates of the three vertices of the triangle coplanar with the target unit node P(x,y) of the pile foundation, They are △P c P2P3, △P c P1P3, △P c The area of ​​P1P2, are the target unit center P of the pile foundation respectively. c (x c ,y c ) the average abrasion rate of the three vertices of a coplanar triangle;

[0122] in The calculation formula is as follows:

[0123]

[0124] Similarly, when the target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the edge P2P3 (region Ω3), the average erosion rate E of the target unit node P(x, y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0125]

[0126] Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the area Ω5 outside P1P3, the average erosion rate E of the target unit node P(x, y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0127]

[0128] 4.3.2, such as Figure 4 As shown, the pile foundation target unit node P (x, y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertex of the coplanar triangle ΔP1P2P3, the average erosion rate E of the target unit node P(x,y) of the pile foundation Pand the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The specific steps are as follows:

[0129] Assume the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertex P2 of the coplanar triangle ΔP1P2P3 (i.e., area Ω2), and PP2 is extended to intersect with P1P3 at point O, with an angle of α. The average erosion rate E of the target unit node P(x, y) of the pile foundation is obtained by linear interpolation theory. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0130]

[0131] in, are the areas of ΔPP1P3, ΔPP1P2, ΔPP2P3 and ΔP1P2P3 respectively, are the average erosion rates of the three vertices of the triangle coplanar with the target unit node P(x,y) of the pile foundation, are the target unit center P of the pile foundation respectively. c (x c ,y c ) the average abrasion rate of the three vertices of a coplanar triangle;

[0132] Among them, the area calculation formulas of ΔPP1P3, ΔPP1P2, ΔPP2P3 and ΔP1P2P3 are as follows:

[0133]

[0134] Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertex P3 (region Ω4), the average erosion rate E of the pile foundation target unit node P (x, y) P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0135]

[0136] Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertex P1 (region Ω6), the average erosion rate E of the pile foundation target unit node P(x, y) P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0137]

[0138] 4.4. Estimate the average erosion rate E of the target unit node of the structural domain pile foundation by the linear interpolation formula inside and outside the triangle in steps 2.3 and 4.3 respectively P and the average erosion rate E at the center of the target unit of the pile foundation C , and then calculate the total average abrasion rate of the target unit in the structure domain according to the following feature point collaborative interpolation algorithm:

[0139]

[0140] Among them, E avg 、E C 、E P 、E i They are the total average abrasion rate of the structural domain target unit, the average abrasion rate of the pile foundation target unit center, the final average abrasion rate of the pile foundation target unit node, and the average abrasion rate of each surface node of the target unit, all in kg / (m 2 ·s); γ∈[0,1] is the weight coefficient, the theoretical value is 2 / 3, and the theoretical value is determined by Simpson's formula.

[0141] According to step 4.4, the feature point collaborative interpolation algorithm is used to calculate the total average wear rate E of the target unit in the structural domain. avg , the annual average abrasion thickness of the target unit in the structural domain is calculated as follows:

[0142]

[0143] Among them, h avg,a is the annual average abrasion thickness, E m is the average abrasion mass (kg / s), R is the radius of the pile foundation before abrasion (m); H is the height of the pile foundation (m), T is the total time of the flood period (s), and the flood period is from June to August each year. t is the total abrasion mass of the pile foundation during the flood period each year (kg), r is the equivalent radius of the pile foundation after abrasion (m), and V is the total volume of the pile foundation abraded (m 3), ρ is the pile density (kg / m 3 ).

[0144] 4.6. According to the Fluent pile foundation abrasion range and the annual average abrasion thickness h of the target unit in the structural domain converted in step 4.5 avg,a , based on the current abrasion thickness and the distance between the centers of each unit, the pile foundation units that should be passivated in the FEM numerical model during the simulated abrasion process are screened and stored as the unit set ELSet2.

[0145] 4.7. Based on the linear interpolation formula inside and outside the triangle and the collaborative interpolation algorithm of characteristic points in steps 2.3 and 4.3, the wave and flow forces of each node of the target unit in the structure domain are calculated based on the wave and flow forces of the pile foundation grid nodes in the fluid domain, and the FEM numerical model considering the erosion effect is as follows: Figure 7 Fluent numerical model considering the erosion effect shown in Figure 2 Figure 8 shown.

[0146] The specific steps for calculating the wave and flow forces at each node of the target unit in the structure domain are as follows:

[0147] For the target unit node in the structural domain contained in the triangular surface formed by the triangulation of the pile foundation mesh node in the fluid domain, the calculation formula is as follows:

[0148]

[0149] Where F is the wave flow force at the node of the structure domain, A F is the area of ​​the current fluid domain triangle, A1 F , They are the areas of each triangle after the structure domain node divides the fluid domain triangle, and F1, F2, and F3 are the wave and flow force data of each vertex of the fluid domain triangle;

[0150] For the structural domain nodes that are not included in the triangular faces formed by the triangulation of the pile foundation mesh nodes in the fluid domain,

[0151] When the structural domain node is located outside the coplanar triangle edge, the target unit node P(x, y) is located in the area Ω1 outside the coplanar triangle ΔP1P2P3 edge P1P2, and intersects with the edge P1P2 at point O. The angle between the straight line PP3 and P1P2 is α. The wave flow force of the target unit node P(x, y) is obtained by linear interpolation theory:

[0152]

[0153] Among them, F1, F2, and F3 are the wave and flow force data of each vertex of the fluid domain triangle;

[0154] Similarly, when the target unit node P(x, y) is located in the area Ω3 outside the edge P2P3 and in the area Ω5 outside the edge P1P3, the wave flow force calculation formulas are:

[0155]

[0156] When the structural domain node is located outside the vertex of the coplanar triangle, the target unit node P(x, y) is located in the area Ω2 outside the vertex P2 of the coplanar triangle ΔP1P2P3, and PP2 is extended to intersect with P1P3 at point O, with an angle of α. The wave flow force of the target unit node P(x, y) is obtained by linear interpolation theory:

[0157]

[0158] Similarly, when the target unit node P(x, y) is located in the region Ω4 outside the vertex P3 and in the region Ω6 outside P1, the wave flow force calculation formulas are:

[0159]

[0160] 5. Based on the life and death unit function of ABAQUS, the corresponding soil unit and pile foundation unit are passivated in the FEM numerical model of rockfall impact bridge, and the corresponding wave and flow forces are applied to construct a numerical model of multi-hazard combined action, such as Fig. 9 shown.

[0161] 5.1. Create a designated scouring analysis step for the scouring process in the FEM numerical model, and use the birth and death unit function to gradually passivate the soil units in the unit set ELSet1 in step 2.4 according to the actual scouring process;

[0162] 5.2. In each scour analysis step in the FEM numerical model of step 5.1, according to the actual erosion process, the pile foundation units in the unit set ELSet2 in step 4.6 are gradually passivated using the birth and death unit function;

[0163] 5.3. In each scour analysis step in the FEM numerical model in step 5.2, wave flow force is applied to the target unit of the pile foundation;

[0164] 5.4. Based on the FEM numerical model that has considered the scouring and abrasion effects in step 5.3, create a specified rockfall impact analysis step for rockfall impact on bridge piers, and finally build a numerical model of rockfall impact on mountain bridges that takes into account the scouring and abrasion effects.

[0165] In summary, the present invention provides a numerical simulation method for the joint action of multiple disasters of bridges based on triangulation and feature point collaborative interpolation. The scattered point interpolation theory is used to process the numerical simulation results of the scouring of the foundation of mountain highway bridges, and the scouring depth data of the center of the target soil unit in the local range around the pile in the FEM numerical model is calculated in combination with the internal linear interpolation theory of the triangle. The soil unit that needs to be passivated is searched according to the scouring depth data, and finally the soil unit is gradually passivated through the life and death unit function to consider the scouring effect of the foundation of mountain highway bridges. In addition, the average abrasion rate and wave flow force of the target unit nodes and centers of the pile foundation wall are calculated based on the internal and external linear interpolation theory of the triangle, and the total average abrasion rate and total wave flow force of the target unit are estimated by the feature point collaborative interpolation algorithm. Then, the annual average abrasion thickness is converted according to the total average abrasion rate of the target unit, and the pile foundation target unit that needs to be passivated in the abrasion process is searched in combination with the abrasion distribution obtained by simulation. Finally, the pile foundation unit is gradually passivated through the life and death unit function to consider the abrasion effect of the pile foundation. The present invention can perform numerical simulation on the piers of highway bridges in mountainous areas under the influence of multiple disasters, thereby providing a reference for the design and defense of the piers of bridges in mountainous areas.

[0166] Example 2

[0167] The present invention discloses a numerical simulation system for the combined effects of multiple disasters on bridges based on triangulation and collaborative interpolation of characteristic points, comprising an initial numerical model construction module, a first processing module, a second disaster numerical construction module, a second processing module and a multiple disaster numerical model construction module.

[0168] The initial numerical model construction module builds a CFD numerical model of mountain highway bridge foundation scour based on REEF3D, and a FEM numerical model of rockfall impact on bridge piers based on ABAQUS.

[0169] The first processing module is used to obtain the simulation data of REEF3D scour, and use two-dimensional Delaunay triangulation and triangle internal linear interpolation theory to process the simulation data to obtain the structural domain scour depth data and screen the soil units that should be passivated in the FEM numerical model.

[0170] Specifically, the riverbed scour depth data in the local area around the REEF3D foundation is extracted and stored as a data set Data1; the data set Data1 is triangulated using two-dimensional Delaunay triangulation to obtain a surface SU1; Figure 1 As shown in the figure, the center P of the target soil unit for which scour depth data is to be extracted in the FEM numerical model is g (x, y) is mapped to the surface SU1, and then the target soil unit center P is obtained g The three vertices P1 of the triangular plane where (x,y) is located g (x1,y1), Then, the center P of the target soil unit is obtained according to the area weight interpolation scheme determined by the following formula: g (x,y) scour depth data:

[0171]

[0172] Among them, γ i is the weighting coefficient (i=1, 2, 3), calculated as follows:

[0173]

[0174] Among them, A is The total area of ​​A1, A2 and A3 are area;

[0175] Based on the linear relationship, it can be seen that the target soil unit center P g The (x,y) scour depth z is estimated by interpolation:

[0176]

[0177] Among them, z1, z2, and z3 are vertex P1 respectively. g (x1,y1), Depth of scour;

[0178] According to the target soil unit center P calculated above g The scour depth data of (x, y) is used to select the soil elements that should be passivated in the FEM numerical model during the foundation scour simulation process based on the current scour depth and the distance between the upper and lower soil elements, and store them as the element set ELSet1.

[0179] In the second disaster numerical construction module, when the scour depth data in REEF3D reaches the set value, the corresponding scour terrain data is extracted and a Fluent numerical model of pile foundation erosion is constructed.

[0180] Specifically, extract the scour depth in REEF3D up to z i =0.8z max Based on the terrain data at that time, the CFD software Fluent was used to build a numerical model of pile foundation erosion under the coupling effect of water and sand two phases, in which the water flow was modeled as a continuous phase and the sediment particles were simulated using the DPM model.

[0181] The second processing module is used to obtain the abrasion rate and wave-current force data obtained by the abrasion simulation, and process the abrasion rate and wave-current force data by using the three-dimensional surface Delaunay triangulation combined with the inner and outer linear interpolation theory of the triangle and the characteristic point collaborative interpolation algorithm, to screen the pile foundation units that should be passivated at each abrasion stage in the FEM numerical model, and calculate the wave-current force that should be applied to each pile foundation unit.

[0182] Specifically, the average wear rate data of each node on the wall of the bridge pile foundation of the Fluent numerical model are extracted and stored as a data set Data2; the data set Data2 of the average wear rate data is triangulated using a three-dimensional surface Delaunay triangulation to obtain a surface SU2; the pile foundation target unit node P(x, y) and the pile foundation target unit center P of the FEM numerical model are searched from the surface SU2. c (x c ,y c ) and estimate the average erosion rate E of the target unit node P(x,y) of the pile foundation according to the area weight interpolation formula. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C , the specific steps are as follows:

[0183]

[0184] Where E P,1 、E P,2 、E P,3 are the average abrasion rates of the three vertices of the triangle where the target unit node P(x, y) of the pile foundation is located, A P is the total area of ​​the triangle where the target unit node P(x,y) is located, They are the areas of three small triangles formed by the three vertices of the triangle where the target unit node P(x, y) is located and the line connecting the target unit node P(x, y);

[0185]

[0186] Where E C,1 、E C,2 、E C,3 are the target unit center P of the pile foundation respectively. c (x c ,y c ) is the average abrasion rate of the three vertices of the triangle, A C is the target unit center of pile foundation c (x c ,y c ) is the total area of ​​the triangle where are the target unit center P of the pile foundation respectively. c (x c ,y c ) and the three vertices of the triangle where the pile foundation target unit center P c (x c ,y c)The area of ​​the three small triangles formed by the connecting lines.

[0187] For the pile target unit nodes P(x, y) and pile target unit centers P that are not included in the triangular plane obtained by Delaunay triangulation of the three-dimensional surface c (x c ,y c ), search for the triangle ΔP1P2P3 that is coplanar with the triangular plane obtained by the three-dimensional Delaunay triangulation of the surface, and divide the exterior of the triangle ΔP1P2P3 into the following six areas: the external area Ω1 of the edge P1P2, the external area Ω3 of the edge P2P3, the external area Ω5 of the edge P1P3, the external area Ω6 of the vertex P1, the external area Ω2 of the vertex P2, and the external area Ω4 of the vertex P3.

[0188] like Figure 3 As shown in the figure, when the pile foundation target unit node P(x, y) and the pile foundation target unit center P c (x c ,y c ) is outside the side of the coplanar triangle ΔP1P2P3:

[0189] Assume the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the coplanar triangle ΔP1P2P3 side P1P2 (i.e., region Ω1), and intersects with side P1P2 at point O. The angle between straight line PP3 and P1P2 is α. The average erosion rate E of the target unit node P(x, y) of the pile foundation is obtained by linear interpolation theory. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0190]

[0191] in, are the areas of ΔPP2P3, ΔPP1P3, ΔPP1P2, and ΔP1P2P3 respectively, are the average erosion rates of the three vertices of the triangle coplanar with the target unit node P(x,y) of the pile foundation, They are △P c P2P3, △P c P1P3, △P c The area of ​​P1P2, are the target unit center P of the pile foundation respectively. c (x c ,yc ) the average abrasion rate of the three vertices of a coplanar triangle;

[0192] in The calculation formula is as follows:

[0193]

[0194] Similarly, when the target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the edge P2P3 (region Ω3), the average erosion rate E of the target unit node P(x, y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0195]

[0196] Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the area Ω5 outside P1P3, the average erosion rate E of the target unit node P(x, y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0197]

[0198] like Figure 4 As shown in the figure, when the pile foundation target unit node P(x, y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertex of the coplanar triangle ΔP1P2P3, the average erosion rate E of the target unit node P(x,y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The specific steps are as follows:

[0199] Assume the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c) is located outside the vertex P2 of the coplanar triangle ΔP1P2P3 (i.e., area Ω2), and PP2 is extended to intersect with P1P3 at point O, with an angle of α. The average erosion rate E of the target unit node P(x, y) of the pile foundation is obtained by linear interpolation theory. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0200]

[0201] in, are the areas of ΔPP1P3, ΔPP1P2, ΔPP2P3 and ΔP1P2P3 respectively, are the average erosion rates of the three vertices of the triangle coplanar with the target unit node P(x,y) of the pile foundation, are the target unit center P of the pile foundation respectively. c (x c ,y c ) the average abrasion rate of the three vertices of a coplanar triangle;

[0202] Among them, the area calculation formulas of ΔPP1P3, ΔPP1P2, ΔPP2P3 and ΔP1P2P3 are as follows:

[0203]

[0204] Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertex P3 (region Ω4), the average erosion rate E of the pile foundation target unit node P(x, y) P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

[0205]

[0206] Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertex P1 (region Ω6), the average erosion rate E of the pile foundation target unit node P(x, y) P and the pile foundation target unit center P c (x c ,yc ) average abrasion rate E C The calculation formulas are:

[0207]

[0208] The average erosion rate E of the target unit node of the pile foundation in the structural domain is estimated by the aforementioned linear interpolation formula inside and outside the triangle. P and the average erosion rate E at the center of the target unit of the pile foundation C , and then calculate the total average abrasion rate of the target unit in the structure domain according to the following feature point collaborative interpolation algorithm:

[0209]

[0210] Among them, E avg 、E C 、E P 、E i They are the total average abrasion rate of the structural domain target unit, the average abrasion rate of the pile foundation target unit center, the final average abrasion rate of the pile foundation target unit node, and the average abrasion rate of each surface node of the target unit, all in kg / (m 2 ·s); γ∈[0,1] is the weight coefficient, the theoretical value is 2 / 3, and the theoretical value is determined by Simpson's formula.

[0211] The total average wear rate E of the target unit in the structural domain is calculated according to the aforementioned feature point collaborative interpolation algorithm. avg , the annual average abrasion thickness of the target unit in the structural domain is calculated as follows:

[0212]

[0213] Among them, h avg,a is the annual average abrasion thickness, E m is the average abrasion mass (kg / s), R is the radius of the pile foundation before abrasion (m); H is the height of the pile foundation (m), T is the total time of the flood period (s), and the flood period is from June to August each year. t is the total abrasion mass of the pile foundation during the flood period each year (kg), r is the equivalent radius of the pile foundation after abrasion (m), and V is the total volume of the pile foundation abraded (m 3 ), ρ is the pile density (kg / m 3 ).

[0214] According to the Fluent pile foundation abrasion range and the annual average abrasion thickness of the structural domain target unit h avg,a , based on the current abrasion thickness and the distance between the centers of each unit, the pile foundation units that should be passivated in the FEM numerical model during the simulated abrasion process are screened and stored as the unit set ELSet2.

[0215] The wave and flow forces of the target unit in the structural domain are calculated based on the linear interpolation formula inside and outside the triangle and the collaborative interpolation algorithm of characteristic points.

[0216] The specific steps for calculating the wave and flow forces at each node of the target unit in the structure domain are as follows:

[0217] For the target unit node in the structural domain contained in the triangular surface formed by the triangulation of the pile foundation mesh node in the fluid domain, the calculation formula is as follows:

[0218]

[0219] Where F is the wave flow force at the node of the structure domain; A F is the area of ​​the current fluid domain triangle, A1 F , They are the areas of each triangle after the structure domain node divides the fluid domain triangle; F1, F2, and F3 are the wave and flow force data of each vertex of the fluid domain triangle;

[0220] For the structural domain nodes that are not included in the triangular surface formed by the triangulation of the pile foundation mesh nodes in the fluid domain,

[0221] When the structural domain node is located outside the coplanar triangle edge, the target unit node P(x, y) is located in the area Ω1 outside the coplanar triangle ΔP1P2P3 edge P1P2, and intersects with the edge P1P2 at point O. The angle between the straight line PP3 and P1P2 is α. The wave flow force of the target unit node P(x, y) is obtained by linear interpolation theory:

[0222]

[0223] Among them, F1, F2, and F3 are the wave and flow force data of each vertex of the fluid domain triangle;

[0224] Similarly, when the target unit node P(x, y) is located in the area Ω3 outside the edge P2P3 and in the area Ω5 outside the edge P1P3, the wave flow force calculation formulas are:

[0225]

[0226] When the structural domain node is located outside the vertex of the coplanar triangle, the target unit node P(x, y) is located in the area Ω2 outside the vertex P2 of the coplanar triangle ΔP1P2P3, and PP2 is extended to intersect with P1P3 at point O, with an angle of α. The wave flow force of the target unit node P(x, y) is obtained by linear interpolation theory:

[0227]

[0228] Similarly, when the target unit node P(x, y) is located in the region Ω4 outside the vertex P3 and in the region Ω6 outside P1, the wave flow force calculation formulas are:

[0229]

[0230] The multi-hazard numerical model construction module, based on the life and death unit function of ABAQUS, passivates the corresponding soil units and pile foundation units in the FEM numerical model of rockfall impact bridges, applies corresponding wave and flow forces, and constructs a multi-hazard combined numerical model.

[0231] Specifically, a designated scour analysis step is created for the scour process in the FEM numerical model, and the soil units in the unit set ELSet1 are gradually passivated using the birth and death unit function according to the actual scour process; in each scour analysis step in the FEM numerical model, the pile foundation units in the unit set ELSet2 are gradually passivated using the birth and death unit function according to the actual erosion process; in each scour analysis step in the FEM numerical model, wave flow force is applied to the pile foundation target unit; based on the FEM numerical model that has considered the scour and abrasion effects, a designated rockfall impact analysis step is created for the rockfall impact bridge, and a numerical model of the rockfall impact mountain bridge that finally considers the scour and abrasion effects is constructed.

Claims

1. A numerical simulation method for the combined action of multiple disasters on bridges based on triangulation and collaborative interpolation of characteristic points, characterized by: The following steps are involved: A CFD numerical model of mountain highway bridge foundation scour was built based on REEF3D, and a FEM numerical model of rockfall impact on bridge piers was built based on ABAQUS. Get the simulation data of REEF3D scour, use two-dimensional Delaunay triangulation and triangle internal linear interpolation theory to process the simulation data, get the structural domain scour depth data, and select the soil units that should be passivated in the FEM numerical model; When the scour depth data in REEF3D reaches the set value, the corresponding scour terrain data is extracted and the Fluent numerical model of pile foundation erosion is constructed; The abrasion rate and wave-current force data obtained from the abrasion simulation are obtained, and the abrasion rate and wave-current force data are processed by using the three-dimensional surface Delaunay triangulation combined with the inner and outer linear interpolation theory of the triangle and the characteristic point collaborative interpolation algorithm, and the pile foundation units that should be passivated at each abrasion stage in the FEM numerical model are selected, and the wave-current force that should be applied to each pile foundation unit is calculated; Based on the life and death unit function of ABAQUS, the corresponding soil units and pile foundation units are passivated in the FEM numerical model of rockfall impact bridge, and the corresponding wave and flow forces are applied to construct a numerical model of multi-hazard combined action.

2. The method for numerical simulation of multi-hazard combined effects on bridges based on triangulation and feature point collaborative interpolation according to claim 1 is characterized by: The specific steps for selecting soil elements that should be passivated in the FEM numerical model are as follows: Extract the riverbed scour depth data in the local area around the REEF3D foundation and store it as data set Data1; The data set Data1 is triangulated using two-dimensional Delaunay triangulation to obtain the surface SU1; The center P of the target soil unit for which scour depth data is to be extracted in the FEM numerical model is g (x, y) is mapped to the surface SU1 to obtain the target soil unit center P g The three vertices P1 of the triangular plane where (x,y) is located g (x1,y1), Calculate the target soil unit center P g (x,y) scour depth data; Target soil unit center P g The (x,y) scour depth z is estimated by interpolation: Among them, z1, z2, and z3 are vertex P1 respectively. g (x1,y1), The scouring depth, A is The total area of ​​A1, A2 and A3 are area; According to the calculated target soil unit center P g The scour depth data of (x, y) is used to select the soil elements that should be passivated in the FEM numerical model during the foundation scour simulation based on the current scour depth and the distance between the upper and lower soil elements, and store them as the element set ELSet1.

3. The method for numerical simulation of multi-hazard combined effects on bridges based on triangulation and feature point collaborative interpolation according to claim 2 is characterized by: The specific steps to construct the Fluent numerical model of pile foundation erosion are as follows: Extract the scour depth up to z in REEF3D i =0.8z max The terrain data at that time was used to construct the Fluent numerical model of pile foundation erosion under the coupling of water and sand in the CFD numerical model; max Refers to the equilibrium scour depth.

4. The method for numerical simulation of multi-hazard combined effects on bridges based on triangulation and feature point collaborative interpolation according to claim 1, characterized in that: The specific steps for selecting pile foundation elements that should be passivated at each erosion stage in the FEM numerical model are as follows: The average abrasion rate data of each node on the bridge pile foundation wall in the Fluent numerical model is extracted and stored as data set Data2; The three-dimensional surface Delaunay triangulation is used to triangulate the data set Data2 to obtain the surface SU2. The pile foundation target unit node P(x, y) and the pile foundation target unit center P of the FEM numerical model are searched in the surface SU2. c (x c ,y c ) are located in the respective triangular planes, and the average erosion rate E of the target unit node P(x, y) of the pile foundation is calculated by weight. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C ; For the pile-based target unit nodes P(x, y) and pile-based target unit centers P of the triangular plane obtained by Delaunay triangulation of the surface not included in the three-dimensional c (x c ,y c ), search for the triangle ΔP1P2P3 that is coplanar with the triangular plane obtained by the three-dimensional surface Delaunay triangulation, divide the outside of the triangle ΔP1P2P3 into 6 areas: the external area Ω1 of the edge P1P2, the external area Ω3 of the edge P2P3, the external area Ω5 of the edge P1P3, the external area Ω6 of the vertex P1, the external area Ω2 of the vertex P2 and the external area Ω4 of the vertex P3, and determine the pile foundation target unit node P(x, y) and the pile foundation target unit center P c (x c ,y c ) belongs to the external area, and calculate the average erosion rate E of the target unit node P(x,y) of the pile foundation respectively P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C ; The average erosion rate E based on the target unit node P(x,y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C Calculate the total average erosion rate E of the target unit in the structural domain avg ; The total average wear rate E based on the structural domain target unit avg , calculate the annual average abrasion thickness h of the target unit in the structural domain avg,a ; The annual average abrasion thickness h based on the structural domain target unit avg,a , based on the current abrasion thickness and the distance between the centers of each unit, the pile foundation units that should be passivated in the FEM numerical model during the simulated abrasion process are selected and stored as the unit set ELSet2; The method for calculating the wave-flow force that should be applied to each pile foundation unit is as follows: the wave-flow force of each node of the target unit in the structural domain is calculated based on the wave-flow force of the pile foundation grid nodes in the fluid domain by using the linear interpolation formula inside and outside the triangle and the characteristic point collaborative interpolation algorithm.

5. The method for numerical simulation of the combined effects of multiple disasters on bridges based on triangulation and feature point collaborative interpolation according to claim 4 is characterized by: Weighted calculation of the average erosion rate E of the target unit node P(x,y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The specific steps are as follows: Where E P,1 、E P,2 、E P,3 are the average abrasion rates of the three vertices of the triangle where the target unit node P(x, y) of the pile foundation is located, A P is the total area of ​​the triangle where the target unit node P(x,y) is located, They are the areas of three small triangles formed by the three vertices of the triangle where the target unit node P(x, y) is located and the line connecting the target unit node P(x, y); Where E C,1 、E C,2 、E C,3 are the target unit center P of the pile foundation respectively. c (x c ,y c ) is the average abrasion rate of the three vertices of the triangle, A C is the target unit center of pile foundation c (x c ,y c ) is the total area of ​​the triangle where are the target unit center P of the pile foundation respectively. c (x c ,y c ) and the three vertices of the triangle where the pile foundation target unit center P c (x c ,y c )The area of ​​the three small triangles formed by the connecting lines.

6. The method for numerical simulation of multi-hazard combined effects on bridges based on triangulation and feature point collaborative interpolation according to claim 4, characterized in that: For the pile-based target unit nodes P(x, y) and pile-based target unit centers P of the triangular plane obtained by Delaunay triangulation of the surface not included in the three-dimensional c (x c ,y c ), when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the edge of the coplanar triangle ΔP1P2P3, the average erosion rate E of the target unit node P(x,y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The specific steps are as follows: Assume the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the outer area Ω1 of the coplanar triangle ΔP1P2P3 side P1P2, and intersects with the side P1P2 at point O. The angle between the straight line PP3 and P1P2 is α. The average erosion rate E of the target unit node P(x, y) of the pile foundation is obtained by linear interpolation theory. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are: in, are the areas of ΔPP2P3, ΔPP1P3, ΔPP1P2, and ΔP1P2P3 respectively, The average erosion rate of the three vertices of the triangle coplanar with the pile target unit node P(x,y), They are △P c P2P3, △P c P1P3, △P c The area of ​​P1P2, and the pile foundation target unit center P c (x c ,y c ) the average abrasion rate of the three vertices of a coplanar triangle; Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the outer area Ω3 of the edge P2P3, the average erosion rate E of the target unit node P(x, y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are: Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the area Ω5 outside P1P3, the average erosion rate E of the target unit node P(x, y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are: When the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertex of the coplanar triangle ΔP1P2P3, the average erosion rate E of the target unit node P(x,y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The specific steps are as follows: Assume the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the outer area Ω2 of the vertex P2 of the coplanar triangle ΔP1P2P3. The extended PP2 intersects with P1P3 at point O, and the angle is α. The average erosion rate E of the target unit node P(x, y) of the pile foundation is obtained by linear interpolation theory. P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are: in, are the areas of ΔPP1P3, ΔPP1P2, ΔPP2P3 and ΔP1P2P3 respectively, The average erosion rate of the three vertices of the triangle coplanar with the pile target unit node P(x,y), and the pile foundation target unit center P c (x c ,y c ) the average abrasion rate of the three vertices of a coplanar triangle; Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located in the region Ω4 outside the vertex P3, the average erosion rate E of the target unit node P(x, y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are: Similarly, when the pile foundation target unit node P(x,y) and the pile foundation target unit center P c (x c ,y c ) is located outside the vertex and within the area Ω6 outside P1, the average erosion rate E of the target unit node P(x, y) of the pile foundation P and the pile foundation target unit center P c (x c ,y c ) average abrasion rate E C The calculation formulas are:

7. The method for numerical simulation of multi-hazard combined effects on bridges based on triangulation and feature point collaborative interpolation according to claim 4, characterized in that: Calculate the total average erosion rate E of the target unit in the structure domain avg The specific steps are as follows: The average erosion rate E of the target unit node of the structural domain pile foundation is estimated by using the linear interpolation formula inside and outside the triangle. P and the average erosion rate E of the target unit center of the pile foundation in the structural domain C , calculate the total average erosion rate E of the target unit in the structure domain according to the following feature point collaborative interpolation algorithm: avg : Among them, E C 、E P 、E i They are the average abrasion rate at the center of the pile foundation target unit, the final average abrasion rate at the nodes of the pile foundation target unit, and the average abrasion rate at each surface node of the target unit, all in kg / (m 2 ·s); γ∈[0,1] is the weight coefficient; Calculate the annual average abrasion thickness h of the target unit in the structural domain avg,a The formula group is as follows: Among them, Em is the average abrasion mass, in kg / s; R is the radius of the pile foundation before abrasion, in m; T is the total time of the flood period, in s; Et is the total abrasion mass of the pile foundation during the annual flood period, in kg; r is the equivalent radius of the pile foundation after abrasion, in m; V is the total volume of the pile foundation abraded, in m3; ρ is the density of the pile foundation, in kg / m3.

8. The method for numerical simulation of multi-hazard combined effects on bridges based on triangulation and feature point collaborative interpolation according to claim 4, characterized in that: The specific steps for calculating the wave and flow forces at each node of the target unit in the structure domain are as follows: For the target unit node in the structural domain contained in the triangular surface formed by the triangulation of the pile foundation mesh node in the fluid domain, the calculation formula is as follows: Where F is the wave flow force at the node of the structure domain, A F is the area of ​​the current fluid domain triangle, They are the areas of each triangle after the structure domain node divides the fluid domain triangle, and F1, F2, and F3 are the wave and flow force data of each vertex of the fluid domain triangle; For the structural domain nodes that are not included in the triangular faces formed by the triangulation of the pile foundation mesh nodes in the fluid domain, When the structural domain node is located outside the coplanar triangle edge, the target unit node P(x, y) is located in the area Ω1 outside the coplanar triangle ΔP1P2P3 edge P1P2, and intersects with the edge P1P2 at point O. The angle between the straight line PP3 and P1P2 is α. The wave flow force of the target unit node P(x, y) is obtained by linear interpolation theory: Among them, F1, F2, and F3 are the wave and flow force data of each vertex of the fluid domain triangle; Similarly, when the target unit node P(x, y) is located in the area Ω3 outside the edge P2P3 and in the area Ω5 outside the edge P1P3, the wave flow force calculation formulas are: When the structural domain node is located outside the vertex of the coplanar triangle, the target unit node P(x, y) is located in the area Ω2 outside the vertex P2 of the coplanar triangle ΔP1P2P3, and PP2 is extended to intersect with P1P3 at point O, with an angle of α. The wave flow force of the target unit node P(x, y) is obtained by linear interpolation theory: Similarly, when the target unit node P(x, y) is located in the region Ω4 outside the vertex P3 and in the region Ω6 outside P1, the wave flow force calculation formulas are:

9. The method for numerical simulation of multi-hazard combined effects on bridges based on triangulation and feature point collaborative interpolation according to claim 1, characterized in that: The specific steps of constructing a numerical model of multi-hazard combined effects are as follows: In the FEM numerical model, a designated scouring analysis step is created for the scouring process, and according to the actual scouring process, the soil elements in the element set ELSet1 are gradually passivated using the birth and death element function; In each scour analysis step in the FEM numerical model, the pile foundation elements in the element set ELSet2 are gradually passivated using the birth and death element function according to the actual erosion process; In each scour analysis step in the FEM numerical model, wave flow force is applied to the target unit of the pile foundation; Based on the FEM numerical model that has considered the scouring and abrasion effects, a specified rockfall impact analysis step is created for the rockfall impact bridge, and a numerical model of the rockfall impact bridge considering the scouring and abrasion effects is constructed.

10. A numerical simulation system for the combined effects of multiple disasters on bridges based on triangulation and collaborative interpolation of characteristic points, characterized by: include: Initial numerical model building module, builds a CFD numerical model of mountain highway bridge foundation scour based on REEF3D, and builds a FEM numerical model of rockfall impact on bridge piers based on ABAQUS; The first processing module is used to obtain the simulation data of REEF3D scour, and use two-dimensional Delaunay triangulation and triangle internal linear interpolation theory to process the simulation data to obtain the structural domain scour depth data and screen the soil units that should be passivated in the FEM numerical model; The second disaster numerical construction module, when the scour depth data in REEF3D reaches the set value, extracts the corresponding scour terrain data and constructs the Fluent numerical model of pile foundation erosion; The second processing module is used to obtain the abrasion rate and wave-current force data obtained by the abrasion simulation, and process the abrasion rate and wave-current force data by using the three-dimensional surface Delaunay triangulation combined with the inner and outer linear interpolation theory of the triangle and the characteristic point collaborative interpolation algorithm, to select the pile foundation units that should be passivated at each abrasion stage in the FEM numerical model, and calculate the wave-current force that should be applied to each pile foundation unit; The multi-hazard numerical model construction module, based on the life and death unit function of ABAQUS, passivates the corresponding soil units and pile foundation units in the FEM numerical model of rockfall impact bridges, applies corresponding wave and flow forces, and constructs a multi-hazard combined numerical model.

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