Bridge pier pile erosion model and simulation method and system based on SPH smooth particles

Abstract

The application discloses a bridge pier pile erosion model and simulation method and system based on SPH smooth particles, which comprises the following steps: defining the range of a calculation domain, setting an import and export boundary based on the range; constructing a water-sand mixture and pier particles, and giving the particles constitutions and types; performing coupling calculation on the water-sand mixture particles, based on selected particles, searching all particles within the radius range of a single particle kernel function, performing viscous stress coupling calculation, and updating the velocity and position information of the selected particles; cyclically traversing all pier wall particles, judging whether there are water-sand mixture particles within the radius range of a single boundary particle kernel function, combining the velocity and position pos information of the mixture particles, calculating the abrasion rate of the pier wall within a specified solution time based on an improved erosion formula; converting the abrasion rate into an abrasion mass, judging whether the particle is deleted or not; and repeating iteration until a specified solution time is reached. The application can more accurately simulate the erosion of a bridge pier pile structure.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of bridge pier erosion simulation, and particularly relates to a bridge pier erosion model and simulation method and system based on SPH smooth particles. BACKGROUND

[0002] Many mountainous bridges are built on rivers and canyons, and natural disasters such as earthquakes, floods and mudslides often occur in the bridge site area of such mountainous bridges. The boulders, sand and other solid impurities mixed in the high-speed water flow will cause continuous transient impact and cutting action on the pier structure of the bridge, thereby causing uneven peeling of the concrete protective layer of the pier structure, and more seriously, causing the reinforcement and aggregate in some areas to be exposed, forming typical bridge erosion characteristics. Long-term erosion will greatly reduce the bearing capacity of the pier structure, and it is necessary to simulate the bridge pier erosion to guide the design of the pier structure. The existing numerical simulation of bridge pier erosion is mostly based on the CFD method, but the accuracy of the method depends on the accuracy of the grid, and it cannot accurately process complex boundaries such as dynamic deletion of wall particles.

[0003] Therefore, it is urgent to solve the above problems. SUMMARY

[0004] The purpose of the application is to provide a bridge pier erosion model and simulation method based on SPH smooth particles, which can more accurately simulate the erosion of the bridge pier structure.

[0005] Technical scheme: To achieve the above purpose, the application discloses a bridge pier erosion model and simulation method based on SPH smooth particles, comprising the following steps:

[0006] S1, define the range of the calculation domain, and set the import and export boundaries based on the set calculation domain range;

[0007] S2, based on the non-Newtonian fluid theory, construct water-sand mixture particles; at the same time, construct pier wall particles; then give different type labels to the water-sand mixture particles and the pier wall particles respectively;

[0008] S3, perform coupling calculation on the water-sand mixture particles in the calculation domain, based on the selected particles, sequentially search all particles within the radius range of the individual particle kernel function, according to the searched particle type label, call the corresponding particle viscosity and the searched particle for viscous stress coupling calculation, and update the velocity and position pos information of the selected particle;

[0009] S4, loop through all the pier wall particles, for a single boundary particle p1, judge whether there is a water-sand mixture particle in the core function radius range, combine the velocity and position pos information of the mixture particle obtained in step S3, based on the improved SPH form Neilson-Gilchrist erosion formula, obtain the discrete form under SPH, calculate the erosion rate of the pier wall within the specified solving time;

[0010] S5, convert the erosion rate into erosion mass, compare the erosion mass with the mass of a single particle, and determine whether the particle is deleted;

[0011] S6, repeat steps S3 to S5 until the specified solving time is reached.

[0012] Optionally, step S1 specifically includes the following steps: defining the range of the calculation domain, specifying that the distance of each side boundary from the center of the pier is at least 5 times the diameter of the pier, or specifying that the distance of each side boundary from the center of the pier is at least 5 times the length of the long side of the section; set the calculation domain as a semi-closed space, i.e. only set the outlet boundary, when the fluid particle exceeds the boundary range, the particle is automatically deleted; then based on the range of the calculation domain, set the size of the water-sand mixture, require the width of the water-sand mixture to be consistent with the width of the calculation domain; set the size and shape of the pier according to the actual situation, and the center is located on the symmetry axis of the calculation domain width.

[0013] Optionally, step S2 specifically includes the following steps:

[0014] S2.1, disperse the water-sand mixture into fluid particles, assign the material parameters of the HBP model, and calculate the apparent viscosity of the fluid according to the following formula, the particle type index of the water-sand mixture is mk1:

[0015]

[0016] In the formula, μ ori is the apparent viscosity of the water-sand mixture; μ is the viscosity coefficient; n is the Herschel-Bulkley power index parameter, which is related to the shear stress; m is the Papanastasiou parameter, which controls the stress index growth rate, so that the stress remains at a small shear rate in the unyielding area and remains linear growth in the yielded area; Π D is a second-order invariant shear strain rate tensor; τ c is the material yield strength;

[0017] S2.2, disperse the pier into wall boundary particles, and the particle type index of the pier is mk2.

[0018] Optionally, step S3 specifically includes the following steps:

[0019] S3.1, coupling calculation is performed on water-sand mixture particles in the basin, the water-sand mixture particles are controlled according to the Navier-Stokes equation, and the SPH discrete form of the mass conservation equation is:

[0020]

[0021] In the formula, subscript a represents a central particle; subscript b represents a field particle; m b is the mass of the field particle; is the Hamiltonian operator for the central particle; p a represents the density of the central particle; p b represents the density of the field particle; u ab is the velocity difference between the central particle and the field particle, and W is the kernel function;

[0022] The SPS term is introduced, and the discrete momentum conservation equation is:

[0023]

[0024] In the formula, μ0 is the kinematic viscosity; t ij is the SPS stress vector; u a is the velocity of the central particle; P a is the pressure of the central particle; P b is the pressure of the field particle; g is the acceleration of gravity; r ab is the distance between the central particle and the field particle, and η is the smoothing length; is the stress vector of the central particle; is the stress vector of the field particle;

[0025] S3.2, for all particles numbered mk1, repeat step S3.1 to perform density and viscous stress coupling calculation, and update the velocity v and position pos information of the selected particles.

[0026] Optionally, step S4 specifically includes the following steps:

[0027] S4.1, loop through all pier wall particles mk2, judge whether there is a water-sand mixture particle in the kernel function radius range, and calculate the impact angle between the wall particle and the mixture particle according to the position pos information of the mixture particle obtained in step S3 according to the following formula:

[0028] θ i = arccos (||v i · n j ||)

[0029] In the formula, v i is the unit velocity normal vector of the water-sand mixture particle i; θi is the impact angle between the two types of particles; n j is the unit outer normal vector of the wall particle j, which is determined based on its relative position information to the center of the circle:

[0030] n j = pos j -pos o

[0031] In the formula, pos j is the position array of the corresponding particle j in the XY plane; pos o is the position array of the center of gravity of the pier in the XY plane;

[0032] S4.2, in combination with the velocity information of the mixture particles obtained in step S3, for the wall particle j, based on the improved SPH form Neilson-Gilchrist erosion formula, the SPH discrete form is obtained, and the erosion rate E of each pier wall particle in a specified solving time is calculated r,j :

[0033]

[0034] In the formula, W is the kernel function; V i is the volume of particle i; E ij is the erosion rate of the fluid particle i within the kernel function radius range of the boundary particle j, which is calculated by using the improved SPH form Neilson-Gilchrist erosion formula:

[0035]

[0036] In the formula, u p,i is the velocity of the fluid particle i colliding with the wall particle j; u r,i is the rebound velocity of the i-th mixture particle colliding with the wall particle; ε D is the deformation coefficient, which is determined by experiment; ε C is the cutting coefficient, which is determined by experiment; S is the compressive strength of concrete, and ω is the roundness coefficient of the sediment particles, where C1 is the circumference of the vertical projection of the sand particles, and C2 is the circumference of the largest inscribed circle in the vertical projection of the sand particles.

[0037] Optionally, step S5 specifically includes the following steps:

[0038] S5.1, based on the erosion rate of step S4, the erosion mass of the boundary particle j is converted:

[0039]

[0040] In the formula, S jis the total erosion mass of the boundary particle j in a year; T is the total time of flood period; E2 is the total erosion mass of the boundary particle j in a flood period per year;

[0041] S5.2, comparing E2 with the mass m of the wall particle j j if E2 >= m j then the wall particle is deleted; if E2 < m j then the wall particle is retained.

[0042] Based on the same inventive concept, the application discloses a bridge pier pile erosion model and simulation system based on SPH smooth particles, which comprises the following steps:

[0043] A preprocessing module is used for defining the range of the calculation domain, setting the import and export boundaries based on the set calculation domain range, constructing water-sand mixture particles based on the non-Newtonian fluid theory, simultaneously constructing pier pile wall particles, and then giving different type labels to the water-sand mixture particles and the pier pile wall particles respectively.

[0044] A control equation solving module is used for coupling calculation of the water-sand mixture particles in the calculation domain, searching all particles within the kernel function radius range of a single particle in turn based on the selected particles, calling the corresponding particle viscosity and the searched particles for viscous stress coupling calculation according to the searched particle type label, and updating the velocity and position pos information of the selected particles.

[0045] An erosion rate calculation module is used for cyclically traversing all pier pile wall particles, judging whether there is a water-sand mixture particle within the kernel function radius range of a single boundary particle p1, combining the velocity and position pos information of the mixture particles obtained in step S3, obtaining the discrete form under SPH based on the improved SPH form Neilson-Gilchrist erosion formula, and calculating the erosion rate of the pier pile wall within a specified solving time.

[0046] A live and dead particle module is used for converting the erosion rate into erosion mass, comparing the erosion mass with the mass of a single particle, and judging whether the particle is deleted.

[0047] An iteration module is used for repeatedly executing the control equation solving module, the erosion rate calculation module and the live and dead particle module until a specified solving time is reached.

[0048] Optionally, the water-sand mixture is discretized into fluid particles in the preprocessing module, material parameters of the HBP model are given, and the apparent viscosity of the fluid is calculated according to the following formula, and the particle type label of the water-sand mixture is mk1:

[0049]

[0050] In the formula, mu oriis the apparent viscosity of the water-sand mixture; μ is the viscosity coefficient; n is the Herschel-Bulkley power index parameter, which is related to the shear stress; m is the Papanastasiou parameter, which controls the stress index growth rate, so that the stress remains at a small shear rate in the unyielding region and linearly increases in the yielded region; Π D is a second-order invariant shear strain rate tensor; τ c is the material yield strength;

[0051] The pier pile is discretized into wall boundary particles, and the particle type label of the pier pile is mk2.

[0052] Optionally, the water-sand mixture particles in the flow domain are coupled and calculated in the control equation solving module, and the water-sand mixture particles are controlled in motion according to the Navier-Stokes equation, and the SPH discrete form of the mass conservation equation is:

[0053]

[0054] In the formula, subscript a represents a center particle; subscript b represents a field particle; m b is the mass of the field particle; is the Hamilton operator for the center particle; ρ a represents the density of the center particle; ρ b represents the density of the field particle; u ab is the velocity difference between the center particle and the field particle, and W is the kernel function;

[0055] The SPS term is introduced, and the momentum conservation equation is discretized as:

[0056]

[0057] In the formula, μ0 is the kinematic viscosity; τ ij is the SPS stress vector; u a is the velocity of the center particle; P a is the pressure of the center particle; P b is the pressure of the field particle; g is the acceleration of gravity; r ab is the distance between the center particle and the field particle, and η is the smoothing length; is the stress vector of the center particle; is the stress vector of the field particle;

[0058] For all particles numbered mk1, the density and viscous stress coupling calculation is repeated, and the velocity v and position pos information of the selected particles are updated.

[0059] Optionally, the abrasion rate calculation module iterates through all pier wall particles mk2, judges whether there are water-sand mixture particles within the kernel function radius range, and calculates the impact angle between the wall particles and the mixture particles according to the position pos information of the mixture particles obtained by the control equation solving module according to the following formula:

[0060] θ i = arccos (‖v i ·n j ‖)

[0061] In the formula, v i is the unit speed normal vector of the water-sand mixture particle i; θ i is the impact angle between the two types of particles; n j is the unit outer normal vector of the wall particle j, which is determined based on its relative position information from the center:

[0062] n j = pos j -pos o

[0063] In the formula, pos j is the position array of the corresponding particle j in the XY plane; pos o is the position array of the pier center of gravity in the XY plane;

[0064] Combined with the speed information of the mixture particles obtained by the control equation solving module, for the wall particle j, the SPH discrete form is obtained based on the improved SPH form Neilson-Gilchrist erosion formula, and the abrasion rate E r,j of each pier wall particle within the specified solving time is calculated.

[0065]

[0066] In the formula, W is the kernel function; V i is the volume of particle i; E ij is the abrasion rate of the fluid particle i within the kernel function radius range of the boundary particle j, which is calculated using the improved SPH form Neilson-Gilchrist erosion formula:

[0067]

[0068] In the formula, u p,i is the speed of the fluid particle i colliding with the wall particle j; u r,i is the rebound speed of the i-th mixture particle colliding with the wall particle; ε D is a deformation coefficient determined by experiment; ε C is a cutting coefficient determined by experiment; S is the compressive strength of concrete, and ω is the roundness coefficient of the sediment particles. Where C1 is the perimeter of the vertical projection of the sand grain, and C2 is the perimeter of the largest inscribed circle in the vertical projection of the sand grain.

[0069] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: The present invention is based on the SPH theory and is developed in a secondary manner. By introducing the abrasion rate calculation formula, it achieves the purpose of numerical simulation of bridge pier erosion based on the meshless method, and has the characteristics of high accuracy and strong operability; The present invention performs numerical simulation of bridge pier erosion based on the SPH theory. By introducing the mass-based birth and death particle discrimination criterion, it can realize the dynamic change of the structural boundary during the pier erosion simulation process, thereby considering the influence of the dynamic boundary of the structure on abrasion in the erosion simulation and improving the accuracy of numerical simulation. Attached Figure Description

[0070] Figure 1 This is a flowchart of the present invention;

[0071] Figure 2 This is a schematic diagram of the included angle between the two types of particles in this invention;

[0072] Figure 3 This is a schematic diagram of the radius range of the kernel function in this invention. Detailed Implementation

[0073] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0074] Example 1

[0075] like Figure 1 As shown, a bridge pier pile erosion model and simulation method based on SPH smooth particles includes the following steps:

[0076] S1. Define the scope of the computational domain and give the boundary conditions of the simulation region; at the same time, based on the scope of the computational domain, set the inlet and outlet boundaries, set the size of the water-sand mixture, and determine the geometry of the pier piles;

[0077] Specifically, the scope of the computational domain is defined, stipulating that the distance from each side boundary to the center of the pier pile is at least 5 times the diameter of the pier pile, or that the distance from each side boundary to the center of the pier pile is at least 5 times the length of the long side of the cross section; an inlet boundary is set, allowing continuous injection of water-sand mixture particles within a specified time, while an outlet boundary is set, automatically deleting particles that exceed this boundary range; then, based on the scope of the computational domain, the size of the water-sand mixture is set, requiring that the width of the water-sand mixture be consistent with the width of the computational domain, and that the volume satisfy the requirement that the abrasion rate of the pier pile can reach periodic stability within the solution time; the size and shape of the pier pile are set according to the actual situation, with its center located on the axis of symmetry of the width of the computational domain;

[0078] S2, based on the theory of non-Newtonian fluid, construct water-sand mixture particles, and construct pier wall particles at the same time; then respectively give different type labels to water-sand mixture particles and pier wall particles: preset water-sand mixture as non-Newtonian fluid, type label of water-sand mixture particles as mk1, preset pier as solid, type label of pier wall particles as mk2;

[0079] Step S2 includes the following specific steps:

[0080] S2.1, discretize the water-sand mixture into fluid particles, give material parameters of the HBP model, and calculate the apparent viscosity of the fluid according to the following formula, the particle type label of the water-sand mixture is mk1:

[0081]

[0082] In the formula, μ ori is the apparent viscosity of the water-sand mixture; μ is the viscosity coefficient; n is the Herschel-Bulkley power index parameter, which is related to the shear stress; m is the Papanastasiou parameter, which controls the stress index growth rate, so that the stress remains at a small shear rate in the unyielding area and remains linear growth in the yielded area; Π D is the second-order invariant shear strain rate tensor; τ c is the material yield strength;

[0083] S2.2, discretize the pier into wall boundary particles, and the particle type label of the pier is mk2;

[0084] S3, perform coupling calculation on the water-sand mixture particles in the calculation domain, based on the selected particles, sequentially search all particles within the radius range of the individual particle kernel function, according to the searched particle type label, call the corresponding particle viscosity and perform viscous stress coupling calculation with the searched particles, and update the velocity and position pos information of the selected particles;

[0085] Step S3 includes the following specific steps:

[0086] S3.1, perform coupling calculation on the water-sand mixture particles in the flow domain, the water-sand mixture particles are controlled by the Navier-Stokes equation, and the SPH discrete form of the mass conservation equation is:

[0087]

[0088] In the formula, subscript a represents the center particle; subscript b represents the field particle; m b is the mass of the field particle; is the Hamiltonian operator for the center particle; ρ a represents the density of the center particle; ρb denotes the density of the domain particles; u ab is the velocity difference between the central particle and the domain particle, W is a kernel function, such as Figure 3 as shown in equation (1), where W(r a -r b |, h) also denotes a kernel function, |r a -r b | is the absolute value of the distance between the central particle and the domain particle, and 2h is the kernel function radius range;

[0089] The SPS term is introduced, and the momentum conservation equation is discretized as:

[0090]

[0091] where μ0 is the kinematic viscosity; τ ij is the SPS stress vector; u a is the velocity of the central particle; P a is the pressure of the central particle; P b is the pressure of the domain particle; g is the gravitational acceleration; r ab is the distance between the central particle and the domain particle, and η is the smoothing length; is the stress vector of the central particle; is the stress vector of the domain particle;

[0092] S3.2, repeat step S3.1 to perform the density and viscous stress coupling calculation, and update the velocity v and position pos information of the selected particle, for all particles numbered mk1;

[0093] S4, loop through all pier wall particles, for a single boundary particle p1, judge whether there is a water-sand mixture particle in the kernel function radius range, combine the velocity and position pos information of the mixture particle obtained in step S3, based on the improved SPH form Neilson-Gilchrist erosion formula, obtain its discrete form under SPH, calculate the abrasion rate of the pier wall within a specified solution time;

[0094] Step S4 includes the following specific steps:

[0095] S4.1, loop through all pier wall particles mk2, judge whether there is a water-sand mixture particle in the kernel function radius range, and calculate the impact angle between the wall particle and the mixture particle according to the position pos information of the mixture particle obtained in step S3 as follows:

[0096] θ i = arccos (||v i · n j ||)

[0097] where v is the unit velocity vector of the water-sand mixture particle; n is the unit outward normal vector of the wall particle, and θ is the included angle between the two types of particles. i i is the impact angle between the two types of particles; n j is the unit outward normal vector of the wall particle j, as shown in Figure 2 where v is the unit velocity vector of the water-sand mixture particle; n is the unit outward normal vector of the wall particle, and θ is the included angle between the two types of particles.

[0098] n is determined based on the relative position information of the center of the circle j :

[0099] n j = pos j - pos o

[0100] where pos j is the position array of the corresponding particle j in the XY plane; pos o is the position array of the center of gravity of the pier in the XY plane.

[0101] S4.2, in combination with the velocity information of the mixture particles obtained in step S3, for the wall particle j, based on the improved SPH form Neilson-Gilchrist erosion formula, the SPH discrete form is obtained, and the erosion rate E of each pier wall particle within the specified solving time is calculated r,j :

[0102]

[0103] where W is the kernel function; V i is the volume of particle i; E ij is the erosion rate of the fluid particle i within the kernel function radius range of the boundary particle j caused by the fluid particle i, which is calculated using the improved SPH form Neilson-Gilchrist erosion formula:

[0104]

[0105] where u p,i is the velocity of the fluid particle i colliding with the wall particle j; u r,i is the rebound velocity of the i-th mixture particle colliding with the wall particle; ε D is the deformation coefficient determined by experiment; ε C is the cutting coefficient determined by experiment; S is the compressive strength of concrete, and ω is the roundness coefficient of the sediment particles, where C1 is the perimeter of the vertical projection of the sand particles, and C2 is the perimeter of the largest inscribed circle in the vertical projection of the sand particles.

[0106] ​S5, convert the erosion rate into erosion mass, compare the erosion mass with the mass of the single particle, and determine whether the particle is deleted according to the comparison result;

[0107] Step S5 includes the following specific steps:

[0108] S5.1, convert the erosion rate of the boundary particle j into erosion mass according to step S4:

[0109]

[0110] In the formula, S j is the erosion boundary particle cross-sectional area; T is the total time of the flood period; E2 is the total erosion mass of the boundary particle j in the flood period per year;

[0111] S5.2, compare E2 with the mass m j of the wall particle j. j If E2 is greater than or equal to m j , the wall particle is deleted; if E2 is less than m j , the wall particle is retained.

[0112] S6, repeat steps S3 to S5 until a specified solution time is reached, for example, the solution time of a single pile can be 20s.

[0113] The present application is based on the SPH theory for secondary development, and the purpose of simulating the bridge pier and pile erosion based on the meshless method is achieved by introducing the erosion rate calculation formula, and the present application has the characteristics of high accuracy and strong operability. In addition, the present application introduces the life and death particle discrimination criterion based on mass, can realize the dynamic change of the structure boundary in the process of simulating the pier and pile erosion, and can consider the influence of the dynamic boundary of the structure on the erosion in the erosion simulation, thereby improving the numerical simulation accuracy.

[0114] Example 2

[0115] As shown in Figure 1 , a bridge pier and pile erosion model and simulation system based on SPH smooth particles comprises:

[0116] A pre-processing module is configured to define the range of the calculation domain, and give the boundary conditions of the simulation area; at the same time, based on the range of the calculation domain, set the inlet and outlet boundaries, set the size of the water-sand mixture, and determine the geometric shape of the pier and pile;

[0117] Specifically, the range of the calculation domain is defined, the distance of each side boundary from the center of the pier is at least 5 times the diameter of the pier, or the distance of each side boundary from the center of the pier is at least 5 times the length of the long side of the section; the inlet boundary is set, the water-sand mixture particles can be continuously injected within a specified time, and the outlet boundary is set, when the fluid particles exceed the boundary range, the particles are automatically deleted; then the size of the water-sand mixture is set based on the range of the calculation domain, the width of the water-sand mixture is required to be consistent with the width of the calculation domain, and the volume is required to satisfy that the erosion rate of the pier within the solving time can reach periodic stability; the size and shape of the pier are set according to the actual situation, and the center of the pier is located on the symmetry axis of the width of the calculation domain;

[0118] Based on the theory of non-Newtonian fluid, the water-sand mixture particles are constructed, and the pier wall particles are also constructed; then different type labels are given to the water-sand mixture particles and the pier wall particles respectively: the water-sand mixture is preset as a non-Newtonian fluid, the type label of the water-sand mixture particles is mk1, and the pier is preset as a solid, the type label of the pier wall particles is mk2;

[0119] The water-sand mixture is discretized into fluid particles, the material parameters of the HBP model are given, and the apparent viscosity of the fluid is calculated according to the following formula, the type label of the water-sand mixture particles is mk1:

[0120]

[0121] In the formula, μ ori is the apparent viscosity of the water-sand mixture; μ is the viscosity coefficient; n is the Herschel-Bulkley power index parameter, which is related to the shear stress; m is the Papanastasiou parameter, which controls the stress index growth rate, so that the stress remains at a small shear rate in the unyielding area and remains linear growth in the yielded area; Π D is a second-order invariant shear strain rate tensor; τ c is the material yield strength;

[0122] The pier is discretized into wall boundary particles, and the type label of the pier particles is mk2;

[0123] The control equation solving module is used for coupling calculation of the water-sand mixture particles in the calculation domain, based on the selected particles, all particles within the radius range of the individual particle kernel function are retrieved in turn, according to the type label of the retrieved particles, the corresponding particle viscosity is called for viscous stress coupling calculation with the retrieved particles, and the velocity and position pos information of the selected particles are updated;

[0124] The water-sand mixture particles in the calculation domain are coupled and calculated, and the water-sand mixture particles are controlled by the Navier-Stokes equation, and the SPH discrete form of the mass conservation equation is:

[0125]

[0126] where subscript a denotes the central particle; subscript b denotes the field particle; m b is the mass of the field particle; is the Hamiltonian operator for the central particle; p a denotes the density of the central particle; p b denotes the density of the field particle; u ab is the velocity difference between the central particle and the field particle, W is a kernel function, as shown in Figure 3 where W(r a -r b |, h) also denotes a kernel function, |r a -r b | is the absolute value of the distance between the central particle and the field particle, and 2h is the kernel function radius range;

[0127] The SPS term is introduced, and the momentum conservation equation is discretized as:

[0128]

[0129] where m0 is the kinematic viscosity; t ij is the SPS stress vector; u a is the velocity of the central particle; P a is the pressure of the central particle; P b is the pressure of the field particle; g is the acceleration of gravity; r ab is the distance between the central particle and the field particle, and h is the smoothing length; is the stress vector of the central particle; is the stress vector of the field particle;

[0130] The density and viscous stress coupling calculation is repeated, and the velocity v and position pos information of the selected particle are updated for all particles numbered mk1.

[0131] The abrasion rate calculation module iterates through all pier wall particles. For a single boundary particle p1, it is determined whether there is a water-sand mixture particle within the kernel function radius range. The velocity and position pos information of the mixture particle obtained by the control equation solving module are combined to obtain the discrete form of the Neilson-Gilchrist erosion formula under SPH, and the abrasion rate of the pier wall within a specified solving time is calculated.

[0132] Iterate through all pile wall particles mk2, determine whether there are water-sand mixture particles within the kernel function radius, and calculate the impact angle between the wall particles and the mixture particles according to the position pos information of the mixture particles obtained from the control equation solving module using the following formula:

[0133] θ i =arccos(||v i ·n j ||)

[0134] In the formula, v i Let θ be the normal vector of the unit velocity of particle i in the water-sand mixture; i The impact angle between the two types of particles; n j Let be the unit outward normal vector of the wall particle j, determined based on its position relative to the center of the circle:

[0135] n j =pos j -pos o

[0136] In the formula, pos j This is the array representing the positions of particle j in the XY plane; pos o This is an array representing the position of the pier's center of gravity in the XY plane;

[0137] Combining the velocity information of the mixed particles obtained from the control equation solving module, for wall particles j, based on the improved SPH form of the Neilson-Gilchrist erosion formula, the discrete form of their SPH is obtained, and the abrasion rate E of each pile wall particle within a specified solution time is calculated. r,j :

[0138]

[0139] In the formula, W is the kernel function value; V i E represents the volume of particle i; ij The erosion rate caused by fluid particles i within the radius of the boundary particle j kernel function is calculated using the modified SPH form of the Neilson-Gilchrist erosion formula:

[0140]

[0141] In the formula, u p,i The velocity of fluid particle i colliding with wall particle j; u r,i ε is the rebound velocity of the i-th mixture particle that collides with the wall particle; D ε is the deformation coefficient, determined experimentally; C ω is the cutting coefficient, determined experimentally; S is the compressive strength of concrete; and ω is the roundness coefficient of the silt particles. C1 is the perimeter of the vertical projection of the sand grain, and C2 is the perimeter of the largest inscribed circle in the vertical projection of the sand grain;

[0142] A life and death particle module is used to convert the erosion rate into the erosion mass, and compare the erosion mass with the mass of the single particle, so as to determine whether the particle is deleted or not;

[0143] The erosion rate conversion boundary particle j is calculated by the erosion rate calculation module:

[0144]

[0145] In the formula, S j is the erosion boundary particle cross-sectional area; T is the total time of the flood period; E2 is the total erosion mass of the boundary particle j in the flood period per year;

[0146] E2 is compared with the mass m j of the wall surface particle j, if E2≥m j , the wall surface particle is deleted; if E2 j < m, the wall surface particle is retained;

[0147] An iteration module is used to repeatedly execute the control equation solving module, the erosion rate calculation module and the life and death particle module until a specified solving time is reached.

Claims

1. A bridge pier pile erosion model simulation method based on SPH smooth particles, characterized in that, It comprises the following steps: S1, defining the range of the calculation domain, and setting the import and export boundaries based on the set calculation domain range; S2, based on the theory of non-Newtonian fluid, constructing water-sand mixture particles; at the same time, constructing pier wall surface particles; then respectively giving different type labels to water-sand mixture particles and pier wall surface particles; S3, performing coupling calculation on water-sand mixture particles in the calculation domain, based on the selected particle, sequentially retrieving all particles within the single particle kernel function radius range of the particle, according to the type label of the retrieved particle, calling the corresponding particle viscosity to perform viscous stress coupling calculation with the retrieved particle, and updating the velocity and position of the selected particle information; S4, loop through all the pier wall particles, for a single boundary particle p1, judge whether there is a water-sand mixture particle in the core function radius range, combined with the velocity and position of the mixture particle obtained in step S3 Information, based on the improved SPH form Neilson-Gilchrist erosion formula, the abrasion rate of the pier wall within the specified solution time is calculated; The step S4 specifically comprises the following steps: S4.1, loop through all the wall particles of the pier, judge whether there is a water-sand mixture particle in the core function radius range, and according to the position of the mixture particle obtained in step S3 The information calculates the impact angle between the wall particle and the mixture particle as follows: , wherein, is the unit speed normal vector of the water-sand mixture particle ; is the impact angle between the two types of particles; is the unit outer normal vector of the wall particle , which is determined based on the relative position information of the center of the circle: ， wherein corresponding particles In XY an array of positions in the plane; with the center of gravity of the pier XY an array of positions in the plane; S4.2, based on the velocity information of the mixture particles obtained in step S3, the erosion rate of each pier pile wall particle within a specified solution time is calculated based on the improved SPH form Neilson-Gilchrist erosion formula , based on the velocity information of the mixture particles obtained in step S3, the erosion rate of each pier pile wall particle within a specified solution time is calculated based on the improved SPH form Neilson-Gilchrist erosion formula : ， where is the kernel function; is the particle volume; is the boundary particle kernel function within the radius of the fluid particle The resulting erosion rate is calculated using the modified SPH form of the Neilson-Gilchrist erosion formula: ， In the formula, To interact with wall particles Colliding fluid particles speed; For the first collision with the wall particles The rebound velocity of the mixed particles; The deformation coefficient is determined experimentally. The cutting coefficient is determined experimentally. This refers to the compressive strength of concrete. This is the roundness coefficient of the sediment particles. ,in Let be the perimeter of the sand grain's vertical projection. Let be the circumference of the largest inscribed circle in the vertical projection of the sand grain; S5, converting the erosion rate into erosion mass, comparing the erosion mass with the mass of a single particle, and judging whether the particle is deleted or not; The step S5 specifically comprises the following steps: S5.1, based on the abrasion rate of step S4, converting the boundary particles of abrasion quality: ， wherein is the abrasive boundary particle cross-sectional area; is the total time of flood period; is the boundary particle is the total abrasive mass per year of flood period; S5.2, contrast with wall particles of mass , if , delete the wall particle; if , keep the wall particle; S6, repeatedly executing steps S3 to S5 until a specified solution time is reached.

2. The bridge pier pile erosion model simulation method based on SPH smooth particles according to claim 1, characterized in that: The step S1 specifically comprises the following steps: defining the range of the calculation domain, stipulating that the distance of each side boundary from the center of the pier is at least 5 times the diameter of the pier, or stipulating that the distance of each side boundary from the center of the pier is at least 5 times the length of the long side of the section; setting the inlet boundary, continuously injecting water-sand mixture particles within a specified time, and setting the outlet boundary, automatically deleting the fluid particles when they exceed the boundary range; setting the size and shape of the pier according to the actual situation, with the center located on the symmetry axis of the calculation domain width.

3. The bridge pier pile erosion model simulation method based on SPH smooth particles according to claim 1, characterized in that: The step S2 specifically comprises the following steps: S2.1, discretizing the water-sand mixture into fluid particles, giving the material parameters of the HBP model, and calculating the apparent viscosity of the fluid according to the following formula, with the particle type label of the water-sand mixture being mk1: ， wherein is the apparent viscosity of the water-sand mixture; is the viscosity coefficient; is the Herschel-Bulkley power index parameter, related to the shear stress; is the Papanastasiou parameter, which controls the rate of stress exponent growth, keeping the stress at small shear rates in the unyielding region and linear growth in the yielded region; is the second order invariable shear strain rate tensor; is the material yield strength; S2.2, discretizing the pier into wall boundary particles, with the particle type label of the pier being mk2.

4. The bridge pier pile erosion model simulation method based on SPH smooth particles according to claim 1, characterized in that: The step S3 specifically comprises the following steps: S3.1, the water-sand mixture particles in the river basin are coupled and calculated, and the water-sand mixture particles are controlled according to the motion equation and the mass conservation equation SPH discrete form of the mass conservation equation is: ， where the subscript denotes the center particle; the subscript denotes the field particle; is the mass of the field particle; is the operator for the center particle; denotes the density of the center particle; denotes the density of the field particle; is the velocity difference between the center particle and the field particle, is the kernel function; Introduction The term, the momentum conservation equation is discretized as: ， wherein is the kinematic viscosity; is is the stress vector; is the velocity of the central particle; is the pressure of the central particle; is the pressure of the domain particle; is the gravitational acceleration; is the distance between the central particle and the domain particle, is the smoothing length; is the stress vector of the central particle; is the stress vector of the domain particle; S3.2, for all particles numbered repeat step S3.1 for density and viscous stress coupling calculations and update the velocity and position information of the selected particle.

5. A bridge pier pile erosion model simulation system based on SPH smooth particles, characterized in that, It comprises the following steps: The preprocessing module is used for defining the range of the calculation domain, and setting the import and export boundaries based on the set calculation domain range; based on the theory of non-Newtonian fluid, constructing water-sand mixture particles; at the same time, constructing pier wall surface particles; then respectively giving different type labels to water-sand mixture particles and pier wall surface particles; The control equation solving module is used for coupling calculation of water-sand mixture particles in the calculation domain, based on the selected particle, all particles in the radius range of the single particle kernel function are searched in turn, according to the searched particle type mark, the corresponding particle viscosity is called to carry out viscous stress coupling calculation with the searched particle, and the velocity and position of the selected particle are updated information; An abrasion rate calculation module is used to cyclically traverse all pier wall particles, and for a single boundary particle, it is judged whether there is a water-sand mixture particle in the core function radius range, and the velocity and position of the mixture particle obtained by the control equation solving module are combined information, based on improved form An erosion formula is obtained, and its discrete form under SPH is obtained, and the abrasion rate of the pier wall within a specified solving time is calculated. Iterate through all particles mk2 on the pile wall surface, determine whether there are water-sand mixture particles within the kernel function radius, and solve for the positions of the mixture particles obtained from the control equation solution module. The impact angle between the wall particles and the mixture particles is calculated using the following formula: In the formula, Water-sand mixture particles The unit velocity normal vector; The impact angle between the two types of particles; For wall particles The unit outward normal vector is determined based on its position relative to the center of the circle: ， wherein corresponding particles in XY an array of positions in the plane; for the pier center of gravity in XY an array of positions in the plane; Combining the velocity information of the mixture particles obtained from the control equation solving module, for wall particles... Based on the improved SPH form of the Neilson-Gilchrist erosion formula, the abrasion rate of particles on the pile wall of each pier within a specified solution time is calculated. : ， where is the kernel function; is the particle volume; is the boundary particle fluid particle within the kernel function radius The resulting erosion rate is calculated using a modified SPH form of the Neilson-Gilchrist erosion formula: ， In the formula, To interact with wall particles Colliding fluid particles speed; For the first collision with the wall particles The rebound velocity of the mixed particles; The deformation coefficient is determined experimentally. The cutting coefficient is determined experimentally. This refers to the compressive strength of concrete. This is the roundness coefficient of the sediment particles. ,in Let be the perimeter of the sand grain's vertical projection. Let be the circumference of the largest inscribed circle in the vertical projection of the sand grain; The live and dead particle module is used for converting the erosion rate into erosion mass, comparing the erosion mass with the mass of a single particle, and judging whether the particle is deleted or not; Abrasion rate conversion boundary particles based on an abrasion rate calculation module of the abrasive mass: ， wherein is the abrasive boundary particle cross-sectional area; is the total time of flood period; is the boundary particle is the total abrasive mass per year of flood period; Comparison With the wall particle The mass If , delete the wall particle; if , keep the wall particle; The iteration module is used for repeatedly executing the control equation solving module, the erosion rate calculation module and the live and dead particle module until a specified solution time is reached.

6. The bridge pier and pile erosion model simulation system based on SPH smooth particles according to claim 5, characterized in that: In the preprocessing module, the water-sand mixture is discretized into fluid particles, the material parameters of the HBP model are given, and the apparent viscosity of the fluid is calculated according to the following formula, with the particle type label of the water-sand mixture being mk1: ， wherein is the apparent viscosity of the water-sand mixture; is the viscosity coefficient; is the Herschel-Bulkley power index parameter, related to the shear stress; is the Papanastasiou parameter, which controls the rate of stress exponent growth, keeping the stress at small shear rates in the unyielded region and linear growth in the yielded region; is the second order invariable shear strain rate tensor; is the material yield strength; The pier is discretized into wall boundary particles, with the particle type label of the pier being mk2.

7. The bridge pier and pile erosion model simulation system based on SPH smooth particles according to claim 5, characterized in that: The control equation solving module performs coupled calculation on the water-sand mixture particles in the flow field, and the water-sand mixture particles are controlled according to the following equations: The SPH discrete form of the mass conservation equation is as follows: ， where the subscript denotes the center particle; the subscript denotes the field particle; is the mass of the field particle; is the operator for the center particle; denotes the density of the center particle; denotes the density of the field particle; is the velocity difference between the center particle and the field particle, is the kernel function; Introduction The term, the momentum conservation equation is discretized as: ， wherein is the kinematic viscosity; is is the stress vector; is the velocity of the central particle; is the pressure of the central particle; is the pressure of the field particle; is the gravitational acceleration; is the distance between the central particle and the field particle, is the smoothing length; is the stress vector of the central particle; is the stress vector of the field particle; For all particles numbered the density and viscous stress coupling calculations are repeated and the velocity and position information of the selected particle is updated.

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