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

Abstract

The invention discloses a bridge pier pile erosion model and simulation method and system based on SPH smoothed particles, and the method comprises the steps: defining the range of a computational domain, and setting an entrance and exit boundary based on the range; constructing a water-sand mixture and pier pile particles, and endowing the particles with constitutive structures and types; coupling calculation is carried out on water-sand mixture particles, all particles in a single particle kernel function radius range are retrieved based on the selected particles, viscosity stress coupling calculation is carried out, and the speed and position information of the selected particles is updated; all pier pile wall surface particles are cyclically traversed, whether water-sand mixture particles exist within the radius range of a single boundary particle kernel function or not is judged, and the abrasion rate of the pier pile wall surface within the specified solving time is calculated based on an improved erosion formula by combining the speed and position pos information of the mixture particles; the abrasion rate is converted into abrasion quality, and whether the particles are deleted or not is judged; and iteration is repeated until the specified solving time is reached. According to the invention, the erosion of the bridge pier pile structure can be simulated more accurately.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge pier erosion simulation, and in particular relates to a bridge pier erosion model based on SPH smooth particles and a simulation method and system. Background Art

[0002] Many mountain bridges are built over rivers and canyons. The bridge sites of such mountain bridges are prone to natural disasters such as earthquakes, floods, and mudslides. The boulders, gravel, and other solid impurities mixed in the high-speed water flow will cause continuous transient impact and cutting on the pier structure of the bridge, causing uneven shedding of the concrete protective layer of the pier structure. More seriously, it will lead to the exposure of steel bars and medium aggregates in some areas, forming typical bridge erosion characteristics. Long-term erosion will greatly reduce the bearing capacity of the pier structure. It is necessary to simulate the erosion of bridge piers to guide the design of pier structures. Existing numerical simulations of bridge pier erosion are mostly based on CFD methods, but the accuracy of this method depends on the accuracy of the grid, and it cannot accurately handle complex boundaries, such as the dynamic deletion of wall particles.

[0003] Therefore, it is urgent to solve the above problems. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a bridge pier pile erosion model and simulation method based on SPH smooth particles, which can more accurately simulate the erosion of bridge pier pile structures.

[0005] Technical solution: To achieve the above purpose, the present invention discloses a bridge pier pile 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, water-sand mixture particles are constructed; at the same time, pier pile wall particles are constructed; and then different type labels are given to the water-sand mixture particles and the pier pile wall particles respectively;

[0008] S3, performing coupling calculation on the water-sand mixture particles in the calculation domain, based on the selected particles, sequentially searching all particles within the radius of the single particle kernel function, calling the corresponding particle viscosity according to the retrieved particle type number to perform viscous stress coupling calculation with the retrieved particle, and updating the speed and position pos information of the selected particle;

[0009] S4, loop through all the pier wall particles, for a single boundary particle p1, determine whether there is a water-sand mixture particle within the radius of its kernel function, 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, and calculate the abrasion rate of the pier wall within the specified solution time;

[0010] S5, converting the abrasion rate into abrasion mass, comparing the abrasion mass with the mass of a single particle, and thereby determining whether the particle should be deleted;

[0011] S6. Repeat steps S3 to S5 until the specified solution time is reached.

[0012] Optionally, step S1 specifically includes the following steps: defining the range of the calculation domain, stipulating that the distance between each side boundary and the center of the pier pile is at least 5 times the diameter of the pier pile, or stipulating that the distance between each side boundary and the center of the pier pile is at least 5 times the length of the long side of the cross section; setting the calculation domain as a semi-closed space, that is, only setting 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, setting the size of the water-sand mixture, requiring the width of the water-sand mixture to be consistent with the width of the calculation domain; setting the size and shape of the pier pile according to actual conditions, with its center located on the symmetry axis of the width of the calculation domain.

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

[0014] S2.1. Discretize the water-sand mixture into fluid particles, assign the material parameters of the HBP model, and calculate the fluid apparent viscosity according to the following formula. The particle type of the water-sand mixture is labeled as 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 exponential parameter, which is related to the shear stress; m is the Papanastasiou parameter, which controls the exponential growth rate of stress, so that the stress maintains a small shear rate in the unyielded area and maintains a linear growth in the yielded area; Π D is the second-order invariant shear strain rate tensor; τ c is the material yield strength;

[0017] S2.2. Discretize the pier into wall boundary particles. The particle type of the pier is labeled as mk2.

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

[0019] S3.1. Coupled calculations are performed on the water-sand mixture particles in the basin. The motion of the water-sand mixture particles is controlled according to the Navier-Stokes equation. The SPH discrete form of the mass conservation equation is:

[0020]

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

[0022] Introducing the SPS term, the momentum conservation equation is discretized as:

[0023]

[0024] Where μ0 is the kinematic viscosity; τ ij is the SPS stress vector; u a is the velocity of the central particle; P a The pressure of the central particle; P b is the pressure of the field particles; g is the gravitational acceleration; r ab is the distance between the central particle and the field particle, 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 calculations, 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 the pier wall particles mk2 to 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 mixture particle position pos information obtained in step S3:

[0028] θ i =arccos(||v i ·n j ||)

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

[0030] n j =pos j -pos o

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

[0032] S4.2. Combined 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, obtain its SPH discrete form, and calculate the abrasion rate E of each pier wall particle within the specified solution time r,j :

[0033]

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

[0035]

[0036] In the formula, u p,i is the velocity of fluid particle i colliding with 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, which is determined by experiment; S is the compressive strength of concrete, ω is the roundness coefficient of sediment particles, Where C1 is the circumference of the vertical projection of the sand grain, and C2 is the circumference of the largest inscribed circle in the vertical projection of the sand grain.

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

[0038] S5.1. Calculate the abrasive mass of the boundary particle j based on the abrasive rate of step S4:

[0039]

[0040] In the formula, S jis the cross-sectional area of ​​the abrasive boundary particles; T is the total flood period; E2 is the total abrasive mass of boundary particle j during the annual flood period;

[0041] S5.2. Compare E2 with the mass m of the wall particle j j , if E2 ≥ m j , then delete the wall particle; if E2<m j , then the wall particle is retained.

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

[0043] The pre-processing module is used to define the range of the calculation domain and set the inlet and outlet boundaries based on the set calculation domain range; construct water-sand mixture particles based on non-Newtonian fluid theory; and construct pier wall particles at the same time; and then give different type labels to water-sand mixture particles and pier wall particles respectively;

[0044] The control equation solving module is used to perform coupling calculation on the water-sand mixture particles in the calculation domain. Based on the selected particles, all particles within the radius of the single particle kernel function are retrieved in sequence. According to the retrieved particle type label, the corresponding particle viscosity is called to perform viscous stress coupling calculation with the retrieved particle, and the speed and position pos information of the selected particle is updated;

[0045] The abrasion rate calculation module is used to loop through all the pier wall particles, and for a single boundary particle p1, determine whether there is a water-sand mixture particle within the radius of its kernel function, and 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, and calculate the abrasion rate of the pier wall within the specified solution time;

[0046] The life and death particle module is used to convert the abrasion rate into the abrasion mass, compare the abrasion mass with the mass of a single particle, and thus determine whether the particle should be deleted;

[0047] The iteration module is used to repeatedly execute the control equation solving module, the abrasion rate calculation module and the birth and death particle module until the specified solution time is reached.

[0048] Optionally, the water-sand mixture is discretized into fluid particles in the pre-processing module, the material parameters of the HBP model are assigned, and the apparent viscosity of the fluid is calculated according to the following formula. The particle type of the water-sand mixture is labeled as mk1:

[0049]

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

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

[0052] Optionally, the control equation solving module performs coupled calculation on the water-sand mixture particles in the watershed, and the motion of the water-sand mixture particles is controlled according to the Navier-Stokes equation. The SPH discretization form of the mass conservation equation is:

[0053]

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

[0055] Introducing the SPS term, the momentum conservation equation is discretized as:

[0056]

[0057] Where μ0 is the kinematic viscosity; τ ij is the SPS stress vector; u a is the velocity of the central particle; P a The pressure of the central particle; P b is the pressure of the field particles; g is the gravitational acceleration; r ab is the distance between the central particle and the field particle, η is the smoothing length; is the stress vector of the central particle; is the stress vector of the field particle;

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

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

[0060] θ i =arccos(‖v i ·n j ‖)

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

[0062] n j =pos j -pos o

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

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

[0065]

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

[0067]

[0068] In the formula, u p,i is the velocity of fluid particle i colliding with 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, which is determined by experiment; S is the compressive strength of concrete, ω is the roundness coefficient of sediment particles, Where C1 is the circumference of the vertical projection of the sand grain, and C2 is the circumference 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 secondary developed based on the SPH theory, and by introducing the abrasion rate calculation formula, the purpose of numerically simulating bridge pier pile erosion based on the gridless method is achieved, and it has the characteristics of high precision and strong operability; the present invention performs numerical simulation of bridge pier pile erosion based on the SPH theory, and by introducing the mass-based dead and alive particle discrimination criterion, the dynamic change of the structural boundary during the pier pile erosion simulation can be realized, thereby considering the influence of the structural dynamic boundary on abrasion in the erosion simulation, and improving the accuracy of numerical simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is a flow chart of the present invention;

[0071] Figure 2 It is a schematic diagram of the angle between two types of particles in the present invention;

[0072] Figure 3 Schematic diagram of the radius range of the kernel function in the present invention. DETAILED DESCRIPTION

[0073] The technical solution of the present invention is further described below in conjunction with 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 area; 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 pile;

[0077] Specifically, the scope of the calculation domain is defined, and the distance between each side boundary and the center of the pier pile is stipulated to be at least 5 times the diameter of the pier pile, or the distance between each side boundary and the center of the pier pile is stipulated to be at least 5 times the length of the long side of the cross section; the inlet boundary is set, and the water-sand mixture particles can be continuously injected within the specified time, and the outlet boundary is set at the same time. When the fluid particles exceed the boundary range, the particles are automatically deleted; then, based on the scope of the calculation domain, the size of the water-sand mixture is set, and the width of the water-sand mixture is required to be consistent with the width of the calculation domain, and the volume must meet 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, and its center is located at the symmetry axis of the width of the calculation domain;

[0078] S2. Based on the non-Newtonian fluid theory, water-sand mixture particles are constructed, and pier pile wall particles are constructed at the same time; then different type labels are given to the water-sand mixture particles and the pier pile 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, the pier pile is preset as a solid, and the type label of the pier pile wall particles is mk2;

[0079] Step S2 includes the following specific steps:

[0080] S2.1. Discretize the water-sand mixture into fluid particles, assign the material parameters of the HBP model, and calculate the fluid apparent viscosity according to the following formula. The particle type of the water-sand mixture is labeled as 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 exponential parameter, which is related to the shear stress; m is the Papanastasiou parameter, which controls the exponential growth rate of stress, so that the stress maintains a small shear rate in the unyielded area and maintains a 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 of the pier is labeled as mk2;

[0084] S3, performing coupling calculation on the water-sand mixture particles in the calculation domain, based on the selected particles, sequentially searching all particles within the radius of the single particle kernel function, calling the corresponding particle viscosity according to the retrieved particle type number to perform viscous stress coupling calculation with the retrieved particle, and updating the speed and position pos information of the selected particle;

[0085] Step S3 includes the following specific steps:

[0086] S3.1. Coupled calculations are performed on the water-sand mixture particles in the basin. The motion of the water-sand mixture particles is controlled according to the Navier-Stokes equation. The SPH discrete form of the mass conservation equation is:

[0087]

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

[0089] Introducing the SPS term, 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 The pressure of the central particle; P b is the pressure of the field particles; g is the gravitational acceleration; r ab is the distance between the central particle and the field particle, η is the smoothing length; is the stress vector of the central particle; is the stress vector of the field particle;

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

[0093] S4, loop through all the pier wall particles, for a single boundary particle p1, determine whether there is a water-sand mixture particle within the radius of its kernel function, 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, and calculate the abrasion rate of the pier wall within the specified solution time;

[0094] Step S4 includes the following specific steps:

[0095] S4.1. Loop through all the pier wall particles mk2 to 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 mixture particle position pos information obtained in step S3:

[0096] θ i =arccos(||v i ·n j ||)

[0097] In the formula, v i is the unit velocity normal vector of particle i of the water-sand mixture; θ i is the impact angle between the two types of particles; n j is the unit external normal vector of the wall particle j, such as Figure 2 As shown, v is the unit velocity normal vector of the water-sand mixture particles; n is the unit external normal vector of the wall particles, and θ is the angle between the two types of particles;

[0098] Determine n based on its relative center position information j :

[0099] n j =pos j -pos o

[0100] In the formula, pos j is the position array of particle j in the XY plane; pos o is the position array of the pier column's center of gravity in the XY plane;

[0101] S4.2. Combined 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, obtain its SPH discrete form, and calculate the abrasion rate E of each pier wall particle within the specified solution time r,j :

[0102]

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

[0104]

[0105] In the formula, u p,i is the velocity of fluid particle i colliding with 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, which is determined by experiment; S is the compressive strength of concrete, ω is the roundness coefficient of sediment particles, Where C1 is the circumference of the vertical projection of the sand grain, and C2 is the circumference of the largest inscribed circle in the vertical projection of the sand grain;

[0106] S5, converting the abrasion rate into abrasion mass, comparing the abrasion mass with the mass of a single particle, and thereby determining whether the particle should be deleted;

[0107] Step S5 includes the following specific steps:

[0108] S5.1. Calculate the abrasive mass of the boundary particle j based on the abrasive rate of step S4:

[0109]

[0110] In the formula, S j is the cross-sectional area of ​​the abrasive boundary particles; T is the total flood period; E2 is the total abrasive mass of boundary particle j during the annual flood period;

[0111] S5.2. Compare E2 with the mass m of the wall particle j j , if E2 ≥ m j , then delete the wall particle; if E2<m j , then the wall particle is retained;

[0112] S6. Repeat steps S3 to S5 until the specified solution time is reached. For example, the corresponding solution time for a single pile may be 20 seconds.

[0113] The present invention is secondary developed based on the SPH theory. By introducing the calculation formula of the abrasion rate, the purpose of numerically simulating the erosion of bridge pier piles based on the meshless method is achieved, and it has the characteristics of high accuracy and strong operability. In addition, by introducing the mass-based dead and alive particle discrimination criterion, the present invention can realize the dynamic change of the structural boundary during the pier pile erosion simulation process, so as to consider the influence of the structural dynamic boundary on the abrasion in the erosion simulation, and improve the accuracy of the numerical simulation.

[0114] Example 2

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

[0116] The pre-processing module is used to define the scope of the computational domain and give the boundary conditions of the simulation area. Based on the scope of the computational domain, the inlet and outlet boundaries are set, the size of the water-sand mixture is set, and the geometry of the pier pile is determined.

[0117] Specifically, the scope of the calculation domain is defined, and the distance between each side boundary and the center of the pier pile is stipulated to be at least 5 times the diameter of the pier pile, or the distance between each side boundary and the center of the pier pile is stipulated to be at least 5 times the length of the long side of the cross section; the inlet boundary is set, and the water-sand mixture particles can be continuously injected within the specified time, and the outlet boundary is set at the same time. When the fluid particles exceed the boundary range, the particles are automatically deleted; then, based on the scope of the calculation domain, the size of the water-sand mixture is set, and the width of the water-sand mixture is required to be consistent with the width of the calculation domain, and the volume must meet 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, and its center is located at the symmetry axis of the width of the calculation domain;

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

[0119] The water-sand mixture is discretized into fluid particles, the material parameters of the HBP model are assigned, and the apparent viscosity of the fluid is calculated according to the following formula. The particle type of the water-sand mixture is labeled as 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 exponential parameter, which is related to the shear stress; m is the Papanastasiou parameter, which controls the exponential growth rate of stress, so that the stress maintains a small shear rate in the unyielded area and maintains a linear growth in the yielded area; Π D is the second-order invariant shear strain rate tensor; τ c is the material yield strength;

[0122] The pier pile is discretized into wall boundary particles, and the particle type of the pier pile is labeled as mk2;

[0123] The control equation solving module is used to perform coupling calculation on the water-sand mixture particles in the calculation domain. Based on the selected particles, all particles within the radius of the single particle kernel function are retrieved in sequence. According to the retrieved particle type label, the corresponding particle viscosity is called to perform viscous stress coupling calculation with the retrieved particle, and the speed and position pos information of the selected particle is updated;

[0124] The water-sand mixture particles in the basin are coupled and calculated. The motion of the water-sand mixture particles is controlled according to the Navier-Stokes equation. The SPH discretization form of the mass conservation equation is:

[0125]

[0126] In the formula, subscript a represents the central particle; subscript b represents the domain particle; m b is the mass of the field particle; is the Hamiltonian operator for the central particle; ρ a represents the density of the central particle; ρ b represents the density of the field particles; u ab is the velocity difference between the central particle and the field particle, and W is the kernel function, such as Figure 3 As shown, where W(r a -r b |,h) also represents the 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 radius range of the kernel function;

[0127] Introducing the SPS term, the momentum conservation equation is discretized as:

[0128]

[0129] Where μ0 is the kinematic viscosity; τ ij is the SPS stress vector; u a is the velocity of the central particle; P a The pressure of the central particle; P b is the pressure of the field particles; g is the gravitational acceleration; r ab is the distance between the central particle and the field particle, η is the smoothing length; is the stress vector of the central particle; is the stress vector of the field particle;

[0130] For all particles numbered mk1, the density and viscous stress coupling calculations are repeated, and the velocity v and position pos information of the selected particles are updated;

[0131] The abrasion rate calculation module loops through all the pier wall particles. For a single boundary particle p1, it determines whether there is a water-sand mixture particle within the radius of its kernel function. Combined with the velocity and position pos information of the mixture particles obtained by the control equation solving module, based on the improved SPH form Neilson-Gilchrist erosion formula, its discrete form under SPH is obtained to calculate the abrasion rate of the pier wall within the specified solution time.

[0132] Loop through all the pier wall particles mk2 to 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 mixture particle position pos information obtained by the control equation solving module:

[0133] θ i =arccos(||v i ·n j ||)

[0134] In the formula, v i is the unit velocity normal vector of particle i of the water-sand mixture; θ i is the impact angle between the two types of particles; n j is the unit external normal vector of the wall particle j, which is determined based on its relative center position information:

[0135] n j =pos j -pos o

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

[0137] Combined with the velocity information of the mixture particles obtained by the control equation solving module, for the wall particle j, based on the improved SPH form Neilson-Gilchrist erosion formula, its SPH discrete form is obtained, and the abrasion rate E of each pier wall particle within the specified solution time is calculated. r,j :

[0138]

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

[0140]

[0141] In the formula, u p,i is the velocity of fluid particle i colliding with 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, which is determined by experiment; S is the compressive strength of concrete, ω is the roundness coefficient of sediment particles, Where C1 is the circumference of the vertical projection of the sand grain, and C2 is the circumference of the largest inscribed circle in the vertical projection of the sand grain;

[0142] The life and death particle module is used to convert the abrasion rate into the abrasion mass, compare the abrasion mass with the mass of a single particle, and thus determine whether the particle should be deleted;

[0143] The abrasive mass of boundary particle j is calculated based on the abrasive rate of the abrasive rate calculation module:

[0144]

[0145] In the formula, S j is the cross-sectional area of ​​the abrasive boundary particles; T is the total flood period; E2 is the total abrasive mass of boundary particle j during the annual flood period;

[0146] Compare E2 with the mass m of the wall particle j j , if E2 ≥ m j , then delete the wall particle; if E2<m j , then the wall particle is retained;

[0147] The iteration module is used to repeatedly execute the control equation solving module, the abrasion rate calculation module and the birth and death particle module until the specified solution time is reached.

Claims

1. A bridge pier pile erosion model and simulation method based on SPH smooth particles, characterized in that: The steps include: S1. Define the range of the calculation domain, and set the import and export boundaries based on the set calculation domain range; S2. Based on the non-Newtonian fluid theory, water-sand mixture particles are constructed; at the same time, pier pile wall particles are constructed; and then different type labels are given to the water-sand mixture particles and the pier pile wall particles respectively; S3, performing coupling calculation on the water-sand mixture particles in the calculation domain, based on the selected particles, sequentially searching all particles within the radius of the single particle kernel function, calling the corresponding particle viscosity according to the retrieved particle type number to perform viscous stress coupling calculation with the retrieved particle, and updating the speed and position pos information of the selected particle; S4, loop through all the pier wall particles, for a single boundary particle p1, determine whether there is a water-sand mixture particle within the radius of its kernel function, combine the velocity and position pos information of the mixture particle obtained in step S3, and calculate the abrasion rate of the pier wall within the specified solution time based on the improved SPH form Neilson-Gilchrist erosion formula; S5, converting the abrasion rate into abrasion mass, comparing the abrasion mass with the mass of a single particle, and thereby determining whether the particle should be deleted; S6. Repeat steps S3 to S5 until the specified solution time is reached.

2. The bridge pier pile erosion model and simulation method based on SPH smooth particles according to claim 1 is characterized by: The step S1 specifically includes the following steps: defining the range of the calculation domain, stipulating that the distance between each side boundary and the center of the pier pile is at least 5 times the diameter of the pier pile, or stipulating that the distance between each side boundary and the center of the pier pile is at least 5 times the length of the long side of the cross section; setting the inlet boundary, so that water-sand mixture particles can be continuously injected within a specified time, and setting the outlet boundary at the same time, when the fluid particles exceed the boundary range, the particles are automatically deleted; setting the size and shape of the pier pile according to actual conditions, and the center of the pier pile is located at the symmetry axis of the width of the calculation domain.

3. The bridge pier pile erosion model and simulation method based on SPH smooth particles according to claim 1 is characterized by: The step S2 specifically includes the following steps: S2.

1. Discretize the water-sand mixture into fluid particles, assign the material parameters of the HBP model, and calculate the fluid apparent viscosity according to the following formula. The particle type of the water-sand mixture is labeled as mk1: 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 exponential parameter, which is related to the shear stress; m is the Papanastasiou parameter, which controls the exponential growth rate of stress, so that the stress maintains a small shear rate in the unyielded area and maintains a linear growth in the yielded area; Π D is the second-order invariant shear strain rate tensor; τ c is the material yield strength; S2.

2. Discretize the pier into wall boundary particles. The particle type of the pier is labeled as mk2.

4. The bridge pier pile erosion model and simulation method based on SPH smooth particles according to claim 1 is characterized by: The step S3 specifically comprises the following steps: S3.

1. Coupled calculations are performed on the water-sand mixture particles in the basin. The motion of the water-sand mixture particles is controlled according to the Navier-Stokes equation. The SPH discrete form of the mass conservation equation is: In the formula, subscript a represents the central particle; subscript b represents the domain particle; m b is the mass of the field particle; is the Hamiltonian operator for the central particle; ρ a represents the density of the central particle; ρ b represents the density of the field particles; u ab is the velocity difference between the central particle and the field particle, W is the kernel function; Introducing the SPS term, the momentum conservation equation is discretized as: Where μ0 is the kinematic viscosity; τ ij is the SPS stress vector; u a is the velocity of the central particle; P a The pressure of the central particle; P b is the pressure of the field particles; g is the gravitational acceleration; r ab is the distance between the central particle and the field particle, η is the smoothing length; is the stress vector of the central particle; is the stress vector of the field particle; S3.

2. For all particles numbered mk1, repeat step S3.1 to perform density and viscous stress coupling calculations, and update the velocity v and position pos information of the selected particles.

5. The bridge pier pile erosion model and simulation method based on SPH smooth particles according to claim 1 is characterized by: The step S4 specifically comprises the following steps: S4.

1. Loop through all the pier wall particles mk2 to 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 mixture particle position pos information obtained in step S3 as follows: i i =arccos(||v i ·n j ||) In the formula, v i is the unit velocity normal vector of particle i of the water-sand mixture; θ i is the impact angle between the two types of particles; n j is the unit external normal vector of the wall particle j, which is determined based on its relative center position information: n j =pos j -pos o In the formula, pos j is the position array of particle j in the XY plane; pos o is the position array of the pier column's center of gravity in the XY plane; S4.2, combined 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, calculate the abrasion rate E of the particles on the wall of each pier within the specified solution time r,j : Where W is the kernel function; V i is the volume of particle i; E ij is the erosion rate caused by fluid particle i within the radius of the kernel function of boundary particle j, and is calculated using the improved SPH form Neilson-Gilchrist erosion formula: In the formula, u p,i is the velocity of fluid particle i colliding with 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, which is determined by experiment; S is the compressive strength of concrete, ω is the roundness coefficient of sediment particles, Where C1 is the circumference of the vertical projection of the sand grain, and C2 is the circumference of the largest inscribed circle in the vertical projection of the sand grain.

6. The bridge pier pile erosion model and simulation method based on SPH smooth particles according to claim 1 is characterized by: The step S5 specifically comprises the following steps: S5.

1. Calculate the abrasive mass of the boundary particle j based on the abrasive rate of step S4: In the formula, S j is the cross-sectional area of ​​the abrasive boundary particles; T is the total flood period; E2 is the total abrasive mass of boundary particle j during the annual flood period; S5.

2. Compare E2 with the mass m of the wall particle j j , if E2 ≥ m j , then delete the wall particle; if E2<m j , then the wall particle is retained.

7. A bridge pier pile erosion model and simulation system based on SPH smooth particles, characterized in that: The steps include: The pre-processing module is used to define the range of the calculation domain and set the inlet and outlet boundaries based on the set calculation domain range; construct water-sand mixture particles based on non-Newtonian fluid theory; and construct pier wall particles at the same time; and then give different type labels to water-sand mixture particles and pier wall particles respectively; The control equation solving module is used to perform coupling calculation on the water-sand mixture particles in the calculation domain. Based on the selected particles, all particles within the radius of the single particle kernel function are retrieved in sequence. According to the retrieved particle type label, the corresponding particle viscosity is called to perform viscous stress coupling calculation with the retrieved particle, and the speed and position pos information of the selected particle is updated; The abrasion rate calculation module is used to loop through all the pier wall particles, and for a single boundary particle p1, determine whether there is a water-sand mixture particle within the radius of its kernel function, and 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, and calculate the abrasion rate of the pier wall within the specified solution time; The life and death particle module is used to convert the abrasion rate into the abrasion mass, compare the abrasion mass with the mass of a single particle, and thus determine whether the particle should be deleted; The iteration module is used to repeatedly execute the coupling calculation module, the abrasion rate calculation module and the judgment module until the specified solution time is reached.

8. The bridge pier pile erosion model and simulation system based on SPH smooth particles according to claim 1 is characterized by: In the pre-processing module, the water-sand mixture is discretized into fluid particles, the material parameters of the HBP model are assigned, and the fluid apparent viscosity is calculated according to the following formula. The particle type of the water-sand mixture is labeled as mk1: 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 exponent parameter, which is related to the shear stress; m is the Papanastasiou parameter, which controls the exponential growth rate of stress, so that the stress maintains a small shear rate in the unyielded region and maintains a linear growth in the yielded region; Π D is the second-order invariant shear strain rate tensor; τ c is the material yield strength; The pier is discretized into wall boundary particles, and the particle type of the pier is labeled mk2.

9. The bridge pier pile erosion model and simulation system based on SPH smooth particles according to claim 1, characterized in that: In the control equation solving module, coupled calculation is performed on the water-sand mixture particles in the watershed, and the motion of the water-sand mixture particles is controlled according to the Navier-Stokes equation. The SPH discrete form of the mass conservation equation is: In the formula, subscript a represents the central particle; subscript b represents the domain particle; m b is the mass of the field particle; is the Hamiltonian operator for the central particle; ρ a represents the density of the central particle; ρ b represents the density of the field particles; u ab is the velocity difference between the central particle and the field particle, W is the kernel function; Introducing the SPS term, the momentum conservation equation is discretized as: Where μ0 is the kinematic viscosity; τ ij is the SPS stress vector; u a is the velocity of the central particle; P a The pressure of the central particle; P b is the pressure of the field particles; g is the gravitational acceleration; r ab is the distance between the central particle and the field particle, η is the smoothing length; is the stress vector of the central particle; is the stress vector of the field particle; For all particles numbered mk1, the density and viscous stress coupling calculations are repeated, and the velocity v and position pos information of the selected particles are updated.

10. The bridge pier pile erosion model and simulation system based on SPH smooth particles according to claim 1, characterized in that: The abrasion rate calculation module loops through all the pier wall particles mk2 to determine whether there are water-sand mixture particles within the kernel function radius, and calculates the impact angle between the wall particles and the mixture particles according to the mixture particle position pos information obtained by the control equation solving module as follows: i i =arccos(||v i ·n j ||) In the formula, v i is the unit velocity normal vector of particle i of the water-sand mixture; θ i is the impact angle between the two types of particles; n j is the unit external normal vector of the wall particle j, which is determined based on its relative center position information: n j =pos j -pos o In the formula, pos j is the position array of particle j in the XY plane; pos o is the position array of the pier column's center of gravity in the XY plane; Combined with the velocity information of the mixture particles obtained by the control equation solving module, for the wall particle j, based on the improved SPH form Neilson-Gilchrist erosion formula, its SPH discrete form is obtained, and the abrasion rate E of each pier wall particle within the specified solution time is calculated. r,j : Where W is the kernel function; V i is the volume of particle i; E ij is the erosion rate caused by fluid particle i within the radius of the kernel function of boundary particle j, and is calculated using the improved SPH form Neilson-Gilchrist erosion formula: In the formula, u p,i is the velocity of fluid particle i colliding with 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, which is determined by experiment; S is the compressive strength of concrete, ω is the roundness coefficient of sediment particles, Where C1 is the circumference of the vertical projection of the sand grain, and C2 is the circumference of the largest inscribed circle in the vertical projection of the sand grain.

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