Scouring riprap grouting joint simulation modeling method based on random convex polyhedral stone

Abstract

The invention relates to the technical field of bridge scour protection, and discloses a scour riprap grouting joint simulation modeling method based on random convex polyhedral stones. Comprising the steps of polyhedron vertex determination, polyhedron inner and outer side face distinguishing, polyhedron entity modeling, bed surface shear stress analysis, grouting simulation analysis, comparison of different stone putting modes and combined protection recommendation of a design scheme. Stone modeling is performed through interaction of Python and AutoCAD, and multi-dimensional simulation analysis is realized from improvement of grouting critical shear stress and consideration of flow velocity and scouring conditions around a pile foundation; the method is easy to program, high in accuracy and strong in operability. Compared with a traditional protection mode, the combined protection efficiency is improved, and the method has more advantages in practical application. The influence of water depth and flow velocity on stone protection efficiency is analyzed, and a basis is provided for design and optimization of a protection scheme.

Description

Technical Field

[0001] The invention relates to the technical field of bridge scour protection, and in particular to a scour riprap grouting joint simulation modeling method based on random convex polyhedron stones. Background Art

[0002] In today's bridge engineering field, the failure of bridge structure function and loss of safety performance are important issues that need to be solved urgently, and hydrological factors are one of the main causes of these problems. This phenomenon has attracted widespread attention from many scholars. During the use of bridges, the scouring effect of water flow on the surrounding areas of pier pile foundations will seriously affect the stability and safety of bridges. The scouring of water flow may cause the silt around the pier pile foundation to be carried away, resulting in a reduction in the buried depth of the pile foundation and a decrease in the bearing capacity of the foundation, which in turn threatens the safety of the entire bridge structure.

[0003] At present, bridge scour protection methods are mainly divided into two categories: active protection and passive protection.

[0004] The core idea of ​​active protection is to change the flow field structure that causes scouring by setting specific structures or structures at different positions of the pier pile foundation, thereby reducing the erosion of sediment by water flow. Among many active protection methods, the effect of retaining ring protection is more significant. Studies have shown that when the retaining ring is set flush with the general scouring surface of the riverbed, its protection effect can reach the best state. However, active protection methods may be limited by many factors in actual application.

[0005] Passive protection is mainly focused on increasing the starting shear stress of the bed. Common passive protection measures include riprap, gabions, concrete blocks and other riprap alternatives, as well as expanded foundation protection. In actual projects, riprap is one of the most commonly used passive protection measures. However, there are some shortcomings in this method. The stability and integrity of direct riprap are relatively weak, and it is easy to move and disperse under the long-term action of water flow. Therefore, secondary protection is usually required, which increases the project cost and construction difficulty.

[0006] With the deepening of research, domestic and foreign researchers have begun to explore combined protection methods based on the traditional single scour protection method. The main idea of ​​this method is to combine two or more protection methods, hoping to achieve a better protection effect than a single protection method. These studies have provided new ideas and directions for bridge scour protection, but they also face many challenges.

[0007] Based on the research status of the above-mentioned bridge scour protection methods, there is an urgent need for a scour riprap grouting combined protection simulation modeling method based on random convex polyhedron stones. Summary of the invention

[0008] The purpose of the present invention is to provide a combined simulation modeling method of scouring riprap grouting based on random convex polyhedral stones, which solves the technical problems raised in the background technology.

[0009] The purpose of the present invention can be achieved by the following technical solutions:

[0010] The scouring riprap grouting joint simulation modeling method based on random convex polyhedron stones includes the following steps:

[0011] StepA1: Determine the vertices of the polyhedron

[0012] Random convex polyhedron stone modeling based on Python and AutoCAD interaction

[0013] StepA1.1. Determine the vertices of the polyhedron using spherical coordinates. The formula is as follows:

[0014]

[0015] Get the vertex coordinates (x, y, z) of the polyhedron;

[0016] Among them, θ and φ are key parameters for determining vertex coordinates, r represents the distance from the vertex to the origin, θ is the elevation angle, which ranges from 0 to π, and φ is the azimuth angle, which ranges from 0 to 2π;

[0017] StepA1.2, by determining the distance between the vertices of the polyhedron, determine whether there is interference between the vertices;

[0018] The formula is as follows:

[0019]

[0020] In the formula, (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two vertices, and L is the distance between the two vertices;

[0021] Compare L with the preset interference distance threshold Lmin:

[0022] If L>Lmin, it means that there is no interference between the two vertices, otherwise, it means that there is interference between the two vertices;

[0023] Step A2: Distinguish the inner and outer sides of the polyhedron

[0024] Distinguish between the outer and inner sides of the polyhedron among the generated random points;

[0025] First, the plane abc formed by any three points in space is defined as the external normal direction vector of the plane:

[0026] Its external normal direction vector The calculation formula is as follows:

[0027]

[0028] in,

[0029]

[0030] Traverse all the vertices of the polyhedron and define the connection direction vector between the vertex and any point in the plane abc as

[0031] The direction vector connecting the vertex to any point in the plane abc The calculation formula is as follows:

[0032]

[0033] If there is If the value is less than 0, that is, the angle between the two vectors is greater than 90°, it means that all points in the space are not on the same side of the plane, and the face does not meet the convexity condition and is not the outer side of the polyhedron, so the face is discarded;

[0034] If any The values ​​of are greater than 0, that is, the angle between the two vectors is less than 90°, which means that all points in the space are on the same side of the plane, and the surface meets the convexity condition, and the plane is defined as the outer side of the polyhedron;

[0035] Step A3: Polyhedron solid modeling

[0036] After determining the outer side surface of the polyhedron, multiple sets of data files containing three points are obtained;

[0037] Determine the output order of the three points on the outer surface, and output the coordinates of the three points in a clockwise direction;

[0038] The purpose is to ensure that when the sphere is sliced, the inner part where the polyhedron is located is retained and the outer part of the polyhedron is discarded;

[0039] The specific operations to determine the clockwise output order of the three points are as follows:

[0040] StepA3.1. Select three points a, b, and c on the outer side of the polyhedron and calculate

[0041] StepA3.2, Calculation and The vector product of

[0042] StepA3.3, Calculation and The dot product of

[0043] If the dot product is less than 0, it means a, b, and c are in clockwise order;

[0044] On the contrary, if a, b, and c are in counterclockwise order, they are re-output in the order of a, c, and b;

[0045] After determining the output order of the three points on the outer side surface, the clockwise output data of the three points on the outer side surface of the polyhedron is obtained, and the sphere is cut using the three-point cutting command in CAD;

[0046] Among them, after each cutting, the outer side surface after cutting is deleted by Boolean operation, and the inner side surface is retained. After traversing all the cutting point sets, the required polyhedron can be obtained;

[0047] StepA4: Bed surface shear stress analysis

[0048] When the bed shear stress exceeds the preset shear stress threshold, the eddy current will carry the particles away from the riverbed and suspend them, and the suspended sediment particles will be carried by the water flow;

[0049] Sedimentation occurs when suspended sediment particles settle to a sand bed due to the combined effects of gravity, buoyancy, and friction;

[0050] Among them, the shear stress threshold is expressed as critical shear stress;

[0051] StepA4.1, bed shear stress is the shear stress of the fluid acting on the surface of the packed bed, which is calculated based on the wall function of three-dimensional turbulence;

[0052] The specific formula is as follows:

[0053]

[0054] In the formula, u τ is the shear speed, τ is the bed shear stress, ρ is the packing density of the mixture of water and sediment; Y is the distance from the boundary wall of the unit grid center point; v is the kinematic viscosity of the fluid; k = 0.4 is the von Karman constant, k s is the roughness, k s =c s d 50 , d 50 is the median particle size of sediment, c s is a custom coefficient. In this embodiment, c s The value is 2.5;

[0055] Among them, in shallow water flow, the quadratic friction law is used to calculate the riverbed shear stress In the formula is the depth-averaged fluid velocity; ρf is the fluid density; C D is the drag coefficient, which is calculated based on the roughness k s Local determination:

[0056] in,

[0057]

[0058] Where h is the water depth, B = 0.71; z0 = k s / 30;

[0059] StepA4.2, Shields number is the dimensionless form of bed shear stress and is defined as:

[0060]

[0061] In the formula, θ n is the Shields number, g is the absolute value of gravity; ρ n is the mass density of sediment particles; d n is the particle diameter;

[0062] First, the physical processes related to bed shear stress are explained, and then its calculation method is introduced, including calculation based on three-dimensional turbulent wall function and calculation based on the law of quadratic friction in shallow water flow. Finally, the dimensionless form of the Shields number is given. They are interrelated and together describe the characteristics of bed shear stress and its influence on sediment movement.

[0063] Step A5: Grouting simulation analysis

[0064] StepA5.1, the grouting part uses the improved critical Shields number of the soil for simulation analysis;

[0065] The specific method is as follows:

[0066] Extract the known critical shear stress of erosion of silt-solidified soil, which is between 2.5-4Pa, and then back-calculate the equivalent critical Shields number of the grouting soil according to the critical Shields number formula;

[0067] The weighted shear stress is then used to evaluate the anti-scouring effect after grouting, and the formula is as follows:

[0068]

[0069] Among them A wcz is the area-weighted shear stress value, τ is the bed surface shear stress, τ cr is the critical shear stress of the bed surface;

[0070] StepA5.2. At the same time, the excess shear stress of the bed surface is extracted to reflect the shear stress distribution around the pile foundation, and then to estimate the scour development trend;

[0071] Among them, the excess shear stress of the bed surface is expressed as the part where the bed surface shear stress exceeds the critical shear stress of sediment;

[0072] The method for extracting the excess shear stress value per unit area is as follows:

[0073]

[0074] In the formula, is the average value of the excess shear stress, which is used to measure the protection effect; τ i is the shear stress value at a certain grid point on the bed surface; A i is the grid area;

[0075] StepA5.3. Conduct relevant analysis based on the fixed-bed scouring model of the stone flow-around analysis;

[0076] The specific method is as follows:

[0077] Extract the excess shear stress data in the 4D range before and after, left and right around the pile foundation, that is, within the nested grid, and use it as the basis for subsequent excess shear stress analysis;

[0078] StepA6. Comparison of different stone placement methods

[0079] Compare and analyze the protection effects of two stone placement methods: staggered circular arrangement and random arrangement

[0080] StepA6.1. For the staggered circular arrangement, the method is as follows:

[0081] The stones are distributed in three layers in total. The interval angle between adjacent stones in each layer is 30°, and the two adjacent layers are staggered by a rotation angle of 15°;

[0082] StepA6.2. For the random arrangement, the method is as follows:

[0083] StepA6.2.1. Randomly place polyhedrons in the set protection area. Consider placing them in the circular ring area, and set the center point of placement using polar coordinates:

[0084]

[0085] In the formula, R1 and R2 are the two radius values used to limit the placement area in the polar coordinate setting; among them, R1 is the inner radius and R2 is the outer radius, indicating that when the polyhedron is placed in the circular ring area, this area is the ring range determined by the radii R1 and R2; ρ is the radial variable in the polar coordinates, representing the distance from the pole to a certain point; among them, the value range of ρ is R1 < ρ < R2, that is, the distance from the placement point of the polyhedron to the center of the placement area should be between R1 and R2, and the pole represents the center of the placement area;

[0086] StepA6.2.2, at the same time, the distance between the centers of any two polyhedrons is controlled within a specified range by a preset lower limit of the distance, the purpose of which is to ensure that the polyhedrons are dispersed around the cylindrical pile foundation as evenly as possible;

[0087] The spacing calculation formula is as follows:

[0088]

[0089] Where L1 min is the preset lower limit of the spacing, which means the minimum distance allowed between the center points of two polyhedrons, and L1 min =3r1, where r1 is the stone particle size, (xb1, yb1, zb1) and (xb2, yb2, zb2) are the coordinates of the two polyhedrons, and L1 is the distance between the center points of the two polyhedrons;

[0090] StepA6.2.3, generate the center point coordinates of the polyhedron (xb i ,yb i ,zb i ), first generate a random polyhedron at the origin (0, 0, 0), and then distribute the random polyhedron around the cylinder by translation to complete the random layout of the random polyhedron;

[0091] StepA7: Recommended design scheme for joint protection

[0092] Perform statistical analysis on the supershear stress grid data in the computational domain;

[0093] The specific method is as follows:

[0094] Divide the statistical data of the supershear stress cloud map into 12 data intervals: [0, 0.1], [0.1, 0.2], [0.2, 0.3], ..., [1.1, 1.2];

[0095] In each data interval, the corresponding frequency and probability density are calculated; the frequency calculation formula is:

[0096]

[0097] where n i is the number of data in the i-th data interval, N is the total number of statistical data; the probability density calculation formula is:

[0098]

[0099] Where L represents the length of the data interval, and L is taken as 0.1 in data analysis.

[0100] The purpose is to explore the distribution of excess shear stress around pile foundations under different stone and grouting parameters in order to obtain the optimal recommended design scheme for combined protection;

[0101] As a further solution of the present invention: in Step A4, fluid analysis calculation is also performed based on Flow-3D;

[0102] Flow-3D uses the continuity equation and the Navier-Stokes equations for incompressible viscous fluids as the governing equations for fluid motion;

[0103] Among them, considering that the fluid is a Newtonian fluid, combined with Flow-3D's unique FAVOR grid technology, the continuity equation and momentum equation contain volume and area fraction parameters;

[0104] As a further solution of the present invention: in Step A4, the bed surface shear stress calculation involves solving the related equations using the generalized minimum residual GMRES algorithm:

[0105] The solution is as follows:

[0106] First, an intermediate velocity is introduced, without considering the influence of the pressure at the new moment on the velocity field, but the pressure correction value at the current moment is introduced;

[0107] The intermediate speeds are obtained by solving the momentum equation, where the momentum equation is an equation describing the change in fluid momentum, and solving it can give the intermediate speeds;

[0108] Then, the relationship between the intermediate velocity and the pressure correction value is substituted into the continuity equation to generate the pressure Poisson equation containing the pressure correction value;

[0109] Finally, the GMRES algorithm is applied to solve the pressure Poisson's equation.

[0110] As a further solution of the present invention: in Step A5, the critical Shields number is used to determine whether the sediment will start to move from a dimensionless perspective;

[0111] The critical Shields number is used to characterize the critical bed shear stress τ cr,n The dimensionless form of the bed shear stress τ ≥ τ cr,n When the mud and sand start to move;

[0112] The specific calculation is as follows:

[0113]

[0114] where θ cr,n is the critical Shields number, θ cr,n According to the properties of sediment, the calculation equation is as follows:

[0115]

[0116] Among them, d *,n is the dimensionless particle size, d *,n It reflects the influence of factors such as sediment particle diameter, gravitational acceleration, density difference between sediment and fluid, and fluid kinematic viscosity on sediment movement. It is a key intermediate parameter for calculating the critical Shields number.

[0117] d *,n The calculation formula is:

[0118]

[0119] Among them, d n represents the diameter of sediment particles, g is the acceleration due to gravity, s n =ρ n / ρ f , ρ n is the mass density of sediment particles, ρ f is the fluid density, s n represents the relative density of sediment and fluid, v f It is the kinematic viscosity of the fluid, which indicates the ability of the fluid to resist deformation and is related to the viscosity of the fluid. The smaller its value is, the easier the fluid flows, and the force on the sediment particles will change accordingly, thereby affecting the movement state of the sediment.

[0120] As a further solution of the present invention: in Step A5, the net exchange rate between the accumulated and suspended sediments is determined by the entrainment velocity and the deposition velocity of the sediment;

[0121] Among them, the entrainment rate and deposition rate of sediment are regarded as two opposite micro-processes occurring simultaneously, which are interrelated and proceed simultaneously;

[0122] The sediment entrainment velocity is calculated according to the following formula:

[0123]

[0124] Among them, α n is the entrainment coefficient of the nth type of sediment, n b is the outward normal vector of the filling bed;

[0125] The sediment settling velocity is calculated according to the following formula:

[0126]

[0127] Where g is the acceleration due to gravity and u settle,n Same direction.

[0128] As a further solution of the present invention: In Step A5, the dimensionless form of the sediment transport rate of the nth layer is defined as:

[0129]

[0130] Among them, Φ n is the sediment transport rate of the nth layer, which is used to comprehensively characterize the intensity and characteristics of sediment transport and facilitate the unified comparison and analysis of sediment transport under different sediment and water flow conditions. b,n is the sediment transport rate per unit width of the bed surface, which refers to the volume of sediment passing through the bed surface per unit width per unit time. It directly reflects the amount of sediment transported on the bed surface and is an important physical quantity for measuring the sediment transport process. b,n The calculation formula is as follows:

[0131] q bn =B n (θ n -θ c,n ) 1.5 c b,n

[0132] Among them, B n is the bed sediment transport coefficient;

[0133] Among them, the low-speed transport coefficient is usually 5.0-5.7, about 8.0 at medium transport rates, and up to 13.0 at high transport rates;

[0134] c bn is the volume fraction of n substances in the bed medium:

[0135]

[0136] As a further solution of the present invention: in Step A7, the expected value of supershear stress is also calculated according to the supershear stress probability density statistical diagram;

[0137] The expected value is calculated as follows:

[0138]

[0139] Where E(X) is the expected value of super shear stress, X i is the median of the ith data interval, P(X i ) is the probability corresponding to the i-th data interval, and n is the total number of data intervals;

[0140] By integrating the information in the supershear stress probability density statistical diagram, an expected value that can represent the average level of supershear stress is obtained, so as to more intuitively understand the overall distribution characteristics of supershear stress.

[0141] Beneficial effects of the present invention:

[0142] The scour riprap grouting combined protection simulation modeling method based on random convex polyhedron stones proposed in the present invention has significant advantages. A random convex polyhedron stone modeling method based on Python and AutoCAD interaction was developed. This innovative modeling method is easy to implement programmatically. Complex polyhedron stone models can be efficiently generated through programming, which reduces the workload and errors of manual modeling, provides an accurate model basis for subsequent scour protection analysis, and greatly improves the efficiency and operability of the entire research process.

[0143] The present invention realizes comprehensive simulation analysis from multiple key dimensions with high accuracy. On the one hand, starting from improving the critical starting shear stress of the grouting part, based on clean water flushing, the grouting part around the pile foundation can be accurately simulated and analyzed. This allows us to have an in-depth understanding of the mechanism of action of grouting in the protection process and its response to different water flow conditions, so as to better optimize the grouting parameters. On the other hand, starting from the flow velocity around the pile foundation, based on fixed bed flushing, the stone disturbance effect is effectively simulated and analyzed. In this way, we can clearly grasp the role of stones in the water flow and how to reduce the scouring of sediment around the pile foundation by changing the water flow state. In addition, starting from the scouring conditions around the pile foundation, a comprehensive simulation analysis of joint protection is realized based on clean water flushing, which fully considers the mutual influence of various factors and provides a reliable basis for the evaluation of the effect of joint protection.

[0144] Based on the analysis of flow velocity, scour pit morphology, scour depth change and other aspects, the stone joint protection of the present invention shows obvious advantages over traditional protection methods such as sacrificial piles, retaining rings, and riprap. The protection efficiency is significantly improved under the joint protection conditions, which is more competitive in practical applications. This advantage is reflected in the long-term and stable protection of the bridge structure, which can effectively reduce maintenance costs and extend the service life of the bridge.

[0145] The present invention uses fixed bed simulation and the change in the mean value of super shear stress as an indicator to deeply analyze the influence of water depth and flow velocity on the stone protection efficiency. The research results show that the water depth factor has little effect on the mean value of super shear stress around the pile foundation, which provides a reference for the protection design under different water depths. At the same time, the relationship between flow velocity and stone protection efficiency is clarified, that is, when the flow velocity is low, the stone protection efficiency increases with the increase of flow velocity, but when the flow velocity reaches a certain value, the improvement of the stone protection efficiency is no longer obvious. This conclusion helps to reasonably select and optimize the protection plan according to the actual water flow velocity, and further improve the pertinence and effectiveness of the protection measures. BRIEF DESCRIPTION OF THE DRAWINGS

[0146] The present invention will be further described below in conjunction with the accompanying drawings.

[0147] Figure 1 It is a flow chart of the simulation modeling method of scour riprap grouting combined protection based on random convex polyhedral stones of the present invention;

[0148] Figure 2 It is a schematic diagram of the protection range and protection corner point coordinates of the multi-pile piers pre-selected by the present invention;

[0149] Figure 3 It is a schematic diagram of the multi-pile pier protection plane layout and top rough surface of the present invention;

[0150] Figure 4 is a schematic diagram of a three-dimensional convex polyhedron of the present invention;

[0151] Figure 5 This is a schematic diagram of the staggered circular placement and random placement of stones used in the present invention;

[0152] Figure 6 It is the flow line diagram around the single pile foundation under no protection and combined protection used in the present invention;

[0153] Figure 7 It is a schematic diagram of the scour morphology of multi-pile foundation piers with and without combined protection used in the present invention.

[0154] In the figure, (x1 rect1 ,y1 rect1 )、(x1 rect1 ,y2 rect1 )、(x2 rect1 ,y2 rect1 )、(x2 rect1 ,y1 rect1 ) is the coordinate of the inner corner point of the protection range; (x1 rect2 ,y1 rect2 )、(x1 rect2 ,y2 rect2 )、(x2 rect2 ,y2 rect2 )、(x2 rect2 ,y1 rect2 ) are the coordinates of the outer corner points of the protection range; 4 is the position of the pile foundation; 5 is the position of the pier; 6 is the rough surface of the top of the riprap protection; 7 is a sphere; 8 is a partially cut sphere; 9 is a polyhedron; 10 is staggered circular placement; 11 is random placement; 12 is the scouring pit shape and streamline of a single pile without protection; 13 is the scouring pit shape and streamline of a single pile with combined protection; 14 is the scouring shape of multi-pile foundation bridge piers without combined protection; 15 is the scouring shape of multi-pile foundation bridge piers with combined protection.

[0155] Figures 2 to 7 It plays a role in visually displaying the content of the invention and verifying the effect of the invention in the full text;

[0156] pass Figures 2 to 5, which can intuitively display the key technical points such as protection range, structural layout, stone modeling and placement method, and can more clearly understand each link of the scour riprap grouting joint protection simulation modeling method based on random convex polyhedron stones;

[0157] Figure 6 and Figure 7 By comparing the scour morphology and depth data under unprotected and combined protection conditions, the effectiveness of the combined protection method is strongly demonstrated. DETAILED DESCRIPTION

[0158] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0159] exist Figure 2 In the process, according to the protection range and the protection corner point coordinates, determine the stone center point coordinates of the protection range;

[0160] It is determined as follows:

[0161] (x∈(x1 rect1 ,x1 rect2 )∩(x2 rect2 ,x2 rect1 ),y∈(y1 rect1 ,y2 rect1 ))∪(x∈

[0162] (x1 rect1 ,x2 rect1 ),y∈(y1 rect1 ,y1 rect2 )∩(y2 rect2 ,y2 rect1 ))

[0163] exist Figure 6 In the scour pit morphology diagram, under the riprap protection condition, due to the high flow velocity on both sides of the pile foundation, the water flow will carry the riprap, and a certain amount of scouring will occur on both sides of the pile foundation, but the overall scouring depth is reduced compared with no protection measures. At the end of 600s, the depth of the scour pit on both sides is 1.166cm, which is lower than the scouring depth (2.939cm) under the condition of no protection measures, and the maximum scouring depth reduction rate is 60.3%;

[0164] exist Figure 7 In the case of combined protection, the maximum scouring depth after scouring for 30 minutes is 0.63m, while the maximum scouring depth after scouring for 30 minutes without combined protection is

[0165] 1.012m. After applying the combined protection, the scour depth on both sides and the rear of the pile foundation cap was improved;

[0166] The specific implementation method of the present invention takes Flow3D as an example, develops a random convex polyhedron stone modeling method based on the interaction of Python and AutoCAD, and establishes a joint protection scour simulation model based on random convex polyhedron stones.

[0167] Embodiment 1

[0168] See also Figure 1 The present invention is a combined simulation modeling method for scouring riprap grouting based on random convex polyhedron stones, including random convex polyhedron stone modeling based on Python and AutoCAD interaction, which includes the following steps:

[0169] StepA1: Determine the vertices of the polyhedron

[0170] Random convex polyhedron stone modeling based on Python and AutoCAD interaction;

[0171] StepA1.1. Determine the vertices of the polyhedron using spherical coordinates. The formula is as follows:

[0172]

[0173] Get the vertex coordinates (x, y, z) of the polyhedron;

[0174] Among them, θ and φ are key parameters for determining vertex coordinates, r represents the distance from the vertex to the origin, θ is the elevation angle, which ranges from 0 to π, and φ is the azimuth angle, which ranges from 0 to 2π;

[0175] StepA1.2, by determining the distance between the vertices of the polyhedron, determine whether there is interference between the vertices;

[0176] The formula is as follows:

[0177]

[0178] In the formula, (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two vertices, and L is the distance between the two vertices;

[0179] Compare L with the preset interference distance threshold Lmin:

[0180] If L>Lmin, it means that there is no interference between the two vertices, otherwise, it means that there is interference between the two vertices;

[0181] Step A2: Distinguish the inner and outer sides of the polyhedron

[0182] Random convex polyhedron stone modeling based on Python and AutoCAD interaction

[0183] Distinguish between the outer and inner sides of the polyhedron among the generated random points;

[0184] First, the plane abc formed by any three points in space is defined as the external normal direction vector of the plane:

[0185] Its external normal direction vector The calculation formula is as follows:

[0186]

[0187] in,

[0188]

[0189] Traverse all the vertices of the polyhedron and define the connection direction vector between the vertex and any point in the plane abc as

[0190] The direction vector connecting the vertex to any point in the plane abc The calculation formula is as follows:

[0191]

[0192] If there is If the value is less than 0, that is, the angle between the two vectors is greater than 90°, it means that all points in the space are not on the same side of the plane, and the face does not meet the convexity condition and is not the outer side of the polyhedron, so the face is discarded;

[0193] If any The values ​​of are greater than 0, that is, the angle between the two vectors is less than 90°, which means that all points in the space are on the same side of the plane, and the surface meets the convexity condition, and the plane is defined as the outer side of the polyhedron;

[0194] Step A3: Polyhedron solid modeling

[0195] Random convex polyhedron stone modeling based on Python and AutoCAD interaction

[0196] After determining the outer side surface of the polyhedron, multiple sets of data files containing three points are obtained;

[0197] Determine the output order of the three points on the outer surface, and output the coordinates of the three points in a clockwise direction;

[0198] The purpose is to ensure that when the sphere is sliced, the inner part where the polyhedron is located is retained and the outer part of the polyhedron is discarded;

[0199] The specific operations to determine the clockwise output order of the three points are as follows:

[0200] StepA3.1. Select three points a, b, and c on the outer side of the polyhedron and calculate

[0201] StepA3.2, Calculation and The vector product of

[0202] StepA3.3, Calculation and The dot product of

[0203] If the dot product is less than 0, it means a, b, and c are in clockwise order;

[0204] On the contrary, if a, b, and c are in counterclockwise order, they are re-output in the order of a, c, and b;

[0205] After determining the output order of the three points on the outer side surface, the clockwise output data of the three points on the outer side surface of the polyhedron is obtained, and the sphere is cut using the three-point cutting command in CAD;

[0206] Among them, after each cutting, the outer side surface after cutting is deleted by Boolean operation, and the inner side surface is retained. After traversing all the cutting point sets, the required polyhedron can be obtained;

[0207] This embodiment realizes the random convex polyhedron stone modeling based on the interaction of Python and AutoCAD. By determining the vertices of the polyhedron, distinguishing the inner and outer sides, and solid modeling, it establishes the foundation for the subsequent protection model and can accurately construct the stone model for scour protection related research.

[0208] Embodiment 2

[0209] As the second embodiment of the present invention, when the present application is implemented, compared with the first embodiment, the technical solution of the present embodiment is different from the first embodiment only in that the present embodiment further includes the following steps:

[0210] StepA4: Bed surface shear stress analysis

[0211] StepA4.1, bed shear stress is the shear stress of the fluid acting on the surface of the packed bed, which is calculated based on the wall function of three-dimensional turbulence;

[0212] The specific formula is as follows:

[0213]

[0214] In the formula, u τ is the shear speed, τ is the bed shear stress, ρ is the packing density of the mixture of water and sediment; Y is the distance from the boundary wall of the unit grid center point; v is the kinematic viscosity of the fluid; k = 0.4 is the von Karman constant, k s is the roughness, k s =c s d 50 , d 50 is the median particle size of sediment, c s is a custom coefficient. In this embodiment, c s The value is 2.5;

[0215] Among them, in shallow water flow, the quadratic friction law is used to calculate the riverbed shear stress In the formula is the depth-averaged fluid velocity; ρ f is the fluid density; C D is the drag coefficient, which is calculated based on the roughness k s Local determination:

[0216] in,

[0217]

[0218] Where h is the water depth, B = 0.71; z0 = k s / 30;

[0219] Among them, the related equations involved in the bed shear stress calculation are solved using the generalized minimum residual GMRES algorithm:

[0220] The solution is as follows:

[0221] First, an intermediate velocity is introduced, without considering the influence of the pressure at the new moment on the velocity field, but the pressure correction value at the current moment is introduced;

[0222] The intermediate speeds are obtained by solving the momentum equation, where the momentum equation is an equation describing the change in fluid momentum, and solving it can give the intermediate speeds;

[0223] Then, the relationship between the intermediate velocity and the pressure correction value is substituted into the continuity equation to generate the pressure Poisson equation containing the pressure correction value;

[0224] Finally, the GMRES algorithm is applied to solve the pressure Poisson equation;

[0225] StepA4.2, Shields number is the dimensionless form of bed shear stress and is defined as:

[0226]

[0227] In the formula, θ nis the Shields number, g is the absolute value of gravity; ρ n is the mass density of sediment particles; d n is the particle diameter;

[0228] When the bed shear stress exceeds the preset shear stress threshold, the eddy current will carry the particles away from the riverbed and suspend them, and the suspended sediment particles will be carried by the water flow;

[0229] Sedimentation occurs when suspended sediment particles settle to a sand bed due to the combined effects of gravity, buoyancy, and friction;

[0230] Among them, the shear stress threshold is expressed as critical shear stress;

[0231] First, the physical processes related to bed shear stress are explained, and then its calculation method is introduced, including calculation based on three-dimensional turbulent wall function and calculation based on the law of quadratic friction in shallow water flow. Finally, the dimensionless form of the Shields number is given. They are interrelated and together describe the characteristics of bed shear stress and its influence on sediment movement.

[0232] In this step, fluid analysis calculations are also performed based on Flow-3D;

[0233] Flow-3D uses the continuity equation and the Navier-Stokes equations for incompressible viscous fluids as the governing equations for fluid motion;

[0234] Among them, considering that the fluid is a Newtonian fluid, combined with Flow-3D's unique FAVOR grid technology, the continuity equation and momentum equation contain volume and area fraction parameters;

[0235] Step A5: Grouting simulation analysis

[0236] StepA5.1, the grouting part uses the improved critical Shields number of the soil for simulation analysis;

[0237] The specific method is as follows:

[0238] Extract the known critical shear stress of erosion of silt-solidified soil, which is between 2.5-4Pa, and then back-calculate the equivalent critical Shields number of the grouting soil according to the critical Shields number formula;

[0239] The weighted shear stress is then used to evaluate the anti-scouring effect after grouting, and the formula is as follows:

[0240]

[0241] Among them A wcz is the area-weighted shear stress value, τ is the bed surface shear stress, τ cr is the critical shear stress of the bed surface;

[0242] Among them, the critical Shields number is used to determine whether the sediment will start to move from a dimensionless perspective;

[0243] The critical Shields number is used to characterize the critical bed shear stress τ cr,n The dimensionless form of the bed shear stress τ ≥ τ cr,n When the mud and sand start to move;

[0244] The specific calculation is as follows:

[0245]

[0246] where θ cr,n is the critical Shields number, θ cr,n According to the properties of sediment, the calculation equation is as follows:

[0247]

[0248] Among them, d *,n is the dimensionless particle size, d *,n It reflects the influence of factors such as sediment particle diameter, gravitational acceleration, density difference between sediment and fluid, and fluid kinematic viscosity on sediment movement. It is a key intermediate parameter for calculating the critical Shields number.

[0249] d *,n The calculation formula is:

[0250]

[0251] Among them, d n represents the diameter of sediment particles, g is the acceleration due to gravity, s n =ρ n / ρ f , ρ n is the mass density of sediment particles, ρ f is the fluid density, s n represents the relative density of sediment and fluid, v f It is the kinematic viscosity of the fluid, which indicates the ability of the fluid to resist deformation and is related to the viscosity of the fluid. The smaller its value, the easier the fluid flows, and the force acting on the sediment particles will change accordingly, thus affecting the movement state of the sediment.

[0252] The dimensionless form of the sediment transport rate of the nth layer is defined as:

[0253]

[0254] Among them, Φ nis the sediment transport rate of the nth layer, which is used to comprehensively characterize the intensity and characteristics of sediment transport and facilitate the unified comparison and analysis of sediment transport under different sediment and water flow conditions. b,n is the sediment transport rate per unit width of the bed surface, which refers to the volume of sediment passing through the bed surface per unit width per unit time. It directly reflects the amount of sediment transported on the bed surface and is an important physical quantity for measuring the sediment transport process. b,n The calculation formula is as follows:

[0255] q bn =B n (θ n -θ c,n ) 1.5 c b,n

[0256] Among them, B n is the bed sediment transport coefficient;

[0257] Among them, the low-speed transport coefficient is usually 5.0-5.7, about 8.0 at medium transport rates, and up to 13.0 at high transport rates;

[0258] c bn is the volume fraction of n substances in the bed medium:

[0259]

[0260] StepA5.2. At the same time, the excess shear stress of the bed surface is extracted to reflect the shear stress distribution around the pile foundation, and then to estimate the scour development trend;

[0261] Among them, the excess shear stress of the bed surface is expressed as the part of the bed surface shear stress exceeding the critical shear stress of the sediment;

[0262] The method for extracting the supershear stress per unit area is as follows:

[0263]

[0264] In the formula, is the mean value of super shear stress, which is used to measure the protection effect; τ i is the shear stress value at a grid point on the bed surface; A i is the grid area;

[0265] StepA5.3, conduct relevant analysis on the fixed bed scour model based on the stone flow analysis;

[0266] The specific method is as follows:

[0267] Extract supershear stress data in the 4D range around the pile foundation, i.e., in the nested grid, and use it as the basis for subsequent supershear stress analysis;

[0268] In this embodiment, the bed shear stress analysis is added, and its calculation method and related physical processes are clarified, including calculation based on three-dimensional turbulent wall functions and the quadratic friction law of shallow water flow. The Shields number is also introduced, and fluid analysis is carried out in combination with Flow-3D. At the same time, the anti-erosion effect is evaluated in the grouting simulation analysis, which can more comprehensively analyze sediment movement and protection effect.

[0269] Embodiment III

[0270] As Embodiment III of the present invention, in the specific implementation of this application, compared with Embodiment I and Embodiment II, the technical solution of this embodiment is to combine and implement the solutions of the above Embodiment I and Embodiment II. The difference between the technical solution of this embodiment and Embodiment I and Embodiment II is only that this embodiment also includes a comparison of different stone placement methods;

[0271] Compare and analyze the protection effects of two stone placement methods, namely staggered circular arrangement and random arrangement. Specifically:

[0272] StepA6.1. For the staggered circular arrangement, the method is as follows:

[0273] The stones are distributed in three layers in total. The interval angle between adjacent stones in each layer is 30°, and the two adjacent layers are staggered by a rotation angle of 15°;

[0274] StepA6.2. For the random arrangement, the method is as follows:

[0275] StepA6.2.1. Randomly place polyhedrons within the set protection area. Considering placing them within a circular ring area, use polar coordinates to set the center point of placement:

[0276]

[0277] In the formula, R1 and R2 are the two radius values used to define the placement area in the polar coordinate setting. Among them, R1 is the inner radius and R2 is the outer radius, indicating that when the polyhedron is placed within the circular ring area, this area is the ring range determined by the radii R1 and R2; ρ is the radial variable in polar coordinates, representing the distance from the pole to a certain point. Among them, the value range of ρ is R1 < ρ < R2, that is, the distance from the placement point of the polyhedron to the center of the placement area should be between R1 and R2, and the pole represents the center of the placement area;

[0278] StepA6.2.2. At the same time, control the distance between the centers of any two polyhedrons within a specified range through a preset lower limit value of the spacing, and the purpose is to ensure that the polyhedrons are as evenly dispersed as possible around the cylindrical pile foundation;

[0279] The spacing calculation formula is as follows:

[0280]

[0281] Where L1 min is the preset lower limit of the spacing, which means the minimum distance allowed between the center points of two polyhedrons, and L1 min =3r1, where r1 is the stone particle size, (xb1, yb1, zb1) and (xb2, yb2, zb2) are the coordinates of the two polyhedrons, and L1 is the distance between the center points of the two polyhedrons;

[0282] StepA6.2.3, generate the center point coordinates of the polyhedron (xb i ,yb i ,zb i ), first generate a random polyhedron at the origin (0, 0, 0), and then distribute the random polyhedron around the cylinder by translation to complete the random layout of the random polyhedron;

[0283] This embodiment compares the protective effects of two stone placement methods, namely, staggered circular arrangement and random arrangement, and through specific arrangement methods and parameter settings, a more optimal stone placement scheme can be found to improve the protection efficiency.

[0284] Embodiment 4

[0285] As the fourth embodiment of the present invention, when the present application is specifically implemented, compared with the first embodiment, the second embodiment and the third embodiment, the difference between the present embodiment and the first embodiment, the second embodiment and the third embodiment is that the present embodiment further includes the steps of: a joint protection recommended design scheme;

[0286] The specific method is as follows:

[0287] Perform statistical analysis on the supershear stress grid data in the computational domain;

[0288] The specific method is as follows:

[0289] Divide the statistical data of the supershear stress cloud map into 12 data intervals: [0, 0.1], [0.1, 0.2], [0.2, 0.3], ..., [1.1, 1.2];

[0290] In each data interval, the corresponding frequency and probability density are calculated; the frequency calculation formula is:

[0291]

[0292] where n i is the number of data in the i-th data interval, N is the total number of statistical data; the probability density calculation formula is:

[0293]

[0294] Where L represents the length of the data interval, and L is taken as 0.1 in data analysis.

[0295] The purpose is to explore the distribution of excess shear stress around pile foundations under different stone and grouting parameters in order to obtain the optimal recommended design scheme for combined protection;

[0296] In this step, the expected value of supershear stress is also calculated based on the supershear stress probability density statistical diagram;

[0297] The expected value is calculated as follows:

[0298]

[0299] Where E(X) is the expected value of super shear stress, X i is the median of the ith data interval, P(X i ) is the probability corresponding to the i-th data interval, and n is the total number of data intervals;

[0300] By integrating the information in the supershear stress probability density statistical diagram, an expected value that can represent the average level of supershear stress is obtained, so as to more intuitively understand the overall distribution characteristics of supershear stress.

[0301] This embodiment performs statistical analysis on the super shear stress grid data, calculates the frequency, probability density and expected value, and can explore the super shear stress distribution around the pile foundation under different parameters, which is helpful to obtain the optimal recommended design scheme for combined protection.

[0302] Embodiment 5

[0303] As the fifth embodiment of the present invention, when the present application is specifically implemented, compared with the first, second, third and fourth embodiments, the technical solution of this embodiment is to combine and implement the solutions of the above-mentioned first, second, third and fourth embodiments.

[0304] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters and thresholds in the formula are set by technicians in this field according to actual conditions.

[0305] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A combined simulation modeling method for scouring and riprap grouting based on random convex polyhedron stones, characterized in that: The steps include: StepA1: Determine the vertices of the polyhedron First, the vertices of the polyhedron are determined by spherical coordinates; then, by determining the distance L between the vertices of the polyhedron, it is determined whether there is interference between the vertices. The determination method is to compare L with the preset interference distance threshold Lmin, and determine whether there is interference between two vertices based on the comparison result: Step A2: Distinguish the inner and outer sides of the polyhedron First, the plane abc formed by any three points in space is defined as the external normal direction vector of the plane: Then traverse all the vertices of the polyhedron and define the connection direction vector between the vertex and any point in the plane abc as Followed by The values ​​determine the outer side of the polyhedron; Step A3: Polyhedron solid modeling After determining the outer side surface of the polyhedron, multiple sets of data files containing three points are obtained; the output order of the three points on the outer side surface is determined, and the coordinates of the three points are output in a clockwise direction; after determining the output order of the three points on the outer side surface, the clockwise output data of the three points on the outer side surface of the polyhedron are obtained, and the sphere is cut using the three-point cutting command in CAD; wherein, after each cutting, the outer side surface after cutting is deleted using Boolean operation, and the inner side surface is retained, and the desired polyhedron is obtained after traversing all the cutting point sets; StepA4: Bed surface shear stress analysis StepA4.1, bed shear stress is the shear stress of the fluid acting on the surface of the filling bed, which is calculated based on the wall function of three-dimensional turbulence; then, according to the preset shear stress threshold of the bed shear stress, it is determined whether the sediment is deposited; StepA4.

2. Determine the dimensionless form of the bed shear stress: Shields number; Step A5: Grouting simulation analysis StepA5.1, the grouting part uses the improved critical Shields number of the soil for simulation analysis; StepA5.2, at the same time, extract the super shear stress of the bed surface, where the super shear stress of the bed surface is expressed as the part of the bed surface shear stress exceeding the critical shear stress of the sediment; StepA5.3, conduct relevant analysis on the fixed bed scour model based on the stone flow analysis; StepA6. Comparison of different stone placement methods Compare and analyze the protective effects of two stone placement methods: staggered circular arrangement and random arrangement; StepA7: Recommended design scheme for joint protection Perform statistical analysis on the supershear stress grid data within the computational domain.

2. The scouring riprap grouting joint simulation modeling method based on random convex polyhedron stones according to claim 1 is characterized in that: In StepA1, if L>Lmin, it means that there is no interference between the two vertices; otherwise, it means that there is interference between the two vertices.

3. The scouring riprap grouting joint simulation modeling method based on random convex polyhedron stones according to claim 1 is characterized in that: In StepA2, the external normal direction vector The calculation formula is as follows: in, The direction vector connecting the vertex to any point in the plane abc The calculation formula is as follows: In StepA2, if there is If the value is less than 0, that is, the angle between the two vectors is greater than 90°, it means that all points in the space are not on the same side of the plane, and the face does not meet the convexity condition and is not the outer side of the polyhedron, so the face is discarded; If any The values ​​of are greater than 0, that is, the angle between the two vectors is less than 90°, which means that all points in the space are on the same side of the plane, and the surface meets the convex condition, and the plane is defined as the outer side of the polyhedron.

4. The scouring riprap grouting joint simulation modeling method based on random convex polyhedron stones according to claim 1 is characterized in that: In StepA3, the specific operations to determine the clockwise output order of the three points are as follows: StepA3.

1. Select three points a, b, and c on the outer side of the polyhedron and calculate StepA3.2, Calculation and The vector product of StepA3.3, Calculation and The dot product of If the dot product is less than 0, it means a, b, and c are in clockwise order; On the contrary, if a, b, and c are in counterclockwise order, they will be re-output in the order of a, c, and b.

5. The scouring riprap grouting joint simulation modeling method based on random convex polyhedron stones according to claim 1 is characterized in that: In shallow water flow, the quadratic friction law is used to calculate the riverbed shear stress In the formula is the depth-averaged fluid velocity; ρ f is the fluid density; C D is the drag coefficient, which is calculated based on the roughness k s Local determination: in, Where h is the water depth, B = 0.71; z0 = k s / 30; In StepA4, the bed shear stress is calculated as follows: First, an intermediate speed is introduced, and at the same time, the pressure correction value at the current moment is introduced; The intermediate velocities are obtained by solving the momentum equation; Then, the relationship between the intermediate velocity and the pressure correction value is substituted into the continuity equation to generate the pressure Poisson equation containing the pressure correction value; Finally, the GMRES algorithm is applied to solve the pressure Poisson equation; In StepA4, when the bed shear stress exceeds the preset shear stress threshold, the eddy current takes the particles away from the riverbed and suspends them, and the suspended sediment particles are carried by the water flow; Sediment deposition occurs when suspended sediment particles settle onto the sand bed under the combined action of gravity, buoyancy, and frictional forces; Among them, the shear stress threshold is expressed as the critical shear stress; The formula in StepA4.1 is as follows: In the formula, u τ is the shear speed, τ is the bed shear stress, ρ is the packing density of the mixture of water and sediment; Y is the distance from the boundary wall of the unit grid center point; v is the kinematic viscosity of the fluid; k = 0.4 is the von Karman constant, k s is the roughness, k s =c s d 50 , d 50 is the median particle size of sediment, c s is a custom coefficient, c s The value is 2.5; StepA4.2, the dimensionless form of the bed shear stress, is defined as: In the formula, θ n is the Shields number, g is the absolute value of gravity; ρ n is the mass density of sediment particles; d n is the particle diameter; In StepA4, fluid analysis calculations are also performed based on Flow-3D; Flow-3D uses the continuity equation and the Navier-Stokes equation for incompressible viscous fluids as the governing equations of fluid motion.

6. The scouring riprap grouting joint simulation modeling method based on random convex polyhedron stones according to claim 1 is characterized in that: In StepA5, the critical Shields number is used to determine whether sediment will start to move from a dimensionless perspective; The critical Shields number is used to characterize the critical bed shear stress τ cr,n The dimensionless form of the bed shear stress τ ≥ τ cr,n When the mud and sand start to move; The specific calculation is as follows: where θ cr,n is the critical Shields number, θ cr,n According to the properties of sediment, the calculation equation is as follows: Among them, d *,n is the dimensionless particle size, d *,n It reflects the influence of factors such as sediment particle diameter, gravitational acceleration, density difference between sediment and fluid, and fluid kinematic viscosity on sediment movement. It is a key intermediate parameter for calculating the critical Shields number. d *,n The calculation formula is: Among them, d n represents the diameter of sediment particles, g is the acceleration due to gravity, s n =ρ n / ρ f , ρ n is the mass density of sediment particles, ρ f is the fluid density, s n represents the relative density of sediment and fluid, v f It is the kinematic viscosity of the fluid, which indicates the ability of the fluid to resist deformation and is related to the viscosity of the fluid. The smaller its value, the easier the fluid flows, and the force acting on the sediment particles will change accordingly, thus affecting the movement state of the sediment. In StepA5, the net exchange rate between deposited and suspended sediments is determined by the entrainment velocity and deposition velocity of the sediment; Among them, the entrainment velocity and deposition velocity of the sediment are regarded as two opposite micro-processes occurring simultaneously, and these two processes are interrelated and occur simultaneously; The sediment entrainment velocity is calculated according to the following formula: Among them, α n is the entrainment coefficient of the nth type of sediment, n b is the outward normal vector of the filling bed; The sediment settling velocity is calculated according to the following formula: Where g is the acceleration due to gravity and u settle,n Same direction; In StepA5, the dimensionless form of the sediment transport rate of the nth layer is defined as: Among them, Φ n is the sediment transport rate of the nth layer, q b,n is the sediment transport rate per unit width of the bed surface, q b,n The calculation formula is as follows: q bn =B n (i n -θ c,n ) 1.5 c b,n Among them, B n is the bed sediment transport coefficient; Among them, c b,n is the volume fraction of n substances in the bed medium.

7. The scouring riprap grouting joint simulation modeling method based on random convex polyhedron stones according to claim 1 is characterized in that: In StepA5.1, the simulation analysis method is as follows: Extract the erosion critical shear stress of the known silt-solidified soil, whose value is between 2.5 - 4 Pa, and then calculate the equivalent critical Shields number of the grouted soil mass by back-calculating according to the critical Shields number formula; Then, the anti-erosion effect after grouting is evaluated using the weighted shear stress, and the formula is as follows: Among them A wcz is the area-weighted shear stress value, τ is the bed surface shear stress, τ cr is the critical shear stress of the bed surface; In StepA5.2, the method for extracting the value of the excess shear stress per unit area is as follows: In the formula, is the mean value of super shear stress, τ i is the shear stress value at a grid point on the bed surface; A i is the grid area; In StepA5.3, the relevant analysis method is to extract the excess shear stress data within the 4D range before and after, left and right of the pile foundation, that is, within the nested grid.

8. The scouring riprap grouting joint simulation modeling method based on random convex polyhedron stones according to claim 1 is characterized in that: For the staggered circular arrangement, the method is as follows: The stones are distributed in three layers in total. The interval angle between adjacent stones in each layer is 30°, and the two adjacent layers are staggered by a rotation angle of 15°; For the random arrangement, the method is as follows: StepA6.2.1, Randomly place polyhedrons within the set protection area. Consider placing them within a circular ring area, and set the center point of placement using polar coordinates: StepA6.2.2, At the same time, control the distance between the centers of any two polyhedrons within the specified range through a preset lower limit value of the spacing; StepA6.2.3, generate the center point coordinates of the polyhedron (xb i ,yb i ,zb i ), first generate a random polyhedron at the origin (0, 0, 0), and then distribute the random polyhedron around the cylinder by translation to complete the random layout of the random polyhedron.

9. The scouring riprap grouting joint simulation modeling method based on random convex polyhedron stones according to claim 1 is characterized in that: In StepA6.2.1, the method for setting the center point of placement using polar coordinates is as follows: In the formula, R1 and R2 are respectively the two radius values used to define the placement area in the polar coordinate setting; among them, R1 is the inner radius and R2 is the outer radius, indicating that when the polyhedron is placed within the circular ring area, this area is the ring range determined by the radii R1 and R2; ρ is the radial variable in polar coordinates, representing the distance from the pole to a certain point; among them, the value range of ρ is R1 < ρ < R2, that is, the distance from the placement point of the polyhedron to the center of the placement area should be between R1 and R2, and the pole represents the center of the placement area; In StepA6.2.2, the spacing calculation formula is as follows: Where L1 min is the preset lower limit of the spacing, which means the minimum distance allowed between the center points of two polyhedrons, and L1 min =3r1, where r1 is the stone particle size, (xb1, yb1, zb1) and (xb2, yb2, zb2) are the coordinates of the two polyhedrons, and L1 is the distance between the center points of the two polyhedrons.

10. The scouring riprap grouting joint simulation modeling method based on random convex polyhedron stones according to claim 1, characterized in that: In StepA7, the statistical analysis method is as follows: Divide the statistical data of the supershear stress cloud map into 12 data intervals: [0, 0.1], [0.1, 0.2], [0.2, 0.3], ..., [1.1, 1.2]; In each data interval, the corresponding frequency and probability density are calculated; the frequency calculation formula is: where n i is the number of data in the i-th data interval, N is the total number of statistical data; the probability density calculation formula is: Where L represents the length of the data interval, and L is taken as 0.1 in data analysis; In StepA7, the expected value of supershear stress is also calculated based on the supershear stress probability density statistical diagram; The expected value is calculated as follows: Where E(X) is the expected value of super shear stress, X i is the median of the ith data interval, P(X i ) is the probability corresponding to the i-th data interval, and n is the total number of data intervals.

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