Near-field dynamics method for soil erosion and piping prediction

Abstract

The invention discloses a near-field dynamics method for soil erosion and piping prediction, and relates to geotechnical engineering, and the method comprises the following steps: S1, building a solid model of a soil body and a water flow area; s2, endowing the model with material attributes according to experimental conditions; s3, performing spatial discretization on the model by adopting an orthogonal uniform discretization method to form material points occupying a specific space, generating a near-field range according to the size, dividing a water flow region and a soil body region, and generating water-water, soil-water and soil-soil bonds; s4, setting initial and boundary conditions, establishing a space integral equation of water flow movement based on near-field dynamics, and solving water flow diffusion by using a static implicit algorithm; s5, reconstructing the Darcy law to calculate the flow velocity of the fluid, and judging whether the soil body is eroded or not according to the flow velocity and the shear strength; and S6, constructing a spatial integral equation of solid expansion and sol migration of bentonite. When the soil body is not eroded, the volume fraction is solved, and otherwise, the migration state is calculated. The model can effectively simulate the fluid diffusion and soil erosion process, and provides a model framework for the prediction of the piping problem.

Description

Technical Field

[0001] The invention belongs to the technical field of geotechnical engineering, and in particular relates to a near-field dynamics method for soil erosion and piping prediction. Background Art

[0002] Soil erosion and piping are two common and complex forms of foundation damage, which are widely present in various projects such as embankments, dam foundations, and riverbeds, and pose a severe challenge to project safety. Soil erosion refers to the process in which soil particles are gradually washed and transported under the action of water flow. As the water flow velocity increases, the hydrodynamic action continuously removes particles on the surface of the soil, causing the soil strength to gradually weaken. When soil erosion occurs inside the soil, soil particles in local areas continue to be lost, resulting in unstable cavities or gaps. Over time, this process gradually develops and forms a continuously expanding channel, which is called piping. The continuous erosion of the soil and piping phenomena not only accelerate the instability of the foundation, but may also cause more serious geological disasters, threatening the safety of infrastructure such as embankments and bridges. Therefore, studying the mechanism, development law and interaction of soil erosion and piping, and proposing effective prevention and control measures are important topics to ensure the safety of engineering structures and prevent disasters.

[0003] At present, most of the publicly published studies on soil erosion and piping are experimental studies. The reason is the complexity of the physical process, which involves multi-physical field coupling, nonlinear behavior of soil, infiltration and erosion. Traditional numerical methods represented by the finite element method are based on the theory of continuous media, and it is difficult to accurately capture the local particle loss and migration of soil particles in the soil. In particular, the piping process also involves problems such as pore destruction and structural instability. Peridynamics (PD) is a new method based on the idea of ​​non-local action. This method uses spatial integral equations to replace the differential equations in the original continuous medium mechanics to describe the movement of discrete points. It is suitable for non-continuous problems such as cracking and destruction, as well as multi-scale and large deformation problems. Compared with traditional numerical methods, peridynamic methods have greater potential in soil erosion and piping problems.

[0004] However, there are still difficulties in applying the existing peridynamic algorithms to soil erosion and piping problems. On the one hand, the seepage process of water in the soil is extremely slow and is often considered a quasi-static process. The erosion and destruction of the soil often take more than 10 hours to gradually form a piping channel. The use of dynamic explicit algorithms commonly used in peridynamics consumes a lot of computing time and resources, so it is necessary to develop a static implicit calculation scheme suitable for soil erosion and piping calculations. However, in the fully implicit calculation process, when soil destruction is involved, it is easy to cause ambiguity in the stiffness matrix, making the calculation difficult, so it is necessary to rebuild the calculation model of soil erosion and piping. Summary of the invention

[0005] In order to solve the technical problems existing in the background technology, the present invention aims to provide a near-field dynamic method for soil erosion and piping prediction, and proposes a new soil erosion model. The model covers physical processes such as soil expansion, water flow and bentonite migration, and introduces a detachment model to solve the discontinuity problem between the solid and solution boundaries. The model was further developed into the piping problem, taking a dam section of Longwanggang as the research object, analyzing the possible evolution process of piping in the dam section, summarizing the evolution process of key parameters when piping occurs, and providing theoretical support and technical reference for actual engineering protection.

[0006] In order to solve the technical problem, the technical solution of the present invention is:

[0007] A peridynamic method for soil erosion and piping prediction, the method comprising:

[0008] S1: Establish a solid model of the soil and water flow area, and assign corresponding material properties to the solid model based on experimental conditions;

[0009] S2: The model is spatially discretized using an orthogonal uniform discretization format to form material points occupying a specific space, which are divided into a water flow area and a soil area, generating various types of connection bonds and the near-field range of the material points;

[0010] S3: Set initial conditions and boundary conditions, establish the spatial integral equation of water flow based on peridynamics theory, and use the static implicit algorithm to solve the diffusion and distribution of water flow;

[0011] S4: Reconstruct Darcy's law to calculate the fluid flow rate, and determine the relationship between shear force and shear strength based on the flow rate and dynamic viscosity to determine whether soil erosion occurs;

[0012] S5: Construct the spatial integral equations for bentonite solid expansion and sol migration, solve for the soil volume fraction when no erosion occurs, and calculate the migration state when erosion occurs.

[0013] Furthermore, in step S2, an orthogonal uniform discrete format is used to spatially discretize the model to form a series of material points occupying a certain space, and the material points are divided into a water flow area and a soil area, and different bond types are generated, including water-water bonds, water-soil bonds and soil-soil bonds, and the near-field range of the material points is generated according to the size of the material points.

[0014] Furthermore, in step S4, Darcy's law is reconstructed in combination with the peridynamic differential operator, the fluid flow rate is calculated, and the shear force of the fluid is calculated based on parameters such as the fluid flow rate and dynamic viscosity, and the magnitude of the shear force and the shear strength are determined. When the shear stress is less than the shear strength, the soil does not erode, and when the shear stress is greater than the shear strength, the soil erodes.

[0015] Furthermore, in step S5, a space integral equation for bentonite solid expansion and a space integral equation for sol migration are constructed based on peridynamic theory. When the soil is not eroded, the soil volume fraction is solved by the solid expansion space integral equation based on a static implicit algorithm. When the soil is eroded, the soil volume fraction is calculated by using the space integral equation for bentonite sol migration based on a static implicit algorithm.

[0016] Furthermore, the construction of the spatial integral equation and the static implicit algorithm include the following steps:

[0017] Establish the water flow motion equation, bentonite solid expansion equation and bentonite sol migration equation; reconstruct the differential equations based on the peridynamics theory to obtain the spatial integral equations of water flow motion, bentonite solid expansion and bentonite sol migration equations; set the initial conditions and boundary conditions of the soil erosion model; assemble the overall stiffness matrix required for implicit solution, and establish the overall matrix solution equation. The boundary conditions are applied through the Lagrange multiplier method, and the direct stiffness method or iterative method is used to solve the material point information at each time step.

[0018] Furthermore, the spatial integral equation of the water flow movement, bentonite solid expansion, and bentonite sol migration equation is:

[0019] The peridynamic equations of water flow are:

[0020]

[0021] Where p is the fluid pore pressure, S is the specific water storage rate, k is the fluid diffusion coefficient. x′ is the other material points in the near field of material point x, H x is the near field of material point x, δ is the near field radius, ξ is the distance vector between material points, ξ=x′-x. V x′ is the volume of the material point x′.

[0022] The peridynamic equation for bentonite solid expansion is:

[0023]

[0024] in, is the soil volume fraction at the material point x, and d(x,x′,t) is the peridynamic microscopic diffusion coefficient of bentonite.

[0025] When erosion occurs, the peridynamic form of the bentonite sol migration equation is:

[0026]

[0027] Wherein, μ(x,x′,t) is the separation function, when the shear stress induced by the water flow exceeds the shear strength, μ(x,x′,t) = 1. When the shear stress does not reach the shear strength, μ(x,x′,t) = 0, and v is the fluid flow rate.

[0028] Furthermore, the initial conditions and boundary conditions are set, the spatial integral equation of water flow motion is established based on the peridynamics theory, and the static implicit algorithm is used to solve the diffusion and distribution of water flow; specifically, it includes:

[0029] For the fluid equation, under steady-state conditions, The matrix equation to be solved between two material points can be written in the following form:

[0030] k p u p =0 (4)

[0031] Where u p =[p i p j ] T , k p is the stiffness matrix, which is specifically expressed as:

[0032]

[0033] According to formula (4), the overall matrix equation is assembled as follows:

[0034] K p U P =0 (6)

[0035] For the bentonite solid expansion equation, the backward difference method is used, and its discretization format is:

[0036]

[0037] The matrix equation to be solved between two material points is expressed as:

[0038]

[0039] In the formula is the stiffness matrix of the bentonite solid expansion equation, specifically:

[0040]

[0041] The r matrix is ​​the known result of the previous step,

[0042] The overall matrix equation of bentonite solid expansion is assembled according to formula (8):

[0043]

[0044] Similarly, when soil erosion occurs, the stiffness matrix is:

[0045]

[0046] Its overall stiffness matrix equation is expressed as:

[0047] K ψ U ψ =R (12)

[0048] Therefore, the three types of control equations are expressed in a unified form:

[0049] K m U m =R m (13)

[0050] in R p =0,

[0051] The boundary conditions are transformed into Introduced into the matrix equation, its form is:

[0052]

[0053] Furthermore, step S4 involves calculation of fluid velocity and determination of whether soil erosion occurs, and the specific process is as follows:

[0054] The non-local form of Darcy's law is constructed by the peridynamic differential operator, and the velocity distribution is solved according to the pressure distribution obtained in step S3; the shear force is solved according to the fluid velocity and compared with the shear strength of the soil to determine whether the soil is eroded; if the required shear force is less than the shear strength, the bentonite solid expansion matrix equation is used to solve the soil volume fraction; if the required shear force is greater than the shear strength, the bentonite sol migration matrix equation is used to solve the soil volume fraction.

[0055] Compared with the prior art, the advantages of the present invention are:

[0056] The present invention proposes a peridynamic method for soil erosion and piping prediction, and the model can simulate the diffusion of fluid, bentonite solid expansion and the diffusion process of bentonite after erosion. Based on the peridynamic theory, the differential equations adopted are all expressed in the form of spatial integral equations, which can be further applied to the analysis of non-continuity problems such as cracking and destruction. The model uses a static implicit algorithm to solve the control equation, which can realize the simulation of soil erosion process under long time scales (such as hundreds of hours), and provides a basic model framework for solving piping problems, further supporting the research on piping prediction. The model effectively avoids the non-continuity problems that may occur in the soil erosion process, and provides a new idea for solving piping. In addition, the establishment and development of the static implicit algorithm has laid a solid foundation for comprehensively describing the whole process of soil erosion and piping evolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a main flow chart of soil erosion calculation provided by the present invention.

[0058] Figure 2 It is a framework diagram of the soil erosion model of the present invention, which explains the relationship between different physical processes.

[0059] Figure 3 It is a soil erosion geometric model.

[0060] Figure 4 The following are the soil erosion results under static water conditions and flow rate of 0.38 ml / min.

[0061] Figure 5 It is the variation curve of the volume fraction of soil at the center line of the model along the distance in the y direction under two working conditions. The simulation results are compared with the experimental results.

[0062] Figure 6 It is the evolution curve of the extrusion (upstream expansion) distance with time under two working conditions. The simulation results are compared with the experimental results.

[0063] Figure 7 It is a geometric model diagram including the dam body and soil foundation, which is constructed based on a certain dam section of Longwanggang.

[0064] Figure 8 It is the water pressure distribution diagram of the dam body and soil foundation before the pipe burst occurs.

[0065] Fig. 9 It is the distribution diagram of water velocity in the dam body and foundation before and after the piping occurs.

[0066] Fig.10 It is a schematic diagram of the results of piping evolution. DETAILED DESCRIPTION

[0067] The specific implementation mode of the present invention is described below in conjunction with embodiments:

[0068] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0069] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0070] Embodiment 1:

[0071] The invention relates to the field of geotechnical engineering technology, and discloses a soil erosion and piping prediction method, comprising the following steps: S1: establishing a physical model of a soil body and a water flow area; S2: assigning corresponding material properties to the physical model according to experimental conditions; S3: using an orthogonal uniform discrete format to perform spatial discretization on the model to form a series of material points occupying a certain space. The material points are divided into a water flow area and a soil body area, and different bond types are generated, including water-water bonds, water-soil bonds and soil-soil bonds. The near-field range of the material point is generated according to the size of the material point; S4: setting initial conditions and boundary conditions. Based on the peridynamic theory, a spatial integral equation of water flow motion is established, and a static implicit algorithm is used to solve the diffusion and distribution of the water flow. S5: Reconstructing Darcy's law in combination with a peridynamic differential operator to calculate the fluid flow rate. The shear force of the fluid is calculated according to parameters such as the fluid flow rate and dynamic viscosity, and the shear force and shear strength are judged. When the shear stress is less than the shear strength, the soil body does not erode, and when the shear stress is greater than the shear strength, the soil body erodes. S6: Based on the peridynamics theory, the space integral equation of bentonite solid expansion and the space integral equation of sol migration are constructed. When the soil is not eroded, the soil volume fraction is solved by the solid expansion space integral equation. When the soil is eroded, the space integral equation of bentonite sol migration is used to calculate the soil volume fraction. Based on the peridynamics theory, the present invention proposes a soil erosion model, which can simulate the fluid diffusion, bentonite solid expansion and the diffusion process of bentonite after erosion. The model uses a static implicit algorithm to solve the control equation, which can realize the simulation of soil erosion process on a long time scale, and provides a basic model framework for solving the piping problem, further supporting the research on piping prediction.

[0072] Specifically, this embodiment proposes a near-field dynamic model of soil erosion, which can simulate the diffusion of fluids, the solid expansion of bentonite, and the diffusion process of bentonite after erosion. The model uses a static implicit algorithm to solve the control equations, which can simulate the soil erosion process on a long time scale, and provides a basic model framework for solving the piping problem, further supporting the research on piping prediction. The model effectively avoids the non-continuity problem that may occur in the soil erosion process, and provides a new idea for solving piping. Figure 1 , is the main flow chart of soil erosion calculation, Figure 2 This is the framework diagram of the soil erosion model. The establishment and solution of the model include the following steps:

[0073] S1: Establish the solid model of soil and water flow area;

[0074] S2: Assign corresponding material properties to the solid model according to the experimental conditions;

[0075] S3: Use the orthogonal uniform discretization format to spatially discretize the model, forming a series of material points occupying a certain space. Divide the material points into water flow areas and soil areas, and generate different types of bonds, including water-water bonds, water-soil bonds, and soil-soil bonds. Generate the near-field range of the material points according to the size of the material points;

[0076] S4: Set initial conditions and boundary conditions. Based on the peridynamic theory, establish the spatial integral equation of water flow motion, and use the static implicit algorithm to solve the diffusion and distribution of water flow.

[0077] S5: Reconstruct Darcy's law by combining the peridynamic differential operator to calculate the fluid velocity. Calculate the shear force of the fluid based on parameters such as the fluid velocity and dynamic viscosity, and determine the magnitude of the shear force and shear strength. When the shear stress is less than the shear strength, the soil will not erode. When the shear stress is greater than the shear strength, the soil will erode.

[0078] S6: Based on the peridynamic theory, the space integral equation of bentonite solid expansion and the space integral equation of sol migration are constructed. When the soil is not eroded, the soil volume fraction is solved by the solid expansion space integral equation. When the soil is eroded, the space integral equation of bentonite sol migration is used to calculate the soil volume fraction.

[0079] Steps S4 and S6 involve the construction of water flow, bentonite spatial integral equation and bentonite sol migration spatial integral equation. The main integral control equations are as follows:

[0080] The peridynamic equations of water flow are:

[0081]

[0082] The peridynamic equation for bentonite solid expansion is:

[0083]

[0084] When erosion occurs, the peridynamic form of the bentonite sol migration equation is:

[0085]

[0086] The nonlocal form of Darcy's law is obtained through the peridynamic differential operator and is expressed as:

[0087]

[0088] Among them, T f is the permeability of a specific fluid (such as clay sol / gel) in the fracture. g(ξ) is the peridynamic vector.

[0089] In steps S4 and S6, the static implicit solution process of multiple equations is involved. The construction of the overall matrix solution equation and the application of boundary conditions are as follows:

[0090] For the fluid equation, under steady-state conditions, The matrix equation to be solved between two material points can be written in the following form:

[0091] k p u p =0 (5)

[0092] Where u p =[p i p j ] T , k p is the stiffness matrix, which is specifically expressed as:

[0093]

[0094] According to formula (5), the overall matrix equation is assembled as follows:

[0095] K p U P =0 (7)

[0096] For the bentonite solid expansion equation, the backward difference method is used, and its discretization format is:

[0097]

[0098] The matrix equation to be solved between two material points is expressed as:

[0099]

[0100] In the formula is the stiffness matrix of the bentonite solid expansion equation, specifically:

[0101]

[0102] The r matrix is ​​the known result of the previous step,

[0103] According to formula (9), the overall bentonite solid expansion matrix equation is assembled:

[0104]

[0105] Similarly, when soil erosion occurs, the stiffness matrix is:

[0106]

[0107] Its overall stiffness matrix equation is expressed as:

[0108] K ψ U ψ =R (13)

[0109] Therefore, the three types of control equations can be expressed in a unified form:

[0110] K m U m =R m (14)

[0111] in R p =0,

[0112] The boundary conditions are transformed into Introduced into the matrix equation, its form is:

[0113]

[0114] By solving the matrix equation (15), we can obtain the fluid pressure and soil volume fraction.

[0115] The present invention will be further described below in conjunction with embodiments and drawings.

[0116] 1) A square calculation area of ​​24 cm (× (24 cm) was established, and the geometric model is as follows Figure 3 As shown, the blue square area is the water area, and the middle circular area (r = 1 (cm) is the soil area.

[0117] 2) Determine the value of the required parameter according to the experimental conditions. Particle surface area S p =9×10 -14 m 2, particle radius a = 200 mm, maximum soil volume fraction Water viscosity η w =1.002×10 -3 , the soil shear strength is set to τ s =5×10 3 The calculation is divided into two working conditions: one is the free expansion process of soil under static water flow, and the other is to set a certain pressure on the left and right boundaries so that the average water flow velocity is 0.38 (ml / min.

[0118] 3) The model was discretized using MATLAB software. The model was composed of a lattice structure of equally spaced material points. The size of the material points was Δx = 0.12 (cm), and the near-field radius was 0.36 (cm).

[0119] 4) Set initial conditions and boundary conditions. At the beginning of the calculation, the solid volume fraction of the initial experimental sample is 0.6, and it is assumed that the solid volume fraction of the central area (r≤2(cm) of the initial sample remains unchanged; the initial bentonite content in the outer area of ​​the sample is set to zero. The left boundary (x(=(-12(cm)) is kept at zero solid volume fraction, and after the soil particles are eroded and stripped, they will exit from the right boundary (x(=(12(cm). The upper and lower boundaries of the model (y(=(-12(cm( and (y(=(12(cm)) are set as impermeable boundary conditions.

[0120] 5) The static implicit algorithm is used to solve the fluid motion matrix equation to obtain the pressure and velocity distribution of the fluid. According to the shear force calculation formula, the shear stress of the fluid on the soil at the soil boundary is calculated. By comparing the shear stress with the shear strength, it is determined whether shear occurs in the soil here.

[0121] 6) When the shear stress is less than the shear strength, the soil in this area is not eroded, and the soil expansion is solved by the bentonite solid expansion matrix equation. When the shear stress is greater than the shear strength, the soil in this area is eroded, and the soil expansion is solved by the bentonite diffusion matrix equation after erosion. Both types of equations are solved using the static implicit strategy to calculate the soil volume fraction of the entire calculation domain.

[0122] 7) Calculate Figure 8 Under static water flow conditions, the soil expands evenly in all directions. Under conditions with a certain water flow rate, the soil may erode in the direction of the water flow.

[0123] 8) In order to verify the accuracy of the calculation results, the variation curves of the volume fraction of soil at the center line along the y direction are selected and compared with the experimental results, such as Figure 5 ; and the evolution curve of the squeezing (upstream expansion) distance over time, such as Figure 6The results show that the numerical calculation results under different working conditions are consistent with the experimental results.

[0124] Embodiment 2:

[0125] The soil erosion model is further extended to predict piping. In this example, a dam section of Longwanggang is used as the calculation object to simulate the entire process of piping from occurrence to development and then to penetration, showing the potential of the proposed model for use in piping problems. This implementation case specifically includes the following steps:

[0126] 1) Construct the actual model of the dam body and soil, such as Figure 7 As shown. The land base is 144(m long, the left side is 9.5(m high, the right side is 15.5(m high, the dam body is 48(m long and 11(m high).

[0127] 2) The permeability coefficient of water flow in soil is 1.0×10 -10 ((m / s, the permeability coefficient in the dam body is 1.0×10 -11 (m / s. The diffusion coefficient of the soil near the dam is 0.001(m 2 / s, and the diffusion coefficient in other areas is 0.01m 2 The remaining parameters are the same as those in the first embodiment.

[0128] 3) The model was discretized using MATLAB software. The model was composed of a lattice structure of equally spaced material points. The size of the material points was Δx = 0.25 (m, the near-field radius was 0.75 (m, and the total number of particles was 32651.

[0129] 4) Set initial conditions and boundary conditions. Assume that the upstream water level is 10 (m, and the pore water pressure of the downstream soil is 10000 (Pa. Piping often occurs in the weak area of ​​the downstream soil layer. When piping occurs, water flows out from the piping, and the pore water pressure is 0 (Pa. The initial water content in the soil is 40%, that is, the initial volume fraction of the soil is 60%.

[0130] 5) Before piping occurs, solve the pressure distribution of the soil foundation and the dam body, and obtain the following Figure 8 The pressure distribution of the pipe is obtained by using Darcy's law to solve the velocity distribution before the pipe burst occurs, as shown in Fig. 9 .

[0131] 6) Calculate the shear stress based on the fluid pressure and velocity. When the shear stress exceeds the shear strength, the soil erodes and piping begins. The fluid velocity distribution at the beginning of piping is as follows: Fig. 9 .

[0132] 7) After the piping occurs, it develops according to certain rules, which requires the following assumptions:

[0133] 7.1) When the soil is eroded, the soil volume fraction is solved by using the soil diffusion equation after erosion. The soil volume fraction decreases continuously. When it is as small as 15%, that is, the water content reaches more than 85%, the soil is considered to be liquid at this time and is defined as the piping boundary.

[0134] 7.2) The boundary of piping is fluid soil, which is easily carried away by water flow. Therefore, the soil volume fraction drops rapidly. The boundary soil volume fraction loss rate is defined as 36% / h.

[0135] 7.3) Considering that the soil near the dam base will be filled and compacted artificially, the diffusion coefficient of the soil near the dam base is much smaller than that of other parts.

[0136] 8) After the piping occurs, the evolution process for 10 hours is calculated. Fig.10 As shown in the figure. In the first hour, the piping develops in the vertical direction. When it develops to a certain depth, the soil in the horizontal direction is carried out by the water flow, causing the piping to develop in the horizontal direction. The piping continues to spread upstream until it penetrates and forms a complete piping channel. The downstream soil and deep soil are eroded, seriously affecting the stability of the dam.

[0137] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0138] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0139] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0140] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0141] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

[0142] Many other changes and modifications may be made without departing from the concept and scope of the present invention.It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A peridynamic method for soil erosion and piping prediction, characterized in that: The method comprises: S1: Establish a solid model of the soil and water flow area, and assign corresponding material properties to the solid model based on experimental conditions; S2: The model is spatially discretized using an orthogonal uniform discretization format to form material points occupying a specific space, which are divided into a water flow area and a soil area, generating various types of connection bonds and the near-field range of the material points; S3: Set initial conditions and boundary conditions, establish the spatial integral equation of water flow based on peridynamics theory, and use the static implicit algorithm to solve the diffusion and distribution of water flow; S4: Reconstruct Darcy's law to calculate the fluid flow rate, and determine the relationship between shear force and shear strength based on the flow rate and dynamic viscosity to determine whether soil erosion occurs; S5: Construct the spatial integral equations for bentonite solid expansion and sol migration, solve for the soil volume fraction when no erosion occurs, and calculate the migration state when erosion occurs.

2. A peridynamic method for soil erosion and piping prediction according to claim 1, characterized in that: In step S2, an orthogonal uniform discretization format is used to spatially discretize the model to form a series of material points occupying a certain space, and the material points are divided into a water flow area and a soil area, and different bond types are generated, including water-water bonds, water-soil bonds and soil-soil bonds. The near-field range of the material points is generated according to the size of the material points.

3. A peridynamic method for soil erosion and piping prediction according to claim 1, characterized in that: In step S4, Darcy's law is reconstructed in combination with the peridynamic differential operator, the fluid flow rate is calculated, and the shear force of the fluid is calculated based on parameters such as the fluid flow rate and dynamic viscosity, and the magnitude of the shear force and the shear strength are determined. When the shear stress is less than the shear strength, the soil does not erode, and when the shear stress is greater than the shear strength, the soil erodes.

4. A peridynamic method for soil erosion and piping prediction according to claim 1, characterized in that: In the step S5, a space integral equation for bentonite solid expansion and a space integral equation for sol migration are constructed based on peridynamic theory. When the soil is not eroded, the soil volume fraction is solved by the solid expansion space integral equation based on a static implicit algorithm. When the soil is eroded, the soil volume fraction is calculated by using the space integral equation for bentonite sol migration based on a static implicit algorithm.

5. A peridynamic method for soil erosion and piping prediction according to claim 4, characterized in that: The construction of the space integral equation and the static implicit algorithm include the following steps: Establish the water flow motion equation, bentonite solid expansion equation and bentonite sol migration equation; reconstruct the differential equations based on the peridynamics theory to obtain the spatial integral equations of water flow motion, bentonite solid expansion and bentonite sol migration equations; set the initial conditions and boundary conditions of the soil erosion model; assemble the overall stiffness matrix required for implicit solution, and establish the overall matrix solution equation. The boundary conditions are applied through the Lagrange multiplier method, and the direct stiffness method or iterative method is used to solve the material point information at each time step.

6. A peridynamic method for soil erosion and piping prediction according to claim 5, characterized in that: The spatial integral equation of the water flow movement, bentonite solid expansion, and bentonite sol migration equation is: The peridynamic equations of water flow are: Where p is the fluid pore pressure, S is the specific water storage rate, k is the fluid diffusion coefficient, x′ is the other material points in the near field of material point x, and H x is the near field of material point x, δ is the near field radius, ξ is the distance vector between material points, ξ=x′-x, V x′ is the volume of the material point x′; Peridynamic equation for bentonite solid expansion: in, is the soil volume fraction at the material point x, d(x,x′,t) is the peridynamic microscopic diffusion coefficient of bentonite; When erosion occurs, the peridynamic form of the bentonite sol migration equation is: Wherein, μ(x,x′,t) is the separation function. When the shear stress induced by the water flow exceeds the shear strength, μ(x,x′,t)=1; when the shear stress does not reach the shear strength, μ(x,x′,t)=0; and v is the fluid flow rate.

7. A peridynamic method for soil erosion and piping prediction according to claim 5, characterized in that: The initial conditions and boundary conditions are set, the spatial integral equation of water flow motion is established based on the peridynamics theory, and the static implicit algorithm is used to solve the diffusion and distribution of water flow; specifically, it includes: For the fluid equation, under steady-state conditions, The matrix equation to be solved between two material points can be written in the following form: k p in p =0 (4) Where u p =[p i p j ] T , k p is the stiffness matrix, which is specifically expressed as: According to formula (4), the overall matrix equation is assembled as follows: K p IN P =0 (6) For the bentonite solid expansion equation, the backward difference method is used, and its discretization format is: The matrix equation to be solved between two material points is expressed as: In the formula is the stiffness matrix of the bentonite solid expansion equation, specifically: The r matrix is ​​the known result of the previous step. The overall matrix equation of bentonite solid expansion is assembled according to formula (8): Similarly, when soil erosion occurs, the stiffness matrix is: Its overall stiffness matrix equation is expressed as: K ψ U ψ =R (12) Therefore, the three types of control equations are expressed in a unified form: K m U m =R m (13) in R p =0, The boundary conditions are transformed into Introduced into the matrix equation, its form is:

8. A peridynamic method for soil erosion and piping prediction according to claim 3, characterized in that: The step S4 involves the calculation of the fluid velocity and the determination of whether the soil is eroded, and the specific process is as follows: The non-local form of Darcy's law is constructed by the peridynamic differential operator, and the velocity distribution is solved according to the pressure distribution obtained in step S3; the shear force is solved according to the fluid velocity and compared with the shear strength of the soil to determine whether the soil is eroded; if the required shear force is less than the shear strength, the bentonite solid expansion matrix equation is used to solve the soil volume fraction; if the required shear force is greater than the shear strength, the bentonite sol migration matrix equation is used to solve the soil volume fraction.

Images