Water-soil coupling single-layer two-phase spf simulation method, device, equipment and medium

Abstract

The present application belongs to the technical field of numerical simulation and geotechnical engineering, and provides a water-soil coupled single-layer two-phase SPH simulation method, device, equipment and medium, wherein the method comprises: discretizing a calculation domain of a single-layer two-phase SPH particle model, giving physical parameters and establishing a neighbor list of particles; adopting Verlet integration to perform twice semi-step updating and once full-step updating; adopting a low-dissipation Riemann solver-based dissipation strategy to process the interaction between particles; according to the updating result, adopting a Drucker-Prager model and a return mapping algorithm to update stress and strain, to obtain an updated stress field; performing diffusion smoothing processing on the updated stress field, to obtain a single-layer two-phase SPH simulation result. The present application has the beneficial effect of realizing efficient, stable and accurate simulation of large deformation processes of geological disasters such as landslides and debris flows under water-soil coupling conditions.

Description

Technical Field

[0001] This invention relates to the fields of numerical simulation and geotechnical engineering technology, and in particular to a method, apparatus, equipment and medium for simulating a single-layer two-phase SPH coupled with water and soil. Background Technology

[0002] Rainfall infiltration is widely considered one of the main triggering factors for geological disasters such as landslides. Under the influence of rainfall, the pore water pressure in unsaturated soil gradually increases, while the matrix suction decreases, leading to a reduction in effective stress. As the shear strength of the soil weakens, the geological mass may lose stability, thereby inducing catastrophic damage such as landslides.

[0003] In conventional engineering practice, slope stability problems caused by rainfall are often analyzed using mesh-based numerical methods (such as the finite element method) for seepage-deformation coupling, especially in studying the triggering mechanisms of geological disaster instability. However, traditional mesh methods are prone to numerical instability and mesh distortion under large deformation conditions, making it difficult to effectively characterize the evolution process after a geological disaster occurs. In fact, in disaster risk assessment and prevention, the dynamic response after failure (such as the movement distance, volume, and potential impact on infrastructure of the sliding body) is of great significance. Therefore, there is an urgent need for novel numerical methods that can simultaneously capture the initiation and post-failure evolution of geological disasters.

[0004] Meshless particle-based methods have gained increasing attention due to their inherent suitability for large deformation calculations. Among them, the Smoothed Particle Hydrodynamics (SPH) method exhibits unique advantages in describing solid-liquid coupling and complex boundary deformations. However, existing SPH coupling methods generally suffer from the following shortcomings: First, they often employ two-layer modeling methods (such as the high-order dual-phase material point method for hydraulically coupled landslide simulation), resulting in low computational efficiency; second, they struggle to realize complex hydraulic boundary conditions, as they only consider fluid-solid interaction forces and neglect the seepage effect of water on the soil; third, they are prone to numerical oscillations and noise in stress field solutions, reducing the stability and prediction accuracy of the simulation. Summary of the Invention

[0005] Aimed at at least in solving one of the technical problems existing in the prior art, the present invention provides a method, apparatus, equipment and medium for simulating a single-layer two-phase SPH coupled with water and soil.

[0006] One aspect of the present invention provides a single-layer two-phase SPH simulation method for soil-water coupling, comprising: A single-layer two-phase SPH particle model of the target slope is constructed. The computational domain of the single-layer two-phase SPH particle model is discretized. Each particle is initialized with physical parameters and a neighbor list of the particles is established. The particles include real particles and boundary particles. The physical parameters include soil phase information and water phase information. The Verlet integral method is used to perform the first half-step update and the first full-step update based on the physical parameters of the particles, and the first update result is obtained. The interactions between particles are handled using a dissipation strategy based on a low-dissipation Riemann solver; A second half-step update is performed on the particles based on the first update result, resulting in the second update result. The first and second update results include updates to the particle's velocity, position, and density. Based on the second update results, the stress and strain of the single-layer two-phase SPH particle model are updated using the Drucker-Prager model and the back-mapping algorithm to obtain the updated stress field. The updated stress field was subjected to diffusion smoothing to obtain the simulation results of a single-layer two-phase SPH.

[0007] According to the aforementioned single-layer two-phase SPH simulation method for soil-water coupling, a single-layer two-phase SPH particle model of the target slope is constructed, the computational domain of the single-layer two-phase SPH particle model is discretized, and each particle is initialized with physical parameters and a neighbor list is established, including: Based on the basic physical parameters, three-dimensional topography, and hydraulic conditions of the target slope, a single-layer two-phase SPH particle model is constructed. Based on the cutoff radius, determine the neighbor list and interaction relationships of particles in the monolayer two-phase SPH particle model; Initialize the physical parameters of the particles, including position, velocity, soil phase mass, water phase mass, soil phase density, water phase density, porosity, saturation, pore water pressure, stress tensor, and strain rate.

[0008] According to the aforementioned single-layer two-phase SPH simulation method for soil-water coupling, the Verlet integral method is used to perform the first half-step update and the first full-step update based on the particle physical parameters, resulting in the first update result, including: At the beginning of each time step, Verlet integrals are used to pre-update the phase fraction and geometric state of half a time step, including updating the porosity, aqueous phase density and particle position of half a time step based on the porosity change rate, aqueous phase density change rate and velocity of the previous step. Based on the porosity and water phase density of the first half-step update, the pore water pressure and saturation are revised using the equation of state and soil-water characteristic curves. Based on physical parameters, the mixing density and mixing mass of particles in a single-layer two-phase SPH particle model are determined, with the first half-step update being:

[0009] in, Porosity For the density of water, The particle position; This indicates the sequence number of the previous step. For time steps; Based on the water density and particle positions updated in the first half-step, each real particle is traversed according to the momentum conservation equation of the mixture. Neighborhood particles Calculate the acceleration of the mixture:

[0010] in, For real particles speed; For neighborhood particles The quality; For real particles Stress tensor; For neighborhood particles Stress tensor; For real particles The density; For neighborhood particles The density; For spatial gradient operators; For kernel functions; For real particles saturation; For real particles pore water pressure; It is the acceleration due to gravity; The total number of particles in the neighborhood; After updating the acceleration of all particles, update the particle velocities to the complete time step:

[0011] in, The first velocity of the particle. The velocity of the particle in the previous step; Using Darcy's law and the seepage control equation, the seepage flux of the aqueous phase is updated in the first full step. The update formula is as follows:

[0012] in, For particles The permeation flow rate; For particles The permeability coefficient; For particles The acceleration.

[0013] According to the aforementioned single-layer two-phase SPH simulation method for soil-water coupling, the interaction between particles is handled using a dissipation strategy based on a low-dissipation Riemann solver, including: For interacting particles and particles In particles Pointing to particles Construct a Riemann problem between particles along the unit vector direction, and replace the average particle variable of the mixture with the Riemann solution of the Riemann problem to obtain the density dissipation term and momentum dissipation term as follows:

[0014] in, For density dissipation, This is the momentum dissipation term; The stress is in the left-hand state; The stress is in the right-hand state; The average density of the left and right states; The velocity in the left state; The velocity in the right state; The initial left state is located in the real particle. ; The initial right state, located in the neighboring particle ; For limiters, it is represented as:

[0015] Among them, the limiter This is used to ensure that the fluid is not dissipated when subjected to an expansion wave, where the expansion wave is represented as... ; These are coefficients used to control numerical dissipation. The reference sound velocity is for the water phase.

[0016] According to the aforementioned single-layer two-phase SPH simulation method for soil-water coupling, a second half-step update is performed on the particles based on the first update result to obtain the second update result, including: Soil phase mass conservation equation Water phase mass conservation equation Calculate the rate of change of porosity and the rate of change of water density for each real particle:

[0017] in, The bulk modulus of water; For real particles The matrix suction; Soil phase mass conservation equation Water phase mass conservation equation Update the real particles in the neighborhood, including the boundary particles. When the density change rate is reached, boundary particles The velocity and seepage flow rate are calculated using the following formula:

[0018] in, Boundary particles speed, Boundary particles The permeation flow rate; Based on the rate of change of porosity, the rate of change of aqueous phase density, and the current particle velocity, the soil porosity, aqueous phase density, and particle position are updated for the second half-step.

[0019] According to the aforementioned simulation method for single-layer two-phase SPH (soil-water coupling) model, based on the second update result, the stress and strain of the single-layer two-phase SPH particle model are updated using the Drucker-Prager model and the back-mapping algorithm to obtain the updated stress field, including: Based on the updated particle positions and velocities from the second update, the actual particle positions and velocities are discretized using SPH. velocity gradient for:

[0020] Based on real particles velocity gradient The strain rate tensor was calculated. and rotation tensor for:

[0021] in, It is the transpose of the tensor; Based on strain rate tensor and rotation tensor The stress rate tensor is calculated using the constitutive relations of the Drucker–Prager model. for:

[0022] in, Shear modulus; For the partial strain rate tensor; Bulk modulus; For strain rate tensor; It is a plastic multiplier; It is the expansion / contraction factor; This is the second deviatoric stress invariant; It is the deviatoric stress tensor; It is a rotation tensor; Unit tensor; Volume stress correction and deviatoric stress correction are performed using a return mapping algorithm, including: satisfy When the body stress is adjusted, the correction is:

[0023] in, To return the mapped stress tensor; To return the stress tensor before mapping; This is the first stress invariant; and The Drucke-Prager constant is calculated as follows:

[0024] in, Let be the friction angle. It is cohesive force; Based on the nonlinear cohesion-softening relationship, the cohesion is calculated to decrease exponentially with equivalent plastic strain. for:

[0025] in, Residual cohesion; Peak cohesion; The softening coefficient; Equivalent plastic strain, equivalent plastic strain and deviation plastic strain increment Related, the calculation method is as follows:

[0026] When satisfied When the deviatoric stress is corrected, the method is as follows:

[0027] in, To return the pre-mapping deviatoric stress tensor; By leveraging the weak compressibility of the aqueous phase, the relationship between pore water pressure and water density is established, where pore water pressure... Calculations are performed using the compressible state equation:

[0028] in, Let the speed of sound be the reference speed for water, and ; This is the reference density for water.

[0029] According to the aforementioned single-layer two-phase SPH simulation method for soil-water coupling, the updated stress field is subjected to diffusion smoothing processing to obtain the single-layer two-phase SPH simulation results, including: The diffusion smoothing process involves adding the diffusion term to the constitutive relation of the Drucker–Prager model, expressed as:

[0030] Among them, diffusion term The calculation formula is as follows:

[0031] in, The coefficient is set to 0.1; For smooth length; It is a position vector; For the diffusion operator, the calculation formula is as follows:

[0032] For the renormalization stress gradient, In Cartesian coordinates, the renormalized stress gradient is:

[0033]

[0034] After diffusion smoothing, the simulation results of a single-layer two-phase SPH include the velocity field, density field, pore water pressure field, saturation cloud map, and stress field during the simulation.

[0035] Another aspect of the present invention provides a single-layer two-phase SPH simulation device for soil-water coupling, comprising: The first module is used to construct a single-layer two-phase SPH particle model of the target slope, discretize the computational domain of the single-layer two-phase SPH particle model, initialize each particle with physical parameters and establish a neighbor list of the particles, where the particles include real particles and boundary particles, and the physical parameters include soil phase information and water phase information. The second module is used to perform the first half-step update and the first full-step update based on the particle's physical parameters using the Verlet integration method, and obtain the first update result. The third module is used to process the interactions between particles using a dissipation strategy based on a low-dissipation Riemann solver; The fourth module is used to perform a second half-step update on the particles based on the first update result, and obtain the second update result. The first update result and the second update result include updates to the particle's velocity, position and density. The fifth module is used to update the stress and strain of the single-layer two-phase SPH particle model based on the second update results, using the Drucker-Prager model and the return mapping algorithm, to obtain the updated stress field. The sixth module is used to perform diffusion smoothing on the updated stress field to obtain the simulation results of a single-layer two-phase SPH.

[0036] Another aspect of the present invention provides an electronic device, including a processor and a memory; The memory is used to store programs; The processor executes the program to implement the method as described above.

[0037] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the methods described above.

[0038] The beneficial effects of this invention are as follows: by precisely controlling numerical dissipation through a low-dissipation Riemann solver and suppressing stress oscillations by combining a stress diffusion term, the stability of the simulation is significantly improved while ensuring computational accuracy. This invention is applicable to the analysis of complex deformation processes of granular materials under water-soil coupling conditions, and can provide a reliable basis for risk assessment and instability prediction of geological disasters such as debris flows and landslides induced by extreme rainfall and other factors; it improves upon the shortcomings of existing SPH methods, such as low computational efficiency due to double-layer modeling and difficulty in handling complex hydraulic boundary conditions; and it solves the problem of numerical oscillations and noise that easily occur during stress field solving, thereby achieving efficient, stable, and accurate simulation of large deformation processes of geological disasters such as landslides and debris flows under water-soil coupling conditions. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the simulation process of a single-layer two-phase SPH for water-soil coupling according to an embodiment of the present invention.

[0040] Figure 2 This is a schematic diagram of particle discreteness according to an embodiment of the present invention.

[0041] Figure 3 This is an approximate particle diagram in the SPH of this invention embodiment.

[0042] Figure 4 This is an embodiment of the invention along the particlei and j Construction diagram of the Riemann problem of interaction lines.

[0043] Figure 5 This is a schematic diagram of the return mapping algorithm according to an embodiment of the present invention.

[0044] Figure 6 This is a one-dimensional seepage diagram of an embodiment of the present invention.

[0045] Figure 7 These are comparison diagrams of one-dimensional seepage results in embodiments of the present invention, where (a) is a one-dimensional seepage result with a resolution of 0.05m; and (b) is a one-dimensional seepage result with a resolution of 0.02m.

[0046] Figure 8 This is a two-dimensional slope model diagram according to an embodiment of the present invention.

[0047] Figure 9 This is a schematic diagram of a two-dimensional rainfall-induced landslide application simulation case according to an embodiment of the present invention, wherein (a) is a saturation cloud map; and (b) is an equivalent plastic strain cloud map.

[0048] Figure 10 This is a schematic diagram of a single-layer two-phase SPH simulation device for water-soil coupling according to an embodiment of the present invention. Detailed Implementation

[0049] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings. Throughout the description, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions. In the following description, suffixes such as "module," "part," or "unit" used to denote elements are used only for the purpose of illustrative purposes and have no specific meaning in themselves. Therefore, "module," "part," or "unit" can be used interchangeably. Terms such as "first," "second," etc., are used only to distinguish technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the sequential relationship of the indicated technical features. In the following description, the consecutive reference numerals for method steps are for ease of review and understanding. Adjusting the implementation order of steps, in conjunction with the overall technical solution of the present invention and the logical relationship between the various steps, will not affect the technical effect achieved by the technical solution of the present invention. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0050] refer to Figure 1 , Figure 1 This is a schematic diagram of the simulation method for a single-layer two-phase SPH (soil-water coupling) system, which includes, but is not limited to, steps S100~S600: S100: Construct a single-layer two-phase SPH particle model of the target slope, discretize the computational domain of the single-layer two-phase SPH particle model, initialize each particle with physical parameters and establish a neighbor list for the particle.

[0051] The particles include real particles and boundary particles, and the physical parameters include soil phase information and water phase information.

[0052] In some embodiments, a single-layer two-phase SPH particle model is constructed based on the basic physical parameters of the target slope, three-dimensional topography, and hydraulic conditions; the neighbor list and interaction relationships of the particles in the single-layer two-phase SPH particle model are determined based on the cutoff radius; the physical parameters of the particles are initialized, including position, velocity, soil phase mass, water phase mass, soil phase density, water phase density, porosity, saturation, pore water pressure, stress tensor, and strain rate.

[0053] Specifically, such as Figure 2 A single-layer two-phase SPH particle model is established, and the computational domain is discretized. Only one layer of particles is used to simultaneously represent the soil and water phases. Since a single-layer particle model is used, each particle in the research object carries information about both the soil and water phases. Therefore, porosity and saturation need to be defined to characterize the material composition of the soil-water mixture at that particle. The density of the mixture can be calculated from the soil-water two-phase density using the following formula:

[0054] in, Total density of the mixture; Porosity; Soil density; Saturation; Water density.

[0055] In some embodiments, such as Figure 2 The particle approximation map in SPH shown is constructed based on the cutoff radius to build a neighbor list and determine the interaction relationships between particles, providing support for subsequent kernel function interpolation and calculation of water-soil two-phase mechanical quantities. All particles are initialized with necessary physical quantities, including position, velocity, soil-water phase mass, soil-water phase density, porosity, saturation, pore water pressure, stress tensor, and strain rate.

[0056] For example, pore water pressure, water density, and saturation are initialized based on actual engineering conditions (target slope), and can be determined by hydrostatic pressure distribution, groundwater level conditions, or measured initial seepage field to ensure consistency between the initial stress state in the numerical simulation and the actual situation. Furthermore, for large-scale engineering cases, reasonable initial stress conditions are required to obtain reliable and accurate results. In this embodiment of the invention, the initial stress distribution is generated by applying gravity to a soil domain with a given pore water pressure distribution. To achieve rapid stabilization in the stress field, a damping force is introduced into the momentum equation, calculated as follows:

[0057] in, The direction is the Cartesian coordinate. For damping force; This is the damping coefficient, which is usually taken as 0.02; It is the elastic modulus; For smooth length; For speed.

[0058] This invention employs the strain softening Drucker-Prager constitutive model to describe the shear yielding characteristics of solid soil, and introduces the effective stress principle and seepage control equation to characterize the water phase effect. The parameters mainly include elastic modulus, Poisson's ratio, friction angle, peak cohesion, residual cohesion, softening coefficient, permeability coefficient, water reference density, water bulk modulus, soil-water characteristic curve, and reference sound velocity.

[0059] S200, based on the particle's physical parameters, uses the Verlet integration method to perform the first half-step update and the first full-step update, obtaining the first update result.

[0060] In some embodiments, the first half-step update is as follows: Predictive computations are performed at the beginning of each time step, using the Verlet integral scheme to pre-update the phase fraction and geometric state for half a time step.

[0061] First, based on the porosity change rate, water phase density change rate, and velocity from the previous step, the porosity, water phase density, and particle position at the half-time step are updated. Then, based on the updated porosity and water phase density, derived state quantities such as mixing density and mixing mass are derived and calculated. The pore water pressure and saturation are corrected by combining the equation of state and the soil-water characteristic curve, providing accurate intermediate state information for the subsequent calculation of interaction forces.

[0062]

[0063] in, Porosity For the density of water, The particle position; This indicates the sequence number of the previous step. For time steps.

[0064] In some embodiments, during the half-step state, hydraulic boundary conditions are simultaneously applied to particles near the boundary of the computational domain to correct pore water pressure or permeation flux, ensuring physical consistency between the inflow and outflow processes.

[0065] Specifically, under heavy rainfall conditions, when the rainfall intensity exceeds the saturated hydraulic conductivity of the soil, the surface suction tends to zero. At this point, due to the lack of neighborhoods for free surface particles, the zero-pressure boundary condition for the free surface can be implicitly satisfied in the established SPH governing equations, thus eliminating the need for additional boundary conditions. However, in the absence of rainfall, the normal permeability of free surface particles must be constrained to zero. Through this step, a reasonable distribution of the pore water pressure field and the stability of the boundary conditions can be effectively maintained in the intermediate state of time progression.

[0066] The first full-step update, under the condition that the half-step density and position are known, traverses each real particle according to the momentum conservation equation of the mixture. i Neighborhood particles j Calculate the acceleration of the mixture:

[0067] in, For particles i speed; For particles j The quality; For particles i Stress tensor; For particles j Stress tensor; For particles i The density; For particles j The density; For kernel functions; For particles i saturation; For particles i pore water pressure; This is the acceleration due to gravity.

[0068] After updating all particle accelerations, use the following formula to update particle velocities to the full time step.

[0069]

[0070] Meanwhile, for the aqueous phase, based on Darcy's law and the seepage control equation, the seepage flux update formula is:

[0071] in, For particles i The permeation flow rate; For particles i The permeability coefficient; For particles i The acceleration.

[0072] It is understood that the embodiments of the present invention employ no-slip boundary conditions. To ensure that boundary particles accurately reflect external constraints, and to guarantee the stability and consistency of the velocity and seepage fields near the boundary, when calculating neighboring particles as boundary particles, the soil stress tensor and the pore water pressure of the water phase are taken as the values ​​of the particles. i Same value.

[0073] S300 employs a dissipation strategy based on a low-dissipation Riemann solver to handle the interactions between particles.

[0074] In some embodiments, to suppress non-physical oscillations and tensile instability that may occur in large deformation simulations using the SPH method, appropriate numerical dissipation needs to be introduced. For example... Figure 4 As shown, the embodiments of the present invention employ a dissipation strategy based on a low-dissipation Riemann solver in the particle... i Pointing to particles j Construct a Riemann problem between particles along the unit vector direction. In this Riemann problem, the initial left state... Right state Located in the particle i and particles j Above, the discontinuity lies at the midpoint between the two particles. The Riemann problem solution yields jumps or average values ​​of the velocity, pressure, and other states at the cross-section.

[0075] Because this invention employs a single-layer two-phase strategy, each particle simultaneously carries information about both the soil and water phases. Furthermore, the momentum conservation equation is based on the mixture rather than a single water or soil phase. Therefore, numerical dissipation can be implicitly introduced simply by replacing the particle-average variable in the mixture's momentum conservation equation with the Riemann solution. The resulting density and momentum dissipation terms are shown below:

[0076] In the formula: For density dissipation, This is the momentum dissipation term; The stress is in the left-hand state; The stress is in the right-hand state; The average density of the left and right states; The velocity in the left state; The velocity in the right state; This represents the total number of particles in the neighborhood.

[0077] In the above formula The limiter is defined as follows:

[0078] Among them, the limiter This is used to ensure that the fluid is not dissipated when subjected to an expansion wave, where the expansion wave is represented as... ; These are coefficients used to control numerical dissipation. This is the reference sound velocity in the water phase. (Coefficient) Used to control numerical dissipation, recommended value ( (Represents the dimension of the model space).

[0079] S400, based on the first update result, performs a second half-step update on the particles to obtain the second update result, where the first update result and the second update result include updates to the particle's velocity, position and density.

[0080] In some embodiments, the soil phase mass conservation equation is adopted. Water phase mass conservation equation Calculate the rate of change of porosity and the rate of change of water density for each real particle:

[0081] in, The bulk modulus of water; For real particles The matrix suction; Since the boundary conditions used in this embodiment of the invention are no-slip boundary conditions, the soil mass conservation equation is adopted. Water phase mass conservation equation Update the real particles in the neighborhood, including the boundary particles. When the density change rate is reached, boundary particles The velocity and seepage flow rate are calculated using the following formula:

[0082] in, Boundary particles speed, Boundary particles The permeation flow rate; Based on the rate of change of porosity, the rate of change of aqueous density, and the current particle velocity, the soil porosity, aqueous density, and particle position are updated in a second half-step. This second half-step update advances the soil porosity, aqueous density, and particle position to the complete time step state, as detailed below:

[0083] Based on the second update results, the stress and strain of the single-layer two-phase SPH particle model are updated using the Drucker-Prager model and the return mapping algorithm to obtain the updated stress field.

[0084] In some embodiments, the particle positions and velocities updated based on the second update result are used to discretize and calculate the real particles using SPH. velocity gradient for:

[0085] Based on real particles velocity gradient The strain rate tensor was calculated. and rotation tensor for:

[0086] in, It is the transpose of the tensor; Based on strain rate tensor and rotation tensor The stress rate tensor is calculated using the constitutive relations of the Drucker–Prager model. for:

[0087] in, Shear modulus; For the partial strain rate tensor; Bulk modulus; For strain rate tensor; It is a plastic multiplier; It is the expansion / contraction factor; This is the second deviatoric stress invariant; It is the deviatoric stress tensor; It is a rotation tensor; Unit tensor; like Figure 5 The schematic diagram of the return mapping algorithm shown illustrates the use of this algorithm for volume stress correction and deviatoric stress correction, including: satisfy When the body stress is adjusted, the correction is:

[0088] in, To return the mapped stress tensor; To return the stress tensor before mapping; This is the first stress invariant; and The Drucke-Prager constant is calculated as follows:

[0089] in, Let be the friction angle. It is cohesive force; Based on the nonlinear cohesion-softening relationship, the cohesion is calculated to decrease exponentially with equivalent plastic strain. for:

[0090] in, Residual cohesion; Peak cohesion; The softening coefficient; Equivalent plastic strain, equivalent plastic strain and deviation plastic strain increment Related, the calculation method is as follows:

[0091] When satisfied When the deviatoric stress is corrected, the method is as follows:

[0092] in, To return the pre-mapping deviatoric stress tensor; By leveraging the weak compressibility of the aqueous phase, the relationship between pore water pressure and water density is established, where pore water pressure... Calculations are performed using the compressible state equation:

[0093] in, Let the speed of sound be the reference speed for water, and ; This is the reference density for water.

[0094] S600 was used to perform diffusion smoothing on the updated stress field to obtain the simulation results of a single-layer two-phase SPH.

[0095] In some embodiments, the diffusion smoothing process includes adding a diffusion term to the constitutive relation of the Drucker–Prager model, expressed as:

[0096] Among them, diffusion term The calculation formula is as follows:

[0097] in, The coefficient is set to 0.1; For smooth length; It is a position vector; For the diffusion operator, the calculation formula is as follows:

[0098] For the renormalization stress gradient, In Cartesian coordinates, the renormalized stress gradient is:

[0099]

[0100] After diffusion smoothing, the simulation results of a single-layer two-phase SPH include the velocity field, density field, pore water pressure field, saturation contour map, and stress field data obtained during the simulation. Figure 9 As shown, it includes a saturation contour plot (a) and an equivalent plastic strain contour plot (b).

[0101] The effects of the embodiments of the present invention are illustrated through the following experiments 1 and 2, as detailed below: Example 1: Two-dimensional granular flow. Infiltration tests were conducted to verify the infiltration boundary conditions and the proposed scheme's ability to solve transient unsaturated seepage problems. More specifically, the infiltration tests simulated water seeping downwards along the top surface of a rigid unsaturated soil column. The model is as follows: Figure 6 As shown. The soil column is initially unsaturated, with a constant matric suction force. Periodic boundary conditions are applied to both sides to achieve one-dimensional water flow. The bottom boundary of the soil column is impermeable, while the top implicitly satisfies the zero-pressure boundary condition. Two sets of particle resolutions, 0.05m and 0.02m, are used to generate 20 and 50 particles along the column height, respectively. Figure 7 The evolution of the ratio of matrix suction to the initial value is shown at two different particle resolutions, where (a) is the one-dimensional seepage result at a resolution of 0.05 m; and (b) is the one-dimensional seepage result at a resolution of 0.02 m. It can be determined that there is good consistency between the numerical results and the analytical solution results of the embodiments of the present invention.

[0102] Example 2: Two-Dimensional Rainfall Landslide Case Study. The proposed numerical method is used to simulate an initially unsaturated slope that becomes unstable due to water infiltration caused by heavy rainfall events. This case study aims to predict landslide occurrence and post-failure deformation. A schematic diagram of the slope geometry is shown below. Figure 8As shown. The bedrock is modeled as an impermeable material using solid wall boundary conditions; a no-slip boundary is used to simulate the perfectly rough interaction between the bedrock and the overlying soil layer. Soil behavior is simulated using an elastic-plastic Drucker-Prager model with strain softening. A linear SWCC model is used to characterize the hydraulic properties of the soil. It is assumed that the slope is initially unsaturated, with the initial groundwater surface located at the bottom of the slope. The initial pore water pressure distribution is set to a hydrostatic distribution, while the initial stress profile is generated by applying a gravity field and using a damping term to achieve rapid equilibrium. Water infiltration is then allowed to initiate the simulation, resulting in the following: Figure 8 Results are given at a particle resolution of 0.2m.

[0103] It can be determined that, at the model level, the single-layer two-phase structure of the embodiments of the present invention can directly describe the momentum exchange and seepage in the soil-water mixture system, avoiding the parameter complexity and numerical instability caused by the multi-phase interface coupling in the double-layer two-phase model; in terms of boundary condition treatment, the single-layer two-phase model is more likely to introduce continuous boundary processes such as rainfall infiltration and reservoir water level fluctuations, and the boundary application method is more direct and the physical meaning is clearer; in terms of computational efficiency, it reduces the number of particles, interphase coupling levels and the number of governing equations, and can significantly reduce the amount of computation and improve computational efficiency while ensuring the ability to characterize soil-water interaction and seepage effects; in terms of numerical methods, compared with the material point method, the SPH method adopts a meshless Lagrangian description method, which has stronger adaptability to large deformation, free interface evolution and material separation, is less prone to mesh distortion problems, and is more suitable for describing the high-speed movement and deposition diffusion process of landslides.

[0104] Figure 10 This is a schematic diagram of a single-layer two-phase SPH simulation device for water-soil coupling according to an embodiment of the present invention. The device includes a first module 1010, a second module 1020, a third module 1030, a fourth module 1040, a fifth module 1050, and a sixth module 1060.

[0105] The system comprises six modules: The first module constructs a single-layer two-phase SPH particle model of the target slope, discretizes the computational domain of the model, initializes each particle with physical parameters, and establishes a neighbor list for each particle (including real particles and boundary particles), with physical parameters including soil and water phase information. The second module performs a first half-step update and a first full-step update based on the particle's physical parameters using the Verlet integral method, yielding the first update result. The third module handles the interactions between particles using a dissipation strategy based on a low-dissipation Riemann solver. The fourth module performs a second half-step update based on the first update result, yielding the second update result, which includes updates to particle velocity, position, and density. The fifth module updates the stress and strain of the single-layer two-phase SPH particle model using the Drucker-Prager model and a back-mapping algorithm based on the second update result, obtaining the updated stress field. The sixth module performs diffusion smoothing on the updated stress field, yielding the single-layer two-phase SPH simulation result.

[0106] Exemplarily, with the cooperation of the first, second, third, fourth, fifth, and sixth modules in the device, the embodiment device can implement any of the aforementioned single-layer two-phase SPH simulation methods for soil-water coupling, namely, constructing a single-layer two-phase SPH particle model of the target slope, discretizing the computational domain of the single-layer two-phase SPH particle model, initializing each particle by assigning physical parameters and establishing a neighbor list for the particles, wherein the particles include real particles and boundary particles, and the physical parameters include soil phase information and water phase information; and performing the first half-step update and the first... A full-step update is performed to obtain the first update result. The interaction between particles is handled using a dissipation strategy based on a low-dissipation Riemann solver. A second half-step update is then performed on the particles based on the first update result, yielding the second update result. Both the first and second update results include updates to the particle velocity, position, and density. Based on the second update result, the stress and strain of the single-layer two-phase SPH particle model are updated using the Drucker-Prager model and a return mapping algorithm, resulting in the updated stress field. The updated stress field is then subjected to diffusion smoothing to obtain the simulation results for the single-layer two-phase SPH. The beneficial effects of this invention are: by precisely controlling numerical dissipation through a low-dissipation Riemann solver and suppressing stress oscillations by combining a stress diffusion term, the stability of the simulation is significantly improved while ensuring computational accuracy. This invention is applicable to the analysis of complex deformation processes of granular materials under water-soil coupling conditions, and can provide a reliable basis for risk assessment and instability prediction of geological disasters such as debris flows and landslides induced by extreme rainfall and other factors. It improves the shortcomings of the existing SPH method, which has low computational efficiency due to double-layer modeling and difficulty in handling complex hydraulic boundary conditions. It also solves the problem of numerical oscillation and noise that easily occur in the stress field solution process, thereby achieving efficient, stable and accurate simulation of large deformation processes of geological disasters such as landslides and debris flows under water-soil coupling conditions.

[0107] This invention also provides an electronic device, which includes a processor and a memory; The memory stores the program; The processor executes a program to perform the aforementioned single-layer two-phase SPH simulation method for soil-water coupling; the electronic device has the function of carrying and running the software system for single-layer two-phase SPH simulation of soil-water coupling provided in the embodiments of the present invention, such as a personal computer, minicomputer, mainframe, workstation, network or distributed computing environment, standalone or integrated computer platform, or communicating with charged particle tools or other imaging devices, etc.

[0108] This invention also provides a computer-readable storage medium storing a program that is executed by a processor to implement the single-layer two-phase SPH simulation method for soil-water coupling as described above.

[0109] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented in the embodiments of this invention. Alternative embodiments are contemplated, in which the order of various operations is changed and sub-operations described as part of a larger operation are executed independently.

[0110] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the aforementioned single-layer two-phase SPH simulation method for soil-water coupling.

[0111] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, considering the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed in the embodiments of the invention, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0112] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0113] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can include, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0114] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0115] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0116] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0117] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0118] The above is a detailed description of the preferred embodiments of the present invention, but the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention, and these equivalent modifications or substitutions are all included within the scope defined by the claims of this application.

Claims

1. A single-layer two-phase SPH simulation method for water-soil coupling, characterized in that, include: A single-layer two-phase SPH particle model of the target slope is constructed. The computational domain of the single-layer two-phase SPH particle model is discretized. Each particle is initialized with physical parameters and a neighbor list of the particles is established. The particles include real particles and boundary particles. The physical parameters include soil phase information and water phase information. The Verlet integral method is used to perform the first half-step update and the first full-step update based on the physical parameters of the particles, and the first update result is obtained. The interactions between particles are handled using a dissipation strategy based on a low-dissipation Riemann solver; A second half-step update is performed on the particles based on the first update result, resulting in the second update result. The first and second update results include updates to the particle's velocity, position, and density. Based on the second update results, the stress and strain of the single-layer two-phase SPH particle model are updated using the Drucker-Prager model and the back-mapping algorithm to obtain the updated stress field. The updated stress field was subjected to diffusion smoothing to obtain the simulation results of a single-layer two-phase SPH.

2. The single-layer two-phase SPH simulation method for water-soil coupling according to claim 1, characterized in that, The construction of a single-layer two-phase SPH particle model of the target slope includes discretizing the computational domain of the single-layer two-phase SPH particle model, initializing each particle with physical parameters, and establishing a neighbor list for each particle, including: Based on the basic physical parameters, three-dimensional topography, and hydraulic conditions of the target slope, a single-layer two-phase SPH particle model is constructed. Based on the cutoff radius, determine the neighbor list and interaction relationships of particles in the monolayer two-phase SPH particle model; Initialize the physical parameters of the particles, including position, velocity, soil phase mass, water phase mass, soil phase density, water phase density, porosity, saturation, pore water pressure, stress tensor, and strain rate.

3. The single-layer two-phase SPH simulation method for water-soil coupling according to claim 2, characterized in that, The first update result, obtained by performing the first half-step update and the first full-step update using the Verlet integration method based on the particle's physical parameters, includes: At the beginning of each time step, Verlet integrals are used to pre-update the phase fraction and geometric state of half a time step, including updating the porosity, aqueous phase density and particle position of half a time step based on the porosity change rate, aqueous phase density change rate and velocity of the previous step. Based on the porosity and water phase density of the first half-step update, the pore water pressure and saturation are revised using the equation of state and soil-water characteristic curves. Based on physical parameters, the mixing density and mixing mass of particles in a single-layer two-phase SPH particle model are determined, with the first half-step update being: in, Porosity For the density of water, The particle position; This indicates the sequence number of the previous step. For time steps; Based on the water density and particle positions updated in the first half-step, each real particle is traversed according to the momentum conservation equation of the mixture. Neighborhood particles Calculate the acceleration of the mixture: in, For real particles speed; For neighborhood particles The quality; For real particles Stress tensor; For neighborhood particles Stress tensor; For real particles The density; For neighborhood particles The density; For spatial gradient operators; For kernel functions; For real particles saturation; For real particles pore water pressure; It is the acceleration due to gravity; The total number of particles in the neighborhood; After updating the acceleration of all particles, update the particle velocities to the complete time step: in, The first velocity of the particle. The velocity of the particle in the previous step; Using Darcy's law and the seepage control equation, the seepage flux of the aqueous phase is updated in the first full step. The update formula is as follows: in, For particles The permeation flow rate; For particles The permeability coefficient; For particles The acceleration.

4. The single-layer two-phase SPH simulation method for water-soil coupling according to claim 3, characterized in that, The interaction between particles is handled using a dissipation strategy based on a low-dissipation Riemann solver, including: For interacting particles and particles In particles Pointing to particles Construct a Riemann problem between particles along the unit vector direction, and replace the average particle variable of the mixture with the Riemann solution of the Riemann problem to obtain the density dissipation term and momentum dissipation term as follows: in, For density dissipation, This is the momentum dissipation term; The stress is in the left-hand state; The stress is in the right-hand state; The average density of the left and right states; The velocity in the left state; The velocity in the right state; The initial left state is located in the real particle. ; The initial right state, located in the neighboring particle ; For limiters, it is represented as: Among them, the limiter This is used to ensure that the fluid is not dissipated when subjected to an expansion wave, where the expansion wave is represented as... ; These are coefficients used to control numerical dissipation. The reference sound velocity is for the water phase.

5. The single-layer two-phase SPH simulation method for water-soil coupling according to claim 3, characterized in that, The process of performing a second half-step update on the particles based on the first update result to obtain the second update result includes: Soil phase mass conservation equation Water phase mass conservation equation Calculate the rate of change of porosity and the rate of change of water density for each real particle: in, The bulk modulus of water; For real particles The matrix suction; Soil phase mass conservation equation Water phase mass conservation equation Update the real particles in the neighborhood, including the boundary particles. When the density change rate is reached, boundary particles The velocity and seepage flow rate are calculated using the following formula: in, For boundary particles speed, For boundary particles The permeation flow rate; Based on the rate of change of porosity, the rate of change of aqueous phase density, and the current particle velocity, the soil porosity, aqueous phase density, and particle position are updated for the second half-step.

6. The single-layer two-phase SPH simulation method for water-soil coupling according to claim 5, characterized in that, Based on the second update result, the stress and strain of the single-layer two-phase SPH particle model are updated using the Drucker-Prager model and the return mapping algorithm to obtain the updated stress field, including: Based on the updated particle positions and velocities from the second update, the actual particle positions and velocities are discretized using SPH. velocity gradient for: Based on real particles velocity gradient The strain rate tensor was calculated. and rotation tensor for: in, It is the transpose of the tensor; Based on strain rate tensor and rotation tensor The stress rate tensor is calculated using the constitutive relations of the Drucker–Prager model. for: in, Shear modulus; For the partial strain rate tensor; Bulk modulus; For strain rate tensor; It is a plastic multiplier; It is the expansion / contraction factor; This is the second deviatoric stress invariant; It is the deviatoric stress tensor; It is a rotation tensor; Unit tensor; Volume stress correction and deviatoric stress correction are performed using a return mapping algorithm, including: satisfy When the body stress is adjusted, the correction is: in, To return the mapped stress tensor; To return the stress tensor before mapping; This is the first stress invariant; and The Drucke-Prager constant is calculated as follows: in, Let be the friction angle. It is cohesive force; Based on the nonlinear cohesion-softening relationship, the cohesion is calculated to decrease exponentially with equivalent plastic strain. for: in, Residual cohesion; Peak cohesion; The softening coefficient; Equivalent plastic strain, equivalent plastic strain and deviation plastic strain increment Related, the calculation method is as follows: When satisfied When the deviatoric stress is corrected, the method is as follows: in, To return the pre-mapped deviatoric stress tensor; By leveraging the weak compressibility of the aqueous phase, the relationship between pore water pressure and water density is established, where pore water pressure... Calculations are performed using the compressible state equation: in, Let the speed of sound be the reference speed for water, and ; This is the reference density for water.

7. The single-layer two-phase SPH simulation method for water-soil coupling according to claim 6, characterized in that, The updated stress field is then subjected to diffusion smoothing processing to obtain the simulation results of a single-layer two-phase SPH. include: The diffusion smoothing process involves adding the diffusion term to the constitutive relation of the Drucker–Prager model, expressed as: Among them, diffusion term The calculation formula is as follows: in, The coefficient is set to 0.

1. For smooth length; It is a position vector; For the diffusion operator, the calculation formula is as follows: For the renormalization stress gradient, In Cartesian coordinates, the renormalized stress gradient is: After diffusion smoothing, the simulation results of a single-layer two-phase SPH include the velocity field, density field, pore water pressure field, saturation cloud map, and stress field during the simulation.

8. A single-layer two-phase SPH simulation device for water-soil coupling, characterized in that, include: The first module is used to construct a single-layer two-phase SPH particle model of the target slope, discretize the computational domain of the single-layer two-phase SPH particle model, initialize each particle with physical parameters and establish a neighbor list of the particles, where the particles include real particles and boundary particles, and the physical parameters include soil phase information and water phase information. The second module is used to perform the first half-step update and the first full-step update based on the particle's physical parameters using the Verlet integration method, and obtain the first update result. The third module is used to process the interactions between particles using a dissipation strategy based on a low-dissipation Riemann solver; The fourth module is used to perform a second half-step update on the particles based on the first update result, and obtain the second update result. The first update result and the second update result include updates to the particle's velocity, position and density. The fifth module is used to update the stress and strain of the single-layer two-phase SPH particle model based on the second update results, using the Drucker-Prager model and the return mapping algorithm, to obtain the updated stress field. The sixth module is used to perform diffusion smoothing on the updated stress field to obtain the simulation results of a single-layer two-phase SPH.

9. An electronic device, characterized in that, Including the processor and memory; The memory is used to store programs; The processor executes the program to implement the single-layer two-phase SPH simulation method for soil-water coupling as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The storage medium stores a program, which is executed by a processor to implement the single-layer two-phase SPH simulation method for soil-water coupling as described in any one of claims 1-7.

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