A numerical simulation method for rock-ice slope failure based on FEM and SPH

Abstract

The application discloses a numerical simulation method for rock-ice slope failure based on FEM and SPH, and relates to the technical field of geotechnical engineering. In the ice body melting stage, the method is based on the SPH method of smooth particle hydrodynamics, the phase change of the material is simulated by controlling the dynamic viscosity of the temperature, and the ice body melting stage is simulated; in the rock mass failure stage, the FEM method based on the stiffness degradation technology is used, the evolution of the damage variable is defined and calculated, the whole process of the rock material from the intact state, the plastic yield, the micro-damage accumulation to the macroscopic fracture instability is quantitatively described, and the rock mass failure stage is simulated; in the fluid-structure coupling stage, the coupling algorithm of the FEM method and the SPH method of smooth particle hydrodynamics is used, the contact force between the SPH particles and the FEM grid is calculated, and the fluid-structure coupling stage is simulated; the simulated ice body melting stage, the rock mass failure stage and the fluid-structure coupling stage are determined as the whole process of the rock-ice slope failure. The method improves the simulation precision of the rock-ice slope failure.

Description

Technical Field

[0001] This application relates to the field of geotechnical engineering technology, and in particular to a numerical simulation method for rock-ice slope failure based on FEM and SPH. Background Technology

[0002] Against the backdrop of global warming, major glaciers worldwide are experiencing accelerated melting, leading to a significant increase in the frequency of large-scale rock and ice collapses in high-altitude mountainous areas. Certain regions, in particular, have become key areas for hydropower development; for example, areas characterized by towering peaks, deep valleys, snow-capped summits, and active tectonics are highly susceptible to massive rock and ice collapses under current climate conditions.

[0003] Dynamic process analysis based on numerical simulation is an important means of quantitatively assessing rock-ice collapse. Fracturing of rock masses in high-altitude, cold regions is the ultimate result of long-term degradation of rock strength and structure induced by freeze-thaw cycles. Warming plays a key role in accelerating the degradation of internal structural surfaces of the rock mass through meltwater from overlying snow and ice. The unloading caused by melting overlying snow and ice reshapes the internal stress state of the slope, leading to rock mass unloading and relaxation. This causes stress concentration at the tips of existing cracks, thereby accelerating crack propagation. Furthermore, meltwater seeps into the cracks, generating seepage within the cracks and increasing internal water pressure. Under the combined action of hydrodynamic pressure and accumulated water pressure, crack tips are more likely to propagate and extend.

[0004] However, existing numerical models of slope failure are mainly based on finite element method and discrete element method. Existing technologies focus on the movement and fluidity of rock and ice collapse, considering only a single factor, which leads to low accuracy in numerical simulation of rock and ice slope failure. Summary of the Invention

[0005] Therefore, it is necessary to provide a numerical simulation method for rock-ice slope failure based on FEM and SPH to address the aforementioned technical problems. This method improves the accuracy of numerical simulation of rock-ice slope failure.

[0006] The following technical solution is adopted in this specification: This specification provides a numerical simulation method for rock-ice slope failure based on FEM and SPH, including: During the ice melting stage, the phase transition of the material is simulated by temperature-controlled dynamic viscosity based on the Smooth Particle Hydrodynamics (SPH) method to simulate the ice melting stage. During the rock mass fracture stage, the finite element method based on stiffness degradation technology quantitatively describes the entire process of rock material from an intact state to plastic yielding, micro-damage accumulation and macro-fracture instability by defining and calculating the evolution of damage variables, so as to simulate the rock mass fracture stage. In the fluid-structure interaction stage, a coupling algorithm based on the finite element method (FEM) and smoothed particle hydrodynamics (SPH) is used to simulate the fluid-structure interaction stage by calculating the contact force between SPH particles and the FEM mesh. The simulated ice melting stage, rock fracturing stage, and fluid-structure interaction stage are defined as the entire process of rock-ice slope failure.

[0007] Optionally, based on the Smooth Particle Hydrodynamics (SPH) method, the phase transition of materials is simulated by temperature-controlled dynamic viscosity to simulate the melting stage of ice, specifically including: In the SPH method, the material temperature and the viscosity related to the material temperature are set; When the material temperature is greater than or equal to the preset temperature, the stress-strain characteristics of the material are described by a power law model, and the rheological properties of the material are made to be solid by a preset viscosity in the power law model. When the material temperature is lower than the preset temperature, the rheological properties of the material are described by the Newton shear model, and the material viscosity is dynamically adjusted according to the temperature change to achieve the ice-water phase change conversion. A smooth transition from solid ice to liquid water is achieved by continuously updating the viscosity, thus simulating the melting stage of ice during heating.

[0008] Optionally, the process of determining the preset viscosity specifically includes: Based on the gas constant, reference temperature, activation energy, and reference flow factor, determine the flow factor that is closely related to temperature; The preset viscosity is determined based on the flow factor and stress, which are closely related to temperature.

[0009] Optionally, a coupled algorithm based on the finite element method (FEM) and smoothed particle hydrodynamics (SPH) is used to simulate the fluid-structure interaction stage by calculating the contact force between SPH particles and the FEM mesh, specifically including: A node-to-surface contact algorithm is used to simulate the interaction between SPH particles and FEM mesh; SPH particles represent water or ice; FEM mesh represents rock. After simulating the interaction between SPH particles and the FEM mesh, the contact forces between the SPH particles and the FEM mesh are calculated; the contact forces include normal contact forces and tangential frictional forces. The fluid-structure interaction stage is simulated based on contact force.

[0010] Optionally, the normal contact force is the product of the penetration depth between the main surface and the node and the material properties.

[0011] Optionally, the tangential friction force is the product of the normal contact force and the coefficient of friction.

[0012] Optionally, the method further includes: When the rock is in an intact state, the damage variable is 1; When the rock undergoes macroscopic fracture instability, the damage variable is 0.

[0013] This specification provides a numerical simulation apparatus for rock-ice slope failure based on FEM and SPH, including: The first simulation module is used to simulate the phase transition of materials during the ice melting stage by using the Smooth Particle Hydrodynamics (SPH) method and temperature-controlled dynamic viscosity. The second simulation module is used to simulate the rock mass fracture stage by using the finite element method based on stiffness degradation technology to quantitatively describe the entire process of rock material from an intact state to plastic yielding, micro-damage accumulation and macro-fracture instability by defining and calculating the evolution of damage variables. The third simulation module is used to simulate the fluid-structure interaction stage by calculating the contact force between SPH particles and the FEM mesh, based on the coupling algorithm of the finite element method (FEM) and smoothed particle hydrodynamics (SPH). The determination module is used to define the simulated ice melting stage, rock fracturing stage, and fluid-structure interaction stage as the entire process of rock-ice slope failure.

[0014] This specification provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described numerical simulation method for rock-ice slope failure based on FEM and SPH.

[0015] This specification provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-described numerical simulation method for rock-ice slope failure based on FEM and SPH.

[0016] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: Based on the Smooth Particle Hydrodynamics (SPH) method, this study simulates the phase transition of ice or snow materials by controlling dynamic viscosity at temperature, thus simulating the ice melting stage. The effect of temperature increase on ice melting is considered. SPH, as a meshless particle method, uses discrete particles to represent the continuous medium, adapting to the large deformation and free surface flow characteristics of ice transitioning from solid to liquid during melting. A finite element method based on stiffness degradation technology is used to simulate the rock mass fracture stage. Stiffness degradation technology gradually reduces the stiffness of elements after damage, simulating the initiation, propagation, and eventual macroscopic fracture of microcracks within the rock mass, closely reflecting the failure evolution of rock materials from continuous to discontinuous under stress. A FEM-SPH coupled algorithm is used to simulate the fluid-structure interaction stage. FEM is used to handle the relatively small deformation of the rock mass, ensuring computational efficiency and boundary treatment accuracy; SPH is used to handle the large deformation of the fluid portion, accurately simulating the fluid flow characteristics. By using a coupling algorithm to realize the mechanical transfer between the two, the stress field and flow field evolution under fluid-structure interaction can be realistically reflected, and the final key stage of rock-ice slope failure can be fully reproduced. The simulated ice melting stage, rock fracturing stage and fluid-structure interaction stage are identified as the entire process of rock-ice slope failure.

[0017] This method improves the simulation accuracy of rock-ice slope failure by accurately matching the core physical laws of each stage through phased modeling. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0019] Figure 1 This document provides a flowchart of a numerical simulation method for rock-ice slope failure based on FEM and SPH. Figure 2 This is a schematic diagram of the basic framework for numerical simulation of ice and rock slope instability provided in this manual. Figure 3 Numerical schematic diagram of the SPH method and its interaction with FEM provided in this specification; Figure 4 A schematic diagram of a numerical simulation device for rock-ice slope failure based on FEM and SPH provided in this specification; Figure 5 This document provides a schematic diagram of a computer device for implementing a numerical simulation method for rock-ice slope failure based on FEM and SPH. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0021] Devices such as desktop computers, servers, and laptops are capable of executing the solutions described in this manual. For ease of explanation, the following description will focus on servers as the primary execution method.

[0022] Although existing techniques can be applied to slope failure analysis, the role of ice melting with increasing temperature is crucial in the failure of rock-ice slopes, yet it is rarely incorporated into quantitative numerical models. In addition to crack propagation and mass separation, simulating rock-ice slope failure also requires considering the ice melting process and the interaction between meltwater and rock, which necessitates fluid-structure interaction and phase transformation capabilities—a significant challenge.

[0023] Current numerical models for slope failure are mainly based on finite element method, discrete element method, smoothed particle hydrodynamics (SPH), or material point method (MPM), which struggle to simultaneously consider the slope's small deformation, fracturing, crack propagation, block interaction, and block detachment. The method proposed in this invention considers all these processes simultaneously. Existing models do not yet consider the impact of warming ice-water phase transition and crack seepage on the numerical simulation of rock-ice slope failure.

[0024] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0025] Figure 1 This is a schematic diagram of a numerical simulation method for rock-ice slope failure based on FEM and SPH, as described in this specification. The method includes the following steps: S101: During the ice melting stage, the phase transition of the material is simulated by temperature-controlled dynamic viscosity based on the Smooth Particle Hydrodynamics (SPH) method to simulate the ice melting stage.

[0026] This invention decomposes the failure process of ice-rock slopes into three key stages for simulation: 1. Ice melting stage: The process of ice melting into water under increasing temperature conditions; 2. Fluid-structure interaction stage: The interaction process between water (or ice-water mixture) and rock mass; 3. Rock mass fracturing stage: The process of formation and propagation of cracks inside the rock mass under the action of seepage.

[0027] For these three stages, the SPH method, the Finite Element Method (FEM)-SPH coupled algorithm, and the Finite Element Method based on stiffness degradation technology were used for simulation, respectively. Figure 2 The basic framework for numerical simulation of ice-rock slope instability provided by this invention is as follows: Figure 2 As shown, this invention proposes a simulation method for the instability of ice-rock slopes based on the finite element method-smooth particle fluid dynamics coupling framework. This method decomposes the failure process of ice-rock slopes into three key stages for simulation: (1) Ice melting stage: the process of ice melting into water under heating conditions; (2) Fluid-structure coupling stage: the interaction process between water (or ice-water mixture) and rock mass; (3) Rock mass fracturing stage: the formation and expansion process of cracks inside the rock mass under seepage.

[0028] In an exemplary embodiment, based on the Smooth Particle Hydrodynamics (SPH) method, the phase transition of materials is simulated by temperature-controlled dynamic viscosity to simulate the melting stage of ice. Specifically, the method includes: setting the material temperature and the viscosity related to the material temperature in the SPH method; when the material temperature is greater than or equal to a preset temperature, describing the stress-strain characteristics of the material using a power-law model, and setting the rheological properties of the material to solid in the power-law model with a preset viscosity; when the material temperature is less than the preset temperature, describing the rheological properties of the material using a Newtonian shear model, and dynamically adjusting the material viscosity according to temperature changes to achieve the ice-water phase transition; and achieving a smooth transition from solid ice to liquid water by continuously updating the viscosity to simulate the melting stage of ice during the heating process.

[0029] In an exemplary embodiment, the process of determining the preset viscosity specifically includes: determining a flow factor closely related to temperature based on a gas constant, a reference temperature, an activation energy, and a reference flow factor; and determining the preset viscosity based on the flow factor closely related to temperature and stress.

[0030] Specifically, for ice and water, different temperatures correspond to different initial viscosities. For example, at 20°C, the initial viscosity of water is approximately 0.89 mPa·s, and at 25°C, it is approximately 0.81 mPa·s. For water above 0°C, the viscosity at 20°C is used as a reference, while for ice below 0°C, a larger value is used to characterize its properties as a solid.

[0031] Specifically, the simulation of the ice melting process (SPH part): The SPH method was used to simulate ice / snow materials.

[0032] Phase transition is simulated by controlling the dynamic viscosity through temperature: when the temperature is below 0°C, the material is given high viscosity (solid ice); when the temperature reaches or exceeds 0°C, the viscosity drops sharply to the viscosity of water (liquid water), thus realizing the phase transition from ice to water.

[0033] Smoothed particle hydrodynamics is a meshless continuous medium method based on a Lagrangian framework. This method replaces the nodes and elements of the traditional finite element method with a set of pseudo-particles, thus enabling effective simulation of large deformation problems without being limited by element distortion. Figure 3 Numerical schematic diagram of the SPH method and its interaction with FEM provided by this invention, as shown below. Figure 3 As shown, Figure 3 The principle of the SPH method and the contact relationship between SPH and FEM are characterized. The symbol represented by the circle in the upper left corner corresponds to formula (1), describing a range of influence of the core particle and a quantitative relationship of the cumulative effect of the surrounding particles on it. Step 1 and Step 2 represent two moments. In step 1, the analysis is performed between the SPH material and the FEM material. In step 2, individual particles in the SPH particle cluster come into contact with the FEM material. The figure shows the calculation of the normal force at the contact moment.

[0034] The core of the SPH method is to quantify the contribution of neighboring particles to the current particle through the kernel function W. Its interpolation approximation formula is formula (1): (1); in, A function of the particle position vector. j For neighboring particle indexing, For smooth length, m The value represents the particle mass, and <> indicates the average value. x For spatial location, x j For particles j Spatial location, m j For the first j The mass of each particle r j For particles j Spatial density, f j For particles j Spatial position vector, W For kernel function, N This represents the number of particles within the smooth length's influence range.

[0035] The continuity equation of the material, expressed in interpolation form, is formula (2): (2); in, r (x () indicates the density distribution of the material.

[0036] The motion of particles follows Newton's second law, as shown in formula (3): ρa = F (3); in, r For particle density, a For particle acceleration, F For the sake of combined efforts.

[0037] The component form of formula (3) is formula (4): F = ρg -∇p + μ∇ 2 u (4); in, ρg For gravity, ∇p For pressure gradient force, μ∇ 2 u It is a viscous shear force.

[0038] Therefore, particles i The acceleration is given by formula (5): a i = g - ( ∇p i ) / r i + ( μ∇ 2 u i ) / r i (5); in, a i The middle is a particle i acceleration, g It is the acceleration due to gravity. ∇p i For particles i The pressure gradient it experiences r i for i Particle density, μ∇ 2 u i It is a viscous phase. m For dynamic viscosity, u i For the velocity vector field, ∇ 2 For the Laplace operator.

[0039] The particle velocity and displacement are defined by the kinematic relationship of formulas (6) and (7), as follows: a t = dv t / dt (6); in, a t For particles in t acceleration at any moment v t for t The speed of time.

[0040] v t = dx t / dt (7); in, x t For particles in t Displacement at any given moment.

[0041] Rheological models based on SPH must satisfy mass conservation, momentum conservation, and energy conservation controlled by the equation of state.

[0042] The mass conservation equation for particles is given by formula (8): (8); in, N The number of influence examples within the smooth length. v(x j ) Neighboring particles j The velocity vector, v(x i ) Neighboring particles i The velocity vector, It is a vector related to the gradient of the kernel function.

[0043] The momentum conservation equation based on particles is Equation (9): (9); in, s Indicates the total stress. Represents stress, For the Laplace operator, Represents kernel function Wᵢ For particles i position vector xᵢ The gradient.

[0044] The equation of state defines pressure as a function of current density and specific internal energy as Equation (10): p = f(ρ, E m ) (10); in, f For function, E m Internal energy per unit mass p For pressure.

[0045] The Mie-Grüneisen equation of state used in the liquid simulation is formula (11): p = [ρ 0 c 0 2 e v / (1 - sε v ) 2 ] (1 - C 0 e v / 2) + C 0 r 0 E m (11); in, r 0 For reference density, c 0 For reference speed of sound, e v For nominal volumetric compressive strain, s For material constants, C 0 For material constants, r 0 For material constants, E m Internal energy per unit mass e v =1 - p 0 / r .

[0046] The interlayer flow of water is described by the Newtonian fluid model as Equation (12): τ = γ (12); in, t It is shear stress. or It is dynamic viscosity. c It is the shear rate.

[0047] Phase change control mechanism: This invention utilizes dynamic viscosity orControlling the ice-water phase transition. When the material is in a solid state (ice), impart a high viscosity parameter (e.g., 1×10⁻⁶). 9 To prevent flow, a viscosity of 0.001 Pa·s is applied, making it behave as a solid. When the material is liquid (water), it is given a viscosity similar to water (e.g., 0.001 Pa·s) to allow flow. By defining the relationship between viscosity and temperature, the phase change process of the material can be controlled using temperature.

[0048] In glaciology and geophysics, ice is generally considered a temperature-dependent viscous fluid (or power-law fluid). Its deformation follows Glen's law of flow, where the strain rate is exponentially related to temperature and proportionally related to stress. n The strain rate is directly proportional to the power of the power. The formula for calculating the strain rate is formula (13):

[0049] (13); in, Indicates strain rate. It is a flow factor that is closely related to temperature. It is stress. It is the stress index, which is usually taken as 3 for ice.

[0050] Based on this, the effective viscosity formulas for ice are derived from the Arrhenius equation as formulas (14) and (15): (14); (15); in, It is the effective viscosity. It is absolute temperature (K). It is the gas constant. This is a reference temperature. It is activation energy. This is the reference flow factor.

[0051] Ice near its pressure melting point ( The effective viscosity at this temperature is calculated under the overburden stress of surface snow (~25 kPa, corresponding to dense wet snow at a depth of less than 5 m). For the temperature range... Parameters used: .

[0052] In this invention, a temperature-dependent constitutive framework is employed. At sub-zero temperatures, ice is modeled as a nonlinear viscous (power-law) fluid following Glen's flow law, exhibiting high effective viscosity (…). This reflects its solid-like creep flow. When the temperature rises above 0°C, the material transforms into a Newtonian fluid, similar to water, with a viscosity several orders of magnitude lower than that of solid ice (approximately...). The rheological characteristic of the ice-water phase transition is a sudden drop in viscosity by an order of magnitude.

[0053] Table 1 shows the effective viscosity of the compound calculated based on Glen's flow law. S102: In the rock mass fracture stage, the finite element method based on stiffness degradation technology quantitatively describes the entire process of rock material from an intact state to plastic yielding, micro-damage accumulation and macro-fracture instability by defining and calculating the evolution of damage variables, so as to simulate the rock mass fracture stage.

[0054] In an exemplary embodiment, the method further includes: when the rock is in an intact state, the damage variable is 1; when the rock is macroscopically fractured and unstable, the damage variable is 0.

[0055] Specifically, simulation of rock failure process (FEM part): The finite element method was used to simulate rock slopes, and a stiffness degradation technique was applied to potential slip zones (weak shear zones). Combining the Drucker-Prager plasticity model and the shear damage model, the entire process of rock deformation from elastic deformation to plastic yielding, then to microscopic damage accumulation, and finally macroscopic fracture was simulated.

[0056] The FEM stiffness degradation technique based on continuous damage mechanics was used to simulate rock slope failure. This method treats material degradation (the initiation and propagation of microcracks and micropores) as a continuous, isotropic or anisotropic process, and introduces damage variables to describe the gradual decrease in material stiffness until final failure occurs and cracks or pores are formed.

[0057] The damage variable D ranges from 0 to 1. D=0 indicates that the element is undamaged, and D=1 indicates that the element is completely destroyed.

[0058] Assuming that the strain in the damaged material is equivalent to the strain generated in the undamaged material under effective stress, the stress-strain constitutive relationship of the damaged element in the direction perpendicular to the cross section is given by formula (16): s n = ( 1 - d n ) · C 0 : e (16); in, s n It is the actual normal stress. d n It is a normal damage variable. C 0 It is the initial elastic stiffness tensor of the material. e It is the normal strain tensor.

[0059] The tangential stress-strain constitutive relation is given by formula (17): t s = [ + (1 - )(1 - d s )] · K s · d s (17); in, t s It is the actual shear stress transmitted through the surface. It is the shear retention factor (residual stress ratio). ds It is a tangential damage variable. Ks It is the initial tangential stiffness. δs It is a tangential slip displacement.

[0060] To quantitatively assess the mechanical behavior of the sliding zone, the Drucker-Prager plasticity model and the shear damage model were used to describe the deformation and failure behavior of the rock, simulating the complete process of the material from initial elastic deformation to plastic deformation, micro-defect nucleation and evolution, until the formation of macroscopic cracks and structural failure.

[0061] The Drucker-Prager model captures the plastic yielding and hardening / softening behavior of materials under high pressure. Its linear yield criterion is given by equation (18):

[0062] F = q - p tanβ - d(ε̄ pl ) = 0 (18); in, q It is the Mises equivalent force. β It is the angle of friction. d It is cohesion, ε̄ pl It is equivalent plastic strain. F is the yield function.

[0063] Using the non-associated flow rule, the direction of plastic flow is determined by the plastic potential function. G Decide, G For formula (19): G = q - p tanψ (19); in, ψ It is the shear expansion angle. G Let be the plastic potential function.

[0064] The plastic strain increment is calculated using formula (20): ε̇ pl= λ̇ (∂G / ∂σ) (20); Among them, ε̇ pl For the increment of plastic strain, l̇ It is a plastic multiplier.

[0065] Equivalent plastic strain ε̄ pl As an internal variable, it serves as a crucial bridge connecting the plasticity model and the damage model. It records the history of plastic deformation development, and its increment is defined by formula (21):

[0066] yes pl = λ̇ (q / σ y ) = λ̇ (twenty one); in, yes pl For equivalent plastic strain, s y This is the stress threshold at which the material begins to yield.

[0067] The plastic displacement criterion is used as the damage initiation threshold. Damage begins when the equivalent plastic strain ε̄... pl Reaching the critical value ε̄0 pl This criterion can be expressed as formula (22):

[0068] ω = ε̄ pl / ε̄0 pl ≥ 1.0 (22); in, oh It is the ratio of the damage initiation criterion, ε̄0 pl This is the critical value of the equivalent plastic strain. When ε̄0 pl When equal to or greater than 1.0, the damage variable D Start by increasing from 0.

[0069] The most common evolutionary assumption is that the energy dissipated during the softening stage equals the fracture energy. The failure value ū is the equivalent plastic displacement. f pl For formula (23):

[0070] G f S = ( 1 / 2 ) s y 0 ū f pl (twenty three); in, ū f pl The failure value is the equivalent plastic displacement. s y 0 This is the yield stress at the onset of damage (usually the peak stress). Therefore, the evolution of the damage variable with respect to the equivalent plastic displacement is given by formula (24):

[0071] D = ū pl / ū f pl (twenty four); in, D For the damage variable, 0 ≤ D ≤ 1.

[0072] When the damage variable in any direction reaches 1, the material point completely loses its load-bearing capacity, forming voids and causing crack propagation. Eventually, the cracks connect with each other, leading to rock instability and resulting in rock slope failure.

[0073] S103: In the fluid-structure interaction stage, a coupling algorithm based on the finite element method (FEM) and smoothed particle hydrodynamics (SPH) is used to simulate the fluid-structure interaction stage by calculating the contact force between SPH particles and the FEM mesh.

[0074] In an exemplary embodiment, a coupled algorithm based on the finite element method (FEM) and smoothed particle hydrodynamics (SPH) simulates the fluid-structure interaction stage by calculating the contact forces between SPH particles and the FEM mesh. Specifically, this includes: using a node-to-surface contact algorithm to simulate the interaction between SPH particles and the FEM mesh; where SPH particles represent water or ice and the FEM mesh represents rock; after simulating the interaction between SPH particles and the FEM mesh, calculating the contact forces between the SPH particles and the FEM mesh; the contact forces include normal contact forces and tangential frictional forces; and simulating the fluid-structure interaction stage based on the contact forces.

[0075] In one exemplary embodiment, the normal contact force is the product of the penetration depth between the primary surface and the node and the material properties.

[0076] In one exemplary embodiment, the tangential frictional force is the product of the normal contact force and the coefficient of friction.

[0077] Specifically, the coupling interaction (FEM-SPH coupling): A node-to-surface contact algorithm is used to handle the interaction between SPH particles (water / ice) and FEM mesh (rock). The algorithm calculates the contact forces, including normal contact forces (based on penetration depth) and tangential frictional forces (based on Coulomb's law of friction).

[0078] The interaction between rock (FEM element) and ice / water (SPH particle) is handled using a node-surface contact algorithm. Figure 2 ).

[0079] Define node-based contact surfaces at the nodes and assume a finite contact thickness. When in contact with the finite element master surface, the node surface acts only as a slave surface, allowing the master surface to penetrate the slave surface, but prohibiting reverse penetration.

[0080] When a pseudo-particle encounters a finite element mesh object, contact forces are calculated. The finite element surface is discretized into nodes, allowing slight interpenetration between the particle and surface nodes to determine the contact force. Contact detection is based on the relative node positions over continuous time steps. Contact force generation is triggered when a particle is penetrated by the finite element surface.

[0081] The normal contact force is perpendicular to the finite element surface, and its magnitude is controlled by the node penetration depth according to formula (25): F n = k p d p (25); in, F n Indicates the normal contact force component. k p Depending on the material properties of the interacting units, d p It is the penetration depth between the main surface and the node.

[0082] The relative tangential motion or impending motion between the pseudoparticle and the finite element surface will generate a tangential contact force (friction) as shown in formula (26): F t = μF n (26); in, F t It is kinetic friction. m It is the Coulomb coefficient of friction.

[0083] S104: The simulated ice melting stage, rock fracturing stage, and fluid-structure interaction stage are defined as the entire process of rock-ice slope failure.

[0084] In one exemplary embodiment, a 2.5D numerical model is established based on an ice avalanche at a specific location on a specific day. The model includes source rock, weak shear zone, bedrock (FEM), and snow / ice cover (SPH). By applying a linear heating boundary condition, the dynamic process of ice melting, meltwater seepage along the trailing edge tension cracks, water pressure erosion of the weak shear zone, stress concentration, fracture of the locked segment, and eventual overall landslide is simulated.

[0085] This invention provides a complete numerical solution for simulating the instability of ice and rock slopes based on FEM-SPH coupling. For the first time, it realizes the temperature-controlled ice-water phase transition, fluid-structure interaction and the progressive failure process of rock mass within a unified framework, providing a powerful quantitative analysis tool for the mechanism research and risk assessment of ice and rock collapse disasters.

[0086] This invention is the first to quantitatively simulate the key triggering factor of temperature-induced ice melting in a numerical model. It clearly reproduces the complete failure chain of rock-ice slopes from "ice melting → seepage → cracking → instability".

[0087] The examples verified that the collapse was caused by stress concentration and eventual rupture of the weak shear zone locking segment due to seepage through the cracks.

[0088] The advantages of this invention include: strong coupling ability of multiple physical processes and clear physical mechanism of the model; it provides an innovative tool for risk assessment and prediction of high-altitude rock and ice collapse.

[0089] When applying the numerical simulation method for rock-ice slope failure based on FEM and SPH provided in this manual, it is not necessary to consider... Figure 1 The steps shown are executed in sequence. The specific execution order of each step can be determined as needed, and this manual does not impose any restrictions on it.

[0090] The above are one or more embodiments of the numerical simulation method for rock-ice slope failure based on FEM and SPH provided in this specification. Based on the same idea, this specification also provides corresponding numerical simulation devices for rock-ice slope failure based on FEM and SPH, such as... Figure 4 As shown.

[0091] Figure 4 A schematic diagram of a numerical simulation device for rock-ice slope failure based on FEM and SPH, provided in this specification, includes: The first simulation module 401 is used to simulate the phase transition of materials by controlling the dynamic viscosity of the material through temperature during the ice melting stage, based on the Smooth Particle Hydrodynamics (SPH) method.

[0092] The second simulation module 402 is used to quantitatively describe the entire process of rock material from an intact state to plastic yielding, micro-damage accumulation and macro-fracture instability in the rock mass fracture stage by defining and calculating the evolution of damage variables based on the finite element method of stiffness degradation technology.

[0093] The third simulation module 403 is used to simulate the fluid-structure interaction stage by calculating the contact force between the SPH particles and the FEM mesh, based on the coupling algorithm of the finite element method (FEM) and smooth particle hydrodynamics (SPH).

[0094] The determination module 404 is used to determine the simulated ice melting stage, rock fracturing stage, and fluid-structure interaction stage as the entire process of rock-ice slope failure.

[0095] Specific limitations regarding the numerical simulation apparatus for rock-ice slope failure based on FEM and SPH can be found in the above section on the limitations of the numerical simulation method for rock-ice slope failure based on FEM and SPH, and will not be repeated here. Each module in the aforementioned numerical simulation apparatus for rock-ice slope failure based on FEM and SPH can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0096] This specification also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 A numerical simulation method for rock-ice slope failure based on FEM and SPH is provided.

[0097] This instruction manual also provides Figure 5 The schematic diagram of the computer device shown is as follows: Figure 5 At the hardware level, the computer device includes a processor, internal bus, network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then runs it to achieve the above-mentioned functions. Figure 1 A numerical simulation method for rock-ice slope failure based on FEM and SPH is provided.

[0098] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0099] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A numerical simulation method for rock-ice slope failure based on FEM and SPH, characterized in that, include: During the ice melting stage, the phase transition of the material is simulated by temperature-controlled dynamic viscosity based on the Smooth Particle Hydrodynamics (SPH) method to simulate the ice melting stage. During the rock mass fracture stage, the finite element method based on stiffness degradation technology quantitatively describes the entire process of rock material from an intact state to plastic yielding, micro-damage accumulation and macro-fracture instability by defining and calculating the evolution of damage variables, so as to simulate the rock mass fracture stage. In the fluid-structure interaction stage, a coupling algorithm based on the finite element method (FEM) and smoothed particle hydrodynamics (SPH) is used to simulate the fluid-structure interaction stage by calculating the contact force between SPH particles and the FEM mesh. The simulated ice melting stage, rock fracturing stage, and fluid-structure interaction stage are defined as the entire process of rock-ice slope failure.

2. The numerical simulation method for rock-ice slope failure based on FEM and SPH as described in claim 1, characterized in that, The Smoothed Particle Hydrodynamics (SPH) method simulates phase transitions in materials by controlling dynamic viscosity at temperature to simulate the melting stage of ice. Specifically, it includes: In the SPH method, the material temperature and the viscosity related to the material temperature are set; When the material temperature is greater than or equal to the preset temperature, the stress-strain characteristics of the material are described by a power law model, and the rheological properties of the material are made to be solid by a preset viscosity in the power law model. When the material temperature is lower than the preset temperature, the rheological properties of the material are described by the Newton shear model, and the material viscosity is dynamically adjusted according to the temperature change to achieve the ice-water phase change conversion. A smooth transition from solid ice to liquid water is achieved by continuously updating the viscosity, thus simulating the melting stage of ice during heating.

3. The numerical simulation method for rock-ice slope failure based on FEM and SPH as described in claim 2, characterized in that, The process of determining the preset viscosity specifically includes: Based on the gas constant, reference temperature, activation energy, and reference flow factor, determine the flow factor that is closely related to temperature; Based on the flow factor and stress that are closely related to temperature, a preset viscosity is determined.

4. The numerical simulation method for rock-ice slope failure based on FEM and SPH as described in claim 1, characterized in that, The coupling algorithm based on the finite element method (FEM) and smoothed particle hydrodynamics (SPH) simulates the fluid-structure interaction stage by calculating the contact force between SPH particles and the FEM mesh, specifically including: A node-to-surface contact algorithm is used to simulate the interaction between SPH particles and FEM meshes; the SPH particles represent water or ice; and the FEM meshes represent rock. After simulating the interaction between SPH particles and the FEM mesh, the contact force between the SPH particles and the FEM mesh is calculated; the contact force includes normal contact force and tangential friction force. Based on the contact force, the fluid-structure interaction stage is simulated.

5. The numerical simulation method for rock-ice slope failure based on FEM and SPH as described in claim 4, characterized in that, The normal contact force is the product of the penetration depth between the main surface and the node and the material properties.

6. The numerical simulation method for rock-ice slope failure based on FEM and SPH as described in claim 4, characterized in that, The tangential friction force is the product of the normal contact force and the coefficient of friction.

7. The numerical simulation method for rock-ice slope failure based on FEM and SPH as described in claim 1, characterized in that, The method further includes: When the rock is in an intact state, the damage variable is 1; When the rock undergoes macroscopic fracture instability, the damage variable is 0.

8. A numerical simulation device for rock-ice slope failure based on FEM and SPH, characterized in that, include: The first simulation module is used to simulate the phase transition of materials during the ice melting stage by using the Smooth Particle Hydrodynamics (SPH) method and temperature-controlled dynamic viscosity. The second simulation module is used to simulate the rock mass fracture stage by using the finite element method based on stiffness degradation technology to quantitatively describe the entire process of rock material from an intact state to plastic yielding, micro-damage accumulation and macro-fracture instability by defining and calculating the evolution of damage variables. The third simulation module is used to simulate the fluid-structure interaction stage by calculating the contact force between SPH particles and the FEM mesh, based on the coupling algorithm of the finite element method (FEM) and smoothed particle hydrodynamics (SPH). The determination module is used to define the simulated ice melting stage, rock fracturing stage, and fluid-structure interaction stage as the entire process of rock-ice slope failure.

9. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the method described in any one of claims 1 to 7.

10. A computer device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any one of claims 1 to 7.

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