Numerical simulation method, device and equipment for ice rock collapse starting and medium

Abstract

The invention discloses a numerical simulation method, device and equipment for ice rock collapse starting and a medium, relates to the technical field of fluid motion simulation, and provides an FDEM-SPH coupling framework. Through a CIE unit in the FDEM method, crack propagation and fracture processes in rock masses are accurately simulated, and after the CIE unit is completely fractured, the FDEM method simultaneously simulates various contact forms between two separated finite units, so that mutual movement and interaction between fractured rock masses can be accurately described; ice and snow melting and movement in the ice-water phase change process are simulated through the smoothed particle flow SPH, and meanwhile, the interaction between ice-water phase change and rock mass fracture movement can be quantified by calculating the contact force between virtual particles in the smoothed particle flow SPH and the surface of a finite element in the finite discrete element method FDEM; the interaction reflects the erosion and impact of the ice-water phase change on the rock mass in the whole process and the actual physical condition in the ice rock collapse starting process, so that the ice rock collapse change more fitting the real condition is described.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid motion simulation, and in particular to a numerical simulation method, device, equipment and medium for ice and rock avalanche initiation. Background Art

[0002] Due to the severe trend of global warming, the high-altitude mountainous areas with originally cold climates and harsh environments have suffered unprecedented impacts in recent years. One of the most notable phenomena is the frequent occurrence and substantial increase in rock and ice avalanches. These special avalanches are different from traditional dry or wet snow avalanches. They use ice as their main component, which makes them extremely fluid and unpredictable when they occur. The hard texture and huge volume of ice, coupled with the speed at which they slide rapidly under the action of gravity, make these avalanches extremely destructive and impactful, and can easily destroy all obstacles encountered along the way, including buildings, transportation facilities and natural landscapes. What is more serious is that this highly fluid rock and ice avalanche poses an extremely serious risk to human life. In addition, avalanches may also trigger secondary disasters such as landslides and mudslides, further expanding the scope and degree of damage of the disaster, and bringing far-reaching impacts to the local social economy and ecological environment.

[0003] Rock-ice avalanches are the predominant form of avalanches in alpine engineering areas. Currently, the main methods for simulating rock-ice avalanche motion include RAMMS software simulation, full-scale and scaled avalanche test simulations, and genetic algorithm-based sliding surface search and numerical simulations. RAMMS software uses advanced numerical models, such as the Voellmy friction model, to simulate the sliding behavior of debris flows and mudflows, and can be used to analyze the dynamic processes of avalanches, mudflows, landslides, and rockfalls. Full-scale and scaled avalanche test simulations. Full-scale avalanche tests are conducted in a real natural environment and can study the motion characteristics and energy release of avalanches. Scaled snow trough experiments use small snow troughs in indoor or controlled outdoor environments to simulate avalanche processes, offering the advantages of controllability, repeatability, and low cost. Genetic algorithm-based sliding surface search and numerical simulations. This method uses a genetic algorithm to search for the most likely sliding surface and establishes a mathematical model for the motion process of the avalanche block. This method can simulate the motion trajectory and energy distribution of the avalanche block, providing a scientific basis for the prediction and prevention of rock-ice avalanches.

[0004] However, the initiation mechanism of ice and rock avalanches in alpine engineering areas is a complex and changeable movement process, which involves not only the movement of rocks but also the movement of ice, snow and water. The current research methods usually involve analysis and physical experiments on rock masses or avalanches. Such analysis and physical experiments are too idealistic and it is difficult to accurately describe the erosion process and the actual physical conditions during the initiation of ice and rock avalanches. As a result, the described initiation mechanism of ice and rock avalanches is quite different from the actual changes in ice and rock avalanches in the region. Summary of the Invention

[0005] The embodiments of the present invention provide a numerical simulation method, device, equipment and medium for ice and rock avalanche initiation, which can solve the problem in the prior art that the current means are too ideal and it is difficult to accurately describe the erosion process during ice and rock avalanche initiation and the actual physical conditions during the ice and rock avalanche initiation process.

[0006] An embodiment of the present invention provides a numerical simulation method for ice and rock avalanche initiation, comprising the following steps: The numerical model of ice-rock avalanche is constructed by simulating the cracking and instability of ice-rock mass using the finite discrete element method (FDEM) and the ice-water phase transition process during the cracking and instability of ice-rock mass using the smooth particle flow (SPH). When simulating the fracture and instability of ice and rock masses on an ice and rock avalanche numerical model, FDEM generates a CIE unit and a finite element mesh. The CIE unit is inserted into the boundary of the finite element mesh and moves. The CIE unit and the finite element mesh generate traction stress and displacement, which characterize the action process of the rock mass during crack propagation and fracture. When the traction stress is reduced to a set value, the CIE unit breaks, and the finite element units on both sides come into contact and friction, resulting in the friction force between the finite element units on both sides. The friction force represents the contact friction process between the fractured rock masses during mutual movement. When simulating the propagation and fracture of rock cracks, as well as the mutual movement between fractured rock masses, the virtual particle collection in the smooth particle flow (SPH) is simulated as an ice-water block during the ice-water phase transition. The virtual particle collection and the finite element surface interpenetrate each other, and the contact force between the virtual particles and the finite element surface is obtained. The contact force represents the interaction between the ice-water phase transition and the rock fracture movement during the rock fracture and mutual movement. Based on the interaction between ice-water phase change and rock fracture movement, the movement process of ice, snow and rock mass when a simulated ice and rock avalanche is initiated is obtained.

[0007] Preferably, the acquisition of the traction stress and displacement includes: When simulating the fracture and instability of ice and rock masses on the numerical model of ice and rock avalanche, the finite discrete element method (FDEM) inserts CIE elements into the finite element mesh boundary. The CIE elements represent the continuous-discontinuous interface elements. The CIE elements and the finite element mesh share nodes to transmit forces and displacements. The CIE unit deforms and fractures according to the traction-separation constitutive response of the stress-displacement law. During the deformation and fracture of the CIE unit, the CIE unit is damaged and fracture energy is generated. The damage of the CIE unit includes tensile damage in the opening mode and shear damage in the sliding mode. The displacement generated by the CIE unit and the finite element mesh is the path generated by the CIE unit from insertion to complete fracture. The traction stress generated by the CIE unit and the finite element mesh is obtained based on the linear relationship between the traction stress and displacement. The linear relationship between the traction stress and displacement of the CIE unit is expressed as: ; in: t represents the traction stress vector; k represents the CIE unit contact stiffness coefficient; δ represents the traction displacement vector; D represents the damage variable; The damage variable D The range is 0-1, where 0 indicates that the CIE unit has no damage and no fracture energy, and 1 indicates that the CIE unit is completely fractured and has fracture energy after complete fracture. The process in which the damage variable changes from 0 to 1 indicates the fracture process of the CIE unit.

[0008] Preferably, the process of breaking the CIE unit includes: Under the single mode conditions of the opening mode and the sliding mode, the CIE unit begins to be damaged after reaching the peak traction stress, and the traction stress begins to decrease; when the traction stress decreases to the minimum value, the CIE unit is completely broken; For the mixed mode of opening mode and sliding mode, the initial damage of CIE unit is determined using the QUADS damage criterion, which is expressed as: ; in: t n 、 t s and t t represent the normal component and tangential component of the crack surface, respectively; t, t, and t represent the peak values of the nominal stresses in the three directions, respectively; <> indicates that the pure compressive stress state will not cause damage; The second power of the fracture energy is used to determine the complete fracture of the CIE unit and is expressed as: ; Where: G, G, and G represent the fracture energy corresponding to complete fracture in the normal direction and the two tangential directions, respectively; G n 、 G s and G t Represent the actual fracture energy in the normal direction and the two tangential directions respectively.

[0009] Preferably, the acquisition of the friction force characterizing the contact friction process between the fractured rock masses during mutual movement includes: After the CIE element is completely fractured, the separated finite elements on both sides have surface-to-surface contact, point-to-surface contact and edge-to-edge contact forms; the surface-to-surface contact, point-to-surface contact and edge-to-edge contact forms represent the mutual motion forms between the fractured rock masses; If the node of the master surface penetrates the slave surface, check whether a normal contact force is generated. The normal contact force on the node is generated by the rebound of the contact surface in the physical mechanism and is perpendicular to the finite element surface. The normal contact force is perpendicular to the finite element surface and its magnitude is determined by the penetration depth of the node. The relationship between the penetration depth of the node and the normal component of the contact force is expressed as: ; in: F n represents the normal component of the contact force; k p Depends on the material properties of the interactive elements; d p represents the penetration distance between the main surface and the node; When a finite element surface has a trend or moves relative to another finite element surface, a tangential contact force is generated. The tangential contact force is the friction force of the contact friction process between the fractured rock masses during mutual movement, which is expressed as: ; in: F t represents friction; μ represents the Coulomb friction coefficient.

[0010] Preferably, the simulation of the interaction between the ice-water phase transition and the rock mass fracture movement includes: The virtual particles in the smooth particle flow (SPH) correspond to a continuous node element in the continuum particle element. The interaction between the virtual particles and the finite element surface depends on the node-based surface in the node-to-surface contact. The node-based surface is composed of the nodes of the finite element mesh. When a virtual particle contacts a finite element surface, the node-based surface acts as a slave surface, and the finite element surface can penetrate the node-based surface, but the node-based surface cannot penetrate the finite element surface; When virtual particles encounter a finite element mesh object, the surface of the finite element is discretized using nodes, and the virtual particles and the finite element surface nodes interpenetrate each other to obtain the contact force between the virtual particles and the finite element surface; The contact force characterizes the interaction between the ice-water phase transition and the rock mass fracture motion when the rock mass fractures and the fractured rock masses move relative to each other.

[0011] Preferably, the ice-water phase transition process is controlled by the conservation of momentum, conservation of energy and conservation of mass; During the ice-water phase transition, inertial forces, pressure gradients, gravity, and viscous forces exist between the ice-water fluids. The motion of the fluid particles in the ice-water fluid follows the conservation of momentum. At the same time, during the ice-water phase transition, the mass of the ice-water fluid remains unchanged, following the conservation of mass. The Navier-Stokes equations for the conservation of mass and momentum are expressed as follows: ; ; During the ice-water phase transition, heat conduction, energy convection, and latent heat of phase change occur between the fluid particles in the ice-water fluid, and energy conservation is followed. The energy conservation is characterized by the EOS equation of state, which is expressed as follows: ; ; ; ; ; in: ρ Indicates the material density; v Indicates speed; σ represents the Cauchy stress; b Indicates physical strength; ρ 0 indicates the material reference density; η represents the nominal compressive strain; c 0 represents the material reference sound velocity; s represents the slope of the Us-Up curve; Γ0 represents the material constant; Γ represents the Grüneisen ratio; E m Indicates the internal energy per unit mass of the material; U s represents the shock wave velocity; U p Indicates the particle velocity.

[0012] Preferably, the ice-water phase transition process simulates the process of ice melting into water in the form of temperature and viscosity coupling; The ice melting process corresponds to a phase transition from an object to a fluid. The melting phase transition is simulated by the change in viscosity caused by the temperature change of each particle. The temperature change is expressed as: ; in: T Indicates temperature; k represents the thermal diffusion constant; When the temperature of a part of the ice cube rises to the melting point, it turns into water; the transition energy during the temperature change J ( T ) is expressed as: ; ; in: T max Indicates the maximum temperature; T min Indicates the minimum temperature; J max represents the highest transition energy; J min represents the minimum transition energy.

[0013] An embodiment of the present invention further provides a numerical simulation device for ice and rock avalanche initiation, comprising: A model building module is used to simulate the fracture and instability of ice-rock mass according to the finite discrete element method (FDEM), and to simulate the ice-water phase transition process during the fracture and instability of ice-rock mass according to the smooth particle flow method (SPH), so as to build a numerical model of ice-rock avalanche; The rock mass motion simulation module is used to simulate the fracture and instability of ice and rock masses on the ice and rock avalanche numerical model. FDEM generates a CIE unit and a finite element mesh, inserts the CIE unit into the finite element mesh boundary and moves it. The CIE unit and the finite element mesh generate traction stress and displacement, which characterize the action process of the rock mass during crack propagation and fracture. When the traction stress is reduced to a set value, the CIE unit breaks, and the finite element units on both sides come into contact and friction, resulting in the friction force between the finite element units on both sides. The friction force represents the contact friction process between the fractured rock masses during mutual movement. The ice and rock avalanche initiation simulation module is used to simulate the propagation and fracture of rock cracks, as well as the mutual movement between fractured rock masses. The virtual particle collection in the smooth particle flow (SPH) is simulated as an ice-water block during the ice-water phase transition. The virtual particle collection and the finite element surface interpenetrate each other, and the contact force between the virtual particles and the finite element surface is obtained. The contact force represents the interaction between the ice-water phase transition and the rock fracture movement during rock fracture and mutual movement. Based on the interaction between ice-water phase change and rock fracture movement, the movement process of ice, snow and rock mass when a simulated ice and rock avalanche is initiated is obtained.

[0014] An embodiment of the present invention further provides an electronic device, including a memory and a processor; The memory is used to store computer programs; The processor is configured to implement the steps of the above-mentioned method for numerical simulation of ice and rock avalanche initiation when executing the computer program stored in the memory.

[0015] An embodiment of the present invention further provides a computer-readable storage medium for storing a computer program, which, when executed by a processor, implements the steps of the above-mentioned method for numerical simulation of ice and rock avalanche initiation.

[0016] The embodiments of the present invention provide a numerical simulation method, device, equipment, and medium for ice and rock avalanche initiation. Compared with the prior art, the methods and devices have the following beneficial effects: The present invention proposes an FDEM-SPH coupling framework that couples the finite discrete element method (FDEM) and the smooth particle flow method (SPH). The FDEM-SPH coupling framework is used to characterize the interaction between the ice and snow phase change and rock fracture during the initiation of ice and rock avalanches. By setting CIE units and finite element meshes in the FDEM method, the crack propagation and fracture processes in the rock mass, as well as the mutual movement and interaction between the fractured rock masses, are simulated and characterized. The smooth particle flow method (SPH) is used to simulate the melting and movement of ice and snow during the ice-water phase change process. At the same time, by calculating the contact force between the virtual particles in the smooth particle flow method (SPH) and the finite element surface in the finite discrete element method (FDEM), the interaction between the ice-water phase change and the rock fracture movement can be quantified. This interaction reflects the erosion and impact of the entire ice-water phase change process on the rock mass. At the same time, this interaction is the most critical factor in the ice and rock avalanche process, which can reflect the actual physical conditions during the initiation of the ice and rock avalanche, thereby describing the ice and rock avalanche changes that are more in line with the real situation.

[0017] In addition, when simulating the fracture movement of rock masses, the present invention sets CIE units and finite element grids in the FDEM method, inserts the CIE units into the finite element grid boundary and moves them. The CIE units and the finite element grid generate traction stress and displacement. During the movement, the traction stress and displacement change accordingly, which can accurately simulate the crack propagation and fracture process in the rock mass. When the traction stress reaches a preset minimum value, the CIE unit is completely broken, and the finite elements on both sides have surface-to-surface contact, point-to-surface contact, and edge-to-edge contact. Contact force is formed in this process, thereby accurately describing the mutual movement and interaction between the fractured rock masses. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 A schematic diagram of the overall process of a numerical simulation method for ice and rock avalanche initiation provided by an embodiment of the present invention; Figure 2 A schematic diagram of a numerical framework of an FDEM method for numerical simulation of ice and rock avalanche initiation provided by an embodiment of the present invention; Figure 3 A schematic diagram of a CIE unit traction-separation constitutive model for a numerical simulation method of ice and rock avalanche initiation provided by an embodiment of the present invention; Figure 4Schematic diagram of an inter-element contact model for a numerical simulation method of ice and rock avalanche initiation provided by an embodiment of the present invention; (a) is a schematic diagram of contact between finite element meshes; (b) is a schematic diagram of contact between finite element meshes and virtual particles; Figure 5 Schematic diagram of the numerical framework of SPH smooth particles for a numerical simulation method of ice and rock avalanche initiation provided by an embodiment of the present invention; (a) is a schematic diagram of traditional finite elements and smooth particles; (b) is a schematic diagram of kernel equations; Figure 6 A schematic diagram of a "Stanford rabbit" simulation melting process for a numerical simulation method of ice and rock avalanche initiation provided by an embodiment of the present invention; Figure 7 A schematic diagram of ice and rock avalanche instability caused by temperature increase under elevated temperature conditions in a numerical simulation method for ice and rock avalanche initiation provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0019] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. The following description sets forth many specific details to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art can make similar modifications without violating the scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0020] See also Figure 1 The embodiment of the present invention provides a numerical simulation method for ice and rock avalanche initiation, specifically: 1. Numerical model of rock mass fracture and movement.

[0021] 1. Numerical model of rock mass fracture.

[0022] Aiming at the main physical processes of ice-rock avalanches in alpine engineering areas under warming conditions, namely temperature rise - ice-water phase transition - dynamic erosion - crack expansion - slope instability, based on the existing FDEM (FEM) and SPH theories, we innovatively proposed a FDEM-SPH coupling framework that combines the characteristics of both methods, and constructed a numerical model of ice-rock avalanches based on the FDEM-SPH numerical framework that considers the microscopic physical process of ice-water phase transition, in which the rock mass is represented by the FDEM (FEM) model framework and the ice and snow are represented by the SPH model.

[0023] In the present study, the rock mass fracture and instability is characterized by the FDEM model, which is a method that combines the characteristics of FEM and DEM. The FDEM model can solve deformation, fracture and motion problems at the same time, expanding the application range of FEM and DEM. The principle of FDEM is to insert CIE into the boundary of the finite element mesh, such as Figure 2 As shown, the CIE and finite element meshes share nodes to transfer forces and displacements.

[0024] CIE can deform and fracture according to the traction-separation constitutive response of the stress-displacement law, e.g. Figure 3 As shown; CIE damage may occur in the opening mode (mode I, tensile damage), sliding mode (mode II, shear damage) and a mixed mode of opening and sliding; the linear relationship between CIE stress and displacement can be expressed as: .

[0025] in: t represents the traction stress vector; k represents the CIE contact stiffness coefficient; δ represents the traction displacement vector; D represents the damage variable.

[0026] Under the conditions of single-mode tensile cracking and sliding, after the CIE reaches the peak traction stress, damage begins to occur and the traction stress begins to decrease. Finally, when the traction stress decreases to the minimum value, the CIE completely breaks. For the mixed mode of tensile cracking and sliding, the QUADS damage failure criterion is used to determine the initial damage of the CIE, which is expressed as: .

[0027] in: t n 、 t s and t t represent the normal and tangential components of the crack surface, respectively; t, t, and t represent the peak values of the nominal stresses in the three directions, respectively; <> indicates that a pure compressive stress state will not cause damage.

[0028] The quadratic power based fracture energy can be used to determine the complete fracture of the CIE and can be expressed as: .

[0029] Where: G, G, and G represent the fracture energy corresponding to complete fracture in the normal direction and the two tangential directions, respectively; G n 、 G s and G t Represent the actual fracture energy in the normal direction and the two tangential directions respectively.

[0030] 2. Block interaction model.

[0031] After the CIE is completely broken, the finite elements separated on both sides can contact each other. The interaction between the two discrete elements is based on the surface contact of the elements. This contact method discretizes the element surface using nodes and allows slight mutual penetration between different surfaces. Whether the two objects are in contact with each other depends on the relative positions of the nodes in different steps. Surface-to-surface contact, point-to-surface contact, and edge-to-edge contact can be detected. For the most common surface-to-surface contact, the master surface and the slave surface are defined, and their roles are exchanged every two calculation steps. If the node of the master surface penetrates the slave surface, check whether a normal contact force is generated, such as Figure 4 As shown in (a); the normal contact force on the node is generated by the rebound of the contact surface in the physical mechanism and is perpendicular to the finite element surface. The normal contact force is perpendicular to the finite element surface and its magnitude is determined by the penetration depth of the node. The penetration depth of the node is calculated by the following formula.

[0032] .

[0033] in: F n represents the normal component of the contact force; k p Depends on the material properties of the interactive elements; d p Represents the penetration distance between the primary surface and the node.

[0034] When a finite element surface has a tendency or moves relative to another finite element surface, a tangential contact force is generated. The tangential contact force is perpendicular to the normal contact force and its magnitude is equal to the sliding force without relative motion or equal to the dynamic friction force with relative motion. The maximum static friction force is assumed to be equal to the dynamic friction force and is calculated by the following formula.

[0035] .

[0036] in: F t represents the kinetic friction; μ represents the Coulomb friction coefficient.

[0037] For edge-to-edge contact, it is based on the cross product of the contact normal direction between the corresponding edges of the two contacts. It is necessary to specify a feature angle, that is, the angle formed between the normals of the two faces connected to an edge, to activate the feature and the perimeter edge to participate in the edge-to-edge contact; in the study of this invention, the feature angle value is set to 1° to accurately detect edge-to-edge contact.

[0038] 3. Block motion model.

[0039] The motion of the object is calculated based on the explicit central difference time integration rule. If the system satisfies the dynamic equilibrium condition, the net force on the node is equal to the node mass matrix M multiplied by the node acceleration ü, which is expressed as: .

[0040] .

[0041] .

[0042] .

[0043] in: M represents the mass matrix; P represents the applied external load vector; I represents the internal force vector.

[0044] 2. Ice-water phase transition model based on SPH.

[0045] 1. SPH basic framework.

[0046] The simulation of ice-water phase transition under warming conditions is characterized by a smooth particle flow model based on SPH. SPH is a continuum mechanics method that is a further evolution of the traditional Lagrangian method. However, unlike the traditional Lagrangian method based on a grid, it has a gridless feature and uses a collection of virtual particles to represent the geometry and force of the material. Therefore, SPH can be used to simulate large deformation problems that are difficult to achieve with traditional grid methods without being restricted by unit distortion, such as Figure 5 As shown in (a) in the figure, the SPH model discretizes the prescribed set of continuum equations by directly interpolating the properties of a discrete set of points distributed on the solution domain. In the computational domain, the behavior of each particle is approximated by a variable field, which is further affected by the cumulative contribution of neighboring particles, as shown in Figure 5 As shown in (b) in the figure, the kernel function W expressed as an equation is often used to describe the contribution of a particle from its neighboring particles, and its equation is expressed as: .

[0047] in: f(x) A function representing the particle position vector; j represents the neighboring particles that can contribute; h Indicates the smoothing length, which determines how many particles affect the interpolation of a specific particle; m Represents the mass of the particle.

[0048] The continuity equation of the material can be expressed as follows: .

[0049] in: P(x)represents the density of a material at a certain location; x represents the spatial position.

[0050] The motion of each particle follows Newton's law of motion, and the force it is subjected to is shown in the following formula: .

[0051] The first term on the right side of the equal sign is gravity, the second term is the force due to the pressure difference, and the third term is the shear force due to the velocity difference.

[0052] 2. Interaction between particles and finite element mesh.

[0053] The virtual particles in SPH are a type of continuous node element corresponding to the continuum particle element. The interaction between SPH virtual particles and Lagrangian finite elements depends on the node-based surface in the node-to-surface contact technology; the node-based surface is defined on the nodes and it is assumed that the nodes have a non-zero contact thickness surface; the contact thickness of the particle is the same as the value specified by the characteristic length. When in contact with the finite element surface (master surface), the node-based surface can only be regarded as a slave surface, which means that the finite element surface can penetrate the node-based surface, but the node-based surface cannot penetrate the finite element surface; when the virtual particle encounters a finite element mesh object, the finite element surface is discretized using nodes, allowing the particles to slightly interpenetrate with the finite element surface nodes to calculate the contact force; whether the virtual particle contacts the finite element mesh object depends on the relative position of the nodes in different steps; in an analysis step, once the particle is penetrated by the finite element surface, a contact force is generated. The normal contact force is perpendicular to the finite element surface and its magnitude is determined by the penetration depth of the node, which can be calculated by the equation described above.

[0054] If there is relative tangential motion or tendency between the pseudo-particle and the finite element surface, a tangential contact force will be generated; the tangential contact force is perpendicular to the normal contact force. If there is a relative tangential motion tendency but no relative tangential motion, the tangential contact force is equal to the sliding force, otherwise the tangential contact force is equal to the kinetic friction force; whether relative tangential motion occurs depends on the relative size of the maximum static friction force and the sliding force, and the maximum static friction force is assumed to be equal to the kinetic friction force.

[0055] 3. Ice-water model governing equations.

[0056] When simulating ice / water, its behavior is governed by the conservation of momentum, energy, and mass. The Navier-Stokes equations for conservation of mass and momentum are shown in the first equation below, while conservation of energy is represented by the EOS equation of state, as shown below.

[0057] .

[0058] .

[0059] .

[0060] .

[0061] .

[0062] .

[0063] in: ρ Indicates the material density; v Indicates speed; σ represents the Cauchy stress; b Indicates physical strength; ρ 0 indicates the material reference density; η represents the nominal compressive strain; c 0 represents the material reference sound velocity; s represents the slope of the Us-Up curve; Γ0 represents the material constant; Γ represents the Grüneisen ratio; E m Indicates the internal energy per unit mass of the material; U s represents the shock wave velocity; U p Indicates the particle velocity.

[0064] 4. Ice-water phase transition simulation.

[0065] The present invention simulates the process of ice melting into water by coupling temperature and viscosity. The ice melting process corresponds to a phase change from an object to a fluid, and this phase change process is simulated according to the change in viscosity caused by the temperature change of each particle. The temperature change is represented by the following heat equation.

[0066] .

[0067] in: T Indicates temperature; k represents the thermal diffusion constant.

[0068] When the temperature of a part of the ice cube rises to the melting point, it turns into water. Assuming that the transition coefficient decreases linearly with respect to the temperature, that is: .

[0069] .

[0070] in: T max Indicates the maximum temperature; T min Indicates the minimum temperature.

[0071] The above model can realize the process of ice melting into water under the action of rising temperature.

[0072] The present invention uses the Stanford rabbit model to roughly simulate the ice melting process, and the simulation results are as follows: Figure 6 shown.

[0073] 5. Numerical simulation of ice and rock avalanche initiation under warming and snowmelt.

[0074] The quantitative assessment model of ice and rock avalanche and ice melt disasters constructed by the present invention based on the above numerical model simulates the process of temperature rising from -5℃ to 10℃. The simulation results are as follows: Figure 7 shown.

[0075] It can be seen that as the temperature rises, the upper ice body gradually melts and dissipates, and the melted ice water infiltrates and seeps along the cracks; under the action of the dynamic and static water pressure of the seepage, the cracks continue to evolve and eventually penetrate, causing the block to fall off under the action of gravity and form an ice and rock avalanche; the entire simulation process is consistent with the situation summarized in the actual ice and rock avalanche case, proving the feasibility of the above-mentioned coupling model in ice and rock avalanche simulation research.

[0076] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A numerical simulation method for ice and rock avalanche initiation, characterized in that: The following steps are involved: The numerical model of ice-rock avalanche is constructed by simulating the cracking and instability of ice-rock mass using the finite discrete element method (FDEM) and the ice-water phase transition process during the cracking and instability of ice-rock mass using the smooth particle flow (SPH). When simulating the fracture and instability of ice and rock masses on an ice and rock avalanche numerical model, FDEM generates a CIE unit and a finite element mesh. The CIE unit is inserted into the boundary of the finite element mesh and moves. The CIE unit and the finite element mesh generate traction stress and displacement, which characterize the action process of the rock mass during crack propagation and fracture. When the traction stress is reduced to a set value, the CIE unit breaks, and the finite element units on both sides come into contact and friction, resulting in the friction force between the finite element units on both sides. The friction force represents the contact friction process between the fractured rock masses during mutual movement. When simulating the propagation and fracture of rock cracks, as well as the mutual movement between fractured rock masses, the virtual particle collection within the smooth particle flow (SPH) is simulated as an ice-water block during the ice-water phase transition. The virtual particle collection and the finite element surface interpenetrate each other, and the contact force between the virtual particles and the finite element surface is obtained. The contact force represents the interaction between the ice-water phase transition and the rock fracture movement during the rock fracture and mutual movement. Based on the interaction between ice-water phase change and rock fracture movement, the movement process of ice, snow and rock mass when a simulated ice and rock avalanche is initiated is obtained.

2. The numerical simulation method for ice and rock avalanche initiation according to claim 1, characterized in that: The acquisition of the traction stress and displacement includes: When simulating the fracture and instability of ice and rock masses on the numerical model of ice and rock avalanche, the finite discrete element method (FDEM) inserts CIE elements into the finite element mesh boundary. The CIE elements represent the continuous-discontinuous interface elements. The CIE elements and the finite element mesh share nodes to transmit forces and displacements. The CIE unit deforms and fractures according to the traction-separation constitutive response of the stress-displacement law. During the deformation and fracture of the CIE unit, the CIE unit is damaged and fracture energy is generated. The damage of the CIE unit includes tensile damage in the opening mode and shear damage in the sliding mode. The displacement generated by the CIE unit and the finite element mesh is the path generated by the CIE unit from insertion to complete fracture. The traction stress generated by the CIE unit and the finite element mesh is obtained based on the linear relationship between the traction stress and displacement. The linear relationship between the traction stress and displacement of the CIE unit is expressed as: ； in: t represents the traction stress vector; k represents the CIE unit contact stiffness coefficient; δ represents the traction displacement vector; D represents the damage variable; The damage variable D The range is 0-1, where 0 indicates that the CIE unit has no damage and no fracture energy, and 1 indicates that the CIE unit is completely fractured and has fracture energy after complete fracture. The process in which the damage variable changes from 0 to 1 indicates the fracture process of the CIE unit.

3. The numerical simulation method for ice and rock avalanche initiation according to claim 2, characterized in that: The process of breaking the CIE unit includes: Under the single mode conditions of the opening mode and the sliding mode, the CIE unit begins to be damaged after reaching the peak traction stress, and the traction stress begins to decrease; when the traction stress decreases to the minimum value, the CIE unit is completely broken; For the mixed mode of opening mode and sliding mode, the initial damage of CIE unit is determined using the QUADS damage criterion, which is expressed as: ； in: t n 、 t s and t t represent the normal component and tangential component of the crack surface, respectively; t, t, and t represent the peak values of the nominal stresses in the three directions, respectively; <> indicates that the pure compressive stress state will not cause damage; The second power of the fracture energy is used to determine the complete fracture of the CIE unit and is expressed as: ； Where: G, G, and G represent the fracture energy corresponding to complete fracture in the normal direction and the two tangential directions, respectively; G n 、 G s and G t Represent the actual fracture energy in the normal direction and the two tangential directions respectively.

4. The numerical simulation method for ice and rock avalanche initiation according to claim 1, characterized in that: The acquisition of the friction force characterizing the contact friction process between the fractured rock masses during mutual movement includes: After the CIE element is completely fractured, the separated finite elements on both sides have surface-to-surface contact, point-to-surface contact and edge-to-edge contact forms; the surface-to-surface contact, point-to-surface contact and edge-to-edge contact forms represent the mutual motion forms between the fractured rock masses; If the node of the master surface penetrates the slave surface, check whether a normal contact force is generated. The normal contact force on the node is generated by the rebound of the contact surface in the physical mechanism and is perpendicular to the finite element surface. The normal contact force is perpendicular to the finite element surface and its magnitude is determined by the penetration depth of the node. The relationship between the penetration depth of the node and the normal component of the contact force is expressed as: ； in: F n represents the normal component of the contact force; k p Depends on the material properties of the interactive elements; d p represents the penetration distance between the main surface and the node; When a finite element surface has a trend or moves relative to another finite element surface, a tangential contact force is generated. The tangential contact force is the friction force of the contact friction process between the fractured rock masses during mutual movement, which is expressed as: ； in: F t represents friction; μ represents the Coulomb friction coefficient.

5. The numerical simulation method for ice and rock avalanche initiation according to claim 1, characterized in that: The simulation of the interaction between the ice-water phase transition and the rock mass fracture movement includes: The virtual particles in the smooth particle flow (SPH) correspond to a continuous node element in the continuum particle element. The interaction between the virtual particles and the finite element surface depends on the node-based surface in the node-to-surface contact. The node-based surface is composed of the nodes of the finite element mesh. When a virtual particle contacts a finite element surface, the node-based surface acts as a slave surface, and the finite element surface can penetrate the node-based surface, but the node-based surface cannot penetrate the finite element surface; When virtual particles encounter a finite element mesh object, the surface of the finite element is discretized using nodes, and the virtual particles and the finite element surface nodes interpenetrate each other to obtain the contact force between the virtual particles and the finite element surface; The contact force characterizes the interaction between the ice-water phase transition and the rock mass fracture motion when the rock mass fractures and the fractured rock masses move relative to each other.

6. The numerical simulation method for ice and rock avalanche initiation according to claim 5, characterized in that: The ice-water phase transition process is controlled by the conservation of momentum, energy and mass. During the ice-water phase transition, inertial forces, pressure gradients, gravity, and viscous forces exist between the ice-water fluids. The motion of the fluid particles in the ice-water fluid follows the conservation of momentum. At the same time, during the ice-water phase transition, the mass of the ice-water fluid remains unchanged, following the conservation of mass. The Navier-Stokes equations for the conservation of mass and momentum are expressed as follows: ； ； During the ice-water phase transition, heat conduction, energy convection, and latent heat of phase change occur between the fluid particles in the ice-water fluid, and energy conservation is followed. The energy conservation is characterized by the EOS equation of state, which is expressed as follows: ； ； ； ； ； in: ρ Indicates the material density; v Indicates speed; σ represents the Cauchy stress; b Indicates physical strength; ρ 0 indicates the material reference density; η represents the nominal compressive strain; c 0 represents the material reference sound velocity; s represents the slope of the Us-Up curve; Γ0 represents the material constant; Γ represents the Grüneisen ratio; E m It represents the internal energy per unit mass of the material; U s represents the shock wave velocity; U p Indicates the particle velocity.

7. The numerical simulation method for ice and rock avalanche initiation according to claim 6, characterized in that: The ice-water phase transition process simulates the process of ice melting into water by coupling temperature and viscosity; The ice melting process corresponds to a phase transition from an object to a fluid. The melting phase transition is simulated by the change in viscosity caused by the temperature change of each particle. The temperature change is expressed as: ； in: T Indicates temperature; k represents the thermal diffusion constant; When the temperature of a part of the ice cube rises to the melting point, it turns into water; the transition energy during the temperature change J ( T ) is expressed as: ； ； in: T max Indicates the maximum temperature; T min Indicates the minimum temperature; J max represents the highest transition energy; J min represents the minimum transition energy.

8. A numerical simulation device for ice and rock avalanche initiation, characterized in that: include: A model building module is used to simulate the fracture and instability of ice-rock mass according to the finite discrete element method (FDEM), and to simulate the ice-water phase transition process during the fracture and instability of ice-rock mass according to the smooth particle flow method (SPH), so as to build a numerical model of ice-rock avalanche; The rock mass motion simulation module is used to simulate the fracture and instability of ice and rock masses on the ice and rock avalanche numerical model. FDEM generates a CIE unit and a finite element mesh, inserts the CIE unit into the finite element mesh boundary and moves it. The CIE unit and the finite element mesh generate traction stress and displacement, which characterize the action process of the rock mass during crack propagation and fracture. When the traction stress is reduced to a set value, the CIE unit breaks, and the finite element units on both sides come into contact and friction, resulting in the friction force between the finite element units on both sides. The friction force represents the contact friction process between the fractured rock masses during mutual movement. The ice and rockfall initiation simulation module is used to simulate the propagation and fracture of rock cracks, as well as the mutual movement between fractured rock masses. The virtual particle collection in the smooth particle flow (SPH) is simulated as an ice-water block during the ice-water phase transition. The virtual particle collection and the finite element surface interpenetrate each other, and the contact force between the virtual particles and the finite element surface is obtained. The contact force represents the interaction between the ice-water phase transition and the rock fracture movement during rock fracture and mutual movement. Based on the interaction between ice-water phase change and rock fracture movement, the movement process of ice, snow and rock mass when a simulated ice and rock avalanche is initiated is obtained.

9. An electronic device, characterized in that: include: memory and processor; The memory is used to store computer programs; The processor is configured to implement the steps of the method for numerically simulating ice and rock avalanche initiation according to any one of claims 1 to 7 when executing the computer program stored in the memory.

10. A computer-readable storage medium, characterized in that Used to store a computer program, which, when executed by a processor, implements the steps of a numerical simulation method for ice and rock avalanche initiation according to any one of claims 1 to 7.

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