Method for simulating conversion process from rock ice avalanche to debris flow

Abstract

The invention belongs to the technical field of disaster simulation, and relates to a method for simulating the conversion process from rock ice avalanche to debris flow. The method comprises the following steps: establishing a fluid phase mass conservation equation, an ice phase mass conservation equation, a rock phase mass conservation equation and a momentum conservation equation of a fluid phase, an ice phase and a rock phase in a conversion process from rock ice avalanche to debris flow, and establishing an energy conservation equation of mass flow to obtain a control equation of a depth average three-phase model; and solving a flux item for the control equation of the depth average three-phase model by adopting a second-order precision finite volume method based on the combination of a finite volume method and a renii approximation Riemann solver to obtain the time and space distribution of the flow depth, the flow velocity, the phase volume fraction and the temperature. By considering the interaction among the rock phase, the ice phase and the fluid phase, a real physical process including positive and negative temperature conversion is simulated, and the conversion process of rock ice avalanche from particle flow to debris flow is described.

Description

Technical Field

[0001] The present invention belongs to the technical field of disaster simulation, and in particular, relates to a method for simulating the transformation process of a rock-ice avalanche into a debris flow. Background Art

[0002] In recent years, due to the rapid melting of glaciers and permafrost in mountainous areas, the transition from rock-ice avalanches to debris flows has become more frequent, causing significant casualties and property losses, and posing severe challenges to the management of alpine environmental disasters.

[0003] The formation mechanism of debris flows transformed from rock-ice avalanches is significantly different from the traditional model due to the phase change and multiphase mixing characteristics of the ice body, and the existing debris flow models are difficult to directly apply. Although both types of flow states involve solid-liquid multiphase interactions, such as phase separation and expansion effects, there is still a lack of coupled modeling for phase change, energy exchange and temperature dynamic changes driven by ice melting.

[0004] Most existing rock-ice avalanche models do not integrate the energy conservation equation, or simplify the temperature dynamics, resulting in distorted simulation of the ice melting process; existing studies analyze rock-ice avalanches and debris flows in isolation, lacking a unified framework to describe the multiphase transformation process driven by ice phase change; frictional heat generation between solid-liquid-ice multiphases, meltwater penetration and flow enhancement effects have not yet been systematically quantified.

[0005] Therefore, it is urgent to develop a new multiphase coupling model that can accurately describe the transformation mechanism of rock and ice avalanches into debris flows by integrating energy conservation, temperature evolution and phase change dynamics, and provide theoretical support for early warning and prevention of alpine disasters. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a method for simulating the transformation process of rock-ice avalanches into debris flows, comprising: A surface induced coordinate system is established. Based on the flow depth, flow velocity, phase volume fraction, time and space evolution of temperature, interphase forces, interaction forces between particles, and ice melting rate, the mass conservation equations of the fluid phase, ice phase, and rock phase in the process of rock-ice avalanche to debris flow are established, as well as the momentum conservation equations of the fluid phase, ice phase, and rock phase in the horizontal direction. At the same time, the energy conservation equation of the mass flow is established to obtain the control equations of the depth-averaged three-phase model. Determine the expressions of interphase forces and interaction forces between particles based on flow depth, flow velocity, phase volume fraction and temperature; According to the expressions of interphase forces and interaction forces between particles, the control equations of the depth-averaged three-phase model are solved by the second-order accuracy finite volume method based on the combination of the finite volume method and the Roy approximate Riemann solver. The time and spatial distribution of flow depth, flow velocity, phase volume fraction and temperature are obtained to describe the transformation process of rock ice avalanches from particle flow to debris flow.

[0007] Based on the above technical solution, the present invention can also be improved as follows.

[0008] Further, suppose is the volume fraction of the rock phase, is the volume fraction of ice phase, is the volume fraction of the fluid phase, is the phase density of the ice phase, is the phase density of the fluid phase, is the depth of the mixture flow, For time, is the melting rate of ice, and is the coordinate axis, For the fluid phase The phase velocity component in the direction, For the fluid phase The phase velocity component in the direction, For ice phase The phase velocity component in the direction, For ice phase The phase velocity component in the direction, Rock phase The phase velocity component in the direction, Rock phase The phase velocity component in the direction; The mass conservation equation for the fluid phase is: ; The mass conservation equation for the ice phase is: ; The mass conservation equation of the rock phase is: .

[0009] Further, suppose is the volume fraction of the rock phase, is the volume fraction of ice phase, is the volume fraction of the fluid phase, is the phase density of the rock phase, is the phase density of the ice phase, is the phase density of the fluid phase, is the depth of the mixture flow, For time, is the melting rate of ice, , and is the coordinate axis, For the fluid phase The phase velocity component in the direction, For the fluid phase The phase velocity component in the direction, is the phase velocity of the ice phase, For ice phase The phase velocity component in the direction, For ice phase The phase velocity component in the direction, is the phase velocity of the rock phase, Rock phase The phase velocity component in the direction, Rock phase The phase velocity component in the direction, is the saturation parameter, is the density ratio between the fluid phase and the rock phase, is the density between the fluid phase and the ice phase, is the bed surface elevation, is the viscosity of the fluid, is the gravitational acceleration The direction of the component, is the gravitational acceleration The direction of the component, is the gravitational acceleration The direction of the component, is the friction coefficient of the ice phase, is the friction coefficient of the rock phase, Fluid phase and ice phase Directional drag, Fluid phase and rock phase Directional drag, Fluid phase and ice phase Directional drag, Fluid phase and rock phase Directional drag, is the inter-particle resistance The direction of the component, is the inter-particle resistance The direction of the component, is the inter-particle resistance The direction of the component, is the force caused by meltwater; Fluid phase The momentum conservation equation in the direction is:

[0010] ; Fluid phase The momentum conservation equation for the direction is;

[0011] ; Ice phase The momentum conservation equation in the direction is:

[0012] ; Ice phase The momentum conservation equation for the direction is;

[0013] ; Rock phase The momentum conservation equation in the direction is:

[0014] ; Rock phase The momentum conservation equation in the direction is:

[0015] .

[0016] Furthermore, the energy conservation equation for mass flow includes heat convection, heat conduction, heat loss due to ice melting, and heat generated by internal friction. is the flow density, is the phase density of the ice phase, is the specific heat of the mixture, is the depth of the mixture flow, is the rock-ice avalanche temperature, is the temperature of the external environment, is the temperature of the ground interface, Phase edge The average speed in the direction, Phase edge The average speed in the direction, is the temperature profile related parameter, is the thermal conductivity, is the latent heat of ice, is the melting rate of ice, is the shape factor of the vertical velocity profile, is the friction resistance at the bottom of the rock-ice avalanche, is the phase average velocity vector, then the energy conservation equation of mass flow is:

[0017] .

[0018] Further, suppose is the particle-fluid drag coefficient, and the Reynolds number is The particle diameter is , is the phase density of the fluid phase, is the velocity of the fluid phase, is the phase velocity, Indicates the phase category, is the viscosity of the fluid, is the volume fraction of the fluid phase, is the phase volume fraction; ; ; The interphase force is: .

[0019] Further, suppose is the particle-drag coefficient, is the interaction force between particles, is the phase density of the ice phase, is the volume fraction of the rock phase, is the volume fraction of the rock phase, is the rock phase velocity vector, is the ice phase velocity vector; The interaction force between particles is: .

[0020] Furthermore, assuming that the melting rate of ice is , is the flow density, is the specific heat of the mixture, is the depth of the mixture flow, is the internal temperature of the rock-ice avalanche, is the temperature threshold at which ice begins to melt, is the phase density of the ice phase, is the latent heat of ice, then the melting rate of ice is: .

[0021] Furthermore, the control equations of the deep averaged three-phase model are solved by a second-order numerical method based on the finite volume method combined with the Roy approximate Riemann solver, including: The control equation of the depth-averaged three-phase model is expressed as a matrix equation, and two sub-matrix equations are obtained by using the fractional stepping method and performing spatial splitting. The two submatrix equations are transformed by the finite volume method to obtain the homogeneous operator equation in discretized form, and the numerical flux is obtained by solving the homogeneous operator equation.

[0022] Furthermore, the control equation of the deep average three-phase model is expressed as a matrix equation, including: and represents the interface flux between adjacent grids, represents the mass transfer flux caused by phase change, represents the momentum flux caused by the phase change, is the volume fraction of the phase, is the depth of the mixture flow, For time, Phase velocity The direction component, For the category of phase, is the phase velocity The direction component, is the rock ice and snow temperature, is the phase side pressure coefficient, , is the specific heat of the mixture, For relative heat, is the atmospheric heat transfer coefficient, , is the bed surface elevation, is the gravitational acceleration The direction component, is the thermal conductivity, is the mass exchange coefficient, is the shape factor of the vertical velocity profile, is the phase density ratio, is the interaction force between particles The direction component, Phase drag force The direction component, Phase drag force The direction component, is the temperature of the external environment, is the temperature of the ground interface, is the phase-averaged basic friction force, is the flow density, is the friction resistance at the bottom, then: ; ; ; ; ; .

[0023] Further, suppose and represents the interface flux between adjacent grids, represents the mass transfer flux caused by phase change, represents the momentum flux caused by the phase change, is the time step, For along The prediction step calculation operator of the direction, For along The correction step calculation operator of the direction, For along Direction prediction operator, For along The correction step calculation operator of the direction, is the total variable matrix before calculation, is the total variable matrix after calculation, is the numerical flux on the right side of the unit interface, is the numerical flux on the left side of the unit interface, is the Jacobian matrix, is the grid length, is the time step, and the fractional stepping method is used to transform the depth averaged three-phase model into: ; Get the solution for the next time step: ; Solve the homogeneous equation, let , based on the finite volume method, the solution for the next time step is obtained: ; Solve using Roy's approximate Riemann solver, let , and obtain the numerical flux.

[0024] The beneficial effects of the present invention are as follows: the present invention adopts a second-order precision finite volume method based on a combination of a finite volume method and a Roy approximate Riemann solver to solve the flux term of the control equation of the depth-averaged three-phase model, thereby significantly improving the calculation stability; by considering the interaction between the rock phase, the ice phase and the fluid phase, the real physical process including the positive and negative temperature conversion is simulated, and the transformation process of the rock-ice avalanche from the particle flow to the debris flow is described. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1A schematic diagram of a method for simulating the transition process of a rock-ice avalanche to a debris flow provided in an embodiment of the present invention; Figure 2 This is a simulation diagram of the depth of the flow body at different times; Figure 3 This is a simulation diagram of the evolution trend of pore pressure during the flow process; Figure 4 This is a simulation diagram of ice volume fraction at the monitoring point; Figure 5 This is a simulation diagram of the temperature change at the monitoring point. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0027] As an example, Figure 1 As shown, in order to solve the above technical problems, this embodiment provides a method for simulating the transformation process of rock ice avalanches into debris flows, including: A surface induced coordinate system is established. Based on the flow depth, flow velocity, phase volume fraction, time and space evolution of temperature, interphase forces, interaction forces between particles, and ice melting rate, the mass conservation equations of the fluid phase, ice phase, and rock phase in the process of rock-ice avalanche to debris flow are established, as well as the momentum conservation equations of the fluid phase, ice phase, and rock phase in the horizontal direction. At the same time, the energy conservation equation of the mass flow is established to obtain the control equations of the depth-averaged three-phase model. Determine the expressions of interphase forces and interaction forces between particles based on flow depth, flow velocity, phase volume fraction and temperature; According to the expressions of interphase forces and interaction forces between particles, the control equations of the depth-averaged three-phase model are solved by the second-order accuracy finite volume method based on the combination of the finite volume method and the Roy approximate Riemann solver. The time and spatial distribution of flow depth, flow velocity, phase volume fraction and temperature are obtained to describe the transformation process of rock ice avalanches from particle flow to debris flow.

[0028] Optional, set is the volume fraction of the rock phase, is the volume fraction of ice phase, is the volume fraction of the fluid phase, is the phase density of the ice phase, is the phase density of the fluid phase, is the depth of the mixture flow, For time, is the melting rate of ice, and is the coordinate axis, For the fluid phase The phase velocity component in the direction, For the fluid phase The phase velocity component in the direction, For ice phase The phase velocity component in the direction, For ice phase The phase velocity component in the direction, Rock phase The phase velocity component in the direction, Rock phase The phase velocity component in the direction; The mass conservation equation for the fluid phase is: ; The mass conservation equation for the ice phase is: ; The mass conservation equation of the rock phase is: .

[0029] Optional, set is the volume fraction of the rock phase, is the volume fraction of ice phase, is the volume fraction of the fluid phase, is the phase density of the rock phase, is the phase density of the ice phase, is the phase density of the fluid phase, is the depth of the mixture flow, For time, is the melting rate of ice, , and is the coordinate axis, For the fluid phase The phase velocity component in the direction, For the fluid phase The phase velocity component in the direction, is the phase velocity of the ice phase, For ice phase The phase velocity component in the direction, For ice phase The phase velocity component in the direction, is the phase velocity of the rock phase, Rock phase The phase velocity component in the direction, Rock phase The phase velocity component in the direction, is the saturation parameter, is the density ratio between the fluid phase and the rock phase, is the density between the fluid phase and the ice phase, is the bed surface elevation, is the viscosity of the fluid, is the gravitational acceleration The direction of the component, is the gravitational acceleration The direction of the component, is the gravitational acceleration The direction of the component, is the friction coefficient of the ice phase, is the friction coefficient of the rock phase, Fluid phase and ice phase Directional drag, Fluid phase and rock phase Directional drag, Fluid phase and ice phase Directional drag, Fluid phase and rock phase Directional drag, is the inter-particle resistance The direction of the component, is the inter-particle resistance The direction of the component, is the inter-particle resistance The direction of the component, is the force caused by meltwater; Fluid phase The momentum conservation equation in the direction is:

[0030] ; Fluid phase The momentum conservation equation for the direction is;

[0031] ; Ice phase The momentum conservation equation in the direction is:

[0032] ; Ice phase The momentum conservation equation for the direction is;

[0033] ; Rock phase The momentum conservation equation in the direction is:

[0034] ; Rock phase The momentum conservation equation in the direction is:

[0035] .

[0036] Optionally, the energy conservation equation for mass flow includes heat convection, heat conduction, heat loss due to ice melting, and heat generated by internal friction. is the flow density, is the phase density of the ice phase, is the specific heat of the mixture, is the depth of the mixture flow, is the rock-ice avalanche temperature, is the temperature of the external environment, is the temperature of the ground interface, Phase edge The average speed in the direction, Phase edge The average speed in the direction, is the temperature profile related parameter, is the thermal conductivity, is the latent heat of ice, is the melting rate of ice, is the shape factor of the vertical velocity profile, is the friction resistance at the bottom of the rock-ice avalanche, is the phase average velocity vector, then the energy conservation equation of mass flow is:

[0037] .

[0038] represents heat convection, represents heat conduction, represents the heat loss caused by melting ice, Indicates the heat generated by internal friction.

[0039] Optional, set is the particle-fluid drag coefficient, and the Reynolds number is The particle diameter is , is the phase density of the fluid phase, is the velocity of the fluid phase, is the phase velocity, Indicates the phase category, is the viscosity of the fluid, is the volume fraction of the fluid phase, is the phase volume fraction; ; ; The interphase force is: .

[0040] The governing equations of the depth-averaged three-phase model describe the temporal and spatial evolution of flow depth, velocity, phase volume fraction, and temperature in the surface-induced coordinate system O-xyz. They consist of the conservation equations of mass, momentum, and energy for each phase, and take into account the effects of phase interaction, temperature evolution, and ice melting on the flow dynamics. In order to solve the model equations efficiently, a second-order accurate finite volume method based on the finite volume method combined with the Roy approximate Riemann solver is used, and the reliability of the model is verified by numerical simulations.

[0041] Optional, set is the particle-drag coefficient, is the interaction force between particles, is the phase density of the ice phase, is the volume fraction of the rock phase, is the volume fraction of the rock phase, is the rock phase velocity vector, is the ice phase velocity vector; The interaction force between particles is: .

[0042] Optionally, assume that the melting rate of ice is , is the flow density, is the specific heat of the mixture, is the depth of the mixture flow, is the internal temperature of the rock-ice avalanche, is the temperature threshold at which ice begins to melt, is the phase density of the ice phase, is the latent heat of ice, then the melting rate of ice is: .

[0043] Optionally, a second-order numerical method based on the finite volume method combined with the Roy approximate Riemann solver is used to solve the governing equations of the deep-averaged three-phase model, including: The control equation of the depth-averaged three-phase model is expressed as a matrix equation, and two sub-matrix equations are obtained by using the fractional stepping method and performing spatial splitting. The two submatrix equations are transformed using the finite volume method to obtain the discretized homogeneous operator equation, and the numerical flux is obtained by solving the homogeneous operator equation.

[0044] Optionally, the governing equations of the deep averaged three-phase model are expressed as a matrix equation, including: and represents the interface flux between adjacent grids, represents the mass transfer flux caused by phase change, represents the momentum flux caused by the phase change, is the volume fraction of the phase, is the depth of the mixture flow, For time, is the phase velocity The direction of the component, For the category of phase, is the phase velocity The direction of the component, is the rock ice and snow temperature, is the phase side pressure coefficient, , is the specific heat of the mixture, For relative heat, is the atmospheric heat transfer coefficient, , is the bed surface elevation, is the gravitational acceleration The direction of the component, is the thermal conductivity, is the mass exchange coefficient, is the shape factor of the vertical velocity profile, is the phase density ratio, is the interaction force between particles The direction of the component, Phase drag force The direction of the component, Phase drag force The direction of the component, is the temperature of the external environment, is the temperature of the ground interface, is the phase-averaged basic friction force, is the flow density, is the friction resistance at the bottom, then: ; ; ; ; ; .

[0045] Optional, set and represents the interface flux between adjacent grids, represents the mass transfer flux caused by phase change, represents the momentum flux caused by the phase change, is the time step, For along The prediction step calculation operator of the direction, For along The correction step calculation operator of the direction, For along Direction prediction operator, For along The correction step calculation operator of the direction, is the total variable matrix before calculation, is the total variable matrix after calculation, is the numerical flux on the right side of the unit interface, is the numerical flux on the left side of the unit interface, is the Jacobian matrix, is the grid length, is the time step, and the fractional stepping method is used to transform the depth averaged three-phase model into: ; Get the solution for the next time step: ; Solve the homogeneous equation, let , based on the finite volume method, the solution for the next time step is obtained: ; Solve using Roy's approximate Riemann solver, let , and obtain the numerical flux.

[0046] The Berkeley rotating drum experiment verifies the effectiveness of the depth-averaged three-phase model in capturing the transition between rock-ice avalanches and debris flows. Figure 2The depth of the flow body at different times is shown, the horizontal axis is the horizontal length of the flow body, the vertical axis is the vertical height of the flow body, S1 represents the calculated data at 3 minutes, M1 represents the experimental monitoring data at 3 minutes, S2 represents the calculated data at 7 minutes, M2 represents the experimental monitoring data at 7 minutes, S3 represents the calculated data at 25 minutes, M3 represents the experimental monitoring data at 25 minutes, S4 represents the calculated data at 39 minutes, and M4 represents the experimental monitoring data at 39 minutes. Figure 2 The experimental simulation results with an ice content of 70% are shown. When the drum starts to rotate and reaches a stable state (t=3 minutes), the mass moves in the direction of the drum's rotation. Due to friction heating and heat transfer from the surrounding environment, the temperature of the mass gradually rises from -10°C to 0°C, followed by an ice melting process. In the early stage (t=7 minutes), the position of the front edge mass retreats slightly, which is due to the fact that a small amount of meltwater enhances the cohesion between particles. As the meltwater increases, the increase in pore water pressure breaks the equilibrium state by reducing the friction resistance of the base, causing the mass to slide downward (t=25 minutes); under the action of gravity, the meltwater is enriched at the front edge to form a nose-shaped protruding feature, which is consistent with the experimental results. Continuous ice melting causes the mass to transition from dry rock-ice particle flow to rock-ice-fluid debris flow (t=39 minutes), and the simulated flow profile is consistent with the measured data.

[0047] As attached Figure 3 As shown, the horizontal axis is the roller angle, unit: °, the vertical axis is the pore pressure, unit: hPa, S5 represents the calculated data at 13 minutes, M5 represents the experimental data at 13 minutes, S6 represents the calculated data at 19 minutes, M6 represents the experimental data at 19 minutes, S7 represents the calculated data at 25 minutes, M7 represents the experimental data at 25 minutes, S8 represents the calculated data at 39 minutes, M8 represents the experimental data at 39 minutes, Appendix Figure 3 The evolution trend of pore pressure during flow is shown. The simulation results are consistent with the observed law that pore pressure gradually increases from the tail to the head. The ice volume fraction at the monitoring point is shown in the attached figure. Figure 4 As shown, the horizontal axis is time, unit: s, and the vertical axis is volume fraction, including four stages: D1, D2, D3 and D4. The temperature changes of the monitoring points are shown in the attached Figure 5As shown in the figure, the horizontal axis is time and the vertical axis is temperature, including five stages: D5, D6, D7, D8 and D9, which intuitively reveals the process of flow state transition. The process can be divided into four stages: (1) After the drum rotates, the flow gradually stabilizes, and the flow depth tends to be stable after initial fluctuations; (2) The stable state is maintained, but the friction heat and environmental heat transfer are not enough to trigger ice melting; (3) After the temperature reaches 0°C, the excess heat triggers ice melting, and the base friction resistance and gravity are unbalanced. During this stage, the temperature remains constant at zero degrees; (4) After the ice particles are completely melted, the flow enters a new steady state, and the temperature rises again due to frictional heat and environmental temperature difference. The numerical simulation successfully reproduces the transition process of the rock-ice avalanche sliding body from granular flow to debris flow, and accurately describes the evolution of key parameters such as phase components and temperature.

[0048] Unlike existing models, the depth-averaged three-phase model proposed in this invention can simulate real physical processes involving positive and negative temperature conversions by introducing energy conservation equations. A key point in ice melting is how to determine when the ice melts by considering the interaction between the rock, ice, and water (produced by ice melting) phases. Due to the influence of friction and heat transfer (e.g., ice and air), the internal temperature of rock-ice avalanches can change from negative to positive and vice versa, which has a great impact on the melting of ice.

[0049] For the analysis of the flow state transition from dry granular flow to solid-liquid multiphase flow during rock-ice avalanche movement, a composite friction law combining solid Coulomb friction and liquid viscous shear is adopted. In addition, a saturation parameter is introduced to quantitatively characterize the effect of pore water pressure on the normal stress of the flowing material, and μ(I)-rheology is combined to optimize the simulation effect of the solid-phase substrate friction coefficient.

[0050] The numerical solution adopts the second-order accurate finite volume method. The second-order accurate finite volume method based on the combination of the finite volume method and the Roy approximate Riemann solver is used to solve the flux term of the control equation of the deep average three-phase model, which significantly improves the calculation stability. Experimental simulation shows that the deep average three-phase model successfully captures the dynamic evolution of rock-ice avalanches under different ice contents (especially ice content>80%). Through the numerical case study of the roller experiment, the model's ability to accurately simulate the transition process from single phase (rock-ice) to multiphase (rock-ice-water) in rock-ice avalanche movement is verified, and the evolution of key parameters such as water content and temperature is effectively tracked. Further numerical experiments show that the increase in fluid viscosity will accelerate the transition rate of rock-ice avalanches from single phase to multiphase by enhancing the friction contact heat generation effect between particles; at the same time, the increase in the particle size ratio of ice particles to rock particles will significantly promote the phase change process by increasing the friction heat generation per unit time. In addition, the cohesive force generated by meltwater will inhibit the movement of low-speed rock-ice avalanches, but the accompanying effects such as the increase in pore water pressure should have a counteracting effect on this inhibition.

[0051] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for simulating the transition process of rock-ice avalanches to debris flows, characterized in that: include: A surface induced coordinate system is established. Based on the flow depth, flow velocity, phase volume fraction, time and space evolution of temperature, interphase forces, interaction forces between particles, and ice melting rate, the mass conservation equations of the fluid phase, ice phase, and rock phase in the process of rock-ice avalanche to debris flow are established, as well as the momentum conservation equations of the fluid phase, ice phase, and rock phase in the horizontal direction. At the same time, the energy conservation equation of the mass flow is established to obtain the control equations of the depth-averaged three-phase model. Determine the expressions of interphase forces and interaction forces between particles based on flow depth, flow velocity, phase volume fraction and temperature; According to the expressions of interphase forces and interaction forces between particles, the control equations of the depth-averaged three-phase model are solved by the second-order accuracy finite volume method based on the combination of the finite volume method and the Roy approximate Riemann solver. The time and spatial distribution of flow depth, flow velocity, phase volume fraction and temperature are obtained to describe the transformation process of rock ice avalanches from particle flow to debris flow.

2. The method for simulating the transition process of rock-ice avalanches to debris flows according to claim 1, characterized in that: set up is the volume fraction of the rock phase, is the volume fraction of the ice phase, is the volume fraction of the fluid phase, is the phase density of the ice phase, is the phase density of the fluid phase, is the depth of the mixture flow, For time, is the melting rate of ice, and is the coordinate axis, For the fluid phase The phase velocity component in the direction, For the fluid phase The phase velocity component in the direction, For ice phase The phase velocity component in the direction, For ice phase The phase velocity component in the direction, Rock phase The phase velocity component in the direction, Rock phase The phase velocity component in the direction; The mass conservation equation for the fluid phase is: ； The mass conservation equation for the ice phase is: ； The mass conservation equation of the rock phase is: 。 3. The method for simulating the transition process of rock-ice avalanches to debris flows according to claim 1, characterized in that: set up is the volume fraction of the rock phase, is the volume fraction of ice phase, is the volume fraction of the fluid phase, is the phase density of the rock phase, is the phase density of the ice phase, is the phase density of the fluid phase, is the depth of the mixture flow, For time, is the melting rate of ice, , and is the coordinate axis, For the fluid phase The phase velocity component in the direction, For the fluid phase The phase velocity component in the direction, is the phase velocity of the ice phase, For ice phase The phase velocity component in the direction, For ice phase The phase velocity component in the direction, is the phase velocity of the rock phase, Rock phase The phase velocity component in the direction, Rock phase The phase velocity component in the direction, is the saturation parameter, is the density ratio between the fluid phase and the rock phase, is the density between the fluid phase and the ice phase, is the bed surface elevation, is the viscosity of the fluid, is the gravitational acceleration The direction of the component, is the gravitational acceleration The direction of the component, is the gravitational acceleration The direction of the component, is the friction coefficient of the ice phase, is the friction coefficient of the rock phase, Fluid phase and ice phase Directional drag, Fluid phase and rock phase Directional drag, Fluid phase and ice phase Directional drag, Fluid phase and rock phase Directional drag, is the inter-particle resistance The direction component, is the inter-particle resistance The direction component, is the inter-particle resistance The direction of the component, is the force caused by meltwater; Fluid phase The momentum conservation equation in the direction is: ； Fluid phase The momentum conservation equation for the direction is; ； Ice phase The momentum conservation equation in the direction is: ； Ice phase The momentum conservation equation for the direction is; ； Rock phase The momentum conservation equation in the direction is: ； Rock phase The momentum conservation equation in the direction is: 。 4. The method for simulating the transition process of rock-ice avalanches to debris flows according to claim 1, characterized in that: The energy conservation equation for mass flow includes heat convection, heat conduction, heat loss due to ice melting, and heat generated by internal friction. is the flow density, is the phase density of the ice phase, is the specific heat of the mixture, is the depth of the mixture flow, is the rock-ice avalanche temperature, is the temperature of the external environment, is the temperature of the ground interface, Phase edge The average speed in the direction, Phase edge The average speed in the direction, is the temperature profile related parameter, is the thermal conductivity, is the latent heat of ice, is the melting rate of ice, is the shape factor of the vertical velocity profile, is the friction resistance at the bottom of the rock-ice avalanche, is the phase average velocity vector, then the energy conservation equation of mass flow is: 。 5. The method for simulating the transition process of rock-ice avalanches to debris flows according to claim 1, characterized in that: set up is the particle-fluid drag coefficient, and the Reynolds number is The particle diameter is , is the phase density of the fluid phase, is the velocity of the fluid phase, is the phase velocity, Indicates the phase category, is the viscosity of the fluid, is the volume fraction of the fluid phase, is the phase volume fraction; ； ； The interphase force is: .

6. The method for simulating the transition process of rock-ice avalanches to debris flows according to claim 1, characterized in that: set up is the particle-drag coefficient, is the interaction force between particles, is the phase density of the ice phase, is the volume fraction of the rock phase, is the volume fraction of the rock phase, is the rock phase velocity vector, is the ice phase velocity vector; The interaction force between particles is: 。 7. The method for simulating the transition process of rock-ice avalanches to debris flows according to claim 1, characterized in that: Assume that the melting rate of ice is , is the flow density, is the specific heat of the mixture, is the depth of the mixture flow, is the internal temperature of the rock-ice avalanche, is the temperature threshold at which ice begins to melt, is the phase density of the ice phase, is the latent heat of ice, then the melting rate of ice is: 。 8. The method for simulating the transition process of rock-ice avalanches to debris flows according to claim 1, characterized in that: The governing equations of the deep averaged three-phase model are solved using a second-order numerical method based on the finite volume method combined with the Roy approximate Riemann solver, including: The control equation of the depth-averaged three-phase model is expressed as a matrix equation, and two sub-matrix equations are obtained by using the fractional stepping method and performing spatial splitting. The two submatrix equations are transformed by the finite volume method to obtain the homogeneous operator equation in discretized form, and the numerical flux is obtained by solving the homogeneous operator equation.

9. The method for simulating the transition process of rock-ice avalanches to debris flows according to claim 1, characterized in that: The control equation of the deep averaged three-phase model is expressed as a matrix equation, including: and represents the interface flux between adjacent grids, represents the mass transfer flux caused by phase change, represents the momentum flux caused by the phase change, is the volume fraction of the phase, is the depth of the mixture flow, For time, is the phase velocity The direction of the component, For the category of phase, is the phase velocity The direction of the component, is the rock ice and snow temperature, is the phase side pressure coefficient, , is the specific heat of the mixture, For relative heat, is the atmospheric heat transfer coefficient, , is the bed surface elevation, is the gravitational acceleration The direction of the component, is the thermal conductivity, is the mass exchange coefficient, is the shape factor of the vertical velocity profile, is the phase density ratio, is the interaction force between particles The direction of the component, Phase drag force The direction of the component, Phase drag force The direction of the component, is the temperature of the external environment, is the temperature of the ground interface, is the phase-averaged basic friction force, is the flow density, is the friction resistance at the bottom, then: ； ； ； ； ； 。 10. The method for simulating the transition process of rock-ice avalanches to debris flows according to claim 9, characterized in that: set up and represents the interface flux between adjacent grids, represents the mass transfer flux caused by phase change, represents the momentum flux caused by the phase change, is the time step, For along The prediction step calculation operator of the direction, For along The correction step calculation operator of the direction, For along Direction prediction operator, For along The correction step calculation operator of the direction, is the total variable matrix before calculation, is the total variable matrix after calculation, is the numerical flux on the right side of the unit interface, is the numerical flux on the left side of the unit interface, is the Jacobian matrix, is the grid length, is the time step, and the fractional stepping method is used to transform the depth averaged three-phase model into: ； Get the solution for the next time step: ； Solve the homogeneous equation, let , based on the finite volume method, the solution for the next time step is obtained: ； Solve using Roy's approximate Riemann solver, let , and obtain the numerical flux.

Images