Simulation Method for the Transformation Process of Rock-Ice Avalanches into Debris Flows

Abstract

The present invention belongs to the technical field of disaster simulation, and relates to a simulation method for the transformation process of rock-ice avalanche into debris flow. The method includes: establishing the fluid-phase mass conservation equation, ice-phase mass conservation equation, and rock-phase mass conservation equation for the transformation process of rock-ice avalanche into debris flow, as well as the momentum conservation equations for the fluid phase, ice phase, and rock phase, and simultaneously establishing the energy conservation equation for the mass flow to obtain the governing equations of the depth-averaged three-phase model; using the second-order accurate finite volume method combined with the finite volume method and Roe approximate Riemann solver to solve the flux terms of the governing equations of the depth-averaged three-phase model to obtain the temporal and spatial distributions of the flow depth, flow velocity, phase volume fraction, and temperature. The present invention simulates the real physical process including the positive and negative conversion of temperature by considering the interactions between the rock phase, ice phase, and fluid phase, and describes the transformation process of rock-ice avalanche from granular flow to debris flow.

Description

Technical Field

[0001] The present invention belongs to the technical field of disaster simulation, and more specifically, relates to a method for simulating the transformation process of rock-ice avalanches into debris flows. Background Art

[0002] In recent years, due to the rapid melting of mountain glaciers and the thawing of permafrost, the transformation from rock-ice avalanches to debris flows has become more frequent, causing significant casualties and property losses, and posing a severe challenge to the management of alpine environmental disasters.

[0003] Debris flows transformed from rock-ice avalanches have a significantly different formation mechanism from traditional models due to the phase change of ice and the characteristics of multiphase mixing. 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 swelling effects, the coupled modeling of phase change, energy exchange, and temperature dynamic changes driven by ice melting is still blank.

[0004] Most existing rock-ice avalanche models do not integrate the energy conservation equation or simplify the temperature dynamic changes, 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; the frictional heat generation, meltwater infiltration, and flow strengthening effects among solid-liquid-ice multiphases have not been systematically quantified.

[0005] Therefore, there is an urgent need to develop a new type of multiphase coupling model to accurately depict the transformation mechanism of rock-ice avalanches into debris flows by integrating energy conservation, temperature evolution, and phase change kinetics, providing theoretical support for alpine disaster warning and prevention. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides a method for simulating the transformation process of rock-ice avalanches into debris flows, including:

[0007] Establish a surface-induced coordinate system, and based on the time and space progress of flow depth, flow velocity, phase volume fraction, temperature, and the interphase force, the interaction force between particles, and the ice melting rate, establish the fluid phase mass conservation equation, ice phase mass conservation equation, and rock phase mass conservation equation for the transformation process of rock-ice avalanches into debris flows, as well as the momentum conservation equation of the fluid phase, ice phase, and rock phase in the horizontal direction. At the same time, establish the energy conservation equation of the mass flow to obtain the control equation of the depth-averaged three-phase model;

[0008] Determine the expressions of the interphase force and the interaction force between particles according to the flow depth, flow velocity, phase volume fraction, and temperature;

[0009] Based on the expressions of the interfacial force and the interaction force between particles, the control equations of the depth-averaged three-phase model are solved using a second-order accurate finite volume method combined with the Roe approximate Riemann solver, and the time and space distributions of the flow depth, flow velocity, phase volume fraction, and temperature are obtained to describe the transition process of rock-ice avalanches from granular flows to debris flows.

[0010] On the basis of the above technical solutions, the present invention can be further improved as follows.

[0011] Furthermore, let be the volume fraction of the rock phase, be the volume fraction of the ice phase, be the volume fraction of the fluid phase, be the phase density of the ice phase, be the phase density of the fluid phase, be the depth of the mixture flow, be the time, be the melting rate of the ice, and be the coordinate axes, be the phase velocity component of the fluid phase in the direction, be the phase velocity component of the fluid phase in the direction, be the phase velocity component of the ice phase in the direction, be the phase velocity component of the ice phase in the direction, be the phase velocity component of the rock phase in the direction, be the phase velocity component of the rock phase in the direction;

[0012] The mass conservation equation of the fluid phase is:

[0013] ;

[0014] The mass conservation equation of the ice phase is:

[0015] ;

[0016] The mass conservation equation of the rock phase is:

[0017] .

[0018] Furthermore, let be the volume fraction of the rock phase, be the volume fraction of the ice phase, be the volume fraction of the fluid phase, be 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, is the time, is the melting rate of the ice, , and are the coordinate axes, is the phase velocity component of the fluid phase in the direction, is the phase velocity component of the fluid phase in the direction, is the phase velocity of the ice phase, is the phase velocity component of the ice phase in the direction, is the phase velocity component of the ice phase in the direction, is the phase velocity of the rock phase, is the phase velocity component of the rock phase in the direction, is the phase velocity component of the rock phase 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 component of the gravitational acceleration in the direction, is the component of the gravitational acceleration in the direction, is the component of the gravitational acceleration in the direction, is the friction coefficient of the ice phase, is the friction coefficient of the rock phase, is the drag force between the fluid phase and the ice phase along the direction, is the drag force between the fluid phase and the rock phase along the direction, is the drag force between the fluid phase and the ice phase along the direction, is the drag force between the fluid phase and the rock phase along the direction, is the component of the inter-particle drag force in the direction, is the component of the inter-particle drag force in the direction, is the component of the inter-particle drag force in the direction, The force caused by meltwater;

[0019] The momentum conservation equation for the fluid phase in direction is:

[0020]

[0021] ;

[0022] The momentum conservation equation for the fluid phase in direction is;

[0023]

[0024] ;

[0025] The momentum conservation equation for the ice phase in direction is:

[0026]

[0027] ;

[0028] The momentum conservation equation for the ice phase in direction is;

[0029]

[0030] ;

[0031] The momentum conservation equation for the rock phase in direction is:

[0032]

[0033] ;

[0034] The momentum conservation equation for the rock phase in direction is:

[0035]

[0036] .

[0037] Furthermore, the energy conservation equation of the mass flow includes heat convection, heat conduction, heat loss caused by ice melting, and heat generated by internal friction. Let be the flow density, be the phase density of the ice phase, be the specific heat of the mixture, be the depth of the mixture flow, be the temperature of the rock-ice avalanche, is the temperature of the external environment, is the temperature of the ground interface, is the average velocity along the phase direction, is the average velocity along the phase direction, is the parameter related to the temperature profile, 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 bottom frictional resistance of the rock-ice avalanche, is the phase average velocity vector, then the energy conservation equation of the mass flow is:

[0038]

[0039] .

[0040] Furthermore, let be the particle-fluid drag coefficient, 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, represents the phase category, is the viscosity of the fluid, is the volume fraction of the fluid phase, is the phase volume fraction;

[0041] ;

[0042] ;

[0043] The inter-phase force is: .

[0044] Furthermore, let be the particle-drag coefficient, be 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;

[0045] The interaction force between particles is:

[0046] .

[0047] Furthermore, let the melting rate of ice be , the flow density, the specific heat of the mixture, the depth of the mixture flow, the internal temperature of the rock-ice avalanche, the temperature threshold at which ice begins to melt, the phase density of the ice phase, the latent heat of ice, then the melting rate of ice:

[0048] .

[0049] Furthermore, the governing equations of the depth-averaged three-phase model are solved by a second-order numerical method combining the finite volume method and the Roe approximate Riemann solver, including:

[0050] The governing equations of the depth-averaged three-phase model are expressed as a matrix equation, and after adopting the fractional step method and performing spatial splitting, two sub-matrix equations are obtained;

[0051] The finite volume method is used to transform the two sub-matrix equations to obtain a discretized homogeneous operator equation, and the homogeneous operator equation is solved to obtain the numerical flux.

[0052] Furthermore, the governing equations of the depth-averaged three-phase model are expressed as a matrix equation, including: Let and represent the interface flux between adjacent grids, represent the mass transfer flux caused by phase change, represent the momentum flux caused by phase change, be the volume fraction of the phase, be the depth of the mixture flow, be the time, be the component of the phase velocity along the direction, be the phase category, be the component of the phase velocity along the direction, be the rock-ice temperature, be the phase-side pressure coefficient, , be the specific heat of the mixture, be the specific heat of the phase, be the atmospheric heat transfer coefficient, , be the bed surface elevation, be the component of the gravitational acceleration in the direction, be the thermal conductivity coefficient, be the mass exchange coefficient, is the shape factor of the vertical velocity profile, is the phase density ratio, is the component of the inter-particle interaction force along direction, is the component of the phase drag force along direction, is the component of the phase drag force along direction, is the temperature of the external environment, is the temperature of the ground interface, is the phase-averaged base friction force, is the flow density, is the phase bottom friction resistance, then:

[0053] ;

[0054] ;

[0055] ;

[0056] ;

[0057] ;

[0058] .

[0059] Furthermore, let and represent the interface flux between adjacent grids, represent the mass transfer flux caused by phase change, represent the momentum flux caused by phase change, is the time step, is the prediction step calculation operator along direction, is the correction step calculation operator along direction, is the prediction calculation operator along direction, is the correction step calculation operator along 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 cell interface, is the numerical flux on the left side of the cell interface, is the Jacobian matrix, is the grid length, is the time step. Using the fractional step method, the depth-averaged three-phase model is transformed into:

[0060] ;

[0061] Obtain the solution at the next time step:

[0062] ;

[0063] Solve the homogeneous equation, let , and based on the finite volume method, obtain the solution at the next time step:

[0064] ;

[0065] Solve using the Roe approximate Riemann solver, let , and obtain the numerical flux.

[0066] The beneficial effects of the present invention are as follows: The present invention uses a second-order accurate finite volume method that combines the finite volume method and the Roe approximate Riemann solver to solve the flux term of the governing equation of the depth-averaged three-phase model, significantly improving the computational stability; by considering the interactions between the rock phase, ice phase, and fluid phase, it simulates the real physical process including the positive and negative conversion of temperature, and describes the transformation process of rock-ice avalanche from granular flow to debris flow. Description of the Drawings

[0067] Figure 1 is the schematic diagram of the simulation method for the transformation process of rock-ice avalanche to debris flow provided by the embodiment of the present invention;

[0068] Figure 2 is the simulation diagram of the depth of the flowing body at different times;

[0069] Figure 3 is the simulation diagram of the evolution trend of pore pressure during the flow process;

[0070] Figure 4 is the simulation diagram of the ice volume fraction at the monitoring point;

[0071] Figure 5 is the simulation diagram of the temperature change at the monitoring point. Specific Embodiments

[0072] To make the objectives, 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 accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations.

[0073] As an embodiment, as shown in the attached Figure 1As shown below, to solve the above technical problems, this embodiment provides a simulation method for the transformation process of rock-ice avalanches into debris flows, including:

[0074] Establish a surface-induced coordinate system. Based on the time and space progress of flow depth, flow velocity, phase volume fraction, temperature, as well as the interphase force, the interaction force between particles, and the ice melting rate, establish the fluid-phase mass conservation equation, the ice-phase mass conservation equation, and the rock-phase mass conservation equation for the transformation process of rock-ice avalanches into debris flows, as well as the momentum conservation equation of the fluid phase, ice phase, and rock phase in the horizontal direction. At the same time, establish the energy conservation equation of the mass flow to obtain the control equations of the depth-averaged three-phase model;

[0075] Determine the expressions of the interphase force and the interaction force between particles according to the flow depth, flow velocity, phase volume fraction, and temperature;

[0076] Solve the control equations of the depth-averaged three-phase model by using the second-order accurate finite volume method based on the combination of the finite volume method and the Roe approximate Riemann solver according to the expressions of the interphase force and the interaction force between particles, and obtain the time and space distributions of the flow depth, flow velocity, phase volume fraction, and temperature to describe the transformation process of rock-ice avalanches from particle flows to debris flows.

[0077] Optionally, let be the volume fraction of the rock phase, be the volume fraction of the ice phase, be the volume fraction of the fluid phase, be the phase density of the ice phase, be the phase density of the fluid phase, be the depth of the mixture flow, be the time, be the ice melting rate, and be the coordinate axes, be the phase velocity component of the fluid phase in the direction, be the phase velocity component of the fluid phase in the direction, be the phase velocity component of the ice phase in the direction, be the phase velocity component of the ice phase in the direction, be the phase velocity component of the rock phase in the direction, be the phase velocity component of the rock phase in the direction;

[0078] The mass conservation equation of the fluid phase is:

[0079] ;

[0080] The mass conservation equation for the ice phase is:

[0081] ;

[0082] The mass conservation equation for the rock phase is:

[0083] .

[0084] Optionally, let be the volume fraction of the rock phase, be the volume fraction of the ice phase, be the volume fraction of the fluid phase, be the phase density of the rock phase, be the phase density of the ice phase, be the phase density of the fluid phase, be the depth of the mixture flow, be the time, be the melting rate of the ice, , and be the coordinate axes, be the phase velocity component of the fluid phase in the direction, be the phase velocity component of the fluid phase in the direction, be the phase velocity of the ice phase, be the phase velocity component of the ice phase in the direction, be the phase velocity component of the ice phase in the direction, be the phase velocity of the rock phase, be the phase velocity component of the rock phase in the direction, be the phase velocity component of the rock phase in the direction, be the saturation parameter, be the density ratio between the fluid phase and the rock phase, be the density between the fluid phase and the ice phase, be the bed surface elevation, be the viscosity of the fluid, be the component of the gravitational acceleration in the direction, be the component of the gravitational acceleration in the direction, be the component of the gravitational acceleration in the direction, be the friction coefficient of the ice phase, be the friction coefficient of the rock phase, be along the fluid phase and the ice phase in the The drag force in the direction is the drag force of the fluid phase and the rock phase along the direction is the drag force of the fluid phase and the ice phase along the direction is the drag force of the fluid phase and the rock phase along the direction is the component of the inter-particle resistance in the direction is the component of the inter-particle resistance in the direction is the component of the inter-particle resistance in the direction is the force caused by meltwater;

[0085] The momentum conservation equation of the fluid phase in the

[0086]

[0087] ;

[0088] The momentum conservation equation of the fluid phase in the

[0089]

[0090] ;

[0091] The momentum conservation equation of the ice phase in the

[0092]

[0093] ;

[0094] The momentum conservation equation of the ice phase in the

[0095]

[0096] ;

[0097] The momentum conservation equation of the rock phase in the

[0098]

[0099] ;

[0100] The momentum conservation equation of the rock phase in the

[0101]

[0102] 。

[0103] Optionally, the energy conservation equation of the mass flow includes heat convection, heat conduction, heat loss due to ice melting, and heat generated by internal friction. Let be the flow density, be the phase density of the ice phase, be the specific heat of the mixture, be the depth of the mixture flow, be the temperature of the rock-ice avalanche, be the temperature of the external environment, be the temperature of the ground interface, be the phase along the average velocity in the direction, be the phase along the average velocity in the direction, be the parameter related to the temperature profile, be the thermal conductivity, be the latent heat of ice, be the melting rate of ice, be the shape factor of the vertical velocity profile, be the bottom friction resistance of the rock-ice avalanche, be the phase average velocity vector, then the energy conservation equation of the mass flow is:

[0104]

[0105] 。

[0106] represents heat convection, represents heat conduction, represents heat loss caused by ice melting, represents heat generated by internal friction.

[0107] Optionally, let be the drag coefficient of the particle-fluid, the Reynolds number is , the particle diameter is , be the phase density of the fluid phase, be the velocity of the fluid phase, be the phase velocity, represent the phase category, be the viscosity of the fluid, be the volume fraction of the fluid phase, be the phase volume fraction;

[0108] ;

[0109] ;

[0110] The interfacial force is: .

[0111] The governing equations of the depth-averaged three-phase model describe the temporal and spatial evolution of flow depth, flow velocity, phase volume fraction, and temperature in the surface-induced coordinate system O-xyz. It consists of the mass, momentum, and energy conservation equations of each phase, and takes into account the effects of phase interaction, temperature evolution, and ice melting on flow dynamics. To effectively solve the model equations, a second-order accurate finite volume method based on the finite volume method and combined with Roe's approximate Riemann solver is adopted, and the reliability of the model is verified through numerical simulations.

[0112] Optionally, let be the particle-drag coefficient, be the interaction force between particles, be the phase density of the ice phase, be the volume fraction of the rock phase, be the volume fraction of the rock phase, be the rock-phase velocity vector, be the ice-phase velocity vector;

[0113] The interaction force between particles is:

[0114] .

[0115] Optionally, let the ice melting rate be , be the flow density, be the specific heat of the mixture, be the depth of the mixture flow, be the internal temperature of the rock-ice avalanche, be the temperature threshold at which ice begins to melt, be the phase density of the ice phase, be the latent heat of ice, then the ice melting rate:

[0116] .

[0117] Optionally, the governing equations of the depth-averaged three-phase model are solved by a second-order numerical method based on the combination of the finite volume method and Roe's approximate Riemann solver, including:

[0118] Express the governing equations of the depth-averaged three-phase model as a matrix equation, and obtain two sub-matrix equations after adopting the fractional step method and performing spatial splitting;

[0119] The finite volume method is used to transform two sub-matrix equations to obtain a homogeneous operator equation in discretized form, and the homogeneous operator equation is solved to obtain the numerical flux.

[0120] Optionally, the governing equations of the depth-averaged three-phase model are expressed as a matrix equation, including: Let and represent the interfacial flux between adjacent grids, represent the mass transfer flux caused by phase change, represent the momentum flux caused by phase change, be the volume fraction of the phase, be the depth of the mixture flow, be the time, be the component of the phase velocity along direction, be the phase category, be the component of the phase velocity along direction, be the temperature of rock ice and snow, be the phase-side pressure coefficient, , be the specific heat of the mixture, be the specific heat of the phase, be the atmospheric heat transfer coefficient, , be the elevation of the bed surface, be the component of the gravitational acceleration in direction, be the thermal conductivity, be the mass exchange coefficient, be the shape factor of the vertical velocity profile, be the phase density ratio, be the component of the inter-particle interaction force along direction, be the component of the phase drag force along direction, be the component of the phase drag force along direction, be the temperature of the external environment, be the temperature of the ground interface, be the phase-averaged base friction force, be the flow density, be the phase bottom friction resistance, then:

[0121] ;

[0122] ;

[0123] ;

[0124] ;

[0125] ;

[0126] .

[0127] Optionally, let and represent the interfacial flux between adjacent grids, represent the mass transfer flux caused by phase change, represent the momentum flux caused by phase change, be the time step, be the prediction step calculation operator along the direction, be the correction step calculation operator along the direction, be the prediction calculation operator along the direction, be the correction step calculation operator along the direction, be the total variable matrix before calculation, be the total variable matrix after calculation, be the numerical flux on the right side of the cell interface, be the numerical flux on the left side of the cell interface, be the Jacobian matrix, be the grid length, be the time step. Using the fractional step method, the depth-averaged three-phase model is transformed into:

[0128] ;

[0129] Obtain the solution at the next time step:

[0130] ;

[0131] Solve the homogeneous equation, let , and based on the finite volume method, obtain the solution at the next time step:

[0132] ;

[0133] Solve using the Roe approximate Riemann solver, let , and obtain the numerical flux.

[0134] The effectiveness of the depth-averaged three-phase model in capturing the transition process of rock-ice avalanches and debris flows is verified through the Berkeley Rotary Drum experiment. As shown in the appendix Figure 2The depth of the fluid at different times is shown. The horizontal axis represents the horizontal length of the fluid, and the vertical axis represents the vertical height of the fluid. 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. Attachment Figure 2 The experimental simulation results with 70% ice content are shown. When the drum starts to rotate and reaches a steady state (t = 3 minutes), the mass body moves in the direction of drum rotation. Due to frictional heating and heat transfer from the surrounding environment, the temperature of the mass body gradually rises from -10 °C to 0 °C, and then the ice melting process occurs. In the initial stage (t = 7 minutes), a slight retreat occurs at the position of the leading-edge mass body, which is caused by a small amount of meltwater enhancing the inter-particle cohesion. As the meltwater increases, the rise in pore water pressure breaks the equilibrium state by reducing the basal friction resistance, resulting in the downward sliding of the mass body (t = 25 minutes); under the action of gravity, the meltwater accumulates at the leading edge to form a nose-like protrusion feature, which is consistent with the experimental results. Continuous ice melting causes the mass body to show a transition from dry rock-ice particles to rock-ice-fluid debris flow (t = 39 minutes), and the simulated flow profile is consistent with the measured data.

[0135] As shown in the attachment Figure 3 As shown, the horizontal axis is the drum angle, unit: °, and 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, and M8 represents the experimental data at 39 minutes. Attachment Figure 3 Shows the evolution trend of pore pressure during the flow process, and the simulation results are consistent with the observed law that the pore pressure gradually increases from the tail to the head. The ice volume fraction at the monitoring point is as shown in the attachment Figure 4 As shown, the horizontal axis is time, unit: s, and the vertical axis is the volume fraction, including four stages D1, D2, D3, and D4. The temperature change at the monitoring point is as shown in the attachment Figure 5As shown, 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. This 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 frictional heat and environmental heat transfer are not sufficient to trigger ice melting; (3) After the temperature reaches 0 °C, the excess heat triggers ice melting, and the basal frictional resistance and gravity are unbalanced. The temperature remains constant at zero in this stage; (4) After the ice particles are completely melted, the flow enters a new stable state, and the temperature rises again due to frictional heat generation and environmental temperature difference. The numerical simulation successfully reproduces the transition process of rock-ice avalanches from granular flow to debris flow and accurately depicts the evolution laws of key parameters such as phase composition and temperature.

[0136] Different from existing models, the depth-averaged three-phase model proposed in the present invention can simulate the real physical process including positive and negative temperature conversion by introducing the energy conservation equation. By considering the interactions between the rock, ice, and water (generated by ice melting) phases, a key point in ice melting is how to determine when the ice melts. Due to the influence of friction and heat transfer (such as between ice and air), the internal temperature of rock-ice-snow avalanches can change from negative to positive and vice versa, which has a great impact on ice melting.

[0137] For the analysis of the flow state transition from dry granular flow to solid-liquid multiphase flow during the movement of rock-ice avalanches, a composite friction law that combines the Coulomb friction of the solid phase and the viscous shear of the liquid phase is adopted. In addition, a saturation parameter is introduced to quantitatively characterize the influence of pore water pressure on the normal stress of the flowing material, and at the same time, the simulation effect of the solid-phase basal friction coefficient is optimized by combining μ(I)-rheology.

[0138] The numerical solution uses the second-order accurate finite volume method. The flux term of the control equation of the depth-averaged three-phase model is solved by using the second-order accurate finite volume method combined with the Roe approximate Riemann solver, which significantly improves the computational stability. Experimental simulations show that the depth-averaged three-phase model successfully captures the dynamic evolution laws of rock-ice avalanches under different ice contents (especially when the ice content > 80%). Through the numerical case study of the drum experiment, the accurate simulation ability of the model for the transition process from single-phase (rock-ice) to multiphase (rock-ice-water) in the movement of rock-ice avalanches is verified, and the evolution laws of key parameters such as water content and temperature are effectively tracked. Further numerical experiments show that: the increase in fluid viscosity will accelerate the transition rate from single-phase to multiphase of rock-ice avalanches by enhancing the frictional 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 frictional heat generation per unit time. In addition, the cohesion 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 have a counteracting effect on this inhibitory effect.

[0139] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, various modifications and variations can be made to the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. Simulation method for the transformation process of rock-ice avalanche into debris flow, characterized in that, Including: Establish a surface-induced coordinate system. Based on the time and space progress of flow depth, flow velocity, phase volume fraction, temperature, as well as the inter-phase force, the interaction force between particles, and the ice melting rate, establish the mass conservation equation of the fluid phase, the mass conservation equation of the ice phase, and the mass conservation equation of the rock phase for the transformation process of rock-ice avalanche into debris flow, as well as the momentum conservation equation of the fluid phase, ice phase, and rock phase in the horizontal direction. At the same time, establish the energy conservation equation of the mass flow to obtain the governing equations of the depth-averaged three-phase model; Quantitatively characterize the influence of pore water pressure on the normal stress of flowing substances by introducing a saturation parameter; Determine the expressions of the interfacial force and the interaction force between particles according to the flow depth, flow velocity, phase volume fraction, and temperature; assume that 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, represents the phase category, is the viscosity of the fluid, is the volume fraction of the fluid phase, is the phase volume fraction; ； ； The interfacial force is as follows: ; Let be the particle-drag coefficient, be the interaction force between particles, be the phase density of the ice phase, be the volume fraction of the rock phase, be the volume fraction of the rock phase, be the rock-phase velocity vector, be the ice-phase velocity vector; The interaction force between particles is: ； According to the expressions of the inter-phase force and the interaction force between particles, use the second-order accurate finite volume method combined with the finite volume method and Roe approximate Riemann solver to solve the governing equations of the depth-averaged three-phase model, and obtain the time and space distributions of flow depth, flow velocity, phase volume fraction, and temperature to describe the transformation process of rock-ice avalanche from granular flow to debris flow.

2. The simulation method for the transformation process of rock-ice avalanche into debris flow according to claim 1, characterized in that, Let be the volume fraction of the rock phase, be the volume fraction of the ice phase, be the volume fraction of the fluid phase, be the phase density of the ice phase, be the phase density of the fluid phase, be the depth of the mixture flow, be the time, be the melting rate of the ice, and be the coordinate axes, be the phase velocity component of the fluid phase in the direction, be the phase velocity component of the fluid phase in the direction, be the phase velocity component of the ice phase in the direction, be the phase velocity component of the ice phase in the direction, be the phase velocity component of the rock phase in the direction, be the phase velocity component of the rock phase in the direction; The mass conservation equation of the fluid phase is: ； The mass conservation equation of the ice phase is: ； The mass conservation equation of the rock phase is: 。 3. The simulation method for the transformation process of rock ice avalanche into debris flow according to claim 1, wherein Let be the volume fraction of the rock phase, be the volume fraction of the ice phase, be the volume fraction of the fluid phase, be the phase density of the rock phase, be the phase density of the ice phase, be the phase density of the fluid phase, be the depth of the mixture flow, be the time, be the melting rate of the ice, , and be the coordinate axes, be the phase velocity component of the fluid phase in the direction, be the phase velocity component of the fluid phase in the direction, be the phase velocity of the ice phase, be the phase velocity component of the ice phase in the direction, be the phase velocity component of the ice phase in the direction, be the phase velocity of the rock phase, be the phase velocity component of the rock phase in the direction, be the phase velocity component of the rock phase in the direction, be the saturation parameter, be the density ratio between the fluid phase and the rock phase, be the density between the fluid phase and the ice phase, be the bed surface elevation, be the viscosity of the fluid, be the component of the gravitational acceleration in the direction, be the component of the gravitational acceleration in the direction, be the component of the gravitational acceleration in the direction, be the friction coefficient of the ice phase, be the friction coefficient of the rock phase, be the drag force between the fluid phase and the ice phase along the direction, be the drag force between the fluid phase and the rock phase along the direction, be the drag force between the fluid phase and the ice phase along the direction, be the drag force between the fluid phase and the rock phase along the direction, be the inter-particle drag force in the Component in the direction, is the component of the drag force between particles in the direction, is the component of the drag force between particles in the direction; is the force caused by meltwater; The momentum conservation equation of the fluid phase in direction is as follows: ； The momentum conservation equation of the fluid phase in direction is as follows; ； The momentum conservation equation for the ice phase in direction is as follows: ； The momentum conservation equation for the ice phase in direction is as follows: ； The momentum conservation equation of the rock facies in direction is as follows: ； The momentum conservation equation of the lithofacies in the direction is as follows: 。 4. The simulation method for the transformation process of rock-ice avalanche into debris flow according to claim 1, characterized in that, The energy conservation equation of the mass flow includes heat convection, heat conduction, heat loss due to ice melting, and heat generated by internal friction. Let be the flow density, be the phase density of the ice phase, be the specific heat of the mixture, be the depth of the mixture flow, be the temperature of the rock-ice avalanche, be the temperature of the external environment, be the temperature of the ground interface, be the phase along the average velocity in the direction, be the average velocity of the phase along the direction, be the parameter related to the temperature profile, be the thermal conductivity, be the latent heat of ice, be the melting rate of ice, be the shape factor of the vertical velocity profile, be the phase average velocity vector. Then the energy conservation equation of the mass flow is: 。 5. The simulation method for the transformation process of rock ice avalanche into debris flow according to claim 1, wherein Let the melting rate of ice be , be the flow density, be the specific heat of the mixture, be the depth of the mixture flow, be the internal temperature of the rock-ice avalanche, be the temperature threshold at which ice begins to melt, be the phase density of the ice phase, be the latent heat of ice, then the melting rate of ice is: 。 6. The method for simulating the transformation process of rock ice avalanche into debris flow according to claim 1, characterized in that, Solve the governing equations of the depth-averaged three-phase model by using the second-order numerical method combined with the finite volume method and Roe approximate Riemann solver, including: Express the governing equations of the depth-averaged three-phase model as a matrix equation, and obtain two sub-matrix equations after using the fractional step method and performing space splitting; Use the finite volume method to transform the two sub-matrix equations to obtain a homogeneous operator equation in discretized form, and solve the homogeneous operator equation to obtain the numerical flux.

7. The method for simulating the transformation process of rock avalanche into debris flow according to claim 1, wherein The governing equations of the depth-averaged three-phase model are expressed as a matrix equation, including: Let and represent the interfacial flux between adjacent grids, represent the mass transfer flux caused by phase change, represent the momentum flux caused by phase change, be the volume fraction of the phase, be the depth of the mixture flow, be the time, be the component of the phase velocity along direction, be the phase category, be the component of the phase velocity along direction, be the rock-ice-snow temperature, be the phase-side pressure coefficient, , be the specific heat of the mixture, be the specific heat of the phase, be the atmospheric heat transfer coefficient, , be the bed surface elevation, be the component of the gravitational acceleration in direction, be the thermal conductivity, be the mass exchange coefficient, be the shape factor of the vertical velocity profile, be the phase density ratio, be the component of the inter-particle interaction force along direction, be the component of the phase drag force along direction, be the component of the phase drag force along direction, be the temperature of the external environment, be the temperature of the ground interface, be the phase-averaged basal friction, be the flow density, be the phase bottom friction resistance, then: ； ； ； ； ； 。 8. The simulation method for the transformation process of rock-ice avalanche into debris flow according to claim 7, characterized in that, Let and represent the interfacial flux between adjacent grids, represent the mass transfer flux caused by phase change, represent the momentum flux caused by phase change, be the time step, be the prediction step calculation operator along the direction, be the correction step calculation operator along the direction, be the prediction calculation operator along the direction, be the correction step calculation operator along the direction, be the total variable matrix before calculation, be the total variable matrix after calculation, be the numerical flux on the right side of the cell interface, be the numerical flux on the left side of the cell interface, be the Jacobian matrix, be the grid length, be the time step. Using the fractional step method, the depth-averaged three-phase model is transformed into: ； Obtain the solution at the next time step: ； Solve the homogeneous equation and let , and based on the finite volume method, obtain the solution at the next time step: ； Solve using the Roe approximate Riemann solver, and let , to obtain the numerical flux.

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