A numerical method for simulating mechanical properties of ice-rock debris with different ice contents

Abstract

The application relates to the technical field of numerical simulation, and particularly discloses a numerical method for simulating the mechanical properties of ice-rock debris with different ice contents, which comprises the following steps: a ring shear apparatus model is established according to a three-dimensional particle flow program PFC; after a given ring shear apparatus speed is given, the shear stress and the angular displacement of the ice-rock debris are monitored; meanwhile, implicit heat transfer calculation is carried out on the ice particles and the rock particles of the upper and lower shear boxes; when the ice-rock debris reaches the residual shear strength, the calculation is stopped; the state diagram of the ice-rock debris after the completion of shearing with different ice contents is simulated; and finally, the relationship diagram of the ice content and the residual shear stress of the ice-rock debris is obtained. The application provides a comprehensive and detailed framework for simulating and analyzing the mechanical properties of the ice-rock debris with different ice contents, which not only helps to scientifically understand the dynamic process of the ice-rock debris flow, but also provides guidance for related engineering applications.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of numerical simulation, in particular to a numerical method for simulating mechanical properties of ice-rock debris with different ice contents. BACKGROUND

[0002] Ice-rock debris is a composite material composed of ice and rock debris. During the movement of high-speed long-range landslides, the ice in the debris changes into water due to friction, and the lubrication effect of ice film and water significantly reduces the frictional resistance of the ice-rock mixture during sliding. Therefore, ice-rock debris with different ice contents exhibits significant differences in high-speed long-range landslides. Since ice-rock debris flow usually occurs in dangerous environments, direct observation may face high safety risks.

[0003] When exploring the mechanical properties of ice-rock debris during shearing, a display solution method is usually used to calculate the heat generated by friction between rocks and the heat absorbed by rock particles and ice particles, i.e., thermodynamic modeling is performed macroscopically, the energy conservation equation during the movement of ice-rock debris is established, and the generation and dissipation of friction heat in each time step are solved. However, the display solution method cannot handle complex glacial environments and has a significant limitation on time step.

[0004] Therefore, to solve the above problems, a numerical method for simulating the mechanical properties of ice-rock debris with different ice contents is needed, which can simulate the shearing properties of ice-rock debris with different ice contents in a ring shear apparatus until the residual shear strength is reached, providing important scientific basis for understanding and predicting the behavior of ice-rock debris flow. SUMMARY

[0005] Therefore, the present application aims to provide a numerical method for simulating the mechanical properties of ice-rock debris with different ice contents, which can simulate the shearing properties of ice-rock debris with different ice contents in a ring shear apparatus until the residual shear strength is reached, providing important scientific basis for understanding and predicting the behavior of ice-rock debris flow.

[0006] The present application provides a numerical method for simulating the mechanical properties of ice-rock debris with different ice contents, which first establishes a ring shear apparatus model with the upper shear box remaining stationary and the lower shear box rotating at a specified rate through PFC discrete element method; simulates the mechanical characteristics of ice-rock debris with different ice contents during shearing based on the ring shear apparatus model until the ice-rock debris reaches the residual shear strength, which includes the following steps:

[0007] S11: After starting and initializing, establish a ring shear apparatus model with different ice contents in the upper shear box and set the initial temperature of the particles;

[0008] S12: Based on the model established in S11, set the speed of the ring shear apparatus and monitor the shear stress and angular displacement of the rock particles in the shear plane;

[0009] S13: calculating the friction heat between the upper and lower rock particles in the shear plane based on the shear stress and the angular displacement determined in S12;

[0010] S14: judging whether the contact type between the particles is rock particles and ice particles; if yes, proceeding to S15; if no, directly proceeding to S16;

[0011] S15: calculating the thermal conductivity between the rock particles and the ice particles based on the particle contact information;

[0012] S16: calculating the heat flux flowing into the rock particles and the ice particles according to the Fourier law;

[0013] S17: establishing a heat conduction equation to calculate the particle temperature;

[0014] S18: judging whether the ice-rock debris body reaches the residual shear strength; if no, returning to S13;

[0015] S19: obtaining a graph of the relationship between the final ice content of the ice-rock debris body and the residual shear strength.

[0016] As a further improvement of the above technical solution, in the ring shear apparatus model in which the upper shear box remains stationary and the lower shear box rotates at a specified rate, the rock particles are represented by spherical particles, the ice particles are represented by flexible clusters, a normal stress is applied, and the contact information and the initial temperature of the rock particles and the ice particles are set.

[0017] As a further improvement of the above technical solution, in step S12, based on the established ring shear apparatus model, the lower shear box is sheared at a specified rate; the shear stress and the angular displacement suffered by the rock particles of the ice-rock debris body are monitored;

[0018] The shear stress suffered by the rock particles of the ice-rock debris body is:

[0019]

[0020] Wherein, M is the moment suffered by the rock particles in the ice-rock debris body, D is the outer ring radius, and d is the inner ring radius.

[0021] The angular displacement of the rock particles of the ice-rock debris body is:

[0022] S = R m θ.

[0023] Wherein, R m is the radius of the position of the rock particles of the ice-rock debris body in the model, and θ is the radian of the rotation of the rock particles when the ring shear apparatus rotates.

[0024] As a further improvement of the above technical solution, in step S13, the friction heat generated between the upper and lower rock particles is:

[0025] Q = τS;

[0026] Where τ is the shear stress experienced by the rock particles of the ice-rock debris body, and S is the angular displacement of the rock particles.

[0027] As a further improvement of the above technical solution, in step S15, the thermal conductivity between the rock particles and the ice particles is:

[0028]

[0029] Where r represents the rock particles, i represents the ice particles, k i is the thermal conductivity of the ice particles, and k r is the thermal conductivity of the rock particles.

[0030] As a further improvement of the above technical solution, in step S16, the process of calculating the heat flux flowing into the ice particles and the rock particles includes:

[0031] Based on the particle temperature information, following the principle that the rock particles with higher temperature transfer heat to adjacent rock particles and ice particles with lower temperature;

[0032] In the heat transfer process, the heat transfer between rock particles-rock particles and rock particles-ice particles is carried out simultaneously;

[0033] The heat flux of the rock particles with higher temperature flowing into the rock particles with lower temperature is:

[0034]

[0035] Where α is a geometric correction factor, is the cross-sectional width formed by adjacent rock particles, is the distance between the centers of adjacent rock particles, is the temperature of the rock particle with higher temperature among the adjacent rock particles, and T r is the temperature of the rock particle with lower temperature among the adjacent rock particles.

[0036] The heat flux of the rock particles flowing into the ice particles is:

[0037]

[0038] Where S ir is the cross-sectional width formed by adjacent ice particles and rock particles, L ir is the distance between the centers of adjacent ice particles and rock particles, T i and T rTemperatures of the ice particles and the rock particles, respectively.

[0039] As a further improvement of the above technical solution, in step S17, the process of calculating the temperature of the particles comprises:

[0040] Based on the heat flux flowing into the ice particles and the rock particles, the temperatures of the ice particles and the rock particles are calculated;

[0041] The temperature of the rock particles is:

[0042]

[0043] wherein, is the temperature of the rock particles at the previous time step, C r is the specific heat capacity of the rock particles, M r is the mass of the rock particles.

[0044] The temperature of the ice particles is:

[0045]

[0046] wherein, is the temperature of the ice particles at the previous time step, C i is the specific heat capacity of the ice particles, M i is the mass of the ice particles.

[0047] As a further improvement of the above technical solution, in step S18, the process of determining whether the ice-rock debris body reaches the residual shear strength comprises:

[0048] Based on the monitored shear stress and the angular displacement, a relationship curve is determined;

[0049] Based on the relationship curve, the residual shear strength is the final stable value reached by the shear stress;

[0050] The residual shear strength of the ice-rock debris body is:

[0051]

[0052] wherein, η is the viscosity coefficient, γ is the shear strain rate, σ is the normal stress, is the internal friction angle, and c is the cohesion.

[0053] As a further improvement of the above technical solution, in step S19, the process of generating a relationship graph of the ice content and the residual shear strength comprises:

[0054] After the simulation is stopped, the residual shear strength of the ice-rock debris body is output;

[0055] According to the residual shear strength corresponding to different ice contents, a relationship graph is generated.

[0056] Compared with the prior art, the present application has the following beneficial technical effects:

[0057] The present application provides a numerical method for simulating the mechanical properties of ice-rock debris with different ice contents, which can simulate the shear properties of ice-rock debris with different ice contents in a ring shear apparatus until the residual shear strength is reached, providing important scientific basis for understanding and predicting the behavior of ice-rock debris flow.

[0058] Specifically, the present application extends the traditional mechanical simulation to the thermodynamic field, especially on this special composite material of ice-rock debris, by combining the PFC discrete element method with the principles of thermodynamics, the mechanical behavior of ice-rock debris under different ice contents is simulated, which provides a more comprehensive perspective to study the shear properties of ice-rock debris; The present application can accurately control the experimental conditions in a virtual environment, such as ice content, ring shear apparatus speed, etc., which is difficult to achieve in physical experiments, thereby improving the controllability and repeatability of the experiment; Numerical simulation allows users to intuitively observe the flow and shear band formation of ice-rock debris during the shearing process under different ice contents, which is very helpful for understanding the internal behavior of the material; Compared with traditional physical experiments, the numerical simulation of the present application can instantly view the results, and can quickly adjust the experimental parameters as needed, thereby saving experimental time and reducing experimental cost; The present application can simulate the dynamic process of ice-rock debris reaching residual shear strength, which is of great significance for predicting and analyzing the stability and danger of ice-rock debris flow; Through implicit heat transfer calculation, the present application can accurately simulate the heat transfer path and efficiency, update the thermal conductivity characteristics of the ice particle and rock particle contact points in real time, and adapt to the dynamic changes of the contact state between particles; The present application comprehensively considers various physical parameters such as shear stress, angular displacement, thermal conductivity, and heat flux, making the simulation results more accurate and reliable; The finally generated ice content and residual shear strength relationship diagram provides an intuitive reference for engineering design and disaster prevention.

[0059] The advantages of the additional aspects of the present application will be partially given in the following description, partially will become apparent from the following description, or will be understood by the practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0060] The drawings accompanying the specification of this application form a part thereof, serve to further illustrate the embodiments of the application, and together with the description, explain the principles of the application.

[0061] Figure 1 The present application is a numerical method for simulating the mechanical properties of ice-rock debris with different ice contents, which can simulate the shear properties of ice-rock debris with different ice contents in a ring shear apparatus until the residual shear strength is reached, providing important scientific basis for understanding and predicting the behavior of ice-rock debris flow.

[0062] Figure 2 The present application is a numerical method for simulating the mechanical properties of ice-rock debris with different ice contents, which can simulate the shear properties of ice-rock debris with different ice contents in a ring shear apparatus until the residual shear strength is reached, providing important scientific basis for understanding and predicting the behavior of ice-rock debris flow.

[0063] Figure 3 is a schematic diagram of the shear stress-angle displacement relationship of different ice contents of the present application;

[0064] Figure 4 is a schematic diagram of the relationship between ice content and residual shear strength. DETAILED DESCRIPTION

[0065] In order for those skilled in the art to better understand the technical solutions of the present application, the present application will be further described in detail below in combination with the drawings and specific embodiments.

[0066] As background, PFC (Particle Flow Code) will first be described.

[0067] The three-dimensional particle flow program PFC (Particle Flow Code) is a particle flow simulation software based on the discrete element method DEM (Discrete Element Method), and the medium materials studied are mainly bulk materials and cohesive materials, which are suitable for studying the macro-micro mechanical properties of materials, the deformation and flow failure process of particle assemblies, the fracture and fracture propagation of solid materials (rock mass, etc.), and can simultaneously consider complex mechanical conditions such as deformation and dynamic load; at the same time, PFC allows detailed simulation at the particle level, can consider the behavior and interaction of each particle, and integrates with the heat conduction model, so as to accurately describe the motion and mechanical properties of ice-rock debris flow.

[0068] PFC is a series of discrete element programs for simulating the behavior of granular materials; it includes 2D and 3D versions for two-dimensional and three-dimensional simulation; PFC 3D is the three-dimensional version of PFC, which is specially used for simulating particle systems in three-dimensional space, such as rock, soil, granular materials, etc.; it can simulate the motion and interaction between spherical particles, and create large particles of any shape by "attaching" two or more small particles; these "group of particles" created by "attaching" can be studied as independent particles; PFC 3D can simulate the fracture problem of solids, and the particle assembly obtained by "bonding" adjacent particles can be regarded as a "solid" with elastic properties, and when the "bond" between particles gradually breaks, the solid will produce "fracture"; the simulation in this embodiment is carried out by using PFC 3D .

[0069] The embodiment provides a numerical method for simulating mechanical properties of ice-rock debris with different ice contents. After collecting relevant actual data, a ring shear apparatus model is established by using a PFC discrete element method, in which an upper shear box is kept stationary and a lower shear box rotates at a specified rate. According to the ring shear apparatus model, mechanical characteristics of ice-rock debris with different ice contents during a shearing process are simulated until the ice-rock debris reaches a residual shear strength. Figure 1 As shown in the figure, the method can specifically include the following steps S11-S19.

[0070] S11: After starting and initializing, a ring shear apparatus model with different ice contents in the upper shear box is established, and the initial temperature of particles is set.

[0071] S12: Based on the model established in S11, the speed of the ring shear apparatus is set, and the shear stress and angular displacement of rock particles in the shear plane are monitored.

[0072] S13: Based on the shear stress and angular displacement determined in S12, the friction heat between the upper and lower rock particles in the shear plane is calculated.

[0073] S14: It is judged whether the contact type between particles is rock particles and ice particles; if yes, S15 is performed; if no, S16 is directly performed.

[0074] S15: Based on the particle contact information, the thermal conductivity between the rock particles and the ice particles is calculated.

[0075] S16: According to Fourier's law, the heat flux flowing into the rock particles and the ice particles is calculated.

[0076] S17: A heat conduction equation is established, and the particle temperature is calculated.

[0077] S18: It is judged whether the ice-rock debris reaches a residual shear strength; if not, S13 is returned.

[0078] S19: A relationship diagram of the ice content of the final ice-rock debris and the residual shear strength is obtained.

[0079] The ring shear apparatus can simulate the shearing behavior of ice-rock debris flow under different ice contents in a controlled environment. Through numerical simulation of ring shear experiments, experimental conditions can be accurately controlled in a virtual environment. The flow of ice-rock debris with different ice contents and the formation of shear bands during the shearing process can be directly observed, and the results can be viewed in real time. Experimental parameters can be quickly adjusted according to needs, which can save experimental time and reduce experimental costs.

[0080] The method of identifying contact for implicit heat conduction between particles can accurately simulate the heat absorption and release process of each particle, more accurately simulate the heat transfer path and efficiency, and real-time update the heat conduction characteristics of the contact points between ice particles and rock particles, and adapt to the dynamic changes of the contact state between particles.

[0081] The physical parameters involved in the calculation include the shear stress on the rock particles of the ice-rock debris body, the thermal conductivity between the ice particles and the rock particles, the heat flux flowing into the rock particles and the ice particles, the angular displacement, the ring shear apparatus speed, and the particle temperature. These are important factors affecting the mechanical properties of the ice-rock debris body. By monitoring the changes of these parameters, the behavior of the material in the shearing process can be better understood.

[0082] In PFC, ball particles (ball) simulate circular rigid particles, which are the most basic particle units used to create models of granular materials; flexible clusters (cluster) are a more advanced particle unit that can simulate non-rigid particles, i.e., flexible particles; a cluster is composed of multiple balls and can simulate irregularly shaped rigid or flexible particles. It is very suitable to use clusters and balls to simulate ice particles and rock particles in the ice-rock debris body; clusters can be used to simulate flexible ice particles, while balls can be used to represent rigid rock particles; in this way, the interaction between ice and rock and their mechanical behavior in the shearing process can be more accurately captured.

[0083] According to the three-dimensional particle flow program PFC, the code for generating ice-rock debris body ring shear apparatus models with different ice contents is generated; the ring shear apparatus is divided into upper and lower shear boxes; the upper shear box remains stationary and is a mixture of flexible clusters (cluster) and ball particles (ball) for the ice-rock debris body; the lower shear box rotates at a set speed and is a rock particle with only ball particles, and contact is applied between the particles. At the same time, a normal stress is applied to the top surface of the ring shear apparatus along the z-axis, and the ring shear apparatus speed is given, so that the ring shear apparatus starts to shear the contact surface between the upper and lower shear boxes when it starts to rotate.

[0084] The upper shear box is the ice-rock debris body, and the lower shear box is the rock particle, i.e., simulating the sliding of the ice-rock debris body in a landslide containing rock; the expression of the normal stress is as follows:

[0085] σ=γh (1)

[0086] Where Y is the bulk density of the ice-rock debris body, and h is the thickness of the ice-rock debris body on the landslide.

[0087] During the rotation of the ring shear apparatus, the relationship between the shear stress and the angular displacement of the ice particles in the ice-rock debris body is monitored to determine whether the rock particles in the ice-rock debris body have reached the residual shear strength. The shear stress of the rock particles is:

[0088]

[0089] Where M is the torque of the rock particle in the ice-rock debris body, D is the outer ring radius, and d is the inner ring radius.

[0090] The angular displacement of the rock particle in the shearing process is:

[0091] S = R m θ (3)

[0092] Where R is the radius of the rock particle in the model, and θ is the radian of the rock particle rotation when the ring shear apparatus rotates. m

[0093] In the process of rotating the shearing box under the ring shear apparatus, the rock particles in the ice-rock debris body of the upper shearing box and the rock particles of the lower shearing box generate heat due to friction, and the generated heat value is:

[0094] Q = τS (4)

[0095] Where τ is the shear stress of the rock particle of the lower shearing box, and S is the angular displacement of the rock particle.

[0096] According to the Fourier theorem, a heat conduction model is established to calculate the heat transfer between particles. In the Fourier law, the relationship between the heat flux per unit area q and the temperature gradient ΔT is:

[0097] q = -kΔT (5)

[0098] Where q is the heat flux, k is the thermal conductivity, and ΔT is the temperature gradient.

[0099] Because the wall of the ring shear apparatus is smooth and frictionless, heat is only generated between rock particles and rock particles during shearing. The temperature of the rock particles on the shearing surface rises due to friction, and the generated heat is transferred to adjacent rock particles and ice particles. If the heat generated by the particles in the model is Q, the temperature rise of the rock particles during friction can be calculated as:

[0100]

[0101] Where Q is the heat generated by friction, t is time, M is the mass of the particle, and C is the specific heat capacity.

[0102] ​The heat in the shearing process of ice-rock debris is assumed to be conducted through a virtual uniform rectangular channel between two particles. After the temperature of the rock particle generating friction is increased, heat transfer is simultaneously conducted between the adjacent rock particles and ice particles. The type of heat transfer is determined by the contact information of the particles. When the contact is between rock particles and the temperatures are different, the heat flux transferred from the rock particle with higher temperature to the rock particle with lower temperature is:

[0103]

[0104] where subscript r represents a rock particle, a r is a geometric correction factor, k r is the thermal conductivity of the rock particle, is the cross-sectional width formed by the adjacent rock particles, is the distance between the centers of the adjacent rock particles, is the temperature of the rock particle with higher temperature among the adjacent rock particles, T r is the temperature of the rock particle with lower temperature among the adjacent rock particles.

[0105] The cross-sectional width formed by the adjacent rock particles is

[0106]

[0107] where R r is the radius of the rock particle.

[0108] When the contact is between a rock particle and an ice particle, the heat flux transferred from the rock particle to the adjacent ice particle is:

[0109]

[0110] where subscript i represents an ice particle, a i is a geometric correction factor, S ir is the cross-sectional width formed by the adjacent ice particle and rock particle, L ir is the distance between the centers of the adjacent ice particle and rock particle, T i and T r are the temperatures of the ice particle and rock particle, respectively, k ir is the thermal conductivity between the rock particle and ice particle.

[0111] The cross-sectional width S ir formed by the adjacent ice particle and rock particle is

[0112] S ir = R i + R r (10)

[0113] where R iThe radius of the ice particle is r.

[0114] The thermal conductivity between the rock particle and the ice particle is k

[0115]

[0116] where k i is the thermal conductivity of the ice particle.

[0117] The geometric correction factor a j is expressed as:

[0118]

[0119] where j is r or i, i.e. is the volume fraction of the rock particles in the model, is the volume fraction of the ice particles in the model, CN r is the average number of neighbors of the rock particles, CN i is the average number of neighbors of the ice particles.

[0120] The volume fraction of the rock particles or the ice particles in the model is is:

[0121]

[0122] where, is the side length of the circumscribed polygon of the rock particle or the ice particle, R j is the radius of the rock particle or the ice particle.

[0123] In the rotation process of the ring shear apparatus, the number of rock particles adjacent to the rock particle r with a higher temperature in the model is n, and the heat flux flowing into the rock particle r is:

[0124]

[0125] where, is the cross-sectional width formed by the adjacent rock particles, is the distance between the centers of the adjacent rock particles, is the temperature of the rock particle with a higher temperature among the adjacent rock particles, T r is the temperature of the rock particle with a lower temperature among the adjacent rock particles.

[0126] Similarly, the number of rock particles near an ice particle i in the model during shearing is p, and the heat flux flowing into the ice particle i is:

[0127]

[0128] Substituting formulas (13) and (14) into formula (5), the temperature changes of the rock particles and the ice particles are respectively:

[0129]

[0130] wherein, is the temperature of the rock particle at the previous time step, C r is the specific heat capacity of the rock particle, M r is the mass of the rock particle.

[0131]

[0132] wherein, is the temperature of the ice particle at the previous time step, C i is the specific heat capacity of the ice particle, M i is the mass of the ice particle.

[0133] During the rotation of the ring shear apparatus, the shear stress experienced by the ice-rock debris body gradually decreases due to the heat generated by the friction of the shear surface until it stabilizes, and the final stable value of the angular stress-shear stress curve of the rock particles in the ice-rock debris body is the residual shear strength, which is expressed as:

[0134]

[0135] wherein, η is the viscosity coefficient, γ is the shear strain rate, σ is the normal stress, is the internal friction angle, and c is the cohesion.

[0136] The shear strain rate γ is:

[0137]

[0138] wherein, d and D are the inner diameter and outer diameter of the ring shear apparatus, respectively, ω is the angular velocity of the rotation of the ring shear apparatus, and H is the height of the ice-rock debris body.

[0139] When the residual shear strength is reached, the rotation of the ring shear apparatus is stopped, and the temperature distribution state diagram of the ice-rock debris body after shearing is generated according to formulas (16) and (17), and finally the relationship diagram of the ice content and the residual shear strength is obtained, as shown in Figure 4 .

[0140] Finally, it should be pointed out that specific examples are applied in this paper to illustrate the principles and implementation modes of the present application, and the above examples are only used to help understand the core idea of the present application, and the present application can be improved and modified in several ways without departing from the principles of the present application, and these improvements and modifications also fall within the protection scope of the present application.

Claims

1. A numerical method for simulating the mechanical properties of ice-rock debris with different ice contents, characterized in that, First, a ring shear apparatus model is established using the PFC discrete element method, with the upper shear box remaining stationary and the lower shear box rotating at a specified rate. Based on this ring shear apparatus model, the mechanical characteristics of ice-rock debris with different ice contents are simulated during the shearing process until the ice-rock debris reaches its residual shear strength. This simulation includes the following steps: S11: After starting and initializing, establish a ring shear model with different ice contents in the upper shear box and set the initial temperature of the particles; S12: Based on the model established in S11, set the speed of the ring shearing apparatus and monitor the shear stress and angular displacement of rock particles in the shearing surface; S13: Based on the shear stress and angular displacement determined in S12, calculate the frictional heat between the upper and lower rock particles in the shear plane; S14: Determine whether the contact type between particles is rock particles and ice particles; if yes, proceed to S15; if no, proceed directly to S16. S15: Calculate the thermal conductivity between rock particles and ice particles based on particle contact information; S16: Calculate the heat flux into the rock particles and ice particles according to Fourier's law; S17: Establish the heat conduction equation and calculate the particle temperature; S18: Determine whether the ice-rock debris has reached the residual shear strength. If not, return to S13. S19: Obtain the relationship between ice content and residual shear stress in the final ice-rock debris.

2. The numerical method for simulating the mechanical properties of ice-rock debris with different ice contents according to claim 1, characterized in that: In a ring shear model where the upper shear box remains stationary and the lower shear box rotates at a specified rate, rock particles are represented as spherical particles and ice particles as flexible clusters. Normal stress is applied, and the contact information and initial temperature of the rock and ice particles are set.

3. The numerical method for simulating the mechanical properties of ice-rock debris with different ice contents according to claim 1, characterized in that: In step S12, based on the established ring shear model, the lower shear box is sheared at a specified rate; the shear stress and angular displacement of the ice-rock debris rock particles are monitored. The shear stress experienced by the rock particles in the ice-rock clastic mass is: Where M is the torque exerted on the rock particles in the ice-rock debris body, D is the outer ring radius, and d is the inner ring radius; The angular displacement of the rock grains in the ice-rock clastic body is: S=R m I; Among them, R m θ represents the radius of the rock particles in the model, and θ is the arc of rotation of the rock particles when the ring shear is rotated.

4. The numerical method for simulating the mechanical properties of ice-rock debris with different ice contents according to claim 1, characterized in that: In step S13, the frictional heat generated between the upper and lower rock particles is: Q = τS; Where τ is the shear stress on the rock particles of the ice-rock debris body, and S is the angular displacement of the rock particles.

5. The numerical method for simulating the mechanical properties of ice-rock debris with different ice contents according to claim 1, characterized in that: In step S15, the thermal conductivity between the rock particles and the ice particles is: Where r represents rock particles, i represents ice particles, and k i k is the thermal conductivity of ice particles. r is the thermal conductivity of the rock particles.

6. The numerical method for simulating the mechanical properties of ice-rock debris with different ice contents according to claim 1, characterized in that: In step S16, the process of calculating the heat flux flowing into the ice particles and rock particles includes: Based on particle temperature information, the principle of transferring heat from higher-temperature rock particles to adjacent lower-temperature rock particles and ice particles is followed. During heat transfer, heat transfer occurs simultaneously between rock particles and between rock particles and ice particles. The heat flux from high-temperature rock particles to low-temperature rock particles is: Among them, a r For geometric correction factor, The width of the cross-section formed by adjacent rock particles. The distance between the centers of adjacent rock particles. T represents the temperature of the rock grain with the higher temperature among adjacent rock grains. r The temperature of adjacent rock particles with lower temperatures; The heat flux from rock particles to ice particles is: Where, k ir S represents the thermal conductivity between rock particles and ice particles. ir L represents the width of the cross-section formed by adjacent ice and rock particles. ir T is the distance between the centers of adjacent ice and rock grains. i and T r These represent the temperatures of ice particles and rock particles, respectively.

7. The numerical method for simulating the mechanical properties of ice-rock debris with different ice contents according to claim 1, characterized in that: In step S17, the process of calculating the particle temperature includes: Calculate the temperature of the ice and rock particles based on the heat flux flowing into them. The temperature of the rock particles is: in, C represents the temperature of the rock particles in the previous time step. r M represents the specific heat capacity of rock particles. r The mass of the rock particles; The temperature of the ice particles is: in, C represents the temperature of the ice particles at the previous time step. i M is the specific heat capacity of ice particles. i This represents the mass of the ice particles.

8. The numerical method for simulating the mechanical properties of ice-rock debris with different ice contents according to claim 1, characterized in that: In step S18, the process of determining whether the ice-rock debris has reached its residual shear strength includes: Based on the monitored shear stress and angular displacement, their relationship curves are determined; Based on its relationship curve, the residual shear strength is the final stable value reached by the shear stress; The residual shear strength of the ice-rock debris is: Where η is the viscosity coefficient, γ is the shear strain rate, and σ is the normal stress. ω is the internal friction angle, and c is the cohesive force.

9. The numerical method for simulating the mechanical properties of ice-rock debris with different ice contents according to claim 1, characterized in that: In step S19, the process of generating a graph showing the relationship between ice content and residual shear strength includes: After the simulation stops, output the residual shear strength of the ice-rock debris. A relationship diagram is generated based on the residual shear strength corresponding to different ice contents.

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