Discrete element method-based resistivity simulation method for frozen soil material

Abstract

The invention discloses a permafrost material resistivity simulation method based on a discrete element method. The permafrost material resistivity simulation method comprises the following steps: generating a three-phase particle system meeting a preset porosity in a set boundary condition; the method comprises the following steps: respectively setting mechanical contact models for different types of contact pairs in combination with interaction characteristics among water, ice and soil in a frozen soil material; traversing all spherical particles in the container, calculating a contact force according to the contact overlapping amount between the current particle and the surrounding particles, and deducing particle motion by using the Newton's second law; setting a contact resistance model among the three-phase particles and between the three-phase particles and the boundary; setting voltage or current boundary conditions, and applying positive and negative voltages at corresponding positions of the boundary; and alternately solving the ohmic conduction equation and the conduction continuity equation to obtain voltage and current distribution. According to the method, the essential influence of ice-water phase change on the electrical characteristics of the frozen soil can be deeply understood, and support can be provided for experimental design and data inversion under the condition of electricity-force multi-field coupling.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical simulation in geotechnical engineering, and particularly to a resistivity simulation method for frozen soil materials based on the discrete element method. Background Art

[0002] As a special geotechnical medium with extremely strong temperature sensitivity, frozen soil is a key geological object that must be faced in the construction of transportation infrastructure such as railways, highways, and airports. Under frozen soil conditions, affected by seasonal freeze-thaw cycles, the ice-water phase change process in the soil will cause strong volume changes and pore structure reconstruction, resulting in engineering diseases such as foundation frost heave, thaw settlement, and frost cracking, seriously threatening the stability of structures such as subgrades, abutments, tunnels, and culverts. The electrical conductivity of frozen soil, as a sensitive indicator of the internal water content state and structural changes, has the characteristics of strong real-time performance, fast response, and easy integration, and has important application values in evaluating the degree of foundation freezing / thawing, identifying the evolution of ice content, and warning of engineering diseases. Therefore, in-depth study of the electrical conduction mechanism of frozen soil materials and construction of an electrical response model reflecting the ice-water phase change process have important theoretical significance and practical value for improving the intelligent monitoring level of transportation infrastructure in cold regions, extending the service life of projects, and ensuring operation safety.

[0003] Traditional studies on the electrical conductivity of frozen soil mostly rely on the fitting of experimental tests and empirical models. Among them, empirical conductivity models represented by the Archie formula, although certain achievements have been made in the study of porous media, are difficult to accurately capture the sudden change phenomenon of the conductive network caused by the ice-water phase change. This sudden change is mainly manifested as the fracture or reconstruction of the conductive path as the temperature decreases and liquid water freezes, resulting in a non-linear drastic change in electrical conductivity, and this process is often simplified in traditional models. In addition, the effects of factors such as pore structure, water saturation state, electrolyte concentration, and interfacial polarization effect in frozen soil on electrical conductivity lack detailed quantitative descriptions in existing models.

[0004] The discrete element method (DEM) has become an important means for studying the microstructure and mechanical behavior of frozen soil due to its strong adaptability to the discontinuity, constitutive nonlinearity, and interactions of granular systems. In recent years, although certain research progress has been made in the mechanical properties, deformation and failure, and inter-particle interactions of frozen soil using DEM, most existing simulations still focus on pure mechanical or thermodynamic behaviors, and research related to electrical conductivity is still in its infancy, especially lacking modeling methods considering the electro-thermal-mechanical multi-physics field coupling mechanism. From the perspective of microscopic mechanisms, the electrical conductivity of frozen soil is not only affected by the moisture distribution and freezing degree but also by complex mechanisms such as ice / water interface polarization, particle contact resistance, and the reconstruction of ice crystal structures. In an ice-water mixed system, the polarization effect enhances the charge migration ability under the action of an electric field, and the change in the contact state between particles during the freezing process also significantly changes the equivalent resistance value. These key electrical behaviors are currently difficult to effectively describe in traditional continuum or pure mechanical discrete models. Summary of the Invention

[0005] Object of the Invention: The object of the present invention is to provide a resistivity simulation method for frozen soil materials based on the discrete element method to meet the need for revealing the electrical conduction mechanism of frozen soil and predicting electrical responses.

[0006] Technical Solution: The resistivity simulation method for frozen soil materials based on the discrete element method described in the present invention includes:

[0007] Step 1: Generate a three-phase particle system with a preset porosity within the set boundary conditions according to the characteristics of frozen soil materials.

[0008] Step 2: Combine the interaction characteristics between water, ice, and soil in frozen soil materials and set mechanical contact models for different types of contact pairs respectively.

[0009] Step 3: Traverse all spherical particles in the container, calculate the contact force based on the contact overlap amount between the current particle and surrounding particles, and deduce the particle motion using Newton's second law.

[0010] Step 4: Based on the intrinsic electrical conductivity and contact characteristics of various particle materials, set the contact resistance models between the three-phase particles and between them and the boundary.

[0011] Step 5: Set voltage or current boundary conditions and apply positive and negative voltages at the corresponding positions of the boundary.

[0012] Step 6: Alternately solve the Ohm's conduction equation and the conduction continuity equation to obtain the voltage and current distributions.

[0013] Further, the three-phase particle system in Step 1 includes three types of particles: soil particles, ice particles, and water particles.

[0014] Further, in Step 1, the random generation method RSA or the hierarchical deposition method is adopted to generate a spherical particle system with a multi-particle size distribution; during the generation process, the coordinates, particle size distribution, phase state information, contact state, and key parameters of the spatial topology structure of each type of particle are recorded synchronously.

[0015] Further, the contact pairs in Step 2 include soil-soil, ice-ice, water-water, ice-water, and soil-water contact pairs.

[0016] Further, in Step 2, considering the differences in contact stiffness, damping coefficient, and friction coefficient parameters, the interface characteristic change mechanism during the phase change process is introduced, and for the contact between particles and boundaries, corresponding boundary contact models are set according to different phase states.

[0017] Further, in Step 3, a discrete element mechanics solution framework is adopted to update the particle displacement, velocity, and acceleration at each time step, and continuous iteration is carried out until the system tends to mechanical equilibrium.

[0018] Further, the contact resistance model in Step 4 includes the contact resistance per unit length between particles and the contact resistance per unit length between particles and boundaries.

[0019] Further, the calculation method for the contact resistance per unit length between particles is as follows:

[0020] Assume that particle i is in contact with particle j, and the contact point is c, then:

[0021] Resistance of particle i:

[0022]

[0023] Resistance of particle j:

[0024]

[0025] Resistance of contact c:

[0026]

[0027] Total contact resistance between particles:

[0028]

[0029] Where: D j =L ij -D i ,ρ i represents the density of particle i, ρ j represents the density of particle j, r j represents the radius of particle j, r i represents the radius of particle i, D iDenotes the distance from the center of the contacting particle i to the contact plane, D j Denotes the distance from the center of the contacting particle j to the contact plane;

[0030] Contact resistivity between particles:

[0031]

[0032] Contact resistance per unit length between particles:

[0033]

[0034] Where: R ij Denotes the total contact resistance between particles, A ij Denotes the contact area between adjacent particles i and j, L ij Denotes the distance between the centers of adjacent particles i and j.

[0035] Furthermore, the calculation method for the contact resistance per unit length of the particle - boundary is:

[0036] Assume that particle i is in contact with the boundary, and the contact point is c, then:

[0037] Resistivity of particle i:

[0038]

[0039] Resistivity of the contact c:

[0040]

[0041] Total resistivity of the particle - boundary contact:

[0042]

[0043] Where: D i = L iw , ρ w Denotes the density of the contact boundary;

[0044] Contact resistivity of the particle - boundary:

[0045]

[0046] Contact resistance per unit length of the particle - boundary:

[0047]

[0048] Where: ρ iw Denotes the density at the contact of the particle and the boundary, A ij Denotes the contact area between adjacent particles i and j, L ij Denotes the distance between the centers of adjacent particles i,

[0049] Furthermore, in Step 6, by coupling the electrical control equation with the mechanical motion equation, electro-mechanical coupling solution is achieved to capture the microscopic structure evolution of the three-phase medium system during the freezing or melting process and its influence on the electrical response.

[0050] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: The present invention not only helps to deeply understand the essential influence of ice-water phase change on the electrical properties of frozen soil, but also provides support for experimental design and data inversion under the condition of electro-mechanical multi-field coupling, further promoting the system construction of the research on the multi-physical field behavior of frozen soil; it can not only simulate the reconstruction and fracture of the conduction path, but also quantify the influence of key physical processes such as ice-water phase change, pore structure adjustment and interface effect on the electrical properties of frozen soil, thus providing support for the in-depth understanding of the conduction mechanism of three-phase media and the development of electrical monitoring technology in cold regions. Brief Description of the Drawings

[0051] Figure 1 is the construction flow chart of the present invention;

[0052] Figure 2 is the contact model diagram of particle resistivity, where (a) is resistance contact and (b) is length contact;

[0053] Figure 3 is the conductive simulation structure diagram of frozen soil material. Detailed Embodiment

[0054] The technical solution of the present invention will be further described below in conjunction with the drawings.

[0055] As Figure 1 shown, the resistivity simulation method of frozen soil material based on the discrete element method described in the present invention includes:

[0056] Step 1: According to the characteristics of frozen soil material, a three-phase particle system with a preset porosity is generated within the set boundary conditions (such as a cubic container); the specimen consists of three types of particles: soil particles, ice particles and water particles, and the proportion of each phase can be set according to the actual composition ratio of frozen soil. The random sequential adsorption (RSA) method or the layered deposition method is used to generate a spherical particle system with a multi-particle size distribution on the basis of ensuring the rationality of the overall pore structure. During the generation process, key parameters such as the coordinates, particle size distribution, phase state information (ice / water / soil), contact state and spatial topological structure of each type of particle are recorded synchronously to provide initial conditions for subsequent physical field coupling calculations.

[0057] Step 2: Combine the interaction characteristics among water, ice, and soil in frozen soil materials, and set mechanical contact models for different types of contact pairs (such as soil-soil, ice-ice, water-water, ice-water, soil-water, etc.); the model should consider the differences in parameters such as contact stiffness, damping coefficient, and friction coefficient, and can introduce the change mechanism of interface characteristics during the phase change process. At the same time, for the contact between particles and boundaries, corresponding boundary contact models should also be set according to different phases.

[0058] Step 3: Traverse all spherical particles in the container, calculate the contact force based on the contact overlap between the current particle and surrounding particles, and deduce the particle motion using Newton's second law; this process adopts a discrete element mechanics solution framework, updating the particle displacement, velocity, and acceleration at each time step, and continuously iterating until the system tends to mechanical equilibrium.

[0059] Step 4: Based on the intrinsic conductivity and contact characteristics of various particle materials, as Figure 2 shown, set the contact resistance models between three-phase particles (such as ice-water, ice-soil, water-soil, etc.) and between them and the boundaries;

[0060] Case 1: Assume that particle i is in contact with particle j, and the contact point is c, then:

[0061] Resistance of particle i:

[0062]

[0063] Resistance of particle j:

[0064]

[0065] Resistance of contact c:

[0066]

[0067] Total contact resistance between particles:

[0068]

[0069] Where: D j =L ij -D i ,ρ i represents the density of particle i, ρ j represents the density of particle j, r j represents the radius of particle j, r i represents the radius of particle i, D i represents the distance from the center of contact particle i to the contact plane, D j represents the distance from the center of contact particle j to the contact plane;

[0070] Inter-particle contact resistivity:

[0071]

[0072] Inter-particle contact resistance per unit length:

[0073]

[0074] Where: R ij represents the total inter-particle contact resistance, A ij represents the contact area between adjacent particles i and j, L ij represents the center distance between adjacent particles i and j.

[0075] Case 2: The calculation method for the particle-boundary contact resistance per unit length is as follows:

[0076] Assume that particle i is in contact with the boundary, and the contact point is c, then:

[0077] Resistivity of particle i:

[0078]

[0079] Resistivity of the contact point c:

[0080]

[0081] Total particle-boundary contact resistivity:

[0082]

[0083] Where: D i = L iw and ρ w represents the density of the contact boundary;

[0084] Particle-boundary contact resistivity:

[0085]

[0086] Particle-boundary contact resistance per unit length:

[0087]

[0088] Where: ρ iw represents the density at the particle-boundary contact, A ij represents the contact area between adjacent particles i and j, L ij represents the center distance between adjacent particles i and j.

[0089] Step 5: Set the voltage or current boundary conditions and apply positive and negative voltages at the corresponding boundary positions.

[0090] Step 6: Alternately solve the Ohm's conduction equation (12) and the conduction continuity equation (13) to enable current to be transmitted in the material and obtain the voltage and current distributions:

[0091]

[0092] Through the construction of a discrete element-circuit coupling calculation model, the present invention can achieve cross-scale analysis of the conductive behavior of frozen soil materials. The principle is as follows: Frozen soil, as a typical water-ice-soil three-phase granular medium system, its conductive properties are jointly affected by the distribution of multiphase substances, phase change behavior, and interfacial electrical properties. Under the framework of the discrete element method (DEM), the core principle of simulating its conductive behavior is to abstract the three-phase granular system into a multiphase-coupled resistor-capacitor network model: Among them, soil particles, ice crystals, and water particles are respectively regarded as components with different dielectric and conductive properties - water particles usually behave as weak electrolyte conductors and are modeled as low-resistance resistors; ice particles are modeled as high-resistance resistors or approximate insulators due to their low conductivity; and soil particles are modeled as resistor or capacitor components according to their material intrinsic conductivity. The contact areas between particles and between them and the boundaries constitute the transmission paths of current and are discretely modeled as resistor branches, and current flows between different-phase particles through these paths. The current distribution follows Ohm's law, and the current input and output of each component satisfy charge conservation. The calculation of contact resistance further introduces the three-phase interface effect. In addition to particle resistance, factors such as contact area, contact pressure, interface polarization between ice / water / soil, charge migration efficiency, and interface microstructure are also considered. Especially during the ice-water phase change process, the generation or melting of ice crystals will significantly change the contact structure and contact conductivity between particles, causing local resistance mutations, thereby affecting the current distribution of the entire system. During the simulation process, the traditional discrete element method is used to simulate the mechanical responses of the three-phase granular system, including mechanical behaviors such as particle motion, mutual contact forces, and volume changes caused by phase changes; while Ohm's law is used to solve the dynamic distributions of current and voltage in the resistor network evolving with the mechanical state. By coupling the electrical control equation and the mechanical motion equation, electro-mechanical coupling solution is realized, and further, the microscopic structure evolution of the three-phase medium system during the freezing / melting process and its influence on electrical responses are captured, as Figure 3 shown. This method can not only simulate the reconstruction and fracture of conductive paths, but also quantify the influence of key physical processes such as ice-water phase change, pore structure adjustment, and interface effect on the electrical properties of frozen soil, thereby providing a theoretical basis for the in-depth understanding of the conductive mechanism of three-phase media and the development of electrical monitoring technologies in cold regions.

Claims

1. A resistivity simulation method for frozen soil materials based on the discrete element method, characterized in that Including: Step 1: Generate a three-phase particle system with a preset porosity within the set boundary conditions according to the characteristics of frozen soil materials; Step 2: Combine the interaction characteristics between water, ice and soil in frozen soil materials, and set mechanical contact models for different types of contact pairs respectively; Step 3: Traverse all spherical particles in the container, calculate the contact force based on the contact overlap between the current particle and the surrounding particles, and deduce the particle motion using Newton's second law; Step 4: Based on the intrinsic conductivity and contact characteristics of various particle materials, set the contact resistance models between the three-phase particles and between them and the boundary; Step 5: Set the voltage or current boundary conditions, and apply positive and negative voltages at the corresponding positions of the boundary; Step 6: Alternately solve the Ohm's conduction equation and the conduction continuity equation to obtain the voltage and current distributions.

2. The resistivity simulation method of frozen soil materials based on the discrete element method according to claim 1, characterized in that The three-phase particle system in Step 1 includes three types of particles: soil particles, ice particles and water particles.

3. The resistivity simulation method of frozen soil materials based on the discrete element method according to claim 1, characterized in that, In Step 1, the random generation method RSA or the layered deposition method is used to generate a spherical particle system with a multi-particle size distribution; During the generation process, the key parameters of the coordinates, particle size distribution, phase state information, contact state and spatial topological structure of each type of particle are recorded synchronously.

4. The resistivity simulation method of frozen soil materials based on the discrete element method according to claim 1, characterized in that The contact pairs in Step 2 include soil-soil, ice-ice, water-water, ice-water and soil-water contact pairs.

5. The resistivity simulation method of frozen soil materials based on the discrete element method according to claim 1, wherein In Step 2, considering the differences in contact stiffness, damping coefficient and friction coefficient parameters, the interface characteristic change mechanism during the phase change process is introduced, and for the contact between particles and the boundary, the corresponding boundary contact models are set according to different phase states.

6. The resistivity simulation method of frozen soil materials based on the discrete element method according to claim 1, wherein In Step 3, a discrete element mechanics solution framework is adopted to update the particle displacement, velocity and acceleration at each time step, and continuous iteration is carried out until the system tends to mechanical equilibrium.

7. The resistivity simulation method of frozen soil materials based on the discrete element method according to claim 1, wherein The contact resistance model in Step 4 includes the unit length contact resistance between particles and the unit length contact resistance between particles and the boundary.

8. The resistivity simulation method of frozen soil materials based on the discrete element method according to claim 7, characterized in that The calculation method of the unit length contact resistance between particles is as follows: Assume that particle i is in contact with particle j, and the contact point is c, then: Resistance of particle i: Resistance of particle j: Resistance of contact c: Total contact resistance between particles: Wherein: D j = L ij - D i , ρ i represents the density of particle i, ρj represents the density of particle j, r j represents the radius of particle j, r i represents the radius of particle i, D i represents the distance from the center of contacting particle i to the contact plane, D j represents the distance from the center of contacting particle j to the contact plane; Contact resistivity between particles: Unit length contact resistance between particles: Where: R ij represents the total inter-particle contact resistance, A ij represents the contact area between adjacent particles i and j, L ij represents the center distance between adjacent particles i and j.

9. The resistivity simulation method of frozen soil materials based on the discrete element method according to claim 7, characterized in that, The calculation method of the unit length contact resistance between particles and the boundary is as follows: Assume that particle i is in contact with the boundary, and the contact point is c, then: Resistivity of particle i: Resistivity of contact c: Total contact resistivity between particles and the boundary: Where: D i = L iw , ρ w represents the density of the contact boundary; Contact resistivity between particles and the boundary: Unit length contact resistance between particles and the boundary: Where: ρ iw represents the density at the contact of particles and boundaries, A ij represents the contact area between adjacent particles i and j, L ij represents the center distance between adjacent particles i and j.

10. The resistivity simulation method of frozen soil materials based on the discrete element method according to claim 1, characterized in that, In Step 6, by coupling the electrical control equation and the mechanical motion equation, electro-mechanical coupling solution is realized to capture the microscopic structure evolution of the three-phase medium system during the freezing or melting process and its influence on the electrical response.

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