A Discrete Element Model Modeling Method Considering Temperature Changes and Its Application

Abstract

The present invention relates to a discrete element model modeling method considering temperature change and its application, belonging to the technical field of geotechnical engineering design. The design key points include: S1: determining the parameters in the DEM model; S2: using PFC 2D to establish a model; S3: preparing the granular specimen by the isotropic compression method, applying a stable compressive stress of 10 kPa laterally and vertically, and then generating a loose granular specimen with a relative density of D r ; S4: establishing a granular specimen model and conducting cyclic thermal consolidation tests; testing the thermal expansion and contraction characteristics of the temperature cycle through the change of the contact force caused by the change of the volume of the particles during the temperature cycle. By using the discrete element model modeling method considering temperature change and its application of the present application, the pore change law of unsaturated soil can be effectively evaluated, and thus a basis can be provided for the design and reinforcement of foundation bases.

Description

Technical Field

[0001] This invention patent relates to the fields of geotechnical engineering design and geotechnical engineering calculation, and particularly relates to a discrete element model modeling method considering temperature change and its application. Background Art

[0002] In recent years, energy-related and temperature-related engineering projects such as energy piles, ground source heat pump technology, nuclear waste disposal, thermal ground treatment, and high-temperature submarine pipelines have been increasing day by day, and the influence of temperature on soil has received more and more attention. Many scholars at home and abroad have carried out a large number of studies on this. The research results show that temperature has a great influence on the properties of soil such as strength, pore characteristics, deformation, and thermal conductivity. And the change of soil properties will inevitably cause the change of the contact between soil and structure.

[0003] Literature 1: Donna A, Ferrari A, Laloui L. Experimental investigations of the soil-concrete interface: physical mechanisms, cyclic mobilization, and behaviour at different temperatures[J]. Canadian Geotechnical Journal, 2016, 53(4): 659-672.

[0004] Literature 2: Yazdani S, Helwany S, Olgun G. Influence of temperature on soil-pile interface shear strength[J]. Geomechanics for Energy and the Environment, 2019, 18: 69-78.

[0005] Literature 1 and Literature 2 studied the experimental devices considering temperature change.

[0006] However, whether it is indoor test or field test, there are certain defects.

[0007] After clearly understanding the defects existing in field tests and laboratory tests, the scientific research personnel developed a numerical calculation method applicable to the engineering field by combining the rapidly developing computer technology. Currently, the more widely used numerical calculation methods include FDM (Finite Difference Method), FEM (Finite Element Method), BEM (Boundary Element Method), DDA (Discontinuous Deformation Analysis), and DEM (Discrete Element Method). Among the above methods, in the program of the particle discrete element method, since the soil mass is regarded as discontinuous discrete blocks, it can not only effectively conduct microscopic simulations of particle contacts, but also conduct a series of studies on the influence of temperature on the characteristics of the soil mass such as the anisotropy of the thermal conductivity, average thermal conductivity, and normal contact stress of the contact.

[0008] However, through the retrieval of existing technologies (CNKI database, Wanfang database, Himmpat retrieval system), it is found that: in the existing technologies, there is no analysis of the cumulative variation laws of the volume compactness, contact distribution, etc. of granular materials under the influence of different variable temperature amplitudes from both macroscopic and microscopic perspectives.

[0009] Therefore, on the premise of only exploring the influence of temperature on the particle volume without considering the heat transfer process of the particles, this application conducts cyclic thermal consolidation experiments on loose granular materials under different variable temperature amplitudes through the 2D PFC software. Analyze the laws of temperature cycle densification and strength weakening macroscopically, and study the influence of temperature on the anisotropy of particle contacts microscopically. Summary of the Invention

[0010] The purpose of the present invention is to provide a discrete element model modeling method considering temperature changes to overcome the deficiencies of the existing technologies.

[0011] Another purpose of the present invention is to provide an evaluation method for the void ratio of soil mass under the cycle of 20° - 80° to overcome the deficiencies of the existing technologies.

[0012] The purpose of the present invention is to provide the variation law of the void ratio of unsaturated soil considering the temperature variable amplitude to facilitate the calculation of settlement deformation.

[0013] A discrete element model modeling method considering temperature changes includes the following steps:

[0014] S1: Determine the parameters in the DEM model: the density ρ of the particles is 2000 kg / m 3 ; the damping coefficient ζ is 0.7; the stiffness ratio K * is 2; the effective modulus E * between the particles and the boundary wall is 1×108 Pa; the thermal expansion coefficient α is 1×10 -6 °C -1 ; the friction coefficient μ b between the particles is 0.5;

[0015] S2: Utilize PFC 2D Establish a model: Divide the grid according to the pre-calculated grid type and set appropriate boundary conditions (Set boundary conditions: the friction coefficient μ between the particles and the boundary wall is 0, that is, the boundary wall is a smooth wall); w is 0, that is, the boundary wall is a smooth wall);

[0016] S3: The preparation of the granular specimen adopts the isotropic compression method, apply a stable compressive stress of 10 kPa laterally and vertically, and then generate a loose granular specimen with a relative density of D r (i.e., the initial density); After the generation of the particles, calculate cyclically until the average unbalance coefficient α inside the specimen f is less than 1e -5 ; The force chains are evenly distributed in the initial state of the specimen;

[0017]

[0018] In the formula: N is the total number of particles; C is the total number of contacts; C i is the number of contacts of the i-th particle; F (ij) is the contact force of the j-th contact of the i-th particle; F b (i) is the body force of the i-th particle; F c (i) is the contact force of the i-th contact;

[0019] S4: Establish a granular specimen model, and then conduct confined compression consolidation on the generated specimen. Its boundary conditions are a stable compressive stress of 100 kPa applied in the y direction, and the wall in the x direction remains fixed;

[0020] After the initial consolidation of the specimen, while keeping the wall in the x direction fixed and the boundary conditions of the wall in the y direction servo-stabilized at 100 kPa unchanged, conduct cyclic thermal consolidation tests;

[0021] Test the thermal expansion and contraction characteristics of the temperature cycle through the change of the contact force caused by the change in the volume of the particles during the temperature cycle. With the change of temperature, the radius of the particles is controlled by the following formula:

[0022] R i =(1 + αΔT)R i0 .

[0023] Furthermore, the process of cyclic thermal consolidation in S4 is as follows: During the cycle, the particles are loaded at a fixed temperature increment ΔT from the initial temperature T0 under the condition of a temperature change amplitude T cyc , that is: T0~T0 + ΔT~T0 + 2ΔT~.......~T0 + T cyc ~T0 + Tcyc -ΔT~T0+T cyc -2ΔT.......~T0~T0-ΔT~T0-2ΔT~.......~T0-T cyc ~T0-T cyc +ΔT~T0-T cyc +2ΔT~T0, which is one cycle.

[0024] Furthermore, the cyclic thermal consolidation recording process in S4 is as follows: During the cycle, the particles are under the condition of the initial temperature T0, and the asymmetric temperature change amplitude T cyc , is loaded with a fixed temperature increment ΔT, that is: T0~T0+ΔT~T0+2ΔT~.......~T0+T cyc ~T0+T cyc -ΔT~T0+T cyc -2ΔT.......~T0 is one cycle.

[0025] A method for evaluating the void ratio of soil under the cycle of 20°~80°, the coefficient of thermal expansion α of the soil is 1×10 -6 °C -1 and the soil is unsaturated sand;

[0026] The initial void ratio of the unsaturated sand is e0, the maximum void ratio is e max , the minimum void ratio is e min , and the relative density Dr = (e max -e0) / (e max -e min );

[0027] After different numbers of cycles Ncyc , e is solved by the following formula:

[0028]

[0029] where N cyc represents the number of temperature cycles;

[0030] where V, A, and B represent calculation parameters and are calculated by the following formula:

[0031]

[0032] Adopting the above technical solution, compared with the prior art, the advantages include the following points.

[0033] First, the modeling method of this application is the first to give a discrete element model modeling method considering temperature changes: The core invention point lies in:

[0034] S3: The preparation of the granular specimen adopts the isotropic compression method. A stable compressive stress of 10 kPa is applied laterally and vertically, and then a loose granular specimen with a relative density of D r (i.e., the initial density) is generated; after the generation of the granules, it is cyclically calculated until the average unbalance coefficient α f inside the specimen is less than 1e -5 ; the force chains are evenly distributed in the initial state of the specimen;

[0035]

[0036] In the formula: N is the total number of granules; C is the total number of contacts; C i is the number of contacts of the i-th granule; F (ij) is the contact force of the j-th contact of the i-th granule; F b (i) is the body force of the i-th granule; F c (i) is the contact force of the i-th contact;

[0037] S4: A granular specimen model is established, and then the generated specimen is subjected to confined compression consolidation. Its boundary condition is a stable compressive stress of 100 kPa applied in the y direction, and the wall in the x direction remains fixed;

[0038] After the initial consolidation of the specimen, while keeping the wall in the x direction fixed and the boundary condition of the wall in the y direction servo-stabilized at 100 kPa unchanged, a cyclic thermal consolidation test is carried out; during the cycle, the granules are under the condition of the initial temperature T0, and under the single-amplitude temperature change amplitude T cyc , the cyclic consolidation based on the volume expansion method is realized through the following formula with a fixed temperature increment ΔT:

[0039] The thermal expansion and contraction characteristics of the temperature cycle are tested by the change of the contact force caused by the change of the volume of the granules during the temperature cycle. With the change of temperature, the radius of the granules is controlled by the following formula:

[0040] R i =(1 + αΔT)R i0

[0041] The above steps S3 and S4 are essential technical features of this application.

[0042] Second, this application provides a method for evaluating the void ratio of soil under a 20° - 80° cycle. The coefficient of thermal expansion α of the soil is 1×10 -6 °C -1 and the soil is unsaturated sand;

[0043] The initial void ratio of the unsaturated sand is e0, and the maximum void ratio is emax , the minimum void ratio is e min , the relative density Dr = (e max - e0) / (e max - e min );

[0044] After different numbers of cycles Ncyc , e is solved by the following formula:

[0045]

[0046] Among them, 0 < N cyc ≤ 20000, N cyc represents the number of temperature cycles;

[0047] A and B represent calculation parameters and are calculated by the following formula:

[0048]

[0049] It should be noted here that when cycling from 20° to 60°, the law of e and N cyc also adopts the above expression form, and the only difference is the calculation method of A and B. Description of the Drawings

[0050] Figure 1 : Diagram of the change in particle volume under the influence of temperature.

[0051] Figure 2 : Particle size distribution curve.

[0052] Figure 3 : Schematic diagram of particle arrangement and force chains in the specimen.

[0053] Figure 4 : Specimen model after primary consolidation.

[0054] Figure 5 : Schematic diagram of temperature change in a single temperature cycle (symmetric loading).

[0055] Figure 6 : Distribution diagram of measurement circles. Detailed Implementation Manner

[0056] Example 1: As Figure 1-6 shown, a discrete element model building method considering temperature changes includes the following steps:

[0057] S1: Use PFC 2D to build the model: Divide the grid according to the pre-calculated grid type and set appropriate boundary conditions;

[0058] S2: The cyclic calculation of the DEM model is achieved through the alternating application of the force-displacement law and Newton's laws of motion; the update of the inter-particle contact force is achieved through the force-displacement law; and the update of the positions of the particles and the boundaries is achieved through Newton's laws of motion. New contacts will be generated after the positions of the particles and the boundaries are updated.

[0059] In the DEM model, the contact force of a particle can be decomposed into a normal contact force and a tangential contact force:

[0060]

[0061] Where: F i is the contact force of the particle; is the normal contact force, is the tangential contact force, and is calculated by the following formula:

[0062]

[0063] Where: K n is the normal stiffness of the contact point; n i is the unit normal vector of the contact surface; is the inter-particle contact overlap; is the tangential contact force at the previous time step; K s is the tangential stiffness of the contact point; is the tangential component of the contact displacement increment, calculated by the formula where is the tangential component of the contact point velocity; Δt is the time step of the calculation.

[0064] In the DEM model, the motion of a particle is divided into translational motion and rotational motion; therefore, during the calculation of the motion of a spherical particle, the translational and rotational motions of the particle are calculated through the following two sets of vector equations:

[0065]

[0066] Formula (3) represents the relationship between the resultant force and translational motion, and formula (4) represents the relationship between the resultant moment and rotational motion.

[0067] Where, m i and I i are the mass and moment of inertia of particle i, respectively; ν and ω are the velocities of displacement and rotation, respectively; F b is the total volume resultant force; N is the number of particles in contact with this particle; F n (k) and are the normal force and tangential force at the kth contact, respectively; R i is the vector from the particle mass point to the contact point, and its magnitude is approximately equal to the particle radius.

[0068] The specimen for DEM simulation determines the stable state of particles by calculating the internal average imbalance coefficient α f (see Equation (5)); generally, it is considered that when α f is less than 1e-5, the particles are in a relatively stable state.

[0069]

[0070] In the formula: N is the total number of particles; C is the total number of contacts; C i is the number of contacts of the i-th particle; F (ij) is the contact force of the j-th contact of the i-th particle; F b (i) is the body force of the i-th particle; F c (i) is the contact force of the i-th contact.

[0071] In this temperature model, it is assumed that the change in temperature only affects the particle volume, while other particle properties (such as stiffness and friction coefficient, etc.) remain unchanged. The change in particle volume will cause changes in the overlap δ i s between particles and the normal vector n i of the contact surface. From Equation (2), it can be obtained that the contact force of the particles will also change. Therefore, this application adopts the following temperature simulation method to test the thermal expansion and contraction characteristics of temperature cycling through the change in contact force caused by the change in particle volume during the temperature cycle, as Figure 1 shown. With the change in temperature, the radius of the particles is controlled by the following formula:

[0072] R i =(1 + αΔT)R i0 (6)

[0073] In the formula: R i0 is the radius of particle i at the reference temperature; α is the volume thermal expansion coefficient of the particle; R is the radius of particle i at the current temperature; ΔT is the temperature change relative to the reference temperature.

[0074] 1.1 Determination of basic parameters in the simulation

[0075] The following are the parameters of contacts and particles involved in the DEM thermal consolidation test: the density ρ of the particles is 2000 kg / m 3 ; the damping coefficient ζ is 0.7; the stiffness ratio K * is 2; the effective modulus E * between the particles and the boundary wall is 1×108 Pa; the thermal expansion coefficient α is 1×10 -6 °C -1 ; the friction coefficient μ between the particlesb is 0.5; the friction coefficient μ between the particles and the boundary wall w is 0, that is, the boundary wall is a smooth wall.

[0076] 1.2 Preparation of particle specimens

[0077] Using the isotropic compression method, a stable compressive stress of 10 kPa is applied laterally and vertically, and a loose particle specimen with a relative density D Figure 2 shown in the figure is generated. The corresponding void ratio is 0.2376. Among them, the minimum particle size is 0.8 mm, the maximum particle size is 2.56 mm, and the average particle size d r is 1.29, and the coefficient of uniformity C 50 is 1.7. The maximum and minimum void ratios are 0.251 and 0.187 respectively. After the particles are generated, the calculation is cycled until the average unbalance coefficient α u in the specimen (see formula (5)) is less than 1e f . -5 . Figure 3 (a) shows the arrangement of the particles. Figure 3 (b) shows the distribution of the force chains between the particles. It can be seen that the force chains are evenly distributed in the initial state of the specimen.

[0078] 1.3 First, a particle specimen model is established by the method in 1.2 using the parameters in 1.1, and then the generated specimen is subjected to confined compression consolidation. The boundary conditions are a stable compressive stress of 100 kPa applied in the y direction, and the walls in the x direction are fixed. The specimen after the initial consolidation is as shown in Figure 4 (a). Under the action of the boundary conditions, the lateral wall spacing remains unchanged at 0.1429 m, and the vertical wall decreases from the initial 0.058 m to 0.0577 m under the action of the compressive stress, and the void ratio also decreases from 0.2376 to 0.2314. From the Figure 4 force chain distribution diagram in (b), it can be seen that the force chains are significantly thickened. The initial state of the specimen referred to in the following text is the state after the confined compression consolidation.

[0079] After the specimen undergoes the initial consolidation, while keeping the walls in the x direction fixed and the boundary conditions of the walls in the y direction servo-stabilized at 100 kPa unchanged, a cyclic thermal consolidation test is carried out. During the cycle, the particles are under the condition of the initial temperature T0 = 20 °C, and in the variable temperature amplitudes T cyc of 20 °C, 40 °C, and 60 °C respectively, and a cyclic consolidation based on the volume expansion method is realized through formula (6) with a fixed temperature increment ΔT = 10 °C. Taking T cyc = 40 °C as an example, the temperature change range is -20 °C (T0 - T cyc ) to 60 °C (T0 + T cyc), the temperature change takes 20°C to 60°C to -20°C to 20°C as one cycle, and the change amount of each temperature during the temperature cycle is ΔT = 10°C. For example, the change from 20°C to 60°C is the change process of 20°C to 30°C to 40°C to 50°C to 60°C. The change situations of different variable temperature amplitudes are as Figure 5 shown.

[0080] Monitor the data of void ratio and lateral confining pressure from a macroscopic perspective. At the same time, in order to understand the void ratio inside the specimen and the stress field distribution inside the specimen, 300 (30×10) measuring circles are uniformly arranged in the specimen model as Figure 6 shown.

[0081] Example 2: The model of the present application can also be used to study asymmetric variable amplitude temperature changes, that is, under the condition that the particles are at the initial temperature T0 = 20°C, with the unilateral variable temperature amplitudes T cyc being 20°C, 40°C, and 60°C respectively, the cyclic consolidation based on the volume expansion method is realized with a fixed temperature increment ΔT = 10°C through formula (6). Taking T cyc = 60°C as an example, the temperature change range is 20° to 80°C (T0 + T cyc ), the temperature change takes 20°C to 80°C to 20°C as one cycle, and the change amount of each temperature during the temperature cycle is ΔT = 10°C. For example, the change from 20°C to 80°C is the change process of 20°C to 30°C to 40°C to 50°C to 60°C to 70°C to 80°C.

[0082] The engineering background corresponding to the above process is: An energy pile is set under a building in a certain place, and the building foundation is constantly in the process of heating - cooling (that is, transferring the heat at the bottom of the foundation to the upper part of the foundation, or transferring the heat at the upper part of the foundation to the bottom of the foundation, and the foundation soil (the part in contact with the energy pile).

[0083] When the soil is constantly cycling from 20° to 80°, through a large number of analyses by the inventor team, for the expansion coefficient, the thermal expansion coefficient α is 1×10 -6 °C -1 , unsaturated sandy soil (saturation ≤ 30%), the initial void ratio of the unsaturated sandy soil is e0, the maximum void ratio is e max , the minimum void ratio is e min , and the relative density Dr = (e max - e0) / (e max - e min );

[0084] The following empirical formula is obtained:

[0085] Under different initial densities, after different numbers of cycles Ncyc , the change rule of e is:

[0086] (i.e., when Ax 2 + Bx + D r is calculated to be greater than 1.0, it is still in the range of 1.0)

[0087] Wherein, 0 < N cyc ≤ 20000:

[0088]

[0089] When N cyc > 20000, e gradually approaches e max (It can also directly take e max ).

[0090] Based on the data analysis of Embodiment 1, it can be known that at different temperatures, the variation law of e-N cyc is different (knowing the variation law of e-N cyc , designers can evaluate the settlement deformation of the soil mass, and then can judge the safety of the building; at the same time, it also provides a basis for the design and reinforcement of the foundation).

[0091] The preferred embodiments of this aspect have been described in detail above. However, it should be understood that after reading the above teachings of the present invention, those skilled in the art can make various changes or modifications to the present invention. These equivalent forms also fall within the protection scope of the appended claims of this application.

Claims

1. A discrete element model modeling method considering temperature changes, characterized in that, It includes the following steps: S1: Determine the parameters in the DEM model: the density ρ of the particles is 2000 kg / m 3 ; the damping coefficient ζ is 0.7; the stiffness ratio K * is 2; the effective modulus E of the particles and the boundary wall * is 1×108 Pa; the thermal expansion coefficient α is 1×10 -6 °C -1 ; The coefficient of friction μ between particles b is 0.5; S2: Use PFC 2D Build a model: Divide the mesh according to the pre-calculated mesh type and set appropriate boundary conditions: the friction coefficient μ w is 0 between the particles and the boundary wall S3: The preparation of the granular specimen adopts the isotropic compression method, applying a stable compressive stress of 10 kPa laterally and vertically, and then generating a loose granular specimen with a relative density of D r ; after the generation of the particles, calculate cyclically until the average imbalance coefficient α f inside the specimen is less than 1e -5 ; in the initial state of the specimen, the force chains are evenly distributed; Where: N is the total number of particles; C is the total number of contacts; C i is the number of contacts of the i-th particle; F (ij) is the contact force of the j-th contact of the i-th particle; F b (i) is the body force of the i-th particle; F c (i) is the contact force of the i-th contact; S4: Establish a granular specimen model, and then conduct lateral confinement compression consolidation on the generated specimen. The boundary condition is a stable compressive stress of 100 kPa applied in the y-direction, and the wall in the x-direction remains fixed; After the specimen undergoes initial consolidation, while keeping the wall in the x-direction fixed and without changing the boundary condition of the wall in the y-direction being servo-controlled at 100 kPa, a cyclic thermal consolidation test is carried out; The thermal expansion and contraction characteristics of the temperature cycle are tested through the change in contact force caused by the change in the volume of the particles during the temperature cycle. With the change in temperature, the radius of the particles is calculated by the following formula: R i = (1 + αΔT)R i0 Where: R i0 is the radius of particle i at the initial temperature; α is the thermal expansion coefficient of the particle; R i is the radius of particle i at the final temperature; ΔT is the difference between the initial temperature and the final temperature.

2. The discrete element model modeling method considering temperature change according to claim 1, characterized in that The cyclic thermal consolidation process in S4 is described as follows: During the cycle, the particles are loaded at a fixed temperature increment Δt from the initial temperature T0 under the condition of variable temperature amplitude T cyc , i.e., T0 ~ T0 + Δt ~ T0 + 2Δt ~....... ~ T0 + T cyc ~ T0 + T cyc - Δt ~ T0 + T cyc - 2Δt....... ~ T0 ~ T0 - Δt ~ T0 - 2Δt ~....... ~ T0 - T cyc ~ T0 - T cyc + Δt ~ T0 - T cyc + 2Δt ~...... T0 is one cycle.

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