Discrete element simulation method for controllable drainage dynamic liquefaction test

Abstract

This invention provides a discrete element method for controlled dynamic liquefaction testing under drainage conditions. It achieves particle sample loading by servo-controlling the velocity of a rigid wall. Using drainage degree parameters as key conditions and combining them with sample geometry information, a drainage condition constraint equation for the wall velocity is established. Using the deviatoric stress loading time history as a key condition and combining it with information on the contact state between the wall and the particles, a deviatoric stress control equation for the wall velocity is established. By simultaneously solving these two equations, an analytical expression for the wall velocity is derived, enabling simultaneous and precise control of specific drainage and stress loading conditions without numerical iteration or trial calculations. This method provides a reliable and efficient technical means for studying the dynamic liquefaction behavior of particulate materials under specified drainage conditions.

Description

Technical Field

[0001] This invention relates to the field of discrete element numerical simulation technology in geotechnical engineering, and in particular to a discrete element simulation method for a controlled dynamic liquefaction test of drainage. Background Technology

[0002] The discrete element method (DEM) is widely used to investigate the dynamic liquefaction behavior and liquefaction mechanism of granular materials such as sand and gravel. Common dynamic liquefaction test forms include biaxial and triaxial dynamic liquefaction tests. In these simulations, stress-controlled loading typically employs the rigid wall servo method. Its basic principle is to control the wall displacement to compress the particles on the wall side, and to transfer force through the contact between the wall and particles and between particles, ultimately completing the overall loading of the granular material.

[0003] Dynamic liquefaction simulation not only requires meeting specific stress loading conditions but also effectively controlling the drainage state of granular samples. Currently, methods for achieving completely undrained conditions are relatively mature. However, soil in actual sites is mostly in a partially drained state, meaning that volume changes occur simultaneously during shearing. This volume change alters the soil's void ratio, thus affecting its shear dilatation characteristics, liquefaction resistance, and other physical and mechanical properties. In discrete element method (DEM)-based dynamic liquefaction simulation, simultaneously achieving partial drainage and specific stress loading conditions using rigid walls is crucial for simulating the dynamic liquefaction behavior of granular materials under a specified drainage level and is also an important foundation for understanding real-world liquefaction behavior and evaluating liquefaction resistance. However, existing DEM simulations lack a scheme that can simultaneously control the stress loading time history and drainage level. Summary of the Invention

[0004] The present invention aims to provide a discrete element method for a controlled dynamic liquefaction test of drainage, so as to simulate the dynamic liquefaction behavior of particulate materials under a specified drainage level.

[0005] To achieve the above objectives, the present invention adopts the following technical solution, comprising the following steps: Step 1: Establish a discrete element model for the dynamic liquefaction test of particle samples; the discrete element model consists of a rigid wall and particles surrounded by the rigid wall; Step 2: Set the drainage parameters for the particle sample; Step 3: Set the deviatoric stress loading time history for the particle sample; Step 4: Within each time step, establish the drainage condition constraint equation for the wall velocity based on the current sample geometry and the drainage degree parameters. Step 5: In each time step, based on the current wall-particle contact state and the deviatoric stress loading time history, establish the deviatoric stress control equation for the wall velocity. Step 6: Within each time step, simultaneously solve the drainage condition constraint equation and the deviatoric stress control equation to obtain the wall velocity; Step 7: Within each time step, calculate the wall displacement increment based on the wall velocity and time step length, and update the wall position; Step 8: Within each time step, the particles inside the sample are compressed by the updated wall to complete the particle sample loading. Step 9: Repeat steps 4 to 8 until the total loading time or the strain of the sample reaches the preset value, and obtain the dynamic liquefaction behavior data of the particle sample under the specified drainage degree.

[0006] Furthermore, in step one, the rigid wall is divided into side walls and end walls, wherein the side walls include the left wall and the right wall, and the end walls include the upper wall and the lower wall.

[0007] Furthermore, in step two, the drainage degree parameter is the strain increment ratio. Its definition is: (1); In the formula, The volumetric strain increment is represented by volumetric expansion; The axial strain increment is positive for tension; parameter The value reflects the degree of drainage of the particulate sample and ranges from [value range missing]. .

[0008] Furthermore, in step three, the deviatoric stress loading time history is a sinusoidal waveform: (2); In the formula, This represents the amplitude of the deviatoric stress. This refers to the loading frequency.

[0009] Furthermore, in step four, the specific form of the drainage condition constraint equation is as follows: (3); In the formula, The ratio of strain increments, and They are respectively The vertical strain increment and horizontal strain increment at time t satisfy: (4); (5); In the formula, and They are respectively The speed of the side walls and end walls at any given time is positive for rightward and upward movement; and They are respectively The height and width of the sample at any given moment; For time step.

[0010] Furthermore, in step five, the specific form of the deviatoric stress control equation is as follows: (6); In the formula, and They are respectively The stresses in the side walls and end walls at any given time satisfy: (7); (8); In the formula, and They are respectively The speed of the side walls and end walls at all times. and They are respectively The gain parameter at time t is calculated as follows: (9); (10); In the formula, and They are respectively The height and width of the sample at any given time. For time step, and They are respectively The number of particles in constant contact with the end walls and side walls. and They are respectively The average normal stiffness of the particles in contact with the end wall and side wall at any given moment.

[0011] Furthermore, in step six, the analytical expression for the wall velocity is: (11); (12); In the formula, and They are respectively The speed of the side walls and end walls at all times. , All are gain parameters. and They are respectively Gain parameters at time t, and They are respectively The height and width of the sample at any given time. , They are respectively , Deviatoric stress at time, This is the ratio of strain increments.

[0012] Furthermore, in step seven, the formula for calculating the wall displacement increment is: (13); (14); In the formula, and They are respectively The speed of the side walls and end walls at all times. For time step.

[0013] Optionally, when When this occurs, the drainage condition constraint degenerates into a completely undrained isochoric condition, i.e. .

[0014] Optionally, It is not limited to a constant, but can also be a time-dependent function. .

[0015] Optionally, the above approach of solving the wall velocity by combining the drainage constraint equations and the deviatoric stress control equations is not only applicable to the two-dimensional case, but can also be extended to the three-dimensional case.

[0016] The technical effects of this invention are as follows: This invention provides a discrete element method for controlled dynamic liquefaction tests under drainage conditions. The core of this method lies in simultaneously solving the drainage constraint equations and the deviatoric stress control equations to directly derive the analytical expression for the wall velocity. This method can achieve precise synchronous control of specific drainage and stress loading conditions without numerical iteration or trial calculations, exhibiting higher computational efficiency. It provides an efficient and reliable technical means for studying the dynamic liquefaction behavior of particulate materials under specified drainage conditions.

[0017] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0018] Figure 1 This is a flowchart of a discrete element simulation method for a controlled dynamic liquefaction test of drainage according to the present invention; Figure 2 This is the calculation result of the dynamic liquefaction behavior in Embodiment 1 of the present invention (partial drainage conditions); wherein, Figure 2 (a) shows the curve of excess pore pressure as a function of vibration frequency. Figure 2 (b) shows the curve of axial strain as a function of vibration order. Figure 2(c) is the deviatoric stress-axial strain relationship curve. Figure 2 (d) is the effective stress path curve; Figure 3 This is the calculation result of the dynamic liquefaction behavior in Embodiment 2 of the present invention (under completely non-drainage conditions); wherein, Figure 3 (a) shows the curve of excess pore pressure as a function of vibration frequency. Figure 3 (b) shows the curve of axial strain as a function of vibration order. Figure 3 (c) is the deviatoric stress-axial strain relationship curve. Figure 3 (d) is the effective stress path curve. Detailed Implementation

[0019] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0020] In the following description, specific details, such as particular internal procedures and techniques, are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will appreciate that the invention may be practiced in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of the invention with unnecessary detail.

[0021] Example 1: like Figure 1 As shown, this invention provides a discrete element simulation method for a controlled dynamic liquefaction test of drainage, comprising the following steps: Step 1: Establish a discrete element model for the dynamic liquefaction test of the particle sample. The model consists of a rigid wall and particles surrounded by the rigid wall. Specifically: Build wide ,high A two-dimensional rectangular discrete element particle sample is enclosed by four rigid walls: side walls on the left and right sides, and end walls at the top and bottom. The total number of particles in the sample is... ,radius R The particles are uniformly distributed within the range of 0.4–0.6 mm, are spherical in shape, and have a density of… The Hertz contact model was used for particle-to-particle contact, and the contact model parameters are shown in Table 1. The wall remains kinematically rigid, meaning its geometry does not change due to the contact force, but the same shear modulus and Poisson's ratio as the particles are used to determine the contact stiffness when calculating the wall-particle contact force.

[0022] Table 1 Contact Model Parameters After particle formation, the initially overlapping particles are allowed to bounce off each other and redistribute under contact force until the particles uniformly fill the entire area and the system reaches mechanical equilibrium. Subsequently, an isotropic consolidation pressure of 100 kPa is applied to the particle sample through four rigid walls. After isobaric consolidation, the porosity of the sample is... .

[0023] Step 2: Set the drainage parameters for the particle sample ; The drainage degree parameter is the strain increment ratio. Its definition is: In the formula, The volumetric strain increment is represented by volumetric expansion; The axial strain increment is positive for tension; parameter The value reflects the degree of drainage of the particulate sample and ranges from [value range missing]. .

[0024] Step 3: Set the deviatoric stress loading time history of the particle sample to a sinusoidal waveform, specifically as follows: In the formula, the amplitude of the deviatoric stress Loading frequency Total loading time The time step is set to... .

[0025] Step 4: At each time step Within this framework, based on the current sample size and drainage parameters, the drainage condition constraint equations for the wall velocity are established. The specific process is as follows: (1) Set the wall velocity: Let the velocity of the right wall be denoted as . The speed of the left wall is The wall-mounting speed is The speed of going down the wall is .

[0026] (2) Obtaining the specimen dimensions: Calculate the current height of the specimen using the coordinates of the rigid wall. and width .

[0027] (3) Calculate the vertical and horizontal strain increments within this time step: (4) Based on the set drainage parameters Establish the drainage condition constraint equations: Step 5, at each time step Internally, based on the current wall-particle contact state and the deviatoric stress loading time history, a deviatoric stress control equation for the wall velocity is established. The specific process is as follows: (1) Count the number of particles in contact with the left and right sidewalls in the current time step, and record the average value of the left and right sidewalls as . Count the number of particles in contact with the upper and lower end walls, and record the average value as follows: .

[0028] (2) Statistically measure the normal stiffness of all contacts between the particle and the sidewalls and endwalls within the current time step, and calculate their average values, denoted as . and For the Hertz contact model used in this embodiment, the normal stiffness of any particle in contact with the wall is... It can be calculated using the following formula: In the formula, g c This represents the normal overlap between the particles and the wall, i.e., the depth to which the particles are embedded in the wall.

[0029] (3) Calculate the gain parameter and : (4) Calculate the vertical stress after the end of this time step. With horizontal stress : (5) Based on the set deviatoric stress loading time history, establish the deviatoric stress control equation: Step Six: Simultaneously establish the drainage constraint equations and the deviatoric stress control equations to solve for the wall velocity. The wall velocity at this time step is: Step 7: Based on the wall velocity and time step obtained in Step 6, calculate the wall displacement increment: Update the position coordinates of the left and right side walls and the upper and lower end walls based on the above displacement increments.

[0030] Step 8: After completing the wall position update, enter the standard discrete element loop for particle-wall contact detection, particle-wall contact force calculation, and particle motion calculation. The motion of each particle in the sample follows Newton's second law.

[0031] Step 9: Repeat steps 4 through 8 until the total loading time reaches 10 seconds or the biaxial axial strain of the specimen reaches 10%. Every 10 seconds... -4 The system outputs data on the horizontal stress, vertical stress, horizontal strain, and vertical strain of the primary specimen. Finally, it obtains data on the particle specimen under partially drained conditions. The calculation results of the dynamic liquefaction behavior under the condition are as follows: Figure 2 (a) Figure 2 (b) Figure 2 (c) Figure 2 As shown in (d).

[0032] Example 2: The only difference between this embodiment and Embodiment 1 is that the drainage level parameter is set. The dynamic liquefaction behavior of particulate materials under completely undrained conditions was simulated. All other parameters (including sample size, number of particles, particle contact constitutive parameters, void ratio, consolidation pressure, deviatoric stress loading waveform, amplitude, frequency, time step, etc.) were exactly the same as in Example 1.

[0033] It should be noted that there is no drainage at all ( The condition described in this invention is the degraded condition under the generalized framework established by the present invention when the drainage degree parameter takes a specific value. In this case, the drainage condition constraint equation of the present invention automatically degenerates into the classical undrained isochoric condition, that is, at any loading moment, the movement of the sidewalls and endwalls always maintains a constant area enclosed by the sample, and the volumetric strain is zero. Therefore, the drainage condition constraint equation degenerates into: Accordingly, the analytical expression for the wall velocity obtained by solving the simultaneous equations in step six degenerates into: The calculation continues until the preset total loading time or the double-amplitude axial strain of the specimen reaches the preset value. Figure 3 (a) Figure 3 (b) Figure 3 (c) Figure 3 (d) shows the calculation results of dynamic liquefaction behavior under completely undrained conditions.

[0034] Optionally, It is not limited to a constant, but can also be a time-dependent function. .

[0035] Optionally, the above approach of solving the wall velocity by combining the drainage constraint equations and the deviatoric stress control equations is not only applicable to the two-dimensional case, but can also be extended to the three-dimensional case.

[0036] Two specific embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A discrete element simulation method for a controlled dynamic liquefaction test of drainage, characterized in that, Includes the following steps: Step 1: Establish a discrete element model for the dynamic liquefaction test of particle samples; the discrete element model consists of a rigid wall and particles surrounded by the rigid wall; Step 2: Set the drainage parameters for the particle sample; Step 3: Set the deviatoric stress loading time history for the particle sample; Step 4: Within each time step, establish the drainage condition constraint equation for the wall velocity based on the current sample geometry and the drainage degree parameters. Step 5: In each time step, based on the current wall-particle contact state and the deviatoric stress loading time history, establish the deviatoric stress control equation for the wall velocity. Step 6: Within each time step, simultaneously solve the drainage condition constraint equation and the deviatoric stress control equation to obtain the wall velocity; Step 7: Within each time step, calculate the wall displacement increment based on the wall velocity and time step length, and update the wall position; Step 8: Within each time step, the particles inside the sample are compressed by the updated wall to complete the particle sample loading. Step 9: Repeat steps 4 to 8 until the total loading time or the strain of the sample reaches the preset value, and obtain the dynamic liquefaction behavior data of the particle sample under the specified drainage degree.

2. The discrete element simulation method for a controlled dynamic liquefaction test of drainage as described in claim 1, characterized in that, In step one, the rigid wall is divided into side walls and end walls, wherein the side walls include the left wall and the right wall, and the end walls include the upper wall and the lower wall.

3. The discrete element simulation method for a controlled dynamic liquefaction test of drainage as described in claim 1, characterized in that, In step two, the drainage degree parameter is the strain increment ratio. Its definition is: （1）； In the formula, The volumetric strain increment is represented by volumetric expansion; The axial strain increment is positive for tension; parameter The value reflects the degree of drainage of the particulate sample and ranges from [value range missing]. .

4. The discrete element simulation method for a controlled dynamic liquefaction test of drainage as described in claim 1, characterized in that, In step three, the deviatoric stress loading time history is a sinusoidal waveform: （2）； In the formula, This represents the amplitude of the deviatoric stress. This refers to the loading frequency.

5. The discrete element simulation method for a controlled dynamic liquefaction test of drainage as described in claim 1, characterized in that, In step four, the specific form of the drainage condition constraint equation is as follows: （3）； In the formula, The ratio of strain increments, and They are respectively The vertical strain increment and horizontal strain increment at time t satisfy: （4）； （5）； In the formula, and They are respectively The speed of the side walls and end walls at any given time is positive for rightward and upward movement; and They are respectively The height and width of the sample at any given moment; For time step.

6. The discrete element simulation method for a controlled dynamic liquefaction test of drainage as described in claim 1, characterized in that, In step five, the specific form of the deviatoric stress control equation is as follows: （6）； In the formula, and They are respectively The stresses in the side walls and end walls at any given time satisfy: （7）； （8）； In the formula, and They are respectively The speed of the side walls and end walls at all times. and They are respectively The gain parameter at time t is calculated as follows: （9）； （10）； In the formula, and They are respectively The height and width of the sample at any given time. For time step, and They are respectively The number of particles in constant contact with the end walls and side walls. and They are respectively The average normal stiffness of the particles in contact with the end wall and side wall at any given moment.

7. The discrete element simulation method for a controlled dynamic liquefaction test of drainage as described in claim 1, characterized in that, In step six, the analytical expression for the wall velocity is: （11）； （12）； In the formula, and They are respectively The speed of the side walls and end walls at all times. , All are gain parameters. and They are respectively Gain parameters at time t, and They are respectively The height and width of the sample at any given time. , They are respectively , Deviatoric stress at time, This is the ratio of strain increments.

8. The discrete element simulation method for a controlled dynamic liquefaction test of drainage as described in claim 1, characterized in that, In step seven, the formula for calculating the wall displacement increment is: （13）； （14）； In the formula, and They are respectively The speed of the side walls and end walls at all times. For time step.

9. The discrete element simulation method for a controlled dynamic liquefaction test of drainage as described in claim 1, characterized in that, When drainage degree parameter At that time, the drainage condition constraint equation degenerates into a completely undrained isochoric condition, i.e., the volumetric strain increment. .

10. The discrete element simulation method for a controlled dynamic liquefaction test of drainage as described in claim 1, characterized in that, The drainage degree parameter For time-related functions .

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