A simulation method for cyclic loading and unloading considering damage accumulation
By introducing damage functions and dynamic weakening of micromechanical parameters into the PFC2D simulation software, the problem of damage accumulation in PFC2D simulation of coal samples was solved, enabling more accurate simulation of coal failure process and guiding the evaluation of coal pillar stability and top coal fragmentation size.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-15
- Publication Date
- 2026-04-03
AI Technical Summary
Existing PFC simulation software cannot simulate the damage accumulation of coal samples during cyclic loading and unloading, which makes it impossible to simulate the damage accumulation of coal in actual situations and the damage accumulation process of coal samples, thus affecting engineering guidance.
This paper proposes a technique in PFC2D simulation software that introduces a global damage variable and calibrates it based on experimental data. The proposed technique includes the following steps: introducing a new device, introducing a cyclic loading and unloading simulation method that considers damage accumulation, adopting a parallel bonding model, defining a damage function, using a global damage variable calibrated based on experimental data, and systematically weakening the micromechanical parameters after each unloading process. This technique overcomes the inherent limitation of the parallel bonding model in PFC2D in simulating material fatigue deterioration.
The simulation of damage accumulation process of coal samples in PFC2D was realized, providing a more accurate simulation of coal failure process, guiding the control of coal pillar stability and the evaluation of top coal fragmentation and venting, and improving the accuracy and reliability of the simulation.
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Figure CN121525420B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of simulation technology for cyclic loading and unloading of samples, and specifically to a simulation method for cyclic loading and unloading that takes into account damage accumulation. Background Technology
[0002] During the longwall mining process of top coal caving faces, both the coal pillar and the top coal are subjected to cyclic loading and unloading actions of varying frequencies and amplitudes. Studying the coal body failure and instability process under cyclic loading and unloading actions is of great significance for guiding the stability control of the coal pillar and evaluating the fragmentation size and caving risk of the top coal. Due to the occurrence characteristics of the coal pillar and top coal, their internal stress distribution and crack propagation are difficult to monitor directly and need to be analyzed through experimental or numerical simulation methods.
[0003] Discrete element method (DEM) numerical simulation has been widely used in mining engineering, geotechnical engineering, slope engineering, and fracture mechanics after years of development. PFC (Particle Flow Code), as a particle flow DEM software, has significant advantages in simulating the process of macroscopic objects from a intact state to fragmentation, and can be used to study the failure process of coal pillars and top coal under cyclic loading and unloading. However, the parallel bonding model in PFC does not have damage accumulation. When using PFC to simulate the loading and unloading of coal samples, it cannot simulate the cumulative damage to the coal specimen caused by loading, i.e., it cannot simulate cyclic loading and unloading environments. For example, if a coal sample has a uniaxial compressive strength of 10 MPa, when using PFC to simulate loading and unloading, under a uniaxial pressure of 6 MPa, regardless of the number of loading cycles, the stress and deformation of the coal sample will be exactly the same, and it will not fail. However, the reality is different. Even a coal sample with a uniaxial compressive strength of 10 MPa will suffer some damage under a single uniaxial pressure of 6 MPa. If subjected to multiple cyclic loading and unloading cycles, the damage to the coal sample will accumulate with each loading cycle, eventually leading to failure under a uniaxial pressure of 6 MPa. Therefore, how to use PFC to simulate cyclic loading and unloading environments while considering cumulative damage has become a challenge for researchers guiding practical engineering. Summary of the Invention
[0004] To address the aforementioned technical problems, this invention proposes a cyclic loading and unloading simulation method considering damage accumulation based on PFC2D simulation software, comprising the following steps: S1. Establishing a coal sample model in PFC2D based on the macroscopic mechanical parameters of the coal sample; S2. Adopting a parallel bonding model and calibrating the microscopic mechanical parameters; S3. Defining the damage function: Selecting a coal sample for cyclic loading and unloading physical experiments, and obtaining different cyclic loading and unloading times of the coal sample. n Corresponding global damage variable D n The number of times to add and unload in a loop n forx Axis, global damage variable D n for y S4. Plot a scatter plot along the axis, then fit an exponential function to obtain the fitted curve, which is the damage function; S5. Design a stress-controlled cyclic loading and unloading path, and apply axial cyclic loading and unloading loads; select a sine wave for the load carrier curve; S6. Determine the unloading stage and capture the current cyclic loading count, then pause the calculation cycle; S7. Calculate the current global damage degree and traverse all interparticle contacts; the global damage degree is the global damage variable. D n The specific value; S7. Dynamically weaken the micromechanical parameters of interparticle contact based on the current global damage degree; S8. After completing the update of the micromechanical parameters of all interparticle contact, resume the calculation cycle, and the coal sample model will carry the weakened new parameters into the next loading and unloading cycle; repeat steps S4-S8 until the preset termination condition is reached.
[0005] Preferably, in step S1, rigid walls are generated at the top, bottom, and left and right sides of the coal sample model.
[0006] Preferably, in step S2, the micromechanical parameters of all particles and interparticle contacts are calibrated. The micromechanical parameters of the particles include: the elastic modulus e of the particles and the stiffness ratio k of the particles; the micromechanical parameters of the interparticle contacts include: the elastic modulus pb_e of parallel bonding, the stiffness ratio pb_k of parallel bonding, the tensile strength pb_t of parallel bonding, the cohesion pb_c of parallel bonding, the internal friction angle pb_fa of parallel bonding, and the friction coefficient fr of parallel bonding.
[0007] Preferably, in step S2, a trial-and-error method is used for calibration. A virtual uniaxial compression experiment is performed on the initial coal sample model, and the output stress-strain curve, peak strength, elastic modulus and failure mode are repeatedly compared with the macroscopic mechanical parameters of the coal sample. When the error is less than the set range, the calibration is considered complete, and the microscopic mechanical parameters at this time are used as the initial microscopic mechanical parameters of the coal sample model.
[0008] Preferably, in step S4, axial cyclic loading and unloading loads are applied by the uniform motion of the top rigid wall.
[0009] Preferably, in step S5, a real-time monitoring and discrimination module is set to continuously monitor the applied axial load. Whenever the axial load is detected to drop to the valley stress, it is determined that an unloading phase has ended and an loading / unloading cycle has been completed. At this time, the calculation cycle is paused, and the number of complete loading / unloading cycles n_c that has been completed is captured and recorded.
[0010] Preferably, in step S6, after obtaining the current number of loading cycles n_c, the damage function in step S3 is called to calculate the current global damage degree D_c; the FISH function is used to traverse each interparticle contact, and its unique ID and current micromechanical parameters are read, including the parallel bond tensile strength pb_t_c, the parallel bond cohesion pb_c_c, the parallel bond internal friction angle pb_fa_c, and the parallel bond friction coefficient fr_c.
[0011] Preferably, in step S7, for each interparticle contact traversed, based on the current global damage degree D_c calculated in step S6, the following weakening rules are executed: Update parallel bond tensile strength: pb_t = pb_t_c × (1-D_c); Update parallel bond cohesion: pb_c = pb_c_c × (1-D_c); Update parallel bond internal friction angle: pb_fa = pb_fa_c × (1-D_c); Update parallel bond friction coefficient: fr = fr_c × (1-D_c); pb_t represents the updated parallel bond tensile strength; pb_c represents the updated parallel bond cohesion; pb_fa represents the updated parallel bond internal friction angle; fr represents the updated parallel bond friction coefficient.
[0012] The beneficial effects of the present invention are as follows: The present invention provides a cyclic loading and unloading simulation method that considers damage accumulation. By introducing a global damage variable that is calibrated by experimental data and is explicitly related to the number of cyclic loading and unloading, and systematically weakening the micromechanical parameters of the coal sample model after each unloading, the inherent limitation of the parallel bonding model in PFC2D in simulating material fatigue deterioration is solved. Attached Figure Description
[0013] Figure 1 This is a flowchart of a cyclic loading and unloading simulation method that considers damage accumulation according to the present invention. Detailed Implementation
[0014] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0015] like Figure 1As shown, this invention provides a cyclic loading and unloading method considering microscopic damage accumulation in the discrete element method (PFC2D) simulation software. This method introduces a global damage variable, calibrated by experimental data and explicitly related to the number of cyclic loading and unloading cycles, and systematically weakens the micromechanical parameters of the coal sample model after each unloading cycle, thereby overcoming the inherent limitation of the parallel bond model in PFC2D in simulating material fatigue degradation. Specifically, this invention proposes a cyclic loading and unloading simulation method considering damage accumulation, comprising the following steps.
[0016] S1. Macroscopic Mechanical Parameter Testing and Numerical Model Establishment. Macroscopic mechanical parameters of coal samples are obtained through laboratory physical experiments, including density, uniaxial compressive strength, elastic modulus, Poisson's ratio, cohesion, and internal friction angle, as well as stress-strain curves, peak strength, and failure modes. Based on the macroscopic mechanical parameters of the coal samples, a corresponding coal sample model is established in PFC2D. The dimensions of the coal sample model are set according to the standard cylindrical sample recommended by the International Society for Rock Mechanics (e.g., 50 mm in diameter and 100 mm in height). Rigid walls are generated at the top, bottom, and left and right sides of the coal sample model.
[0017] S2. Micromechanical Parameter Calibration. A parallel bonding model is used to calibrate the micromechanical parameters of all particles and interparticle contacts. The micromechanical parameters of particles include: elastic modulus e and stiffness ratio k. The micromechanical parameters of interparticle contacts include: parallel bonding elastic modulus pb_e, parallel bonding stiffness ratio pb_k, parallel bonding tensile strength pb_t, parallel bonding cohesion pb_c, parallel bonding internal friction angle pb_fa, and parallel bonding friction coefficient fr. Specifically, a trial-and-error method is used for calibration. A virtual uniaxial compression experiment is performed on the initial coal sample model. The output stress-strain curve, peak strength, elastic modulus, and failure mode are repeatedly compared with the macromechanical parameters obtained from the physical experiment in step S1. When the error is less than a set range (less than 2% in this embodiment), the calibration is considered complete, and the micromechanical parameters at this point are used as the initial micromechanical parameters of the coal sample model.
[0018] S3. Define the damage function. The core innovation of this invention lies in constructing a damage function that connects the macroscopic load history with the evolution of microscopic mechanical parameters; the method for determining this damage function is as follows: select a coal sample and conduct cyclic loading and unloading physical experiments to obtain the coal sample at different cyclic loading and unloading times. n Corresponding global damage variable D n The number of times to add and unload in a loop n for x Axis, global damage variable D n for yA scatter plot is drawn along the axes, and then an exponential function is fitted. The resulting fitted curve is the damage function. In this embodiment, the expression for the damage function is: In the formula, D max For constant terms, For the first i There are 10 index items, totaling 100 index items. m Each index item, m Depends on the coefficient of determination of the damage function R 2 , must meet R 2 >0.95, C i 、t i The first i The coefficient constants and degree constants of each exponential term; D max , C i 、t i The value is determined by the macroscopic mechanical parameters of the coal sample selected for the cyclic loading and unloading physical experiment; this damage function expression describes the global damage variable as increasing exponentially with the number of cyclic loading and unloading cycles and eventually tending to a saturation value. D max The evolution law. In this application, the damage variable is called the global damage variable because step S7 dynamically weakens and assigns values to the micromechanical parameters of the contact between multiple particles based on a damage degree.
[0019] S4. Design a cyclic loading and unloading path under stress control. A stress control mode is adopted, applying axial cyclic loading and unloading loads through the uniform motion of the top rigid wall; the load carrier waveform is selected as a sine wave, and the peak stress σ_max and valley stress σ_min are set; in this embodiment, the peak stress σ_max is 0.6 times the uniaxial compressive strength in step S1, and the valley stress σ_min is 0.1 times the uniaxial compressive strength in step S1.
[0020] S5. Unloading Phase Judgment and Current Cycle Loading Count n Capture. To achieve discrete accumulation of damage, the model needs to be updated at the end of each unloading cycle. A real-time monitoring and judgment module is set up to continuously monitor the applied axial load. Whenever the axial load is detected to drop to the valley stress σ_min, it is determined that an unloading phase has ended and a loading / unloading cycle has been completed. At this time, the calculation cycle is paused, and the current number of complete cycle loading / unloading counts n_c is captured and recorded.
[0021] S6. Calculate the current global damage degree and iterate through all interparticle contacts. After obtaining the current number of loading cycles n_c, call the damage function in step S3 to calculate the current global damage degree D_c; use the FISH function to iterate through each interparticle contact, read its unique ID and current micromechanical parameters, including parallel bond tensile strength pb_t_c, parallel bond cohesion pb_c_c, parallel bond internal friction angle pb_fa_c, and parallel bond friction coefficient fr_c; where the global damage degree is the global damage variable D. n The specific value.
[0022] S7. Dynamically weaken and assign values to the micromechanical parameters of interparticle contacts based on the current global damage level. For each interparticle contact traversed, based on the current global damage level D_c calculated in step S6, execute the following weakening rules: Update parallel bond tensile strength: pb_t = pb_t_c × (1-D_c); Update parallel bond cohesion: pb_c = pb_c_c × (1-D_c); Update parallel bond internal friction angle: pb_fa = pb_fa_c × (1-D_c); Update parallel bond friction coefficient: fr = fr_c × (1-D_c); pb_t represents the updated parallel bond tensile strength; pb_c represents the updated parallel bond cohesion; pb_fa represents the updated parallel bond internal friction angle; fr represents the updated parallel bond friction coefficient.
[0023] S8. Resume calculation and determine loop termination. After updating the micromechanical parameters of all interparticle contacts, resume the calculation loop. The coal sample model will carry the weakened new parameters into the n_c+1th loading and unloading loop; repeat steps S4-S8 until the preset termination condition is met.
[0024] The results can be output and analyzed in the following ways: After the simulation is completed, the crack propagation, failure mode, and stress curve data of the whole process can be output, and the final crack distribution pattern can be visualized; the stiffness degradation and energy dissipation characteristics can be studied by analyzing the morphological changes of hysteresis loops (such as envelope contraction and area reduction); and the damage localization and macroscopic fracture surface formation mechanism can be revealed through the spatiotemporal evolution of cracks.
[0025] The above description of the disclosed embodiments is presented in a progressive manner to enable those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A cyclic loading and unloading simulation method considering damage accumulation, characterized in that, Includes the following steps: S1. Establish a corresponding coal sample model in PFC2D based on the macroscopic mechanical parameters of the coal sample; S2. A parallel bonding model was adopted and the micromechanical parameters were calibrated. S3. Define the damage function: Select a coal sample and conduct cyclic loading and unloading physical experiments to obtain the number of cyclic loading and unloading cycles for the coal sample. n Corresponding global damage variable D n The number of times to add and unload in a loop n for x Axis, global damage variables D n for y Plot a scatter plot on the axis, then fit an exponential function to obtain the fitted curve, which is the damage function. S4. Design a cyclic loading and unloading path under stress control, and apply axial cyclic loading and unloading loads; select a sine wave for the load carrier waveform. S5. Determine the unloading phase and capture the current loop loading count, then pause the loop calculation; S6. Calculate the current global damage level and iterate through all interparticle contacts. The global damage level is the global damage variable. D n The specific value; S7. Dynamically weaken and assign values to the micromechanical parameters of interparticle contact based on the current global damage level; S8. After updating the micromechanical parameters of all interparticle contacts, resume the calculation cycle. The coal sample model will carry the weakened new parameters into the next loading and unloading cycle. Repeat steps S4-S8 until the preset termination condition is reached. In step S2, the micromechanical parameters of all particles and their interparticle contacts are calibrated. The micromechanical parameters of the particles include: the elastic modulus of the particles. e stiffness ratio of particles k The micromechanical parameters of interparticle contact include: parallel adhesive modulus. pb_e Parallel bond stiffness ratio pb_k Parallel bond tensile strength pb_t Parallel adhesive cohesion pb_c Parallel bonding internal friction angle pb_fa and parallel adhesive friction coefficient fr The calibration was performed using a trial-and-error method. A virtual uniaxial compression test was conducted on the initial coal sample model. The stress-strain curve, peak strength, elastic modulus and failure mode output by the model were repeatedly compared with the macroscopic mechanical parameters of the coal sample. The calibration was considered complete when the error was less than the set range. The microscopic mechanical parameters at this time were taken as the initial microscopic mechanical parameters of the coal sample model. In step S5, a real-time monitoring and discrimination module is set to continuously monitor the applied axial load. Whenever the axial load is detected to drop to the valley stress, it is determined that an unloading phase has ended and a loading / unloading cycle has been completed. At this time, the calculation cycle is paused, and the number of complete loading / unloading cycles that have been completed is captured and recorded. n _ c ; In step S6, after obtaining the current loop loading count... n _ c Then, the damage function in step S3 is called to calculate the current global damage level. D _ c The FISH function is used to iterate through each interparticle contact, reading its unique ID and current micromechanical parameters, including parallel bond tensile strength. pb_t _ c Parallel adhesive cohesion pb_c _ c Parallel bonding internal friction angle pb_fa _ c and parallel adhesive friction coefficient fr _ c ; In step S7, for each interparticle contact encountered, the current global damage level is calculated based on the value obtained in step S6. D _ c Perform the following weakening rule: Update the parallel bond tensile strength: pb_t = pb_t_c *(1- D_c Update parallel bond cohesion: pb_c = pb_c_c *(1- D_c Update the internal friction angle of parallel bonding: pb_fa = pb_fa_c *(1- D_c Update the parallel bonding friction coefficient: fr = fr_c *(1- D_c ); pb_t This indicates the updated parallel bond tensile strength; pb_c This indicates the updated parallel bond cohesion. pb_fa This indicates the updated internal friction angle of the parallel bonding; fr This represents the updated parallel adhesive friction coefficient.
2. The cyclic loading and unloading simulation method considering damage accumulation according to claim 1, characterized in that, In step S1, rigid walls are generated at the top, bottom, and left and right sides of the coal sample model.
3. The cyclic loading and unloading simulation method considering damage accumulation according to claim 1, characterized in that, In step S4, axial cyclic loading and unloading loads are applied through the uniform motion of the top rigid wall.
Citation Information
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