At the laboratory scale, locating acoustic emission (AE) events is a comparatively mature method for evaluating cracks in rock materials, and the method plays an important role in numerical simulations. This study is aimed at developing a quantitative method for the measurement of acoustic emission (AE) events in numerical simulations. Furthermore, this method was applied to estimate the crack initiation, propagation, and coalescence in rock materials. The discrete element method-acoustic emission model (DEM-AE model) was developed using an independent subprogram. This model was designed to calculate the scalar seismic tensor of particles in the process of movement and further to determine the magnitude of AE events. An algorithm for identifying the same spatiotemporal AE event is being presented. To validate the model, a systematic physical experiment and numerical simulation for argillaceous sandstones were performed to present a quantitative comparison of the results with confining pressure. The results showed good agreement in terms of magnitude and spatiotemporal evolution between the simulation and the physical experiment. Finally, the magnitude of AE events was analyzed, and the relationship between AE events and microcracks was discussed. This model can provide the research basis for preventing seismic hazards caused by underground coal mining.
An increasing number of underground engineering and physical experiments have focused on investigating the failure or fracture properties of rocks [
Among the numerical methods that have been used to study the deformation and cracks in rock materials, the finite element method (FEM) or Fast Lagrangian Analysis of Continua (FLAC) cannot generate actual cracks, and the majority of investigations have focused mainly on studying the plastic or damaged zones [
In DEM, if each generated microcrack is considered an individual AE event, the magnitude of the AE event caused by the hypocenter of microcrack inversion is almost the same for each event. At the laboratory scale or at the field scale, the magnitude of AE events is generally in line with the exponential distribution [
Because the stress and movement of unit particles are already known, in this study, a new module was developed incorporating an independent subprogram to calculate the moment tensor of rock materials as cracks developed, so that the magnitude of AE events could be established. An algorithm for identifying the same spatiotemporal AE event was developed. This new model was defined as the DEM-AE model. Physical experiments were conducted for a quantitative analysis of the spatiotemporal relationship of the AE events as cracks were generated in argillaceous sandstones under different confining pressures. A validation analysis was performed on the model. A comparison of the magnitude and spatiotemporal relationship of AE events in the numerical simulations and the physical experiments demonstrated that the simulations were in good agreement with the experimental data. Finally, in this study, we also analyzed the magnitude of AE events under different confining pressures in numerical simulations and discussed the relationship between AE events and the number of microcracks.
A common representation of an explicit DEM is the Particle Flow Code (PFC). PFC theory assumes that macroscopic rock materials are composed of many bonded microscopic particles, which is a mechanical behavior of representing macroscopic rock materials by the relative motion of microscopic particles [
A parallel bond in PFC. (a) Components of a contact. (b) Parallel bond model. (c) Schematic of constitutive law of contact forces at the interface between two particles.
In PBM, the movement of particles causes changes in force and moment. The resultant force and moment can be divided into normal- and shear-directed components, which can be expressed as follows:
Other parameters
In PBM, the maximum tension and shear stress between particles are subject to
The radius of the cross section is described by
In the normal and shear direction, the relationship between stress and displacement of the contact points depends on
The interparticle bond breaks and the corresponding mechanical behaviors. (a) Normal component of bond breaks. (b) Shear component of bond breaks.
If
The contact behavior of shear stress
If
Due to the growth of new cracks, friction motion in rock materials will create AE signals. At the laboratory scale, in order to estimate the damage zone and the crack location of rocks, signal monitoring is generally carried out by using an AE instrument [
The scalar seismic moment is defined as
In DEM, since the stress and movement of particles can be derived directly from calculations, it is easier to determine the scalar seismic moment based on the change of contact force between particles as new cracks develop. As shown in Figure
AE event with one microcrack. (a) Stress schematic of the particles after generation of the microcrack. (b) Calculation chart of seismic moment tensor.
The maximum scalar moment of the moment tensor is
The magnitude of AE events is calculated as per the empirical equation
Only when new cracks occur at other contact points of the source particles (Particles
The definition of excitation time of an AE event is shown in Figure
Definition of the same AE event in terms of time; the occurrence order of microcracks is Cracks 1, 5, 2, 3, and 4, in which Cracks 1, 2, and 3 belong to the same AE event.
Definition of the same AE event in terms of space, in which Cracks 1, 2, and 3 belong to the same AE event.
As shown in Figures
The rock materials used in this study were argillaceous sandstones from the Shanxi Formation at Shanxi Province, China, created to
Preparing the physical specimens.
As illustrated in Figure
Schematic diagram of the two data acquisition procedures under uniaxial compression. (
Table
Test results for the specimens.
Specimen number |
|
|
|
|
---|---|---|---|---|
I-1 | 0.5 | 19.55 | 20.11 | 0.194 |
II-1 | 0.5 | 18.86 | 20.70 | 0.216 |
III-1 | 0.5 | 18.23 | 21.67 | 0.235 |
I-2 | 2.0 | 20.97 | 20.64 | 0.204 |
II-2 | 2.0 | 21.02 | 19.87 | 0.174 |
III-2 | 2.0 | 20.14 | 20.24 | 0.210 |
I-3 | 4.0 | 24.60 | 22.16 | 0.224 |
II-3 | 4.0 | 25.47 | 21.25 | 0.195 |
III-3 | 4.0 | 24.31 | 22.04 | 0.203 |
I-4 | 6.0 | 29.08 | 21.88 | 0.201 |
II-4 | 6.0 | 30.35 | 22.87 | 0.214 |
III-4 | 6.0 | 29.67 | 21.41 | 0.224 |
Test results versus confining pressure for all specimens. (a) Deviatoric stress (
According to Table
The discrete element model must be calibrated to the associated microscopic parameters in order to describe the macroscopic mechanical behaviors of rock materials (i.e., deviatoric stress and Young’s modulus). Although the calculation equations for parameters such as cohesion, stiffness, and friction angle are included in the manual of the PFC software [ Young’s modulus and strength parameters (i.e., cohesion and internal friction angle) were calibrated first. The calibration standard was subjected to the cohesion and the internal friction angle obtained from physical experiments, rather than using only the uniaxial compressive strength of argillaceous sandstones as the basis. Initial microscopic properties were assigned in accordance with the relationship between microscopic parameters and macroscopic mechanical behaviors of rock materials. In the DEM, a servo system was used for compression tests with the confining pressure set at 0.5, 2.0, 4.0, and 6.0 MPa, respectively. In this case, trial and error was applied to determine microscopic parameters, until Young’s modulus reached 21.34 GPa and the peak deviatoric stress was roughly consistent with the envelope line resulting from physical experiments. Microscopic parameters of argillaceous sandstones after calibration are shown in Table The established DEM-AE model was compared with the results of the physical experiment (mainly including the spatiotemporal location of AE events and magnitude), and the comparison results are presented in Section
Microscopic parameters of the simulated specimen after calibration.
Microparameters | Symbol | Unit | Value |
---|---|---|---|
The minimum particle radius |
|
mm | 1.0 |
Ratio of maximum and minimum particle radius |
|
/ | 1.67 |
Particle density |
|
kg/m3 | 2800 |
Particle friction coefficient |
|
/ | 0.55 |
Young’s modulus of the particle |
|
GPa | 14.4 |
Parallel bond radius multiplier |
|
/ | 1.0 |
Young’s modulus of the parallel bond |
|
MPa | 14.4 |
Normal stiffness of the parallel bond (mean) |
|
MPa | 14.7 |
Normal stiffness of the parallel bond (std. deviation) |
|
MPa | 3.6 |
Shear stiffness of the parallel bond (mean) |
|
MPa | 9.2 |
Shear stiffness of the parallel bond (std. deviation) |
|
MPa | 2.4 |
After ensuring that the macroscopic parameters of the argillaceous sandstone specimens in the physical experiments were consistent with those of the numerical simulations, the contrastive analysis of the DEM-AE model was carried out. Figure
Deviatoric stress and ratio of cumulative events during confined compression test. (a) 0.5 MPa; (b) 2.0 MPa; (c) 4.0 MPa; (d) 6.0 MPa.
Under the different confining pressures, the results showed good agreement for the ratio of cumulative AE events in the physical experiments and in the DEM-AE model. It is worth noting that, in the physical experiment, cumulative AE events demonstrated linear growth at the initial loading stage; therefore, AE events could be detected even at this loading stage in the physical experiment, causing deviation from the numerical simulation. The detailed reasons are described in Section
With the different confining pressures, the number of AE events prior to loading to the peak deviatoric stress was very small, especially in the numerical simulation. There were nearly no AE events at the linear elastic stage, followed by a small number of microcracks in the specimens. In the DEM-AE model, only a small number of AE events were monitored as well. Most AE events developed after the peak and cumulative failure events increased exponentially at the postpeak stage. In particular, as for specimens with lower confining pressure (
Based on the microscopic parameters after calibration, the failure modes of the argillaceous sandstones under different confining pressures can be seen in Figure
Comparison of failure modes between experiments and DEM simulations.
Statistical quantity of microcracks under different confining pressures.
The temporal evolution of AE events at the stages of 50% peak deviatoric stress, peak deviatoric stress, and postpeak stage is shown in Figures
Comparison of spatial AE events between experiments and DEM simulations at a confining pressure of 0.5 MPa.
Comparison of spatial AE events between experiments and DEM simulations at a confining pressure of 2.0 MPa.
Comparison of spatial AE events between experiments and DEM simulations at a confining pressure of 4.0 MPa.
Comparison of spatial AE events between experiments and DEM simulations at a confining pressure of 6.0 MPa.
At the peak deviatoric stress, the AE events in the physical experiments and the numerical simulations accounted for 20%~35% of the cumulative total, while no obvious macroscopic cracks occurred in the specimens during the loading procedure. Until loading to 90% of postpeak strength, the physical experiments and numerical simulations resulted in relatively obvious cracks among the specimens with the confining pressures of 0.5, 2.0, and 4.0 MPa, accounting for 40%~55% of the cumulative total of AE events. It is worth noting that there were obvious macroscopic cracks in specimens with the confining pressure of 6.0 MPa only until 80% of postpeak strength.
During monitoring of the spatial distribution of AE events, the magnitude of AE events can be calculated in the DEM-AE model as well. As shown in Figure
Statistical number of AE events at different gradients under different confining pressures: (a) 0.5 MPa; (b) 2.0 MPa; (c) 4.0 MPa; (d) 6.0 MPa.
Figure
The relationship between the number of AE events and the number of microcracks. (a) 0.5 MPa; (b) 2.0 MPa; (c) 4.0 MPa; (d) 6.0 MPa.
As described in Section
In addition, because of the closing of initial cracks or holes in the physical experiments, the AE events of specimens could be monitored even at the initial loading stage, which was not observed in the numerical simulations. Nevertheless, AE events at the initial loading stage accounted for only a small proportion of the entire loading process.
In this paper, a DEM-AE model was presented based on the movement of particles during the loading process. The fundamental principle of the process was the calculation of the scalar moment of the moment tensor and the determination of the magnitude of AE events. An algorithm for identifying the spatiotemporal location of the same AE event was put forward. With this method, it was possible to analyze and quantify the spatiotemporal location and the magnitude during the process of crack initiation, propagation, and coalescence. This model was applied to the compression test with different confining pressures of argillaceous sandstones. A systematic contrastive analysis was conducted with the results from the physical experiment and the numerical simulation, leading to a good agreement between both cases in terms of spatiotemporal distribution as well as the magnitude of AE events. Furthermore, this model was used to analyze the magnitude of AE events and discuss the relationship between AE events and microcracks.
With this model, an authentic simulation of AE events in physical experiments can be reproduced using numerical simulations. In the near future, this model will be applied to the production process at the field scale. The performance of this model makes it possible to evaluate and prevent seismic hazards caused by roadway excavation and coal mining.
The authors declare that they have no conflicts of interest.
Financial support for this work is provided by the National Natural Science Foundation of China (no. 51474208), the National Key Research and Development Program of China (2016YFC0600904), and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). The financial support provided by China Scholarship Council (CSC, Grant no. 201606420013) is also gratefully acknowledged.