Acoustic emission fractal-permeability model and experimental study of coal specimens under hydraulic-loading coupling

The fracture (pore) development of coal specimen under axial stress loading and hydraulic permeability affects directly the mechanical indexes and the permeability characteristics. In this paper, using theoretical analysis and mechanical test methods, the relationships between permeability and fractal dimension, ringing count response under coal specimen fracture (pore) were analyzed, and the acoustic emission fractal-permeability model of coal specimens under hydraulic-loading coupling were established. The permeability experiments of coal specimens with hydraulic-loading coupling in different confining pressures (2−5 MPa, Δp_w/p'_c=0.75) were carried out, and the mechanical behavior, permeability characteristics and acoustic emission rules of coal specimens in different confining pressures (water pressure) were analyzed, and the relationship between the failure morphology of coal samples under different confining pressures and the acoustic emission positioning was discussed. The strength enhancement characteristics and the relationships between failure pattern and acoustic emission location of coal specimens under confining pressures were discussed. The rationality of the fractal-permeability model of coal specimens under hydraulic-loading coupling was verified. The results showed that the fracture (pore) change of coal specimen was consistent with acoustic emission ringing, the fracture (pore) development was closely related to the fractal dimension and the permeability, and the acoustic emission fractal and permeability could be characterized by the volume strain in the permeability experiments. The acoustic emission fractal-permeability model of coal specimen under hydraulic-loading coupling could be analyzed by a two-stage mathematical model. The permeability of the coal specimen showed the process of short-term decrease, long-term slow increase, rapid increase and slight decline, and the ringing count showed the wave-like development of rapid increase - decrease - increase - decrease during the total stress-strain process of coal specimen, the minimum permeability lagged behind the critical point of volume strain compression and expansion, and the minimum permeability varied from 0.124×10⁻¹⁷ m² to 1.250×10⁻¹⁷ m². With the increase of confining pressure (2−5 MPa), the peak deviating stress, peak axial strain and peak volume strain of coal specimen all showed an increasing trend, the linear characteristics were significant, the lag of peak permeability behind peak strength showed a decreasing trend, the reduction reached 93.34%, and the loudest ringing count (corresponding to the peak strength) showed an increasing trend. The effective cohesion and the effective internal friction angle of the coal specimen increased to 6.511 6 MPa and 36.56º under hydraulic coupling, respectively. With confining pressure (2−5 MPa) increase, the acoustic emission information of coal specimen changed from single inclined plane to irregular inclined plane, the angle of the main fracture plane from small angle to high angle, and the instability mode from single block shear to multi-block compression, and the specimen fracture could be expressed by acoustic emission positioning ringing count. Three experiment curves of acoustic emission fractal-volume strain, permeability and volume strain, and fractal and permeability of the coal specimens were consistent with the theoretical curves, the correlation during compression stage with confining pressure 2−5 MPa was 0.882−0.999, 0.950−0.998 and 0.849−0.997, respectively. The correlation during the expansion stage was 0.937−0.996, 0.891−0.998 and 0.873−0.966, respectively.