## 3 Results and Discussion
### Changes in Acoustic Wave Properties  
In conventional creep characterisation studies, strain-time relationships are established on the assumption that the laboratory-scale sample is homogeneous so that the macroscopic deformation can be averaged over the whole sample to represent the mechanical responses of the rock material. However, the pronounced inhomogeneity of the coal samples used in this study introduced considerable irregularity into the creep strain data with increasing stress levels, which highlights the shortcomings of the conventional method for studying creep in coal. Therefore, in this section, ultrasonic wave velocities and attenuations measured during the creep tests are presented to provide more detailed information about the structural deformation within the samples. The P- and S-wave velocities recorded during the creep tests were normalised by their initial values (\(v_{po}\) and \(v_{so}\)) and plotted versus time in Figure 9. Because the tests at 11.02, 15.99, and 17.97 MPa were of short duration, those data are plotted against a time scale in minutes (Figure 9b or Figure 9d). From Figure 9a or Figure 9c, it can be seen that the velocities of P- and S-waves from long-term creep during each creep test fluctuate moderately with similar amplitudes. During the creep tests, the fluctuations ranged from 7.2% to 2.1% for P-wave velocities and 6.9% to 1.8% for S-wave velocities. This implies that the internal structure was being continuously altered during the tests. However, the magnitudes of the velocities, and thus the forms of the fluctuation curves, vary significantly as the stress level is increased from \(\sim\)8 MPa to \(\sim\)17 MPa and the relationship cannot be formulated as any comprehensible mathematical equation. In contrast, the P- and S- wave velocities for the 11.02, 15.99, and 17.97 MPa tests all show a general downward trend (Figure 9b or Figure 9d). The overall declines are 5.4%, 4.9%, and 3.4% for P-wave velocities generated at of 11.02, 15.99, and 17.97 MPa, respectively, and the velocity decreases for S-waves at the same three pressures are 12.5%, 9.6%, and 7.7% (the data is supplemented in Table 2) The decrease of the S-wave velocities is about twice as large as that of the P-wave velocities. It is well known that the velocity of S-waves is more sensitive to microcracks oriented parallel to the propagating direction of wave (in this case, it is the loading direction), whereas P-wave velocity is more sensitive to the microcracks oriented perpendicular to the propagation direction of the ultrasound wave. Therefore, the larger decline in the S-wave velocities indicates that the main mechanism triggering sample failure is the development of microcracks parallel or subparallel to the sample's axis. Several previous studies using triaxial loading experiments on sandstone [42; 43; 44] observed that the S-wave/P-wave velocity decline ratio ranged from about 2.5 to 5, which is consistent with the results obtained by this work. The consistency of these results implies that, even when the materials being deformed are different and are subjected to different forms of stress, the damage generated in brittle rock materials may possibly be developed by the same mechanisms. Figure 9: \(Cont.\)Figure 9: Graphs showing the changes in ultrasonic velocities during creep tests: (**a**) P-wave velocities of coal samples measured at 8.03 MPa, 8.98 MPa, 10.00 MPa, 11.98 MPa, 13.00 MPa, 14.02 MPa, 14.97 MPa, and 17.01 MPa; (**b**) P-wave velocities of coal samples measured at 11.02 MPa, 15.99 MPa, and 17.97 MPa; (**c**) S-wave velocities of coal samples measured at 8.03 MPa, 8.98 MPa, 10.00 MPa, 11.98 MPa, 13.00 MPa, 14.02 MPa, 14.97 MPa, and 17.01 MPa; (**d**) S-wave velocities of coal samples measured at 11.02 MPa, 15.99 MPa, and 17.97 MPa. Given the complexities of the normalised ultrasonic wave velocity plotted in Figure 9a or Figure 9c, dynamic moduli (\(E_{d}\)) of the velocities were calculated to supplemented examination of the damage generated during creep.