## 3 Results and Discussion
### Changes in Acoustic Wave Properties
As for long-term creep, in spite of the measures to reduce the effects of sample inhomogeneity, the variations in the normalised dynamic moduli are still independent of stress level to a certain extent. This suggests that the structural deformation in the sample is not completely dominated by the compression-induced tensile cracking just described above. Further evidence can be obtained by examining the fluctuations of the normalised dynamic moduli over time. Except for the relatively stable moduli at 10.00 MPa and 13.00 MPa, all of the moduli in Figure 10a exhibit fluctuations that are difficult to explain with a single deformational mechanism. We attributed the fluctuations to the active involvement of multiple structural deformations such as particle dislocation, pore closure, matrix cracking, compaction of clay mineral, and so forth. It has been shown that ultrasonic velocity is determined by the fastest wave front passing through the most favourable portion of the rock. In practice, this means the velocity is the speed of the wave front affected by the fewest defects [51]. However, the multiple deformations alter the internal structure of the sample in different ways over long periods of time and this results in the ultrasonic velocity (and its dynamic modulus) fluctuating. This means a more precise ultrasonic parameter is required to interpret the inner deformational mechanisms of long-term creep correctly. [PERSON] et al. [51] proposed a spatial attenuation parameter (\(\alpha_{\mathrm{s}}\)) summing the wave attenuation caused by both defects and discontinuities in the rock. Hence, this parameter should allow an investigator to improve their assessment of the deformation  
Figure 12: Sketch showing the creep stress induced deterioration in a sample of anthracite. The arrow indicates the progression of structural degradation. in the sample. This spatial attenuation parameter is thus is a more appropriate tool for evaluating long-term creep data. The \(\alpha_{\mathrm{s}}\) is expressed as  
\[\alpha_{\mathrm{s}}=\frac{20\times log\left(\frac{A_{m1}}{A_{m2}}\right)}{L}, \tag{8}\]  
where \(A_{m1}\) is the maximum amplitude generated by the transducer, \(A_{m2}\) is the maximum amplitude recorded by the receiver, and \(L\) is the length of the sample. By using Equation (8), the spatial attenuation parameters for long-term creep can be obtained. As explained in Section 3.1, for this investigation creep has been classified into three types. In order to explore the deformation underlying different creep mechanisms, the spatial attenuation parameters and the fitting curves for Types 1 and 2 strain rates are plotted versus time in Figures 13 and 14, respectively. (In Figure 13, two sets of representative experimental data are selected to present). In contrast to the irregular fluctuations observed in ultrasonic velocities and dynamic moduli, the spatial attenuation parameters show clear trends. For Type 1 creep, the spatial attenuation parameters at both \(\sim\)8 MPa and \(\sim\)12 MPa gradually decline to a relatively stable value and then begin to rise. The initial reduction is expected because the samples are being subjected to a high compressive strain rate along their axis which results in a denser packing pattern along the direction of axial stress, but the subsequent flat and increasing portions of the curve cannot be explained by compression. Through examining the correlation between the strain rates and the spatial attenuation parameter, we found that the presence of the transition point (from the decline to a stable stage) of \(\alpha_{\mathrm{s}}\) is slightly later than it of the peak value of axial strain rate. The peak of axial strain rate is the beginning of the deceleration of compaction. Obviously, a different mechanism balances the influence of compaction on attenuation and tends to dominate the \(\alpha\)s curve at the stage of secondary creep. The most probable mechanism that can achieve this result is micro-cracking in the coal matrix.