## 3 Results and Discussion
### Changes in Acoustic Wave Properties
The competition between compaction and micro-cracking can also be seen on the spatial attenuation curves for Type 2 creep (Figure 14). Both the \(\sim\)10 MPa and the \(\sim\)17 MPa curves show a small increase at initial dilatancy (corresponding to a high radial strain rate) and then follow a downtrend similar to the Type 1 curves when axial compression begins to dominate the creep. The shift point to a moderate increase still closely follows the beginning of the deceleration of compaction, indicating that micro-cracking temporarily becomes a more important mechanism than compaction. However, this increase lasts only 1.5 h and 1 h for samples compressed at 10.00 MPa and 17.01 MPa, respectively, before becoming a stable phase. The stable phase then lasts until the end of test and must mean that the influences of micro-cracking and compression are balanced. Figure 9:0 _Cont._  
Figure 9:1 Graphs showing the spatial attenuation parameters and strain rates plotted versus time for Type 2 creep. Results are shown for tests at: (**a**) 10.00 MPa; (**b**) 17.01 MPa. \(\tau_{a}\), \(\tau_{v}\), \(\tau_{r}\), and \(\alpha_{s}\) denote axial strain rate, volumetric strain rate, radial strain rate, and spatial attenuation parameter, respectively. The dashlines denote the transition points of creep stages. Figure 9:2 Graphs showing the spatial attenuation parameters and strain rates plotted versus time for Type 1 creep. Results are shown for tests at; (**a**) 8.03 MPa; (**b**) 11.98 MPa. \(\tau_{a}\), \(\tau_{v}\), \(\tau_{r}\), and \(\alpha_{s}\) denote axial strain rate, volumetric strain rate, radial strain rate, and spatial attenuation parameter, respectively. The dashlines denote the transition points of creep stages. Motivated by curiosity, we also calculated the spatial attenuation parameter for short-term creep corresponding to Type 3 creep. Two sets of representative data are shown in Figure 15, data for the tests at 11.02 MPa and 15.99 MPa. Probably reflecting the development of vertical cracks depicted in Figure 12, both spatial attenuation curves end with an apparent increase. An initial decline and a U-shaped curve are evident for the sample compressed at 11.02 MPa; this clearly reflects the competition between compaction and cracking. As for the sample compressed at 15.99 MPa, if the interval of sampling were small enough, a curve of similar shape might be visible. During the stages of secondary creep and tertiary creep, the increase of both spatial attenuation curves indicate a dramatic development of micro-cracks, which can also be verified by the high volumetric strain rate and radial strain rate. These observations appear to confirm an inherent consistency between short-term and long-term creep. The mechanical response of samples under creep compression is a result of competition between compaction and cracking, in which the cracking deteriorates the structure and increases the ultrasonic attenuation, whilst the compaction causes the densification along axial axis and reduces attenuation. Figure 9:3 Graph of spatial attenuation parameters and strain rates versus time for Type 3 creep. Results are shown for tests at: (**a**) 11.02 MPa; (**b**) 15.99 MPa. \(\text{r}_{\text{a}}\), \(\text{r}_{\text{v}}\), \(\text{r}_{\text{r}}\), and \(\alpha_{\text{s}}\) denote axial strain rate, volumetric strain rate, radial strain rate, and spatial attenuation parameter, respectively. The dashlines denote the transition points of creep stages.