# Creep and Hardening Characteristics of Anthracite under Graded Static-Dynamic Coupled Loading
## 4 Discussion  
### Relation between the Strain Increment at Each Stress Level and Graded Loading Rate  
In order to investigate the effect of loading rate on sample strain, the strain increments of the samples at each stress level were analyzed. The composition of the strain increments at each stress level substantially differs for different graded loading rates (Table 5). The variation in the proportion of the instantaneous strain increment with the graded loading rate is depicted in Figure 8.  
The sensitivities of the axial and radial strains to the loading are characterized based on the percentage of the instantaneous strain increments to the total strain increments  
Figure 8: Relation between the instantaneous strain increment proportion and the graded loading rate.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample Number**} & \multirow{2}{*}{
\begin{tabular}{c} **Graded Loading** \\ **Rate** \(V_{I}\) **(mm**\(\cdot\)**s\({}^{-1}\)**)** \\ \end{tabular} } & \multicolumn{2}{c}{\(\Delta\epsilon_{I}\)/\(\Delta\epsilon_{I}\) **(\%)**} & \multicolumn{2}{c}{\(\Delta\epsilon_{I}\)/\(\Delta\epsilon_{I}\) **(\%)**} \\  & & **(Axial)** & \multicolumn{2}{c}{**(Radial)**} \\  & & **Minimum**–**Maximum** & **Average** & **Minimum**–**Maximum** & **Average** \\ \hline H-04 & 0.01 & 57.69–73.85 & 66.54 & 8.85–12.92 & 9.58 \\ H-05 & 0.02 & 52.96–66.61 & 59.27 & 7.12–16.03 & 10.77 \\ H-06 & 0.04 & 33.33–56  
to quantitatively explain the effect of the graded loading rates on the strain increments. Figure 5 shows that these sensitivities and the graded loading rate exhibit an exponential relation. When the graded loading rate is \(<\)0.04 mm/s, the axial strain is dominated by the instantaneous strain, and the radial strain is dominated by the creep strain. Moreover, the radial strain exhibits clear hysteresis. With increasing loading rates, the sensitivities of the axial and radial strains to the loading decrease and increase, respectively. When the loading rate is increased from 0.01 mm/s to 0.1 mm/s, the sensitivity of the axial strain decreases from 66.54% to 28.64%, while that of the radial strain increases from 9.58% to 65.24%.  
A comprehensive analysis shows that with increasing graded loading rate, the sensitivity of the axial strain to the axial loading gradually decreases. Moreover, the axial strain generated by the samples during the loading stage decreases. The axial strain hysteresis effect gradually becomes clear. The sensitivity of the axial strain to the loading shows the most reduction in the linear elasticity stage. Moreover, it exhibits a linear relation with the hierarchical graded loading rate, indicating that the ability of the sample to resist deformation in the linear elasticity stage rapidly increases with increasing graded loading rate, and the hardening characteristics of the samples become clear. The overall sensitivity of the radial strain to the loading exhibits an increasing trend, and the macroscopic performance indicates that the radial expansion of the sample during the loading stage is clear, especially when the graded loading rate is \(>\)0.04 mm/s. The sensitivity of the radial strain to the axial loading is considerably improved with increasing graded loading rate. The results reflect that the axial and radial strains of the samples during the creep process show obvious asynchrony, and the radial strain shows obvious hysteresis, which was also proved in the literature [19].