## 4 Experimental Results and Discussion
### Volume Change of Soil Specim  
As previously stated, the soil specimen volume change is measured by the volume change indicator, whereas pore water pressure is measured by tensiometer during each test. Combining this volume change and the initial void ratio, the void ratio at any period, e, can be calculated as follows:  
\[e=\frac{G_{\mathrm{s}}\rho_{\mathrm{w}}}{\frac{\rho_{d}V_{0}}{(V_{0}+\Delta V )}}-1 \tag{12}\]  
where \(G_{\mathrm{s}}\) is specific gravity, \(\rho_{d}\) is the dry density of compacted soil specimen, \(V_{0}\) is the volume of soil specimen at an initial state, and \(\Delta V\) is its volume change. Figure 8 shows the change in void ratio obtained from this study and [PERSON]'s research for the soil specimens at steady state [54]. The numbers denote negative pore water pressure at that void ratio. The negative pore water pressure with the gravimetric water content of 0.07 has exceeded the measurement range of the tensiometer (i.e., 500 kPa), which is not shown in Figure 8. At each given temperature, the void ratio increases with its gravimetric water content. It is due to the relative movement of the water phase in the soil specimen. Similar changes can also be found in [PERSON] et al. [54; 55]. On the other hand, at each given gravimetric water  
Figure 7: Comparison of average volumetric air flow rate under different pressure drops across the specimen (data obtained from [PERSON] et al. [24]).  
content, as the temperature increases, the negative pore water pressure decreases, whereas the void ratio increases. It is because the increase in the temperature leads to a decrease in the surface tension of contractile skin [56; 57] and thus a negative pore water pressure with a maximum decrease of 11.1%. As the negative pore water pressure decreases, the force equilibrium between soil particles is broken, and thus the volume of the soil specimen swells as well. For the volume change, when the temperature increases from 25 \({}^{\circ}\)C to 60 \({}^{\circ}\)C and the initial gravimetric water content is 0.3, the void ratio exhibits an increase of 0.053, corresponding to a maximum increment of 5.4%. These results differ from those obtained from [PERSON] and [PERSON] [58], in which the specific volume (the inverse of density) decreased as the temperature increased from 25 to 60 \({}^{\circ}\)C. It is noted that the condition used by [PERSON] and [PERSON] [58] was suction-controlled. The influence of the temperature on pore water pressure was ignored.  
In addition, in order to verify the reliability of the obtained data, the volumetric shrinkage curve fitted by the experimental data is compared with the curve in the published research. [PERSON]'s equation [47] of estimating the volumetric shrinkage curve is best fitted to the experimental data of soil specimens. The fitting parameters (A\({}_{\text{sh}}\), B\({}_{\text{sh}}\), and C\({}_{\text{sh}}\)) in [PERSON] et al.'s equation, the best fitted curves, and [PERSON]'s fitted curve [54] are illustrated in Figure 8. The curve obtained in this study has the same trend as [PERSON]'s curve. As the water content increases, the void ratio remains unchanged at first, and then the change rate of the void ratio gradually rises until it reaches a constant value. The difference between the curves is significant for the initial constant minimum void ratio, curvature, and rate of change of void ratio. The three differences are represented by three parameters (A\({}_{\text{sh}}\), B\({}_{\text{sh}}\), and C\({}_{\text{sh}}\)), respectively. Moreover, it is noteworthy that an increase in A\({}_{\text{sh}}\) corresponds to a proportional increase in B\({}_{\text{sh}}\), aligning with [PERSON]'s findings [59; 60] and further validating the reliability of the acquired data.