# Investigating the Physical Mechanisms of Quicksand Using a Custom-Designed Experimental Apparatus
## 3 Result  
### Permeability Analysis of Quartz Quicksand  
Experimental results delineate the permeability variation patterns of quartz sand under distinct particle gradation. The relationship between median particle diameter (d\({}_{50}\)) and seepage discharge is plotted in Figure 3a. Key findings reveal that seepage discharge remains independent of d\({}_{50}\) across all hydrodynamic velocity conditions, indicating minimal influence of median particle size on porosity for the five specimen groups.  
To ensure the accurate quantification of the seepage process, the outflow at the top of the permeameter was measured for each sample group under five different water injection rates. This allowed the total seepage for each stage to be determined. Theoretical seepage discharge values were calculated based on hydrodynamic velocity and duration, as shown in Figure 3a. Comparing the actual seepage flow with the theoretical seepage values helps reveal the impact of particle structure reconstruction on the changes in seepage channels while also quantifying the relationship between dynamic water rate and seepage response. The specific details are as follows: Experimental results demonstrate that when the hydrodynamic velocity ranges between 25 and 50 mL/min, interparticle flow resistance causes the actual discharge to be slightly lower than theoretical values. In the 50-150 mL/min range, particle reorganization in the quartz sand specimens accelerates water flow, resulting in actual discharge values that closely match theoretical predictions. At 200 mL/min, the actual discharge of all specimens exceeds theoretical values due to significant particle spatial rearrangement and the combined effects of capillary siphoning in interparticle pores, which collectively increase flow velocity.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{4}{c}{**Water Injection Rate/(mL-min\({}^{-1}\))**} & \multicolumn{2}{c}{**Water**} \\ \cline{2-7}  & **Stage 1** & **Stage 2** & **Stage 3** & **Stage 4** & **Stage 5** & **Temperature/\({}^{0}\)C** \\ \hline
1\# & 25 & 50 & 100 & 150 & 200 & \\
2\# & 25 & 50 & 100 & 150 & 200 & \\
3\# & 25 & 50 & 100 & 150 & 200 & \\
4\# & 25 & 50 & 100 & 150 & 200 & \\
5\# & 25 & 50 & 100 & 150 & 200 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Design of water injection rates for various groups of quartz sands with different gradations.  
Figure 2(a) clearly demonstrates that the seepage discharge of quartz sand specimens exhibits a marked increase with rising hydrodynamic velocities. The relationship between seepage discharge and hydrodynamic velocity is plotted in Figure 2(b), revealing a distinct positive correlation that remains consistent across all particle gradations. This correlation primarily results from the linear, proportional increase in injection rates controlled by the water supply unit. These findings further validate that the median particle diameter (d50), as an indicator of different gradations, has limited influence on permeability characteristics. In civil engineering practice, the use of quartz sand with particle sizes ranging from 0.080 to 8.000 mm for fill applications does not significantly alter permeability behavior, aligning with the performance of natural sandy soil foundations.