## 2 Experimental Principles and Method
### Darcy Flow Experiment  
In order to obtain the actual permeability coefficient of the quartz sand samples and calculate the permeability, a Darcy seepage experiment device was used to conduct seepage experiments on quartz sand samples with different grain sizes. Since the sample was highly water-permeable, the measurement was carried out via the constant head method. The experimental instrument is shown in Figure 5; the current experiment system is mainly comprised of five parts:  
* Water supply device: This ensured the continuous replenishment of the experimental water and kept the water head stable during the experiment. * Permeation device: An acrylic cylinder was used to place the experiment sample, the upper end was equipped with a water inlet, the side was equipped with a pressure measuring hole, the lower end was equipped with a water outlet and the bottom was equipped with a permeable filter plate. * Pressure measuring device: This connected the pressure-measuring tube with the pressure-measuring hole to measure the pressure head on different sections. * Drainage device: This set a series of round holes in the piezometric tube to adjust the drainage water level. * Other equipment: A stopwatch, 1000 mL measuring cylinder, beaker, funnel, glass rod, thermometer, tube clamp, rubber tube, suction balloon, etc. Before the formal experiment, we first determined the relationship between the permeability of the quartz sand sample and the head loss and tested the experimental instrument. After confirming that the experimental instrument was in good condition, a permeability measurement of 8 kinds of homogeneous quartz sand samples with different grain  
Figure 4: Experiment in outdoor laboratory tank. Figure 5: Schematic diagram of Darcy seepage tester. sizes was carried out. Furthermore, according to [PERSON]'s law, the seepage flow (\(Q\)) of the cross-section through the infiltration device was found to be proportional to the column cross-section (\(A\)) and the hydraulic slope (\(I\)) and was related to the hydraulic conductivity, \(K\)[31]. \[Q=KAI \tag{1}\]  
\[I=(H_{2}-H_{1})/L. \tag{2}\]  
Here, \(I\) represents the hydraulic gradient, \(H_{1}\) and \(H_{2}\) are the heads of the piezometer and \(L\) is the length of the seepage path and the units are meters. The experimental process was as follows:  
* Connecting the instrument: Check the state of the instrument (for example, whether the piezometer tube and the infiltration device are airtight) and record the inner diameter of the infiltration device, the distance between the piezometer tubes and other parameters. * Filling the sample: First, we installed a permeable filter plate at the bottom of the infiltration device, then loaded the sample. Each time a certain thickness was loaded, a certain degree of vibration was performed with a glass rod. * Saturated sample: We injected water from top to bottom until a water film appeared on the surface of the sample. * Experimental measurement: After the water level of the piezometric pipe was stable, we recorded the piezometric water level and started to measure the seepage flow out of the permeation device within a certain period of time. After repeating the measurement, we changed the hydraulic slope of the device and repeated the above process for subsequent measurements. In order to prevent the osmotic pressure of the device from changing too drastically and damaging the original structure of the sample, the hydraulic gradient was increased or decreased step by step to avoid jumping changes. The permeability coefficient (\(K\)) can be used to evaluate the difficulty of the fluid passing through the pore framework of rock and soil, and its definition is shown in Equation (3). \[K=k\rho g/\mu \tag{3}\]  
Here, \(\rho\) is the fluid density, \(g\) is the acceleration due to gravity and \(\mu\) is the hydrodynamic viscosity coefficient. The Darcy seepage experiment can be used to test samples of different grain sizes.