The following is the first draft of an academic paper. Please help me polish the language.
<3.2.2 Average depth
Figure 7 shows the variation of the average depth of the pipe cross-section with pipe length in Test-1 and Test-2. The sand layer in Test-1 was in contact with a smooth acrylic plate, and the sand layer in Test-2 was in contact with a coarse silicone plate. Except for the part near the outlet hole, the depth of the pipe in Test-2 was greater than that in Test-1, indicating that the roughness degree of the contact surface between the sand layer and the cover plate has a significant impact on the pipe depth. When the cover plate was smooth, the depth of the pipe near the outlet hole was larger. As the length of the pipe increased, the depth of the pipe first rapidly decreased and then stabilized. When the pipe length in Test-1 was greater than 50 mm, the pipe depth changed little and fluctuated around a fix value. The average depth of the whole pipe in Test-1 was 3.1 mm, which was 11.1 times that of d50.
When the sand layer directly contacted the silicone plate, the pipe depth slowly decreased with the increase of the pipe length, and the relationship between the pipe depth and length was approximately linear. The average depth of the entire pipe in Test-2 was 4.0 mm, which was 14.3 times d50. The relationship between pipe depth and length was fitted using the following linear formula:
In this formula, D is the average depth of the pipe cross-section, L is the length of the pipe. The linear correlation coefficient of this formula was -0.69.
Fig. 7  Variation of average depth of pipe cross-section with pipe length in Test-1 and Test-2
The relative compactness of sand sample in Test-2 and Test-3 was 59.6% and 74.9%, respectively, and the variation law of pipe depth in these two tests was similar. The average depth for the whole pipe in Test-2 and Test-3 was 4.0 mm (14.3d50) and 3.8 mm (13.6d50), respectively, with a slight decrease in pipe depth in Test-3. As the compactness of sand layer increased, the depth of the pipe decreased to a certain extent.

3.3 Width characteristics of pipes
Figure 8 shows the variation of the average width of  pipe cross-section with pipe length in Test-1 and Test-2, which can be used to analyze the influence of the roughness degree of the cover plate on the pipe width. Overall, the width of the pipe in Test-2 was greater than that in Test-1, indicating that the rougher the cover plate, the larger the pipe width. The width of the pipe near the outlet hole was greater compared to other parts, mainly due to the continuous erosion of sand near the outlet hole. For Test-1 with a smooth acrylic plate, the pipe width showed a linear decreasing trend as the pipe length increased, indicating the presence of secondary erosion. Secondary erosion is defined as an erosion mechanism that causes the widening and deepening of the pipe [20,21], governed by the shear stress that is exerted by the water on the grains that form the pipe. The relationship between pipe width (W) and length in Test-1 was fitted using the following linear formula:
In this formula, W is the average width of the pipe cross-section and L is the length of the pipe. The linear correlation coefficient of this formula was -0.81, and the absolute value was greater than 0.8, indicating a highly linear correlation.
For Test-2, the sand layer was in contact with a silicone plate, and the average pipe width also showed a slow linear decrease trend as the pipe length increased. By removing four data points with significant deviations from linearity which were close to the outlet hole, and the average pipe width could be fitted using the following linear formula:
The linear correlation coefficient of this formula was -0.92, and the absolute value was greater than 0.8, indicating a highly linear correlation.
Fig. 8 Variation of the average width of pipe cross-section with pipe length in Test-1 and Test-2
Figure 9 shows the variation of average pipe width with pipe length in Test-2 and Test-3, and the relative density of sand samples in Test-2 and Test-3 was 59.6% and 74.9%, respectively. The width of the pipe in Test-3 changed relatively little with the increase of pipe length compared that in Test-2. Within the entire length of the pipe, the average width of the pipe in Test-2 and Test-3 was 31.1 mm and 25.6 mm, respectively. This indicates that the greater the compactness of sand, the smaller the width of the pipe.
Fig. 9 Variation of the average width of pipe cross-section with pipe length in Test-2 and Test-3

3.4 Ratio of width to depth of pipes
The ratio of the average width of the pipe cross-section to average depth is an important indicator for describing the pipe morphology. Figure 10 shows the variation of the width-to-depth ratio in Test-1 and Test-2. The magnitude and change rule of the width-to-depth ratio of the pipe for two tests were similar. As the length of the pipe increased, the width-to-depth ratio first increased and then decreased. The reason for the low value of the ratio near the outlet hole was that the depth of the pipe was relatively large in this part. As the length of the pipe continuously increases, the decrease in width-to-depth ratio was mainly due to the decline of pipe width. The average width-to-depth ratio for the whole pipe in Test-1 and Test-2 were 8.1 and 7.8, respectively.
Fig. 10 Variation of width-to-depth ratio of the pipe with pipe length in Test-1 and Test-2
Table 3 presents the key results of the experiment. With the increase of the roughness degree of cover plate and the compactness of the sand sample, a greater hydraulic gradient for sand boil and pipe reaching upstream level was required. This founding is consistent with existing research findings [22]. The average depth and width of the pipe in Test 2 were the largest, but the average width-to-depth ratios of pipes in the three tests were similar.
Table 3  Key results of the experiment>