*4.1. E*ff*ect of Particle Size on the Dispersion Coe*ffi*cient*

In order to uncover the effect of particle size on the one-dimensional dispersion coefficient, dispersion tests were performed on a total of six groups of single-grained coral sand samples, with the sample groups having a particle sizes of < 0.1 mm, 0.1–0.25 mm, 0.25–0.5 mm, 0.5–1 mm, 1–2 mm, and 2–5 mm; the groups had particle size ranges within the categories of silt, fine sand, medium sand, coarse sand, gravelly sand, and crushed stone (angular gravel), respectively. These groupings were determined according to the soil classification method in the Code for the Investigation of Geotechnical Engineering (GB50021-2001) (Ministry of Construction of the People's Republic of China, 2009) [16]. The dry density of all samples was 1.3 g/cm<sup>3</sup> .

Figure 7 presents a one-dimensional dispersion curve for single-grained coral sands, which indicates that when the particle size was 0–0.1 mm, the dispersion process consisted of three stages: a drainage stage, a displacement stage, and a stabilization stage. In the drainage stage, the original saturated fluid in the soil column was discharged outward under the displacement of the tracer, a circumstance in which the discharged fluid had the same concentration as the original saturated fluid, thereby leading to a flat dispersion curve. In the displacement stage, with the continuous injection of the tracer, the tracer underwent diffusion in the original saturated solution, in addition to producing the displacement effect. The diffusion "interface" existed in the form of a concentration transition zone between the original saturated fluid and the tracer. When the edge of the transition zone reached the sensor position, the measured concentration of the discharged fluid began to increase, indicative of the onset of the displacement stage, as manifested by the curve slope starting to increase. In the stabilization stage, when the tracer had completely displaced the original saturated fluid, the discharged fluid had a concentration similar to that of the tracer, with the curve reaching the highest value and tending to flatten. *J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 10 of 21

**Figure 7.** One-dimensional dispersion curves of single-grained coral sands*.*  **Figure 7.** One-dimensional dispersion curves of single-grained coral sands.

As revealed by the above observations, different sample groups of different particle sizes exhibited dispersion pattern similarities, although the drainage stage gradually shortened with increasing particle size. The curve's slope in the displacement stage, i.e., the diffusion rate, increased with increasing particle size, and the time taken for the concentration to reach the stabilization stage gradually shortened with increasing particle size. With the exception of the 0–0.1 mm group, the As revealed by the above observations, different sample groups of different particle sizes exhibited dispersion pattern similarities, although the drainage stage gradually shortened with increasing particle size. The curve's slope in the displacement stage, i.e., the diffusion rate, increased with increasing particle size, and the time taken for the concentration to reach the stabilization stage gradually shortened with increasing particle size. With the exception of the 0–0.1 mm group, the other three groups were relatively similar to each other in terms of the parameters of the three stages,

Figure 8 shows the variation pattern of the one-dimensional dispersion coefficient with respect to particle size. The dispersion coefficient of coral sands increased with increasing particle size. When the particle size exceeded 0.25 mm, the dispersion coefficient increased rapidly, with the dispersion coefficient differing by a factor of 202. When the particle size was 0.1–2 mm (i.e., fine sands–gravels), the dispersion coefficient was between 0.152–2.37 cm2/s, with the difference being a factor of approximately 15. However, when the particle size was greater than 2 mm, the change in the dispersion coefficient with respect to particle size became smaller, with the dispersion coefficient tending to reach a constant value as the particle size increased, finally reaching a value of 2.5 cm2/s in this test condition. These observations suggest that 0.25 mm and 2 mm could be considered the

other three groups were relatively similar to each other in terms of the parameters of the three stages,

indicating a significant difference in dispersion characteristics between the particle size 0–0.1 mm and the other particle sizes.

Figure 8 shows the variation pattern of the one-dimensional dispersion coefficient with respect to particle size. The dispersion coefficient of coral sands increased with increasing particle size. When the particle size exceeded 0.25 mm, the dispersion coefficient increased rapidly, with the dispersion coefficient differing by a factor of 202. When the particle size was 0.1–2 mm (i.e., fine sands–gravels), the dispersion coefficient was between 0.152–2.37 cm<sup>2</sup> /s, with the difference being a factor of approximately 15. However, when the particle size was greater than 2 mm, the change in the dispersion coefficient with respect to particle size became smaller, with the dispersion coefficient tending to reach a constant value as the particle size increased, finally reaching a value of 2.5 cm<sup>2</sup> /s in this test condition. These observations suggest that 0.25 mm and 2 mm could be considered the characteristic particle sizes of coral sands. *J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 11 of 21

#### **Figure 8.** Dispersion coefficients of single-grained soils*. 4.2. E*ff*ect of Dry Density on the Dispersion Coe*ffi*cient*

*4.2. Effect of Dry Density on the Dispersion Coefficient*  The effect of the degree of compactness on the one-dimensional dispersion coefficient was investigated using the group of coral sands having a particle size range of 0.25–0.5 mm and dry densities of 1.2 g/cm3 (relative degree of compactness of 1.021), 1.3 g/cm3 (relative degree of compactness of 1.212), and 1.4 g/cm3 (relative degree of compactness of 1.375). The test results, which are shown in Figure 9, indicate that with the increase in density, the displacement stage became longer, the diffusion rate decreased, and the time spent before reaching a steady state increased. reveals that the dispersion coefficient decreased linearly with increasing dry density. **Figure 8.** Dispersion coefficients of single-grained soils. The effect of the degree of compactness on the one-dimensional dispersion coefficient was investigated using the group of coral sands having a particle size range of 0.25–0.5 mm and dry densities of 1.2 g/cm<sup>3</sup> (relative degree of compactness of 1.021), 1.3 g/cm<sup>3</sup> (relative degree of compactness of 1.212), and 1.4 g/cm<sup>3</sup> (relative degree of compactness of 1.375). The test results, which are shown in Figure 9, indicate that with the increase in density, the displacement stage became longer, the diffusion rate decreased, and the time spent before reaching a steady state increased. Figure 10 represents the variation of the dispersion coefficient with the change in dry density, which reveals that the dispersion coefficient decreased linearly with increasing dry density.

Figure 10 represents the variation of the dispersion coefficient with the change in dry density, which

*4.2. Effect of Dry Density on the Dispersion Coefficient* 

reveals that the dispersion coefficient decreased linearly with increasing dry density.

**Figure 8.** Dispersion coefficients of single-grained soils*.* 

The effect of the degree of compactness on the one-dimensional dispersion coefficient was investigated using the group of coral sands having a particle size range of 0.25–0.5 mm and dry densities of 1.2 g/cm3 (relative degree of compactness of 1.021), 1.3 g/cm3 (relative degree of compactness of 1.212), and 1.4 g/cm3 (relative degree of compactness of 1.375). The test results, which are shown in Figure 9, indicate that with the increase in density, the displacement stage became longer, the diffusion rate decreased, and the time spent before reaching a steady state increased. Figure 10 represents the variation of the dispersion coefficient with the change in dry density, which

**Figure 9.** One-dimensional dispersion curves of coral sands with different dry densities.

**Figure 10.** One-dimensional diffusion coefficients of coral sands with different dry densities*.*  **Figure 10.** One-dimensional diffusion coefficients of coral sands with different dry densities.
