*4.3. E*ff*ect of Particle Gradation on the Dispersion Coe*ffi*cient*

in Figure 12.

*4.3. Effect of Particle Gradation on the Dispersion Coefficient*  To simulate natural-gradation sands, stepwise removal of the particles smaller than a certain size was conducted in order to change the gradation [17]. This was followed by one-dimensional dispersion tests on coral sands of different gradations to investigate the effect of particle gradation on the one-dimensional dispersion coefficient. The sample dry density was 1.3 g/cm3 and the gradation parameters of each sample are listed in Table 2 [18]. As shown by the data, all the samples were poorly graded coral sands, with the exception of the natural gradation sands. The gradation To simulate natural-gradation sands, stepwise removal of the particles smaller than a certain size was conducted in order to change the gradation [17]. This was followed by one-dimensional dispersion tests on coral sands of different gradations to investigate the effect of particle gradation on the one-dimensional dispersion coefficient. The sample dry density was 1.3 g/cm<sup>3</sup> and the gradation parameters of each sample are listed in Table 2 [18]. As shown by the data, all the samples were poorly graded coral sands, with the exception of the natural gradation sands. The gradation curves of the samples are displayed in Figure 11 and the dispersion coefficient curves are illustrated in Figure 12.


No. 5 2.55 1.5 1.2 0.735 2.125

curves of the samples are displayed in Figure 11 and the dispersion coefficient curves are illustrated **Table 2.** Gradation parameters of the samples.

**Figure 11.** Gradation curves of the samples*.* 

in Figure 12.

**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*.* 

**Table 2.** Gradation parameters of the samples. **Sample d60 d30 d10 Cc Cu** No. 1 2.5 0.52 0.05 2.163 50.000 No. 2 2.5 0.52 0.15 0.721 16.667 No. 3 2.5 0.6 0.31 0.465 8.065 No. 4 2.5 0.9 0.6 0.540 4.167

To simulate natural-gradation sands, stepwise removal of the particles smaller than a certain size was conducted in order to change the gradation [17]. This was followed by one-dimensional dispersion tests on coral sands of different gradations to investigate the effect of particle gradation on the one-dimensional dispersion coefficient. The sample dry density was 1.3 g/cm3 and the gradation parameters of each sample are listed in Table 2 [18]. As shown by the data, all the samples were poorly graded coral sands, with the exception of the natural gradation sands. The gradation curves of the samples are displayed in Figure 11 and the dispersion coefficient curves are illustrated

*4.3. Effect of Particle Gradation on the Dispersion Coefficient* 

**Figure 11.** Gradation curves of the samples.

**Figure 12.** One-dimensional dispersion coefficients of samples with different gradations.

**Figure 12.** One-dimensional dispersion coefficients of samples with different gradations*.*  As shown in Figure 12, the dispersion coefficient of the coral sands gradually increased with increasing d10. Following the removal of soil particles smaller than 0.25 mm (d10 increased to 0.31 mm from the initial 0.05 mm), the dispersion coefficient of the coral sands increased dramatically. After removal of the soil particles smaller than 0.5 mm (d10 exceeded 0.6 mm), the dispersion coefficient of the coral sands tended to reach a constant value. These results suggest that 0.25 mm and 2 mm were As shown in Figure 12, the dispersion coefficient of the coral sands gradually increased with increasing d10. Following the removal of soil particles smaller than 0.25 mm (d<sup>10</sup> increased to 0.31 mm from the initial 0.05 mm), the dispersion coefficient of the coral sands increased dramatically. After removal of the soil particles smaller than 0.5 mm (d<sup>10</sup> exceeded 0.6 mm), the dispersion coefficient of the coral sands tended to reach a constant value. These results suggest that 0.25 mm and 2 mm were the characteristic particle sizes for the dispersion properties of graded coral sands.

### the characteristic particle sizes for the dispersion properties of graded coral sands. **5. Analysis of the Dispersion Mechanisms in Coral Sands**

dispersion tests, were performed on the coral sands in this study.

*5.1. Molecular Diffusion in Coral Sands* 

**5. Analysis of the Dispersion Mechanisms in Coral Sands**  There are many significant factors affecting solute transport, such as convection, mechanical dispersion, molecular diffusion, interactions between the solid phase and solute (such as dissolution and adsorption), chemical reactions within the solution, and other source–sink solute interactions (such as attenuation of radioactive elements and absorption of certain solutes by crop roots) [19]. Among these, mechanical dispersion and molecular diffusion are collectively referred to as dispersion. Studies have shown that mechanical dispersion and molecular diffusion generally occur simultaneously during solute transport, although they exhibit different variation patterns with changing average pore flow velocity. When the flow velocity is low, molecular diffusion is stronger than mechanical dispersion. In contrast, when the flow velocity is high, mechanical dispersion is There are many significant factors affecting solute transport, such as convection, mechanical dispersion, molecular diffusion, interactions between the solid phase and solute (such as dissolution and adsorption), chemical reactions within the solution, and other source–sink solute interactions (such as attenuation of radioactive elements and absorption of certain solutes by crop roots) [19]. Among these, mechanical dispersion and molecular diffusion are collectively referred to as dispersion. Studies have shown that mechanical dispersion and molecular diffusion generally occur simultaneously during solute transport, although they exhibit different variation patterns with changing average pore flow velocity. When the flow velocity is low, molecular diffusion is stronger than mechanical dispersion. In contrast, when the flow velocity is high, mechanical dispersion is stronger than molecular diffusion. In order to reveal the roles of these two mechanisms in the solute dispersion process of coral sands,

stronger than molecular diffusion. In order to reveal the roles of these two mechanisms in the solute

Figure 13 depicts a curve showing the diffusion concentrations of solute molecules in coral sands having different particle sizes. *ENaCl* is the conductivity measured by the left sensor and *Ewater* is measured by the right sensor, with *EMed* = (*ENaCl* + *Ewater*)/2. When there was a concentration gradient in the saturated porous medium and the pore flow velocity was 0, the NaCl solution concentrations gradually decreased and increased in the left and right samples, respectively, until the two concentrations reached a relative equilibrium. It is noteworthy that the concentrations of the NaCl solution on both sides were not necessarily the same when equilibrium was reached; this was due to the fact that when the concentration gradient was low (defined as the limiting concentration gradient at equilibrium, ranging from 0–1, with larger values representing larger concentration gradients at pore tortuosity tests, as well as molecular and mechanical dispersion tests, were performed on the coral sands in this study.
