## 4 Particle Gradation Change after Leaching  
When the leaching of each rare earth sample was completed, a quantity of rare earth particles around the observation points A-D was taken out from the model tank by using a ring knife. After drying these particles, screen tests were carried out to acquire the particle gradation of the rare earth after the leaching. Through comparing the particle masses before and after the leaching, the rate of the mass change for each particle grade can be obtained as follows:  
\[\eta=\frac{M_{\rm a}-M_{\rm b}}{M_{\rm b}}\times 100\% \tag{2}\]  
where \(\eta\) denotes the change rate of the particle mass, \(M_{\rm a}\) is the particle mass after leaching, and \(M_{\rm b}\) is the particle mass before leaching. Figure 12 shows the change rate of the particle mass for each particle grade in the four soil samples. It is clearly seen that after the leaching, the mass of each particle grade changed at different degrees at various observation points. This indicates that the migration of rare earth particles occurs in the entire pile during the leaching. In the standard soil sample S1 (see Figure 12a), the mass change rate of the fine particles that were smaller than 0.15 mm increases monotonically from the observation point A to the observation point D. This means that under the lateral liquid injection conditions, the fine particles migrated from the liquid injection end to the liquid outlet end, and eventually, they settled down near the outlet end. Notably, in the vicinity of the liquid injection end, when the fine particles migrated out, there were no fine particles to replenish it. As a result, the soil near the liquid injection end was dominated by coarse and medium particles. This is also the reason why the permeability coefficient near the liquid injection end \(K_{\rm AB}\) is greater than that at other locations. Figure 11: Variations of the seepage flow with the hydraulic head of leaching liquid. Figure 12: _Cont._Among the four soil samples, the change rate of the particle mass for the fine-medium particle soil sample S2 is the smallest (see Figure 12b). This shows that in this soil sample, the gap between the rare earth particles is smaller, and the fine particles cannot migrate as easily. It corresponds to the slower change of the permeability coefficient in the soil sample S2, as described in Figure 6. In comparison, the particle mass of the medium-coarse particle soil sample S3 changed significantly before and after the leaching (see Figure 12c). Similar to the soil sample S1, the mass change rate of the medium particles within 0.25-0.60 mm increases monotonically from the liquid injection end to the liquid outlet end. It is demonstrated that in this soil sample, the medium particles (also the finer particle component) easily migrate under the lateral liquid injection conditions due to the larger gap between the particles. Consequently, the permeability coefficient in the soil sample S3 is more sensitive to the increasing hydraulic head of the leaching liquid than that in the soil sample S2. Figure 12: Change rate of the particle mass for each grade at different observation points: (**a**) soil sample S1; (**b**) soil sample S2; (**c**) soil sample S3; (**d**) soil sample S4. For the coarse-fine particle soil sample S4 (see Figure 12d), the relative change of the fine particle mass after the leaching was not significant, although its permeability coefficient varied most noticeably among the four soil samples. This because the soil sample S4 has the largest mass of fine particles before the leaching. Unlike the other soil samples, in the soil sample S4, the mass change rate of the fine particles that were smaller than 0.15 mm first increases from the point A to the point C, and then, it decreases from the point C to the point D. This is because in this soil sample, a large number of fine particles exude from the outlet end during the leaching (see Figure 10), resulting in a slump in the fine particle content near the outlet end.