# One-Dimensional Consolidation of Multi-Layered Unsaturated Soil with Impeded Drainage Boundaries
## 4 Verifications and Examples
### Worked Examples
The difference resulting from this influence is slightly small in the initial stage, and then it gradually increases with time passing. Later, the induced difference decreases or even disappears. Furthermore, Figure 7a,b show the evolutions of normalized soil settlement under constant and exponential loads, respectively. Being similar to the results in Figure 5a,b, the normalized soil settlement undergoes two distinct developing stages and the influence of the drainage parameter above mainly occurs at the first stage. The larger the drainage parameter of the air phase is, the faster the soil settles. Once the value of this drainage parameter is larger than 100, the curves of the soil settlement also tend to develop as the same pattern. Under this scenario, the influences stemming from the drainage parameter related to the air phase can be ignored, and the top surface approaches full drainage to the air phase. Figure 4: Pore-air pressure evolutions with different \(R_{\text{ta}}\): (**a**) constant load; and (**b**) exponential load. The second worked example adopts the changing drainage parameter of the water phase at the top surface whereas that of the air phase is taken as \(R_{\text{ta}}=5\). For this example, the evolutions of excess pore-air pressure under the external excitations of constant load and exponential load are shown in Figure 8a,b, and the evolutions of excess pore-water pressure for the same external excitations are illustrated in Figure 9a,b, respectively. As observed, this drainage parameter has no influence upon the evolution of excess pore-air pressure while it shows a pronounced effect on the dissipation of excess pore-water pressure. This influence is different from that caused by the drainage parameter of air phase, as shown in Figures 4 and 5. This phenomenon can be explained that the excess pore-water pressure dissipates significantly after the excess pore-air pressure dissipates completely, as depicted in Figures 5 and 9. Herein, the drainage parameter of the water phase mainly induces a pronounced difference during the later period of the dissipation of excess pore-water pressure. Thus, a change in this drainage parameter will not produce an increase in the dissipation of excess pore-water pressure. Figure 5: Pore-water pressure evolutions with different \(R_{\text{ta}}\): (**a**) constant load; and (**b**) exponential load. Figure 7: Evolutions of soil settlement with different \(R_{\text{ta}}\): (**a**) constant load; and (**b**) exponential load. effect on the evolution of excess pore-air pressure. In general, the larger drainage parameter of the water phase gives rise to a faster dissipation of excess pore-water pressure. When the value of this drainage parameter is larger than 100, its influences on the evolution of excess pore-water pressure can be disregarded. Furthermore, for the situation of the constant load, the distributions of excess pore-air pressures and those of excess pore-water pressures at different times are shown in Figure 10a,b. The results show that the drainage parameter of the water phase does not influence the distributions of excess pore-air pressure at all, but it affects those of excess pore-water pressure significantly. This phenomenon is identical to that in Figures 8 and 9. For the excess pore-water pressure, the larger drainage parameter generally brings about a quicker dissipation. During the consolidation process, the difference caused by this drainage parameter firstly increases to a noticeable value, then gradually decreases or even disappears. Being similar to the phenomena of Figure 6a,b, this drainage parameter initially delivers a noticeable influence at the position near the top surface, and then gradually affects the positions far away. Furthermore, Figure 11a,b demonstrate the changes of the soil settlement induced by the constant and exponential loads, respectively. As seen, the drainage parameter of the water phase mainly produces a noticeable influence during the later period of the soil settling process.