# Study on Reinforcement Mechanism and Reinforcement Effect of Saturated Soil with a Weak Layer by DC
## 4 Numerical Analysis
### Parametric Analysis
#### 4.2.1 Influences of Thickness of the Embedded Weak Layer  
The numerical simulation of DC was performed with the thickness of soft interlayer ranging from 0.4 to 2.0 m to investigate the effect of the thickness of the weak interlayer on the reinforcement effect of soft soil stratum and the rising of pore water pressure in embedded weak layer. The left half of each figure presents the foundation without an embedded weak layer, while the right half represents the foundation with an embedded weak layer (see cases 1 to 4 in Table 4).  
Figure 10 shows the distribution of \(\mathrm{I_{r}}\) in grounds with a weak layer of different thicknesses. The white curve represents the zone of \(\mathrm{I_{r}}\) = 7.7%. Figure 11 describes cloud lines of \(\mathrm{I_{r}}\) = 7.7% for different thickness of embedded weak layer. It can be found that the zone of \(\mathrm{I_{r}}\) = 7.7% of the soil above the weak layer basically did not change with the thickness of the interlayer, whereas the reinforcement range of the soil below the weak layer decreased with the increase of the thickness of the interlayer. In ground with a thin interlayer (Figure 10a,b), the damping energy can penetrate through the embedded weak layer into the underlying soil. However, as the embedded weak layer became thicker, the improvement effect to the lower soil became weakened, indicating that the embedded weak layer prevented the transmission of damping energy.  
Figure 12 shows the distribution of the excess pore water pressure ratio in grounds with embedded weak layer of different thickness. It can be seen that the liquefied zone (\(\mathrm{\Delta r_{u}}\) < 1.0) was mainly in the embedded weak layer, and the range of liquefied zone increased with the increase of the thickness of the embedded weak layer. The results indicate that the excess pore pressure in the ground with an embedded weak layer accumulated as DC continued, resulting in failure of effective reinforcement to the embedded weak layer. Moreover, the maximum excess pore pressure ratio of the upper soil without a weak interlayer was generally less than 0.2, indicating that the pore pressure dissipated quickly, and a better reinforcement effect was obtained. The excess pore water pressure ratio \(\mathrm{\Delta r_{u}}\) within the soil below the embedded weak layer was greater than that in the ground without an embedded weak layer at the same depth. It can be concluded that the presence of an embedded weak layer makes the pore water cannot be drained in time, resulting in a continuous accumulation of pore water pressure.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case**} & **Groundwater** & **Depth of Soft** & **Thickness of Soft** & **Tamping** \\  & **Table (m)** & **Interlayer (m)** & **Interlayer (m)** & **Energy (kN\(\cdot\)m)** \\ \hline
1 & 2.0 & 3.0 & 0.4 & 3000 \\
2 & 2.0 & 3.0 & 1.0 & 3000 \\
3 & 2.0 & 3.0 & 1.6 & 3000 \\
4 & 2.0 & 3.0 & 2.0 & 3000 \\
5 & 2.0 & 0.4 & 0.4 & 300  
Figure 11: Cloud lines of I\({}_{\rm r}\) = 7.7% for different thickness of embedded weak layer.  
Figure 10: Distributions of I\({}_{\rm r}\) in grounds with different thickness of embedded weak layer. (**a**) 0.4 m; (**b**) 1 m; (**c**) 1.6 m; (**d**) 2.0 m.