# Study on Reinforcement Mechanism and Reinforcement Effect of Saturated Soil with a Weak Layer by DC
## 4 Numerical Analysis
### Improvement Mechanism of Nonhomogeneous Saturated Soil Foundation under DC  
To quantify the improvement effect of DC to layered saturated soil foundation, three parameters--effective stress increment \(\Delta\)S\({}_{\text{y}}\)', excess pore water pressure \(\Delta\)p, and the relative degree of reinforcement I\({}_{\text{r}}\)--proposed by [PERSON] and [PERSON] [14] are used. \[\text{I}_{\text{r}}=\frac{\text{D}_{\text{r}}-\text{D}_{\text{r}0}}{100-\text{ D}_{\text{r}0}}\times 100\% \tag{11}\]  
where D\({}_{\text{r}0}\) and D\({}_{\text{r}}\) are the relative density of soil before and after DC, respectively. The relative degree of reinforcement I\({}_{\text{r}}\) is used as it can eliminate the influence of different soil types on the effect of soil improvement [14]. The index of excess pore water pressure ratio \(\Delta\)r\({}_{\text{u}}\) is defined to quantify the liquefaction potential, which is characterized as:  
\[\Delta\text{r}_{\text{u}}=\frac{\Delta\text{u}}{\sigma_{\text{s}}^{\prime}} \tag{12}\]  
where \(\Delta\)u is the excess pore water pressure generated during DC, and \(\sigma_{\text{s}}^{\prime}\) is the initial effective stress before implying the dynamic load. Soil liquefaction is supposed to happen as \(\Delta\)r\({}_{\text{u}}\) reaches 1.0. In Figures 7-9, the evolutions of \(\Delta\)S\({}_{\text{y}}\)', I\({}_{\text{r}}\), and \(\Delta\)p in a foundation without weak layers are plotted in the left half of each figure, while those in a foundation with an embedded weak layer with a thickness of 1.0 m are plotted in the right half of each figure. Other parameters in these foundations were set as identical. It is shown that at the first stage of loading (t = 0.01 s), the excess pore water pressure of these two conditions had a similar distribution law. As a continuation of wave propagation (Figure 7b,c), it can be observed that the maximum value of pore pressure bulk occurred nearby the embedded weak layer. For the foundation without a weak layer and with a weak layer, the excess pore water pressure reached the same values of 750 kPa at 0.01 s, which increased to 1500 kPa for the soil with an embedded weak layer and attenuated to 425 kPa for soil without an embedded weak layer at 0.04 s. The dissipation of the excess pore water pressure in the foundation with an embedded weak layer took a long time due to the lower permeability of the weak layer. In contrast, the excess pore water pressure dissipates rapidly in the ground without an weak layer due to the relatively high permeability of soil. It is easy to conclude that the presence of an embedded weak layer has a significant influence on the distribution of the excess pore pressure. The dynamic reinforcement effect greatly depends on transformation efficiency of the impact load (i.e., effective stress increment), which is finally transferred to the soil skeleton, compacting the soil into a denser state. As shown in Figure 8, at the initial stage of DC, increments of the effective stresses in the foundation with a weak layer were transmitted into the upper soil of weak interlayer, whose distribution is basically in consistent with that of the soil without a weak interlayer. In contrast, the pore water pressure at the same time propagated into the embedded weak layer. It is indicated that the wave characteristic of excess pore pressure and effective stress belong to fast wave and slow compressional wave, respectively [35]. Then, the effective stress wave penetrated into the embedded weak soil layer. However, the increase in effective stress became zero in the embedded weak layer, which was around 215 kPa for soil without an embedded weak layer at the same position. This is because the continuous DC induced the development of pore water pressure in the embedded weak layer of silty clay and the excess pore pressure slowly dissipated, leading the majority of the impact load to be transformed into the excess pore water pressure. Only a small part of the impact load went through the embedded weak interlayer and entered the lower soil.