# Complex Variable Solution for Stress and Displacement of Layered Soil with Finite Thickness
## 4 Analysis and Discussion
### Influence of Layered Soil on Surface Settlement and Additional Stress Distribution in Soil  
When \(H_{1}=H_{2}=30\;m\), \(G_{1}=1.0\;\)MPa, \(\mu_{1}=\mu_{2}=0.2\), the distribution of base pressure is \(p_{y}(x_{1})=-3(4-x_{1}^{2})/8\), and other parameters are the same as those described in Section 4.1. Figure 11 shows the surface settlement curve when \(G_{2}/G_{1}\) is \(0.1,0.5,1.0,20\) and \(10.0\), respectively. It can be seen from Figure 11 that the smaller the shear modulus ratio \(G_{2}/G_{1}\), the greater the surface settlement. The influence of the change in \(G_{2}/G_{1}\) on the surface settlement can be divided into two scenarios: when \(G_{2}/G_{1}>1\), the change in \(G_{2}/G_{1}\) has little influence on the surface settlement, when \(G_{2}/G_{1}<1\), the change in \(G_{2}/G_{1}\) has a great influence on the surface settlement. Figure 12 shows the \(\sigma_{1,x}\) curves (solid line) of the lower boundary of the first layer when \(G_{2}/G_{1}\) is \(0.1,0.5,1.0,20\) and \(10.0\) and the \(\sigma_{2,x}\) curves (dotted line) of the upper boundary of the second layer when \(G_{2}/G_{1}\) is \(0.1,\) and \(10.0\). Figure 13 shows the \(\sigma_{1,y}\) curve on the contact surface, and Figure 14 shows the \(\tau_{1,xy}\) curve on the contact surface. Figure 11: Effect of layered soil on surface settlement. Figure 12: Effect of layered soil on horizontal normal stress at interface. Figure 13: Effect of layered soil on vertical normal stress at interface. It can be seen from Figure 12 that with the decrease in the shear modulus ratio \(G_{2}/G_{1}\) of the two layers of soil, the maximum value of \(\sigma_{1,x}\) (absolute value) of the lower boundary of the first layer of soil decreases at first and then increases, and the tensile stress occurs. Moreover, with the decrease in \(G_{2}/G_{1}\), the tensile stress increases. Compared with the first layer, \(\sigma_{2,x}\) on the upper boundary of the second layer is very small and the change in \(G_{2}/G_{1}\) has little effect on \(\sigma_{2,x}\). Therefore, this paper only shows the \(\sigma_{2,x}\) curves when \(G_{2}/G_{1}\) is 01, 100 respectively. As can be seen from Figure 13, when the soft soil layer is covered by the hard soil layer (\(G_{2}/G_{1}>1\)), near \(x=0\), the \(\sigma_{1,y}\) (absolute value) on the contact surface is larger than that of homogeneous soil (\(G_{2}/G_{1}=1\)), but in the distance, it is smaller than that of homogeneous soil, that is, the stress concentration phenomenon occurs near \(x=0\). When the hard soil layer covers the soft soil layer (\(G_{2}/G_{1}<1\)), the \(\sigma_{1,y}\) on the contact surface is smaller near \(x=0\) than that of the homogeneous soil layer, but larger in the distance than that of the homogeneous soil layer, which is known as the stress diffusion phenomenon. At this time, the vertical normal stress distribution on the contact surface is relatively uniform, so the vertical deformation of the lower soil will be relatively uniform, but it can be seen from Figure 12 that the horizontal tensile stress of the lower boundary of the upper soil will be relatively large. It can be seen from Figure 14 that with the decrease in \(G_{2}/G_{1}\), the shear stress \(\tau_{1,xy}\) (absolute value) on the contact surface gradually decreases. When \(G_{2}/G_{1}>1\), the change in \(G_{2}/G_{1}\) has little effect on the shear stress distribution on the contact surface, while when \(G_{2}/G_{1}<1\), the change in \(G_{2}/G_{1}\) has a greater effect on the shear stress. Taking the same parameters as described in Section 4.1, since the base pressure is symmetrical about the \(y\)-axis, there are only two normal stress components on the \(y\)-axis, and the shear stress component is 0. Figure 15 shows the variation in the two normal stresses on the \(y\)-axis with depth \(h\). At the surface, the horizontal normal stress is basically equal to the vertical normal stress.