# Seismic Isolation Effect of Non-Water Reacted Two-Component Polymeric Material Coating on Tunnels
## 4 Results and Discussion of Numerical Analysis
### Effect of Layer Density and Elastic Modulus(Case 1 to 8)  
The tensile stresses and absolute values of compressive stress on the lining and NRTCPM layer decrease obviously when the layer density decreases, and their variations tend to be similar, as shown in Figures 9-12.  
Taking the eight points on the NRTCPM layer as an example, as the layer density decreases from 0.54 g/cm\({}^{3}\) to 0.17 g/cm\({}^{3}\), the elastic modulus decreases from 228 MPa to 17.2 MPa and the Poisson's ratio increases from 0.1 to 0.25, while the compressive and tensile principal stresses go down at the same time (Figures 9 and 10). When the coating layer density decreases from 0.33 g/cm\({}^{3}\) to 0.28 g/cm\({}^{3}\) and from 0.28 g/cm\({}^{3}\) to 0.2 g/cm\({}^{3}\), the tensile stresses and absolute values of the compressive stress decrease sharply, while when the density decreases from 0.2 g/cm\({}^{3}\) to 0.17 g/cm\({}^{3}\), the tensile stresses and absolute values of the compressive stress decrease gradually. The reduction rate of the tensile stresses and absolute values of the compressive stress differs at different stages. We can see from Figure 9 that the tensile stress declines slowly at every point as the density of NRTCPM decreases from 0.54 g/cm\({}^{3}\) to 0.4 g/cm\({}^{3}\), and then rapidly within the medium density. Finally, the tensile stress at every point declines gently again. To be specific, the largest tensile stress drop value from Point No. 9 to Point  
Figure 8: Vertical time histories (**a**) and Fourier amplitude spectra (**b**).  
No. 16 is 261 KPa at Point No. 14 when the density of the NRTCPM layer decreases from 0.33 g/cm\({}^{3}\) to 0.28 g/cm\({}^{3}\), and 125 KPa at Point No. 12 when its density decreases from 0.28 g/cm\({}^{3}\) to 0.2 g/cm\({}^{3}\), respectively. As shown in Figure 10, the compressive stress increases by 326 KPa at Point No. 12 when the density of the NRTCPM layer decreases to 0.28 g/cm\({}^{3}\) from 0.33 g/cm\({}^{3}\), and the compressive stress goes up 127 KPa at Point No. 15 when the density of the NRTCPM layer decreases to 0.2 g/cm\({}^{3}\) from 0.28 g/cm\({}^{3}\).  
Figure 11: Compressive stress of eight points on the lining.  
Figure 9: Tensile stress of eight points on the NRTCPM layer.  
The changing trends of the tensile stresses and absolute values of the compressive stress on the lining shown in Figures 11 and 12 are the same as the changing trends of these stresses on the NRTCPM layer from Figures 9 and 10. When the density of the isolation layer is 0.2 g/cm\({}^{3}\), the tensile stress and absolute value of the compressive stress on the lining can be reduced by 80% on average compared with a tunnel without the condition of an isolation layer around it. It can be seen from Figure 11 that the compressive stresses increase by an average of 2902 KPa and 1304 KPa on all points when the density of the NRTCPM layer changes from 0.33 g/cm\({}^{3}\) to 0.28 g/cm\({}^{3}\) and from 0.28 g/cm\({}^{3}\) to 0.2 g/cm\({}^{3}\). Figure 12 shows that the tensile stress values decrease by 2902 KPa and 1088 KPa when the density of the NRTCPM layer changes from 0.33 g/cm\({}^{3}\) to 0.28 g/cm\({}^{3}\) and from 0.28 g/cm\({}^{3}\) to 0.2 g/cm\({}^{3}\).  
In conclusion, the lower the density of the NRTCPM layer is, the more the seismic energy is taken in, and the better the seismic isolation effect performs. As the density decreases, the elastic modulus decreases too (Table 4). 0.2 g/cm\({}^{3}\) is suggested as an optimum density in view of the compressive and tensile strength reduction rate. Furthermore, the lower the density is, the lower the cost is.