# Seismic Response Analyses of a Large-Span Powerhouse Cavern Considering Rock-Structure Interaction
## 5 Results and Discussion  
### 2D Analyses  
The dynamic analyses using the 2D model were performed first, with the purpose to obtain the seismic response of the cavern when subjected separately to seismic inputs in the E-W, vertical, and both directions. With only the accelerogram A1 adopted, the deformed shapes of the cavern cross-section obtained are shown in Figure 5.  
The ovaling or racking deformation of the shotcrete, induced by the propagation of shear and pressure waves in the plane of the cross-section of the tunnel, is generally considered as the most critical deformation pattern during a seismic event. In this study, it can be inferred from Figure 6 that the horizontal component of motion generates shear deformations of the rock mass and then ovaling of the cavern cross-section, typical of that produced by a vertically propagating S wave. On the other hand, the application of the vertical component generates a deformation typical of a vertical propagating P wave.  
It is noted that the deformed shape and the displacements computed with the two components of motion can be derived by the superimposition of the results obtained for each component. This is due to the dynamic motion producing effects that are completely in the elastic field.  
Figure 7 shows the distribution of the thrust force along the shotcrete lining when the horizontal, vertical, and both components are applied. The thrust induced by vertical motion is larger than that resulting from horizontal motion. Moreover, the thrust induced by both the components of motion is slightly smaller than the superimposition of the results of the two separate analyses. Moreover, the thrust force time history of the lateral bottom element, when subjected to three types of seismic input, is shown in Figure 8, and the results indicate that the thrust force of shotcrete is more dependent on P wave than on S wave in this case, which is in accordance with the conclusions obtained by [PERSON] [27]. Accordingly, it may be concluded that the effect of P-wave propagation should be properly  
Figure 5: E-W and vertical components of the selected accelerogram A1.  
Figure 6: Deformed shapes of the cavern cross–section when the model is loaded by horizontal, i.e., E–W (**a**), vertical (**b**), and both components (**c**).  
considered during the seismic design of underground structures, though generally, only more attention has been given to the effect of shear wave propagation.  
Ground shaking by seismic events induces redistribution of stresses around the opening. Seven analyses using the selected seven groups of accelerograms containing two components (in the E-W and vertical directions) were performed, and the average seismic response could then be obtained. Figure 9 shows the average minimum principal stress distribution around the cavern induced after the application of the two components of motion. The maximum tensile stress value, equal to 0.5 MPa, is very close to the tensile strength (0.51 MPa).  
Figure 8: Thrust force time histories of the studied beam element subjected to P wave, S wave, and both waves.  
Figure 7: Thrust force along the shotcrete subjected to horizontal (**a**), vertical (**b**), and both (**c**) components of ground motion.