A Study on the Effect of Seismic Wave Incident Angle on Lining Strains Imposed to Underground Rectangular 2D Structures

Soil-Structure Interaction (SSI) problems are usually broken down into four fundamental parts. The first step is the estimation of free field motion (FFM). FFM is representative of the field motion in the absence of any activity relating to the building construction procedure. The second step is the calculation of excavated field motion (EFM), which translates the effect of including void on alternation in FFM. This later motion usually is defined in the perimeter of the cavity. The third step accounts for kinematic aspects of SSI. In this part, foundation deformations due to EFM are estimated. In the fourth and final step, the previously calculated deformations are used to impose the acceleration history on structural mass. In current practice, it is known that the third step has the highest influence on underground structures and hence it dictates the design criteria for such systems.
To implement the above-mentioned analysis plan, FFM is usually considered as shear waves with upward propagation direction. Such assumption has formed the popular simplified seismic design method for underground structures. Though, this common assumption may not be valid for topographic urban areas were wave fields reach the surface through different incident angles. Such inclination would lead to various states of confrontation between embedded structures and wave fields. The state variety, in turn, causes underground constructions to experience different stress fields and hence dissimilar lining deformations. Therefore, there is a serious need to uncover the role of face-off orientation of wave field and the structure on lining strain demands.
Here, the effect of face-off angle between shear wave field and rectangular underground structures, on lining strains is investigated. For this purpose, a 2D isotropic soil model including homogeneity is included under statically simulated seismic shear deformations. The analysis was performed through finite element method regarding different aspect ratios for underground structure and subsequently lining strains were reported. To drive strain demands, in the analyzed model, first, the axial, shear and moment demands are estimated. Then the results are normalized to proper parameters that lead to relative strains. Beside these three types of strain, with a combination of strains resulted from axial and moment forces, the total axial strain is also extracted. This parameter is commonly used in any structural member design. The analysis was repeated for three aspect ratios of 1, 2 and 4. Besides, four face-off angles of 0, -15, -30 and -45 degrees were considered while the flexibility ratio was set to 10. The outcomes were reported in contour format. There in each graph, the variation of strains was illustrated by changing incident angle in one axis against different sections along the target element in the other axis. The first part of this research examines the performance of perfect rectangular structures against different incident angles. The second part deals with samples of semi-rectangular sections. The selected cases, which belong to different metro stations in Kobe metropolitan, possess rectangular sub-parts.
With an overview of results for perfect rectangles, it can be figured out that the total axial strain is notably governed by moment induced strain rather than pure axial strain. In that case, the maximum strain at corners belongs to zero incident angle while in the middle part of the element, the confrontation angle of -45 degree takes the highest strain values. For shear strains, zero face-off angle caps all results for both corner and middle parts. For the case of semi-rectangular sections, the effect of variation in incident angle on demands becomes highlighted. From the results, it can be seen that for more than 50 percent of elements, face-off angles other than zero dominate the results. It is worth mentioning that to reach a comprehensive influence map on the critical face-off angle, further investigation is required.