An Investigation on Seismically Induced Local Distortions to Underground Rectangular 2D Cavities: The Case of Shear Wave Field of Motion with Different Incident Angles

A classical approach to soil-structure interaction problems includes three analysis stages. The first is the estimation of free field motion (FFM). The second stage accounts for the effect of excavation on FFM alternations in the perimeter of excavated part. The third and final step deals with soil-structure interaction, usually in two sub-parts, i.e. kinematic and inertial interactions. For the case of underground systems, the first two stages and also the first sub-part of the third stage, govern the forces imposed to embedded structures. To implement the above analysis plan, FFM is usually considered as shear waves with upward propagation direction. Such assumption has formed the popular simplified seismic design method of underground structures [1-6]. Though, this common assumption may not be valid for topographic urban areas were wave fields reach surface through different incident angles. Such inclination would lead to various states of confrontation between embedded cavities and wave fields. The state variety, in turn, cause underground openings to experience different stress fields and hence dissimilar void-wall deformations. The tractions that affect embedded structures are the results of such deformations. Therefore, there is a serious need to uncover the role of wave field-cavity face-off orientation on void-wall distortions. Here, the effect of face-off angle, between shear wave field and rectangular cavities, on semi-local distortions 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 the finite element method regarding different aspect ratios for cavity and subsequently global distortions were reported. To drive semi-local distortions, in the analyzed model, the cavity junctions were initially connected by strait lines. Then, the divergences from perpendicularity between adjacent edge lines of the opening were calculated. This approach would provide the same results for different corners of perfect rectangular cavities. However, this is not the case for imperfect rectangles were the responses would not take similar values for different junctions. The first part of this research examines the performance of perfect cavities against different incident angles. The second part deals with the samples of semi-rectangular sections. With an overview on results for perfect rectangles, it can be figured out that the traditional formulations for cavity distortion estimation just cover special incident angles, which are close to zero value and also specified to square sections rather than general rectangular shapes. However, as the incident angle varies from zero to 45 degrees and also sections tend to more slender shapes, usual suggestions would become in many cases conservative and also in a number of occasions unconservative. For instance, in the case of 45 and -45 incident angles, global distortion of sections vanishes in spite of existence of local arching shapes. This means that wall deformations are totally different from what is expected in the case of zero confrontation angle. Furthermore, the above investigation is extended to two of semi-rectangular sections. The selected cases, which belong to different metro stations in Kobe and Athens metropolitans, possess rectangular sub-parts at the bottom. These sub-parts make deviations from perfect rectangles. In the former case, the added part is placed in the middle length with which one of two symmetry axis is removed and the other one still remains. In the later one, the added part is placed at an arbitrary position that removes both symmetry axes. In this second round of analysis, as distortions vary from node to node, each nodal distortion is reported separately. Due to the results, it is seen that by approach to the position of added parts, deformations become more different from perfect states. This difference may result in more than 50% increase in corner angle adjustments. That is while far regions from added inclusions experience approximately the similar responses to perfect rectangles. It is worth mentioning that to reach a comprehensive influence map on the effect face-off angle, further investigation is required. Besides, it is important to note that this document has focused on edge junctions for the calculation of nodal distortions. Other local deformations were out of the scope of this paper.