# Numerical Study of the Seismic Response of an Instrumented Building with Underground Stories
## 1 Introduction  
Designing structures requires adequate modeling of its different elements, loads, and--especially in earthquake-prone countries like Chile--simulations of the seismic loads. In the modeling process, the structural building system can be divided into three groups: the superstructure above the soil surface, the foundation that transfers the load from the structure to the earth, and the substructure below the ground surface known as thebasement. However, the current state-of-practice in the seismic analysis and design of buildings with subterranean stories is still controversial since incorporating underground stories' effects in modeling is based on approximations and the designer's expertise and judgment. This controversy still lacks adequately formulated recommendations in most building codes and standards, where the approach followed for analyzing civil building structures with surface foundations is also used in buildings with low and medium-rise regular subterranean levels [1; 2; 3]. It is well-known that underground levels can affect the superstructure's behavior because the subterranean levels will receive loads directly from the soil. However, it has become a common practice in engineering offices to model and analyze the soil-structure interaction (SSI) with vertical elements fixed at their bases, including a certain number of basement floors, and rarely, including all the underground floors. On the other hand, in buildings with multiple high-density wall underground levels, the building superstructure and substructure are analyzed and designed separately. While the superstructure is cropped at the ground floor level and analyzed as an embedded structure founded on the ground surface, the substructure is designed for the seismic base shear and moment demand resulting from the superstructure in addition to the seismic earth pressure acting on the subterranean walls due to the side soil mass oscillation. Although also commonly used in practice, this two-step strategy depends on the building's seismic analysis procedure. Furthermore, the aforementioned modeling strategies consider the structure supported on non-deformed support, which may be realistic when embedded in very stiff soil or solid rock [4]. However, the supporting and adjacent soil will always deform under loading, which under strong ground shaking, it will behave nonlinearly, affecting the SSI [5; 6]. SSI may affect a structure's performance in many ways, such as altering the input ground motion due to foundation flexibility and modifying the period of vibration of a structure due to foundation movement. Additionally, SSI also affects the damping of a structure by providing additional damping through energy dissipation in soil or by reducing the expected damping the structure would have on a rigid foundation. Thus, it becomes increasingly important to incorporate the underground stories, subterranean walls, side soil, and foundation soil explicitly in the structure's numerical model to assess the effect of the underground part of the building adequately on its seismic response. Moreover, design codes are trending to a performance-based design methodology that encourages incorporating SSI effects in the seismic analysis of structures [7]. To this end, three major approaches can be found in the literature to consider soil and foundation nonlinearity, namely continuum models, plasticity-based macroelement (PBM), and beam-on nonlinear Winkler foundation (BNWF). Continuum models, based on the employment of brick or shell elements (for 3D and 2D analyses, respectively) to represent the soil behavior and the soil-structure interaction, are commonly referred to as the most exact and accurate for the prediction of the response of the complete soil-foundation-structure system.