# Numerical Study of the Seismic Response of an Instrumented Building with Underground Stories
## 1 Introduction
This kind of modeling technique is time-consuming due to many degrees of freedom considered to represent the entire system, and therefore, its application has been focused on very large and stiff structures, like nuclear power plants, mostly for academic purposes [8; 9; 10]. However, the fast increase in the processing capabilities of computers is expected to make this methodology suitable for design purposes in the mid-term. A thorough review of the application of continuum mechanics for the analysis of dynamic soil-structure interaction can be found in [10]. PBM's represent the foundation's behavior by a system of generalized variables, primarily forces and displacements at the foundation center [11], and consider three mechanisms (elasticity, plasticity and uplift of the foundation). They are much less time-consuming than the continuum models described above and have proven to be accurate comparing the results of the modeling with that of laboratory modeling. Research has been conducted aimed to test the performance of this modeling technique in the assessment of the dynamic response of structures, but the complexity of the model and the calibration of the parameters involved remains an issue that still to is investigated. The BNWF approach is the most popular given its simplicity in defining the parameters involved in the model and its capabilities for capturing the rocking and sliding effects as well as the permanent settlement of the footing for both linear and nonlinear soil behavior [4]. However, this modeling technique presents some disadvantages, such as (1) the idealization of the soil continuum with discrete soil reactions that are uncoupled, (2) inadequate performance in modeling problems involving significant kinematic interaction and ground motion effects, and (3) incapacity to account for the cyclic SSI response [12]. Numerous studies have been conducted in the past decades to understand and analyze the seismic performance of structures with subterranean levels [13; 14; 15; 16; 17; 18; 19; 20; 21]. In the study done by [PERSON] and [PERSON] [17], the seismic performance of moment-resisting frame steel buildings with multiple underground stories and varying building heights was evaluated through a 3D nonlinear finite element model (FEM) by considering the seismic hazard of Vancouver, Canada, and the use of BNWF model to simulate the essential aspects of the nonlinear behavior of the foundation and side soil. The results indicated that SSI could considerably affect the seismic response of buildings with subterranean stories founded on soft soil conditions by increasing the base shear and moment demands by up to 25% of the fixed-based buildings' values. Similar results were obtained by [PERSON] et al. [19]. They investigated SSI's impact on the seismic design of reinforced concrete (RC) buildings and compared buildings modeled with the fixed condition at ground level and buildings with different numbers of underground levels. The results showed that SSI plays a significant role in increasing the story shear and moment demands for relatively low-rise buildings with subterranean levels. [PERSON] et al. [20] evaluated the influence of SSI on seismic demands in the gravity-load-resisting system of a 12-story RC shear wall building with underground stories through nonlinear time history analyses (NLTHAs) for soil classes ranging from stiff to soft. The results showed that underground structure cracking should be included in the building's structural analyses and that foundation movement should be explicitly considered for soil class D and softer. Recently, [PERSON] et al. [21] showed that basement floors' addition could minimize the roof-floor displacement, the structure's natural fundamental period, and axial column forces when considering SSI effects. Moreover, the effects of SSI on the dynamic response of other types of structures have also been assessed.