مدل نوسانی- جنبشی برای ارزیابی پاسخ لرزه ای سازه های قرار گرفته بر فونداسیون سطحی

ABSTRACT A simplified Nonlinear Sway-Rocking model for evaluation of seismic response of structures on shallow foundations

During the past decade, the interest in the topic of seismic SoilStructure Interaction (SSI) has seen a gradual shift from the superstructure to the foundation soil. Recent research studies on SSI have shown reduced seismic ductility demands of structures due to nonlinearity that arises mainly from the mobilisation of the ultimate capacity and the uplifting response of shallow foundations. These studies have mainly focused on stiff slender structures on small foundations, such as shear walls [1], bridge piers [2,3], and framed structures [4,5] supported by spread footings. It has been found that the lifting off of one side of the footing not only results in geometric nonlinearity at the soil-footing interface, but causes yielding of soil on the other side, which in turn increases the uplift. Allowing mobilisation of the foundation bearing capacity through soil yielding and foundation uplifting limits the maximum loads that can act on the superstructure, and also leads to a considerable amount of energy dissipation due to the hysteretic damping in the soil [6].

On the other hand, structures supported on spread footings may experience unexpectedly high differential settlements during strong shaking. This phenomenon, induced by either heavy structural loads that are unevenly distributed across the footing, poor soil conditions, or the combination of both, can lead to failure of structural components and hence, non-repairable damage or collapse of structures [7]. Mat (or Raft) foundations, in these cases, are more suitable to spread the loads from the structure to the ground. Unlike the shear walls or bridge piers, structures supported on mat foundations are usually designed with a medium slenderness ratio. This leads to a strong interaction between the sway and rocking motions of the foundation when subjected to the horizontal component of strong ground motion.

It has been shown that nonlinearities in the soil (corresponding to large strains) and at the soil-foundation interface are almost unavoidable in strong seismic events [8]. Performance-based seismic design methodology embraces these nonlinearities, provided that the responses of both structural and geotechnical components satisfy the performance targets. The role of nonlinear seismic soil-structure interaction on dynamic response of buildings has recently been emphasised by Pecker et al. [9] and Gazetas [10]. In this context, it is important to develop reliable design tools that provide sufficient accuracy to assess the seismic performance of SSI while maintaining simplicity so as to be easily understood and accepted by engineers.

In recent years, the concept of a macro-element, which simplifies the dynamic interaction between soil and foundation by integrating the nonlinearities (in the soil and/or at the soilfoundation interface) into a single plasticity-based element, has attracted considerable attention (e.g. [11–13]). However, this macro element for practical engineers remains a “black box” where the multi-yield (and sometimes multi-mechanism) complexity makes it difficult to be implemented into computer codes [14].

On the other hand, using spring-type models to simulate the dynamic response of soil-structure systems is popular in design practice because of their ease of use and clear physical meaning.

Examples include (1) the linear dynamic impedance models (e.g. cone model [15]) used in the analysis of foundation vibrations on an elastic soil medium, (2) Winkler-based linear/nonlinear springbed models (e.g. [16,17]), and (3) the nonlinear rotational spring model [18] for the analysis of rocking-dominant nonlinear foundation behaviour. These models usually assume that the foundation soil is homogeneous, whereas in most cases the soil stiffness and strength increase with depth due to the effects of overburden stress. There is a lack of an effective and efficient spring-type model which is able to capture both Nonlinear Sway-Rocking response of shallow foundations and soil non-homogeneity.

This paper presents a simplified Nonlinear Sway-Rocking (NSR) model that is capable of simulating the load-displacement response of mat foundations subjected to seismic excitations. Compared with the linear/nonlinear spring-type models in the literature, the present model in this study is able to simulate the nonlinear foundation sway-rocking response which can be significantly affected by the load path of the seismically-excited SSI system. The effect of soil non-homogeneity is also considered. The model is developed using the OpenSees platform [23] and verified using data obtained from more rigorous Finite Difference (FD) analyses conducted using FLAC3D. The simplified model is well suited for heavily-loaded structures with a moderate slenderness ratio for which the nonlinear sway response is strongly coupled with the rocking response. The paper is organised into six main sections. First, an overview of the problem is provided, followed by a description of a FLAC3D numerical model and static analyses conducted to identify the foundation load-displacement relations and bearing capacities.

The NSR model is then developed based on calibration of analytical foundation backbone curves with load-displacement relations obtained from the FLAC3D static push-over tests. The process by which the coupling between swaying and rocking motions is taken into account in the proposed model is also described. The efficiency of the NSR model to predict load-displacement and moment-rotation responses of shallow foundations to dynamic loading is demonstrated using results obtained from additional dynamic FLAC3D numerical simulations. Finally, the limitations of the model are discussed and conclusions are provided.