This study employs system identification using the Extended Kalman Filter to investigate variations in the stiffness and damping of shallow foundations during earthquakes. System identification results showed that the elastic stiffness of different foundations was significantly smaller than specifications proposed by FEMA 356 for the SE site class. As the earthquake load increased, a partial uplift of the foundation occurred. Following this uplift, the time domain inelastic stiffness decreased due to variations in contact area between the foundation and sub-soil. The inelastic stiffness at the maximum response was less than the elastic stiffness, according to the effective peak ground acceleration (EPGA) and the contact area ratio. After uplift in the foundation, the EPGA increased, the contact area ratio decreased, and the damping ratio increased by up to 20%. On the basis of these system identification results, we determined relationships between elastic stiffness and the ratio of bearing stress demand to the soil-foundation system capacity.

Introduction

The interaction between the soil foundational structure and the rocking effect commonly observed within shallow foundations (which can affect the structural dynamic response) have been investigated since Housner’s critical study [1]. To investigate the dynamic behavior of shallow foundations, Antonellis et al. [2] and Madaschi et al. [3] performed full-scale dynamic tests, where Wittich et al. [4], Drosos et al. [5], and Anastasopoulos et al. [6] used small-scale shake table tests. Recently, experimental studies have used centrifuge tests to investigate rocking effects observed within shallow foundations. For example, these tests were used to study a rocking foundation used as the base isolation for a bridge pier [7], the seismic behavior of a framewall-rocking foundation system [8], the structure-soil-structure interaction [9], and rotational damping effects on the structural earthquake response [10]. Numerical studies have been used to predict the dynamic behavior of shallow foundations. For example, Antonellis and Panagiotou [11] compared the seismic response of bridges with unattached rocking foundations to that of fixed-base bridges using numerical analysis. Anastasopoulos and Kontoroupi [12], Chen and Shi [13], and Lu et al. [14] all proposed simplified models to evaluate the seismic response of shallow foundations. Gajan and Kutter [15] used results of centrifuge tests to propose a contact interface model for shallow foundations. These experimental and numerical studies have led to new design concepts that consider shallow foundation rocking effects. This includes studies by Allmond and Kutter [16], who proposed design considerations for rocking foundations that are not connected through piles, Deng et al. [17], who used a displacement-based methodology, and Gazetas et al. [18], who proposed a geotechnical design concept for structures with safety factors that are less than 1.0.