Base-Modified Post-Tensioned Rocking Walls for Tailored Seismic Response and Damage Reduction

Abstract

Recent studies on the socio-economic impact of earthquakes have led to the development of several novel lateral force-resisting systems. These systems aim to improve the seismic performance and resilience of structures by reducing the residual drift and protecting the main structural components. The post-tensioned rocking wall is one of the novel systems that has shown promising results by limiting bending and shear stress on the wall via post-tensioned bars/strands and rocking. However, despite the many benefits of this system - such as redirecting the seismic energy into energy dissipation devices, and re-centering after seismic events - there remain challenges. This work introduces the concept of base-modified rocking walls (both curved and tapered base), a modification over traditional rectangular profile walls, and analytically/numerically investigates the potential benefits of this simple geometric modification. In this work, three levels of analysis are used to characterize the base-modified wall behavior. The three levels gradually increase in system fidelity to shift from qualitative to quantitative prediction, but also necessarily from closed-form analysis to numerical simulation. At the first level, Lagrange's equations are employed in formulating the analytical equations to study the static and dynamic behavior of a simplified curved-base rocking wall in concert with a gravity frame. The parameter sensitivities and nonlinear dynamic behaviors are identified using the analytical equations. Furthermore, the advantages of the curved-base rocking walls are explored. Alongside the analytical model, a finite element model of the rocking walls was developed to validate the analytical model and to later extend the study to more generalized rocking walls. The second level was the extension of the analytical model to capture the behavior of flexible rocking walls. The objective was to characterize the interaction of rocking and wall deformation and by using the framework of nonlinear normal modes, an extension of linear normal modes. The study used a two degrees-of-freedom model consisting of one degree-of-freedom for the base rotation angle and a second degree-of-freedom for the wall deformation. The analytical model was able to capture the amplitude-frequency behavior of different modes, characterize the transition between fixed-base vibration and rocking, and show co-existing steady-state solutions. Lastly, a finite element model of flexible tapered-base rocking wall systems was develop to more accurately explore the potential benefits of the geometric base modification using ground motions. Moreover, the model broadens the scope by generalizing elements that were previously simplified/omitted. To evaluate the seismic performance of the the modified wall, case studies of a two-story and ten-story wall were done. The studies showed the modified rocking walls resulted in lower base damage than the equivalent rectangular rocking wall without causing issues in (and sometimes even reducing) other demands, e.g., base shear, interstory drift, or floor acceleration.