Seismic Design of Rocking Shallow Foundations: Displacement-Based Methodology

Abstract

This paper proposes a direct displacement-based design (DDBD) methodology for seismic design of rocking shallow foundations for ordinary bridges under earthquake loads. A multilinear model is developed to represent the backbone curve of the nonlinear moment-rotation behavior. In addition, a new empirical relationship is proposed that correlates the initial rotational stiffness to the moment capacity of a rocking foundation; this correlation is proposed as an alternative to calculation of stiffness based upon elasticity theory. In the proposed design procedure, a bridge system consisting of a deck mass, a rocking foundation, and a damped elastic column is integrated into a single element from which the equivalent linear damping and period can be determined. The DDBD methodology uses the equivalent system damping and period along with a design displacement response spectrum to determine the seismic displacement demand. The approach is checked by comparing displacements predicted by this method to those computed using nonlinear time-history analyses. The methodology also includes provisions to determine footing dimensions to obtain acceptable performance in terms of foundation settlement and lateral sliding. The DDBD methodology is further illustrated with a design example.