Simplified Displacement Loading Patterns for Incorporation of Spatially Variable Ground Motions in Bridge Seismic Design Codes

Abstract

This paper derives simplified differential displacement loading patterns, in lieu of spatially variable seismic excitations, for use in the seismic design of bridges, based on the displacement sets originally presented in the European seismic design codes. The most significant difference between the patterns derived herein and those of the European seismic design codes is that the patterns derived in this work have a clear physical interpretation. First, the relationship between the space and time derivatives of ground motions in the free field is discussed, and an estimate for the differential ground motions at different locations on the ground surface with respect to a reference point is derived. Second, a deterministic methodology is developed to produce simplified displacement loading patterns, consistent with the propagation characteristics of seismic waves, for the evaluation of the nonuniform excitation of bridge supports when the soil properties along the structure do not vary significantly. The proposed displacement loading patterns are compared with the ones recommended by the European seismic design codes for the consideration of the multisupport excitation of long-span bridges. The numerical results of this study indicate that the displacement loading pattern proposed by the European seismic design codes for the case in which the adjacent bridge supports move in opposite directions may provide unrealistic values for the differential ground motions.