Viscous damping formulation and high frequency motion propagation in non-linear site response analysis

Non-linear time domain site response analysis is widely used in evaluating local soil effects on propagated ground motion. This approach has generally provided good estimates of field behavior at longer periods but has shortcomings at relatively shorter periods. Viscous damping is commonly employed in the equation of motion to capture damping at very small strains and employs an approximation of Rayleigh damping using the first natural mode only. This paper introduces a new formulation for the viscous damping using the full Rayleigh damping. The new formulation represents more accurately wave propagation for soil columns greater than 50 m thick and improves non-linear site response analysis at shorter periods. The proposed formulation allows the use of frequency dependent viscous damping. Several examples, including a field case history at Treasure Island, California, demonstrate the significant improvement in computed surface response using the new formulation. q 2002 Elsevier Science Ltd. All rights reserved.