ABSTRACT
The new formulae with three factors and one factor for calculating the stress reduction coefficient rd at depths of 0–50 m are proposed in this paper. A more reliable database of rd curves is established using models for actual sites, the corresponding real seismic records from the KiK-net downhole array. Then, a quantitative analysis of the factors influencing rd is performed, and the important factors affecting rd are reasonably selected. The basic pattern of the rd curves and their unified mathematical expression for depths of 0–50 m are determined and the three-factor and one-factor formulae for calculating rd are presented.