Calculation of site fundamental period in the case of oblique incidence

The site fundamental period is a crucial variable for site effect models and serves as a significant index for seismic site classification. The existing methods for obtaining site fundamental period assume that the angle of incident seismic wave at the site base are vertical. These commonly used methods include simulation and empirical method based on the vertical SH wave propagation in seismic site. The empirical method of layer by layer single degree of freedom method is adopted in the Japanese seismic design code for its simple calculation and the results are equivalent to the simulation method. Nonetheless, the assumption of vertical incidence does not align with the actual incidence angle of ground motion at the site base. This paper addresses this discrepancy by focusing on establishing a method for the calculation of the basic period under obliquely incident seismic wave. First, the 2D SH wave propagation in seismic site under the action of oblique incidence wave is characterized as vertical 1D apparent propagation to establish the SH wave propagation model based on Snell law. Building upon this foundation, a wave propagation simulation model is applied to establish a numerical method and modified layer by layer single degree of freedom method for the calculation of the basic period and then applied to KiK-net stations. The findings indicate that the fundamental period decreases with an increasing incident angle. For the statistical average result of the base incident wave angle at 57 degrees, the average deviation can be 11%. The modified method accurately considers the influence of the seismic wave incident angle, while maintaining calculation simplicity equivalent to the original method. Finally, the paper discusses the influence of selecting the bedrock surface burial depth on the calculated site fundamental period. The results demonstrate a high correlation between the basic period of the site and different depths if the top of the soil layer, with a shear wave velocity larger than 700 m/s, is defined as the bedrock surface.