Hidenori Mogi

Analysis of Scattered Waves on Ground with Irregular Topography Using the Direct Boundary Element Method and Neumann Series Expansion

It is well known that ground with irregular topographic surfaces causes complicated seismic responses. The complex seismic response is mainly caused by scattering and wave conversions. However, the specific locations of the surface where the scattering mainly occurs and the extent of their effects are not yet clear. In this study, we investigated the excitation process of complicated seismic responses induced by irregular ground surfaces in terms of the contribution of scattered waves. First, the formulation of scattered-wave contribution in a two-dimensional SH -wave field based on the direct boundary element method and the Neumann series expansion of the bem matrix was shown. In the formulation process, it was pointed out that the mathematical expression of the first-order scattered-wave contribution has a form consisting of a wave function and an inclination factor, which was similar to that obtained by the Huygens–Fresnel principle. Next, numerical analyses were conducted for a ground that had a sinusoidal-shaped surface at the center and flat parts at both ends. A comparison of the results showed that the complicated waveforms of the responses were caused by the arrivals of the scattered waves. Finally, the contributions of the first-order scattered waves at the reference points were closely examined based on the mathematical expression; the following conclusions were drawn: (1) The polarity of the first-order scattered waves in the time domain is attributed to the inclination factor, which depends only on the geometrical relationship between the reference point and the source point from which the scattered waves emanate. (2) At the bottom of a valley, the scattered waves generated at its nearby surface are dominant because of the short distance from the source of the scattered waves. These scattered waves appear nearly at the same time of arrival as the incident wave and always reduce the amplitude of the incident wave because of their negative polarity. (3) On the contrary, at the peak of a hill, the scattered waves generated at the nearby surface have positive polarity, and they always enhance the amplitude response.

GRAVITY EFFECTS ON EARTHQUAKE RESPONSE OF A FLEXURE BUILDING: A SHEAR BUILDING COMPARISON

An analytical building model including the nonlinear effects caused by gravity is presented in this paper. Governing equations are derived for both single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) models with large displacements taken into account, and solutions are obtained by direct integration and modal analysis. The response of typical structures subjected to harmonic ground excitation was expressed in exact and approximate forms, compared with the response of an equivalent shear building. Numerical examples show that while gravity generally decreases the natural frequency of elastic SDOF systems with small displacement approximations, actual natural frequency increases with ground motion. The difference in the natural frequency and response of MDOF systems to the equivalent shear building is not only due to gravity, but also caused by the geometry of the structure. Exact solution shows that the frequency varies with ground motion amplitude.

Analyzing Spatial Intraevent Variability of Peak Ground Accelerations as a Function of Separation Distance

Peak ground acceleration (PGA) as a measure of earthquake motion intensity is an important factor in the earthquake-resistant design and reliability analysis of structures. The purpose of this paper is to examine the spatial variability of PGAs (recorded at the same epicentral distance) as a function of separation distance. To do this, we define PGA ratios as spatial intra-event variations of PGAs and examine their statistical characteristics. We analyze the probability distribution of the ratios, and formulate equations for their probability density functions, mean values, standard deviations and percentiles. The above-mentioned statistics are then estimated using accelerometer arrays of the Chiba, SMART1, and SIGNAL databases. Then, the relationship between these statistics and the station separation distances is analyzed. We found that the means and standard deviations have an almost linear relationship with the logatithrn of the station separation distances ranging from several meters to one hundred kilometers. Finally, based on the 5oth and 95th percentiles, the differences between PGAs at two different sites due to future earthquakes are discussed.