Hideji Kawakami

Modeling wave propagation by using normalized input-output minimization (NIOM)

A new method for modeling wave propagation is described here, its application is discussed, and its results are compared with those obtained using the conventional correlation and unit impulse response methods. The method uses spectral analysis by minimizing the mean square values of the system input and output when subjected to a constraint, and is effective in detecting arrival times of incident and reflected waves and in revealing their relative amplitudes as well. The method is applied to simple models and to the strong motion records obtained at the TTRL (Koto-ku, Minamisuna) and Chiba vertical arrays during three earthquakes in Japan. The travel times evaluated by the NIOM method agree with the results obtained by the geophysical measurements of S-wave velocity at the sites. The method is also effective in showing the amplification property of shallow layers at the TTRL and Chiba sites.

Normalized input–output minimization analysis of wave propagation in buildings

Abstract In previous studies on the earthquake response of buildings, vibration approaches were used more often than wave propagation approaches; thus, wave propagation through a building has not been sufficiently investigated. This paper presents a wave propagation modeling analysis of strong motion records for actual buildings in comparison with an analysis of those in elastic soil media and in analytical building models. We use the normalized input–output minimization (NIOM) method, which can model wave propagation in multiple linear systems by considering the statistical correlation among the strong motions at different observation locations. Output wave models simplified by the NIOM method show two clear peaks that correspond to incident and reflected waves propagating through the building in the vertical direction. Obtained wave propagation properties, such as wave travel time and wave amplitude ratio, at each story of the building are found to reflect the structural properties like rigidity and damping at that story. Thus, the NIOM method is shown to be an effective new method of investigating structural behavior of buildings during earthquakes.

A New Method for Propagation Analysis of Earthquake Waves in Damaged Buildings : Evolutionary Normalized Input-Output Minimization (NIOM)

We have developed a new method for wave-propagation analysis--called evolutionary normalized input output minimization (NIOM)-that models time-variant wave propagation by considering the time-variant statistical correlation between the strong motions recorded at different levels in the building. The NIOM results for actual damaged and undamaged buildings (which experienced the 1994 Northridge earthquake or the 1971 San Fernando earthquake), as well as those from an analytical elastic building model, were compared. All of these results showed two clear peaks that correspond to the incident and reflected waves propagating through the building in the vertical direction. The wave travel time was determined from these two peaks. In the case of the damaged buildings, the travel time increased during the earthquake; however, in the cases of the undamaged buildings and the elastic model, it remained almost constant during the earthquake. It was found that the change in the travel time is related to the change in the structural properties and to the degree of damage to a building. These results show that evolutionary NIOM is an effective new method for investigating the change in structural properties and the damage to buildings.

Wave Propagation Modeling Analysis of Earthquake Records for Buildings

This paper introduces an application of wave propagation modeling to building response investigation. We have analyzed the computed responses of analytical building models and the obtained strong-motion records for forty-one actual buildings during five different earthquakes by using the normalized input output minimization (NIOM) method. This method can model wave propagation in multiple linear systems by considering the statistical correlation of the earthquake motions at different observation locations, and can reveal the arrival times of incident and reflected waves as well as their relative amplitudes. From these values, the fundamental period and the damping ratio of the building could be simply estimated. The estimated values were then compared with the values for the analytical building models, the values estimated in the previous studies for the actual buildings, and the building code formula.

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.

Statistical study of spatial variation of response spectrum using free field records of dense strong motion arrays

Spatial variation of acceleration response spectra is examined using strong motion records for a large number of events from dense accelerometer arrays at Chiba in Japan and SMART-1 in Lotung, Taiwan. The effects of earthquake component, structural damping, earthquake magnitude, focal depth, epicentral distance, structural time period, and station separation on the intra-event variation of response spectra are examined first through an empirical analysis and then through a least-square regression fit for parametric study. A very large scatter of the response spectra ratio is observed for both arrays, especially for SMART-1 array. The mean values of the ratio vary from 10 to 20 per cent for Chiba array while they vary from 25 to 50 per cent for SMART- 1 array. The coefficients of variation of the ratio range from 5 to 25 per cent for Chiba array and 30 to 50 per cent for SMART-I array. The correlation among response spectra is found to be inversely proportional to station separation and shows frequency dependence. For larger time periods, the correlation is lower and not higher. The correlation is also lower for UD earthquake component as compared to the two horizontal components. For higher damping ratio, the correlation among spectra is higher. The effect of the earthquake magnitude, focal depth and epicentral distance on the spatial variation is complex. The three parameters having implicit interdependence, considering their combined effect, a positive contribution to the value of ratio of response spectra is observed in the case of larger earthquake events. Furthermore, as mentioned above, the spatial variation for SMART-1 array is much larger than that for Chiba array. This difference can be attributed mainly to the difference in distance between the instruments in the two arrays. However, some of the difference is considered to be due to site specific characteristics.

On the characteristics of non-linear soil response and dynamic soil properties using vertical array data in Japan

Non-linear response of the soil is investigated by comparing the spectral ratios (uphole/downhole) using weak and strong motions. Data from seven vertical arrays in Japan are analysed in this study. The frequency-dependent transfer function of soil is calculated as a ratio of the spectrum at uphole to the spectrum at downhole, considering the horizontal component of shear wave. In spectral ratio analysis auto- and cross-spectra are employed. The reduction in the predominant frequency of the transfer function with increases in excitation level reflects the non-linear response of the soil. Results of analysis demonstrate a significant non-linear ground response at six sites with surface PGA exceeding 90 gal. However, the results of one site show the linear response up to 130 gal surface PGA. Furthermore, the in situ strain-dependent soil behaviour is examined through the shear modulus - shear strain relationship. When compared, the actual and laboratory results of the shear strain - shear modulus relationship are in agreement. Additionally, a good consistency between the tendency of reduction in shear modulus ratio with shear strain increases, and reduction of predominant frequency with ground motion increases, confirms the significance of non-linearity in site effects study.

A simplified input output relation method using AR model for earthquake wave propagation analysis

This paper introduces a Simplified Input Output Relation Method (SIORM) using multiple-variable autoregression (AR) model which can be used to determine ground wave propagation properties. Using the AR model, a method is developed to establish the basis for the formulation of SIORM. The degree of accuracy of this method is evaluated. SIORM is applied to actual ground acceleration records taken at Minamisuna and Etchujima sites in Japan and its results are discussed in this paper.

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.

Analysis Of Earthquake Wave PropagationIn Buildings

This paper presents a wave propagation modelling analysis of strong motion records for actual buildings in comparison with an analysis of simple building models. In previous studies on earthquake response of buildings, vibration approaches were used more often than wave propagation approaches; thus, wave propagation through a building has not been investigated enough. We use the normalized input output minimization (NIOM) method, which can model wave propagation in multiple linear systems by considering the statistical correlation among the strong motions at different observation locations. Output wave models simplified by this method show two clear peaks that correspond to incident and reflected waves propagating through the building in the vertical direction. The obtained wave propagation properties, such as wave travel time and wave amplitude ratio, at each story of the building are found to reflect the structural properties like rigidity and damping ratio at that story. Further, a new method for wave-propagation analysis—called evolutionary normalized input-output minimization—is developed. It models time-variant wave propagation by considering the time-variant statistical correlation between strong motions recorded at different levels in the building. In the case of damaged buildings, the travel time increased during the earthquake; however, in the cases of undamaged buildings and the elastic model, it remained almost constant during the earthquake.