Effects of foundation size on Fourier spectrum amplitudes of earthquake accelerations recorded in buildings V. W. LEE, M. D. TRIFUNAC and C. C. FENG Department of Civil Engineering, University of Southern California, Los Angeles, CA 90007 Hypotheses that typical building foundations attenuate amplitudes of incident earthquake motions by scattering mechanism has been investigated. By analysis of normalized spectra of motions recorded inside building foundations it is found that the effect of size of building foundation if present is much smaller than the inherent variance of the data so far recorded in 57 buildings. Through comparison with theoretical results for vibration of rigid hemispherical and the disk foundations it is concluded that the relative rigidity of foundation may play a major role in influencing the degree to which foundations size influences strong motion recorded in building basements. INTRODUCTION Comparisons of the amplitudes of strong shaking recorded within the building foundations and in the vicinity outside the buildings have suggested that there exists a systematic relationship between the two recordings which would be governed by the phenomenon associated with soil-structure interaction] '4,s'll Studies of wave scattering and diffrac- tion by some sort of a rigid inclusion which could also be used to model simple building foundations lead to a general observation that the amplitudes of short incident seismic waves may be reflected back into the half space thus reduc- ing the high frequency motions of the foundation. 6' 7 While in general the high frequency energy tends to be reflected off the foundation so that it can be viewed as a 'low-pass' filter it has been pointed out also that the inertial forces acting on the rigid mass may lead to the motions which are, for some frequencies, larger than the amplitudes of incident waves)' 6 Currently available theoretical techniques for analysis of soil-structure interaction are not yet capable of predicting some of its detailed aspects that are needed in design prac- tice. Therefore, caution must be exercised in using simpli- fied methods of analysis especially while the experimental data is limited in number and quality. In the high-frequency range of interest for earthquake engineering applications, strong motions recorded in and outside the basement of the Hollywood Storage building, 4 for example, lead to the response spectrum amplitudes in the building that are smaller than the corresponding amplitudes in the adjacent parking lot. This observation has so far been frequently quoted in support of the attenuation of incident motions by the building foundation. However, recent recordings in the Imperial Valley, California, suggest that the opposite is possible as well. Horizontal motions and the response spec- trum amplitudes of recording 340 ft outside the Imperial Valley County Services building are, in the high frequency range, smaller than the corresponding motions and spec- trum amplitudes recorded at the building foundation (Fig. 1, Table 1). The vertical motions recorded there (Table 1) and the corresponding vertical spectra, however, suggest some attenuation of high frequency amplitudes. In experimental observations, where measurements are available near or on ground surface close to the building Table 1 Ground floor Free field NS UP EW N02E UP N92E Peak acceleration 288 154 332 195 215 215 (cm/s~) Peak velocity (cm/s) 45 15 66 35 17 63 Peak displacement (cm) 19 7 29 15 7 29 foundation and on the building foundation, one often does not have direct means of recording incident motions, but registers the so called free field motions which include incident waves plus the family of waves scattered from the building foundations and from other nearby inhomo- geneities. By taking ratios of spectral amplitudes recorded inside the building foundation and at some nearby outside 'free field' station one can obtain a 'transfer function' which does not always decay at high frequencies. 7 This suggests that computing of such transfer functions may lead to erroneous conclusions unless enough is known about the nature of wave motions outside foundation and in particu- lar whether scattering, focusing and shadow zones are likely to affect the computed ratios. 7 This therefore calls for a method of analysis which is not sensitive to such effects. The purpose of this work is to try a different method of analysis by examining the dependence of the spectral ampli- tudes of strong shaking recorded in building only and to analyze in particular whether these amplitudes depend in a systematic way on the dimensions of buildings where the recordings have been taken. This analysis will ignore any recordings outside buildings so that the requirement for detailed understanding of incident motions will not be present. METHOD OF ANALYSIS The analyses of strong shaking recorded in buildings do not depend on the soil-structure interaction of each structure and its setting only but also on numerous other features of the earthquake source, transmission path and the effects near the building site. To study the effects of building foundation on the recorded motions there it is necessary 0261-7277/82/020052-0752.00 52 Soil Dynamics and Earthquake Engineering, 1982, Vol. 1, No. 2 © 1982 CML Publications