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The present analysis is one part of a three-part !,tudy of the dynamic response of a nuclear reactor structural and surrounding soil that is subjected to earthquake motion. A previous part of the study by I IT (Research Institute uses the finite element method to compute the response of ft reactor structure whose foundation is on the ground surface. A parallel study of this problem using analytic or closed-form techniques has been performed by the University of Toledo. The present study also considers this problem, but its main subject is the more typical case of a reactor structure whose foundation is embedded below ground surface. The structure and soil are represented by an assembly of two-dimensional finite elements. In some examples, elastic properties are assumed for the soil, and In others, inelastic properties are assumed. The computer programs used to perform the analyses and the version of plasticity theory used to represent Inelastic soil properties are described. The study indicates that the horizontal response of the structure foundation, as measured either by its response spectrum or peal< acceleration. Is less than the corresponding response at the surface of the free field. The structural response appears to be suppressed by a greater amount if its natural frequencies are about the same as the dominant frequencies of the earthquake Input. Suppression Is also greater if the stiffness of the soil Is decreased. The ratio of horizontal response spectra (foundation response/free field response) varies from about 0.2 to 1.0. A typical suppression ratio for elastic soils In the frequency range of 3 to 5 cps is 0.5, while for Inelastic soils it Is 0.3. The vertical response spectrum of the foundation is ampHfled by 1.0 to 1.5 relative to that of the free field at 1 to 3 cps and suppressed by 0.2 to 1.0 at 3 to 8 cps. The scope of the study Is too limited, however, to draw oroad conclusions on the amount of suppression over a wide range of soils, types of structures, and earthquake motions. li AjA R-6915-1200 stresses In the soli adjacent to the structure differ from the stress which would have occurred at the same point In the free field. The horizontal stress beneath the foundation Is considerably less than the corresponding free field stress. Also, the stress In the soil adjacent to the structure appears to be uniquely related to the velocity of the structure; however, a quantitative relationship Is not established. Finally, an attempt Is made t6 correlate the translatlonal and rotational response spectra of the foundation to the peak acceleration of the single-degree-of-freedom oscillators representing the containment and Internal support structures. Since the peak accelerations of the oscillators are less than the sum of the two response spectra at the appropriate frequencies, It Is concluded that rocking and translation are out of phase v/lth each other, and their response spectra should not be superposed.

This is a case study where the goal is to predict the vibration environment due to a footfall excitation in the vicinity of a replacement Magnetic Resonance Imaging (MRI) unit on a hospital floor. A new MRI unit with a weight of 19,000 lbs replaces an existing, much heavier unit with a weight of 82,000 lbs. Dynamic characteristics of the floor will change when the new unit is installed, affecting the vibration environment of the unit that is generated by nearby footfalls.In this study we use physical heel drop measurements of the existing conditions to calibrate a computer model that we then use to predict the vibrations and compare the calculated vibrations with the criteria for the new unit.The results show that the vibration levels predicted for the new MRI unit do not exceed its vibration criterion. The paper will present detailed analytical model and analysis procedure, together with conclusions.