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Title: Earth vibration effects and abatement for military facilities. Report 2, The particle motion field generated by the torsional vibration of a circular footing on sand
Authors: Heller, Lyman W.
Keywords: Foundations
Mathematical models
Publisher: Soils and Pavements Laboratory (U.S.)
Series/Report no.: Technical Report;S-71-14, Report 2
Abstract: Abstract: Over the past few years, it has been demonstrated that the self-excited vibratory motion of a circular footing on various types of soil can be successfully predicted by a mathematical model derived by assuming that the foundation soil is represented by a homogeneous elastic half-space. This finding suggested that the same model, or variations thereof, might be useful for predicting the particle motion generated within a soil foundation by a vibrating footing. The objective of this study was to test the hypothesized utility of the half-space model for predicting the motion field generated in a natural soil deposit by the forced torsional vibration of a circular footing. The test involved the computation of half-space motion, the measurement of soil motion, and a comparison of the computations to the measurements. A 5-ft-diam footing was vibrated at 5 different frequencies on a natural sand deposit with a shear modulus that varied from about 1,800 psi at a depth of 1 ft to about 23,000 psi at a depth of 35 ft. Resultant particle motions were measured on the footing and at radial distances to 90 ft and at depths to 35 ft. Homogeneous half-space particle motions were computed using a shear modulus of 9,480 psi. The average measured particle displacement, neglecting damping, was between 1/3 and 1/4 of the computed displacement. The measured displacements were 1/10 of the calculated displacements at the deeper locations and 3 times the calcu1ated displacements near the ground surface. Near the footing, the displacements were in good agreement. Recent literature on the stress conditions in a nonhomogeneous elastic half-space suggested that the particle displacements in a homogeneous half-space could be used to determine the particle displacements in a nonhomogeneous half-space. When the sand deposit was considered as a nonhomogeneous half-space and damping was neglected, the displacements were in good agreement near the footing, the average measured displacement was 60 percent of the computed displacement, and the measured displacements were 1/4 to 2-1/2 times the computed displacements. The material damping effect on the propagating body waves agreed with previous determinations for this effect on surface waves at a similar test site. The correlation between the ratio of the computed displacement to the measured displacement and the cone bearing capacity of the sand deposit at various depths suggested that a more accurate and detailed determination of the shear modulus of the sand would improve the correspondence between measured and computed results. Because the accuracy of the particle displacement predictions was adequate to classify transmitted vibrations as either undetectable, readily apparent, or intolerable, the elastic half-space model, adjusted for nonhomogeneous site conditions, was considered a potentially useful analytical representation of a natural soil deposit subjected to torsional footing vibrations.
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