Perhaps the leading question to be answered about soil-structure interaction is: 'For what soil conditions will the rigid base assumption lead to significant errors in the response calculations?' Veletsos and Meek (1974) have suggested that consideration of soil-structure interaction is only warranted for values of the ratio vs
fh where vs is the shear-wave velocity in the soil half-space, f is the fixed-base frequency of the single-degree-of-freedom structure, and h is its height. Substituting f & 30/h for framed buildings and f & 45/h for shear wall buildings in the above equation implies that soil-structure interaction effects may be important for framed buildings when vs < 600 m/s, or for shear wall buildings when vs < 900 m/s. As seen from Table 5.1, these shear-wave velocities cover the full range of ground conditions softer than bedrock. Obviously, this is too general to be of much use in predicting when soil-structure interaction effects are likely to be substantial.
It is of interest that equation (5.34) correctly predicts that soil-structure interaction is important for the concrete gravity oil platforms studied by Watt et al. (1976). Radiation damping effects were found to reduce the base shear of a platform on 'very hard' ground (vs = 480 m/s) by about 50% (the relevant value of vs/fh was 6.6), despite the fact that the foundation was effectively rigid regarding its effect on the mode shapes and periods. It is relevant that these offshore structures have a high mass density factor, m/pnR2h, where p is the density of the soil and m is the participating mass of the structure.
Research by Zhao (1990) has shown that if the fundamental period of the structure is less than the fundamental period of the site, ignoring the soil-structure interaction may sometimes be dangerous, while if the fundamental period of the structure is longer than the fundamental period of the site, the soil-structure effects would reduce the response of the structure even without the effects of radiation damping. If the fundamental periods of the structure and the site are similar, the displacement response of the structure relative to the free-field responses are generally very large. It has been found that, in most cases, the period shift is the more important factor affecting the structural response than is the energy dissipation by plastic deformations in the structure and radiation of energy into the flexible soil. Radiation damping is only significant when the natural frequency of the soil-structure system is greater than the natural frequency of the site itself.
In a study by Mylonakis and Gazetas (2000), it was found that soil-structure interaction has detrimental effects in certain seismic and soil conditions, as follows:
• By comparing conventional code design spectra to actual response spectra, it was shown that an increase in fundamental natural period of a structure due to soil-structure interaction does not necessarily lead to smaller response, and that the prevailing view in structural engineering of the always beneficial role of soil-structure interaction is an oversimplification which may lead to unsafe design.
• Ductility demand in fixed-base structures is not necessarily a decreasing function of structural period, as suggested by traditional design procedures. Analysis of motions recorded on soft soils has shown increasing trends in ductility demand at periods higher than the predominant period of the motions.
• Soil-structure interaction in inelastic bridge piers supported on deformable soil may cause significant increases in ductility demand in piers, depending on the characteristics of the motion and the structure. However, inappropriate generalization of ductility concepts and geometric considerations may lead to the wrong conclusion when assessing the seismic performance of such structures.
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