Abstract:In this study, the formulation of Lysmer's analog method is presented briefly first. The radiation damping ratio, stiffness, and vibrational mass for a certain amount of soil may be obtained from a half-space system that is equivalent to a mass-spring system. Subsequently, a combination of both systems is discussed. On the basis of measurement, analysis, and application, the damping ratio is reduced:this is a modification for modeling non-homogeneous soil and is more practical. For a long time, a larger damping ratio has been considered to be unsafe and thus not used; this constraint may disappear and subsequently the practical use of half-space theory will become more common. The focal point of this study is the practical use of the method. First, two experimental tests have revealed that the damping ratio of our state code is very small and the half-space is significantly larger. Therefore, the results from measuring a large number of vibrator foundations and models demonstrate that the damping ratio of the half-space must be modified.(1) The damping ratio of homogeneous soil must be reduced. Although some energy of wave propagation is consumed, wave reflection or refraction is performed by soil or hard layers. The energy consumed is less, and the damping ratio is not as large with a discount coefficient of 0.5~0.7.(2) The former Soviet code of 1979 used a reduction of 30% on the half-space damping ratio for the design of dynamic machine foundation, which is equal to the upper reduction limit of our measurement results. In 1996, a Russian academician who had been the chief editor of that code came to China to deliver lectures and explained that the reduction value was obtained from a large number of comparisons obtained by measuring.(3) The reduced damping ratio of homogeneous soil is practical. The reduced damping ratio is still greater than that of our state code and will be both more economical and safer for the design of dynamic foundations.
