Uniqueness of Damping and Stiffness Distributions in the Identification of Soil and Structural Systems

As the interest in the seismic design of structures has increased considerably over the past few years, accurate predictions of the dynamic responses of soil and structural systems has become necessary. Such predictions require a knowledge of the dynamic properties of the systems under consideration. This paper is concerned with the uniqueness of the results in the identification of such properties. More specifically, the damping and stiffness distributions, which are of importance in the linear range of response, have been investigated. An N-storied structure or an N-layered soil medium is modeled as a coupled, N-degree-of-freedom, lumped system consisting of masses, springs, and dampers. Then, assuming the mass distribution to be known, the problem of identification consists of determining the stiffness and damping distributions from the knowledge of the base excitation and the resulting response at any one mass level. It is shown that if the response of the mass immediately above the base is known, the stiffness and damping distributions can be uniquely determined. Following this, some nonuniqueness problems have been discussed in relation to the commonly used ideas of system reduction in the study of layered soil media. A numerical example is provided to verify some of these concepts and the nature of nonuniqueness of identification is indicated by showing how two very different (yet physically reasonable) systems could yield identical excitation-response pairs. Errors in the calculation of the dynamic forces, due to erroneous identification have also been illustrated thus making the results of the present study useful from the practical standpoint of the safe design of structures to ground shaking.