DYNAMIC CHARACTERISTICS OF STRUCTURES ON PILES AND FOOTINGS

In this paper, novel analytical solutions are presented for single degree-of-freedom (SDOF) oscillators founded on footings and piles on compliant soil. First, exact formulas for the fundamental natural period of the above structures, encompassing the frequency dependence of the various impedance terms, are derived. Second, closed-form solutions for the corresponding damping coefficients are derived. It is shown that the common approximation of neglecting higher-order terms involving products of damping coefficients is unnecessary and potentially inaccurate for highly-damped soilstructure systems. To address the issue of coupled swaying-rocking oscillations at the pile head, the reference system is translated to the depth below the pile head where the resultant soil reaction to the pile is applied, to ensure a diagonal impedance matrix. Third, the amounts of radiation damping generated from a single pile and a footing are compared. To this end, the concept of statically and geometrically equivalent SSI systems is introduced. It is shown that a structure founded on a pile may generate twice the amount of radiation damping of a similar structure on a spread footing. Results are provided in ready-to-use graphs and charts that elucidate the salient features of the problem and can be directly implemented in design. The paper complements and extends the seminal studies in the subject by Parmelee, Veletsos, Bielak and their co-workers.