Evaluation of Winkler Model and Pasternak Model for Dynamic Soil-Structure Interaction Analysis of Structures Partially Embedded in Soils

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Department of Civil and Environmental Engineering


This paper reports a comprehensive study including detailed experimental, theoretical, and numerical analyses to evaluate the performance of two predominant soil-structure interaction models, that is, the Winkler model and Pasternak model, in predicting the predominant natural frequency (PNF) of structures partially embedded in soils. For the evaluation, PNF-based scour detection, a nondestructive testing technique that has been receiving increasing attention, was adopted. First, a series of lab experiments was conducted using idealized piers partially embedded in two representative soils, that is, a sand and a clay, to measure the PNF-scour depth relationship. Next, a mathematical model was established and numerically implemented to predict the PNF of the idealized piers for scour detection. The soil-structure interaction was formulated using the Winkler model, which only considers the modulus of subgrade reaction for soils, and the Pasternak model, which considers the shear interaction in addition to the modulus. The numerically computed PNFs were then compared with those from the experiments in this study and a documented field test. Our results clearly show that when structures are partially embedded in soils, the Winkler model yields a better PNF prediction than the Pasternak model, regardless of the types of test piers and soils. This finding is different from those obtained in the dynamic response of structures resting on or fully embedded in an elastic foundation (i.e., not partially embedded), where the Pasternak model yields more realistic results than the Winkler model because of its consideration of the continuity of foundation media via the shear interaction. Because of the shear interaction, the PNFs predicted with the Pasternak model in this study are about 24%–38% and 31%–39% higher than the predictions with the Winkler model and the measured PNFs, respectively.

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International Journal of Geomechanics