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Numerous physical models using frequency-independent elements have been developed to reproduce impedance functions for the purposes of time-domain soil–foundation interaction analysis. Most of the models have been developed to simulate homogeneous soils. However, the physical models developed in past research for layered soils are mostly focused on surface foundations only. Accordingly, this study proposes a representative simplified model to simulate the three-dimensional layered soil for square foundations embedded in a non-uniform layer, overlying a uniform half-space, subjected to vertical forced vibrations. The non-uniform layer has shear-wave velocities linearly varying with depth. Non-dimensional charts are presented to determine the model parameters as per foundation embedment ratios, layer depth ratios, and shear-wave velocity ratios of layered soil. The capability of the proposed model is demonstrated through the analysis of frequency-response curves of the foundation to a constant-force type oscillator in the frequency domain and of the displacement history of the foundation to a non-periodic loading in the time domain. The proposed model is found to give results consistent with those obtained from a dynamic soil-structure interaction analysis program. The proposed model may be of practical value for analysis of dynamically loaded foundations.

A simplified model of layered soil for analyzing vertical vibration of loaded foundations