Presented is an energy dissipation analysis framework for granular material that is based on thermodynamics. Theoretical formulations are derived from the second law of thermodynamics, in conjunction with a few plausible assumptions on energy transformation and dissipation. The role of plastic free energy is emphasized by a conceptual experiment showing its physical nature. Theoretical formulation is adapted in order to be applied in elasticplastic finite element method (FEM) simulations. Developed methodology is verified through comparison of input work, stored energy, and energy dissipation of the system. Separation of plastic work into plastic free energy and energy dissipation removes a common mistake, made in a number of publications, where energy dissipation can attain negative values (energy production) which is impossible.

This study presents a finite element based approach to evaluate the linear and nonlinear frequency-amplitude response of floating piles subject to rotating machine induced vertical vibrations. A Matlab program is developed to compute the response of a single pile with floating tip condition for a linear and two nonlinear soil models. The variation of complex soil stiffness parameters with frequency has also been presented using different boundary zone parameters (shear modulus reduction ratio, thickness ratio and damping ratio). A detailed investigation of soil-pile system stiffness and damping parameters has been done considering different values of soil-pile separation lengths and boundary zone parameters. To verify the effectiveness of this proposed approach vertical vibration tests were conducted in the field on a single pile of diameter 0.114 m and length of 2.85 m by constructing floating tip condition. The frequencyamplitude response obtained from field vibration test has been compared with the theoretical results for all the soil models. From the comparison results it is observed that the proposed theory can predict the nonlinear response of floating piles very efficiently with proper inclusion of boundary zone parameters and soil-pile separation lengths.

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