only damping in rotation, , is influenced by the stiffness of the pile-soil system as demonstrated by the small spacing among all damping curves prior to approaching resonance frequency. At resonance, all damping modes experience a sudden increase, followed by an approximate linearly trending increase with increasing frequencies. In stiff soil conditions (), damping and align well with each other throughout the entire frequency range. Differences between fixed and hinged tip piles are obvious near resonance for in stiff soils. Beyond = 1, differences between fixed tip and hinged tip pile damping become more pronounced. While damping ratios and for medium stiff soils follow each other closely, larger differences are noticeable for . Results obtained for soft soil conditions show a strong divergence across all damping modes. Comparison with Winkler model The proposed model is compared against stiffness and damping formulations obtained from literature. Springs and dashpots proposed by Baranov-Novak (, ), Dobry , Gazetas and Dobry , Makris and et al. Gazetas , and Mylonakis as summarized by Anoyatis and Lemnitzer are implemented in a Winkler model and compared with results from Eqs. 10 15 in Figs. 14 and 15. – Note that the stiffness matrix from the Winkler model () can be expressed as: (16) where (17) and , where is the pile cross sectional area. Figure 14 compares the dynamic stiffness of the proposed model with results from Winkler based formulations. The expressions suggested by Dobry fail to represent the pile stiffness across the et al. entire frequency range. As expected, the plane strain spring and dashpot by Baranov-Novak cannot capture the dynamic effects associated with resonance but can be used to estimate pile stiffness at frequency ratios of 3. While Makris and Gazetas does not perform well for , better performance is achieved for beyond resonance and at high frequencies. Solutions obtained using Gazetas and Dobry , provide a good estimation for beyond resonance and for and beyond 3. Even though Mylonakis underestimates the resonance stiffness in swaying and rotation, the expression renders the Winkler model capable of predicting the dynamic stiffness in swaying-rotation over the whole frequency range. Figure 15 compares pile damping ratios for all modes. With the exception of Baranov-Novak, the Winkler model using the simple expressions is capable of capturing damping below resonance. At
only damping in rotation, , is influenced by the stiffness of the pile-soil system as demonstrated by the small spacing among all damping curves prior to approaching resonance frequency. At resonance, all damping modes experience a sudden increase, followed by an approximate linearly trending increase with increasing frequencies. In stiff soil conditions (), damping and align well with each other throughout the entire frequency range. Differences between fixed and hinged tip piles are obvious near resonance for in stiff soils. Beyond = 1, differences between fixed tip and hinged tip pile damping become more pronounced. While damping ratios and for medium stiff soils follow each other closely, larger differences are noticeable for . Results obtained for soft soil conditions show a strong divergence across all damping modes. Comparison with Winkler model The proposed model is compared against stiffness and damping formulations obtained from literature. Springs and dashpots proposed by Baranov-Novak (, ), Dobry et al. , Gazetas and Dobry , Makris and Gazetas , and Mylonakis as summarized by Anoyatis and Lemnitzer are implemented in a Winkler model and compared with results from Eqs. 10 – 15 in Figs. 14 and 15. Note that the stiffness matrix from the Winkler model () can be expressed as: (16) where (17) and , where is the pile cross sectional area. Figure 14 compares the dynamic stiffness of the proposed model with results from Winkler based formulations. The expressions suggested by Dobry et al. fail to represent the pile stiffness across the entire frequency range. As expected, the plane strain spring and dashpot by Baranov-Novak cannot capture the dynamic effects associated with resonance but can be used to estimate pile stiffness at frequency ratios of 3. While Makris and Gazetas does not perform well for , better performance is achieved for beyond resonance and at high frequencies. Solutions obtained using Gazetas and Dobry , provide a good estimation for beyond resonance and for and beyond 3. Even though Mylonakis underestimates the resonance stiffness in swaying and rotation, the expression renders the Winkler model capable of predicting the dynamic stiffness in swaying-rotation over the whole frequency range. Figure 15 compares pile damping ratios for all modes. With the exception of Baranov-Novak, the Winkler model using the simple expressions is capable of capturing damping below resonance. At
Anoyatis%20et%20al%202017.docx