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# Dynamic Analysis For Laterally Loaded Piles And Dynamic P-y Curves

M Hesham El Naggar, Kevin J Bentley

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Pile foundations are often subjected to lateral dynamic loading due to forces on the supported structure. In this study, a simple two-dimensional analysis was developed to accurately model the pile response to dynamic loads. The proposed model incorporates the static p-y curve approach (where p is the static soil reaction and y is the pile deflection) and the plane strain assumptions to represent the soil reactions within the frame of a Winkler model. The p-y curves are used to relate pile deflections to the nonlinear soil reactions. Wave propagation and energy dissipation are also accounted for along with discontinuity conditions at the pile-soil interface. The inclusion of damping with the static unit transfer curves results in increased soil resistance, thus producing "dynamic p-y curves." The dynamic p-y curves are a function of the static p-y curve and velocity of the soil particles at a given depth and frequency of loading. The proposed model was used to analyze the pile response to the lateral Statnamic load test, and the predicted response compared well with the measured response. Closed-form solutions for dynamic p-y curves were established by curve fitting the dynamic soil reactions for a range of soil types and loading frequencies. These solutions can be used to model soil reactions for pile vibration problems in readily available finite element analysis (FEA) and dynamic structural analysis packages. A simple spring and dashpot model was also proposed to be used in equivalent linear analyses of transient pile response. The proposed models were incorporated into an FEA program (ANSYS) which was used to compute the response of a laterally loaded pile. The computed responses compared well with the predictions of the two-dimensional analysis.Key words: dynamic, transient, lateral, piles, p-y curves, inertial interaction.