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Elastic lateral dynamic impedance functions are defined as the ratio of the lateral dynamic force/moment to the corresponding lateral displacement/rotation at the top ending of a foundation at very small strains. Elastic lateral dynamic impedance functions have a defining influence on the natural frequencies of offshore wind turbines supported on cylindrical shell type foundations, such as suction caissons, bucket foundations, and monopiles. This paper considers the coupled horizontal and rocking vibration of a cylindrical shell type foundation embedded in a fully saturated poroelastic seabed in contact with a seawater half-space. The formulation of the coupled seawater-shell-seabed vibration problem is simplified by treating the shell as a rigid one. The rigid shell vibration problem is approached by the integral equation method using ringload Green's functions for a layered seawater-seabed half-space. By considering the boundary conditions at the shell-soil interface, the shell vibration problem is reduced to Fredholm integral equations. Through an analysis of the corresponding Cauchy singular equations, the intrinsic singular characteristics of the problem are rendered explicit. With the singularities incorporated into the solution representation, an effective numerical method involving Gauss-Chebyshev method is developed for the governing Fredholm equations. Selected numerical results for the dynamic contact load distributions, displacements of the shell, and lateral dynamic impedance functions are examined for different shell length-radius ratio, poroelastic materials, and frequencies of excitation.where 0 ≤ θ ≤ 2π, 0 ≤ z ≤ l. Eqn. (27) is a set of Fredholm integral equations about the interfacial forces p z (z), p r (z), and p θ (z) which can be solved numerically. To deal with the singular tractions at the top and bottom of the shell, the method in [9] will be employed. It entails studying the corresponding Cauchy singular equations 516 R. HE, R. Y. S. PAK AND L. WANG

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Discrete bio-gas bubbles commonly form in fine-grained marine sediments and have modified many aspects of the behavior of these sediments, including strength, stiffness, and permeability. Although the level of such modifications is known to govern by bubble shape and size, limited studies have been undertaken, mainly due to difficulty in nondestructively characterizing bubbles within a soil under in situ stresses. In this study, a mini-loading device was developed to perform one-dimensional loading tests on gassy marine clay and gassy silt in a microcomputed tomography (μCT). The evolving bubble shape, size, and pressure during loading were quantified, and the resulting stress fields around the bubble cavities were evaluated via elliptical cavity contraction analysis considering stress anisotropy. As the vertical load increased, bubble cavities were found to compress predominantly along the vertical loading direction, with little horizontal compression, because localized soil failure (LSF) and thus cavity collapse occurred mainly near the roof of the at-rest lateral earth pressure coefficient (K0)-stressed elliptical bubble cavities. The evolution of bubble shape and size under loading is significantly affected by stress anisotropy, which governs the extent and location of the LSF. A Gaussian mixture model is adopted to quantify the evolving distributions of bubble structure parameters, which are essential for developing more physically rigorous gassy soil models.

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