• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.1
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• pp.44-51
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• 1996

The accurate calculation of run-up heights of long waves along the coastline is important in the view of engineering. In this paper the run-up heights of long waves are estimated by using the cnoidal wave theory which also covers both sinusoidal and solitary waves. However, the generation and the calculation of run-up heights of cnoidal waves are difficult both in laboratory and numerical experiments. In this study, the maximum run-up heights of cnoidal waves on steep slopes are computed by using the boundary integral equation model. It has been shown that the run-up heights of cnoidal waves are less than those of solitary waves, while they are larger than those of sinusoidal waves having the same wavelengths and heights. The variation of run-up heights of cnoidal waves is not a monotonic function of the wavelength. However, the run-up heights of cnoidal waves asymptotically approach that of a solitary wave as the wavelength approaches infinity. The calculated run-up heights agreed reasonably with experimental data.

• Geomechanics and Engineering
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• v.31 no.5
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• pp.477-488
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• 2022

Pile composite foundation (PCF) has been commonly applied in practice. Existing research has focused primarily on semi-infinite media having equal pile lengths with little attention given to the effects of inclined bedrock and dissimilar pile lengths. This investigation considers the effects of inclined bedrock on vertical loaded PCF with dissimilar pile lengths. The pile-soil system is decomposed into fictitious piles and extended soil. The Fredholm integral equation about the axial force along fictitious piles is then established based on the compatibility of axial strain between fictitious piles and extended soil. Then, an iterative procedure is induced to calculate the PCF characteristics with a rigid cap. The results agree well with two field load tests of a single pile and numerical simulation case. The settlement and load transfer behaviors of dissimilar 3-pile PCFs and the effects of inclined bedrock are analyzed, which shows that the embedded depth of the inclined bedrock significantly affects the pile-soil load sharing ratios, non-dimensional vertical stiffness N₀/wdE_s, and differential settlement for different length-diameter ratios of the pile l/d and pile-soil stiffness ratio k conditions. The differential settlement and pile-soil load sharing ratios are also influenced by the inclined angle of the bedrock for different k and l/d. The developed model helps better understand the PCF characteristics over inclined bedrock under vertical loading.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.21 no.2
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• pp.131-136
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• 1985

The calculation of the resulting fluid motion is an important problem of ship hydrodynamics. For a partially immersed body the condition of constant pressure at the free surface can be linearized. The resulting linear boundary-value problem for the velocity potential is the Neumann-Kelvin problem. The two-dimensional Neumann-Kelvin problem is studied for the half-immersed circular cylinder by Ursell. Maruo introduced a slender body approach to simplify the Neumann-Kelvin problem in such a way that the integral equation which determines the singularity distribution over the hull surface can be solved by a marching procedure of step by step integration starting at bow. In the present pater for the two-dimensional Neumann-Kelvin problem, it has been suggested that any solution of the problem must have singularities in the corners between the body surface and free surface. There can be infinitely many solutions depending on the singularities in the coroners.