Three-dimensional investigation of wave–pile group interaction using the scaled boundary finite element method. Part I: Theoretical developments

Abstract In this study, the three-dimensional wave–pile group interaction mechanism is investigated by addressing both wave behaviour and pile group responses. The Scaled Boundary Finite Element Method (SBFEM) is employed to develop the computational model. This paper, Part I of the study, mainly focuses on the theoretical development of the problem. A SBFEM model is developed to formulate both equations governing the wave motion and the structural behaviour. The proposed model, with its accuracy verified by wave interaction with a single pile foundation, is capable of addressing wave interaction with any arbitrary number of piles with various cross-sections and spatial layouts.

[1]  Zhenjun Yang.  Application of scaled boundary finite element method in static and dynamic fracture problems , 2006 .

[2]  Jun Liu,et al.  Three-dimensional investigation of wave–pile group interaction using the scaled boundary finite element method—Part II: Application results , 2013 .

[3]  Miao Li,et al.  Structural Response of Offshore Monopile Foundations to Ocean Waves , 2010 .

[4]  Gao Lin,et al.  The scaled boundary finite element method applied to electromagnetic field problems , 2010 .

[5]  J. Wolf,et al.  Finite-element modelling of unbounded media , 1996 .

[6]  Miao Li,et al.  Study of offshore monopile behaviour due to ocean waves , 2011 .

[7]  J. N. Newman,et al.  Wave diffraction by a long array of cylinders , 1997, Journal of Fluid Mechanics.

[8]  Subrata K. Chakrabarti,et al.  Scaled boundary FEM solution of short-crested wave diffraction by a vertical cylinder , 2007 .

[9]  N Nordenstrom,et al.  SAFETY OF OFFSHORE STRUCTURES , 1985 .

[10]  Hong Guan,et al.  Schur decomposition in the scaled boundary finite element method in elastostatics , 2010 .

[11]  Peter L. Monkmeyer,et al.  A PROGRAMMABLE IRREGULAR WAVE GENERATOR , 1974 .

[12]  Andrew Deeks,et al.  A semi-analytical solution method for two dimensional Helmholtz Equation , 2006 .

[13]  Hao Song,et al.  Modelling of water wave interaction with multiple cylinders of arbitrary shape , 2010, J. Comput. Phys..

[14]  Yoshimi Goda,et al.  Random Seas and Design of Maritime Structures , 1985 .

[15]  Guido Benassai,et al.  Introduction to Coastal Dynamics and Shoreline Protection , 2006 .

[16]  D. Yue,et al.  Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method , 1986, Journal of Fluid Mechanics.

[17]  A. Sommerfeld.  Partial Differential Equations in Physics , 1949 .

[18]  D. Evans,et al.  The interaction of waves with arrays of vertical circular cylinders , 1990, Journal of Fluid Mechanics.

[19]  J. Wolf,et al.  Consistent infinitesimal finite-element cell method for diffusion equation in unbounded medium , 1996 .

[20]  Chongmin Song.  A matrix function solution for the scaled boundary finite-element equation in statics , 2004 .

[21]  Atilla Incecik,et al.  Analytical solutions of the diffraction problem of a group of truncated vertical cylinders , 1998 .

[22]  Andrew Deeks,et al.  Fully-automatic modelling of cohesive crack growth using a finite element-scaled boundary finite element coupled method , 2007 .

[23]  J. D. Wheeler,et al.  Methods for Calculating Forces Produced by Irregular Waves , 1969 .

[24]  R. E. Taylor,et al.  Wave diffraction from linear arrays of cylinders , 2005 .

[25]  John P. Wolf,et al.  The scaled boundary finite-element method: analytical solution in frequency domain , 1998 .

[26]  C. Z. Wang,et al.  Time domain analysis of second-order wave diffraction by an array of vertical cylinders , 2007 .

[27]  C. Mei.  The applied dynamics of ocean surface waves , 1983 .

[28]  Chongmin Song,et al.  The scaled boundary finite-element method—alias consistent infinitesimal finite-element cell method—for elastodynamics , 1997 .

[29]  J. Wolf,et al.  Consistent Infinitesimal Finite-Element Cell Method: Three-Dimensional Vector Wave Equation , 1996 .

[30]  Spyros A. Mavrakos,et al.  An analytical approach for the solution of the hydrodynamic diffraction by arrays of elliptical cylinders , 2010 .

[31]  P. Gould.  Introduction to Linear Elasticity , 1983 .

[32]  Masashi Kashiwagi,et al.  Hydrodynamic interactions among a great number of columns supporting a very large flexible structure , 2000 .

[33]  Gao Lin,et al.  A coupled FE and scaled boundary FE-approach for the earthquake response analysis of arch dam-reservoir-foundation system , 2010 .

[34]  Eiichi Watanabe,et al.  An eigenfunction expansion-matching method for analyzing the wave-induced responses of an elastic floating plate , 1995 .

[35]  Subrata K. Chakrabarti,et al.  Spacing Effect on Hydrodynamics of Two Adjacent Offshore Caissons , 2009 .

[36]  Hsien Hua Lee,et al.  Dynamic behavior of tension-leg platform with net-cage system subjected to wave forces , 2001 .

[37]  Boning Li.  Extending the scaled boundary finite-element method to wave diffraction problems , 2007 .

[38]  Song-Ping Zhu,et al.  Diffraction of short-crested waves around a circular cylinder , 1993 .