Bang-Fuh Chen

Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank

Abstract A time-independent finite-difference method and a fifth-order Runge–Kutta–Felhberg scheme were used to analyze the dynamic responses of sea-wave-induced fully non-linear sloshing fluid in a floating tank. The interaction effect between the fully non-linear sloshing fluid and the floating tank associated with coupled surge, heave and pitch motions of the tank are analyzed for the first time in the present pilot study. For the analysis of fluid motion in the tank, the coordinate system is moving (translating and rotating) with tank motion. The time-dependent water surface of the sloshing fluid is transformed to a horizontal plane and the flow field is mapped on to a rectangular region. The Euler equations as well as the fully non-linear kinematic free surface condition were used in the analysis of the sloshing fluid. The strip theory for linearized harmonic sea-wave loading was adopted to evaluate the regular encounter wave force. In addition, the dynamic coefficients used in the dynamic equations of tank motion were also derived based on strip theory and a harmonic motion of the tank. The characteristics of free and forced tank motions with and without the sloshing effect are studied. By the damping effect, the response of free oscillation will damp out and that of forced oscillation will approach a steady state. Without sea-wave action, the contribution of the sloshing load would enlarge the angular response of tank motion as well as the rise of free surface and the sloshing effect will delay the damping effect on angular displacement. On the contrary, under sea-wave action, the sloshing effect will decrease the dynamic response of tank motion and rise of free surface. The interaction, sloshing and coupling effects are found to be significant and should be considered in the analysis and design of floating tanks.

Viscous free surface effect on coastal embankment hydrodynamics

Abstract A finite-differnece method was used to calculate the nonlinear hydrodynamic pressures acting on the coastal embankment faces by seismic-wave actions. The nonlinearity of free surface flow, convective acceleration, viscosity and surface tension of fluid are included in the analysis. The kinematic and dynamic free surface boundary conditions are employed for calculating the horizontal fluid velocity, pressure at the free surface and the surface profile of the fluid. The time-dependent water surface is transformed to the horizontal plane, and the flow field is mapped onto a rectangular, making it convenient to model the complex sea bottom geometry and the wavy water surface by the finite-difference method. Fully nonlinear and weakly nonlinear dynamic free surface conditions are used and compared. The effects of surface tension of fluid are also discussed. The nonslip boundary condition is applied on the most part of the interface between fluid and solid face, except the region near the intersection between free surface and wall face. The numerical results are presented for various water depths and ground motion intensities, and their associate viscous effects on coastal embankment hydrodynamics are discussed.

The significance of earthquake-induced dynamic forces in coastal structures design

Abstract The dynamic forces of sea water and backfill soil acting on coastal embankments and the hydrodynamic forces on offshore breakwaters have been analyzed using a finite-difference scheme. A non-horizontal sea bottom is considered in the analysis. Both rigid and flexible embankments are included in the study. For a coastal embankment, the hydrodynamic pressure of sea water acting on the embankment face significantly increases as the slope of the sea bottom increases. On the other side of the embankment, the pore pressure and the interaction force between the soil and fluid will augment significantly when the backfill soil is compressed during earthquakes. When the sea-embankment-backfill soil interaction is included, the dynamic forces acting on a flexible embankment are much larger than those on a rigid one. The comparison of evaluating the sliding of a cassion in a case study of SPM by a conventional analysis and the present seismic analysis was made. The earthquake-induced dynamic pressures on both sides of the embankment (or breakwater) could be much larger than the force generated by the storm surge. The hydrodynamic (or seismic) analysis incorporating the effect of an earthquake should be included in the coastal embankment or offshore breakwater design, especially for the area with active earthquakes.

Nonlinear hydrodynamic pressures generated by a moving high-rise offshore cylinder

Both analytical (small time expansion) and numerical (finite-difference) approaches have been used to solve the earthquake-induced nonlinear hydrodynamic pressure acting on a rigid high rise offshore cylinder. For the high rise offshore cylinder, the most part of the flow field is independent of z and a three dimensional hydrodynamic analysis can be reduced to a two dimensional analysis. At onset, the dimensionless ground displacement ϵ2 = 0 for the two dimensional analysis, the normalized hydrodynamic pressures across cylinder face is a constant and is independent of the radius of the cylinder. The normalized horizontal force coefficient Cfx is independent of intensity of ground acceleration and is approximately linear and proportional to ϵ2 and its onset value is equal to π. For a linear analysis i.e. neglecting nonlinear convective acceleration, the normalized hydrodynamic pressure coefficient is also independent of the radius of cylinder. The analytical method was good for ground motion in a single direction, the results of simultaneous action of two components of ground acceleration can be obtained by the superposition of the results due to separate excitation. But the superposition method is only valid in the linear analysis. For highly nonlinear problem, the present finite difference approach is recommended.

Hybrid three-dimensional finite-difference and finite-element analysis of seismic wave induced fluid–structure interaction of a vertical cylinder

Abstract The two-dimensional finite-difference scheme has been extended to three dimensions to solve nonlinear hydrodynamic pressures and structural responses of a deformable, vertical and circular surface-piercing offshore cylinder during earthquakes. A complete three-dimensional analysis has been made with both the three-dimensional equations of motion and the simultaneous action of three components of ground acceleration included in the analysis. Not only the magnitude but also the direction of the acting ground motion can be varied with time. The dynamic response of a cylinder is approximated by the displacements in the fundamental modes of vibration. A comparison of the dynamic displacement of the cylinder with and without surrounding sea water has been made. The flexibility of the offshore cylinder can significantly increase the hydrodynamic pressures acting on cylinder faces, that is, the fluid–structure interaction is necessary in offshore cylinder analysis. Although the hydrodynamic pressure induced by the vertical ground acceleration of the El Centro 1979 earthquake is significant, the calculated structural dynamic response of a cylinder is very small and the corresponding resultant hydrodynamic force is almost nil. The hydrodynamic force induced by two-horizontal ground acceleration is about the same as that by three simultaneous components of ground acceleration. For a solid and stubbier circular cylinder, the vertical component of ground acceleration may be neglected.

Hydrodynamic forces on concrete sea wall and breakwater during earthquakes: effects of bottom sediment layers and back-fill soil

Abstract The objective of this paper is to present the effect of sediment characteristics on the dynamic response of sea walls and breakwaters during earthquakes. A finite-difference method is used to calculate the earthquake-induced hydrodynamic pressures of seawater and the pore water in seabed sediment. The water-filled soil mixture is used to model sediment and back-fill soil. The dynamic response of a rigid coastal structure induced by constant ground acceleration is studied, using variable sediment depths and porosity. The dynamic characteristics of the water–embankment–sediment system are investigated, applying four earthquake-records as exciting forces. The result of a quay-walled caisson demonstrates the significance of the seismic-induced dynamic force and the seismic effects should be considered for the design of coastal structures in seismic zone. The damaged wharves of Taichung Port during Chi-Chi earthquake, 21 September 1999 is also reported in the paper.