Hydrodynamic Load Models

The Morison generalized equation is an empirical formulation used for calculations of hydrodynamic loads on slender structures, i.e. slender versus wavelength and wave height. Morison’s equation can be used when the the wavelength is large relative to the diameter.

The MacCamy-Fuchs method may be used to provide acceptable hydrodynamic forces outside the region for which Morison’s equation is valid.
Note that the requirement for slender structural elements for applying beam theory still applies.
For large diameter circular columns, diffraction effects become important in short waves.
The MacCamy-Fuchs analytical solution for first order diffraction for a vertical surface-piercing cylinder has been implemented as pre-generated wave forces calculated before the dynamic simulation using the static coordinates.
This approach is applicable for finite water depth and gives depth- and frequency-dependent wave loads up to the still water level.
For linear wave theory, the results are exact for a pile whose diameter is much greater than the wave height.

The solution is given for an earth fixed pile with constant diameter but is assumed to be applicable for cases where the diameter does not change too rapidly.
The local diameter, vertical position, and components of the wave potential are the only required input to the force computation.

For elements with MacCamy-Fuchs type loading, the formulation for the inertia and diffraction forces follows (MacCamy and Fuchs, 1954 and Dean and Dalrymple, 1991), with modifications for the irregular wave history.

Note that the loads act in the horizontal plane.

Time series for the MacCamy-Fuchs wave excitation loads are generated during pre-stochastic analysis and applied during dynamic analysis.
Interpolation is applied if the simulation time step differs from the pre-generated interval

To extend the use of MacCamy-Fuchs loads on bottom-fixed cylindrical monopiles to be applicable for floating single column systems a simple load model representing the radiation forces is implemented.
The radiation loads are based on an added mass coefficient and a damping coefficient and included as:

The forces based on MacCamy-Fuchs load model including radiation contributions are calculated at the center of an element and distributed to the element ends (nodes).

Note that in the tangential direction the wave excitation forces are calculated in a similar manner as the corresponding load term in the generalized Morison equation. (\f\(dF_T\f\))
The drag terms are calculated as described for the generalized Morison equation and act in the local element system.

The hydrodynamic element forces based on potential theory (WAMIT) has been implemented in RIFLEX. However, this functionality is still under development and not commercially supported. The purpose of implementing hydrodynamic element forces based on potential theory (WAMIT) results, is to provide adequate hydrodynamic forces outside the area for which Morison’s equation is valid. It also accounts for interaction effects, e.g. with other structural member, sea floor etc.

Use of the implementation requires manual runs of:

1. WAMIT
2. User written scripts to integrate the WAMIT pressures
3. SIMATOOL_retfun.exe that calculates retardation functions from frequency dependent added mass and damping and does a polynominal fitting to the retardation function.

Note that only translation components of pressure and forces are considered (3 degrees of freedom). Time series for the wave excitation forces are generated during pre-stochastic analysis and applied during dynamic analysis. If the time integration step is different to the pre-generated time step, the pre-generated time series will be interpolated.

The forces based on this method are calculated at the mid-point of the element and distributed to the element ends (nodes). The drag terms are calculated as described for the generalized Morison equation.

If the Froude-Krylov pressure is included in the longitudinal component of the calculated loads, the Froude-Krylov scaling factor in tangential direction must be deactivated, so that this term is not included twice.

The Froude-Krylov force is a part of the Morsion’s Generalized Equation, and is related to the undisturbed pressure field. Both MacCamy-Fuchs and Potential flow use the Morison’s Generalized Equation formulation for the tangential loads. For the potential flow formulation it is important to deactivate the Froude-Krylov force in tangential direction if this is included in the potential theory calculations.