## Environment: Seabed data |

The seabed data fall naturally into two distinct groups, governing the shape of the seabed and its properties.

Three types of seabed shape are available:

- A flat seabed is a simple plane, which can be horizontal or sloping.
- A profiled seabed is one where the shape is specified by a 2D profile in a particular direction. Normal to that profile direction the seabed is horizontal.
- A 3D seabed allows you to specify a fully general 3D surface for the seabed, by defining the depth at a series of $X,Y$ positions, with a choice of linear or cubic polynomial interpolation in between.

The **seabed origin** is a point on the seabed and it is the origin relative to which the seabed data are specified. It is defined by giving its coordinates with respect to global axes.

For a flat seabed, if you enter a value for the seabed origin $Z$ coordinate, then the **depth** value (the water depth at the seabed origin) will be updated accordingly, and vice versa: if you enter a depth, the $Z$ coordinate will be updated, based on the value of sea surface Z.

For profile and 3D seabeds, the $Z$ coordinate and water depth at the seabed origin are displayed but they are not editable: they are determined by the $Z$ values in the profile or 3D geometry data and the given sea surface Z.

The **seabed direction** follows the OrcaFlex direction conventions, so is measured positive anti-clockwise from the global $X$ axis when viewed from above. The meaning of this direction depends on the type of seabed in use:

- For a flat seabed, the direction is that of maximum upwards slope. For example, 0° means sloping upwards in the global $X$ direction, 90° means sloping up in the in the global $Y$ direction.
- For a profile seabed, the direction is that in which the 2D profile is defined.
- For a 3D seabed, the direction and the seabed origin together define a frame of reference, relative to which the seabed data points are specified.

This is the maximum upward slope, in degrees above the horizontal. A flat seabed is modelled as a plane passing through the seabed origin and inclined at this angle in the seabed direction. The model is only applicable to small slopes. OrcaFlex will accept slopes of up to 45° but the model becomes increasingly unrealistic as the slope increases, because the bottom current remains horizontal.

The profile table defines the seabed shape in the vertical plane through the seabed origin in the seabed direction. The shape is specified by giving the either the seabed **Z coordinate** relative to global axes, or the **depth**, at a series of points specified by their **distance from seabed origin** in the seabed direction (negative values representing points in the opposite direction). If a $Z$ coordinate is entered then the depth is updated to match, and vice versa.

Seabed $Z$ values in between profile points are obtained by interpolation, with a choice of **interpolation method**. The seabed is assumed to be horizontal. The seabed is assumed to be horizontal in the direction normal to the seabed profile direction and beyond the ends of the table.

Warning: | Linear interpolation can cause difficulties for static and dynamic calculations. If you are having problems with static convergence or unstable simulations then you should try one of the other interpolation methods. |

Note: | You cannot model a true vertical cliff by entering two points with identical distances from seabed origin but differing $Z$ coordinates – the second point will be ignored. You can, however, specify a near-vertical cliff. If you do this, to avoid interpolation overshoot you may need to either specify several extra points just either side of the cliff or use linear interpolation. |

The view profile button displays a graph of the seabed profile, showing the specified profile points and the interpolating curve. The seabed is horizontal beyond the ends of the graph.

You should check that the interpolated shape is satisfactory, in particular that the interpolation has not introduced overshoot – i.e. where the interpolated seabed is significantly higher or lower than desired. Overshoot can be solved by adding more profile points in the area concerned and carefully adjusting their coordinates until suitable interpolation is obtained.

The 3D seabed is defined by specifying a set of **x**, **y** and **Z** coordinates of the seabed. The $x$ and $y$ coordinates are given with respect to a right-handed frame of reference with origin at the seabed origin, $Z$ vertically upwards, $x$-axis horizontal in the specified seabed direction and $y$-axis horizontal and normal to that $x$-direction. The $Z$ coordinate is specified relative to the global origin. Equivalently, you may give **depth** values instead of $Z$ coordinates. If a $Z$ coordinate is entered then the depth is updated to match, and vice versa.

OrcaFlex forms a triangulation of the input data and interpolates this with either the **linear** or **cubic polynomial** method. We normally recommend using cubic polynomial: this provides a smooth interpolation which makes both static and dynamic calculations more stable and robust than the linear method.

The linear method has been provided for the special case in which the seabed data are limited to only depth and slope at each line anchor point. The linear interpolation method then allows you to build a seabed which is effectively a number of different flat sloping seabeds for each line.

The **minimum edge triangulation angle**, $\alpha$, provides a degree of control over the triangulation. Some data sets (for example those which are concave) can result in unusual artefacts around the edges of the data; if this happens, you may find that setting $\alpha$ to a value greater than zero helps. With $\alpha{\gt}0$, triangles at the edge of the triangulation with internal angles less than $\alpha$ are removed. On the other hand, this may lead to significant portions of your triangulated seabed being removed, so unless you see these artefacts we recommend that you choose $\alpha{=}0$.

Note: | The seabed generated by OrcaFlex only extends as far as the data given and, at any point outside the horizontal area specified, the sea is considered to be infinitely deep. You must therefore provide data covering the whole area of seabed which might be contacted by any model object. |

Two seabed models are available, an elastic model (which may be linear or nonlinear) and a nonlinear soil model. In summary,

- The elastic seabed behaves as a simple elastic spring in directions normal and tangential to the seabed plane. The normal direction stiffness may be defined independently of the stiffness for the tangential directions. The normal stiffness may be linear or nonlinear; tangential stiffness is linear.
- The nonlinear soil model is a more sophisticated model of the normal direction seabed resistance. It includes the nonlinear hysteretic behaviour of seabed soil in the normal direction, including modelling of suction effects when a penetrating object rises up. As with the elastic model, tangential stiffness is linear.

The data requirements for these two models are described below.

The elastic model treats the seabed as a simple elastic spring, which may be either linear or nonlinear in both the seabed normal and the seabed shear directions. This gives a seabed normal resistance that is proportional to the penetration, and a seabed tangential resistance that is proportional to the tangential displacement of the contact point (e.g. a node on a line) from its undisturbed position.

In addition, when explicit integration is used the elastic model includes linear damping in the normal and tangential directions, giving extra damping resistance that is proportional to the rate of penetration (for the normal direction) or the rate of tangential movement (for the tangential directions). The linear damper in the normal direction acts only when penetration is increasing and not when it is decreasing, i.e. suction effects are not modelled.

The **seabed normal stiffness** specifies the properties for the normal spring. To specify a linear stiffness, enter a single stiffness value that is the reaction force that the seabed applies per unit depth of penetration per unit area of contact. For nonlinear stiffness, use variable data to specify a table of reaction force per unit area of contact against depth of penetration.

The **seabed shear stiffness** is used by the friction calculation. A value of 0 disables friction. A value of ~ indicates that the seabed normal stiffness value is to be used: in the case that the normal stiffness is nonlinear, then the value corresponding to zero penetration is used.

The **seabed damping** is the constant of proportionality of the damping force, and is a percentage of critical damping. Seabed damping is always zero when using the implicit integration scheme.

The nonlinear soil model has been developed in collaboration with Prof. Mark Randolph FRS (Centre for Offshore Foundation Systems, University of Western Australia). It builds upon earlier models which used a hyperbolic secant stiffness formulation, such as those proposed by Bridge et al and Aubeny et al, and is documented in Randolph and Quiggin (2009).

The nonlinear soil model is more sophisticated than the elastic model. It models the nonlinear and hysteretic properties of seabed soil in the normal direction, including modelling of suction effects. (In the tangential directions the seabed is modelled in the same way as for the linear elastic model.)

The nonlinear soil model is suited to modelling soft clays and silty clays, and is particularly appropriate for typical deep water seabeds where the mudline undrained shear strength is only a few kPa or less, and where the seabed stiffness response to catenary line contact is dominated by plastic penetration rather than elastic response. This model is not suitable for caprock conditions, and using it to model sand requires very careful choice of soil data and model parameters to represent sand response.

For further details of the model, see the seabed theory and nonlinear soil model theory topics.

Note: | For dynamic analysis using implicit integration you might find that you need to use a shorter time step with the nonlinear soil model than with the elastic model. |

The data for the nonlinear soil model are divided into three groups:

These specify the undrained shear strength and saturated density of the seabed soil. They should be obtained from geotechnical survey of the site.

The shear strength is determined by the undrained **shear strength at mudline**, $s_\mathrm{u0}$, and the undrained **shear strength gradient**, $\rho$. The undrained shear strength at any given penetration distance $z$ is then
\begin{equation}
s_\mathrm{u}(z) = s_\mathrm{u0} + \rho z
\end{equation}
The **saturated soil density** is the density of the seabed soil when fully saturated with sea water. It is used by the nonlinear seabed model to model the extra buoyancy effect that arises when a penetrating object displaces seabed soil.

Site-specific data should be used. Typical saturated soil densities are in the range 1.4 to 1.6 te/m^{3}. Typical deep water sediments have essentially negligible undrained shear strength at mudline (0 to 5 kPa) and an undrained shear strength gradient of 1.3 to 2 kPa/m. Seabed soils are typically stronger in shallow water than in deep water.

These specify the strength of the tangential linear spring-damper that is used to model the shear resistance. These data are the same as those described above for the elastic model. The shear damper is only used for explicit integration; for implicit integration the shear damper strength is zero.

The shear stiffness can be given as the default value '~', to get OrcaFlex to calculate a value based on the soil shear strength data given by the soil properties. The formula used is \begin{equation} \text{Shear stiffness} = \frac{20}{d}\ (s_\mathrm{u0} + \rho\ \tfrac12 d) \end{equation} where $d$ is the contact diameter of the penetrating object; the term in brackets is the soil undrained shear strength at a penetration depth of $d/2$.

These parameters appear on a separate page on the environment data form. They are non-dimensional parameters that control how the seabed soil is modelled; their use is detailed under the nonlinear soil model theory topic.