Wave-loaded seabed response: `rodAndSeabed`

Prepared by Philip Cardiff, Ivan Batistić, and Tian Tang

Tutorial Aims

Demonstrate the anisotropic poroelastic soil model.
Demonstrate seabed response under prescribed wave-induced pressure loading.

Case Overview

This case solves the poroelastic response of a seabed domain subjected to time-varying pressure on the upper seabed patch. The pressure loading is prescribed from precomputed mapped boundary data rather than generated by a live water-column or structure calculation during the run.

The case was adapted, with modifications, from Tian Tang's minigeotechfoam cases [4].

The setup follows the wave-structure-seabed interaction modelling approach of Li et al. [1,3], where time-varying wave pressure is transferred to the seabed solver through mapped boundary data. The current tutorial keeps only the seabed-response part of that workflow.

The computational domain is a rectangular seabed block. The top surface is the seabed patch, the lateral boundaries are grouped in the sides patch, and the lower boundary is the bottom patch. The mesh spans \(84\) m in the \(x\) direction, \(42.5\) m in the \(y\) direction, and \(10\) m in depth.

Table 1 - Poroelastic material properties used in the current case

Parameter	Symbol	Value
Density	\(\rho\)	\(2650\) kg/m\(^3\)
Young's modulus, x	\(E_x\)	\(1.2\cdot10^7\) Pa
Young's modulus, y	\(E_y\)	\(1.2\cdot10^7\) Pa
Young's modulus, z	\(E_z\)	\(2.0\cdot10^7\) Pa
Poisson's ratio, xy	\(\nu_{xy}\)	\(0.2\)
Poisson's ratio, yz	\(\nu_{yz}\)	\(0.24\)
Poisson's ratio, zx	\(\nu_{zx}\)	\(0.4\)
Shear modulus, xy	\(G_{xy}\)	\(0.5\cdot10^7\) Pa
Shear modulus, yz	\(G_{yz}\)	\(1.2\cdot10^7\) Pa
Shear modulus, zx	\(G_{zx}\)	\(1.2\cdot10^7\) Pa
Hydraulic conductivity	\(k\)	\(1.0\cdot10^{-3}\) m/s
Porosity	\(n\)	\(0.2\)
Water specific weight	\(\gamma_w\)	\(9.807\cdot10^3\) N/m\(^3\)
Degree of saturation	\(S_r\)	\(0.9\)
Water bulk modulus	\(K_w\)	\(2.15\cdot10^9\) Pa

Table 2 - Boundary conditions for displacement and pressure

Boundary	\(D\)	\(p\)
`seabed`	`solidTraction`	`timeVaryingMappedFixedValue`
`sides`	`slip`	`zeroGradient`
`bottom`	`slip`	`zeroGradient`

The seabed pressure condition reads the mapped pressure values from constant/boundaryData/seabed. Since the solved field is named p, the active time directories contain files named p, for example:

constant/boundaryData/seabed/0/p
constant/boundaryData/seabed/0.05/p
constant/boundaryData/seabed/0.1/p
constant/boundaryData/seabed/0.15/p
constant/boundaryData/seabed/0.2/p
constant/boundaryData/seabed/0.25/p
  

The same directory also contains points and faces, which define the source patch geometry used for mapping. The p_w files are present as auxiliary data, but they are not referenced by the p boundary condition.

Note: some current case settings differ from the values reported in [1]. The porosity is \(0.2\), the degree of saturation is \(0.9\), and the hydraulic conductivity is specified uniformly in all directions as \(1.0\cdot10^{-3}\) m/s.

Expected Results

The main result is the transient pore-pressure and displacement response of the anisotropic seabed under the prescribed wave-induced pressure field. A wave crest produces positive pore pressure in the seabed, while a wave trough produces negative pore pressure. The response is expected to show a phase lag with depth because the pore pressure diffuses through the porous soil.

This tutorial differs from the full WSSI workflow described by Li et al. [1,3]. In the full workflow, the pressure loading is generated by separate wave and structure simulations and then transferred to the seabed solver. In this tutorial, those pressure values are already available as mapped boundary data, so only the seabed response is solved.