As an additional feature of the OASES 2.0 environmental model layers modelled as fluid saturated porous media (Biot model) may be included with other layer types. The Biot model and its implementation is described in Appendix A.
A porous sediment layer is flagged by stating the usual parameter line for the layer in the environmental data block:
| D | cc | cs | [L] |
with negative values for both cc and cs. Only the interface depth D has significance and must be stated correctly; the other parameters listed on this data line are dummy. This line is immediately followed by a line containing the 13 parameters specifying the properties of the porous sediment layer in the order:
| Kf | Kr | a | K | cm |
where
| is the density of the pore fluid in | |
| Kf | is the bulk modulus of the pore fluid in Pa |
| is the viscosity of the pore fluid in kg/m-s | |
| is the grain (solid constituent) density in | |
| Kr | is the grain bulk modulus in Pa |
| is the sediment porosity | |
| is the sediment permeability in | |
| a | is the pore size factor in m |
| is the sediment frame shear modulus in Pa | |
| K | is the sediment frame bulk modulus in Pa |
| is the sediment frame shear attenuation | |
| is the sediment frame bulk attenuation | |
| cm | is a dimensionless virtual mass parameter |
The sediment frame properties pertain to the drained structure and are assumed to be dissipative. In particular, for harmonic motion the frame shear and bulk moduli are taken to be complex in the form . The imaginary parts of the moduli are specified through and where corresponds to the attenuation measured in dB/ of shear waves in the sediment frame (as in the data specification for elastic layers) when the attenuation is low; is related to the attenuation of both compression and shear waves. However, it should be noted that in contrast to the elastic layer case, the Biot porous sediment model will yield complex wavespeeds even if the frame is elastic since dissipation is inherent in the relative motion of the pore fluid with respect to the frame.
The pore size parameter a is treated as an empirical constant which depends on the average grain size and shape; for spherical grains of diameter d the value has been suggested[6]. The virtual mass parameter cm (called the `structure factor' or `tortuosity' by some authors and often denoted ) is also treated as an empirical constant which depends on the pore structure of the frame. For moderate frequencies (long wave length compared to `average pore size') and porosities from 25% to 50%, Yavari and Bedford[7] have made finite element calculations which suggest that Berryman's relation may be used in the absence of more reliable data. More thorough discussions of the material parameters defining the Biotmodel may be found in other references[8].
If the K option is invoked, then recievers in a porous sediment layer will output (negative) pore fluid pressure rather than bulk stress as called for in other fluid or solid layers. The Z option, which creates a velocity profile plot, shows the zero frequency limit wavespeeds in porous sediment layers. Note that at present the modifications do NOT permit sources in Biot layers.
The following presents a modification of SAFARI-FIP case 3 to replace the elastic sediment layer by a poro-elastic layer,
SAFARI-FIP case 3. Poroelastic. N C A D J 30 30 1 0 5 0 0 0 0 0 0 0 0 1500 -999.999 0 0 1 0 # SVP continuous at z = 30 m 30 1480 -1490 0 0 1 0 100 -1 -1 0 0 0 0 0 # Cp<0 Cs<0 flag poro-elastic layer 1 2.E9 .001 2.65 9.E9 .4 2.E-9 1.E-5 3.13E8 5.14E9 .8 1.55 1.25 120 1800 600 0.1 0.2 2.0 0 50 0.1 120 41 40 1350 1E8 -1 1 950 0 5 20 1 20 80 12 10 0 120 12 20 40 70 6