FLAC3D Theory and Background • FluidMechanical Interaction
Calculation Modes for FluidMechanical Interaction
The calculation mode and commands required for a porepressure analysis
depend on whether the grid has been configured for fluid flow
(i.e., whether the model configure fluid
command has been specified).
The flow calculation can be performed independent of, or coupled to,
the mechanical deformation calculation when model configure fluid
is specified.
It is also possible to conduct simplified, uncoupled, fluidmechanical calculations with FLAC3D such as slope stability analyses, without configuring the grid for fluid flow. This option, when applicable, provides faster solution than the fluid flow configuration.
Grid Not Configured for Fluid Flow and Grid Configured for Fluid Flow reflect the two possibilities. For convenience, all commands described below are summarized in Input Instructions for FluidFlow Analysis, at the end of this section.
Grid Not Configured for Fluid Flow
If the command model configure fluid
has not been given,
then a fluidflow analysis cannot be performed,
but it is still possible to assign pore pressure at gridpoints.
In this calculation mode, pore pressures do not change, but failure,
which is controlled by the effectivestress state,
may be induced when plastic constitutive models are used.
A porepressure distribution can be specified at gridpoints,
with the zone gridpoint initialize porepressure
command with a gradient,
or with the zone water plane
(or zone water set
) command.
If the zone water plane
command is used,
a hydrostatic porepressure distribution is calculated automatically by the code,
below the given water table level.
In this case, the fluid density
(zone water density
) and gravity (model gravity
) must also be specified.
The fluid density value and water table location can be printed with the zone list fluiddensity
command,
and the water table can be plotted,
if the water table is defined by zone water set
or zone water plane
command.
In both cases, zone pore pressures are calculated by averaging from the gridpoint values,
and used to derive effective stresses for use in the constitutive models.
In this calculation mode, the fluid presence is not automatically accounted for in the calculation of body forces:
wet and dry medium densities must be assigned by the user, below and above the water level, accordingly.
The commands zone gridpoint list porepressure
and zone list porepressure
print gridpoint and zone pore pressures, respectively.
plot add zone contour porepressure
plots contours of gridpoint pore pressures.
A simple example application of this calculation mode is given in the topic The Effect of Water in the Problem Solving section.
Grid Configured for Fluid Flow
If the command model configure fluid
is given, a transient fluidflow analysis can be performed,
and change in pore pressures,
as well as change in the phreatic surface, can occur.
Pore pressures are calculated at gridpoints, and zone values are derived using averaging.
Both effectivestress (static porepressure distribution)
and undrained calculations can be carried out in model configure fluid
mode.
In addition, a fully coupled analysis can be performed,
in which changes in pore pressure generate deformation,
and volumetric strain causes the pore pressure to evolve.
If the grid is configured for fluid flow, dry densities must be assigned by the user (both below and above the water level), because FLAC3D takes the fluid influence into account in the calculation of body forces.
A fluidflow model must be assigned to zones when running in model configure fluid
mode.
Isotropic flow is prescribed with the zone fluid cmodel assign isotropic
command;
anisotropic flow with the command zone fluid cmodel assign anisotropic
.
An impermeable material is assigned to zones with the zone fluid cmodel assign null
command.
Note that zones that are made null mechanically are not automatically made null for fluid flow.
Fluid properties are assigned to either zones or gridpoints.
Zone fluid properties include isotropic permeability, porosity, Biot coefficient, undrained thermal coefficient and fluid density.
Zone fluid properties are assigned with the zone fluid property
command, with the exception of fluid density,
which is assigned with the zone initialize fluiddensity
command.
(Note that fluid density can also be specified globally with the zone water density
command.)
For isotropic flow, permeability is specified using the permeability property keyword. For anisotropic flow, the three principal values of permeability are specified using the property keywords permeability1, permeability2 and permeability3, and the orientation is defined using the keywords dip, dipdirection, and rotation. The principal directions of permeability correspond to \(k_1\), \(k_2\), \(k_3\), and form a righthanded system. The properties dip and dipdirection are the dip angle and dip direction angle of the plane in which \(k_1\) and \(k_2\) are defined. The dip angle is measured from the global \(xy\)plane, positive down (in negative \(z\)direction). The dip direction angle is the angle between the positive \(y\)axis and the projection of the dipdirection vector on the \(xy\)plane (positive clockwise from \(y\)axis). The property rotation is the rotation angle between the \(k_1\)axis and the dip vector in the \(k_1\)\(k_2\)plane (positive clockwise from dipdirection vector). See Figure 1.
Biot coefficient is assigned using the biot keyword; porosity is assigned using the porosity keyword. If not specified, Biot coefficient = 1 and porosity = 0.5, by default.
Gridpoint fluid properties are assigned with the zone gridpoint initialize
command.
These properties include fluid bulk modulus, Biot modulus, fluid tension limit and saturation.
Each of the gridpoint properties can also be given a spatial variation.
Table 1 summarizes the ways the various properties can be specified. The fluid properties are described further in Properties and Units for FluidFlow Analysis.
property 
keyword 
specific 
command 

Permeability (isotropic) 
permeability 
in zones 

Perm. princ. val. (aniso) 
permeability1 
in zones 

Perm. princ. val. (aniso) 
permeability2 
in zones 

Perm. princ. val. (aniso) 
permeability3 
in zones 

Perm. princ. val. (aniso) 
permeabilityxx 
in zones 

Perm. princ. val. (aniso) 
permeabilityxy 
in zones 

Perm. princ. val. (aniso) 
permeabilityxz 
in zones 

Perm. princ. val. (aniso) 
permeabilityyy 
in zones 

Perm. princ. val. (aniso) 
permeabilityyz 
in zones 

Perm. princ. val. (aniso) 
permeabilityzz 
in zones 

Perm. princ. dir. (aniso) 
dip 
in zones 

Perm. princ. dir. (aniso) 
diddirection 
in zones 

Perm. princ. dir. (aniso) 
rotation 
in zones 

Porosity 
porosity 
in zones 

Biot coefficient 
biot 
in zones 

Undrained thermal coeff. 
undrainedthermalcoefficient 
in zones 

Fluid modulus 
fluidmodulus 
at gridpoints 

Biot modulus 
biotmodulus 
at gridpoints 

Saturation 
saturation 
at gridpoints 

Fluid tension limit 
fluidtension 
at gridpoints 

Fluid density 
fluiddensity 
at zones 

density 
globally 
Note that fluid compressibility is defined in one of two ways in the model configure fluid
mode:
1) Biot coefficient and Biot modulus are specified; or
2) fluid bulk modulus and porosity are specified.
The first case accounts for the compressibility of the solid grains
(Biot coefficient is set to 1 for incompressible grains).
In the second case, solid grains are assumed to be incompressible
(see Biot Coefficient and Biot Modulus).
The zone properties can be printed with the zone fluid list property
command,
and the gridpoint properties can be printed with the zone gridpoint list
command.
Fluid density, along with the location of the water table (if specified) can be printed with the zone water list
command.
The fluidflow properties can be plotted as a contour plot.
For anisotropic flow, the global components of the permeability tensor are available for plotting and printing,
using the zone property keywords
permeabilityxx,
permeabilityyy,
permeabilityzz,
permeabilityxy,
permeabilityxz and
permeabilityzz
(please note that these global components cannot be initialized directly).
An initial gridpoint porepressure distribution is assigned the same way
for the model configure fluid
mode as for the nonmodel configure fluid
mode
(i.e., either with the zone gridpoint initialize porepressure
command
or the zone water set
or zone water plane
command).
Pore pressures can be fixed (and freed) at selected gridpoints with the zone gridpoint fix porepressure
(or zone gridpoint free porepressure
) command.
Fluid sources and sinks can be applied with the zone apply well
command.
See describes the various FluidFlow Boundary and Initial Conditions.
The fluidflow solution is controlled by the zone fluid active
on and model solve
commands.
Several keywords are available to help the solution process.
For example, zone fluid active
on or off turns on or off the fluid flow calculation mode.
The application of these commands and keywords depends on the level of coupling required in the fluid flow analysis.
The section in Solving FlowOnly and CoupledFlow Problems
describes the various coupling levels and the recommended solution procedure.
Example applications, ranging from flowonly to coupled mechanicalflow calculations, are also described in this section.
Results from a fluidflow analysis are provided in several forms.
The commands zone gridpoint list porepressure
and zone list porepressure
print gridpoint and zone pore pressures, respectively.
Histories of gridpoint and zone pore pressures can be monitored
with the command zone history porepressure
and specify source.gridpoint and source.zone, respectively.
And for a transient calculation, the pore pressure can be plotted versus real time
by monitoring the flow time with the model history fluid timetotal
command.
plot add zone contour porepressure
plots contours of gridpoint pore pressures.
plot add zone contour saturation
plots contours of saturation.
The plot add flow
command plots specific discharge vectors.
General information on the model configure fluid
calculation mode is printed with the model fluid list
command.
Several fluidflow variables can be accessed through FISH.
These are listed in Input Instructions for FluidFlow Analysis.
There is one gridrelated variable, gp.flow
, that can only be accessed through a FISH function;
this corresponds to the net inflow or outflow at a gridpoint.
The summation of such flows along a boundary where the pore pressure is fixed is useful
because it can provide a value for the total outflow or inflow for a system.
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