FLAC3D Theory and Background • Fluid-Mechanical Interaction

# Fluid-Mechanical Interaction

FLAC3D models the flow of fluid through a permeable solid, such as soil. The flow modeling may be done by itself, independent of the usual mechanical calculation of FLAC3D, or it may be done in parallel with the mechanical modeling, in order to capture the effects of fluid/solid interaction. One type of fluid/solid interaction is consolidation, in which the slow dissipation of pore pressure causes displacements to occur in the soil. This type of behavior involves two mechanical effects. First, changes in pore pressure cause changes in effective stress, which affect the response of the solid. (For example, a reduction in effective stress may induce plastic yield.) Second, the fluid in a zone reacts to mechanical volume changes by a change in pore pressure.

The basic flow scheme handles both fully saturated flow and flow in which a phreatic surface develops. In this case, pore pressures are zero above the phreatic surface, and the air phase is considered to be passive. This logic is applicable to coarse materials when capillary effects can be neglected. In order to represent the evolution of an internal transition between saturated and unsaturated zones, the flow in the unsaturated region must be modeled so that fluid may migrate from one region to the other. A simple law that relates the apparent permeability to the saturation is used. The transient behavior in the unsaturated region is only approximate (due to the simple law used), but the steady-state phreatic surface should be accurate (see Steady-State Fluid Flow with a Free Surface and Spreading of a Groundwater Mound for examples).

1. Two fluid-transport laws corresponding to isotropic and anisotropic permeability are available. The fluid-flow null model is also provided to specify impermeable materials in the flow domain.
2. Different zones may have different fluid-flow models (isotropic, anisotropic or null) and properties.
3. Fluid pressure, flux, and leaky and impermeable boundary conditions may be prescribed.
4. Fluid sources (wells) may be inserted into the material as either point sources or volume sources. These sources correspond to either a prescribed inflow or outflow of fluid, and vary with time.
5. Both explicit and implicit fluid-flow solution algorithms are available for fully saturated simulations. An explicit method of solution is used for saturated/unsaturated flow.
6. Any of the mechanical and thermal models may be used with the fluid-flow models. In coupled problems, the compressibility and thermal expansion of the saturated material are allowed.
7. Coupling between fluid and mechanical calculations due to deformable grains is provided through the Biot coefficient, $$\alpha$$.
8. Coupling to the thermal conduction calculation is provided through the linear thermal expansion coefficient, $${\alpha}_t$$, and the undrained thermal coefficient, $$\beta$$.
9. The thermal-conduction fluid-flow logic is based on a linear theory that assumes constant material properties and neglects convection. Fluid and solid temperatures are locally equilibrated. Nonlinear behavior can be specified by access to pore pressures and material properties via FISH. Thermal coupling to the conduction logic is addressed in Mathematical Description.
10. An advection model to take the transport of heat by convection into account is also provided. This includes temperature-dependent fluid density and thermal advection by the fluid. See Advection for a description of this thermal-fluid coupling.

Fluid-flow and coupled undrained and drained calculations using the basic flow scheme can be very slow when 1) the bulk modulus of the fluid is large compared to the drained confined modulus, $$K + (4/3)G$$, 2) there is a large contrast in permeability and/or porosity, or 3) there is a large variation in grid size. A different numerical technique, saturated fast-flow logic, is provided to speed the calculation for fully saturated, coupled fluid-mechanical simulations, when the fluid can be considered as incompressible when compared to the drained material compressibility. The logic is invoked with the zone fluid fastflow on command. The scheme and theoretical background is described in Fully Saturated Fast Flow, and efficiency demonstrations and application of this logic are presented in 1D Consolidation and Consolidation Settlement.

Dynamic pore-pressure generation and liquefaction due to cyclic loading can also be modeled with FLAC3D (Liquefaction Modeling contains the documentation on this topic). FLAC3D does not represent capillary, electrical or chemical forces between particles of a partially saturated material. However, it is possible to introduce such forces by writing a FISH function that supplies the appropriate internal stresses, based on the local saturation, porosity and/or any other relevant variable. Similarly, the effect of variable fluid stiffness due to dissolved air is not explicitly modeled, but a FISH function may be used to vary the local fluid modulus as a function of pressure, time or any other quantity.

This section is divided into eight major parts:

1. The mathematical model description and the corresponding numerical formulation for fluid flow and coupled fluid flow-mechanical and fluid-flow thermal-conduction processes. (see Mathematical Description and Numerical Formulation).
2. The calculation modes and associated commands for analyses involving fluid flow. (link)
3. Material properties required for a fluid-flow analysis, and includes the appropriate units for these properties. ((link))
4. Initial conditions, and a description of the different boundary conditions and fluid sources and sinks that can be applied in a FLAC3D model. (link)
5. The recommended procedures for solving both flow-only and coupled-flow problems. This section also contains several examples that illustrate the application of these procedures. We recommend that you work through these examples before attempting your own fluid analysis. (link)
6. Several verification problems that demonstrate the accuracy of the fluid-flow logic in FLAC3D.
7. Modeling techniques for specific fluid applications: Several topics are covered: modeling solid weight, buoyancy forces and seepage forces in a coupled analysis; relation between initialization of pore pressures and deformation in a coupled analysis; and effect of the Biot coefficient.
8. Finally, a summary of all the commands and FISH functions related to fluid flow. A special zone-based pore pressure logic is also included in this section.

The user is strongly encouraged to become familiar with the operation of FLAC3D for simple mechanical problems before attempting to solve problems in which flow and mechanical effects are both important. Coupled flow and mechanical behavior are often very complicated, and require a good deal of insight to interpret correctly. Before starting a big project, it is very important to spend time experimenting with a small-grid version of the proposed simulation, to try out various boundary conditions and modeling strategies. The time “wasted” on these experiments will be amply repaid in terms of an overall reduction in both staff time and execution time.