Pore Fluid Flow

Pore fluid flow can be prescribed in coupled pore fluid diffusion/stress analysis (see Coupled Pore Fluid Diffusion and Stress Analysis) and in the geostatic stress field procedure (see Geostatic Stress State). Pore fluid flow can be prescribed by:

defining seepage coefficients and sink pore pressures on element faces or surfaces;
defining drainage-only seepage coefficients on element faces or surfaces that are applied only when surface pore pressures are positive; or
prescribing an outward normal flow velocity directly at nodes, on element faces, or on surfaces.

This page discusses:

Defining Pore Fluid Flow as a Function of the Current Pore Pressure in Consolidation Analysis
Prescribing Seepage Flow Velocity and Seepage Flow Directly in Consolidation Analysis

Defining Pore Fluid Flow as a Function of the Current Pore Pressure in Consolidation Analysis

In consolidation analysis you can provide seepage coefficients and sink pore pressures on element faces or surfaces to control normal pore fluid flow from the interior of the region modeled to the exterior of the region.

The surface condition assumes that the pore fluid flows in proportion to the difference between the current pore pressure on the surface, $u_{w}$ , and some reference value of pore pressure, $u_{w}^{\infty}$ :

v_{n} = k_{s} (u_{w} - u_{w}^{\infty}),

where

$v_{n}$: is the component of the pore fluid velocity in the direction of the outward normal to the surface;
$k_{s}$: is the seepage coefficient;
$u_{w}$: is the current pore pressure at this point on the surface; and
$u_{w}^{\infty}$: is a reference pore pressure value.

Specifying Element-Based Pore Fluid Flow

To define element-based pore fluid flow, specify the element or element set name; the distributed load type; the reference pore pressure, $u_{w}^{\infty}$ ; and the reference seepage coefficient, $k_{s}$ . The face of the elements upon which the normal flow is enforced is identified by a seepage distributed load type. The seepage types available depend on the element type (see About the Element Library).

Input File Usage

FLOW
element number or element set name, Qn,   $u_{w}^{\infty}$ ,  $k_{s}$

Specifying Surface-Based Pore Fluid Flow

To define surface-based pore fluid flow, specify a surface name, the seepage flow type, the reference pore pressure, and the reference seepage coefficient. The element-based surface (see Element-Based Surface Definition) contains the element and face information.

Input File Usage

SFLOW
surface name, Q,  $u_{w}^{\infty}$ ,  $k_{s}$

Defining Drainage-Only Flow

Drainage-only flow types can be specified for element-based or surface-based pore fluid flow to indicate that normal pore fluid flow occurs only from the interior to the exterior region of the model. The drainage-only flow surface condition assumes that the pore fluid flows in proportion to the magnitude of the current pore pressure on the surface, $u_{w}$ , when that pressure is positive:

\begin{matrix} v_{n} & = k_{s} u_{w}, u_{w} > 0 \\ v_{n} & = 0 u_{w} \leq 0, \end{matrix}

where

$v_{n}$: is the component of the pore fluid velocity in the direction of the outward normal to the surface;
$k_{s}$: is the seepage coefficient; and
$u_{w}$: is the current pore pressure at this point on the surface.

Figure 1 illustrates this pore pressure–velocity relationship. This surface condition is designed for use with the total pore pressure formulation (see Coupled Pore Fluid Diffusion and Stress Analysis), mainly for cases where the phreatic surface intersects an exterior surface that is free to drain. See Calculation of phreatic surface in an earth dam for an example of this type of calculation.

When surface pore pressures are negative, the constraint will properly enforce the condition that no fluid can enter the interior region. When surface pore pressures are positive, the constraint will permit fluid flow from the interior to the exterior region of the model. When the seepage coefficient value, $k_{s}$ , is large, this flow will approximately enforce the requirement that the pore pressure should be zero on a freely draining surface. To achieve this condition, it is necessary to choose the value of $k_{s}$ to be much larger than a characteristic seepage coefficient for the material in the underlying elements:

k_{s} ≫ k / γ_{w} c,

where

k: is the permeability of the underlying material;
$γ_{w}$: is the fluid specific weight; and
c: is a characteristic length of the underlying elements.

Values of $k_{s} \approx 10^{5} k / γ_{w} c$ will be adequate for most analyses. Larger values of $k_{s}$ could result in poor conditioning of the model. In all cases the freely draining flow type represents discontinuously nonlinear behavior, and its use may require appropriate solution controls (see Commonly Used Control Parameters).

Input File Usage

Use the following option to define element-based drainage-only flow:

FLOW
element number or element set name, QnD,   $k_{s}$

Use the following option to define surface-based drainage-only flow:

SFLOW
surface name, QD,  $k_{s}$

Modifying or Removing Seepage Coefficients and Reference Pore Pressures

Seepage coefficients and reference pore pressures can be added, modified, or removed as described in About Loads.

Specifying a Time-Dependent Reference Pore Pressure

The magnitude of the reference pore pressure, $u_{w}^{\infty}$ , can be controlled by referring to an amplitude curve. If different variations are needed for different portions of the flow, repeat the flow definition with each referring to its own amplitude curve. See About Loads and Amplitude Curves for details.

Defining Nonuniform Flow in a User Subroutine

To define nonuniform flow, the variation of the reference pore pressure and the seepage coefficient as functions of position, time, pore pressure, etc. can be defined in user subroutine FLOW.

Input File Usage

Use the following option to define a nonuniform element-based flow:

FLOW
element number or element set name, QnNU

Use the following option to define a nonuniform surface-based flow:

SFLOW
surface name, QNU

Prescribing Seepage Flow Velocity and Seepage Flow Directly in Consolidation Analysis

You can directly prescribe an outward normal flow velocity, $v_{n}$ , across a surface or an outward normal flow at a node in consolidation analysis.

Prescribing Element-Based Seepage Flow Velocity

To prescribe an element-based seepage flow velocity, specify the element or element set name, the seepage type, and the outward normal flow velocity. The face of the element for which the seepage flow is being defined is identified by the seepage type. The seepage types available depend on the element type (see About the Element Library).

Input File Usage

DFLOW
element number or element set name, Sn,  $v_{n}$

Prescribing Surface-Based Seepage Flow Velocity

To prescribe a surface-based seepage flow velocity, specify a surface name, the seepage flow type, and the pore fluid velocity. The element-based surface (see Element-Based Surface Definition) contains the element and face information.

Input File Usage

DSFLOW
surface name, S,  $v_{n}$

Prescribing Node-Based Seepage Flow

To prescribe node-based seepage flow, specify the node or node set name and the magnitude of the flow per unit time.

Input File Usage

CFLOW
node number or node set name,  , magnitude

Prescribing Seepage Flow at Phantom Nodes for Enriched Elements

For an enriched element (see Modeling Discontinuities as an Enriched Feature Using the Extended Finite Element Method), you can specify the seepage flow at a phantom node that is originally located coincident with the specified real node.

Alternatively, you can specify the seepage flow at a phantom node located at an element edge between two specified real corner nodes directly or indicate that the pore pressure applied to a phantom node located at an element edge is interpolated from the specified real corner nodes.

Input File Usage

Use the following option to specify the seepage flow at a phantom node originally located coincident with the specified real node:

CFLOW, PHANTOM=NODE
node number,  , magnitude

Use the following option to specify the seepage flow at a phantom node located at an element edge:

CFLOW, PHANTOM=EDGE
first corner node number, second corner node number,  magnitude

Use the following option to indicate that the pore pressure applied to a phantom node located at an element edge will be interpolated automatically from the specified real corner nodes when the enriched element is cracked:

CFLOW, PHANTOM=INCLUDED
node or node set name, , magnitude

Modifying or Removing Seepage Flow Velocities and Seepage Flow

Seepage flow velocities can be added, modified, or removed as described in About Loads.

Specifying Time-Dependent Flow Velocity and Flow

The magnitude of the seepage velocity, $v_{n}$ , can be controlled by referring to an amplitude curve. To specify different variations for different flows, repeat the seepage flow velocity or seepage flow definition with each referring to its own amplitude curve. See About Loads and Amplitude Curves for details.

Defining Nonuniform Flow Velocities in a User Subroutine

To define nonuniform element-based or surface-based flow, the variation of the seepage magnitude as a function of position, time, pore pressure, etc. can be defined in user subroutine DFLOW. If the optional seepage velocity, $v_{n}$ , is specified directly, this value is passed into user subroutine DFLOW in the variable used to define the seepage magnitude.

Input File Usage

Use the following option to define nonuniform element-based flow:

DFLOW
element number or element set name, SnNU,  $v_{n}$

Use the following option to define nonuniform surface-based flow:

DSFLOW
surface name, SNU,  $v_{n}$