FourNodeQuad u-p Element
This command is used to construct an eFourNodeQuadUP element object. A FourNodeQuadUP element is a four-node plane-strain element using bilinear isoparametric formulation. This element is implemented for simulating dynamic response of solid-fluid fully coupled material, based on Biot’s theory of porous medium. Each element node has 3 degrees-of-freedom (DOF): DOF 1 and 2 for solid displacement (u) and DOF 3 for fluid pressure (p). The arguments for the construction of this element are:
element quadUP $eleTag $Node1 $Node2 $Node3 $Node4 $thick $matTag $bulk $fmass $PermX \(PermY <\)b1=0 $b2=0 \(t=0></strong></p></td> </tr> </tbody> </table> <hr /> <table> <tbody> <tr class="odd"> <td><code class="parameter-table-variable">eleTag</code></td> <td><p>unique element object tag</p></td> </tr> <tr class="even"> <td><p><strong>\)Node1 .. \(Node4</strong></p></td> <td><p>Four element node (previously defined) numbers in counter-clockwise order around the element</p></td> </tr> <tr class="odd"> <td><code class="parameter-table-variable">thick</code></td> <td><p>Element thickness</p></td> </tr> <tr class="even"> <td><code class="parameter-table-variable">matTag</code></td> <td><p>Tag of an NDMaterial object (previously defined) of which the element is composed</p></td> </tr> <tr class="odd"> <td><code class="parameter-table-variable">bulk</code></td> <td><p>Combined undrained bulk modulus Bc relating changes in pore pressure and volumetric strain, may be approximated by: where Bf is the bulk modulus of fluid phase (2.2x106 kPa for water), and n the initial porosity.</p></td> </tr> <tr class="even"> <td><code class="parameter-table-variable">fmass</code></td> <td><p>Fluid mass density</p></td> </tr> <tr class="odd"> <td><code class="parameter-table-variable">PermX</code></td> <td><p>Permeability coefficient in X direction</p></td> </tr> <tr class="even"> <td><code class="parameter-table-variable">PermY</code></td> <td><p>Permeability coefficient in Y direction</p></td> </tr> <tr class="odd"> <td><p><strong>\)bX, $bY |
Optional gravity acceleration components in X and Y directions respectively (defaults are 0.0) |
t
|
Optional uniform element normal traction, positive in tension (default is 0.0) |
NOTE:
- This element requires 3 degrees-of-freedom (ndf=3), the 3rd degree-of-freedom being pore pressure. The Pore pressure can be recorded at an element node using OpenSees Node Recorder:
recorder Node <-file \(fileName> <-time> <-node (\)nod1 $nod2 …)> -dof 3 vel
- The valid queries to a quadUP element when creating an ElementRecorder are ‘force’, and ‘material matNum matArg1 matArg2 …’, where matNum represents the material object at the corresponding integration point.
- TYPICAL RANGE OF PERMEABILITY COEFFICIENT (cm/s)
Gravel |
Sand |
Silty Sand |
Silt |
Clay |
>1.0x10-1 |
1.0x10-3 ~ 1.0x10-1 |
1.0x10-5 ~ 1.0x10-3 |
1.0x10-7 ~ 1.0x10-5 |
<1.0x10-7 |
Examples
Please visit http://cyclic.ucsd.edu/opensees for examples.
REFERENCES:
Code Developed by: Zhaohui Yang, UC San Diego