Nine Four Node Quad u-p Element

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Nine_Four_Node_QuadUP is a 9-node quadrilateral plane-strain element. The four corner nodes have 3 degrees-of-freedom (DOF) each: DOF 1 and 2 for solid displacement (u) and DOF 3 for fluid pressure (p). The other five nodes have 2 DOFs each for solid displacement. This element is implemented for simulating dynamic response of solid-fluid fully coupled material, based on Biot's theory of porous medium.

Please click here for examples.


Pore pressure can be recorded at an element node using OpenSees Node Recorder:

recorder Node <-file $fileName> <-time> <-node ($nod1 $nod2 …)> -dof 3 vel

See OpenSees command manual (McKenna and Fenves 2001) for nodal displacement, velocity, or acceleration recorders.

The valid queries to a Nine_Four_Node_QuadUP element when creating an ElementRecorder are 'force', 'stiffness', or 'material matNum matArg1 matArg2 ...', where matNum represents the material object at the corresponding integration point.

element 9_4_QuadUP $eleTag $Node1 $Node2 $Node3 $Node4 $Node5 $Node6 $Node7 $Node8 $Node9 $thick $matTag $bulk $fmass $hPerm $vPerm <$b1=0 $b2=0>

Elem9 4QuadUp.png

$eleTag A positive integer uniquely identifying the element among all elements
$Node1,… $Node9 Nine element node (previously defined) numbers (see figure above for order of numbering).
$thick Element thickness
$matTag Tag of an NDMaterial object (previously defined) of which the element is composed
$bulk Combined undrained bulk modulus Bc relating changes in pore pressure and volumetric strain, may be approximated by:

Bc ≈ Bf/n

where Bf is the bulk modulus of fluid phase (2.2x106 kPa (or 3.191x105 psi) for water), and n the initial porosity.

$fmass Fluid mass density
$hPerm, $vPerm Permeability coefficient in horizontal and vertical directions respectively.
$b1, $b2 Optional gravity acceleration components in horizontal and vertical directions respectively (defaults are 0.0)

Code Developed by: UC San Diego (Dr. Zhaohui Yang):

UC San Diego Soil Model: