Nine Four Node Quad u-p Element
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 $b2=0>|
|$eleTag||A positive integer uniquely identifying the element among all elements|
|$Node1,… $Node9||Nine element node (previously defined) numbers (see figure above for order of numbering).|
|$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:
- Element Command
- NDMaterial Command
- UC San Diego soil models (Linear/Nonlinear, dry/drained/undrained soil response under general 2D/3D static/cyclic loading conditions (please visit UCSD for examples)
- UC San Diego Saturated Undrained soil
- Related References