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> |
| $eleTag | unique element object tag |
| $Node1 .. $Node4 | Four element node (previously defined) numbers in counter-clockwise order around the element |
| $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: where Bf is the bulk modulus of fluid phase (2.2x106 kPa for water), and n the initial porosity. |
| $fmass | Fluid mass density |
| $PermX | Permeability coefficient in X direction |
| $PermY | Permeability coefficient in Y direction |
| $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 |
EXAMPLE:
Please visit http://cyclic.ucsd.edu/opensees for examples.
REFERENCES:
Code Developed by: Zhaohui Yang, UC San Diego