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 $iNode $jNode $kNode $lNode $thick $matTag $bulk $fmass $hPerm $vPerm <$b1=0 $b2=0 $t=0> |
| $eleTag | unique element object tag |
| $iNode $jNode $kNode $lNode | 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 |
| $hPerm | Permeability coefficient in horizontal direction |
| $vPerm | Permeability coefficient in vertical direction |
| $b1, $b2 | Optional gravity acceleration components in horizontal and vertical 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