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>

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$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:

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Code Developed by: Zhaohui Yang, UC San Diego