# Four Node Quad u-p Element

FourNodeQuadUP 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).

OUTPUT INTERFACE: 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 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 quadUP \$eleTag \$iNode \$jNode \$kNode \$lNode \$thick \$matTag \$bulk \$fmass \$hPerm \$vPerm <\$b1=0 \$b2=0 \$t=0>

 \$eleTag A positive integer uniquely identifying the element among all elements \$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: 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) \$t Optional uniform element normal traction, positive in tension (default is 0.0)

TYPICAL RANGE OF PERMEABILITY COEFFICIENT

 Gravel Sand Silty Sand Silt Clay >1.0x10-1 cm/s (or 3.94x10-2 in/s) 1.0x10-3 cm/s (or 3.94 x10-4 in/s) ~ 1.0x10-1 cm/s (or 3.94 x10-2 in/s) 1.0x10-5 cm/s (or 3.94 x10-6 in/s) ~ 1.0x10-3 cm/s (or 3.94 x10-4 in/s) 1.0x10-7 cm/s (or 3.94 x10-8 in/s) ~ 1.0x10-5 cm/s (or 3.94 x10-6 in/s) <1.0x10-7 cm/s (or 3.94x10 -8 in/s)

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

UC San Diego Soil Model: