# 4.2.11.5. 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.

element('9_4_QuadUP', eleTag, *eleNodes, thick, matTag, bulk, fmass, hPerm, vPerm, <b1=0, b2=0>)
 eleTag (int) unique element object tag eleNodes (list (int)) a list of nine element nodes thick (float) Element thickness matTag (int) Tag of an NDMaterial object (previously defined) of which the element is composed bulk (float) Combined undrained bulk modulus Bc relating changes in pore pressure and volumetric strain, may be approximated by: $$B_c \approx B_f/n$$ where $$B_f$$ is the bulk modulus of fluid phase ($$2.2\times 10^6$$ kPa (or $$3.191\times 10^5$$ psi) for water), and n the initial porosity. fmass (float) Fluid mass density hPerm, vPerm (float) Permeability coefficient in horizontal and vertical directions respectively. b1, b2 (float) Optional gravity acceleration components in horizontal and vertical directions respectively (defaults are 0.0)