Fully-coupled PWP Generation Model

In the FEM engine, excess pore pressure is not generated from an empirical cyclic r_u model. Instead, generation arises naturally from the coupled Biot u-p formulation through volumetric deformation of the soil skeleton.

At each time step, the I-Soil constitutive model updates effective stress under the imposed strain increment. Plastic volumetric coupling is controlled by the volumetric-response parameters A₀ and η_dsr which allows contractive or dilative plastic volumetric strain to develop during cyclic shear.

That volumetric strain increment then drives the excess pore-pressure source term in the Biot equation:

Eq. 1

with the generation source related to volumetric strain by

Eq. 2

and fluid storage

Eq. 3

where ε_v = ε_xx + ε_yy +ε_zz is volumetric strain, n is porosity, and K_f  is the bulk modulus of the pore fluid. In discrete form, the change in pore pressure increment is therefore

Eq. 4

In this engine, the porosity is set to 1.0 which leads to the magnitude of pore pressure to be controlled solely by the fluid stiffness. Contractive volumetric response increases excess pore pressure; dilative response decreases it. Generation acts only in saturated elements below the water table. Because generation enters through q_u in Eq. 1, pore-pressure generation and dissipation occur simultaneously during shaking.