Undrained Pore Fluid Flow and Stress Analysis

A porous medium typically consists of a solid skeleton of numerous solid grains that are "loosely packed" and a pore fluid that flows through a system of interconnected pores among these solid grains. An example of a porous medium is soil containing ground water. When subjected to loading, both the soil and water respond in a manner that leads generally to a fully coupled response where the deformation in the soil influences the pressure of the water and vice versa. In addition, water flows through the porous medium driven by pressure gradients. To simulate the fully coupled response, a fully coupled pore pressure and stress analysis is necessary (see Coupled Pore Fluid Diffusion and Stress Analysis).

In some situations when the loading rate is significantly faster than the rate at which pore fluid can drain from the porous medium, the fluid diffusion terms can be ignored. This corresponds to the undrained conditions.

The undrained pore fluid flow and stress analysis functionality in Abaqus/Explicit is intended for the simulation of fully saturated porous media under undrained conditions. The functionality enables modeling the increase in stiffness of the soil in applications such as trenching, gouging, and pile driving. Another typical class of problems that can be modeled is soil liquefaction, such as quicksand, quick clay, turbidity currents, and earthquake-induced liquefaction. In all of these applications, fluid diffusion terms can be ignored when the rate of loading is fast compared to the characteristic time of the diffusion process.

For problems where the fluid diffusion terms are important and fluid can rapidly diffuse, a fully coupled pore pressure and stress analysis must be performed (see Coupled Pore Fluid Diffusion and Stress Analysis).

DYNAMIC, EXPLICIT, PORE PRESSURE=UNDRAINED

For the coupled pore fluid flow and stress analysis, the continuity equation for the fluid diffusion is given by

$u_w$

is the fluid pore pressure,

$K_w$

is the bulk modulus of the fluid,

$K_g$

is the bulk modulus of the solid grains,

$n$

is the porosity of the medium,

${\rho }_w$

is the density of the fluid,

${\rho }_w^0$

is the density of the fluid in the reference configuration,

${\stackrel{\mathrm{.}}{\epsilon }}_{vol}$

is the volumetric strain rate in the porous medium,

${\stackrel{\mathrm{.}}{\epsilon }}_w^{th}$

is the volumetric thermal expansion rate in the porous fluid,

${\stackrel{\mathrm{.}}{\epsilon }}_g^{th}$

is the volumetric thermal expansion rate in the porous solid skeleton,

$v_w$

is the average velocity of the fluid relative to the solid phase,

$\alpha$

is the Biot parameter defined as $\alpha =1-K/K_g$ , and

$K$

is the bulk elastic modulus of the porous material skeleton.

Under undrained conditions, the fluid velocity terms can be set to zero in the continuity equation:

Integrating in time, the incremental pore fluid pressure is given by

The porosity evolution is

The total stress and strain are given by

In the above expression $\mathit{\sigma }$ is the total stress, and $\overline{\mathit{\sigma }}$ is the effective stress that is a function of the effective strain $\overline{ϵ}$ and the constitutive response of the porous material skeleton (see Effective stress principle for porous media).