This paper presents an unified mathematical and computational framework for mechanics-coupled “anomalous” transport phenomena in porous media. The anomalous diffusion is mainly due to variable fluid flow rates caused by spatially and temporally varying permeability. This type of behaviour is described by a fractional pore pressure diffusion equation. The diffusion transient phenomena is significantly affected by the order of the fractional operators. In order to solve 3D consolidation problems of large scale structures, the fractional pore pressure diffusion equation is implemented in a finite element framework adopting the discretised formulation of fractional derivatives given by Grunwald–Letnikov (GL). Here the fractional pore pressure diffusion equation is implemented in the commercial software Abaqus through an open-source UMATHT subroutine. The similarity between pore pressure, heat and hydrogen transport is also discussed in order to show that it is possible to use the coupled thermal-stress analysis to solve fractional consolidation problems.

本文提出了一个统一的数学和计算框架，用于多孔介质中力学耦合的“异常”传输现象。异常扩散主要是由于渗透率随空间和时间变化引起的可变流体流速。这种类型的行为由分数孔隙压力扩散方程描述。扩散瞬态现象受分数算子顺序的显着影响。为了解决大规模结构的 3D 固结问题，分数孔隙压力扩散方程在采用 Grunwald-Letnikov (GL) 给出的分数阶导数的离散公式的有限元框架中实现。这里的分数孔隙压力扩散方程是通过开源 UMATHT 子程序在商业软件 Abaqus 中实现的。