A unified non-local fluid transport model is proposed for heterogeneous saturated porous media. First, a non-local governing equation of fluid transport is presented based on the Non-ordinary State-based Peridynamics (NOSB-PD), and a novel flux vector state and a non-local Darcy’s law is proposed to illustrate non-local fluid transport effects in heterogeneous saturated porous media. The proposed flux state vector ensures the non-local governing equation of fluid transport model in heterogeneous saturated porous media degenerates into the local one when the horizon of each material point approaches to zero. A non-local pressure gradient at each material point can be obtained by averaging all the flux state vectors in its horizon, which unifies the weak and strong discontinuities of pressure in heterogeneous saturated porous media in a consistent way. Second, a variational formulation of the unified non-local fluid transport model is developed. This variational formulation enables the proposed model to deal with complex boundary conditions, which is difficult or even impossible for current fluid transport models based on Bond-based Peridynamics (BB-PD) and Ordinary State-based Peridynamics (OSB-PD). Third, a fully implicit algorithm combined with the Newton–Raphson method is introduced to solve the general non-linear problems in the heterogeneous saturated porous media. The penalty function method is employed to eliminate the zero-energy mode oscillation in NOSB-PD. Further, numerical examples demonstrate that the proposed model is accurate and can well capture the weak and strong discontinuities of pressure at the material interfaces and crack surfaces in the heterogeneous saturated porous media. Numerical examples also indicate that the model can effectively eliminate the zero-energy mode oscillation inherently rooted in the NOSB-PD, and thus reaches a stable numerical solution.

针对非均质饱和多孔介质提出了统一的非局部流体输运模型。首先，基于非普通状态近场动力学（NOSB-PD）提出了流体输运的非局部控制方程，并提出了一种新的通量矢量状态和非局部达西定律来说明非局部流体非均质饱和多孔介质中的输运效应。所提出的通量状态向量保证了非局部控制方程在非均质饱和多孔介质中的流体传输模型在每个材料点的视界接近零时退化为局部控制方程。非局部压力梯度在每个材料点处，可以通过对其视界内的所有通量状态向量求平均值来获得，从而以一致的方式统一了非均质饱和多孔介质中压力的弱和强不连续性。二、变分公式开发了统一的非局部流体传输模型。这种变分公式使所提出的模型能够处理复杂的边界条件，这对于当前基于债券的近场动力学 (BB-PD) 和基于普通状态的近场动力学 (OSB-PD) 的流体输运模型来说是困难的甚至不可能的。第三，引入了一种结合Newton-Raphson方法的全隐式算法来解决非均质饱和多孔介质中的一般非线性问题。采用惩罚函数法消除NOSB-PD中的零能量模式振荡。此外，数值例子表明所提出的模型是准确的，可以很好地捕捉压力的弱和强不连续性。非均质饱和多孔介质中的材料界面和裂纹表面。数值算例还表明，该模型可以有效消除NOSB-PD固有的零能量模式振荡，从而达到稳定的数值解。