Experimental observation demonstrates that both negative and positive dispersion relations are possible for porous media, which classical Biot theory fails to predict and interpret. The present paper establishes a higher-order strain gradient nonlocal poroelasticity considering both the size effects and heterogeneity structure effects to describe the specific physical characteristics of material and structure for porous media. The theoretical frame of Biot theory is reserved, and two length parameters, nonlocal parameter and scale factor are introduced to improve the classical Biot theory. Such an amendment yields remarkable merits as compared with the classical Biot theory because the nonlocality considers interactions among the solid grains with different sizes, while the high-order poromechanics only consider the locality of strain field. The differential-form constitutive relation and the governing equations of motion associated with boundary conditions are proposed by using variational method. The theory is finally applied to analyze the wave propagation characteristics in porous media, on which based both negative and positive dispersion relations as observed in the experiments can be successfully reproduced. The essential mechanism of softening and hardening effects in porous media is the result of competition of scale factor and nonlocal parameter. Thus, this higher-order strain gradient nonlocal poroelasticity is a general and complete theoretical scheme, which is capable of interpreting dynamical behaviors of porous media in a wide frequency of range.

实验观察表明，多孔介质的正和负色散关系都是可能的，而经典的毕奥特理论无法预测和解释。本文建立了一个高阶应变梯度非局部孔隙弹性，同时考虑了尺寸效应和异质结构效应，以描述多孔介质材料和结构的特定物理特性。保留了毕奥特理论的理论框架，并引入了两个长度参数（非局部参数和比例因子）来改进经典毕奥特理论。与经典的毕奥特理论相比，这种修正产生了显着的优点，因为非局部性考虑了具有不同尺寸的固体颗粒之间的相互作用，而高次体力学仅考虑了应变场的局部性。利用变分方法，提出了微分形式的本构关系和边界条件下的运动控制方程。该理论最终被应用于分析多孔介质中的波传播特性，从而可以成功地再现实验中观察到的负和正色散关系。多孔介质中软化和硬化作用的基本机理是比例因子和非局部参数竞争的结果。因此，这种高阶应变梯度非局部多孔弹性是一个通用而完整的理论方案，它能够在很宽的频率范围内解释多孔介质的动力学行为。