The current study presents superposition‐based concurrent multiscale approaches for porodynamics, capable of capturing related physical phenomena, such as soil liquefaction and dynamic hydraulic fracture branching, across different spatial length scales. Two scenarios are considered: superposition of finite element discretizations with varying mesh densities, and superposition of peridynamics (PD) and finite element method (FEM) to handle discontinuities like strain localization and cracks. The approach decomposes the acceleration and the rate of change in pore water pressure into subdomain solutions approximated by different models, allowing high‐fidelity models to be used locally in regions of interest, such as crack tips or shear bands, without neglecting the far‐field influence represented by low‐fidelity models. The coupled stiffness, mass, compressibility, permeability, and damping matrices were derived based on the superposition‐based current multiscale framework. The proposed FEM‐FEM porodynamic coupling approach was validated against analytical or numerical solutions for one‐ and two‐dimensional dynamic consolidation problems. The PD‐FEM porodynamic coupling model was applied to scenarios like soil liquefaction‐induced shear strain accumulation near a low‐permeability interlayer in a layered deposit and dynamic hydraulic fracturing branching. It has been shown that the coupled porodynamic model offers modeling flexibility and efficiency by taking advantage of FEM in modeling complex domains and the PD ability to resolve discontinuities.

中文翻译：

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基于叠加的并发多尺度孔隙动力学方法


目前的研究提出了基于叠加的并发多尺度孔隙动力学方法，能够捕获不同空间长度尺度的相关物理现象，例如土壤液化和动态水力裂缝分支。考虑两种情况：具有不同网格密度的有限元离散的叠加，以及近场动力学 (PD) 和有限元方法 (FEM) 的叠加，以处理应变局部化和裂纹等不连续性。该方法将孔隙水压力的加速度和变化率分解为由不同模型近似的子域解，允许在感兴趣的区域（例如裂纹尖端或剪切带）局部使用高保真模型，而不会忽略远场低保真度模型所代表的影响。耦合刚度、质量、压缩性、渗透性和阻尼矩阵是基于基于叠加的当前多尺度框架导出的。所提出的 FEM-FEM 孔隙动力耦合方法针对一维和二维动态固结问题的解析或数值解进行了验证。 PD-FEM 孔隙动力耦合模型适用于层状沉积物中低渗透夹层附近土壤液化引起的剪切应变积累和动态水力压裂分支等场景。事实证明，耦合孔隙动力学模型通过利用 FEM 建模复杂域以及 PD 解决不连续性的能力，提供了建模灵活性和效率。