Abstract

This article derives the effective poroelastic properties of N-layered composite assemblage. The derivation is based on the Hashin composite sphere assemblage (CSA) model and the linear elastic solution of n-layer coated inclusion-reinforced materials proposed by Hervé and Zaoui. The contribution of this study consists in the consideration of the poromechanical coupling to derive not only the bulk and shear drained moduli but also the Biot coefficient and the solid Biot modulus. The theoretical solutions are used for studying the oolitic limestone from Bourgogne (France), in which the microstructure exhibits generally an assemblage of oolite grains surrounded by a matrix. They are linked via interphase where most of the macropores locate. A two-step homogenisation scheme is proposed. The first step consists in upscaling the mesoscopic poroelastic properties of each porous phase by using the differential self-consistent scheme. In the second step, the three different porous constituents (oolite, ITZ and matrix) are homogenised using the CSA model. Results are validated against the data collected from the open literature.

摘要

本文推导了N的有效多孔弹性特性- 分层复合组合。推导基于Hashin复合球体组合（CSA）模型和Hervé和Zaoui提出的n层包覆夹杂物增强材料的线弹性解。本研究的贡献在于考虑了孔隙力学耦合，不仅可以导出体积和剪切排水模量，还可以导出毕奥系数和固体毕奥模量。理论解决方案用于研究来自勃艮第（法国）的鲕状灰岩，其中微观结构通常表现为被基质包围的鲕粒组合。它们通过大多数大孔所在的相间相连接。提出了两步均化方案。第一步包括通过使用微分自洽方案来放大每个多孔相的介观孔隙弹性。在第二步中，三种不同的多孔成分（鲕粒岩、ITZ 和基质）使用 CSA 模型进行均质化。结果根据从公开文献中收集的数据进行验证。