Pores, vugs, and cracks configurations affect physical and mechanical properties of porous and fractured (PF) media, specifically the percolations of pores/vugs/cracks trigger the dramatic change of conductive-like properties such as thermal conductivity, diffusivity, elastic modulus of PF media. It has been a key but unresolved issue how to accurately capture the percolation thresholds of these complex networks interacted by anisotropic-shaped pores and cracks, and their quantitative effects on the thermal conductivity and elastic modulus of PF media. This work proposes numerical and theoretical strategies for the accurate determination of percolation thresholds of penetrable spheroidal inclusions over a broad range of aspect ratios κ representing prolate pores (1 < κ ≤ 200), vugs (κ = 1) and oblate cracks (0.001 ≤ κ < 1), and the reliable predictions of effective thermal conductivity, diffusivity, and elastic modulus of PF media. The numerical and theoretical strategies include: (1) an extensive Monte Carlo finite-size scaling analysis (MCFSS) for obtaining the statistical values of percolation threshold of porous and fracture networks with κ from 200 to 0.001; (2) a Padé-type percolation model for predicting the percolation thresholds of penetrable spheroidal inclusions over a broad range of aspect ratios; (3) a continuum percolation-based generalized effective medium theory (CP-GEMT) for predicting effective thermal conductivity, diffusivity, and elastic modulus of PF media over the whole range of volume fractions of spheroidal inclusions, including near the percolation threshold. Comparison with extensive experimental, numerical and theoretical results confirms that the present models are capable of accurately determining the percolation thresholds of porous and fracture networks and the effective thermal conductivity, diffusivity, and elastic modulus of PF media as resemble to conductor-superconductor and insulator-conductor. The models can be regarded as a general theoretical framework to shed light on the intrinsic and complex interaction of components, structures and transport and elastic properties in porous and fracture materials, meanwhile the proposed models can be also well utilized to predict the percolation thresholds of spheroidal carbon nanotubes (CNTs) and graphenes, and the effective transport and elastic properties of CNT-/graphene-based composites.

孔，孔洞和裂缝的形态会影响多孔和破裂（PF）介质的物理和机械性能，特别是孔/孔洞/裂缝的渗漏会触发类似导电性质的剧烈变化，例如PF的导热系数，扩散系数和弹性模量媒体。如何准确地捕获由各向异性形状的孔和裂缝相互作用的复杂网络的渗透阈值，以及它们对PF介质的热导率和弹性模量的定量影响，是一个关键但尚未解决的问题。这项工作提出了一种数值和理论策略，可在宽长比κ代表宽孔（1 < κ≤200）的宽孔比（vug）（κ  = 1）和扁圆形裂纹（0.001≤κ <1），以及PF介质有效导热率，扩散率和弹性模量的可靠预测。数值和理论策略包括：（1）广泛的蒙特卡洛有限尺寸尺度分析（MCFSS），用于获得具有κ的多孔和裂缝网络的渗流阈值的统计值200至0.001; （2）Padé型渗滤模型，用于预测宽高比范围内的可渗透球状夹杂物的渗滤阈值；（3）基于连续渗流的广义有效介质理论（CP-GEMT），用于预测球形包裹体体积分数整个范围内（包括在渗流阈值附近）的PF介质的有效导热率，扩散率和弹性模量。与大量实验，数值和理论结果进行的比较证实，本模型能够准确确定多孔和断裂网络的渗流阈值，以及类似于导体-超导体和绝缘子的PF介质的有效导热率，扩散率和弹性模量。导体。