Permeability of Microcracked Porous Solids: Modeling from Homogenization to Percolation

Abstract

This paper establishes a comprehensive modeling for permeability of porous solids incorporating cracks with clustering extent ranging from nonoverlapping to percolation. The geometry of cracks is characterized through the crack density, orientation, connectivity, and fractal dimension of crack networks. The interaction direct derivative (IDD) model from effective medium theory is developed to predict the permeability of solids with nonoverlapping cracks and further extended by a two-step scheme to account for cracks with local clustering. The continuum percolation theory is adopted to build the permeability scaling law for crack networks approaching percolation. The comprehensive model thus established was validated against numerical simulations for crack networks with different geometry characteristics. The obtained results show that (1) the classical IDD model can predict satisfactorily the permeability for nonoverlapping cracks and the crack opening has nearly no impact on overall permeability, (2) the extended IDD model considers successfully the local clustering of cracks, the prediction range is greatly enhanced for overall permeability, and the impact of crack opening is still limited, and (3) as crack networks approachi percolation, the overall permeability observes a scaling law highlighting the importance of crack connectivity, and the impact of crack opening assumes a power law with the exponent related to the fractal dimension of crack networks.

Computational methods of mass transport in concrete under stress and crack conditions: A review

“…[30], © Elsevier Ltd., 2012; (c) four-point bending method [32,33], reproduced with permission from Ref. [32], © ASCE, 2011; (d) center expansion method [27]; (e) splitting method [4,24]; and (f) Wedge splitting method [34,35], reproduced with permission from Ref. [34], © RILEM, 2007.…”

“…Due to differences in concrete materials and testing equipment, the compressive stress thresholds obtained by different scholars are not consistent, ranging from 30% to 70%. For prestressed concrete members, the permeability coefficient of chloride ions decreases with increasing pressure when the construction load is less than 55% of the compressive strength (f c ) of the concrete [24]. Picandet et al [42] observed the permeability of concrete by unloading concrete specimens subjected to axial compressive loads, and the experimental results showed that the permeability of concrete would increase significantly when the stress level reached 90% of the ultimate strength.…”

“…Based on the obtained concentration distribution curves, a series of significant influencing factors have been further elucidated, including water-cement ratio, interface transition zone effects, external chloride ion concentration, aggregate volume fraction, and internal Grey correlation analysis was further conducted to rank the relevant factors affecting chloride ion diffusion under FTCs. They also took into account the influence of coarse aggregate shape [24] and applied the Bayesian method to integrate common patterns of numerical models with experimental individual information. By updating the penetration depth, a more reasonable penetration depth can be calculated.…”

“…The study of transport characteristics in cracked concrete has emerged as a popular research topic in the field of concrete materials science. Numerous scholars [22][23][24][25][26][27][28][29] have conducted in-depth investigations in this area and proposed various models and theories to describe the transport characteristics of cracked concrete. These models include empirical models based on experimental data and theoretical models based on physical principles.…”