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STRESS-DEPENDENT MODELS FOR PERMEABILITY AND POROSITY OF FRACTURED ROCK BASED ON FRACTAL THEORY

TONGJUN MIAO

School of Physics and Electronic Engineering, Xinxiang University, Xinxiang, Henan 453003, P. R. China

E-mail Address: mtong2004@163.com

Corresponding author.

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AIMIN CHEN

School of Chemistry and Material Engineering, Xinxiang University, Xinxiang, Henan 453003, P. R. China

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ZUN LI

School of Physics and Electronic Engineering, Xinxiang University, Xinxiang, Henan 453003, P. R. China

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DAPING LIU

School of Physics and Electronic Engineering, Xinxiang University, Xinxiang, Henan 453003, P. R. China

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, and

BOMING YU

School of Physics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China

E-mail Address: yubm_2012@hust.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0218348X23500937Cited by:4 (Source: Crossref)

Abstract

The hydro-mechanical coupling behavior of the fractured rock is constitutive in accurately modeling the seepage properties such as permeability and porosity. In this work, the stress-dependent models for permeability and porosity of the fractured rock are proposed by employing the fractal geometry theory and the two-part Hooke’s model (TPHM). The proposed models for the permeability and porosity are related to the effective stress and the microstructures of fractures, such as the fractal dimension ( $D_{0, f}$ and $D_{σ, f})$ , the maximum fracture length $l_{σ, max}$ , and fracture orientations ( $𝜃$ and $φ)$ as well as porosities ( $ϕ_{0}$ and $ϕ_{σ})$ . The validity of the proposed permeability model coupled with stress is validated by comparison with the available experimental data. The model predictions agree well with the experimental data. The effects of microstructures of fracture networks in fractured rock on the dimensionless stress-dependent permeability and porosity as well as the fractal dimension for fracture areas are also discussed in detail. The proposed models may shed much light on the fundamental behavior of coupled hydro-mechanical properties of fractured rock.

Keywords:

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