Models for liquid relative permeability of cementitious porous media at elevated temperature: comparisons and discussions

Pan Zeng; Linlong Mu; Yiming Zhang; Pan Zeng; Linlong Mu; Yiming Zhang

doi:10.3934/mbe.2019198

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 4007-4035. doi: 10.3934/mbe.2019198

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Models for liquid relative permeability of cementitious porous media at elevated temperature: comparisons and discussions

1.
School of Civil and Transportation Engineering, South China University of Technology, Wushan Road 381, 510641 Guangzhou, P.R.China
2.
Department of Geotechnical Engineering, Tongji University, Siping Road 1239, 200092 Shanghai, P.R.China
3.
State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Siping Road 1239, 200092 Shanghai, P.R.China
4.
School of Civil and Transportation Engineering, Hebei University of Technology, Xiping Road 5340, 300401 Tianjin, P.R.China

Received: 21 February 2019 Accepted: 23 April 2019 Published: 06 May 2019

Fire-loaded cementitious material such as concrete experiences a rapid and dramatic pore pressure buildup, resulting in potential explosive spalling—sudden loss of the heated section—which can jeopardize the structure. Pore pressure buildup processes in heated concrete are closely related to the relative permeabilities of concrete to gas and liquid denoted by $k^{rg}$ and $k^{rl}$, respectively. While $k^{rg}$ has been widely investigated experimentally, $k^{rl}$ is conventionally determined by semi-analytical meth-ods such as Mualem's model, the reliability of which has been questioned by indirect experimentation but is not fully understood. In this work, we discuss the potential overestimation of $k^{rl}$ by conventional model in consideration of the achievements of previous research. Then, by using different models, the influences of $k^{rl}$ on the pore pressure $p^g$ are shown and compared through numerical simulations with a well established thermo-hydro-chemical (THC) multifield framework, revealing that the conventional model provides smaller values of $p^g$ than other models. Finally, through a comparison with water con-tent results obtained from nuclear magnetic resonance (NMR) tests in publications ^[1], we prove that some other models produce results that are more agreeable than those of the conventional model, which cannot reproduce the steep increase in the moisture content with depth observed experimentally.
- fire-loaded cementitious material,
- relative permeability,
- multiphase flow in porous media,
- coupled multifield analysis,
- numerical simulations
Citation: Pan Zeng, Linlong Mu, Yiming Zhang. Models for liquid relative permeability of cementitious porous media at elevated temperature: comparisons and discussions[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4007-4035. doi: 10.3934/mbe.2019198

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Abstract

Fire-loaded cementitious material such as concrete experiences a rapid and dramatic pore pressure buildup, resulting in potential explosive spalling—sudden loss of the heated section—which can jeopardize the structure. Pore pressure buildup processes in heated concrete are closely related to the relative permeabilities of concrete to gas and liquid denoted by $k^{rg}$ and $k^{rl}$, respectively. While $k^{rg}$ has been widely investigated experimentally, $k^{rl}$ is conventionally determined by semi-analytical meth-ods such as Mualem's model, the reliability of which has been questioned by indirect experimentation but is not fully understood. In this work, we discuss the potential overestimation of $k^{rl}$ by conventional model in consideration of the achievements of previous research. Then, by using different models, the influences of $k^{rl}$ on the pore pressure $p^g$ are shown and compared through numerical simulations with a well established thermo-hydro-chemical (THC) multifield framework, revealing that the conventional model provides smaller values of $p^g$ than other models. Finally, through a comparison with water con-tent results obtained from nuclear magnetic resonance (NMR) tests in publications ^[1], we prove that some other models produce results that are more agreeable than those of the conventional model, which cannot reproduce the steep increase in the moisture content with depth observed experimentally.

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