### Mathematical Biosciences and Engineering

2019, Issue 5: 4007-4035. doi: 10.3934/mbe.2019198
Research article Special Issues

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

• 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.

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

### Related Papers:

• 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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