An entropic model for the rock water absorption process
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ORIGINAL PAPER
An entropic model for the rock water absorption process Zhongfan Zhu1 • Jie Dou2,3 • Hongrui Wang1
Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The interaction between rock and surrounding water is an important research topic in geotechnical engineering. In this study, the temporal variation in rock moisture content when immersed in water is investigated using the probability method based on the entropy theory. An analytical mathematical expression is derived by assuming the rock moisture content to be a random variable, maximizing the entropy function subject to a constraint condition and adopting a hypothesis regarding the rock moisture content cumulative distribution function. The proposed entropy-based expression models the temporal evolution of rock moisture content as immersion time progresses from null to infinity. Furthermore, the derived model is tested against eight experimental data sets from the literature, with good agreement, a high correlation coefficient (0.9689) and a low mean absolute relative error (0.0664). Based on previous experimental results, the impacts of three main factors—rock type, rock porosity and outer water pressure on the maximum capacity for moisture content growth, a key parameter of the proposed expression—are discussed. The entropy-based method is a useful tool for predicting the variation of rock moisture content with different immersion times during the water absorption process. Keywords Entropy Probability distribution Water absorption process Rock
1 Introduction Rock’s stiffness and strength often make it resistant to external pressure under natural conditions; however, it can expand, soften and disintegrate in water, decreasing its mechanical performance (e.g., Hadizadeh and Law 1991; Lockner 1998; He et al. 2002; Liu et al. 2011). These characteristics may lead to large deformations or even collapse in some geotechnical projects (e.g., He et al. 2002; Liu et al. 2011). Therefore, understanding the interaction between rock and the surrounding water is important for the protection, management and operation of certain & Hongrui Wang [email protected] 1
Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Beijing 100875, China
2
Three Gorges Research Center for Geo-Hazards, Ministry of Education, China University of Geosciences, Wuhan 430074, China
3
Department of Civil and Environmental Engineering, Nagaoka University of Technology, 1603-1, Kami-Tomioka, Nagaoka 940-2188, Japan
geotechnical engineering projects (e.g., Zhou et al. 2005; Lian and Chai 2011; Ren et al. 2017). As He et al. (2008), Lian and Chai (2011) and Liu et al. (2011) summarized, many investigations into water–rock interaction have been performed, mainly focusing on the following aspects: the mechanical properties of water-containing rock (e.g., Van Eeckhout and Peng 1975; Meng et al. 2002; Li and Reddish 2004; Wang et al. 2006; Vasarhelyi 2005; Cheng et al. 2006), the e
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