Elastic Properties of Swelling Clay Particles at Finite Temperature upon Hydration

Abstract

The knowledge of mechanical properties of swelling clays on the scale of the clay layer is of crucial importance to build predictive hydromechanical macroscopic constitutive laws in a bottom-up approach. In this work, we computed the elastic properties of particles of a swelling clay (i.e., montmorillonite) by molecular dynamics simulations. Because of the softness of the material in the direction orthogonal to the clay layer with increasing water content, the computation of the whole stiffness tensor was not trivial: we needed to implement the elastic bath method, 1 which allows us to attenuate thermal strains and compute the stiffness via strain fluctuations in isothermal−isobaric simulations. We investigated the effect of water content, temperature, and the interlayer cation on the elastic properties of swelling clays. In particular, we showed that the out-of-plane stiffness coefficients computed at 300 K differed significantly from the same coefficients computed at 0 K. The out-of-plane coefficients were very sensitive to both temperature and water content. In contrast, the dependence of the in-plane coefficients to temperature was slight. Moreover, the decrease of the in-plane coefficients with water content could be entirely explained by the change of geometry of the system due to the swelling of the interlayer space. The interlayer cation impacted the elastic properties of montmorillonite only in the driest states.

Measurement of the elastic properties of swelling clay minerals using the digital image correlation method on a single macroscopic crystal

“…However, experimental data obtained by acoustic or elastic wave measurements are known to provide higher values of elastic parameters than static measurements i.e., those associated with slower loading rates (e.g., Santamarina et al, 2001), as is the case for this study. Finally, the estimated undrained uniaxial Young's modulus provided by this study, i.e., 32.3 ± 3.9 GPa as well as the experimental data obtained by Zhang et al (2009) on a natural rectorite crystal and the theoretical results obtained by Carrier et al (2014) are found to be almost consistent. The Young's modulus of approximately 18 GPa obtained by Zhang et al (2009) for a single crystal of rectorite, which corresponds to the regular alternation of illite and montmorillonite layers, appears to logically lie in-between the values obtained by Carrier et al (2014) for dehydrated and monohydrated montmorillonite, respectively.…”

“…Finally, the estimated undrained uniaxial Young's modulus provided by this study, i.e., 32.3 ± 3.9 GPa as well as the experimental data obtained by Zhang et al (2009) on a natural rectorite crystal and the theoretical results obtained by Carrier et al (2014) are found to be almost consistent. The Young's modulus of approximately 18 GPa obtained by Zhang et al (2009) for a single crystal of rectorite, which corresponds to the regular alternation of illite and montmorillonite layers, appears to logically lie in-between the values obtained by Carrier et al (2014) for dehydrated and monohydrated montmorillonite, respectively. This study's value of 32.3 ± 3.9 GPa lies between the theoretical data obtained by Carrier et al (2014) for the Na-montmorillonite with 1 or 0 interlayer water sheet.…”

“…The Young's modulus of approximately 18 GPa obtained by Zhang et al (2009) for a single crystal of rectorite, which corresponds to the regular alternation of illite and montmorillonite layers, appears to logically lie in-between the values obtained by Carrier et al (2014) for dehydrated and monohydrated montmorillonite, respectively. This study's value of 32.3 ± 3.9 GPa lies between the theoretical data obtained by Carrier et al (2014) for the Na-montmorillonite with 1 or 0 interlayer water sheet. This observation can tentatively be assigned to the more rigid interlayer organization of water and cations in Mg 2+ -vermiculite compared to Na-montmorillonite, likely resulting from the increased layer charge and the presence of divalent cation in the former sample (De la Calle and Suquet, 1988;Michot et al, 2012).…”

“…In mineral physics, investigating how the mineral elasticity of nanoscale clay minerals and the distribution of water molecules in the interlayer space affect the mechanical behavior of the clay crystals or tactoids is of scientific interest (e.g., Ulm et al, 2005;Ichikawa et al, 2004;Carrier et al, 2014;Ebrahimi et al, 2014). In geophysics, because clay minerals are an integral part of many geological formations, reservoir characterization using seismic waves requires the elastic parameters of solid components and pore fluids to be known (e.g., Wang et al, 2001;Vanorio et al, 2003;Mondol et al, 2008;Mavko et al, 2009).…”

“…Here, the elastic properties are primarily obtained from molecular dynamics (MD) simulations. Although these types of calculations have been applied to clay minerals (e.g., Shroll and Smith, 1999), the theoretical estimation of elastic properties as a function of hydration is rather recent (Militzer et al, 2011;Carrier et al, 2014). The results emphasized the crucial role of the interlayer water molecules on the mechanical response of the swelling clay crystal.…”