|
|
|
| Molecular dynamics simulation of small-strain anisotropy of unsaturated montmorillonite |
| QIAN Jiangu1, 2*, ZHOU Gaoyun1, SHI Zhenhao1 |
(1. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China;
2. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China) |
|
|
|
|
Abstract Anisotropy is a fundamental characteristic of the small-strain behavior of unsaturated clay minerals, with its microscopic mechanisms governed by the coupled effects of interparticle hydration and stress levels. To elucidate the multiscale mechanisms through which confining pressure and suction influence the small-strain stiffness of clay minerals, this study employs a mesoscale coarse-grained molecular dynamics (CGMD) approach, calibrated against full-atomistic potential of mean force (PMF) calculations. An interparticle potential function that explicitly accounts for macroscopic relative humidity (RH) is introduced by incorporating an exponentially decaying oscillatory term, enabling the quantitative characterization of the periodic oscillatory decay of interparticle forces arising from the ordering of water molecules. Montmorillonite platelets are idealized as oblate ellipsoidal particles, and the evolution of small-strain elastic anisotropy is systematically investigated under various RH and confining pressure conditions. Mesoscale simulations are performed using the LAMMPS platform to capture the small-strain elastic response of clay minerals, and the simulation results exhibit a consistent trend with experimental data at both macro- and microscopic scales. The evolution of stiffness anisotropy is further analyzed in relation to fabric evolution, elucidating the microscopic mechanisms underlying the effects of pressure and RH. The results indicate that under constant RH, increasing confining pressure enhances small-strain stiffness and anisotropy, with the fabric progressively evolving toward an ordered, transversely isotropic structure characterized by face-to-face particle stacking. Under low confining pressures, an increase in RH leads to a reduction in stiffness, a slight decrease in anisotropy, and a tendency toward fabric loosening, accompanied by reduced stacking density and order. Furthermore, a well-defined linear correlation is observed between the macroscopic anisotropy parameter and the mesoscopic order parameter.
|
|
|
|
|
|
[1] LIAO J J,WANG C. Elastic solutions for a transversely isotropic half-space subjected to a point load[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1998,22(6):425–447.
[2] GRAHAM J,HOULSBY G. Anisotropic elasticity of a natural clay[J]. Géotechnique,1983,33(2):165–180.
[3] EBRAHIMI D. Multiscale modeling of clay-water systems[Ph. D. Thesis][D]. Cambridge:Massachusetts Institute of Technology,2013.
[4] UNDERWOOD T R,BOURG I C. Large-scale molecular dynamics simulation of the dehydration of a suspension of smectite clay nanoparticles[J]. The Journal of Physical Chemistry C,2020,124(6):3 702–3 714.
[5] 杨仲轩,廖 栋,钱建固,等. 土的基本特性及本构关系[J]. 土木工程学报,2025,58(4):88–107. (YANG Zhongxuan,LIAO Dong,QIAN Jiangu,et al. Fundamental behaviors and constitutive relationships of soil[J]. China Civil Engineering Journal,2025,58(4):88–107. (in Chinese))
[6] MITARITONNA G,AMOROSI A,COTECCHIA F. Experimental investigation of the evolution of elastic stiffness anisotropy in a clayey soil[J]. Géotechnique,2014,64(6):463–475.
[7] 杜子博,钱建固,郭院成,等. 天然软黏土主应力轴循环旋转塑性效应的本构模拟[J]. 岩土工程学报,2022,44(8):1 493–1 501. (DU Zibo,QIAN Jiangu,GUO Yuancheng,et al. Constitutive modeling of plastic effects of cyclic principal stress rotation of natural soft clay[J]. Chinese Journal of Geotechnical Engineering,2022,44(8):1 493–1 501.(in Chinese))
[8] MOHYLA T,BOHá? J,MAŠÍN D. Small-strain behaviour of unsaturated silty clay:experiments and model interpretation[J]. Acta Geotechnica,2021,16(9):2 837–2 849.
[9] WONG K S,MAŠÍN D,NG C W W. Modelling of shear stiffness of unsaturated fine grained soils at very small strains[J]. Computers and Geotechnics,2014,56:28–39.
[10] EBRAHIMI D,WHITTLE A J,PELLENQ R J M. Mesoscale properties of clay aggregates from potential of mean force representation of interactions between nanoplatelets[J]. The Journal of Chemical Physics,2014,140(15):154309.
[11] ZHU H,WHITTLE A J,PELLENQ R J M. Potential of mean force for face-face interactions between pairs of 2:1 clay mineral platelets[J]. Langmuir,2022,38(43):13 065–13 074.
[12] ZHU H,WHITTLE A J,PELLENQ R J M. Mesoscale simulation of the compression and small-strain elastic shear behavior of illite nanoparticle assemblies[J]. Acta Geotechnica,2025,20(2):781–802.
[13] EBRAHIMI D,WHITTLE A J,PELLENQ R J M. Effect of polydispersity of clay platelets on the aggregation and mechanical properties of clay at the mesoscale[J]. Clays and Clay Minerals,2016,64(4):425–437.
[14] DU J,WHITTLE A J,HU L,et al. Coupling grid nanoindentation and surface chemical analysis to infer the mechanical properties of shale mineral phases[J]. Engineering Geology,2023,325:107304.
[15] DU J,YUEN K V,WHITTLE A J,et al. Characterization of mechanical properties of shale constituent minerals using phase-identified nanoindentation[J]. Computer-Aided Civil and Infrastructure Engineering,2025,40(4):542–558.
[16] SIWEI M,ZIHAN Z,JIAPING T,et al. A novel upscaling method for evaluating mechanical properties of the shale oil reservoir based on cluster analysis and nanoindentation[J]. Journal of Energy Resources Technology,2023,145(11):112901.
[17] GAY J,BERNE B. Modification of the overlap potential to mimic a linear site-site potential[J]. The Journal of Chemical Physics,1981,74(6):3 316–3 319.
[18] BERARDI R,FAVA C,ZANNONI C. A Gay-Berne potential for dissimilar biaxial particles[J]. Chemical Physics Letters,1998,297(1/2):8–14.
[19] ZHANG Y,OESTREICHER J,BINNS W J,et al. A coarse-grained interaction model for sodium dominant montmorillonite[J]. Langmuir,2022,38(43):13 226–13 237.
[20] ZHOU G,SHI Z,QIAN J. Mesoscale analysis of coupled deformation-hydration behaviors of unsaturated clay accounting for atomistic-scale interactions[J]. Computers and Geotechnics,2025,187:107489.
[21] BROCHARD L. Swelling of montmorillonite from molecular simulations:hydration diagram and confined water properties[J]. The Journal of Physical Chemistry C,2021,125(28):15 527–15 543.
[22] 孟筠青,牛家兴,夏捃凯,等. 纳米尺度下煤的力学性质及破坏机制研究[J]. 岩石力学与工程学报,2020,39(1):84–92.(MENG Junqing,NIU Jiaxing,XIA Junkai,et al. Study on mechanical properties and failure mechanisms of coal at the nanometer scale[J]. Chinese Journal of Rock Mechanics and Engineering,2020,39(1):84–92.(in Chinese))
[23] DELAFARGUE A,ULM F J. Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters[J]. International Journal of Solids and Structures,2004,41(26):7 351–7 360.
[24] BOBKO C,ULM F J. The nano-mechanical morphology of shale[J]. Mechanics of Materials,2008,40(4/5):318–337.
[25] MARCUSON III W F,WAHLS H E. Time effects on dynamic shear modulus of clays[J]. Journal of the Soil Mechanics and Foundations Division,1972,98(12):1 359–1 373. |
|
|
|