Technical Papers
Oct 3, 2024

All-Atomic Modeling of the Compaction of Montmorillonite Clays: Fabric Evolution and Energy Conversion

Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 150, Issue 12

Abstract

Compaction is an essential compression process for sedimentary soils. Compared with in-depth studies on granular soil behaviors, numerical modeling of clay compaction is still in its infancy. This study presents an all-atomic modeling framework to investigate the compaction of anhydrous montmorillonite from initially fully exfoliated platelets. The total number of interparticle contacts increased, and the mesopores were dominant during the formation of card-house structures. As the local fabrics evolved into book-house structures, the contact evolutions became predominant, and partial mesopores transformed into micropores. The coordinated deformations during the formation of compacted aggregates dramatically increased interparticle contacts, and so the micropores became dominant. After rebound, the interparticle contacts decreased and partial micropores were restored. The total potential energy decreased during contact evolutions due to the significant reduction in interaction potential energy between clay particles, while hysteresis was observed during coordinated deformations and rebound due to the changes in internal potential energy within deformed clay particles. The internal potential energy was primarily determined by the electrostatic forces except under significant deformations, where the van der Waals forces became dominant. The interaction potential energy remained unchanged with specific contact types but decreased significantly due to electrostatic interaction when contacts evolved. As computational capacity develops, a greater number of larger hydrated clay particles can be used to improve simulations of compaction and other macroscopic behaviors via all-atomic molecular dynamics simulations.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

Acknowledgments

The financial support received from the National Natural Science Foundation of China (NSFC, Grant Nos. 51988101 and 42077241) are gratefully acknowledged. Hang-Jun Wu in the Centre of Cryo-Electron Microscopy (CCEM), Zhejiang University, is greatly appreciated for his technical assistance.

References

Ahmed, H. R., and S. N. Abduljauwad. 2017. “Nano-level constitutive model for expansive clays.” Géotechnique 67 (3): 187–207. https://doi.org/10.1680/jgeot.15.P.140.
Allen, M. P., and D. J. Tildesley. 2017. Computer simulation of liquids. Oxford, UK: Oxford University Press.
Aminpour, P., and K. J. Sjoblom. 2019. “Multi-scale modelling of kaolinite triaxial behaviour.” Geotech. Lett. 9 (3): 178–185. https://doi.org/10.1680/jgele.18.00194.
Anandarajah, A. 1994. “Discrete-element method for simulating behavior of cohesive soil.” J. Geotech. Eng. 120 (9): 1593–1613. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:9(1593).
Anandarajah, A., and J. Chen. 1995. “Single correction function for computing retarded van der Waals attraction.” J. Colloid Interface Sci. 176 (2): 293–300. https://doi.org/10.1006/jcis.1995.9964.
Anandarajah, A., and N. Lu. 1991. “Numerical study of the electrical double-layer repulsion between non-parallel clay particles of finite length.” Int. J. Numer. Anal. Methods Geomech. 15 (10): 683–703. https://doi.org/10.1002/nag.1610151002.
Anoukou, K., A. Zaoui, F. Zaïri, M. Naït-Abdelaziz, and J. M. Gloaguen. 2015. “Structural and thermodynamics properties of organo-modified montmorillonite clay.” Physica E 65 (Jun): 56–60. https://doi.org/10.1016/j.physe.2014.07.025.
Arun, K. S., T. S. Huang, and S. D. Blostein. 1987. “Least-squares fitting of two 3-D point sets.” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9 (5): 698–700. https://doi.org/10.1109/TPAMI.1987.4767965.
Bandera, S., C. O’Sullivan, P. Tangney, and S. Angioletti-Uberti. 2021. “Coarse-grained molecular dynamics simulations of clay compression.” Comput. Geotech. 138 (Sep): 104333–104350. https://doi.org/10.1016/j.compgeo.2021.104333.
Bayesteh, H., and A. A. Mirghasemi. 2013. “Numerical simulation of pore fluid characteristic effect on the volume change behavior of montmorillonite clays.” Comput. Geotech. 48 (Sep): 146–155. https://doi.org/10.1016/j.compgeo.2012.10.007.
Benhamida, A., I. Djeran-Maigre, H. Dumontet, and S. Smaoui. 2005. “Clay compaction modelling by homogenization theory.” Int. J. Rock Mech. Min. Sci. 42 (7–8): 996–1005. https://doi.org/10.1016/j.ijrmms.2005.05.021.
Bhattacharya, S., and K. E. Gubbins. 2006. “Fast method for computing pore size distributions of model materials.” Langmuir 22 (18): 7726–7731. https://doi.org/10.1021/la052651k.
Carrier, B., M. Vandamme, R. J. Pellenq, M. Bornert, E. Ferrage, F. Hubert, and H. Van Damme. 2016. “Effect of water on elastic and creep properties of self-standing clay films.” Langmuir 32 (5): 1370–1379. https://doi.org/10.1021/acs.langmuir.5b03431.
Chen, J., and A. Anandarajah. 1996. “van der Waals attraction between spherical particles.” J. Colloid Interface Sci. 180 (2): 519–523. https://doi.org/10.1006/jcis.1996.0332.
Cheng, Z., and J. Wang. 2018. “A particle-tracking method for experimental investigation of kinematics of sand particles under triaxial compression.” Powder Technol. 328 (Sep): 436–451. https://doi.org/10.1016/j.powtec.2017.12.071.
Cundall, P. A., and O. D. L. Strack. 1979. “A discrete numerical model for granular assemblies.” Géotechnique 29 (1): 47–65. https://doi.org/10.1680/geot.1979.29.1.47.
Cygan, R. T., J. A. Greathouse, and A. G. Kalinichev. 2021. “Advances in CLAYFF molecular simulation of layered and nanoporous materials and their aqueous interfaces.” J. Phys. Chem. C 125 (32): 17573–17589. https://doi.org/10.1021/acs.jpcc.1c04600.
Cygan, R. T., J.-J. Liang, and A. G. Kalinichev. 2004. “Molecular models of hydroxide, oxydroxide, and clay phases and the development of a general force field.” J. Phys. Chem. B 108 (4): 1255–1266. https://doi.org/10.1021/jp0363287.
de Bono, J., and G. McDowell. 2023a. “Particle-scale simulations of the compression and shearing of kaolin clay.” Geotechnique 413 (Jan): 1–13. https://doi.org/10.1680/jgeot.22.00423.
de Bono, J., and G. McDowell. 2023b. “Simulating multifaceted interactions between kaolinite platelets.” Powder Technol. 413 (Jan): 118062. https://doi.org/10.1016/j.powtec.2022.118062.
Ebrahimi, D. 2014. “Multiscale modeling of clay water systems.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology.
Ebrahimi, D., R. J. M. Pellenq, and A. J. Whittle. 2016a. “Mesoscale simulation of clay aggregate formation and mechanical properties.” Granular Matter 18 (3): 49. https://doi.org/10.1007/s10035-016-0655-8.
Ebrahimi, D., A. J. Whittle, and R. J. M. Pellenq. 2014. “Mesoscale properties of clay aggregates from potential of mean force representation of interactions between nanoplatelets.” J. Chem. Phys. 140 (15): 154309. https://doi.org/10.1063/1.4870932.
Ebrahimi, D., A. J. Whittle, and R. J. M. Pellenq. 2016b. “Effect of polydispersity of clay platelets on the aggregation and mechanical properties of clay at the mesoscale.” Clays Clay Miner. 64 (4): 425–437. https://doi.org/10.1346/CCMN.2016.0640407.
Ece, Ö. I., F. Z. Çoban, N. Güngör, and F. Suner. 1999. “Clay mineralogy and occurrence of ferrian smectites between serpentinite saprolites and basalts in Biga Peninsula, Northwest Turkey.” Clays Clay Miner. 47 (3): 241–251. https://doi.org/10.1346/CCMN.1999.0470301.
Everaers, R., and M. R. Ejtehadi. 2003. “Interaction potentials for soft and hard ellipsoids.” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 67 (4): 041710. https://doi.org/10.1103/PhysRevE.67.041710.
Frankel, D., and B. Smit. 2002. Understanding molecular simulation: From algorithms to applications. Bodmin, Cornwall: Academic Press.
Gay, J. G., and B. J. Berne. 1981. “Modification of the overlap potential to mimic a linear site–site potential.” J. Chem. Phys. 74 (6): 3316–3319. https://doi.org/10.1063/1.441483.
Gu, X., J. Hu, and M. Huang. 2015. “K0 of granular soils: A particulate approach.” Granular Matter 17 (6): 703–715. https://doi.org/10.1007/s10035-015-0588-7.
Guo, Y., and X. Yu. 2017. “Characterizing the surface charge of clay minerals with atomic force microscope (AFM).” AIMS Mater. Sci. 4 (3): 582–593. https://doi.org/10.3934/matersci.2017.3.582.
Guo, Y., and X. Yu. 2019. “A holistic computational model for prediction of clay suspension structure.” Int. J. Sediment Res. 34 (4): 345–354. https://doi.org/10.1016/j.ijsrc.2018.12.002.
Ho, T. A., J. A. Greathouse, Y. Wang, and L. J. Criscenti. 2017. “Atomistic structure of mineral nano-aggregates from simulated compaction and dewatering.” Sci. Rep. 7 (1): 15286. https://doi.org/10.1038/s41598-017-15639-4.
Hockney, R. W., and J. W. Eastwood. 1989. Computer simulation using particles. Bristol, UK: Adam Hilger.
Honorio, T., L. Brochard, M. Vandamme, and A. Lebee. 2018. “Flexibility of nanolayers and stacks: Implications in the nanostructuration of clays.” Soft Matter 14 (36): 7354–7367. https://doi.org/10.1039/C8SM01359D.
Humphrey, W., A. Dalke, and K. Schulten. 1996. “VMD: Visual molecular dynamics.” J. Mol. Graphics 14 (1): 33–38. https://doi.org/10.1016/0263-7855(96)00018-5.
Imseeh, W. H., A. M. Druckrey, and K. A. Alshibli. 2018. “3D experimental quantification of fabric and fabric evolution of sheared granular materials using synchrotron micro-computed tomography.” Granular Matter 20 (2): 24. https://doi.org/10.1007/s10035-018-0798-x.
Jaradat, K. A., and S. L. Abdelaziz. 2019. “On the use of discrete element method for multi-scale assessment of clay behavior.” Comput. Geotech. 112 (Aug): 329–341. https://doi.org/10.1016/j.compgeo.2019.05.001.
Jaradat, K. A., and S. L. Abdelaziz. 2023. “Simplifying the physico-chemical contacts in cohesive soils for efficient DEM simulations.” Comput. Geotech. 154 (Feb): 105155. https://doi.org/10.1016/j.compgeo.2022.105155.
Jiang, M. J. 2019. “New paradigm for modern soil mechanics: Geomechanics from micro to macro.” Chin. J. Geotech. 41 (2): 195–254. https://doi.org/10.11779/CJGE201902001.
Kang, X., H.-M. Sun, W. Yang, and R.-P. Chen. 2020. “Wettability of clay aggregates—A coarse-grained molecular dynamic study.” Appl. Surf. Sci. 532 (Dec): 147423. https://doi.org/10.1016/j.apsusc.2020.147423.
Kaufhold, S., M. Plötze, M. Klinkenberg, and R. Dohrmann. 2013. “Density and porosity of bentonites.” J. Porous Mater. 20 (1): 191–208. https://doi.org/10.1007/s10934-012-9589-7.
Khabazian, M., A. A. Mirghasemi, and H. Bayesteh. 2018. “Compressibility of montmorillonite/kaolinite mixtures in consolidation testing using discrete element method.” Comput. Geotech. 104 (Dec): 271–280. https://doi.org/10.1016/j.compgeo.2018.09.005.
Lammers, L. N., I. C. Bourg, M. Okumura, K. Kolluri, G. Sposito, and M. Machida. 2017. “Molecular dynamics simulations of cesium adsorption on illite nanoparticles.” J. Colloid. Interface Sci. 490 (Mar): 608–620. https://doi.org/10.1016/j.jcis.2016.11.084.
Lavikainen, L. P., J. T. Hirvi, S. Kasa, T. Schatz, and T. A. Pakkanen. 2015. “Stability of dioctahedral 2:1 Phyllosilicate edge structures based on pyrophyllite models.” Theor. Chem. Acc. 134 (9): 112. https://doi.org/10.1007/s00214-015-1715-6.
Leong, Y.-K., P. Liu, P.-I. Au, P. Clode, and J. Liu. 2022. “Microstructure and time-dependent behavior of STx-1b calcium montmorillonite suspensions.” Clays Clay Miner. 69 (6): 787–796. https://doi.org/10.1007/s42860-021-00170-5.
Lowenstein, W. 1954. “The distribution of aluminum in the tetrahedra of silicates and aluminates.” Am. Mineral. 39 (1–2): 92–96.
Lu, N., and A. Anandarajah. 1992. “Empirical estimation of double-layer repulsive force between two inclined clay particles of finite length.” J. Geotech. Eng. 118 (4): 628–634. https://doi.org/10.1061/(ASCE)0733-9410(1992)118:4(628).
Lu, T., and F. Chen. 2012. “MultiWFN: A multifunctional wavefunction analyzer.” J. Comput. Chem. 33 (5): 580–592. https://doi.org/10.1002/jcc.22885.
Martins, D. M. S., M. Molinari, M. A. Gonçalves, J. P. Mirão, and S. C. Parker. 2014. “Toward modeling clay mineral nanoparticles: The edge surfaces of pyrophyllite and their interaction with water.” J. Phys. Chem. C 118 (47): 27308–27317. https://doi.org/10.1021/jp5070853.
Mazo, M. A., L. I. Manevitch, E. B. Gusarova, M. Y. Shamaev, A. A. Berlin, N. K. Balabaev, and G. C. Rutledge. 2008. “Molecular dynamics simulation of thermomechanical properties of montmorillonite crystal. 1. Isolated clay nanoplate.” J. Phys. Chem. B 112 (Sep): 2964–2969. https://doi.org/10.1021/jp076022q.
Michot, L. J., and F. Villiéras. 2006. “Surface area and porosity.” In Handbook of clay science, edited by F. Bergaya, B. K. G. Theng, and G. Lagaly, 965–978. Amsterdam, Netherlands: Elsevier.
Mitchell, J. K., and K. Soga. 2005. Fundamentals of soil behavior. Hoboken, NJ: Wiley.
Mouzon, J., I. U. Bhuiyan, and J. Hedlund. 2016. “The structure of montmorillonite gels revealed by sequential cryo-XHR-SEM imaging.” J. Colloid Interface Sci. 465 (Mar): 58–66. https://doi.org/10.1016/j.jcis.2015.11.031.
Nie, J.-Y., Z.-J. Cao, D.-Q. Li, and Y.-F. Cui. 2021. “3D DEM insights into the effect of particle overall regularity on macro and micro mechanical behaviours of dense sands.” Comput. Geotech. 132 (Apr): 103965. https://doi.org/10.1016/j.compgeo.2020.103965.
O’Sullivan, C. 2011. Particulate discrete element modelling: A geomechanics perspective. Abingdon, UK: Spron Press.
Pagano, A. G., V. Magnanimo, T. Weinhart, and A. Tarantino. 2020. “Exploring the micromechanics of non-active clays by way of virtual DEM experiments.” Géotechnique 70 (4): 303–316. https://doi.org/10.1680/jgeot.18.P.060.
Pedrotti, M., and A. Tarantino. 2018. “An experimental investigation into the micromechanics of non-active clays.” Géotechnique 68 (8): 666–683. https://doi.org/10.1680/jgeot.16.P.245.
Pouvreau, M., J. A. Greathouse, R. T. Cygan, and A. G. Kalinichev. 2017. “Structure of hydrated gibbsite and brucite edge surfaces: DFT results and further development of the CLAYFF classical force field with Metal–O–H angle bending terms.” J. Phys. Chem. C 121 (27): 14757–14771. https://doi.org/10.1021/acs.jpcc.7b05362.
Pouvreau, M., J. A. Greathouse, R. T. Cygan, and A. G. Kalinichev. 2019. “Structure of hydrated kaolinite edge surfaces: DFT results and further development of the CLAYFF classical force field with Metal–O–H angle bending terms.” J. Phys. Chem. C 123 (18): 11628–11638. https://doi.org/10.1021/acs.jpcc.9b00514.
Prishchenko, D. A., E. V. Zenkov, V. V. Mazurenko, R. F. Fakhrullin, Y. M. Lvov, and V. G. Mazurenko. 2018. “Molecular dynamics of the halloysite nanotubes.” Phys. Chem. Chem. Phys. 20 (8): 5841–5849. https://doi.org/10.1039/C7CP06575B.
Quirk, J. P., and L. A. G. Aylmore. 1971. “Domains and quasi-crystalline regions in clay systems.” Soil Sci. Soc. Am. J. 35 (4): 652–654. https://doi.org/10.2136/sssaj1971.03615995003500040046x.
Rouquerol, J., D. Avnir, C. W. Fairbridge, D. H. Everett, J. H. Haynes, N. Pernicone, J. D. F. Ramsay, K. S. W. Sing, and K. K. Unger. 1994. “Recommendations for characterisation of porous solids (technical report).” Pure Appl. Chem. 66 (8): 1739–1758. https://doi.org/10.1351/pac199466081739.
Santagata, M., A. Bobet, A. E. Howayek, F. Ochoa, J. V. Sinfield, and C. T. Johnston. 2014. “Building a nanostructure in the pore fluid of granular soils.” In Proc., Geomechanics from Micro to Macro, 1377–1382. London: Taylor & Francis Group.
Santamarina, J. C. 2003. “Soil behavior at the microscale: Particle forces.” In Proc., Symp. on Soil Behavior and Soft Ground Construction Honoring, edited by C. C. Ladd, 25–56. Reston, VA: ASCE.
Schaettle, K., L. Ruiz Pestana, T. Head-Gordon, and L. N. Lammers. 2018. “A structural coarse-grained model for clays using simple iterative Boltzmann inversion.” J. Chem. Phys. 148 (22): 222809. https://doi.org/10.1063/1.5011817.
Sjoblom, K. J. 2016. “Coarse-grained molecular dynamics approach to simulating clay behavior.” J. Geotech. Geoenviron. Eng. 142 (2): 06015013. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001394.
Skipper, N. T., F.-R. C. Chang, and G. Sposito. 1995. “Monte Carlo simulation of interlayer molecular structure in swelling clay minerals. 1. Methodology.” Clays Clay Miner. 43 (3): 285–293. https://doi.org/10.1346/CCMN.1995.0430303.
Souli, H., J. M. Fleureau, M. Trabelsi-Ayadi, and S. Taibi. 2013. “A multi-scale study of the effect of zinc and lead on the hydromechanical behaviour and fabric of a montmorillonite.” Géotechnique 63 (10): 880–884. https://doi.org/10.1680/geot.13.P.016.
Sperry, J. M., and J. J. Peirce. 1999. “Ion exchange and surface charge on montmorillonite clay.” Water Environ. Res. 71 (3): 316–322. https://doi.org/10.2175/106143098X121798.
Suter, J. L., R. L. Anderson, H. Christopher Greenwell, and P. V. Coveney. 2009. “Recent advances in large-scale atomistic and coarse-grained molecular dynamics simulation of clay minerals.” J. Mater. Chem. 19 (17): 2482–2493. https://doi.org/10.1039/b820445d.
Tarantino, A., and E. De Col. 2008. “Compaction behaviour of clay.” Géotechnique 58 (3): 199–213. https://doi.org/10.1680/geot.2008.58.3.199.
Thompson, A. P., et al. 2022. “LAMMPS—A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales.” Comput. Phys. Commun. 271 (Feb): 108171–108204. https://doi.org/10.1016/j.cpc.2021.108171.
Underwood, T. R., and I. C. Bourg. 2020. “Large-scale molecular dynamics simulation of the dehydration of a suspension of smectite clay nanoparticles.” J. Phys. Chem. C 124 (6): 3702–3714. https://doi.org/10.1021/acs.jpcc.9b11197.
van Olphen, H. 1977. An introduction to clay colloid chemistry: For clay technologists, geologists and soil scientists. New York: Wiley.
Vijayan, A., Y. Gan, and R. K. Annabattula. 2020. “Evolution of fabric in spherical granular assemblies under the influence of various loading conditions through DEM.” Granular Matter 22 (2): 34. https://doi.org/10.1007/s10035-020-1000-9.
Wang, X., S. Ramirez-Hinestrosa, J. Dobnikar, and D. Frenkel. 2020. “The Lennard-Jones potential: When (not) to use it.” Phys. Chem. Chem. Phys. 22 (19): 10624–10633. https://doi.org/10.1039/C9CP05445F.
Wei, X., M. Hattab, J.-M. Fleureau, and R. Hu. 2013. “Micro–macro-experimental study of two clayey materials on drying paths.” Bull. Eng. Geol. Environ. 72 (3–4): 495–508. https://doi.org/10.1007/s10064-013-0513-4.
White, G. N., and L. W. Zelazny. 1988. “Analysis and implications of the edge structure of dioctahedra phyllosilicates.” Clays Clay Miner. 36 (2): 141–146. https://doi.org/10.1346/CCMN.1988.0360207.
Whittaker, M. L., L. R. Comolli, B. Gilbert, and J. F. Banfield. 2020. “Layer size polydispersity in hydrated montmorillonite creates multiscale porosity networks.” Appl. Clay Sci. 190 (Jun): 105548. https://doi.org/10.1016/j.clay.2020.105548.
Xiong, W., J. Wang, and M. Wu. 2024. “Effects of morphological gene decay and mutation on the micro–macro mechanical behaviours of granular soils.” Géotechnique 74 (11): 1076–1094. https://doi.org/10.1680/jgeot.21.00180.
Yao, M. 2002. “Three-dimensional discrete element method analysis of cohesive soil.” Ph.D. thesis, Dept. of Civil Engineering, John Hopkins Univ.
Yin, Z., P. Wang, and S. Dai. 2023. “Microstructures and micromechanics of geomaterials.” J. Zhejiang Univ.-Sci. A 24 (4): 299–302. https://doi.org/10.1631/jzus.A2300MMG.
Zhao, B., J. Wang, M. R. Coop, G. Viggiani, and M. Jiang. 2015. “An investigation of single sand particle fracture using X-ray micro-tomography.” Géotechnique 65 (8): 625–641. https://doi.org/10.1680/geot.4.P.157.
Zhao, J., and N. Guo. 2013. “Unique critical state characteristics in granular media considering fabric anisotropy.” Géotechnique 63 (8): 695–704. https://doi.org/10.1680/geot.12.P.040.
Zhu, H., A. J. Whittle, R. J. M. Pellenq, and K. Ioannidou. 2019. “Mesoscale simulation of aggregation of imogolite nanotubes from potential of mean force interactions.” Mol. Phys. 117 (22): 3445–3455. https://doi.org/10.1080/00268976.2019.1660817.
Zhu, L., W. Shen, J. Shao, and M. He. 2021. “Insight of molecular simulation to better assess deformation and failure of clay-rich rocks in compression and extension.” Int. J. Rock Mech. Min. Sci. 138 (Feb): 104589. https://doi.org/10.1016/j.ijrmms.2020.104589.

Information & Authors

Information

Published In

Go to Journal of Geotechnical and Geoenvironmental Engineering
Journal of Geotechnical and Geoenvironmental Engineering
Volume 150Issue 12December 2024

History

Received: Sep 21, 2023
Accepted: Jul 2, 2024
Published online: Oct 3, 2024
Published in print: Dec 1, 2024
Discussion open until: Mar 3, 2025

Permissions

Request permissions for this article.

Authors

Affiliations

Sheng-Jie Wei [email protected]
Ph.D. Candidate, Ministry of Education Key Laboratory of Soft Soils and Geoenvironmental Engineering, Dept. of Civil Engineering, Zhejiang Univ., Hangzhou 310058, China. Email: [email protected]
Professor, School of Engineering, Cardiff Univ., Cardiff CF24 3AA, UK. ORCID: https://orcid.org/0000-0002-4005-5319. Email: [email protected]
Yun-Min Chen, Ph.D. [email protected]
Professor, Ministry of Education Key Laboratory of Soft Soils and Geoenvironmental Engineering, Dept. of Civil Engineering, Zhejiang Univ., Hangzhou 310058, China. Email: [email protected]
Yu-Chao Li, Ph.D. [email protected]
Professor, Ministry of Education Key Laboratory of Soft Soils and Geoenvironmental Engineering, Dept. of Civil Engineering, Zhejiang Univ., Hangzhou 310058, China (corresponding author). Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share