New Unsaturated Dynamic Porosity Hydromechanical Coupled Model and Experimental Validation
Publication: International Journal of Geomechanics
Volume 22, Issue 10
Abstract
Constitutive coupled modeling has developed rapidly in recent decades, with numerous new models published. However, few models consider dynamic porosity, and experimental validation of such a model remains a challenge due to multiple variables. In this study, a new constitutive model for unsaturated soil with dynamic porosity was developed based on mixture theory and nonequilibrium thermodynamics, then the model was validated using test data from two experimental studies that yielded good results (relative average error AVRE = 0.8631–1.3046, R2 = 0.9028–0.9981). The sensitivity of the model to the four primary parameters was analyzed to investigate the influence of model properties on the hydraulic and mechanical behavior. Results show that the calculation of volumetric strain is most sensitive to Young’s modulus (E), while the calculation of specific water volume is most sensitive to permeability (k). In addition, the sensitivity of the parameters changes with their value. Modeled results show that the porosity change significantly affects both hydraulic and mechanical behavior, even when soil undergoes relatively low deformation. Relative calculation error decreases notably after porosity change is considered (44.9% and 35.2% improvement in two different calculations). This study also finds that dynamic porosity affects the deformation energy of solids.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was supported by the National Key R&D Program of China (No. 2019YFC1805503), the National Key R&D Program of China (No. 2018YFC1800905) and the Key Science and Technology Projects of the Inner Mongolia Autonomous Region (2019ZD001).
References
Abdollahipour, A., H. Soltanian, Y. Pourmazaheri, E. Kazemzadeh, and M. Fatehi-Marji. 2019. “Sensitivity analysis of geomechanical parameters affecting a wellbore stability.” J. Cent. South Univ. 26 (3): 768–778. https://doi.org/10.1007/s11771-019-4046-2.
Alonso, E. E., and J. Alcoverro. 1999a. Catsius clay project. Calculation and testing of behaviour of unsaturated clay as barrier in radioactive waste repositories. Stage 2: Validation exercises at laboratory scale. Madrid, Spain: Empresa Nacional de Residuos Radiactivos.
Alonso, E. E., and J. Alcoverro. 1999b. Catsius clay project: Calculation and testing of behaviour of unsaturated clay as barrier in radioactive waste repositories: Stage 3: Validation exercises at a large in situ scale. Madrid, Spain: Empresa Nacional de Residuos Radiactivos.
Biglari, M., A. d’Onofrio, C. Mancuso, M. K. Jafari, A. Shafiee, and I. Ashayeri. 2012. “Small-strain stiffness of Zenoz kaolin in unsaturated conditions.” Can. Geotech. J. 49 (3): 311–322. https://doi.org/10.1139/t11-105.
Biot, M. A. 1941. “General theory of three-dimensional consolidation.” J. Appl. Phys. 12 (2): 155–164. https://doi.org/10.1063/1.1712886.
Biot, M. A. 1962. “Mechanics of deformation and acoustic propagation in porous media.” J. Appl. Phys. 33 (4): 1482–1498. https://doi.org/10.1063/1.1728759.
Charlier, R., F. Collin, B. Pardoen, J. Talandier, J.-P. Radu, and P. Gerard. 2013. “An unsaturated hydro-mechanical modelling of two in-situ experiments in Callovo-Oxfordian argillite.” Eng. Geol. 165: 46–63. https://doi.org/10.1016/j.enggeo.2013.05.021.
Chen, X., and M. A. Hicks. 2011. “A constitutive model based on modified mixture theory for unsaturated rocks.” Comput. Geotech. 38 (8): 925–933. https://doi.org/10.1016/j.compgeo.2011.04.008.
Chen, X., and M. A. Hicks. 2013. “Unsaturated hydro-mechanical-chemo coupled constitutive model with consideration of osmotic flow.” Comput. Geotech. 54: 94–103. https://doi.org/10.1016/j.compgeo.2013.06.001.
Chen, X., W. Pao, and X. Li. 2013. “Coupled thermo-hydro-mechanical model with consideration of thermal-osmosis based on modified mixture theory.” Int. J. Eng. Sci. 64: 1–13. https://doi.org/10.1016/j.ijengsci.2012.12.005.
Chen, X., W. Pao, S. Thornton, and J. Small. 2016a. “Unsaturated hydro-mechanical-chemical constitutive coupled model based on mixture coupling theory: Hydration swelling and chemical osmosis.” Int. J. Eng. Sci. 104: 97–109. https://doi.org/10.1016/j.ijengsci.2016.04.010.
Chen, X., S. F. Thornton, and W. Pao. 2018. “Mathematical model of coupled dual chemical osmosis based on mixture-coupling theory.” Int. J. Eng. Sci. 129: 145–155. https://doi.org/10.1016/j.ijengsci.2018.04.010.
Chen, Y.-F., J.-M. Hong, H.-K. Zheng, Y. Li, R. Hu, and C.-B. Zhou. 2016b. “Evaluation of groundwater leakage into a drainage tunnel in Jinping-I arch dam foundation in Southwestern China: A case study.” Rock Mech. Rock Eng. 49 (3): 961–979. https://doi.org/10.1007/s00603-015-0786-y.
Cheviron, B., and Y. Coquet. 2009. “Sensitivity analysis of transient-MIM HYDRUS-1D: Case study related to pesticide fate in soils.” Vadose Zone J. 8 (4): 1064–1079. https://doi.org/10.2136/vzj2009.0023.
Edip, K., V. Sesov, C. Butenweg, and J. Bojadjieva. 2018. “Development of coupled numerical model for simulation of multiphase soil.” Comput. Geotech. 96: 118–131. https://doi.org/10.1016/j.compgeo.2017.08.016.
Félix, B., P. Lebon, R. Miguez, and F. Plas. 1996. “A review of the ANDRA's research programmes on the thermo-hydromechanical behavior of clay in connection with the radioactive waste disposal project in deep geological formations.” Eng. Geol. 41 (1–4): 35–50. https://doi.org/10.1016/0013-7952(95)00025-9.
Heidug, W. K., and S. W. Wong. 1996. “Hydration swelling of water-absorbing rocks: A constitutive model.” Int. J. Numer. Anal. Methods Geomech. 20 (6): 403–430. https://doi.org/10.1002/(SICI)1096-9853(199606)20:6%3C403::AID-NAG832%3E3.0.CO2-7.
Jin, W.-z., Z.-j. Luo, and X.-h. Wu. 2016. “Sensitivity analysis of related parameters in simulation of land subsidence and ground fissures caused by groundwater exploitation.” Bull. Eng. Geol. Environ. 75 (3): 1143–1156. https://doi.org/10.1007/s10064-016-0897-z.
Lewis, E. R., K. Morgan, B. Schrejler, E. Hinton, P. Bettess, O. Zienkiewicz, E. C. Desai, R. Gallagher, R. Wood, and J. Alex. 1987. The finite element method in the deformation and consolidation of porous media. Hoboken, NJ: Wiley.
Lewis, R. and B. Schrefler 1982. “Finite element simulation of the subsidence of a gas reservoir undergoing a waterdrive.” In Vol. 4 of Finite element in fluids, 179–199. Hoboken, NJ: Wiley.
Li, W., and Q. Yang. 2018. “Hydromechanical constitutive model for unsaturated soils with different overconsolidation ratios.” Int. J. Geomech. 18 (2): 04017142. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001046.
Li, X., R. Li, and B. A. Schrefler. 2006. “A coupled chemo-thermo-hygro-mechanical model of concrete at high temperature and failure analysis.” Int. J. Numer. Anal. Methods Geomech. 30 (7): 635–681. https://doi.org/10.1002/nag.495.
Lisjak, A., P. Kaifosh, L. He, B. S. A. Tatone, O. K. Mahabadi, and G. Grasselli. 2017. “A 2D, fully-coupled, hydro-mechanical, FDEM formulation for modelling fracturing processes in discontinuous, porous rock masses.” Comput. Geotech. 81: 1–18. https://doi.org/10.1016/j.compgeo.2016.07.009.
Ma, Y., X. H. Chen, L. J. Hosking, H. S. Yu, H. R. Thomas, and S. Norris. 2021. “The influence of coupled physical swelling and chemical reactions on deformable geomaterials.” Int. J. Numer. Anal. Methods Geomech. 45 (1): 64–82. https://doi.org/10.1002/nag.3134.
Masoudian, M. S., M. A. Hashemi Afrapoli, A. Tasalloti, and A. M. Marshall. 2019. “A general framework for coupled hydro-mechanical modelling of rainfall-induced instability in unsaturated slopes with multivariate random fields.” Comput. Geotech. 115: 103162. https://doi.org/10.1016/j.compgeo.2019.103162.
Meroi, E. A., B. A. Schrefler, and O. C. Zienkiewicz. 1995. “Large strain static and dynamic semisaturated soil behaviour.” Int. J. Numer. Anal. Methods Geomech. 19 (2): 81–106. https://doi.org/10.1002/nag.1610190203.
Raghavan, R., and L. Y. Chin. 2004. “Productivity changes in reservoirs with stress-dependent permeability.” SPE Reservoir Eval. Eng. 7 (4): 308–315. https://doi.org/10.2118/88870-pa.
Sanavia, L., B. A. Schrefler, and P. Steinmann. 2002. “A formulation for an unsaturated porous medium undergoing large inelastic strains.” Comput. Mech. 28 (2): 137–151. https://doi.org/10.1007/s00466-001-0277-8.
Sawangsuriya, A., T. B. Edil, and C. H. Benson. 2009. “Effect of suction on resilient modulus of compacted fine-grained subgrade soils.” Transp. Res. Rec. 2101: 82–87. https://doi.org/10.3141/2101-10.
Schwartz, M. O. 2018. “Modelling groundwater contamination above a potential nuclear waste repository in the Columbia River Basalt, USA.” Environ. Earth Sci. 77 (12): 1–12. https://doi.org/10.1007/s12665-018-7615-z.
Seetharam, S. C., H. R. Thomas, and P. J. Cleall. 2007. “Coupled thermo/hydro/chemical/mechanical model for unsaturated soils—Numerical algorithm.” Int. J. Numer. Methods Eng. 70 (12): 1480–1511. https://doi.org/10.1002/nme.1934.
Selvadurai, P., P. A. Selvadurai, and M. Nejati. 2019. “A multi-phasic approach for estimating the Biot coefficient for Grimsel granite.” Solid Earth 10 (6): 2001–2014. https://doi.org/10.5194/se-10-2001-2019.
Stormont, J. C., and J. J. K. Daemen. 1992. “Laboratory study of gas permeability changes in rock salt during deformation.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 29 (4): 325–342. https://doi.org/10.1016/0148-9062(92)90510-7.
Terzaghi, K. 1943. “Theory of consolidation.” In Theoretical soil mechanics, 265–296. Hoboken, NJ: Wiley.
Truesdell, C. 1962. “Mechanical basis of diffusion.” J. Chem. Phys. 37 (10): 2336–2344. https://doi.org/10.1063/1.1733007.
van Genuchten, M. T. 1980. “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J. 44 (5): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Vassallo, R., C. Mancuso, and F. Vinale. 2007. “Effects of net stress and suction history on the small strain stiffness of a compacted clayey silt.” Can. Geotech. J. 44 (4): 447–462. https://doi.org/10.1139/t06-129.
Zhang, R., Z. Liu, J. Zheng, and J. Zhang. 2020. “Experimental evaluation of lateral swelling pressure of expansive soil fill behind a retaining wall.” J. Mater. Civ. Eng. 32 (2): 04019360. https://doi.org/10.1061/(asce)mt.1943-5533.0003032.
Information & Authors
Information
Published In
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 13, 2022
Accepted: May 14, 2022
Published online: Jul 25, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 25, 2022
ASCE Technical Topics:
- Coupling
- Dynamic models
- Engineering fundamentals
- Errors (statistics)
- Geomechanics
- Geotechnical engineering
- Hydraulic models
- Hydrologic models
- Material mechanics
- Material properties
- Materials engineering
- Mathematics
- Methodology (by type)
- Models (by type)
- Porosity
- Research methods (by type)
- Soil dynamics
- Soil mechanics
- Statistics
- Structural engineering
- Structural members
- Structural systems
- Validation
Authors
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.
Cited by
- Kai Wang, Jiahui Zhou, Yue Ma, Aizhong Ding, Xiaohui Chen, Constitutive and numerical modeling for the coupled thermal-hydro-mechanical processes in dual-porosity geothermal reservoir, Applied Thermal Engineering, 10.1016/j.applthermaleng.2023.120027, 223, (120027), (2023).