Fully coupled global equations for hydro-mechanical analysis of unsaturated soils.

*(English)*Zbl 07360496Summary: Fully coupled global equations are proposed for enhancing the performance of Finite Element analysis of unsaturated soils. The governing equation describing mechanical equilibrium is formulated in terms of net stress, and in the mass conservation equation the contribution of this net stress in determining the change of degree of saturation is also included. The novelty of this paper is the development of new global finite element equations that can be used to find an approximate solution to these governing equations. The new equations have a mechanical term appearing in the flow matrix that is additional to the usual hydraulic term. This is in contrast to previous studies in which the coupling matrices ignore this effect. A performance study has been conducted for undrained footing problems, which shows that the additional mechanical term appearing in the flow matrix has a large influence on the accuracy of the numerical results.

##### MSC:

74-XX | Mechanics of deformable solids |

##### Software:

UDAM
PDF
BibTeX
XML
Cite

\textit{Y. Zhang} et al., Comput. Mech. 67, No. 1, 107--125 (2021; Zbl 07360496)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Alonso, EE; Gens, A.; Josa, A., Constitutive model for partially saturated soils, Géotechnique, 40, 405-430 (1990) |

[2] | Ehlers, W.; Ehlers, W.; Bluhm, J., Foundations of multiphasic and porous materials, Porous Media (2002), Berlin: Springer, Berlin · Zbl 1062.76050 |

[3] | Ehlers, W.; Graf, T.; Ammann, M., Deformation and localization analysis of partially saturated soil, Comput Methods Appl Mech Eng, 193, 27-29, 2885-2910 (2004) · Zbl 1067.74543 |

[4] | Gatmiri, B.; Delage, P.; Cerrolaza, M., Udam: a powerful finite element software for the analysis of unsaturated porous media, Adv Eng Softw, 29, 29-43 (1998) |

[5] | Guo L (2017) Field monitoring and numerical analysis of the influence of trees on soil moisture and ground movement in an urban environment. Doctor of Philosophy, Ph.D., RMIT University |

[6] | Hillel D (1971) Soil and water: physical principles and processes. Academic Press |

[7] | Hu, R.; Chen, Y-F; Liu, H-H; Zhou, C-B, A coupled two-phase fluid flow and elastoplastic deformation model for unsaturated soils: theory, implementation, and application, Int J Numer Anal Methods Geomech, 40, 1023-1058 (2015) |

[8] | Hu, R.; Hong, J-M; Chen, Y-F; Zhou, C-B, Hydraulic hysteresis effects on the coupled flow-deformation processes in unsaturated soils: numerical formulation and slope stability analysis, Appl Math Model, 54, 221-245 (2018) · Zbl 07166588 |

[9] | Khalili, N.; Habte, M.; Zargarbashi, S., A fully coupled flow deformation model for cyclic analysis of unsaturated soils including hydraulic and mechanical hystereses, Comput Geotech, 35, 872-889 (2008) |

[10] | Kohgo, Y.; Nakano, M.; Miyazaki, T., Theoretical aspects of constitutive modelling for unsaturated soils, Soils Found, 33, 49-63 (1993) |

[11] | Li, X.; Zienkiewicz, O., Multiphase flow in deforming porous media and finite element solutions, Comput Struct, 45, 211-227 (1992) · Zbl 0769.76031 |

[12] | Liakopoulos, AC, Theoretical solution of the unsteady unsaturated flow problems in soils, Int Assoc Sci Hydrol Bull, 10, 5-39 (1965) |

[13] | Liu, X.; Zhou, A.; Shen, SL; Li, J.; Sheng, D., A micro-mechanical model for unsaturated soils based on DEM, Comput Methods Appl Mech Eng, 368, 113183 (2020) |

[14] | Loret, B.; Khalili, N., An effective stress elastic-plastic model for unsaturated porous media, Mech Mater, 34, 97-116 (2002) |

[15] | Ma, T.; Wei, C.; Chen, P.; Wei, H., Implicit scheme for integrating constitutive model of unsaturated soils with coupling hydraulic and mechanical behavior, Appl Math Mech, 35, 1129-1154 (2014) · Zbl 1298.74035 |

[16] | Mun, W.; McCartney, JS, Constitutive model for the undrained compression of unsaturated clay, J Geotech Geoenviron Eng, 143, 4, 04016117 (2017) |

[17] | Pereira, J-M; Wong, H.; Dubujet, P.; Dangla, P., Adaptation of existing behaviour models to unsaturated states: application to CJS model, Int J Numer Anal Methods Geomech, 29, 1127-1155 (2005) · Zbl 1140.74505 |

[18] | Rahardjo, H.; Fredlund, DG, Experimental verification of the theory of consolidation for unsaturated soils, Can Geotech J, 32, 749-766 (1995) |

[19] | Romero, E.; Jommi, C., An insight into the role of hydraulic history on the volume changes of anisotropic clayey soils, Water Resources Res, 44, W12412 (2008) |

[20] | Roscoe KH, Burland J (1968) On the generalized stress-strain behaviour of wet clay. In: Proceedings of a conference on engineering plasticity, Cambridge, UK, March 1968, pp 535-609 · Zbl 0233.73047 |

[21] | Santagiuliana, R.; Schrefler, BA, Enhancing the Bolzon-Schrefler-Zienkiewicz constitutive model for partially saturated soil, Transp Porous Media, 65, 1-30 (2006) |

[22] | Sheng, D.; Zhou, AN, Coupling hydraulic with mechanical models for unsaturated soils, Can Geotech J, 48, 5, 826-840 (2011) |

[23] | Sheng, D.; Fredlund, DG; Gens, A., A new modelling approach for unsaturated soils using independent stress variables, Can Geotech J, 45, 511-534 (2008) |

[24] | Sheng, D.; Sloan, SW; Gens, A., A constitutive model for unsaturated soils: thermomechanical and computational aspects, Comput Mech, 33, 453-465 (2004) · Zbl 1115.74347 |

[25] | Sheng, D.; Sloan, SW; Gens, A.; Smith, DW, Finite element formulation and algorithms for unsaturated soils. Part I: theory, Int J Numer Anal Methods Geomech, 27, 745-765 (2003) · Zbl 1085.74515 |

[26] | Sheng, D.; Sloan, SW; Yu, H., Aspects of finite element implementation of critical state models, Comput Mech, 26, 185-196 (2000) · Zbl 0989.74072 |

[27] | Sun, DA; Sheng, D.; Sloan, SW, Elastoplastic modelling of hydraulic and stress-strain behaviour of unsaturated soils, Mech Mater, 39, 212-221 (2007) |

[28] | Tamagnini, R., An extended Cam-clay model for unsaturated soils with hydraulic hysteresis, Géotechnique, 54, 223-228 (2004) |

[29] | Tsiampousi, A.; Smith, PGC; Potts, DM, Coupled consolidation in unsaturated soils: an alternative approach to deriving the governing equations, Comput Geotech, 84, 238-255 (2017) |

[30] | Van Genuchten, MT, A closed-form equation for predicting the hydraulic conductivity of unsaturated soils1, Soil Sci Soc Am J, 44, 892-898 (1980) |

[31] | Wheeler, S.; Sharma, R.; Buisson, M., Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils, Géotechnique, 53, 41-54 (2003) |

[32] | Wheeler, S.; Sivakumar, V., An elasto-plastic critical state framework for unsaturated soil, Géotechnique, 45, 35-53 (1995) |

[33] | Wu, S.; Zhou, A.; Li, J.; Kodikara, J.; Cheng, WC, Hydromechanical behaviour of overconsolidated unsaturated soil in undrained conditions, Can Geotech J, 56, 1609-1621 (2019) |

[34] | Zhang, F.; Ikariya, T., A new model for unsaturated soil using skeleton stress and degree of saturation as state variables, Soils Found, 51, 67-81 (2011) |

[35] | Zhang, Y.; Zhou, A.; Nazem, M.; Carter, JP, Finite element implementation of a fully coupled hydro-mechanical model and unsaturated soil analysis under hydraulic and mechanical loads, Comput Geotech, 110, 222-241 (2019) |

[36] | Zhou, A.; Sheng, D., An advanced hydro-mechanical constitutive model for unsaturated soils with different initial densities, Comput Geotech, 63, 46-66 (2015) |

[37] | Zhou, A.; Sheng, D.; Sloan, SW; Gens, A., Interpretation of unsaturated soil behaviour in the stress-saturation space: II: constitutive relationships and validations, Comput Geotech, 43, 111-123 (2012) |

[38] | Zhou, A.; Sheng, D.; Sloan, SW; Gens, A., Interpretation of unsaturated soil behaviour in the stress-saturation space, I: volume change and water retention behaviour, Comput Geotech, 43, 178-187 (2012) |

[39] | Zhou, A.; Wu, S.; Li, J.; Sheng, D., Including degree of capillary saturation into constitutive modelling of unsaturated soils, Comput Geotech, 95, 82-98 (2018) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.