Fully coupled global equations for hydro-mechanical analysis of unsaturated soils
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ORIGINAL PAPER
Fully coupled global equations for hydro-mechanical analysis of unsaturated soils Yue Zhang1 · Annan Zhou2
· Majidreza Nazem2 · John Carter3
Received: 18 October 2019 / Accepted: 1 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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. Keywords Global equations · Finite element · Hydro-mechanical coupled analysis · Unsaturated soils
List of symbols a1
a2 ad , m d and m d aw , m w and m w b b Bu CTσv ξ
B
Fitting parameter that defines the variation of compression index with the degree of saturation Fitting parameter that defines the variation of Sr under constant suction Fitting parameters for the main drying curve Fitting parameters for the main wetting curve Fitting parameter for non-linear hysteresis Body force vector Strain–displacement matrix Coefficient of the volumetric strain due to the net stress change
Annan Zhou [email protected]
1
School of Transportation Science and Engineering, Beihang University, Beijing 100191, China
2
School of Engineering, Royal Melbourne Institute of Technology, Melbourne, VIC 3001, Australia
3
ARC Centre of Excellence for Geotechnical Science and Engineering, University of Newcastle, Callaghan, NSW 2308, Australia
De Dep f F h H H and S k Kep L and L M mT n Nu and Nw p pc q qw Q s shnew
Elastic stiffness matrix Elastoplastic stiffness matrix Yield function Force Depth Total depth Flow matrices Matrix of the permeability Global elastoplastic stiffness matrix Coupling matrices Stress ratio at the critical state Transformation vector and equals to {1, 1, 1, 0, 0, 0} Porosity Matrix of shape functions Effective mean stress Preconsolidation pressure Deviator stress Prescribed fluid flux on the boundary of the domain Quantities of flow Suction Suction increment obtained from using the new proposed equation
123
Computational Mechanics
shGES
S Se Sr t t U Uw and u w δuT V v Wep γw ε εv p εv θw κ λ ν ρw σ σ ∇¯
Suction increment obtained from using the governing equation given by Sheng et al. [25] Surface tractions Effective degree of saturation Degree of saturation Traction forces T
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