Time-step constraints in coupled hydro-mechanical finite element analysis of unsaturated soils

In the finite element (FE) modelling of transient coupled problems for soils, the associated equations need to be integrated numerically over a time interval during the solution process. A minimum time-step size has been observed to exist, below which spatial oscillations in the obtained solutions can occur. These oscillations might lead to an accumulation of the resultant errors, eventually leading to invalid final predictions. This paper presents an analytical approach for deriving the time-step constraints for FE modelling of the transient behaviour of unsaturated soils with a fully coupled hydro-mechanical (HM) formulation. The effects of both element type and nonlinear soil properties are accounted for in the derivation. The proposed time-step constraints were subsequently verified through a series of coupled HM FE analyses of unsaturated soils, showing an excellent agreement. The present work shows that, when dealing with unsaturated soils, the minimum time-step size depends on the suction range investigated. This dependency derives from the nonlinear variation of water content and permeability with suction, as demonstrated through a set of comparative studies with three different types of unsaturated clays.