Dynamic analysis of unsaturated porous media under moving loads by the time domain FEM using moving coordinates

Transport systems such as highways and railways are constructed on earthworks that experience fluctuating levels of saturation. This can range from dry to fully saturated, however most commonly they are in a state of partial saturation. When numerically modelling such problems, it is important to capture the response of the solid, liquid and gas phases in the material. However, multi-physics solutions are computationally demanding and as a solution this paper presents a finite element approach for the dynamic analysis of unsaturated porous media in a moving coordinate system. The first novelty of the work is the development of a principle of relative motion for a three-phase medium, where the moving load is at rest while the unsaturated porous medium moves relative to the load. This makes it particularly efficient for moving load problems such as transport. The second novelty is a parametric investigation of the three-phase response of a partially saturated medium subject to a moving load. The paper starts by presenting the time domain model in terms of its constitutive relationships and equations for mass and momentum conservation. Next the model is validated using three case studies: the consolidation of a saturated soil column, the dynamics of an unsaturated soil column and finally the response of a saturated foundation to a moving load. It is then used to study a moving 2D plane strain load problem and its performance is compared to that of a standard FEM solution which does not employ a moving coordinate system. Similar accuracy is obtained while computational efficiency is improved by a factor of ten. Finally, the model is used to investigate the effect of degree of saturation and moving load speed on the response of an unsaturated porous medium. It is found that both variables have a significant impact on the dynamic response.