Which software has the feature to model soil settlement due water drawdown?
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Abaqus with user subroutine: for example use C3D8T element: With this Temperature element water flow can be modeled
COMSOL. This tutorial could be of great help :
https://www.comsol.fr/model/biot-poroelasticity-483
This can be done by most of the software here. For Plaxis, see this tutorial: https://www.plaxis.com/support/tutorials/plaxis-3d-tutorial-rapid-drawdown-analysis/