Modeling of the three-dimensional subsidence diffusion–convection problem above a trapdoor


  • In memoriam of Professor Ioannis Vardoulakis

Correspondence to: E. Vairaktaris, School of Applied Mathematical and Physical Sciences, Section of Mechanics, NTU of Athens, Athens, Greece.



In a series of previous works, the plane strain and the axisymmetric cases of the so-called active trapdoor problem have been modeled by virtue of Litwiniszyn's theory of deep subsidence. However, in reality, there exist trapdoor base geometries—in plan view—which can be very well approximated by an elliptical boundary. Following the elliptical shape of the trapdoor, the contour lines of subsidence also appear to be similar ellipses. In this work, an elliptic model of deep subsidence is presented, the mentioned hypothesis of the self-similar subsidence contour lines is validated, and finally a simplified model is presented. For completeness of the present three-dimensional model analysis, a rectangular model is also considered. Results are finally presented and compared with those of plane strain and axisymmetric problems. Some suggestions that have been proposed in previous similar works are also evaluated and compared with the results of the present study. Finally, some estimates are proposed for different trapdoor base geometries. Copyright © 2011 John Wiley & Sons, Ltd.