Uncertainty quantification of axisymmetric spherical cavities with lining in coupled saturated thermo-poro-elastic media via adaptive second-order central high resolution schemes

摘要

The main aim of our study is to investigate uncertainty quantification of an axisymmetric cavity with lining subjected to the unit step function of compression traction on the inner boundary of the lining. The uncertainties are due to the thickness, density and porosity of the lining. Discontinuous propagating waves develop both in the lining and the surrounding medium. To handle such discontinuous solutions, the second-order central high resolution schemes working on irregular (adaptive) cells are utilised. These schemes, however, are sensitive for cell-irregularities. To remedy this drawback, in general, flux-limiter definitions and variation of cell densities should be controlled. Regarding the uncertainty quantification, the Box-Behnken experimental design and corresponding response surface are utilised. For both the lining and the surrounding medium the fully coupled saturated thermo-poro-elastic theory is used. For such problems, however, the performance of the Box-Behnken experimental design should be investigated carefully (measured here by the determination factor). Since, the saturated thermo-poroelastic problems include discontinuous responses which can change solution patterns considerably even by marginal altering of soil/lining properties. At the end, to quantify uncertainties, the response surfaces are provided for the pressure component in the contact interface, between the soil and the lining.