Event Detail

Event Type: 
M.Sc. Presentation
Friday, February 26, 2021 - 15:00 to 16:00
Zoom - If you are interested in attending this presentation, please send an email to Nikki Sullivan - nikki.sullivan@oregonstate.edu - to request Zoom log in details.

The necessitation for modeling various mechanical processes in porous media, such as consolidation and compaction, arises in several applied sciences. Within the context of sedimentary basins, we develop a model for consolidation with a permanent effect, a phenomena commonly observed in basin floors. In conjunction with the fundamental stress-porosity equation (4) derived in Holland and Showalter [12], we utilize a multi-valued constraint relation defined by (8) to obtain a non-trivial model depicting the stress-porosity relationship of porous media during cyclical processes of loading/unloading. Irreversible changes to the porous structure of the medium relate to the inclusion of a permanent damage component, which leads to a lagging response, (or hysteresis), between the porosity and effective stress. The full rheology (10) consists of elastic and viscoelastic components in addition to the previously mentioned damage component. However, the numerical simulations present in Section 3 focus on the viscoelastic and damaging behaviors exhibited by the classic Kelvin Voigt equation (10b) and our damage model (10c) respectively. Two numerical methods are implemented, where the first employs a well-known Runga-Kutta based solver ODE45, and the second, following Peszynska and Showalter [18], approximates the differential equations by an implicit backward difference scheme, where the resolvent operator is then recursively applied. We conclude the approach using the resolvent operator is stable and significantly more effective in comparison to ODE45.