14–17 May 2018
New Orleans
US/Central timezone

A Dynamic Symplectic Manifold Analysis for Wave Propagation in Porous Media

17 May 2018, 14:56
15m
New Orleans

New Orleans

Oral 20 Minutes GS 1: Fundamental theories of porous media Parallel 11-G

Speaker

Mr Karl Igor Martins Guerra (Pontifical Catholic University of Rio de Janeiro)

Description

This study aims to understand with more amplitude and clarity the behavior of a porous medium where a pressure wave travels, translated into relative displacements inside the material, using mathematical tools derived from topology and symplectic geometry. The paper starts with a given partial differential equation based on the continuity and conservation theorems to describe the travelling wave through the porous body. A solution for this equation is proposed after all boundary and initial conditions are fixed and it’s accepted that the solution lies in a manifold U of purely spatial dimensions and that is embedded in the n-dimensional Real manifold, with spatial and kinectic dimensions. It’s shown that the U manifold of lower dimensions than IRna, where it is embedded, inherits properties of the vector spaces existing inside the topology it lies on. Then, a second manifold (U*), embedded in another space called IRnb of stress dimensions, is proposed and there’s a non degenerative function that maps it into the U manifold. This relation is proved as a transformation in between two corresponding admissible solutions of the differential equation in distinct dimensions and properties, leading to a more visual and intuitive understanding of the whole dynamic process of a stress wave through a porous medium and also highlighting the dimensional invariance of Terzaghi’s theory for any coordinate system.

Acceptance of Terms and Conditions Click here to agree

Primary authors

Mr Karl Igor Martins Guerra (Pontifical Catholic University of Rio de Janeiro) Prof. Luciana Andrade Peixoto Silva (University of the State of Rio de Janeiro)

Presentation materials

There are no materials yet.