A Mathematical Model for Voigt Poro-Visco-Plastic Deformation

TL;DR

This paper develops a mathematical model for poro-visco-plastic deformation in sediments, capturing different regimes of pressure and permeability, validated through numerical simulations and analytical solutions.

Contribution

It introduces a Voigt-type rheological model for poro-visco-plastic deformation, linking experimental data with nonlinear hyperbolic equations and numerical validation.

Findings

Model captures slow and rapid deformation regimes

Analytical and numerical solutions show good agreement

Provides insights into pressure solution and compaction processes

Abstract

A mathematical model for poro-visco-plastic compaction and pressure solution in porous sediments has been formulated using the Voigt-type rheological constitutive relation as derived from experimental data. The governing equations reduce to a nonlinear hyperbolic heat conduction equation in the case of slow deformation where permeability is relatively high and the pore fluid pressure is nearly hydrostatic, while travelling wave exists in the opposite limit where over-pressuring occurs and the pore fluid pressure is almost quasi-lithostatic. Full numerical simulation using a finite element method agree well with the approximate analytical solutions.