Numerical modeling for geotechnics use formulations which take into consideration simplifying hypotheses for porous media physical behavior. However, these simplifications neglect effects which could contribute in model's accuracy. In this paper, a fully coupled hydro-mechanical formulation considering fluid and solids compressibility is presented. This formulation was tested for a two-dimensional consolidation case. A sensitivity analysis for the fluid compressibility parameter was performed, with comparison of the simulation results to Biot's analytical solution. Results show that the values of vertical displacements are lower to cases with compressible fluids than to those with incompressible fluids. Instantaneously after load application, fluid pressure increases to a maximum value and it dissipates as load is gradually transferred to solid matrix. For compressible fluids, however, there is a delay in fluid pressure dissipation, which makes effective stress lower than expected. Therewith, stress-strain relations are affected, with low soil strain rate values, justifying vertical displacement decrease.
When evaluating physical behavior of porous media, such as soils and rocks, one can observe that stress strain state is affected by fluid pressures and viceversa. Therewith, it is intuitive the understanding that both mechanical and hydraulic effects are interconnected. This proves the importance of coupled analyses, which describe more precisely how mechanical and hydraulic behavior are related.
Using numerical modeling for behavior prediction is largely employed in geotechnics, more specifically in geomechanics. Formulations are previewed to reproduce porous media behavior. However, the complexity of the phenomena evaluated may induce some simplification of the numerical models. This may interfere in model responses, with simulation results not correspondent to the observed behavior of the studied case.
The compressibility of the solids which form the solid matrix of a porous medium and the compressibility of the fluids within this medium are not taken into account in traditional models in geotechnics or related areas, such as reservoir geomechanics, in petroleum engineering. This type of consideration could enhance modeling, contributing to more accurate results in behavior prediction.