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Two-scale coupled flow and geomechanics: continuum modeling and stabilized finite elements

Natural and engineered geomaterials such as fractured rocks and structured soils often exhibit a bimodal pore size distribution that leads to intricate hydromechanical coupling at two scales.
Fluids in the two pore scales impact the mechanical behavior of the solid matrix concurrently but with highly contrasting rates.
Structural degradation of the solid matrix induces markedly heterogeneous porosity reduction in the two scales.
In this work, we present a theoretical and computational framework that couples flow and geomechanics at the two scales.
Using mixture theory we formulate conservation laws incorporating thermodynamically consistent
effective stress and constitutive relations.
For efficient computation we develop stabilized mixed finite elements that allow equal-order linear interpolation of the displacement and two pore pressures throughout the entire range of drainage condition.
A critical state model is enhanced to capture two-scale porosity reduction associated with structural degradation. We present a numerical example that demonstrates the impact of two-scale coupling on the strain localization.

Author(s):

Jinhyun Choo    
Stanford University
United States

Ronaldo Borja    
Stanford University
United States