Poromechanics Solutions to Plane Strain and Axisymmetric Mandel-Type Problems in Dual-Porosity and Dual-Permeability Medium

摘要

The two-dimensional Mandel-type problem geometry is well-known to bio-ngeomechanicians for testing rocks, cartilages, and bones with solutions in Cartesianncoordinates for rectangular specimens or polar coordinates for cylindrical and disknsamples. To date, all existing solutions are only applicable to single-porosity and single-npermeability models, which could fall short when the porous material exhibits multi-nporosity and/or multipermeability characteristics, such as secondary porosity or fracture.nThis paper extends the plane strain and axisymmetric Mandel-type solutions fromnsingle-to dual-porosity and dual-permeability poromechanics. The solutions are pre-nsented in explicit analytical forms and account for arbitrary time-dependent externalnloading conditions, e.g., cyclic and ramping. The derived analytical solutions and resultsnexhibit general behaviors characterized by two time scales. Stresses, pore pressures, andndisplacements are plotted for various time scale ratios to illustrate the interplaying ef-nfects of permeability and stiffness contrast of both porous regions, in addition to theninterporosity exchange, on the overall responses of the system. Also, examples with re-nalistic loading conditions for laboratory testing or field simulation such as cyclic andnramping are provided to demonstrate the engineering applications of the presented dual-nporoelastic formulation and solutions. u0001DOI: 10.1115/1.3172146