Master Curves for Poroelastic Spherical Indentation

Theoretical and numerical analyses are conducted to rigorously construct master curves that can be used for interpretation of spherical indentation test for poroelasticity characterization. Poroelastic contact between a rigid sphere and a fully saturated porous medium consisting of slightly compressible solid and fluid phases is considered in this work. Both displacement-controlled load relaxation test and force-controlled creep test with a surface drainage condition assumed to be fully permeable, fully impermeably or impermeable over the contact area but permeable everywhere else are examined.

 

We may view such contact problems as the poroelastic extension of the Hertzian contact. In principle, mechanical properties could be determined from the undrained and drained limits while the hydraulic diffusivity is reflected in the transient response. Theoretical solutions are first derived within the framework of Biot's theory using the McNamee-Gibson displacement function method. We show that for this class of poroelastic contact problems, relaxation of the normalized indentation force or displacement is affected by material properties through a single derived material constant only. Finite element analysis is then performed in order to examine the differences between the theoretical solutions, obtained by imposing the normal displacement or force over the contact area, and the numerical results where frictionless contact between a rigid sphere and the poroelastic medium is explicitly modeled. Master curves based on the theoretical solutions with the validity supported by the numerical analysis are proposed. Our analyses indicate that between the two testing approaches, the normalized indentation response from the displacement-controlled method appears to be less sensitive to uncertainties in material properties, suggesting that the displacement-controlled method is more reliable for determining hydraulic diffusivity from a theoretical point of view. Application of these master curves for the ramp-hold loading scenario is also discussed.