On the Role of Capillary Energy in Inducing Damage and Possibility of Fractures in Partially Saturated Porous Media

  • Ommi, Siddhartha Harsha (Sapienza Universit√† di Roma)
  • Sciarra, Giulio (Ecole Centrale Nantes)
  • Nardinochhi, Paola (Sapienza Universit√† di Roma)

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When a non-wetting fluid invades a pore network a priori saturated by a wetting fluid, both fluids being immiscible, capillary forces generate a tensile effect on the pore walls resulting in a tendency of bulk contraction. If the pore network is formed by a weakly cohesive solid phase, more so in cohesion-less granular media, fracture initiation is exceedingly driven by capillary forces (Shin and Santamarina, 2010; Jain and Juanes, 2009; Shin and Santamarina, 2011; Holtzman et al., 2012), rather than purely mechanistic tensile stresses generated by constraints that restrain the bulk contraction. To investigate this fracture driving mechanism, in Ommi et al. (2022) a variational modeling approach has been put forward within the framework of continuum-scale poromechanics. A scalar internal variable has been employed, inspired by the damage variable in gradient-damage models (Marigo et al., 2016), that modulates the macro-scale interfacial energy implicating it in the dissipation during fracture formation. In this framework possibility of periodic initiation of fractures is associated with the bifurcation and eventual localization of homogeneous damage solutions. In this work, this possibility is investigated by setting up a boundary value problem involving desiccation driven by a boundary flux that implies a homogeneous solution at early times. A bifurcation analysis reveals if this homogeneous solution bifurcates onto another solution branch at a finite time indicating fracture initiation, while the wave-number of bifurcation represents the fracture spacing.