Universal Percolation Threshold Mixing Law in Fractured Porous Media: Unifying Shape and Size Polydispersity and Dimensionality Coupling

Percolation in fractured porous media is governed by the coupled connectivity of pores and fractures, yet simultaneously addressing mixed dimensionality and broad shape variability remains elusive. Here, we derive a mixing law for hybrid networks composed of overlapping 3D pores (superovoids) and 2D fractures (superovals) embedded in the same 3D domain. This law applies to constituent sets that permit polydispersity in size and shape within each constituent while maintaining equivalent size, namely R_{eqp}=R_{eqf} for monosized systems and R_{eqp,max}=R_{eqf,max} for polysized systems. We validate the prediction against our simulations and representative literature datasets across 2D, 3D, and mixed-dimensional settings. By revealing overlooked interdependencies within multidistribution couplings, it bridges theoretical frameworks with engineering applications, enabling morphology-targeted optimization for subsurface hydrology and nanocomposite design.