“…When observed at the mesoscale, concrete materials are typical examples, since the main compositions include aggregates, cements and C-S-H phase, each with distinct permeability. The overall permeability of concretes is determined by this mesoscale structure, which responds for barrier performance, concrete durability (Hall, 1994, Hanžič, et al, 2010, Navarro, et al, 2006, etc. However, earlier work on overall flow properties of heterogeneous porous media (Durlofsky, 1991, Pettersen, 1987, Warren, et al, 1961 focuses on effective permeability instead of detailed imbibition processes, e.g., the evolution of liquid front, whilst recent work are mostly limited to layered configuration (Bal, et al, 2011, Debbabi, et al, 2017, Ern, et al, 2010, Guerrero-Martínez, et al, 2017, Helmig, et al, 2007, Patel, et al, 2017, Reyssat, et al, 2009, Schneider, et al, 2017.…”