“…Understanding variably saturated flow (VSF) in fractured porous media has great significance to many environmental and geotechnical applications, such as groundwater recharge in karst aquifers, (Mudarra and Andreo, 2011;de Rooij et al, 2013de Rooij, 2019, epikarst (Chang et al 2019) and unconfined chalk aquifers (Ireson et al, 2009), geological disposal of nuclear waste such as at Yucca Mountain in the United States where the unsaturated zone is estimated as potential site for disposal of high-level nuclear waste (Hayden et al, 2012;Ye et al, 2007), contaminant transport and infiltration of landfill leachate (Brouyère, 2006;Ben Abdelghani et al, 2015), infiltration through unsaturated saprock in hillslopes with shallow fractured shale bedrock (Guo et al, 2019), unsaturated flow and contaminant transport in saprolite (Van der Hoven et al, 2003;Alazard et al, 2016), water flow in cracked soils and stability of soil slopes with cracks (Pouya et al, 2013;Wang at al., 2019;Yang and Liu, 2020), seepage through fissured dams (Jiang et al, 2014), tunnel excavation (Gokdemir et al, 2019) and protection of structure foundations in contact with water (Zhao et al 2019).…”