New analytical models are introduced to describe the motion of a Herschel–Bulkley fluid slumping under gravity in a narrow fracture and in a porous medium. A useful self-similar solution can be derived for a fluid injection rate that scales as time $t$ ; an expansion technique is adopted for a generic injection rate that is power law in time. Experiments in a Hele-Shaw cell and in a narrow channel filled with glass ballotini confirm the theoretical model within the experimental uncertainty.

Environmentally sensitive areas along coastlines may be adversely affected by saltwater intrusion (SI), a condition which can be worsened by extensive groundwater extraction. Given the uncertainty of problem parameters, the risk of contamination of the vegetation capture zone needs to be cast in a probabilistic framework. In order to exemplify real situations existing along the Adriatic coast of Emilia-Romagna, a case study involving a pinewood strip and a well field drawing freshwater from an unconfined coastal aquifer was examined. On the basis of a widely adopted sharp interface formulation, key hydrogeological problem parameters were modeled as random variables, and a global sensitivity analysis was carried out to determine their influence on the position of the interface. This analysis utilized an efficient model reduction technique based on Polynomial Chaos Expansion. The risk that saltwater intrusion affects coastal vegetation was then evaluated via a two-step procedure by computing the probability that (i) the leading edge of the saltwater wedge reaches the sensitive area in the horizontal plane, and (ii) the freshwater/saltwater interface reaches the capture zone. The influence of the design parameters of the well field on the overall probability of contamination was investigated, revealing the primary role of the pumping discharge in the examined configuration.