To quantify the effects of differential settlement on leakage through a geomembrane (GMB) hole in waste (landfill/mine tailings) covers, field experiments were conducted at Queen's University Experimental Liner Test Site on two sections, each with a 4H : 1V slope. Over 13 months, measurements showed that a 3 m × 2 m × 0.12–0.17 m depression in Section B led to a 51-fold increase in leakage when compared to Section A, which had no such depression (493 l vs 11.1 l). Notably, in Section B, 284 mm of precipitation between November and February resulted in 281 l of leakage, whereas 537 mm of precipitation between June and September led to a mere 142 l of leakage. A 3D numerical investigation provides encouraging agreement with the experimental measurements and confirms a counterintuitive 43% increase in leakage with a decrease in the temperature of cover sand from 21.9°C to 1°C, due to the influence of temperature-dependent viscosity on the hydraulic conductivity of the cover soil. This paper offers insights for optimizing waste cover design and inspection procedures to mitigate the challenges of contaminant control.