Analytical Solution for Contaminant Transport Through a Damaged Geomembrane into the Underlying Unsaturated Soil Layer

A one-dimensional analytical model was developed to simulate the transport of organic contaminants through a defective geomembrane into the underlying unsaturated soil layer. This model accounted for geomembrane defects and incorporated the unsaturated properties of the soil, providing a more accurate representation of contaminant migration mechanisms in unsaturated soil. By applying boundary transformation, the displacement theorem, the Laplace transform, and its inverse, an analytical solution describing the variation of contaminant concentration with time and depth was derived. Additionally, the unsaturated soil layer was reduced to a saturated soil layer, and typical case studies were conducted to calculate contaminant concentration distributions. The obtained results were compared with existing research data, demonstrating a high degree of consistency. A systematic analysis was then conducted to investigate the effects of three key factors (i.e., geomembrane wrinkle rate, the number of perforations, and the soil unsaturated index) on the temporal and spatial evolution of normalized contaminant concentration in the unsaturated soil layer. The results indicate that, at a given depth, the geomembrane wrinkle rate and the number of perforations are positively correlated with the contaminant migration rate, whereas the soil unsaturated index exhibits a negative correlation. Similarly, at a given time, the critical depth at which the normalized contaminant concentration becomes zero deepens with the increase of the geomembrane wrinkle rate and the number of perforations, but shallows with the increase of the soil unsaturated index. Moreover, the impact of geomembrane defects on contaminant migration is significantly greater than that of soil unsaturated properties. This study provides a theoretical reference for the optimization of informal landfills, the prediction of contaminant concentration evolution in natural unsaturated soil layers, and the related contamination prevention and control measures.