Two-dimensional migration characteristics for contaminant considering time-dependent contaminant source and GM defect

Geomembranes (GMs) are often used as the first liner in landfills to block the upper leachate and prevent toxic substances from migrating to the underlying soil layer (SL). However, during the construction or service periods, defects are easily caused in GM by external forces, which can greatly reduce the barrier capacity of GM. In view of this, a two-dimensional migration model of contaminant transporting through the defected GM to the underlying SL was established with time-dependent pollution source. Laplace transform, Fourier transform, and boundary transformation method were applied to obtain the semi analytical solution for contaminant concentration. Later, the correctness and reliability of this study were verified by comparing the results of numerical and semi analytical solutions. The migration characteristics of pollutants in SL through defected GM were investigated against different parameters under the temporal and spatial domains. Results indicate that the migration is faster with bigger defect rate, and the smaller defect rate leads to the higher the sensitivity to concentration variations. In addition, peak values of concentration exist when the exponential concentration function is adopted, and the higher and later peak is produced with the larger the concentration function parameter.