New simplified design methods for engineering barriers around contaminated sites with Cauchy boundaries

Since the 1980s, low-permeability slurry trench cutoff walls have been widely constructed as barriers to retard the migration of contaminants. The thickness of the cutoff walls is a key determinant of the wall service life. Through a series of theoretical derivations, simplified methods for determining the flux limit and concentration limit were proposed to determine the thickness of cutoff walls for contaminated sites with constant pollutant flux. The relative errors of both the flux-based and concentration-based methods increase as the breakthrough criterion of the ratio between the specified limit concentration of the contaminant to the source concentration (C^*) and the ratio of the limited value of contaminant flux to the constant source flux (F^*) increases, with a given Peclet number P_L. The maximum relative error reaches 4% and 6% when C^* and F^* are both 0.1, which covers most practical situations in cutoff wall design. Good agreements of wall thickness were obtained between the proposed simplified methods and analytical solutions via a clear example. The proposed method can efficiently simplify the design process of cutoff walls with high accuracy, providing a basis for containing contaminated sites.