The study presented herein links to a regression analysis that ties into three mathematical models from the Brutsaert, Mualem and Burdine equations respectively. The paper describes a series of experimental investigations on the characteristic permeation and interaction of three clayey soil types as barrier liners with landfill leachate from around the City of Johannesburg (CoJ), South Africa. From the outcomes therefrom, sequence of logarithmic relationships were projected towards proposing rational approximations of the best curve-fitting bounds using the Grain Size Distribution (GSD) and Atterberg Limits (AL) of the respective soils as selected classification properties. The outcomes which generally revealed reasonable indicative values were expressed using the weighted Plasticity Indices (PI) of the respective soils in conformance to Sitarenios et al. The two curve-fitting parameters x and z incorporated to simulate the Liner-Leachate Interaction Curve (LLIC) of the three clayey soils sampled from respective landfills around the CoJ, South Africa yielded 118, 0.6; 1211, 0.6; 1058, 0.6 in the Brutsaert model, 0.1, 1.2; 0.0, 1.5; 0.0, 1.5 in the Mualem model and 0.1, 2.4; 0.0, 2.6; 0.0, 2.7 in the Burdine model for samples A, B and C respectively, with a general R2 value of 0.904.