The Use of Lagrangian Interpolation Polynomial to Predict the Safe Distances for a Borehole Location in the Cemetery Vicinity

Abstract

Abstract Leachate formation and migration from cemeteries is a major threat to underground water bodies due to toxic chemicals released during decomposition. This study uses Lagrangian Interpolation Polynomial (LIP) to predict safe distances for locating hand-dug wells in the vicinity of a cemetery in Ede (Latitude 7.7349 o N and Longitude 4.4439 o E). Eleven (11) soil samples were collected using hand augers at 20.0 m intervals from the center of the cemetery to the outside of the sloppy side of it at a maximum depth of 2.0 m; they were analyzed in the laboratory for the presence of leachate ionic concentrations (LIC) (nitrate, sulphate, and carbonate). The analysis results were substituted into LIP to obtain a Model Equation (ME) for the predicted concentration (PC) of each ion. The graphs of LIC and PC against distance were plotted for each ionic component to compare and test for accuracy. The ME of PC for different ionic components was combined to obtain a General Model Equation (GME) for PC. The results of the correlation coefficient (CC) of LIC and PC for each model revealed that there is a strong correlation between them for nitrate (R RN = 0.9278, R PN = 0.9273), sulphate (R RS = 0.9394 and R PS = 0.9384), and carbonates (R RC = 0.9706 and R PC = 0.9701). The CC of GME of LIC and PC indicated a close correlation. Hence, Therefore, LIP can be used to calculate safe distances from cemeteries for hand-dug wells and boreholes.