Interpretation of Falling-Head Tests in Presence of Random Measurement Error

Abstract

Field data are tainted by random and several types of systematic errors. The paper presents a review of interpretation methods for falling-head tests. The statistical robustness of each method is then evaluated through the use of synthetic data tainted by random error. Six synthetic datasets are used for this evaluation. Each dataset has an average relative error for water elevation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Z</mml:mi></mml:math>, respectively, of 0.04%, 0.11%, 0.22%, 0.34%, 0.45%, and 0.90% (absolute errors on elevation are, respectively, 0.10, 0.25, 0.50, 1.0, and 2.0 mm for a range of water elevation change of 150 mm during test). Each synthetic dataset is composed of 40 synthetic tests (each test consisting of 18 data couples of synthetic falling-head measurements). Results show that the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Z</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi></mml:math>method is the most accurate and precise, followed by the Hvorslev method when a correction is applied and the velocity method when appropriately interpreted. Advice on how to interpret falling-head tests tainted by random error concludes the study.