Quantifying Measurement Uncertainty in the Critical Secant Gradient Function

The critical secant gradient function (CSGF) is a spatial function that defines the hydraulic conditions causing the progression of backward erosion piping, a significant internal erosion failure mode for dams and levees. While recent studies have defined the CSGF analytically and have also demonstrated how to measure it in the laboratory, uncertainty in measurements of the CSGF has not yet been quantified. In this study, a preliminary assessment of the uncertainty in measuring the CSGF is developed by analyzing the residual errors between the best estimate of the CSGF for each experiment and the measured values of the secant gradient at specific points. The results indicate that the errors in the best estimate of the measured CSGF are approximately normally distributed with a standard deviation of 7% for the experimental configuration used. Further research is needed to assess if this level of error is acceptable in practice.