A Consolidation Curve Reproduction Based on Sigmoid Model: Evaluation and Statistical Assessment

Abstract

In the present study, various shapes of laboratory consolidation curves were numerically reproduced using a four-parametric sigmoid function. Sixteen consolidation curves were selected based on one-dimensional oedometer tests to statistically evaluate the sigmoid model and to determine the appropriate deviation statistics. Comparisons between observed and predicted data were performed using the following statistical metrics: mean error (E), root mean square error (RMSE), mean absolute error (MAE), weighted error (WE), revised Nash–Sutcliffe efficiency index (CE1) and refined index of model performance (dr). The weighted error (WE) was chosen as the optimization target in a first-order iterative optimization algorithm to determine a local minimum of a differentiable function. Comparing the simulated and observed settlements showed close correspondence in the values of CE1 and dr in terms of model performance. Based on statistical assessment, the maximum values of RMSE and MAE for the average degree of consolidation were 0.029 (-) and 0.021 (-), respectively. In turn the settlement data RMSE and MAE were 0.039 mm and 0.025 mm, respectively. These results indicated that the sigmoid expression effectively reproduced the shape of the consolidation curve.