Fig 1.
(a) Schematic of the leakage simulation apparatus: 1 – Water supply tank, 2 – Water pump, 3 – Pressure gauge, 4 – Soil containment box with a leaking pipe, 5 – Primary pipeline with an upward-directed leakage, 6 – Pressure control valve, 7 – Leakage water outlet, 8 – Pipes and fittings.
(b) Measured parameters in the experiments.
Table 1.
Characteristics of the soils used in the experiments.
Fig 2.
Grain size distribution curves of the soils used in the experiments.
Fig 3.
Workflow from data preprocessing to model development and evaluation.
Fig 4.
Algorithm of ensemble machine learning models used in: a) Bagging model (Random Forest), b) Boosting model (XGBoost), and c) Stacking model (MLP, SVR).
Table 2.
Assigned values for the hyperparameters of each model.
Fig 5.
Time evolution of fluidization at Qleak = 1.01E-04 m3/s: (a) Before the pump is activated, (b) At the start of the experiment, (c) At t = 4 s, (d) At t = 5 s, (e) At t = 20 s, (f) Immediately after t = 20 s, (g) At t = 25 s, (h) At t = 65 s, (i) At t = 75 s, (j) At t = 168 s, (k) At t = 900 s.
Fig 6.
Variation of Hf/d50 with: a) Frd for different Cu values in downward-directed leakage, (b) d50/√(Aleak) in downward-directed leakage, (c) Frd2 for different ranges of Aleak/(CDd50) in upward-directed leakage, and (d) Frd2 for different Cu values in upward-directed leakage.
Fig 7.
Density plot of observed and predicted data points from Eqs. (1) and (2) around the best-fit trend line ((Hf/d50)perd = (Hf/d50)actual) for: a) downward-directed leakage, and b) upward-directed leakage.
Fig 8.
Density plot of observed and predicted data points from Eqs. (3) and (4) around the best fit trend line ((√Af/d50)perd = (√Af/d50)actual) for: a) downward-directed leakage, and b) upward-directed leakage.
Fig 9.
Taylor diagram based on R², RMSE, and correlation values for the equations of maximum height and area of the fluidized region.
Table 3.
Sensitivity analysis for and
in upward-directed and downward-directed leakage.
Table 4.
Optimized hyperparameters of ensemble learning models.
Table 5.
Evaluation metric (R², RMSE, and Correlation coefficient) in the train and test phases for ensemble learning models estimating Hf/d50 and√(Af)/d50.
Fig 10.
Taylor diagram for comparison and evaluation of ensemble learning models in estimating: a) Hf/d50, and b) √(Af)/d50.
Table 6.
Evaluation metrices (R2, RMSE, and correlation coefficient) for the equations and the test phase of ensemble learning models.