Pressure fluctuations beneath hydraulic jumps potentially endanger the stability of stilling basins. This paper deals with the mathematical modeling of the results of laboratory-scale experiments to estimate the extreme pressures. Experiments were carried out on a smooth stilling basin underneath free hydraulic jumps downstream of an Ogee spillway. From the probability distribution of measured instantaneous pressures, pressures with different probabilities could be determined. It was verified that maximum pressure fluctuations, and the negative pressures, are located at the positions near the spillway toe. Also, minimum pressure fluctuations are located at the downstream of hydraulic jumps. It was possible to assess the cumulative curves of pressure data related to the characteristic points along the basin, and different Froude numbers. To benchmark the results, the dimensionless forms of statistical parameters include mean pressures (P*_m), the standard deviations of pressure fluctuations (σ*_X), pressures with different non-exceedance probabilities (P*_k%), and the statistical coefficient of the probability distribution (N_k%) were assessed. It was found that an existing method can be used to interpret the present data, and pressure distribution in similar conditions, by using a new second-order fractional relationships for σ*_X, and N_k%. The values of the N_k% coefficient indicated a single mean value for each probability.

In this paper, two artificial intelligence (AI) techniques, including Deep Learning (DL) and Multi-Layer Perceptron (MLP), have been applied to predict the pressure fluctuations coefficient (Cʹ_P) along the submerged and free jumps at the bottom of the USBR Type II stilling basin, based on the geometric and hydraulic parameters. This coefficient is significant for evaluating the uplift and cavitation phenomena within the stilling basins. The measurements were conducted in a laboratory flume using the pressure transducers and the data acquisition system. The maximum values of Cʹ_P occurred at the beginning of the stilling basin. The DL algorithm contains three hidden layers using (100,100,100) hidden neurons. The optimal structure for the MLP model was found to be 5–10‒1. In the testing set, using the DL model, the values of determination coefficient (R²), root mean square error (RMSE), mean absolute error (MAE), and Legate and McCabe’s Index (LMI) were obtained 0.915, 0.003, 0.002, and 0.743, respectively. For the MLP model, the same values were obtained 0.522, 0.009, 0.007, and 0.199, respectively. It was verified that the DL model gives more accurate results for the Cʹ_P coefficient.

Dissipation basins are usually constructed downstream of spillways to dissipate energy, causing large pressure fluctuations underneath hydraulic jumps. Little systematic experimental investigation seems available for the pressure parameters on the bed of the US Department of the Interior, Bureau of Reclamation (USBR) Type II dissipation basins in the literature. We present the results of laboratory-scale experiments, focusing on the statistical modeling of the pressure field at the centerline of the apron along the USBR Type I and II basins. The accuracy of the pressure transducers was ±0.5%. The presence of accessories within basin_II reduced the maximum pressure fluctuations by about 45% compared to basin_I. Accordingly, in some points, the bottom of basin_II did not collide directly with the jet due to the hydraulic jump. As a result, the values of pressure and pressure fluctuations decreased mainly therein. New original best-fit relationships were proposed for the mean pressure, the statistical coefficient of the probability distribution, and the standard deviation of pressure fluctuations to estimate the pressures with different probabilities of occurrence in basin_I and basin_II. The results could be useful for a more accurate, safe design of the slab thickness, and reduce the operation and maintenance costs of dissipation basins.

Knowledge of extreme pressures and fluctuations within the stilling basins is of the utmost importance, which may cause potential severe damages. It is complicated to measure the fluctuating pressures of hydraulic jumps in the real-scale structures. Therefore, little information is available on pressure fluctuations in the literature. In this paper, minimal and maximal pressures are analyzed on the flat bed of a stilling basin downstream of an Ogee spillway. Attention has been focused on dimensionless pressures related to the low and high cumulative probabilities of occurrence (P*_0.1 and P*_99.9%), respectively. The results are presented based on laboratory-scale experiments. These parameters for the relatively high Froude numbers have not been investigated. The total standard uncertainty for the dimensionless mean pressures (P*_m) is obtained around 1.87%. Spectral density analysis showed that the dominant frequency in the classical hydraulic jumps is about 4 HZ. Low-frequency of pressure fluctuations indicates the existence of large-scale vortices. In the zone near the spillway toe, P*_0.1% reached to negative values around – 0.3. The maximum values of pressure coefficients, namely |C_P0.1%|_max and C_P99.9%max, were achieved around 0.19 and 0.24, respectively. New original expressions were proposed for P*_0.1 and P*_99.9%, which are useful for estimating extreme pressures.

Pressure fluctuations beneath hydraulic jumps downstream of Ogee spillways potentially damage stilling basin beds. This paper deals with the extreme pressures underneath free hydraulic jumps along a smooth stilling basin. The experiments were conducted in a laboratory flume. From the probability distribution of measured instantaneous pressures, the pressures with different non-exceedance probabilities (P*a%) could be determined. It was verified that the maximum pressure fluctuations, as well as the negative pressures, are located at the positions closest to the spillway toe. The minimum pressure fluctuations are located at the downstream of hydraulic jumps. It was possible to assess the cumulative curves of P*a% related to the characteristic points along the basin, and different Froude numbers. To benchmark, the results, the dimensionless forms of mean pressures, standard deviations, and pressures with different non-exceedance probabilities were assessed. It was found that an existing methodology can be used to interpret the present data, and pressure distribution in similar conditions, by using a new third-order polynomial relationship for the standard deviation (σ*X) with the determination coefficient (R2) equal to 0.717. It was verified that the new optimized adjustment gives more accurate results for the estimation of the maximum extreme pressures than the minimum extreme pressures.