European Geosciences Union
Informational Entropy and Bridge Scour Estimation under Complex Hydraulic Scenarios
Alonso Pizarro (1,2), Oscar Link (2), Mauro Fiorentino (1), Caterina Samela (1), and Salvatore Manfreda (1) (1) University of Basilicata, 85100 Potenza, Italy (
[email protected]), (2) University of Concepción, 4030000, Concepción, Chile.
Introduction
BRISENT model under Flood Waves
Bridges are important for society because they allow social, cultural, and economic connectivity being a key piece in the development process and progress. At the same time, bridges continually suffer the action of natural hazards like earthquakes, landslides and floods, which expose the road network service at risk. The main cause of bridge collapse is related to hydraulic conditions [Briaud et al., 2007], where flood events can compromise the safety of the whole structure up to the complete failure. (a)
EGU2017-14956-2, 2017
Effective Flow Work Parameter: W*
(b)
Figure 2. Hydrographs for unsteady runs: [Oliveto and Hager, 2002, 2005]: (1) 11.11.00; (3) 11.11.00; (1) 4.3.01. [Link et al., 2016]: C-1; C-2.
Figure 3. Schematic view of the experimental installation and discharge control scheme used by [Link et al., 2016].
Figure 4. Properties of the Effective flow work W*. Literature data by [Lança et al. , 2013)].
Figure 1. Bridge failure due to Scour. Source: (a) Prendergast and Gavin (2014). (b) UFROMEDIOS (2016).
BRISENT model
Acknowledgments
One goal of our research is to introduce a new scour model exploiting the Principle of Maximum Entropy and applying it on the dimensionless Effective flow work, W* [Pizarro et al., 2017], that allows to extend the analysis with views to discharge unsteadiness. Thus, the called BRIdge-pier Scour ENTropic (BRISENT) model has born. The entropy concept and its theory have been used before in statistical mechanics, information theory, hydrology and water resources [e.g. Chiu, 1987; Moramarco et al., 2013; Singh, 2010], providing good results and an easy way for introducing probabilities into hydraulic. The dimensionless Effective flow work W*, Informational entropy of scour H(z*), and Brisent model are presented in Eq. (1), Eq. (2), and Eq. (3), respectively.
1 u t 0.5uc dt tR uR 4
W tend *
tend
0
* zmax
f z ln f z dz
H z
*
*
*
*
1
2
0
The authors would like to thank Prof. Giuseppe Oliveto (University of Basilicata) for the provided experimental data and the support from the European Commission under the -ELARCH program (Project Reference number: 552129-EM-1-2014-1-IT-ERA MUNDUS-EMA21). This publication reflects only the authors’ view and the Commission is not liable for any use that may be made of the information contained therein.
References Figure 5. Time-dependent scour depth in contrast with the BRISENT model.
Figure 4. Flume at University of Concepción employed for carried out unsteady scour experiements.
Chiu, C.-L. (1987), Entropy and probability concepts in hydraulics, Journal of Hydraulic Engineering, 113(5), 583-599. Lança, R. M., C. S. Fael, R. J. Maia, J. P. Pêgo, and A. H. Cardoso (2013), Clearwater scour at comparatively large cylindrical piers, Journal of Hydraulic Engineering, 139(11), 1117-1125.
Experimental data were compiled from available studies in literature. Altogether, 5 runs were analysed pertained to [Oliveto and Hager, 2002, 2005] and [Link et al., 2016]. Note that experiments C-1 and C-2 are highly unsteady runs conducted in a novel installation able to reproduce any hydrograph with high precision in laboratory flumes at University of Concepcion, Chile [Link et al., 2016]. Figure 2 shows the hydrographs for the five unsteady runs and Figure 5 contrasts measured scour points with BRISENT model over time. Calibration process were carried out minimizing RMSE function.
Link, O., C. Castillo, A. Pizarro, A. Rojas, B. Ettmer, C. Escauriaza, and S. Manfreda (2016), A model of bridge pier scour during flood waves, Journal of Hydraulic Research, 1-14. Moramarco, T., G. Corato, F. Melone, and V. P. Singh (2013), An entropy-based method for determining the flow depth distribution in natural channels, Journal of Hydrology, 497, 176-188. Oliveto, G., and W. H. Hager (2002), Temporal evolution of clear-water pier and abutment scour, Journal of Hydraulic Engineering, 128(9), 811820. Oliveto, G., and W. H. Hager (2005), Further results to time-dependent local scour at bridge elements, Journal of Hydraulic Engineering, 131(2), 97105. Figure 6. Local scour after flood waves.
* 1 W * * z ln 1 * exp zmax 1 Wmax
Conclusion 3
Briaud, J.-L., L. Brandimarte, J. Wang, and P. D'Odorico (2007), Probability of scour depth exceedance owing to hydrologic uncertainty, Georisk, 1(2), 77-88.
Bridge-pier scour evolution was analysed using the first mathematical formulation for simulating the scour phenomena based on energy concepts and entropy theory. The proposed BRISENT model has been established on the effective flow work parameter and on the principle of maximum entropy. The model has only one fitting coefficient and is able to reproduce the main dynamic of the scour process. In particular, RMSE values are less than 0.52 cm for the analysed dataset. The BRISENT model represents a good candidate for estimating the time-dependent scour depth under complex hydraulic scenarios. The authors are keen to apply this idea for describing the scour behaviour during a real flood event.
Pizarro, A., B. Ettmer, S. Manfreda, A. Rojas, and O. Link (2017), Dimensionless Effective Flow Work for Estimation of Pier Scour Caused by Flood Waves, Journal of Hydraulic Engineering, 06017006. Prendergast, L. J., and K. Gavin (2014), A review of bridge scour monitoring techniques, Journal of Rock Mechanics and Geotechnical Engineering, 6(2), 138-149. Singh, V. P. (2010), Entropy theory for derivation of infiltration equations, Water resources research, 46(3). UFROMEDIOS (2016), Caen tren de carga al río Toltén luego que colapsara el puente ferroviario de Pitrufquén, in UFROMEDIOS, edited.
