Document Type : Original/Review Paper

Authors

1 Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran.

2 Department of Architecture Engineering, University of Sistan and Baluchestan, Zahedan, Iran.

3 Department of Civil Engineering, Bozorgmehr University of Qaenat, Qaen, Iran.

10.22044/jadm.2020.10085.2147

Abstract

Scouring, occurring when the water flow erodes the bed materials around the bridge pier structure, is a serious safety assessment problem for which there are many equations and models in the literature to estimate the approximate scour depth. This research is aimed to study how surrogate models estimate the scour depth around circular piers and compare the results with those of the empirical formulations. To this end, the pier scour depth was estimated in non-cohesive soils based on a subcritical flow and live bed conditions using the artificial neural networks (ANN), group method of data handling (GMDH), multivariate adaptive regression splines (MARS) and Gaussian process models (Kriging). A database containing 246 lab data gathered from various studies was formed and the data were divided into three random parts: 1) training, 2) validation and 3) testing to build the surrogate models. The statistical error criteria such as the coefficient of determination (R2), root mean squared error (RMSE), mean absolute percentage error (MAPE) and absolute maximum percentage error (MPE) of the surrogate models were then found and compared with those of the popular empirical formulations. Results revealed that the surrogate models’ test data estimations were more accurate than those of the empirical equations; Kriging has had better estimations than other models. In addition, sensitivity analyses of all surrogate models showed that the pier width’s dimensionless expression (b/y) had a greater effect on estimating the normalized scour depth (Ds/y).

Keywords

[1] A.M. Shirhole and R.C. Holt, “Planning for a comprehensive bridge safety program,” Transportation Research Record, vol. 1290, pp.39-50, 1999.

[2] H.N.C. Breusers, G. Nicollet and H.W. Shen, “Local scour around cylindrical piers,” Journal of Hydraulic Research, vol. 15, pp. 211–252, Jun  1977.

[3] B.W. Melville and S.A. Coleman, “Bridge Scour,” Water Resources Publications, Highlands ranch, Colorado, USA, 2000.

[4] E.V. Richardson and S.R. Davis, “Evaluating scour at bridges, Hydraulic Engineering Circular no. 18,” FHWA NHI, Washington DC, USA, Rep. FHWA NHI, 2001.

[5] D.M. Sheppard and Jr. W. Miller, “Live-bed local pier scour experiments,” Journal of Hydraulic Engineering, vol. 132, pp. 635–642, July 2006.

[6] R. Ettema, B.W. Melville and B. Barkdoll, “Scale effect in pierscour experiments,” Journal of Hydraulic Engineering, vol. 124, pp. 639–642, 1998.

[7] S.M. Bateni, S.M. Borghei and D.S. Jeng, “Neural network and neuro-fuzzy assessments for scour depth around bridge piers,” Engineering Applications of Artificial Intelligence, vol. 20, pp. 401–414, April 2007.

[8] S.M. Bateni, H.R. Vosoughifar, B. Truce and D.S. Jeng, “Estimation of Clear-Water Local Scour at Pile Groups Using Genetic Expression Programming and Multivariate Adaptive Regression Splines,” Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 145, pp. 04018029, January 2019. 

[9] R.V. Raikar, C.Y. Wang, H.P. Shih and J.H. Hong, “Prediction of contraction scour using ANN and GA,” Flow Measurement and Instrumentation, vol. 50, pp. 26–34, 2016.

[10] Q. Zhang, X.L. Zhou and J.H. Wang, “Numerical investigation of local scour around three adjacent piles with different arrangements under current,” Ocean Engineering, vol. 142, pp. 625–638, September 2017.

[11] Y. Hassanzadeh, A. Jafari-Bavil-Olyaei, M.T. Aalami and N. Kardan, “Experimental and numerical investigation of bridge pier scour estimation using ANFIS and teaching–learning-based optimization methods,” Engineering with Computers, vol. 35, pp. 1103-1120, October 2018.

[12] N.M. Dang, D.T. Anh and T.D. Dang, “ANN optimized by PSO and Firefly algorithms for predicting scour depths around bridge piers,” Engineering with Computers, vol. 18, pp. 1-11, July 2019. 

[13] M. Fatahi and B. Lashkar-Ara, “Estimating scour below inverted siphon structures using stochastic and soft computing approaches,” Journal of AI and Data Mining, vol. 5, pp. 55–66, October 2016.

[14] M. Firat and M. Gungor, “Generalized regression neural networks and feed forward neural networks for prediction of scour depth around bridge piers,” Advances in Engineering Software, vol. 40, pp. 731–737, August 2009.

[15] M. Najafzadeh, G.A. Barani and H.M. Azamathulla, “GMDH to predict scour depth around a pier in cohesive soils,” Applied Ocean Research, vol. 40, pp. 35–41, March 2013.

[16] S. Qin, Y.L. Zhou, H. Cao and M.A. Wahab, “Model Updating in Complex Bridge Structures using Kriging Model Ensemble with Genetic Algorithm,” KSCE Journal of Civil Engineering, vol. 22,  pp. 3567-3578, November 2017.    

[17] X. Fan, P. Wang and F. Hao, “Reliability-based design optimization of crane bridges using Kriging-based surrogate models,” Structural and Multidisciplinary Optimization, vol. 59, pp. 993-1005, January 2019.

[18] P. Lu, Z. Xu, Y. Chen and Y. Zhou, “Prediction method of bridge static load test results based on Kriging model Pengzhen,” Engineering Structures, vol. 214, pp. 110641, July 2020.

[19] H.M. Azamathulla, A.A. Ghani, N.A. Zakaria and A. Guven, “Genetic programming to predict bridge pier scour,” Journal of Hydraulic Engineering, vol. 136, pp. 165–169, March 2010.

[20] M. Najafzadeh and H.M. Azamathulla, “Neuro-fuzzy GMDH systems to predict the scour pile groups due to waves,” Journal of Computing in Civil Engineering, vol. 29, pp. 04014068, 2013.

[21] N. Ghaemi, A. Etemad-Shahidi and B. Ataie-Ashtiani, “Estimation of current- induced pile groups scour using a rule based method,” Journal of Hydroinformatics, vol. 15, pp. 516–528, 2013.

[22] A.M. Sattar, “Gene expression models for the prediction of longitudinal dispersion coefficients in transitional and turbulent pipe flow,” Journal of Pipeline Systems Engineering and Practice, vol. 5, pp. 04013011, February 2014.

[23] H. Shan, R. Kilgore, J. Shen and K. Kerenyi, “Updating HEC-18 Pier Scour Equations for Noncohesive Soil,” United States, Federal Highway Administration, Office of Infrastructure Research and Development, 2016.

[24] E.M. Laursen and A. Toch, “Scour around bridge piers and abutments,” Ames, IA: Iowa Highway Research Board, 1956.

[25] P.A. Johnson, “Reliability-based pier scour engineering,” Journal of Hydraulic Engineering, vol. 118, pp. 1344–1358, Jan 1992.

[26] E.V. Richardson, L.J. Harrison, J. Richardson and S. Davis, “Evaluating scour at bridges (No. HEC 18 (2nd edition)),” Administration (FHwA), Washington. D.C, 1993.

[27] Y.M. Chiew, “Local Scour at Bridge Piers,” School of Engineering, The Univ. of Auckland, Auckland, New Zealand, Rep. 355, 1984.

[28] J. Chabert and P. Engeldinger, “Etude des affouillements autor des piles de ponts,” Chatou, Rep. Natl. Hydraul Lab., 1956.

[29] R.K. Chee, “Live-bed scour at bridge piers,” Auckland University, New Zealand, Rep. 290, 1982.

[30] S.C. Jain and E.E. Fischer, “Scour around bridge piers at high Froude numbers,” Federal Highway Administration, U.S. Department of Transportation, Washington, D.C, 1979. 

[31] S.C. Jain and E.E. Fischer, “Scour around bridge piers at high flow velocities” Journal of Hydraulic Engineering, vol. 106, pp. 1827–1842, 1980.

[32] A.H. Chen, “Local scour around circular piers,” Ph.D. dissertation, Asian Institute of Technology, Bangkok, Thailand, 1980.

[33] B.W. Melville and A.J. Sutherland, “Design method for local scour at bridge piers,” Journal of Hydraulic Engineering, vol. 114, pp. 1210-1226, October 1988.

[34] A.J. Keane and P.B. Nair, “Computational approaches for aerospace design: the pursuit of excellence” John Wiley&Sons, Ltd, West Sussex 582, 2005.

[35] A.G. Ivakhnenko, “The group method of data handling in prediction problems,” Soviet Automatic Control, vol. 9, pp. 21-30, 1976.      

[36] G.C. Onwubolu, “GMDH-methodology and implementation in MATLAB,” London: Imperial College Press, 2016.

[37] J. Sacks, W.J. Welch, T.J. Mitchell and H.P. Wynn, “Design and analysis of computer experiments,” Statistical Science, vol. 1, pp. 409–423, 1989.    

[38] D.R. Jones, “A taxonomy of global optimization methods based on response surfaces,” Journal of Global Optimization, vol. 21, pp.345–383, December 2001.           

[39] J.H. Friedman, “Multivariate adaptive regression splines,” Annals of Statistics, vol. 1, pp. 1–67, 1991.

[40] W. Zhang, “MARS Applications in Geotechnical Engineering Systems,” Springer Nature Customer Service Center LLC, 2020.

[41] T. Hastie, R. Tibshirani and J. Friedman, “The elements of statistical learning,” Springer New York, New York, 2009.

[42] R.H. McCuen, “Mdeling Hydrologic Change: Statistical Methods,” Lewis Publishers CRC Press, Boca Raton, 2016.

[43] M. Najafzadeh, “Neuro-fuzzy GMDH systems based evolutionary algorithms to predict scour pile groups in clear water conditions,” Ocean Engineering, vol. 99, pp. 85-94, May 2015.