1. Raudkivi, A., Loose Boundary Hydraulics, A.A. Balkema, Rotterdam, Brook_eld, Netherlands (1998). 2. Karimaei Tabarestani, M. and Zarrati, A.R. Local scour calculation around bridge pier during ood event", KSCE J. Civil Eng., 21(4), pp. 1462{1472 (2017). 3. Zarrati, A.R., Nazariha, M., and Mashahir, M.B. Reduction of local scour in the vicinity of bridge pier groups using collars and riprap", J. Hydraul. Eng., 132(2), pp. 154{162 (2006). 4. Karimaei Tabarestani, M. and Zarrati, A.R. E_ect of collar on time development and extent of scour hole around cylindrical bridge piers", Int. J. Eng., Transactions C, 25(1), pp. 11{16 (2011). 5. Melville, B.W. and Had_eld, A.C. Use of sacri_cial piles as pier scour countermeasures", J. Hydraul. Eng., 125(11), pp. 1221{1224 (1999). 6. Chiew, Y.M. Scour protection at bridge piers", J. Hydraul. Eng., 118(9), pp. 1260{1269 (1992). 7. Gaudio, R., Tafarojnoruz, A., and Calomino, F. Combined ow-altering countermeasures against bridge pier scour", J. Hydraul. Res., 50(1), pp. 35{43 (2012). 8. Tafarojnoruz, A., Gaudio, R., and Calomino, F. Evaluation of ow-altering countermeasures against bridge pier scour", J. Hydraul. Eng., 138(3), pp. 297{305 (2012). 9. Chiew, Y.M. Mechanics of riprap failure at bridge pier", J. Hydraul. Eng., 121(9), pp. 635{643 (1995). 10. Richardson, E.V. and Davis, S.R. Evaluating scour at bridges", Hydraul. Eng. Circular, No. 18 (HEC-18 Fourth Edition), FHWA NHI 01-001, Federal Highway Administration, Washington, D.C. (2001). 11. Lagasse, P.F., Clopper, P.E., Zevenbergen, L.W., and Girard, L.G. Countermeasures to protect bridge piers from scour", NCHRP Report 593, TRB, NAS, Washington D.C. (2007). 12. Mashahir, M.B., Zarrati, A.R., and Mokallaf, E. Application of riprap and collar to prevent scouring around piers rectangular bridge", J. Hydraul. Eng., 136(3), pp. 183{187 (2009). 13. Karimaei Tabarestani, M. and Zarrati, A.R. Design of stable riprap around aligned and skewed rectangular bridge piers", J. Hydraul. Eng., 139(8), pp. 911{916 (2013). 14. Karimaei Tabarestani, M. and Zarrati, A.R. Design of riprap stone around bridge piers using empirical and neural network method", Civil Eng. Infrast. J., 48(1), pp. 175{188 (2015a). 15. Karimaei Tabarestani, M., Zarrati, A.R., Mashahir, M.B., and Mokallaf, E. Extent of riprap layer with di_erent stone sizes around rectangular bridge piers with or without an attached collar", Scientia Iranica, Trans. A, 22(3), pp. 709{716 (2015b). 16. Karimaei Tabarestani, M., Azarmidokht, H.R., Zarrati, A.R., and Anvary, S. Optimum design of riprap extension with di_erent stone size at rectangular bridge piers with and without protective collar", I. Hydraul. J., 10(4), pp. 51{64 (2016) (In Persian). 17. Froehlich, D.C. Protecting bridge piers with loose rock riprap", J. App. Wat. Eng. & Res., 1(1), pp. 39{ 57 (2013). 18. Chiew, Y.M. and Lim, F.H. Failure behavior of riprap layer at bridge piers under live-bed condition", J. Hydraul. Eng., 126(1), pp. 43{55 (2000). 19. Chiew, Y.M. Local scour and riprap stability at bridge piers in a degrading channel", J. Hydraul. Eng., 130(3), pp. 218{226 (2004). 20. Lauchlan, C.S. and Melville, B.W. Riprap protection at bridge piers", J. Hydraul. Eng., 127(5), pp. 412{418 (2001). Gh. Khademghaeiny et al./Scientia Iranica, Transactions A: Civil Engineering 27 (2020) 588{595 595 21. Unger, J. and Hager, W.H. Riprap failure at circular bridge piers", J. Hydraul. Eng., 132(4), pp. 354{362 (2006). 22. Rajaratnam, N. and Nwachukwu, B.A. Erosion near groynelike structures" J. Hydraul. Res., 21(4), pp. 277{287 (1983). 23. Oliveto, G. and Hager, W.H. Temporal evolution of clear-water pier and abutment scour", J. Hydraul. Eng., 128(9), pp. 811{820 (2002). 24. Garde, R.J. and Ranga Raju, K.G., Mechanics of Sediment Transportation and Alluvial Stream Problems, Wiley Eastern Limited, New Delhi (1977). 25. Raudkivi, A. and Ettema, R. E_ect of sediment gradation on clear water scour", J. Hydraul. Div., 103(HY10), pp. 1209{1213 (1977). 26. Melville, B.W. and Sutherland, A.J. Design method for local scour at bridge piers", J. Hydraul. Eng., 114(10), pp. 1210{1226 (1988).