NUMERICAL SIMULATION OF FLOW AND MORPHOLOGICAL EVALUATIONS IN RIVERS UNDER DAM-BREAK FLOWS

M.D. Saikia and A.K. Sarma

References

  1. [1] A. Ritter, Die Fortpfazung der Wasser-wellen, Zeitschrift des Vereins Deutscher Ingenieure, 36(33), 1892, 947–954.
  2. [2] F.E. Hicks, P.M. Steffler, & N. Yasmin, One dimensional dam break solutions for variable width channel, Journal of Hydraulic Engineering, 123(5), 1997, 464–468. Figure 7. Change in the cross-section at (a) 200 m downstream and (b) 1,500 m downstream. 6. Numerical Comparison The computational accuracy has been tested for the proposed simple FD model, by simulating the flow profiles with the second-order TVD MacCormak scheme with Veen Leer’s Limiter. It has been presented in Saikia and Sarma [45], where couple modelling was done for the Dibang dam failure. Here both coupling and decoupling modelling models have been done with same numerical model along with a new addition that is the simulation of the change in the cross-section in the original channel of Dibang due to the dam-break flow. 7. Model Assessment The performance of the proposed numerical model is assessed by simulating and comparing the discharge and bed elevation hydrographs for the rectangular channel which had previously been taken by Cao et al. [19] in their dam-break flow analysis. The channel length has been set to 50 km. Initially, the dam was considered to be located at the middle of the channel, i.e., at x = 25 km. The initial static water depths upstream and downstream of the dam were considered 40 m and 2 m, respectively. The trend of the discharge hydrographs and change in the bed elevations in three channel cross sections have been checked. The sections were considered at 20 km upstream of the dam, one at the dam site (i.e., at 25 km), and the other at 30 km downstream of the dam. The outputs obtained by proposed FD model is found to be in good agreement with 295
  3. [3] B.F. Sanders, High-resolution and non-oscillatory solution of the St. Venant equations in non-rectangular and non-prismatic channels, Journal of Hydraulic Research, 39(3), 2001, 321–330.
  4. [4] C. Zoppou & S. Roberts, Explicit schemes for dam-break simulations, Journal of Hydraulic Engineering, 129(1), 2003, 11–34.
  5. [5] F. Macchione & G. Viggiani, Simple modeling of dam failure in a natural river, Journal of Water Management, ICE, WA157(1), 2004, 53–60.
  6. [6] N.D. Katopodes, Two dimensional surges and shocks in open channels, Journal of Hydraulic Division, ASCE, 110(6), 1984, 794–812.
  7. [7] A. Hromadka, Two dimensional dam-break flood plain model, Advances in Water Resources 8, 1985, 7–14.
  8. [8] A.A. Akanbi & N.D. Katopodes, Model for flood propagation on initially dry land, Journal of Hydraulic Engineering, 114(7), 1988, 689–706.
  9. [9] D.H. Zhao, H.W. Shen, J.S. Lai, & G.Q. Tabios, III, Approximate Riemann solver in FVM for 2D hydraulic shock wave modeling, Journal of Hydraulic Engineering, 122(12), 1996, 692–702.
  10. [10] A.K. Sarma, A study of two-dimensional flow propagating from an opening in the river dike, Ph.D. Thesis, Assam Engineering College, Gauhati University, Assam, India, 1999.
  11. [11] F. Aureli & P. Mignosa, Flooding scenarios due to levee breaking in the Po river, Journal of Water Management, ICE, WA157(1), 2004, 3–12.
  12. [12] H. Capart & D.L. Young, Formation of a jump by the dam break wave over a granular bed, Journal of Fluid Mechanics, 372, 1998, 165–187.
  13. [13] L. Fraccarollo & H. Capart, Riemann wave description of erosional dam-break flows, Journal of Fluid Mechanics, 461, 2002, 183–228.
  14. [14] L. Fraccarollo & A. Armanin, A semi-analytical solution for the dambreak problem over a movable bed, Proc. European Concerted Action on Dam-Break Modeling, Munich, 1998.
  15. [15] A. Paquire & P. Balayn, Unsteady cases of validation for a 1-D sediment transport model, Proc. European Concerted Action on Dam-Break Modeling, Munich, 1998.
  16. [16] A. Paquire, Sediment transport models used by Cemagref during Impact project, Proc. Impact 1st Impact Workshop, PAQUIER 1–7, HR Wallingford, 16–17 May, 2002.
  17. [17] R.M.L. Ferreira & J.G.A.B. Leal, 1D mathematical modelling of the instantaneous -dam-break flood wave over mobile bed: Application of TVD AND flux splitting schemes, Proc. European Concerted Action on Dam-Break Modeling, Munich, 1998.
  18. [19] in their dam-break flow analysis. The channel length has been set to 50 km. Initially, the dam was considered to be located at the middle of the channel, i.e., at x = 25 km. The initial static water depths upstream and downstream of the dam were considered 40 m and 2 m, respectively. The trend of the discharge hydrographs and change in the bed elevations in three channel cross sections have been checked. The sections were considered at 20 km upstream of the dam, one at the dam site (i.e., at 25 km), and the other at 30 km downstream of the dam. The outputs obtained by proposed FD model is found to be in good agreement with 295 [3] B.F. Sanders, High-resolution and non-oscillatory solution of the St. Venant equations in non-rectangular and non-prismatic channels, Journal of Hydraulic Research, 39(3), 2001, 321–330. [4] C. Zoppou & S. Roberts, Explicit schemes for dam-break simulations, Journal of Hydraulic Engineering, 129(1), 2003, 11–34. [5] F. Macchione & G. Viggiani, Simple modeling of dam failure in a natural river, Journal of Water Management, ICE, WA157(1), 2004, 53–60. [6] N.D. Katopodes, Two dimensional surges and shocks in open channels, Journal of Hydraulic Division, ASCE, 110(6), 1984, 794–812. [7] A. Hromadka, Two dimensional dam-break flood plain model, Advances in Water Resources 8, 1985, 7–14. [8] A.A. Akanbi & N.D. Katopodes, Model for flood propagation on initially dry land, Journal of Hydraulic Engineering, 114(7), 1988, 689–706. [9] D.H. Zhao, H.W. Shen, J.S. Lai, & G.Q. Tabios, III, Approximate Riemann solver in FVM for 2D hydraulic shock wave modeling, Journal of Hydraulic Engineering, 122(12), 1996, 692–702. [10] A.K. Sarma, A study of two-dimensional flow propagating from an opening in the river dike, Ph.D. Thesis, Assam Engineering College, Gauhati University, Assam, India, 1999. [11] F. Aureli & P. Mignosa, Flooding scenarios due to levee breaking in the Po river, Journal of Water Management, ICE, WA157(1), 2004, 3–12. [12] H. Capart & D.L. Young, Formation of a jump by the dam break wave over a granular bed, Journal of Fluid Mechanics, 372, 1998, 165–187. [13] L. Fraccarollo & H. Capart, Riemann wave description of erosional dam-break flows, Journal of Fluid Mechanics, 461, 2002, 183–228. [14] L. Fraccarollo & A. Armanin, A semi-analytical solution for the dambreak problem over a movable bed, Proc. European Concerted Action on Dam-Break Modeling, Munich, 1998. [15] A. Paquire & P. Balayn, Unsteady cases of validation for a 1-D sediment transport model, Proc. European Concerted Action on Dam-Break Modeling, Munich, 1998. [16] A. Paquire, Sediment transport models used by Cemagref during Impact project, Proc. Impact 1st Impact Workshop, PAQUIER 1–7, HR Wallingford, 16–17 May, 2002. [17] R.M.L. Ferreira & J.G.A.B. Leal, 1D mathematical modelling of the instantaneous -dam-break flood wave over mobile bed: Application of TVD AND flux splitting schemes, Proc. European Concerted Action on Dam-Break Modeling, Munich, 1998. [18] D. Pritchard & A. Hogg, On sediment transport under dam break flow, Journal of Fluid Mechanics, 473, 2002, 265–274. [19] Z. Cao, G. Pender, S. Wallis, & P. Carling, Computational dam-break hydraulics over erodible sediment bed, Journal of Hydraulic Engineering, 130(7), 2004, 689–703.
  19. [20] W. Wu & S.S.Y. Wang, 1-D numerical simulation of morphodynamic processes under dam break and overtopping flows, World Environmental and Water Resources Congress, 21–25 May, Omaha, Nabeska, USA, EWRI, ASCE, 2006.
  20. [21] Z. Cao, Equilibrium near-bed concentration of suspended sediment, Journal of Hydraulic Engineering, 125(12), 1999, 1270– 1278.
  21. [22] C.H. Hembree, B.R. Colby, H.A Swenson, & J.R. Davis, Sedimentation and chemical quality of water in the Powder River drainage basin, Wyoming and Montana, Circular 170, U.S. Geological Survey, Washington, DC, 1952.
  22. [23] E.W. Lane & V.A. Koelzer, Density of sediments deposited in reservoirs. Rep. No. 9 of a Study of Methods Used in Measurement and Analysis of Sediment Loads in Streams, Engineering District, St. Paul, Minn, 1953.
  23. [24] B.R. Colby, Discussion of ‘Sediment transportation mechanics: Introduction and properties of sediment’, Journal of Hydraulic Division, ASCE, 89(1), 1963, 266–268.
  24. [25] S. Komura, Discussion of ‘Sediment transportation mechanics: Introduction and properties of sediment’, Journal of Hydraulic Division, ASCE, 89(1), 1963, 263–266.
  25. [26] Q.W. Han, Y.C. Wang, & X.L. Xiang, Initial dry density of sediment deposit, Journal of Sediment Research, 1 (in Chinese), 1981.
  26. [27] W. Wu & S.S.Y. Wang, Formulas for sediment porosity and settling velocity, Journal of Hydraulic Engineering, 132(8), 2006, 858–862.
  27. [28] P. Trask, Compaction of sediments, Bulletin of the America Association of Petroleum Geologists, 15, 1931, 271–276.
  28. [29] L.G. Straub, Missouri River report, House Document 238, Appendix XV, Corps of Engineers, U.S. Dept. of the Army to 73rd U.S. Congress, 2nd Session, 1935, 1156.
  29. [30] P.P. Brown & D.F. Lawler, Sphere drag and settling velocity revisited, Journal of Environmental Engineering, 129(3), 2003, 222–231.
  30. [31] P.K. Swamee & C.S.P. Ojha, Drag coefficient and fall velocity of nonspherical particles, Journal of Hydraulic Engineering, 117(5), 1991, 660–667.
  31. [32] W.E. Dietrich, Settling velocity of natural particles, Water Resources Research, 18(6), 1982, 1615–1626.
  32. [33] N.S. Cheng, Simplified settling velocity formula for sediment particle, Journal of Hydraulic Engineering, 123(2), 1997, 149– 152.
  33. [34] J.P. Ahrens, The fall-velocity equation, Journal of Water, Port, Coastal, and Ocean Engineering, 126(2), 2000, 99–102.
  34. [35] P. Diplas & G. Vigilar, Hydraulic geometry of threshold channels, Journal of Hydraulic Engineering, 118(4),1992, 597– 614.
  35. [36] S.R. Khodashenas & A. Paquier, A geometrical method for computing the distribution of boundary shear stress across irregular straight open channels, Journal of Hydraulic Research, 37(3),1999, 381–388.
  36. [37] S.R. Khodashenas & A. Paquier, River bed deformation calculated from boundary shear stress, Journal of Hydraulic Research, 40(5), 2002, 603–609.
  37. [38] S.R. Khodashenas, Simulation of the deformation of a river by a 1D-3D model, Joint International Conference of Civil and Building Engineering, Montreal, Canada, June 14–16, 2006.
  38. [39] S. Ikeda, Incipient motion of sand particles on sand slopes, Journal of the Hydraulics Division, 108(HY1), 1982, 95–114.
  39. [40] A.K. Sarma & M.D. Saikia, Dam break hydraulics in natural channel, World Environmental and Water Resources Congress, 21–25 May, Omaha, Nabeska, USA, EWRI, ASCE, 2006.
  40. [41] M.D. Saikia & A.K. Sarma, Numerical simulation model for computation of dam break flood in natural flood plain topography, Journal of Dam Engineering, 17(1), 2006, 31–50.
  41. [42] J.A. Cunge, F.M. Holly, Jr & A. Verwey, Practical aspects of computational river hydraulics (Boston: Pitman Advanced Publishing Program, 1980).
  42. [43] A.J.C. Saint-Venant, Theorie dumouvement non permanent des eaux, avec application aux crues des rivieres et al’introduction de marees dans leurs lits, Comptes rendus des seances del’ Academie des Sciences, 36, 1871, 174–154.
  43. [45], where couple modelling was done for the Dibang dam failure. Here both coupling and decoupling modelling models have been done with same numerical model along with a new addition that is the simulation of the change in the cross-section in the original channel of Dibang due to the dam-break flow. 7. Model Assessment The performance of the proposed numerical model is assessed by simulating and comparing the discharge and bed elevation hydrographs for the rectangular channel which had previously been taken by Cao et al. [19] in their dam-break flow analysis. The channel length has been set to 50 km. Initially, the dam was considered to be located at the middle of the channel, i.e., at x = 25 km. The initial static water depths upstream and downstream of the dam were considered 40 m and 2 m, respectively. The trend of the discharge hydrographs and change in the bed elevations in three channel cross sections have been checked. The sections were considered at 20 km upstream of the dam, one at the dam site (i.e., at 25 km), and the other at 30 km downstream of the dam. The outputs obtained by proposed FD model is found to be in good agreement with 295 [3] B.F. Sanders, High-resolution and non-oscillatory solution of the St. Venant equations in non-rectangular and non-prismatic channels, Journal of Hydraulic Research, 39(3), 2001, 321–330. [4] C. Zoppou & S. Roberts, Explicit schemes for dam-break simulations, Journal of Hydraulic Engineering, 129(1), 2003, 11–34. [5] F. Macchione & G. Viggiani, Simple modeling of dam failure in a natural river, Journal of Water Management, ICE, WA157(1), 2004, 53–60. [6] N.D. Katopodes, Two dimensional surges and shocks in open channels, Journal of Hydraulic Division, ASCE, 110(6), 1984, 794–812. [7] A. Hromadka, Two dimensional dam-break flood plain model, Advances in Water Resources 8, 1985, 7–14. [8] A.A. Akanbi & N.D. Katopodes, Model for flood propagation on initially dry land, Journal of Hydraulic Engineering, 114(7), 1988, 689–706. [9] D.H. Zhao, H.W. Shen, J.S. Lai, & G.Q. Tabios, III, Approximate Riemann solver in FVM for 2D hydraulic shock wave modeling, Journal of Hydraulic Engineering, 122(12), 1996, 692–702. [10] A.K. Sarma, A study of two-dimensional flow propagating from an opening in the river dike, Ph.D. Thesis, Assam Engineering College, Gauhati University, Assam, India, 1999. [11] F. Aureli & P. Mignosa, Flooding scenarios due to levee breaking in the Po river, Journal of Water Management, ICE, WA157(1), 2004, 3–12. [12] H. Capart & D.L. Young, Formation of a jump by the dam break wave over a granular bed, Journal of Fluid Mechanics, 372, 1998, 165–187. [13] L. Fraccarollo & H. Capart, Riemann wave description of erosional dam-break flows, Journal of Fluid Mechanics, 461, 2002, 183–228. [14] L. Fraccarollo & A. Armanin, A semi-analytical solution for the dambreak problem over a movable bed, Proc. European Concerted Action on Dam-Break Modeling, Munich, 1998. [15] A. Paquire & P. Balayn, Unsteady cases of validation for a 1-D sediment transport model, Proc. European Concerted Action on Dam-Break Modeling, Munich, 1998. [16] A. Paquire, Sediment transport models used by Cemagref during Impact project, Proc. Impact 1st Impact Workshop, PAQUIER 1–7, HR Wallingford, 16–17 May, 2002. [17] R.M.L. Ferreira & J.G.A.B. Leal, 1D mathematical modelling of the instantaneous -dam-break flood wave over mobile bed: Application of TVD AND flux splitting schemes, Proc. European Concerted Action on Dam-Break Modeling, Munich, 1998. [18] D. Pritchard & A. Hogg, On sediment transport under dam break flow, Journal of Fluid Mechanics, 473, 2002, 265–274. [19] Z. Cao, G. Pender, S. Wallis, & P. Carling, Computational dam-break hydraulics over erodible sediment bed, Journal of Hydraulic Engineering, 130(7), 2004, 689–703. [20] W. Wu & S.S.Y. Wang, 1-D numerical simulation of morphodynamic processes under dam break and overtopping flows, World Environmental and Water Resources Congress, 21–25 May, Omaha, Nabeska, USA, EWRI, ASCE, 2006. [21] Z. Cao, Equilibrium near-bed concentration of suspended sediment, Journal of Hydraulic Engineering, 125(12), 1999, 1270– 1278. [22] C.H. Hembree, B.R. Colby, H.A Swenson, & J.R. Davis, Sedimentation and chemical quality of water in the Powder River drainage basin, Wyoming and Montana, Circular 170, U.S. Geological Survey, Washington, DC, 1952. [23] E.W. Lane & V.A. Koelzer, Density of sediments deposited in reservoirs. Rep. No. 9 of a Study of Methods Used in Measurement and Analysis of Sediment Loads in Streams, Engineering District, St. Paul, Minn, 1953. [24] B.R. Colby, Discussion of ‘Sediment transportation mechanics: Introduction and properties of sediment’, Journal of Hydraulic Division, ASCE, 89(1), 1963, 266–268. [25] S. Komura, Discussion of ‘Sediment transportation mechanics: Introduction and properties of sediment’, Journal of Hydraulic Division, ASCE, 89(1), 1963, 263–266. [26] Q.W. Han, Y.C. Wang, & X.L. Xiang, Initial dry density of sediment deposit, Journal of Sediment Research, 1 (in Chinese), 1981. [27] W. Wu & S.S.Y. Wang, Formulas for sediment porosity and settling velocity, Journal of Hydraulic Engineering, 132(8), 2006, 858–862. [28] P. Trask, Compaction of sediments, Bulletin of the America Association of Petroleum Geologists, 15, 1931, 271–276. [29] L.G. Straub, Missouri River report, House Document 238, Appendix XV, Corps of Engineers, U.S. Dept. of the Army to 73rd U.S. Congress, 2nd Session, 1935, 1156. [30] P.P. Brown & D.F. Lawler, Sphere drag and settling velocity revisited, Journal of Environmental Engineering, 129(3), 2003, 222–231. [31] P.K. Swamee & C.S.P. Ojha, Drag coefficient and fall velocity of nonspherical particles, Journal of Hydraulic Engineering, 117(5), 1991, 660–667. [32] W.E. Dietrich, Settling velocity of natural particles, Water Resources Research, 18(6), 1982, 1615–1626. [33] N.S. Cheng, Simplified settling velocity formula for sediment particle, Journal of Hydraulic Engineering, 123(2), 1997, 149– 152. [34] J.P. Ahrens, The fall-velocity equation, Journal of Water, Port, Coastal, and Ocean Engineering, 126(2), 2000, 99–102. [35] P. Diplas & G. Vigilar, Hydraulic geometry of threshold channels, Journal of Hydraulic Engineering, 118(4),1992, 597– 614. [36] S.R. Khodashenas & A. Paquier, A geometrical method for computing the distribution of boundary shear stress across irregular straight open channels, Journal of Hydraulic Research, 37(3),1999, 381–388. [37] S.R. Khodashenas & A. Paquier, River bed deformation calculated from boundary shear stress, Journal of Hydraulic Research, 40(5), 2002, 603–609. [38] S.R. Khodashenas, Simulation of the deformation of a river by a 1D-3D model, Joint International Conference of Civil and Building Engineering, Montreal, Canada, June 14–16, 2006. [39] S. Ikeda, Incipient motion of sand particles on sand slopes, Journal of the Hydraulics Division, 108(HY1), 1982, 95–114. [40] A.K. Sarma & M.D. Saikia, Dam break hydraulics in natural channel, World Environmental and Water Resources Congress, 21–25 May, Omaha, Nabeska, USA, EWRI, ASCE, 2006. [41] M.D. Saikia & A.K. Sarma, Numerical simulation model for computation of dam break flood in natural flood plain topography, Journal of Dam Engineering, 17(1), 2006, 31–50. [42] J.A. Cunge, F.M. Holly, Jr & A. Verwey, Practical aspects of computational river hydraulics (Boston: Pitman Advanced Publishing Program, 1980). [43] A.J.C. Saint-Venant, Theorie dumouvement non permanent des eaux, avec application aux crues des rivieres et al’introduction de marees dans leurs lits, Comptes rendus des seances del’ Academie des Sciences, 36, 1871, 174–154. [44] A.J.C. Saint-Venant, Theorie du mouvement non permanent des eaux avec application aux crues des rivieres eta l’introduction de marees dans leurs lits, Comptes rendus des seances de l’ Academie des Sciences, 36, 1871, 237–240. [45] M.D. Saikia & A.K. Sarma, Numerical model for simulating flow and river bed profiles in a natural river under dam failure condition, The 15th IASTED International Conference on Applied Simulation and Modelling (ASM 2006), June 26–28, Rhode, 2006. 296

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