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Two-dimensional mobile-bed dam-break model Tang, Gaven 2012-10-19

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   TWO-DIMENSIONAL MOBILE-BED DAM-BREAK MODEL  by  GAVEN TANG B.Sc., University of Alberta, 2010  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Civil Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  October 2012  Β© Gaven Tang, 2012   ii ABSTRACT Sudden and catastrophic dam-breaks typically induce high bed shear stresses downstream as the flood-wave propagates over the alluvial channel and flood plain. In fact, the non-dimensionalized shear stresses are often high enough that they are comparable to those typically seen in the transport of sand. Despite the existence of these shear stresses, industry typically ignores sediment transport altogether and assumes a fixed-bed when modelling dam-breaks. This thesis will examine the validity of the fixed-bed assumption and create a depth-averaged 2D mobile- bed dam-break model. This model will then be tested by simulating the Malpasset (France) dam- break of 1959, and a sensitivity analysis will then be performed on the parameters of grain roughness, vegetation roughness, friction angle, grain size, and depth to bedrock to examine differences in inundation and flood-wave propagation.   iii TABLE OF CONTENTS ABSTRACT ................................................................................................................................... ii TABLE OF CONTENTS ............................................................................................................ iii LIST OF TABLES ....................................................................................................................... vi LIST OF FIGURES .................................................................................................................... vii LIST OF EQUATIONS .............................................................................................................. xv LIST OF SYMBOLS AND ABBREVIATIONS ..................................................................... xvi ACKNOWLEDGEMENTS .................................................................................................... xviii 1 INTRODUCTION ................................................................................................................. 1 1.1 CURRENT PRACTICE ................................................................................................... 1 1.2 DAM-BREAK CASE STUDIES ..................................................................................... 2 1.3 CURRENT METHODS OF MODELLING DAM-BREAK ........................................... 8 1.4 STATEMENT OF PROBLEM ........................................................................................ 9 2 LITERATURE REVIEW ................................................................................................... 10 2.1 2D MOBILE-BED MODELS ........................................................................................ 10 2.1.1 WOLF 2D MODEL ................................................................................................ 10 2.1.2 RIVER2D-MORPHOLOGY MODEL ................................................................... 11 2.1.3 QUANHONG’S MODEL ....................................................................................... 12 2.1.4 XIA ET AL.’S MODEL ......................................................................................... 12 2.1.5 CONCLUSIONS..................................................................................................... 13 2.2 SEDIMENT TRANSPORT EQUATIONS ................................................................... 13 2.2.1 DAM-BREAK SHEAR STRESS ESTIMATES .................................................... 14 2.2.2 REVIEW OF SELECT BEDLOAD TRANSPORT EQUATIONS ....................... 15 2.2.2.1 ENGELUND AND FREDSOE EQUATION ................................................. 15 2.2.2.2 MEYER-PETER AND MULLER EQUATION ............................................. 16 2.2.2.3 WONG AND PARKER EQUATION ............................................................. 17 2.2.2.4 WILSON EQUATION .................................................................................... 18 2.2.2.5 CHENG EQUATION ...................................................................................... 19 2.2.2.6 PARKER EQUATION .................................................................................... 19 2.2.3 SUSPENSION ........................................................................................................ 20 2.2.4 DISCUSSION ......................................................................................................... 21 iv 2.2.5 CONCLUSIONS..................................................................................................... 24 2.3 FLOOD PLAIN VEGETATION EFFECTS ................................................................. 26 3 MODELLING METHODOLOGY .................................................................................... 27 3.1 TELEMAC VERSION 6.1 ............................................................................................. 27 3.1.1 TELEMAC2D ......................................................................................................... 28 3.1.1.1 HYDRODYNAMICS ...................................................................................... 28 3.1.1.2 COMPUTATIONAL OPTIONS IMPLEMENTED ....................................... 29 3.1.2 SISYPHE ................................................................................................................ 30 3.1.2.1 MOBILIZATION OF THE BED .................................................................... 30 3.1.2.2 SEDIMENT TRANSPORT EQUATION ....................................................... 30 3.1.2.3 VERTICAL AND SPATIAL VARIATION OF SEDIMENT AND RIGID BOUNDARY .................................................................................................................... 32 3.1.2.4 COMPUTATIONAL OPTIONS IMPLEMENTED ....................................... 32 3.2 MODEL VALIDATION ................................................................................................ 32 3.2.1 SOARES-FRAZAO AND ZECH (2002) ............................................................... 32 3.2.2 VASQUEZ AND LEAL (2006) ............................................................................. 35 3.2.3 VASQUEZ (2005) .................................................................................................. 39 4 CASE STUDY: INPUT DATA AND MODELLING ASSUMPTIONS ......................... 41 4.1 STUDY SITE: MALPASSET DAM, FRANCE............................................................ 41 4.1.1 BACKGROUND .................................................................................................... 41 4.1.2 MALPASSET DAM-BREAK MODEL ................................................................. 42 4.2 SENSITIVITY ANALYSIS PARAMETERS ............................................................... 44 4.2.1 MEAN GRAIN SIZE (𝑑50) ................................................................................... 44 4.2.2 DEPTH TO BEDROCK (𝑑𝑏) ................................................................................. 44 4.2.3 GRAIN ROUGHNESS (𝑛𝑔) .................................................................................. 45 4.2.4 VEGETATION ROUGHNESS (𝑛𝑣) AND FRICTION ANGLE (πœ™β€²) ................... 45 4.2.4.1 DELINEATION OF VEGETATED AND URBANIZED ZONES ................ 45 5 RESULTS AND ANALYSIS .............................................................................................. 48 5.1 EFFECT OF VARYING GRAIN ROUGHNESS ......................................................... 51 5.1.1 CROSS-SECTIONS OF HIGH-WATER MARKS AND BED CHANGE ........... 51 5.1.2 2D BED EVOLUTION........................................................................................... 60 v 5.1.3 FLOOD-WAVE PROPAGATION TIME .............................................................. 63 5.1.3.1 MOBILE-BED SIMULATIONS .................................................................... 63 5.1.3.2 FIXED-BED SIMULATIONS ........................................................................ 69 5.2 EFFECT OF VARYING VEGETATION ROUGHNESS AND FRICTION ANGLE . 75 5.2.1 CROSS-SECTIONS OF HIGH-WATER MARKS AND BED CHANGE ........... 75 5.2.2 2D BED EVOLUTION........................................................................................... 83 5.2.3 FLOOD-WAVE PROPAGATION TIME .............................................................. 87 5.2.3.1 MOBILE-BED SIMULATIONS .................................................................... 87 5.2.3.2 FIXED-BED SIMULATIONS ........................................................................ 90 5.2.4 PRE-/POST-DAM-BREAK STEADY-STATE HYDRODYNAMICS ................ 93 5.3 EFFECT OF VARYING MEAN GRAIN SIZE ............................................................ 99 5.3.1 CROSS-SECTIONS OF HIGH-WATER MARKS AND BED CHANGE ........... 99 5.3.2 2D BED EVOLUTION......................................................................................... 103 5.3.3 FLOOD-WAVE PROPAGATION TIME ............................................................ 108 5.4 EFFECT OF VARYING DEPTH TO BEDROCK...................................................... 111 5.4.1 CROSS-SECTIONS OF HIGH-WATER MARKS AND BED CHANGE ......... 111 5.4.2 2D BED EVOLUTION......................................................................................... 116 5.4.3 FLOOD-WAVE PROPAGATION TIME ............................................................ 122 6 SUMMARY ........................................................................................................................ 126 6.1 CONCLUSIONS .......................................................................................................... 126 6.1.1 SENSITIVITY ANALYSIS ................................................................................. 126 6.1.2 THE FIXED-BED ASSUMPTION ...................................................................... 128 6.1.3 RESEARCH CONTRIBUTION ........................................................................... 128 6.2 LIMITATIONS ............................................................................................................ 128 6.3 FUTURE WORK ......................................................................................................... 129 REFERENCES .......................................................................................................................... 130 APPENDIX A – SAMPLE TELEMAC2D INPUT FILE ..................................................... 134 APPENDIX B – SAMPLE SISYPHE INPUT FILE .............................................................. 135 APPENDIX C – SAMPLE FORTRAN INPUT FILE ........................................................... 136    vi LIST OF TABLES Table 2-1: Valid 𝜏 βˆ— ranges of reviewed bedload transport equations .......................................... 23 Table 3-1: Initial conditions of Leal et al.'s (2002) experiments .................................................. 36 Table 4-1: Sensitivity parameter - mean grain sizes ..................................................................... 44 Table 4-2: Sensitivity parameter - depth to bedrock ..................................................................... 44 Table 4-3: Sensitivity parameter - grain roughness ...................................................................... 45 Table 4-4: Sensitivity parameter - vegetation density .................................................................. 45 Table 5-1: Flood-wave propagation time after dam-break to the Mediterranean Sea on mobile- bed ................................................................................................................................................. 67 Table 5-2: Flood-wave propagation time after dam-break to the Mediterranean Sea on fixed-bed ....................................................................................................................................................... 73 Table 5-3: Flood-wave propagation time after dam-break to the Mediterranean Sea on mobile- bed with varied 𝑑𝑏 ...................................................................................................................... 125    vii LIST OF FIGURES Figure 1-1: Ha! Ha! Lake outbreak flood outcome photographs: (a) photo mosaic showing eroded river-bank; (b) and (c) aerial photographs of the river course before and after the flood, respectively. (Capart et al., 2007; Β© Taylor & Francis, 2007, by permission) ............................... 3 Figure 1-2: Topography of the river channel before and after the Tangjiashan Barrier Lake dam- break (Liu et al., 2010; Β© ASCE, 2010, by permission) ................................................................. 5 Figure 1-3: Before and after cross-sections of the river following the Tangjiashan Barrier Lake dam-break. (a) to (l) are cross-sections at various points along the river. (Liu et al., 2010; Β© ASCE, 2010, by permission) .......................................................................................................... 7 Figure 2-1: 3D-view in WOLF 2D (Dewals et al., 2002; Courtesy of WIT Press from: Third International Conference Computer Simulation in Risk Analysis and Hazard Mitigation, Risk Analysis III, page 66) .................................................................................................................... 11 Figure 2-2: Parker's Shields diagram (Mays, 1999; Β© The McGraw-Hill Companies, Inc., 1999, by permission) ............................................................................................................................... 15 Figure 2-3: Data collected by Meyer-Peter and Muller (1948) (Β© IAHR, 1948, by permission) 17 Figure 2-4: Modified Meyer-Peter Muller relation (Wong and Parker, 2006; Β© ASCE, 2006, by permission) .................................................................................................................................... 18 Figure 2-5: Cheng’s (2002) bedload transport relation (Β© ASCE, 2002, by permission) ............ 19 Figure 2-6: Criteria for the initiation of suspension (van Rijn, 1984; Β© ASCE, 1984, by permission) .................................................................................................................................... 21 Figure 2-7: Comparison of various bedload transport relations for a wide range of 𝜏 βˆ— .............. 22 Figure 2-8: Comparison of various bedload transport relations for verified ranges of 𝜏 βˆ— ........... 23 Figure 2-9: Proposed combination bedload transport equation .................................................... 25 Figure 3-1: Soares-Frazao and Zech’s (2002) experimental set-up (Β© ASCE, 2002, by permission) .................................................................................................................................... 33 Figure 3-2: Graphical comparison of water levels between Soares-Frazao and Zech's (2002) model and TELEMAC2D output. The left part shows Soares-Frazao and Zech’s (2002) simulated water levels, and the right part shows TELEMAC2D simulated water levels. (left part Β© ASCE, 2002, by permission) .................................................................................................... 34 viii Figure 3-3: Graphical comparison of velocity field between Soares-Frazao and Zech's (2002) model and TELEMAC2D output (left part Β© ASCE, 2002, by permission) ................................ 35 Figure 3-4: Graphical comparison of velocity field between Soares-Frazao and Zech's (2002) experimental results and TELEMAC2D output (left part Β© ASCE, 2002, by permission) ......... 35 Figure 3-5: Initial conditions of Leal et al.'s (2002) experiments (Vasquez and Leal, 2006; Β© Jose Vasquez, 2006, by permission) ..................................................................................................... 36 Figure 3-6: Experimental and simulated results for experiment Ts.25 (Β© Jose Vasquez, 2006, adapted by permission) ................................................................................................................. 37 Figure 3-7: Experimental and simulated results for experiment Ts.28 (Β© Jose Vasquez, 2006, adapted by permission) ................................................................................................................. 38 Figure 3-8: LFM secondary flow experiment (Β© Jose Vasquez, 2005, by permission) ............... 39 Figure 3-9: Comparison of model outputs and experimental results of secondary flow effects on LFM flume experiment for left and right banks (Β© Jose Vasquez, 2005, adapted by permission) ....................................................................................................................................................... 40 Figure 4-1: Malpasset dam-break model topography mesh (aerial photograph of Frejus [FR 177- 150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ............................................................... 43 Figure 4-2: Vegetated and urbanized zones (aerial photograph of Frejus [3544-3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) ................................................................................ 47 Figure 5-1: Cross-sections (aerial photograph of Frejus [3544-3644, #41 to #121] in 1955 Β© IGN, 2012, by permission)............................................................................................................ 49 Figure 5-2: Location of 2D bed elevation plot of evolution (aerial photograph of Frejus [3544- 3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) ........................................................... 50 Figure 5-3: HWM at cross-section 1 varying 𝑛𝑔 on a fixed-bed.................................................. 53 Figure 5-4: HWM and bed elevation at cross-section 1 varying 𝑛𝑔 on a mobile-bed ................. 53 Figure 5-5: HWM at cross-section 2 varying 𝑛𝑔 on a fixed-bed.................................................. 54 Figure 5-6: HWM and bed elevation at cross-section 2 varying 𝑛𝑔 on a mobile-bed ................. 54 Figure 5-7: HWM at cross-section 3 varying 𝑛𝑔 on a fixed-bed.................................................. 55 Figure 5-8: HWM and bed elevation at cross-section 3 varying 𝑛𝑔 on a mobile-bed ................. 55 Figure 5-9: HWM at cross-section 4 varying 𝑛𝑔 on a fixed-bed.................................................. 56 Figure 5-10: HWM and bed elevation at cross-section 4 varying 𝑛𝑔 on a mobile-bed ............... 56 Figure 5-11: HWM at cross-section 5 varying 𝑛𝑔 on a fixed-bed ............................................... 57 ix Figure 5-12: HWM and bed elevation at cross-section 5 varying 𝑛𝑔 on a mobile-bed ............... 57 Figure 5-13: HWM at cross-section 6 varying 𝑛𝑔 on a fixed-bed ............................................... 58 Figure 5-14: HWM and bed elevation at cross-section 6 varying 𝑛𝑔 on a mobile-bed ............... 58 Figure 5-15: HWM at cross-section 7 varying 𝑛𝑔 on a fixed-bed ............................................... 59 Figure 5-16: HWM and bed elevation at cross-section 7 varying 𝑛𝑔 on a mobile-bed ............... 59 Figure 5-17: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ..................................... 62 Figure 5-18: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ..................................... 62 Figure 5-19: Bed evolution of case where: 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ..................................... 62 Figure 5-20: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ... 66 Figure 5-21: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑣 = 0.033, πœ™β€² = 49Β°, and 𝑑50 = 1 π‘šπ‘š (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ... 66 Figure 5-22: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑣 = 0.067, πœ™β€² = 60Β°, and 𝑑50 = 1 π‘šπ‘š (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ... 66 Figure 5-23: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑣 = 0.090, πœ™β€² = 70Β°, and 𝑑50 = 1 π‘šπ‘š (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ... 66 Figure 5-24: Flood-wave propagation time versus total roughness for varying grain roughnesses in mobile-bed model ..................................................................................................................... 69 Figure 5-25: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑣 = 0.000 (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ........................................................ 72 x Figure 5-26: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑣 = 0.033 (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ........................................................ 72 Figure 5-27: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑣 = 0.067 (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ........................................................ 72 Figure 5-28: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑣 = 0.090 (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ........................................................ 72 Figure 5-29: Flood-wave propagation time versus total roughness for varying grain roughnesses in fixed-bed model ........................................................................................................................ 74 Figure 5-30: HWM at cross-section 1 varying 𝑛𝑣 and πœ™β€² on a fixed-bed .................................... 76 Figure 5-31: HWM and bed elevation at cross-section 1 varying 𝑛𝑣 and πœ™β€² on a mobile-bed .... 76 Figure 5-32: HWM at cross-section 2 varying 𝑛𝑣 and πœ™β€² on a fixed-bed .................................... 77 Figure 5-33: HWM and bed elevation at cross-section 2 varying 𝑛𝑣 and πœ™β€² on a mobile-bed .... 77 Figure 5-34: HWM at cross-section 3 varying 𝑛𝑣 and πœ™β€² on a fixed-bed .................................... 78 Figure 5-35: HWM and bed elevation at cross-section 3 varying 𝑛𝑣 and πœ™β€² on a mobile-bed .... 78 Figure 5-36: HWM at cross-section 4 varying 𝑛𝑣 and πœ™β€² on a fixed-bed .................................... 79 Figure 5-37: HWM and bed elevation at cross-section 4 varying 𝑛𝑣 and πœ™β€² on a mobile-bed .... 79 Figure 5-38: HWM at cross-section 5 varying 𝑛𝑣 and πœ™β€² on a fixed-bed .................................... 80 Figure 5-39: HWM and bed elevation at cross-section 5 varying 𝑛𝑣 and πœ™β€² on a mobile-bed .... 80 Figure 5-40: HWM at cross-section 6 varying 𝑛𝑣 and πœ™β€² on a fixed-bed .................................... 81 Figure 5-41: HWM and bed elevation at cross-section 6 varying 𝑛𝑣 and πœ™β€² on a mobile-bed .... 81 Figure 5-42: HWM at cross-section 7 varying 𝑛𝑣 and πœ™β€² on a fixed-bed .................................... 82 Figure 5-43: HWM and bed elevation at cross-section 7 varying 𝑛𝑣 and πœ™β€² on a mobile-bed .... 82 Figure 5-44: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ..................................... 86 Figure 5-45: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.033, πœ™β€² = 49Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ..................................... 86 xi Figure 5-46: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.067, πœ™β€² = 60Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ..................................... 86 Figure 5-47: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.090, πœ™β€² = 70Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ..................................... 86 Figure 5-48: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.025, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑛𝑣 = 0.000 and πœ™β€² = 40Β°, blue – 𝑛𝑣 = 0.033 and πœ™β€² = 49Β°, red – 𝑛𝑣 = 0.067 and πœ™β€² = 60Β°, green – 𝑛𝑣 = 0.090 and πœ™β€² = 70Β°) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ........................................................ 89 Figure 5-49: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.030, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑛𝑣 = 0.000 and πœ™β€² = 40Β°, blue – 𝑛𝑣 = 0.033 and πœ™β€² = 49Β°, red – 𝑛𝑣 = 0.067 and πœ™β€² = 60Β°, green – 𝑛𝑣 = 0.090 and πœ™β€² = 70Β°) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ........................................................ 89 Figure 5-50: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.035, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑛𝑣 = 0.000 and πœ™β€² = 40Β°, blue – 𝑛𝑣 = 0.033 and πœ™β€² = 49Β°, red – 𝑛𝑣 = 0.067 and πœ™β€² = 60Β°, green – 𝑛𝑣 = 0.090 and πœ™β€² = 70Β°) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ........................................................ 89 Figure 5-51: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑔 = 0.025 (orange – 𝑛𝑣 = 0.000, blue – 𝑛𝑣 = 0.033, red – 𝑛𝑣 = 0.067, green – 𝑛𝑣 = 0.090) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) .............. 92 Figure 5-52: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑔 = 0.030 (orange – 𝑛𝑣 = 0.000, blue – 𝑛𝑣 = 0.033, red – 𝑛𝑣 = 0.067, green – 𝑛𝑣 = 0.090) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) .............. 92 Figure 5-53: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑔 = 0.035 (orange – 𝑛𝑣 = 0.000, blue – 𝑛𝑣 = 0.033, red – 𝑛𝑣 = 0.067, green – 𝑛𝑣 = 0.090) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) .............. 92 Figure 5-54: Pre-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š3/𝑠 (aerial photograph of Frejus [3544-3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) ................................................ 98 xii Figure 5-55: Post-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š3/𝑠 (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ................................................ 98 Figure 5-56: Pre-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.033, πœ™β€² = 49Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š3/𝑠 (aerial photograph of Frejus [3544-3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) ................................................ 98 Figure 5-57: Post-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.033, πœ™β€² = 49Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š3/𝑠 (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ................................................ 98 Figure 5-58: Pre-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.067, πœ™β€² = 60Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š3/𝑠 (aerial photograph of Frejus [3544-3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) ................................................ 98 Figure 5-59: Post-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.067, πœ™β€² = 60Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š3/𝑠 (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ................................................ 98 Figure 5-60: Pre-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.090, πœ™β€² = 70Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š3/𝑠 (aerial photograph of Frejus [3544-3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) ................................................ 98 Figure 5-61: Post-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.090, πœ™β€² = 70Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š3/𝑠 (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ................................................ 98 Figure 5-62: HWM and bed elevation at cross-section 1 varying 𝑑50 on a mobile-bed ........... 100 Figure 5-63: HWM and bed elevation at cross-section 2 varying 𝑑50 on a mobile-bed ........... 100 Figure 5-64: HWM and bed elevation at cross-section 3 varying 𝑑50 on a mobile-bed ........... 101 Figure 5-65: HWM and bed elevation at cross-section 4 varying 𝑑50 on a mobile-bed ........... 101 Figure 5-66: HWM and bed elevation at cross-section 5 varying 𝑑50 on a mobile-bed ........... 102 Figure 5-67: HWM and bed elevation at cross-section 6 varying 𝑑50 on a mobile-bed ........... 102 Figure 5-68: HWM and bed elevation at cross-section 7 varying 𝑑50 on a mobile-bed ........... 103 Figure 5-69: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ................................... 107 xiii Figure 5-70: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 5 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ................................... 107 Figure 5-71: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 10 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ................................... 107 Figure 5-72: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 20 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ................................... 107 Figure 5-73: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 40 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ................................... 107 Figure 5-74: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, and πœ™β€² = 40Β° (orange – 𝑑50 = 1 π‘šπ‘š, blue – 𝑑50 = 5 π‘šπ‘š, red – 𝑛𝑣 = 𝑑50 = 10 π‘šπ‘š, green – 𝑛𝑣 = 𝑑50 = 20 π‘šπ‘š, black – 𝑑50 = 40 π‘šπ‘š) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ...................................................... 110 Figure 5-75: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.090, and πœ™β€² = 70Β° (orange – 𝑑50 = 1 π‘šπ‘š, blue – 𝑑50 = 5 π‘šπ‘š, red – 𝑛𝑣 = 𝑑50 = 10 π‘šπ‘š, green – 𝑛𝑣 = 𝑑50 = 20 π‘šπ‘š, black – 𝑑50 = 40 π‘šπ‘š) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ...................................................... 110 Figure 5-76: HWM and bed elevation at cross-section 1 varying 𝑑𝑏 on a mobile-bed .............. 112 Figure 5-77: HWM and bed elevation at cross-section 2 varying 𝑑𝑏 on a mobile-bed .............. 112 Figure 5-78: HWM and bed elevation at cross-section 3 varying 𝑑𝑏 on a mobile-bed .............. 113 Figure 5-79: HWM and bed elevation at cross-section 4 varying 𝑑𝑏 on a mobile-bed .............. 113 Figure 5-80: HWM and bed elevation at cross-section 5 varying 𝑑𝑏 on a mobile-bed .............. 114 Figure 5-81: HWM and bed elevation at cross-section 6 varying 𝑑𝑏 on a mobile-bed .............. 114 Figure 5-82: HWM and bed elevation at cross-section 7 varying 𝑑𝑏 on a mobile-bed .............. 115 Figure 5-83: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 2 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ............................... 121 xiv Figure 5-84: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 5 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ............................... 121 Figure 5-85: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 5 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ............................... 121 Figure 5-86: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 10 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ............ 121 Figure 5-87: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 10 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ............ 121 Figure 5-88: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 15 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ............ 121 Figure 5-89: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 15 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) ............ 121 Figure 5-90: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑑𝑏 = 2 π‘š, blue – 𝑑𝑏 = 5 π‘š, red – 𝑑𝑏 = 10 π‘š, green – 𝑑𝑏 = 15 π‘š) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission).......................................................................................................... 124 Figure 5-91: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑑𝑏 = 2 π‘š, blue – 𝑑𝑏 = 5 π‘š, red – 𝑑𝑏 = 10 π‘š, green – 𝑑𝑏 = 15 π‘š) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission).......................................................................................................... 124 Figure 5-92: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑑𝑏 = 2 π‘š, blue – 𝑑𝑏 = 5 π‘š, red – 𝑑𝑏 = 10 π‘š, green – 𝑑𝑏 = 15 π‘š) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission).......................................................................................................... 124  xv LIST OF EQUATIONS Equation 2-1: Engelund and Fredsoe (1976) equation ................................................................. 15 Equation 2-2: Meyer-Peter and Muller (1948) equation ............................................................... 16 Equation 2-3: Modified Meyer-Peter and Muller equation (Wong and Parker, 2006) ................. 17 Equation 2-4: Wilson (1966) equation .......................................................................................... 18 Equation 2-5: Cheng (2002) equation ........................................................................................... 19 Equation 2-6: Parker (1979) equation ........................................................................................... 19 Equation 2-7: Proposed combination sediment transport equation .............................................. 25 Equation 3-1: Continuity............................................................................................................... 28 Equation 3-2: Momentum along 𝒙 ................................................................................................ 28 Equation 3-3: Momentum along π’š ................................................................................................ 28 Equation 3-4: Transport of π’Œ and 𝜺 (a) ......................................................................................... 29 Equation 3-5: Transport of π’Œ and 𝜺 (b) ......................................................................................... 29 Equation 3-6: Exner Equation ....................................................................................................... 30 Equation 3-7: Meyer-Peter and Muller (1948) equation ............................................................... 30 Equation 3-8: Logarithmic interpolation between Meyer-Peter and Muller (1948) and Wilson (1966) ............................................................................................................................................ 31 Equation 3-9: Wilson (1966) equation .......................................................................................... 31 Equation 3-10: Li and Millar’s (2011) shear stress partitioning ................................................... 31    xvi LIST OF SYMBOLS AND ABBREVIATIONS 1D  = one-dimensional 2D  = two-dimensional 3D  = three-dimensional ASCE  = American Society of Civil Engineers BRGM = Bureau de Recherches GΓ©ologiques et MiniΓ¨res DHL  = Delft Hydraulics Laboratory EDF  = ElectricitΓ© de France EWRI  = Environmental and Water Resources Institute HWM  = High-water mark IAHR  = International Association for Hydro-Environment Engineering & Research IGN  = Institut GΓ©ographique National KE  = k-epsilon turbulence model LFM  = Laboratory of Fluid Mechanics NSERC = Natural Sciences and Engineering Research Council of Canada USACE = U.S. Army Corps of Engineers π·βˆ—  = particle parameter 𝐷50  = mean grain diameter 𝐷𝑠  = mean grain diameter 𝐾𝑠  = Nikuradse roughness height 𝑅𝑒𝑝  = particle Reynolds number 𝑑50  = mean grain diameter 𝑑𝑏  = thickness of alluvium layer to bedrock 𝑛  = Manning’s roughness coefficient 𝑛𝑔  = grain component of Manning’s roughness coefficient 𝑛𝑣  = vegetation component of Manning’s roughness coefficient π‘žβˆ—  = non-dimensional transport rate π‘’βˆ—  = shear velocity 𝑒𝑏  = mean transport velocity of particles moving as bedload πœβˆ—  = non-dimensional bed shear stress xvii πœπ‘  = bed shear stress πœπ‘ βˆ—  = non-dimensional critical shear stress πœπ‘” βˆ—   = grain component of total non-dimensional bed shear stress πœπ‘£ βˆ—  = vegetation component of total non-dimensional bed shear stress 𝑔  = acceleration of gravity 𝑠  = specific gravity 𝑑  = time 𝑣  = flow velocity 𝑀  = settling velocity 𝛩  = πœβˆ— 𝛷  = π‘žβˆ— 𝛹  = 1/𝛩 𝜌  = density πœ™β€²  = friction angle   xviii ACKNOWLEDGEMENTS I give my gratitude to Dr. Faye Hicks and Dr. Nallamuthu Rajaratnam, my former professors in the field of Water Resources Engineering at the University of Alberta, for inspiring me to pursue further studies and a career in this field. This work would have not been possible without guidance and support from Dr. Robert Millar, my supervisor at the University of British Columbia. Dr. Millar also provided an opportunity for me to travel to Paris for the XVIIIth TELEMAC Users Club Conference. This memorable trip to Europe was the first of many to come.  I am also very grateful for the modelling assistance that Dr. Jose Vasquez and Mr. Faizal Yusuf provided in the early stages of my research. I must give special thanks to Dr. Stephen Kwan for giving so much of his personal time to troubleshoot my models and provide extensive technical guidance. In the later stages of research, Dr. Jean-Michel Hervouet and the online TELEMAC community provided much needed programming support. I dedicate this work to my family and friends for always supporting me in my decisions, and for encouraging me to continuously better myself. I also need to give special recognition to my best friend, Mr. Lawrence Lau, for never declining my requests to proofread and edit my papers. Lastly, I would like to thank my officemates, Mr. Curtis VanWerkhoven and Mr. Yapo Alle- Ando, for the Risk games and lunches that we were able to share. 1 1 INTRODUCTION 1.1 CURRENT PRACTICE Dam-break analysis is commonly performed to create inundation maps and to determine flood- wave propagation time to populated regions or locations of critical infrastructure in the event of dam failure. Typically, one-dimensional fixed-bed simulations are used in the modelling of dam- break floods.  From Newlin (2007) and the USACE (1997) dam-break analysis guideline, it is apparent that dam-break analyses performed by industry have not progressed in quite a few years. The four steps involved in performing the industry standard dam-break analysis are as follows (USACE, 1997):  (1) Dam-Breach Analysis: The causes of dam failure and dam-breach characteristics are determined. (2) Dam Failure Hydrograph: A failed dam outflow hydrograph is produced based on input parameters (i.e., precipitation hydrograph, hydraulic and hydrologic routing, dam characteristics, and downstream river morphology). (3) Dam-Break Routing: A usually one-dimensional, full unsteady flow routing model is run. (4) Inundation Mapping: Maps of predicted inundated land are produced to assist in the identification of hazard zones and creation of evacuation plans. It is of note that the USACE (1997) guideline to performing a dam-break analysis neither references sediment transport nor changes in river morphology; hence, the analysis is performed with the assumption that the riverbed is fixed. A fixed-bed assumption for the analysis of sudden dam-break flows in an alluvial river may or may not be appropriate depending on application. However, it is well recognized in the fluvial geomorphology community that flows equal to or greater than bankfull flows are channel forming. Thus, if sudden dam-break flows are channel- forming flows, the stream morphology may evolve.  Research to examine the morphologic change in a river following a dam-break will require the assumption of a mobile riverbed. In making this assumption, it is extremely likely that steps (3) 2 and (4) of the above USACE (1997) guideline will be impacted. By incorporating mobile-bed conditions, the process of performing dam-break analyses will be advanced. 1.2 DAM-BREAK CASE STUDIES In 1996, the Ha! Ha! Lake in Quebec experienced a breach whereby a small earthen dyke situated south of the main concrete dam was overtopped. This resulted in a new channel being incised, allowing water to bypass the dam. The lake’s water level rapidly dropped by 9 π‘š with an estimated peak outflow of 1010 π‘š3/𝑠 (Capart et al., 2007). The Ha! Ha! Lake outbreak flood likely led to large amounts of sediment being entrained from the lake and floodway and being deposited downstream. Such a large mobilization of bed sediment caused morphologic changes along the entire downstream reach of the Ha! Ha! River as evidenced in Figure 1-1. In the figure, (b) shows the before aerial photograph of the river, and (c) shows the after. By comparing (b) and (c) it can be interpreted that following the lake outbreak, the channel was widened along the entire length of the river and there was lateral migration of some meanders. Both of these feed into the notion that flows on the scale of those observed following a sudden dam-break, or in this case, dyke-breach, will cause morphologic change. 3  Figure 1-1: Ha! Ha! Lake outbreak flood outcome photographs: (a) photo mosaic showing eroded river-bank; (b) and (c) aerial photographs of the river course before and after the flood, respectively. (Capart et al., 2007; Β© Taylor & Francis, 2007, by permission)4 In 2008, a magnitude 8.0 earthquake shook Wenchuan, Sichuan Province, Southwest China, resulting in the formation of a barrier lake at Tangjiashan. Approximately a month after its formation, the lake breached and the water level in the lake fell 22 π‘š as it emptied. Peak discharge was determined to be about 6500 π‘š3/𝑠 (Liu et al., 2010). Similar to the Ha! Ha! Lake outbreak, the Tangjiashan Barrier Lake breach also entrained and deposited large amounts of sediment. Figure 1-2 shows a longitudinal profile of the original bed elevation and topography, before and after the dam-break. Comparing the original bed slope to the bed slope after the dam-breach, it can be seen that the slope angle has increased and up to 40 π‘š of sediment has been deposited on top of the original bed. It is also likely that the material deposited on top of the original riverbed has a different grain size distribution than that of the original bed. Both of these factors contribute to the development of a new morphology. Figure 1-3 shows the cross-sections of the river channel with the original bed elevation and the bed elevation after the dam-breach. As a part of a changing morphology, the channel geometry has also changed.  5  Figure 1-2: Topography of the river channel before and after the Tangjiashan Barrier Lake dam-break (Liu et al., 2010; Β© ASCE, 2010, by permission) 6  Figure 1-3a 7  Figure 1-3b Figure 1-3: Before and after cross-sections of the river following the Tangjiashan Barrier Lake dam-break. (a) to (l) are cross-sections at various points along the river. (Liu et al., 2010; Β© ASCE, 2010, by permission)8 The Ha! Ha! Lake and Tangjiashan Barrier Lake incidents both highlight the fact that dyke- breaches and dam-breaks are events with flows that can mobilize large amounts of sediment. Such large mobilizations of sediment are bound to have significant impacts on river morphology. Thus, it is more appropriate to assume mobile-bed conditions when attempting to model dam- break flows over alluvial rivers. 1.3 CURRENT METHODS OF MODELLING DAM-BREAK The current state of practice, study of dam-break flows on alluvial rivers involves both numerical simulations and scaled physical models. Most scaled physical models are created to verify their numerical simulation counterparts (Quanhong, 2009; Vasquez and Leal, 2006; Vasquez et al., 2007; Xia et al., 2010; Capart and Young, 1998). After a numerical model is verified, there can be confidence in the output yielded when applying the model to a case study. Numerical simulation involves one-, two-, or three-dimensional models. Traditionally, 1D models have been widely used because they require the least computer resources. As the processing power of computers has grown over the years, 2D models have become more practical. Eventually, once computer processing power reaches the point where simulation time is reduced to an acceptable level, 3D models will become the standard. Having a mobile-bed over a fixed-bed also increases computational requirements; therefore, fixed-bed simulations are more prevalent for all three categories of numerical models (Vasquez and Roncal, 2009; Cao et al., 2004; Ferrari et al., 2010; Hardy et al., 2005). Scaled physical models of dam-break flows on alluvial rivers are typically used to develop and verify numerical models. Verification of a 1D model would entail the use of a simple rectangular or trapezoidal prismatic channel, such as that of Soares Frazao et al. (2001), while verification of a 2D or 3D model would entail the use of more complex channel geometries and morphologies such as those of Soares Frazao and Zech (2002), Vasquez and Roncal (2009), and Vasquez and Leal (2006). The bed of this type of set-up may or may not contain mobile sediment, depending on the type of numerical simulation being tested.  Because the focus of this research is on the morphologic impacts of dam-break flows over alluvial rivers, the different modeling methodologies will be examined within the context of mobile-bed. 9 1.4 STATEMENT OF PROBLEM Dam-breaks can lead to a multitude of environmental and community impacts, including impacts on fish populations, river morphology, and human life. A topic of particular interest to stakeholders is the immediate impact of a dam-break on the morphology of a river, as this will allow the assessment of ecological recovery and resilience. Research into this area will allow the examination of sediment transport, with and without vegetation influences, and the prediction of possible changes in channel geometry. The scour, transport, and deposition that occur during dam-break may also affect travel time, duration, and inundation levels of the dam-break flood. The Malpasset dam in France, which failed catastrophically in 1959, will be used as a case study. A 2D mobile-bed model will be developed and used to examine the morphologic effect of having a dam-break flood propagate through the Reyran Valley downstream of the Malpasset Dam. Potential morphologic effects of dam-break floods will be studied through a sensitivity analysis that allows for the examination of differences in inundation and flood-wave characteristics for both the mobile-bed and fixed-bed simulations. This research is part of a larger NSERC-funded project that involves BC Hydro as an industry partner. It will assist BC Hydro, other utilities, and stakeholders in performing appropriate planning and design exercises where dam-breaks are a concern.  10 2 LITERATURE REVIEW 2.1 2D MOBILE-BED MODELS To model a dam-break flood over a mobile-bed, a 1D model would not be sufficient as it is cross-sectionally averaged, and a 3D model would require extensive computing resources. A 2D depth-averaged model would be sufficient as it is capable of simulating changes in river depth and width, allowing subsequent examination of changes to morphology and channel geometry. There have been relatively few attempts at modelling dam-break flows for mobile-bed rivers using 2D depth-averaged approaches in order to examine morphologic impacts on alluvial rivers. A search of the literature has yielded four studies: Dewals et al., 2002; Vasquez and Leal, 2006; Quanhong, 2009; and  Xia et al., 2010. This work is discussed below. 2.1.1 WOLF 2D MODEL The WOLF 2D model was developed by the University of Liege to solve 2D shallow-water equations on any evolutive grid, dealing with natural topography and mobile-beds. The sediment transport module in WOLF 2D assumes that only bedload transport occurs. This software suite was developed over a period of years to be an efficient analysis and optimization tool, and thus it features helpful graphical display techniques in powerful pre- and post-processing analyses (Dewals et al., 2002). To demonstrate the WOLF 2D model, Dewals et al. (2002) successfully applied it in the simulation of a hypothetical instantaneous and total failure of the large Eupen dam in Belgium. The focus of this study was to create functional risk maps, but the model was also able to monitor changes in bed topography due to erosion and deposition. This is particularly useful in monitoring how the morphology in an alluvial river changes over time after a sudden dam-break. While the accuracy of the model simulation of the Eupen dam is not stated by Dewals et al. (2002), the tone suggests that the results had an acceptable level of accuracy. During a simulation run, WOLF 2D is capable of displaying a 3D rendering of what is occurring at a specific location along the channel. This provides an additional perspective when trying to understand what is happening during the simulation. Figure 2-1 is a sample of the 3D rendering 11 capabilities of WOLF 2D. While this example is presented in black and white, coloured renderings are also possible.  Figure 2-1: 3D-view in WOLF 2D (Dewals et al., 2002; Courtesy of WIT Press from: Third International Conference Computer Simulation in Risk Analysis and Hazard Mitigation, Risk Analysis III, page 66) 2.1.2 RIVER2D-MORPHOLOGY MODEL River2D-Morphology (R2DM) is a 2D mobile-bed river morphology model developed as an extension of River2D (R2D), a fixed-bed hydrodynamic model (Vasquez et al., 2007; Steffler and Blackburn, 2002). Similar to WOLF 2D, sediment transport in R2DM also accounts only for bedload transport.  Vasquez and Leal (2006) used R2DM to simulate a sudden release of water from a reservoir into an initially wetted channel with a 90Β° bend, and used experimental results to assess the model simulations. R2DM was capable of simulating the concavity of the bed and the formation of bars. It was also capable of predicting water levels with reasonable accuracy when compared 12 to experimental results. However, since the downstream water level had to be fixed, the accuracy of results deteriorated over time (Vasquez and Leal, 2006). It should be noted that Vasquez and Leal's (2006) study involved an idealized rather than a real dam-break scenario. Water was only allowed to propagate along initially wetted channel cells and not on initially dry flood plain cells. Later testing by Vasquez and Roncal (2009) found that R2DM is not well suited to dam-break modelling in alluvial rivers due to the way that R2D handles wetting and drying of the bed. R2D always assumes that water moves over a pervious bed with a defined transmissivity, thus allowing some surface water to flow into an imaginary underlying aquifer when water depth decreases below a minimum low value. It was found that when the bed slope intersects the dam-break flood-wave, up to 100% of the incoming flood- wave could disappear into the aquifer. One possible solution to mitigate this was to reduce the groundwater transmissivity, but this caused numerical instabilities in River2D. As such, River2D-Morphology is not a candidate for use in researching morphologic change in alluvial rivers due to sudden dam-breaks. 2.1.3 QUANHONG’S MODEL Quanhong (2009) developed a 2D morphodynamic model for a PhD thesis. However, this model has only been verified for straight channels without bends. In terms of dam-break simulations, it has only been tested on ideal dam-break and laboratory partial dam-break scenarios. This model is not suitable for simulating sudden dam-breaks since it is an uncoupled model with simplified governing equations. Quanhong's (2009) approach appears to be similar to early renditions of River2D during its development. 2.1.4 XIA ET AL.’S MODEL Xia et al. (2010) developed a 2D morphodynamic model that accounts for suspended-load and bedload sediment transport. It is noteworthy that this model couples the computation of flow motion and sediment transport. To verify the model output, Xia et al. (2010) compared simulation data to existing numerical model outputs and experimental results. After the model was verified, it was used to simulate dam-break flows over a fixed-bed and then over a mobile-bed to examine the differences in 13 flood-wave speed and depth. Results indicated that dam-break flows behave substantially different over mobile-beds than over fixed-beds. Xia et al.'s (2010) findings justify the need to closely examine the differences between dam-break models with fixed-beds and mobile-beds. 2.1.5 CONCLUSIONS The only models used to date to simulate real-case dam-breaks are WOLF2D, which was discussed above, and TELEMAC2D, which will be discussed in a later section. WOLF2D is the only model that has truly been verified to simulate mobile-bed dam-breaks. However, its development and popularity pales in comparison to the TELEMAC suite of models. It is therefore proposed that the TELEMAC models, TELEMAC2D and SISYPHE, be used for this research to simulate mobile-bed dam-breaks. 2.2 SEDIMENT TRANSPORT EQUATIONS Dams are usually constructed on mountain streams, which are normally gravel-bed rivers. Since sediment starvation occurs downstream of dams, it is reasonable to assume that all rivers downstream of dams are gravel-bed. In gravel-bed rivers, bedload transport typically occurs at or slightly above the threshold of motion of the gravel sediment  (Mays, 1999). As a consequence, most bedload transport equations for gravel-bed rivers are designed and verified at relatively low non-dimensional bed shear stresses (πœβˆ—), and thus are unverified for cases of high πœβˆ—. However, during dam-break analysis, πœβˆ— will exceed the threshold of motion and, as a result, greatly exceed the intended and/or verified regions of validity for most bedload transport equations. It is, therefore, of interest to examine the degree to which the values of bed πœβˆ— developed during dam-break flows deviate from verified πœβˆ— regions. This examination will allow the selection of a suitable bedload transport relation to use during extreme flows. For the determination of morphologic change downstream of a dam-break, it is of great interest to know what other regimes of sediment transport may occur or dominate. Consequently, suspension criteria will also be briefly examined.  14 2.2.1 DAM-BREAK SHEAR STRESS ESTIMATES In order to determine the range of bed shear stresses (πœπ‘), PHOENICS, a 3D hydrodynamic model developed by CHAM, was employed to simulate a model previously created by Vasquez and Roncal (2009).  It should be noted that this simulation only examines shear stresses that develop because of immobile boundary (bed) conditions; hence, the output shear stresses may not necessarily be representative of what would happen in an actual dam-break. For the purpose of quantifying the approximate degree of πœβˆ— deviation, the condition of the mobile or immobile boundary is of no consequence.  It was found that under dam-break conditions, the maximum πœβˆ— was on the order of 10, a value 100 times greater than the typical gravel transport condition. A preliminary observation from plotting the computed πœβˆ— value on Parker’s Shields Diagram (Mays, 1999) in Figure 2-2 is that it plots much higher than the area specified for gravel-bed rivers. This indicates that under the dam-break scenario, flows are great enough to induce intense shear stresses. In addition, it can be deduced that the primary mode of sediment transport should be suspended-load transport since πœβˆ— plots above the boundary where the ratio of shear velocity (π‘’βˆ—) to settling velocity (𝑀) is 1.  Although the primary mode of sediment transport was determined to be suspension for the computed maximum value of πœβˆ—, a review of bedload sediment transport equations is still warranted, as a wide range of πœβˆ— was experienced by the river channel during the dam-break simulation. 15  Figure 2-2: Parker's Shields diagram (Mays, 1999; Β© The McGraw-Hill Companies, Inc., 1999, by permission) 2.2.2 REVIEW OF SELECT BEDLOAD TRANSPORT EQUATIONS A number of bedload transport equations were examined and underlying assumptions in their development and verified ranges of πœβˆ— compared. The purpose of comparing these bedload transport equations was to determine whether there exists a suitable π‘žβˆ— (non-dimensional transport rate) versus πœβˆ— relationship that has been verified for values of πœβˆ— up to 10. 2.2.2.1 ENGELUND AND FREDSOE EQUATION Equation 2-1: Engelund and Fredsoe (1976) equation π‘žβˆ— = 18.74(πœβˆ— βˆ’ πœπ‘ βˆ—) οΏ½πœβˆ— 1 2 βˆ’ 0.7πœπ‘ βˆ— 1 2οΏ½ πœπ‘ βˆ— = 0.05 16 This bedload transport equation was developed by first semi-empirically determining the motion of an immersed particle travelling as bedload. This allowed Engelund and Fredsoe (1976) to create a relationship between friction velocity (π‘’βˆ—) and mean transport velocity of particles moving as bedload (𝑒𝑏), which then further allowed them to relate 𝜏 βˆ— and π‘žβˆ—. The relationship developed assumed uniform grain size throughout the bed. This formulation was verified for various 𝑒𝑏 through laboratory experiments, where Meland and Normann (1966) used spherical glass beads moving over a bed of rhombohedrally packed spherical beads. Experiments were run where the beads travelling over the bed were larger, smaller, or the same size as the packed spherical beads. The verified range of πœβˆ— for Engelund and Fredsoe's (1976) formulation is 0.04 to 0.3, which covers the lower πœβˆ— range of the gravel-bed river region in Figure 2-2. 2.2.2.2 MEYER-PETER AND MULLER EQUATION Equation 2-2: Meyer-Peter and Muller (1948) equation π‘žβˆ— = 8(πœβˆ— βˆ’ πœπ‘ βˆ—) 3 2 πœπ‘ βˆ— = 0.047 The classic Meyer-Peter and Muller (1948) bedload transport equation was empirically developed through laboratory experiments in a rectangular flume. The experiments used a uniform grain size of 5.05 π‘šπ‘š and uniform flow conditions where friction slope equated to bed slope. Sediments of varying specific gravity were also used. Figure 2-3 shows the experimental data that was collected by Meyer-Peter and Muller (1948) in creating their transport relation. It is noted that they were able to verify the relation for a πœβˆ— range of 0.073 to 0.18. 17  Figure 2-3: Data collected by Meyer-Peter and Muller (1948) (Β© IAHR, 1948, by permission) 2.2.2.3 WONG AND PARKER EQUATION Equation 2-3: Modified Meyer-Peter and Muller equation (Wong and Parker, 2006) π‘žβˆ— = 4.93(πœβˆ— βˆ’ πœπ‘ βˆ—)1.6 πœπ‘ βˆ— = 0.047 Wong and Parker (2006) re-examined Meyer-Peter and Muller’s (1948) derivation of their bedload transport equation and proposed that an unnecessary bed roughness correction was applied to cases of plane-bed morphodynamic equilibrium. They also highlighted that the characterization of flow resistance using Nikaradse roughness height (𝐾𝑠) has been shown to be inappropriate in cases of mobile-bed rough conditions in rivers. Lastly, they proposed the incorporation of an improved correction of the boundary shear stress due to sidewall effects. Thus, Wong and Parker (2006) re-derived the Meyer-Peter and Muller (1948) formulation to create the Modified Meyer-Peter and Muller equation. 18 Figure 2-4 shows Wong and Parker’s (2006) fit of the same dataset from Meyer-Peter and Muller (1948). It can be observed that πœβˆ— is valid for the same range as the original Meyer-Peter and Muller (1948) method since no new data was used to verify this relationship.  Figure 2-4: Modified Meyer-Peter Muller relation (Wong and Parker, 2006; Β© ASCE, 2006, by permission) 2.2.2.4 WILSON EQUATION Equation 2-4: Wilson (1966) equation π‘žβˆ— = 12(πœβˆ— βˆ’ πœπ‘ βˆ—) 3 2 πœπ‘ βˆ— π‘“π‘œπ‘’π‘›π‘‘ π‘“π‘Ÿπ‘œπ‘š π‘ β„Žπ‘–π‘’π‘™π‘‘π‘  π‘‘π‘–π‘Žπ‘”π‘Ÿπ‘Žπ‘š The Wilson (1966) bedload transport relation is an empirical relation that was fit to high rates of bedload transport. In particular, this relation is used extensively to estimate the transport of sand and industrial materials in pressurized flows (EWRI, 2008). The range of πœβˆ— used to fit this relation was 0.5 to 10 (Cheng, 2002).  19 2.2.2.5 CHENG EQUATION Equation 2-5: Cheng (2002) equation π‘žβˆ— = 13πœβˆ— 3 2 expοΏ½βˆ’ 0.05 πœβˆ— 3 2 οΏ½ Cheng (2002) created this bedload transport equation by fitting a continuous exponential function through data collected by Meyer-Peter Muller (1948), Gilbert (1914), and Wilson (1966). The relation was fit to data over the range of πœβˆ— from 0.03 to 10 (Figure 2-5).  Figure 2-5: Cheng’s (2002) bedload transport relation (Β© ASCE, 2002, by permission) 2.2.2.6 PARKER EQUATION Equation 2-6: Parker (1979) equation π‘žβˆ— = 11.2(πœβˆ— βˆ’ 0.03)4.5 πœβˆ—3  20 According to EWRI (2008), Parker (1979) developed this relation as a simplified fit to the Einstein (1950) method for the range of πœβˆ— most likely to occur in gravel-bed rivers. This range of πœβˆ— is the same as that in Figure 2-2.  The verified range of πœβˆ— is thus 0.03 to 0.07, which makes Parker's (1979) relation reasonable to use for most gravel-bed rivers. Once again, however, this method only verifies a very minute portion of the dam-break range of πœβˆ—. 2.2.3 SUSPENSION The suspension boundary in Figure 2-2 was proposed by Bagnold (1966). He stated that a particle remains in suspension when turbulent eddies have vertical velocity components that exceed the particle fall velocity. After detailed studies were performed on turbulence, it was determined that the bed-shear velocity was on the same order as the maximum value of vertical turbulent velocity. Hence, Bagnold’s (1966) suspension criterion of π‘’βˆ— 𝑀 = 1 was formulated, where π‘’βˆ— is the bed-shear velocity, and 𝑀 is the particle fall velocity. Around the same time, Engelund (1965) developed a similar relation using a β€œrather crude” stability analysis (van Rijn, 1984). This criterion was also based on a ratio between π‘’βˆ— and 𝑀: π‘’βˆ— 𝑀 = 0.25. Reducing the value from 1 to 0.25 indicates that Engelund (1965) thought that suspension occurred at much lower πœβˆ— for a given sediment grain size. Finally, based on experimental research performed at Delft Hydraulics Laboratory (DHL, 1982), van Rijn (1984) developed a new set of suspension criteria that falls between the previous two criteria. He quantified the initiation of suspension as when the instantaneous upward turbulent motions of particles caused jump lengths of about 100 particle diameters. The developed suspension criteria were: π‘’βˆ— 𝑀 = 4 π·βˆ—  for 1 < π·βˆ— ≀ 10, and π‘’βˆ— 𝑀 = 0.4 for π·βˆ— > 10, where π·βˆ— = 𝐷50 οΏ½ (π‘ βˆ’1)𝑔 𝑣2 οΏ½ 1 3 is the dimensionless particle parameter. Figure 2-6 presents a comparison between the three different suspension criteria, where the vertical axis is πœβˆ—. The large variation between the suspension criteria is noteworthy because it indicates the need for more research into when the initiation of suspension actually occurs.  21  Figure 2-6: Criteria for the initiation of suspension (van Rijn, 1984; Β© ASCE, 1984, by permission) 2.2.4 DISCUSSION From the review of select bedload transport equations in Section 2.2.2, a trend is observed in that π‘žβˆ— is proportional to πœβˆ— 3 2. Consequently, for low values of πœβˆ—, the bedload transport relation can be approximated by π‘žβˆ— = π΅πœβˆ— 3 2, where 𝐡 is a coefficient used by each of the methods to fit the transport relation to their dataset. Figure 2-7 is a plot of the bedload transport relations reviewed in this paper for a wide range of πœβˆ—. It is apparent that all of the relations plot similar in shape and form, but with a vertical shift along the π‘žβˆ— axis. This shift is caused by the fact that each relation was created based on fits of different datasets.  22  Figure 2-7: Comparison of various bedload transport relations for a wide range of πœβˆ— In the lower πœβˆ— region of Figure 2-7, it is observed that π‘žβˆ— is very sensitive to the value of πœβˆ—. Therefore, slight differences in the fitting of bedload transport relations to different datasets can lead to dramatically different computed values of π‘žβˆ—. This may explain the variation in π‘žβˆ—, since most of the relations were verified based on small πœβˆ— values. Table 2-1 shows the validated πœβˆ— range of each reviewed bedload transport equation from Figure 2-7. Figure 2-8 is similar to Figure 2-7, except that only the verified values of πœβˆ— are plotted for each bedload transport relation. From the plot, it is observed that the relations developed by Wilson (1966) and Cheng (2002) have verified πœβˆ— ranges that are suitable for the computed πœβˆ— value due to dam-break flows (πœβˆ— on the order of 10). However, it should be noted that the data used to verify these bedload transport relations were from sand-bed rivers rather than gravel-bed rivers. Hence, the validity of these equations in gravel-bed rivers remains 23 questionable, even though the predicted π‘žβˆ— in Figure 2-7 falls between the relations of Engelund and Fredsoe (1976) and Meyer-Peter and Muller (1948).  Table 2-1: Valid πœβˆ— ranges of reviewed bedload transport equations Sediment Transport Relation Valid π‰βˆ— Range   Engelund and Fredsoe (1976) 0.04 to 0.3 Meyer-Peter and Muller (1948) 0.073 to 0.18 Wong and Parker (2006) 0.073 to 0.18 Wilson (1966) 0.5 to 10 Cheng (2002) 0.03 to 10 Parker (1979) 0.03 to 0.07   Figure 2-8: Comparison of various bedload transport relations for verified ranges of πœβˆ— Figure 2-6 shows a range of πœβˆ— where initiation of suspension occurs. However, each of the three suspension criteria have a different definition of what suspension actually is. Bagnold (1966) 24 and Engelund (1965) defined suspension as where a particle would remain suspended in the flow due to vertical velocity components of turbulent eddies, while van Rijn (1984) defined suspension as when particles jump, or saltate, 100 particle diameters. As such, it is not entirely clear when sediment becomes entrained as suspended-load, and a better definition of the initiation of suspended-load transport is required before attempting to integrate it into a morphological model. 2.2.5 CONCLUSIONS From the work of van Rijn (1984), since maximum πœπ‘ βˆ—  plots beyond all three suspension criteria (Figure 2-6) for the case of a catastrophic dam release, it can be concluded that sediments in that particular area of the simulated river will be transported in suspension. As such, none of the relations mentioned above for bedload transport and for grain flows apply. It is recommended that suspended-load transport relations be used in the case of extreme πœβˆ—.  Since a spectrum of πœβˆ— exists during a catastrophic dam release, the sediment transport regimes of bedload and suspended-load must both be considered together. For bedload transport, Cheng’s (2002) relation was verified for the largest range of πœβˆ—, and hence, ideally, it should be used to estimate bedload transport for all πœβˆ— values. The problem with the use of Cheng’s (2002) relation is that, being an average of multiple bedload transport relations, it does not incorporate the feature of πœπ‘ βˆ—. Thus, it would not be possible to vary the critical shear stress at which sediment transport is initiated. It is therefore proposed that, for the mobile-bed dam-break model constructed for this research, a combination Meyer-Peter and Muller (1948) and Wilson (1966) equation (Equation 2-7) be created, whereby each equation would be used for its known range of validity with a logarithmic interpolation bridging the two. This is demonstrated in Figure 2-9.   25 Equation 2-7: Proposed combination sediment transport equation π‘žβˆ— = ⎩ βŽͺ βŽͺ ⎨ βŽͺ βŽͺ ⎧ 8(πœβˆ— βˆ’ πœπ‘ βˆ—) 3 2                                                         πœβˆ— ≀ 0.18 8(0.18βˆ’ πœπ‘ βˆ—) 3 2  οΏ½ πœβˆ— 0.18 οΏ½ logοΏ½ 12(0.5βˆ’πœπ‘βˆ—) 3 2 8(0.18βˆ’πœπ‘ βˆ—) 3 2 οΏ½ logοΏ½ 0.5 0.18οΏ½               0.18 < πœβˆ— < 0.5 12(πœβˆ— βˆ’ πœπ‘ βˆ—) 3 2                                                       πœβˆ— β‰₯ 0.5   Figure 2-9: Proposed combination bedload transport equation   26 2.3 FLOOD PLAIN VEGETATION EFFECTS Simulating a dam-break flood over a mobile-bed requires consideration of the effect of varying levels of vegetation on sediment transport rates. To account for this effect, Li and Millar (2011) introduced the concept of partitioning roughness into grain and vegetation components. This leads to a partitioning of πœ™β€² and πœβˆ—, friction angle and bed shear stress respectively, whereby only the grain component (πœπ‘” βˆ—) of πœβˆ— would contribute to the transport of sediment. This is based on the work of Meyer-Peter and Muller (1948) and Einstein (1950), who partitioned shear stress into grain and form components. The partitioning of πœβˆ— yields two components: πœπ‘” βˆ—  and πœπ‘£ βˆ—. πœπ‘£ βˆ— is the portion of shear stress acting on any vegetation present, while πœπ‘” βˆ—  is the remainder of the shear stress acting upon the sediment responsible for inducing sediment transport. The presence of any appreciable amount of vegetation, hence πœπ‘£ βˆ—, would lead to a reduced portion of πœπ‘” βˆ—  available for sediment transport. This translates to a decrease in π‘žβˆ— as vegetation density increases. Another effect of vegetation is that its roots can hold and stabilize the soil around it. For sediment with no vegetative root networks, the value of πœ™β€² = 40Β° (the angle of repose of gravel sediment). As vegetation density increases, so does the stability of the sediment, and hence πœ™β€² would also increase. To represent this in a model, πœπ‘ βˆ— can be increased through the relation πœπ‘ βˆ— = 𝑐 π‘‘π‘Žπ‘›πœ™β€², where 𝑐 is a constant that can be determined by setting πœπ‘ βˆ— to πœπ‘ βˆ— of the sediment transport equation being used, and πœ™β€² = 40Β° represents no vegetation being present.   The concept of partitioning πœβˆ— and varying πœπ‘ βˆ— based on varied levels of vegetation is incorporated into the 2D mobile-bed dam-break model developed.    27 3 MODELLING METHODOLOGY 3.1 TELEMAC VERSION 6.1 After more than a decade of development, Hervouet and Petitjean (1999) used TELEMAC2D to model the Malpasset dam failure of 1959. What was unique about the Malpasset dam-break was the availability of parameters such as flood-wave travel time and high-water marks for validating physical and numerical models. The fixed-bed model that Hervouet and Petitjean (1999) created to simulate this dam-break yielded valid results. Yet they did not perform a mobile-bed dam-break analysis even though SISYPHE, a sediment transport module, could be coupled with TELEMAC2D to perform such an analysis. The research in this thesis takes the work of Hervouet and Petitjean (1999) one step further and incorporates sediment transport into their Malpasset dam-break model.  TELEMAC2D is a 2D hydrodynamic model that is part of the TELEMAC suite of models developed by ElectricitΓ© de France (EDF). This suite also contains a 2D sediment transport module that can be coupled with TELEMAC2D. With this tool it would be simple to convert the Malpasset dam-break simulation from a fixed-bed model to a mobile-bed model. Another advantage of the TELEMAC suite of models is that the source code is available and can be modified.  The TELEMAC suite of models was initially built at ElectricitΓ© de France (EDF) for dimensioning and impact studies. In 2010, TELEMAC became open source after 17 years of commercial distribution in order to improve access by consultants and researchers. The suite of models and a support forum can now be accessed at http://www.opentelemac.org.  The TELEMAC system contains a wide range of models to simulate free surface flows in a variety of conditions. These are listed below: β€’ TELEMAC2D: 2D hydrodynamics using Saint-Venant equations β€’ TELEMAC3D: 3D hydrodynamics using Navier-Stokes equations β€’ ARTEMIS: Hydrodynamics of waves in harbours β€’ TOMAWAC: Hydrodynamics of costal wave propagation β€’ SISYPHE: 2D sediment transport of bedload and suspended load 28 β€’ SEDI-3D 3D sediment transport of suspended load β€’ ESTEL-2D: 2D groundwater flow β€’ ESTEL-3D: 3D groundwater flow All of the models listed above can be run as coupled models. To simulate a dam-break flood over a mobile-bed, TELEMAC2D was coupled with SISYPHE to perform a morphodynamic simulation of a dam-break. TELEMAC2D and SISYPHE would interact at every timestep to update the bed elevation of the flood plain and channel for the next hydrodynamic computation. The reason behind using these TELEMAC models is that Hervouet and Petitjean (1999) have applied TELEMAC2D, with fixed-bed assumptions, to simulate a real-case dam-break flood, the Malpasset dam failure of 1959. TELEMAC is versatile because it is open source and because all computations are coded as separate modules that can be easily modified. Overall, TELEMAC was chosen due to its versatility and because it has been verified as a means of simulating real- case dam-breaks. 3.1.1 TELEMAC2D 3.1.1.1 HYDRODYNAMICS This is the 2D hydrodynamic model of the TELEMAC suite. This code solves the depth- averaged shallow water Saint-Venant equations that follow (EDF, 2010): Equation 3-1: Continuity πœ•β„Ž πœ•π‘‘ + 𝑒 βˆ™ βˆ‡οΏ½βƒ— (β„Ž) + β„Ž 𝑑𝑖𝑣(𝑒�⃗ ) = π‘†β„Ž Equation 3-2: Momentum along 𝒙 πœ•π‘’ πœ•π‘‘ + 𝑒�⃗ βˆ™ βˆ‡οΏ½βƒ— (𝑒) = βˆ’π‘” πœ•π‘ πœ•π‘₯ + 𝑆π‘₯ + 1 β„Ž 𝑑𝑖𝑣(β„Žπœˆπ‘‘βˆ‡οΏ½βƒ— 𝑒) Equation 3-3: Momentum along π’š πœ•π‘£ πœ•π‘‘ + 𝑒�⃗ βˆ™ βˆ‡οΏ½βƒ— (𝑣) = βˆ’π‘” πœ•π‘ πœ•π‘¦ + 𝑆𝑦 + 1 β„Ž 𝑑𝑖𝑣(β„Žπœˆπ‘‘βˆ‡οΏ½βƒ— 𝑣) 29 Where: β€’ β„Ž = depth of water (π‘š) β€’ 𝑒, 𝑣 = velocity components (π‘š/𝑠) β€’ 𝑔 = gravity acceleration (π‘š/𝑠2) β€’ πœˆπ‘‘ = momentum diffusion coefficient (π‘š2/𝑠) β€’ 𝑍 = free surface elevation (π‘š) β€’ 𝑑 = time (𝑠) β€’ π‘₯, 𝑦 = horizontal space coordinates (π‘š) β€’ π‘†β„Ž = source of sink of fluid (π‘š/𝑠) β€’ 𝑆π‘₯, 𝑆𝑦 = source or sink terms in dynamic equations (π‘š/𝑠2) Turbulent viscosity may be specified or determined by a model through the transport of turbulent quantities π‘˜ (turbulent kinetic energy) and πœ€ (turbulent dissipation). The equations are as follows: Equation 3-4: Transport of π’Œ and 𝜺 (a) πœ•π‘˜ πœ•π‘‘ + 𝑒�⃗ βˆ™ βˆ‡οΏ½βƒ— (π‘˜) = 1 β„Ž 𝑑𝑖𝑣 οΏ½β„Ž πœˆπ‘‘ πœŽπ‘˜ βˆ‡οΏ½βƒ— π‘˜οΏ½+ 𝑃 βˆ’ πœ€ + π‘ƒπ‘˜π‘£ Equation 3-5: Transport of π’Œ and 𝜺 (b) πœ•πœ€ πœ•π‘‘ + 𝑒�⃗ βˆ™ βˆ‡οΏ½βƒ— (πœ€) = 1 β„Ž 𝑑𝑖𝑣 οΏ½β„Ž πœˆπ‘‘ πœŽπœ€ βˆ‡οΏ½βƒ— πœ€οΏ½+ πœ€ π‘˜ (𝑐1πœ€π‘ƒ βˆ’ 𝑐2πœ€πœ€) + π‘ƒπœ€π‘£ After completing a computation, TELEMAC2D is able to output β„Ž (water depth), 𝑒 (velocity in the π‘₯-direction), and 𝑣 (velocity in the 𝑦-direction) at each node. For a coupled model, this output is then fed into SISYPHE to calculate bed evolution. 3.1.1.2 COMPUTATIONAL OPTIONS IMPLEMENTED A sample input file for TELEMAC2D is provided in APPENDIX A. Refer to EDF’s (2010) TELEMAC2D manual for a translation and description of the computational options implemented. APPENDIX C contains fortran-coded scripts that were modified or created for TELEMAC2D or SISYPHE to enable the simulation of mobile-bed dam-break modelling. 30 3.1.2 SISYPHE 3.1.2.1 MOBILIZATION OF THE BED The volume of sediment transported is computed through the Exner equation: Equation 3-6: Exner Equation (1βˆ’ 𝑛) πœ•π‘π‘“ πœ•π‘‘ + 𝑑𝑖𝑣�𝑄𝑏����⃗ οΏ½ = 0  Where: β€’ 𝑍𝑓 = bed elevation (π‘š) β€’ 𝑄𝑏 = bedload transport per unit width (π‘š2/𝑠) β€’ 𝑛 = porosity β€’ 𝑑 = time (𝑠) 3.1.2.2 SEDIMENT TRANSPORT EQUATION Modifications to the sediment transport code were made to implement a combination Meyer- Peter and Muller (1948) and Wilson (1966) equation and to incorporate the effect of vegetation on the sediment transport rate.  As stated in previous sections, the Meyer-Peter and Muller (1948) and Wilson (1966) equations have different ranges of πœβˆ— for which πœβˆ— has been validated, πœβˆ— = 0.073 to 0.18 and πœβˆ— = 0.5 to 10 respectively. Thus, this dam-break model implements the Meyer-Peter and Muller (1948) equation for πœβˆ— ≀ 0.18 and the Wilson (1966) equation for πœβˆ— β‰₯ 0.5. For the πœβˆ— range of 0.18 to 0.5, a logarithmic interpolation is used to bridge the two equations. Since the Meyer-Peter and Muller (1948) equation is used at the lower bounds of πœβˆ—, it is assumed that πœπ‘ βˆ— = 0.047. The following are the sediment transport equations implemented in the SISYPHE code: Equation 3-7: Meyer-Peter and Muller (1948) equation π‘žβˆ— = 8(πœβˆ— βˆ’ πœπ‘ βˆ—) 3 2 31 Equation 3-8: Logarithmic interpolation between Meyer-Peter and Muller (1948) and Wilson (1966) π‘žβˆ— = 8(0.18βˆ’ πœπ‘ βˆ—) 3 2  οΏ½ πœβˆ— 0.18 οΏ½ logοΏ½ 12(0.5βˆ’πœπ‘βˆ—) 3 2 8(0.18βˆ’πœπ‘ βˆ—) 3 2 οΏ½ logοΏ½ 0.5 0.18οΏ½  Equation 3-9: Wilson (1966) equation π‘žβˆ— = 12(πœβˆ— βˆ’ πœπ‘ βˆ—) 3 2 To account for the effect of vegetation on the sediment transport rate, πœβˆ— is partitioned into πœπ‘” βˆ—  and πœπ‘£ βˆ— components, and πœπ‘ βˆ— is adjusted based on πœ™β€². The shear stress partitioning is accomplished through Li and Millar’s (2011) shear stress partitioning equation: Equation 3-10: Li and Millar’s (2011) shear stress partitioning πœπ‘” βˆ— = πœβˆ— 𝑛𝑔 �𝑛𝑔2 + 𝑛𝑣2οΏ½ 1 2  Where: β€’ 𝑛𝑔  = Manning’s grain roughness β€’ 𝑛𝑣  = Manning’s vegetation roughness Adjustments of πœπ‘ βˆ— are accomplished by assuming that πœπ‘ βˆ— = 𝑐 π‘‘π‘Žπ‘›πœ™β€², where 𝑐 is a constant, and that sediment with no vegetation influence has πœ™β€² = 40Β°. Since πœπ‘ βˆ— = 0.047 for conditions with no vegetation (Meyer-Peter and Muller, 1948), then 𝑐 = 0.056. πœβˆ— can then be calculated for increasing πœ™β€², which corresponds to increasing levels of vegetation.  Adjustments to πœπ‘ βˆ— are limited to the top 1 π‘š of the original bed elevation. The assumption was made that vegetation would only affect the top 1 π‘š of sediment, and thus, when this top layer of sediment is eroded away, πœπ‘ βˆ— reverts to a value with no vegetation influence (0.047). Any sediment deposited on top of the original bed elevation is also assumed not to be influenced by vegetation and has a πœπ‘ βˆ— = 0.047.  32 A similar scheme is used to adjust Manning’s roughness. In regions where vegetation is present, 𝑛 = �𝑛𝑣 2 + 𝑛𝑔 2οΏ½ 0.5  in only the top 1 π‘š of sediment. After sediment is eroded past the top 1 π‘š from the original bed elevation, or if sediment is deposited on top of the original bed elevation, 𝑛 = 𝑛𝑔. 3.1.2.3 VERTICAL AND SPATIAL VARIATION OF SEDIMENT AND RIGID BOUNDARY In SISYPHE, it is possible to vertically stratify and spatially vary sediment by specifying up to 10 different sediment layers at each node. Each of these layers can be assigned different 𝑑50, 𝑛, πœ™β€², πœπ‘ βˆ—, and thickness. SISYPHE also has a subroutine to define bedrock elevation, or the rigid boundary; however, this may cause simulations to become unstable. As a remedy to these possible instabilities, it was found that defining one sediment layer with πœπ‘ βˆ— = ∞ effectively makes it into a rigid boundary. The solution was implemented for all simulations run for this research. 3.1.2.4 COMPUTATIONAL OPTIONS IMPLEMENTED A sample input file for TELEMAC2D is provided in APPENDIX B. Refer to EDF’s (2010) SISYPHE manual for a translation and description of the computational options implemented. APPENDIX C contains fortran-coded scripts that were modified or created for TELEMAC2D or SISYPHE to enable the simulation of mobile-bed dam-break modelling. 3.2 MODEL VALIDATION To verify that TELEMAC2D outputs reasonable hydrodynamic results and that TELEMAC2D coupled with SISYPHE outputs reasonable morphodynamic results for the case of sudden dam- breaks, a series of models were created to simulate experiments run by Soares-Frazao and Zech (2002), Vasquez and Leal (2006), and Vasquez (2005).  3.2.1 SOARES-FRAZAO AND ZECH (2002) Soares-Frazao and Zech (2002) conducted a laboratory experiment to simulate how water would flow along a sharp 90Β° bend during a sudden dam-break style release from an upstream reservoir. This set-up consisted of a rectangular reservoir filled with water that was suddenly 33 released into a plastic channel containing a sharp 90Β° bend. Figure 3-1 shows a schematic of the experimental set-up. Velocity of the fluid particles was measured using the Voronoi digital imaging technique, and water level measurements were taken at various times over the course of the experiment. This experimental data was used to validate a 2D hydrodynamic model that Soares-Frazao and Zech (2002) had created.   Figure 3-1: Soares-Frazao and Zech’s (2002) experimental set-up (Β© ASCE, 2002, by permission) To verify the TELEMAC2D’s hydrodynamic outputs, a model with Soares-Frazao and Zech's (2002) specifications was created. A graphical comparison of the simulated water level was made in Figure 3-2 at 𝑑 = 3, 5, 7 and 14 𝑠 between Soares-Frazao and Zech's (2002) model and the TELEMAC2D model, which showed that both were in relatively good agreement.  34  Figure 3-2: Graphical comparison of water levels between Soares-Frazao and Zech's (2002) model and TELEMAC2D output. The left part shows Soares-Frazao and Zech’s (2002) simulated water levels, and the right part shows TELEMAC2D simulated water levels. (left part Β© ASCE, 2002, by permission) A graphical comparison of the velocity field of the bend at 𝑑 = 7 𝑠 was then made between the model output from the Soares-Frazao and Zech (2002) and the TELEMAC2D models as shown in Figure 3-3, and between the measured experimental results and TELEMAC2D model output as shown in Figure 3-4. It is apparent that both models are in reasonable agreement with the experimental results. Therefore, it is verified that TELEMAC2D outputs reasonable hydrodynamic results in this situation. 35  Figure 3-3: Graphical comparison of velocity field between Soares-Frazao and Zech's (2002) model and TELEMAC2D output (left part Β© ASCE, 2002, by permission)  Figure 3-4: Graphical comparison of velocity field between Soares-Frazao and Zech's (2002) experimental results and TELEMAC2D output (left part Β© ASCE, 2002, by permission) 3.2.2 VASQUEZ AND LEAL (2006) Leal et al. (2002) performed dam-break experiments in a rectangular flume that contained a stepped sediment-filled bed and a lift-gate in the middle. Figure 3-5 shows the initial conditions of the experiment. Vasquez and Leal (2006) used the results from two sets of initial conditions, detailed in Table 3-1, to compare with the output of River2D. 36  Figure 3-5: Initial conditions of Leal et al.'s (2002) experiments (Vasquez and Leal, 2006; Β© Jose Vasquez, 2006, by permission) Table 3-1: Initial conditions of Leal et al.'s (2002) experiments Test 𝒉𝒖 (m) 𝒉𝒅 (m) 𝒉𝒔𝒖 (m) 𝒉𝒔𝒅 (m) Ts.25 0.400 0.000 0.190 0.071 Ts.28 0.400 0.075 0.190 0.071  With the same initial conditions and model parameters as Leal et al.’s (2002) experimental set- up, the two tests were run in TELEMAC2D coupled with SISYPHE. Water surface elevations and bed elevations are compared at 𝑑 = 1 and 4 𝑠 in Figure 3-6 and Figure 3-7. The TELEMAC results appear to be in relatively good agreement with River2D and the experimental results. Thus, it is verified that a mobile-bed dam-break simulation in TELEMAC2D coupled with SISYPHE produces realistic and valid morphodynamic results. 37  Figure 3-6: Experimental and simulated results for experiment Ts.25 (Β© Jose Vasquez, 2006, adapted by permission) 38  Figure 3-7: Experimental and simulated results for experiment Ts.28 (Β© Jose Vasquez, 2006, adapted by permission) 39 3.2.3 VASQUEZ (2005) Accounting for secondary flows in morphodynamic simulations would yield significantly different bed topography where a channel meanders or bends. A subroutine exists in SISYPHE to account for such secondary flow effects. This subroutine was validated by simulating the Laboratory of Fluid Mechanics (LFM) experiment consisting of a long flume that has a 180Β° bend as shown in Figure 3-8.  Figure 3-8: LFM secondary flow experiment (Β© Jose Vasquez, 2005, by permission) A TELEMAC2D coupled with SISYPHE steady-state simulation was run to examine morphodynamics accounting for secondary flow effects. The parameters used in the numerical experiment were 𝑄 = 170 𝐿/𝑠, β„Ž = 20 π‘π‘š, 𝑆 = 0.18 %, 𝐷50 = 0.78 π‘šπ‘š, and π‘˜ = 0.083. A comparison of modelled and experimental results, shown in Figure 3-9, suggests that the secondary flow correction built into SISYPHE does not fully capture the effect on morphology. However, it is not expected that morphodynamic evolution of the bed as a result of secondary 40 flow effects would dominate in the case of sudden dam-breaks. Therefore, the secondary flow correction in SISYPHE is considered adequate for the purposes of creating a 2D mobile-bed dam-break model.   Figure 3-9: Comparison of model outputs and experimental results of secondary flow effects on LFM flume experiment for left and right banks (Β© Jose Vasquez, 2005, adapted by permission)   41 4 CASE STUDY: INPUT DATA AND MODELLING ASSUMPTIONS 4.1 STUDY SITE: MALPASSET DAM, FRANCE 4.1.1 BACKGROUND The Malpasset dam failed explosively at 9:14 p.m. on December 2, 1959. This dam, built for irrigation and water storage, was located in a narrow gorge of the Reyran River approximately 12 π‘˜π‘š upstream of Frejus, France. It was a double-curvature arch dam with a maximum height of 66.5 π‘š and a crest length of 223 π‘š. The reservoir could store a maximum of 55 π‘₯ 106 π‘š3 (Hervouet, 2000; Hervouet and Petitjean, 1999). In the days preceding November 30, 1959, the reservoir had been filling slowly, but, due to exceptionally heavy rains, the last 4 π‘š were filled in three days. In response, the dam operators opened the bottom outlet gate at 6 p.m. on December 2 to prevent the dam from overtopping. Although this strategy was correct, the dam still failed following a violent trembling of the ground and a brief rumble. A massive flood-wave surged from the gorge and overran inhabited areas near Frejus. The Malpasset disaster caused 433 casualties (Hervouet, 2000; Hervouet and Petitjean, 1999). Engineering investigations after the accident showed that the reasons for the Malpasset dam failing were the pore pressure in the rock, the nature of the rock, and a geotechnical fault downstream of the dam. As the water level in the reservoir increased, the increased load caused the arch to separate from its foundation and rotate about its upper right end. Parts of the dam collapsed as this occurred (Hervouet, 2000; Hervouet and Petitjean, 1999). This disaster is an example of a catastrophic-type dam-break with a nearly instantaneous breach. As far as modelling considerations are concerned, this would be the worst-case scenario to model for dam-break analyses, yielding maximum high-water marks and maximum scouring of the channel bed and flood plain.  This disaster also supports the notion that it might be unreasonable to model dam-breaks with the fixed-bed assumption. The dam-break flood-wave eroded into the flood plain alluvium, and a wide, poorly defined channel developed, thus altering the morphology of the lower slopes and 42 bottom of the Reyran Valley. Post-dam-break investigators that visited the Reyran Valley witnessed undercut bridge abutments and pieces of the dam deposited far downstream, further exemplifying the morphologic changes that had occurred (Hervouet, 2000; Hervouet and Petitjean, 1999).  Because the Malpasset dam-break was an example of a sudden and catastrophic dam-break, and because there was clear evidence that extreme sediment transport processes were involved, this presents a well-documented case study to test the use of a 2D mobile-bed dam-break model. 4.1.2 MALPASSET DAM-BREAK MODEL To test the capabilities of the TELEMAC2D hydrodynamic model, Hervouet and Petitjean (1999) modelled the Malpasset dam-break with a fixed-bed simulation. It utilized the pre-event topography in generating the rather high-resolution bottom-elevation mesh, with mesh sizes ranging from 2 π‘š to 150 π‘š, 53081 nodes, and 104000 elements (Figure 4-1). To simulate the sudden dam-break, the water level in the reservoir was initialized to an elevation yielding a 55 π‘š high wall of water at the location of the dam. This wall of water was instantaneously released into the valley when the simulation started. Calibration of the fixed-bed model indicated that setting a Manning’s 𝑛 = 0.033 across the entire domain would be appropriate to sufficiently match multiple recorded high-water marks and transit times between two transformers. This model is now available to the public at www.opentelemac.org in the TELEMAC validation cases package. Using the Hervouet and Petitjean (1999) TELEMAC2D model as a base fixed-bed model, the SISYPHE module, subsequent subroutines and simulation options (section 3.1) were appended to create a new mobile-bed model of the Malpasset dam-break. It would have been ideal to be able to calibrate this new mobile-bed model of the Malpasset dam-break, but post-dam-break topographical data was not available as no post-dam-break survey had been performed. Thus, it was decided that a sensitivity analysis be run to examine differences in inundation and flood- wave characteristics (such as propagation time and maximum wave-heights). 43  Figure 4-1: Malpasset dam-break model topography mesh (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Malpasset Dam Frejus Mediterranean Sea Reservoir 44 4.2 SENSITIVITY ANALYSIS PARAMETERS After an extensive literature search and consultations with both Institut GΓ©ographique National (IGN) and Bureau de Recherches GΓ©ologiques et MiniΓ¨res (BRGM), very little to no information about grain sizes and alluvium thicknesses (depth to bedrock) could be found. As a result, these parameters, coupled with the parameters of grain roughness, vegetation roughness, and friction angle, were varied in a sensitivity analysis to examine differences in inundation and flood-wave characteristics for both the mobile-bed and fixed-bed simulations. 4.2.1 MEAN GRAIN SIZE (𝑑50) Table 4-1 lists the mean grain sizes that were considered reasonable ranges for the Reyran River and its flood plain. Table 4-1: Sensitivity parameter - mean grain sizes Aggregate Class π’…πŸ“πŸŽ (π’Žπ’Ž) Coarse Sand 1 Fine Gravel 5 Medium Gravel 10 Coarse Gravel 20 Very Coarse Gravel 40  4.2.2 DEPTH TO BEDROCK (𝑑𝑏) Table 4-2 lists the alluvium thicknesses (depths to bedrock) that were assumed throughout the whole domain for each sensitivity iteration. Table 4-2: Sensitivity parameter - depth to bedrock 𝒅𝒃 (π’Ž) 0 2 5 10 15  45 4.2.3 GRAIN ROUGHNESS (𝑛𝑔) Table 4-3 lists the grain roughnesses in the form of Manning’s 𝑛, which encompasses the fixed- bed calibrated roughness of 𝑛𝑔 = 0.033. This will ensure that a somewhat realistic result is produced even with the influence of mobile-bed processes. Table 4-3: Sensitivity parameter - grain roughness π’π’ˆ 0.025 0.030 0.035  4.2.4 VEGETATION ROUGHNESS (𝑛𝑣) AND FRICTION ANGLE (πœ™β€²) Table 4-4 lists the vegetation roughness and friction angle combinations that range from no vegetation to heavy vegetation. This allows the examination of vegetation influences on sediment transport. Total roughness was computed using 𝑛 = �𝑛𝑔 2 + 𝑛𝑣 2οΏ½ 0.5 , which allows for the shear stress partitioning where πœβˆ— = πœπ‘” βˆ— + πœπ‘£ βˆ—. Table 4-4: Sensitivity parameter - vegetation density Vegetation Density 𝒏𝒗 𝝓′ None 0.000 40 Light 0.033 49 Medium 0.067 60 Heavy 0.090 70  4.2.4.1 DELINEATION OF VEGETATED AND URBANIZED ZONES Vegetated zones were delineated from 1959 IGN aerial photographs of the Frejus area. A similar exercise was completed for urbanized areas. To avoid the complexity of determining calibrated roughnesses and friction angles for buildings and urban infrastructure, it was decided that urbanized areas would be treated as vegetated zones. To simplify this further, vegetated and urbanized zones would be assigned a uniform global 𝑛𝑣 and πœ™β€² for each simulated sensitivity iteration. Figure 4-2 shows the delineated vegetated and urbanized regions in red. As noted in 46 Section 3.1.2.2, the vegetation effects are limited to the top 1 π‘š of sediment. After the top 1 π‘š of sediment has been eroded away, the roughness and friction angle revert to the base values of 𝑛𝑔 of the specific scenario and 40Β°, respectively.  47  Figure 4-2: Vegetated and urbanized zones (aerial photograph of Frejus [3544-3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) Malpasset Dam Frejus Mediterranean Sea Reservoir 48 5 RESULTS AND ANALYSIS The flood plain inundation is examined using two approaches. The first is the high-water mark left by the propagation of the dam-break flood-wave towards the Mediterranean Sea; this is output by the transient simulations. The second is the extent of inundation during a mean annual flood event in the Reyran River, arbitrarily assumed to be 100 π‘š3/𝑠 due to a lack of available hydrological data; this is output by the steady-state simulations. The steady-state simulations were run for a limited number of scenarios with varying degrees of vegetation as a proof-of- concept trial. The two methods combined paint a clear picture of how varying each of the sensitivity parameters would affect inundation. The main method of examining flood-wave characteristics is by measuring the travel time for the flood-wave to reach the Mediterranean Sea and the distance the flood-wave has propagated at a certain time (30 minutes in this case). There is no need to examine maximum wave-height as this is accounted for by examining the HWMs left by the propagating dam-break flood-wave. The change in morphology is quantified by comparing initial and final bed elevations at a sample of cross-sections and by looking at 2D plots of bed evolution for different simulations. This will help quantify morphological change due to the variation of sensitivity parameters. Figure 5-1 shows the location of seven cross-sections where HWMs and final bed elevations will be compared. Figure 5-2 shows the location of the 2D plots of bed evolution. 49  Figure 5-1: Cross-sections (aerial photograph of Frejus [3544-3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) Malpasset Dam Frejus Mediterranean  Reservoir 1   21   31   41   51   61   71   50  Figure 5-2: Location of 2D bed elevation plot of evolution (aerial photograph of Frejus [3544-3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) Malpasset Dam Frejus Mediterranean Sea Reservoir 51 5.1 EFFECT OF VARYING GRAIN ROUGHNESS The grain roughness (𝑛𝑔) was varied with the values in Table 4-3 for both mobile-bed and fixed- bed simulations. HWM and bed change were compared at the seven cross-sections (Figure 5-1) for both simulation types, and the 2D bed evolution at the location in Figure 5-2 was examined for only the mobile-bed cases. Flood-wave propagation times were then compared for both the mobile-bed and fixed-bed simulations. Only one set of results is presented for the comparison of cross-sections and 2D plots of bed evolution, but similar results are replicated when comparing scenarios with differing levels of vegetation and 𝑑50. A full set of results is presented for flood-wave propagation time, as the number of plots is more manageable. 5.1.1 CROSS-SECTIONS OF HIGH-WATER MARKS AND BED CHANGE The set of fixed-bed simulations used constant values of the following parameters: 𝑛𝑣 = 0.000, and 𝑑 = 2 β„Žπ‘œπ‘’π‘Ÿπ‘ . To test the effect of grain roughness on high water levels, the value of 𝑛𝑔 is varied among the three values of 0.025, 0.030, and 0.035. All of the cross-sections also display the original bed elevation (before dam-break) as a basis for comparison. Results demonstrate that varying 𝑛𝑔 does have a significant effect on the HWM for fixed-bed simulations. As 𝑛𝑔 increases, the HWM (Figure 5-3, Figure 5-5, Figure 5-7, Figure 5-9, Figure 5-11, Figure 5-13, Figure 5-15) decreases in cross-sections 1 and 2 and in parts of 3, 4, 5, and 6, and increases in cross-section 7 and in parts of 3, 4, 5, and 6. The largest HWM difference was found to be a decrease of 5.4 π‘š when 𝑛𝑔 increased from 0.025 to 0.035 in cross- section 2. The set of mobile-bed simulations used constant values of the following parameters: 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, 𝑑𝑏 = 2 π‘š, and 𝑑 = 2 β„Žπ‘œπ‘’π‘Ÿπ‘ . To test the effect of grain roughness on high water levels, the value of 𝑛𝑔 is varied among the three values of 0.025, 0.030, and 0.035. All of the cross-sections also display the original bed elevation (before dam-break) as a basis for comparison. 52 Results demonstrate that varying 𝑛𝑔 does have a significant effect on the HWM for mobile-bed simulations. As 𝑛𝑔 increases, the HWM (Figure 5-4, Figure 5-6, Figure 5-8, Figure 5-10, Figure 5-12, Figure 5-14, Figure 5-16) decreases in cross-section 1 and in parts of 2, 3, 4, 5, and 6, and increases in cross-section 7 and in parts of 2, 3, 4, 5, and 6. The largest HWM difference was found to be a decrease of 5.5 π‘š when 𝑛𝑔 increased from 0.025 to 0.035 in cross- section 2. The effect of 𝑛𝑔 on bed elevation is not discernible using this method of comparing cross-sections. The maximum change in HWM and bed elevation when comparing fixed-bed and mobile-bed simulations with the same 𝑛𝑔 was found to be 3.1 π‘š and 78.9 π‘š, respectively. Comparing the fixed-bed and mobile-bed HWM for each cross-section (Figure 5-3 to Figure 5-16) shows that the high water levels are relatively unaffected whether the dam-break is simulated with a fixed- or mobile-bed.    53  Figure 5-3: HWM at cross-section 1 varying 𝑛𝑔 on a fixed-bed  Figure 5-4: HWM and bed elevation at cross-section 1 varying 𝑛𝑔 on a mobile-bed 54  Figure 5-5: HWM at cross-section 2 varying 𝑛𝑔 on a fixed-bed  Figure 5-6: HWM and bed elevation at cross-section 2 varying 𝑛𝑔 on a mobile-bed 55  Figure 5-7: HWM at cross-section 3 varying 𝑛𝑔 on a fixed-bed  Figure 5-8: HWM and bed elevation at cross-section 3 varying 𝑛𝑔 on a mobile-bed 56  Figure 5-9: HWM at cross-section 4 varying 𝑛𝑔 on a fixed-bed  Figure 5-10: HWM and bed elevation at cross-section 4 varying 𝑛𝑔 on a mobile-bed 57  Figure 5-11: HWM at cross-section 5 varying 𝑛𝑔 on a fixed-bed  Figure 5-12: HWM and bed elevation at cross-section 5 varying 𝑛𝑔 on a mobile-bed 58  Figure 5-13: HWM at cross-section 6 varying 𝑛𝑔 on a fixed-bed  Figure 5-14: HWM and bed elevation at cross-section 6 varying 𝑛𝑔 on a mobile-bed 59  Figure 5-15: HWM at cross-section 7 varying 𝑛𝑔 on a fixed-bed  Figure 5-16: HWM and bed elevation at cross-section 7 varying 𝑛𝑔 on a mobile-bed 60 5.1.2 2D BED EVOLUTION Although the effect of varying 𝑛𝑔 on bed elevation was indiscernible using the previous cross- sections, the effect of increasing 𝑛𝑔 is clearly demonstrated in the 2D bed evolution plots (Figure 5-17, Figure 5-18, and Figure 5-19). As 𝑛𝑔 is increased, the zones of significant erosion (blue) and deposition (red) shrink. This indicates that πœβˆ— experienced by the bed decreases as 𝑛𝑔 is increased. 61  Figure 5-17  Figure 5-18 62  Figure 5-19 Figure 5-17: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-18: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-19: Bed evolution of case where: 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission)   63 5.1.3 FLOOD-WAVE PROPAGATION TIME 5.1.3.1 MOBILE-BED SIMULATIONS Figure 5-20 to Figure 5-23 show the extent that the dam-break flood-wave has propagated after 𝑑 = 30 π‘šπ‘–π‘› with assumptions of no vegetation to heavy vegetation for a mobile-bed. As the effect of vegetation increases, it can be observed that the distance travelled by the flood-wave after 𝑑 = 30 π‘šπ‘–π‘› decreases; this is due to the increase in friction experienced by the flood-wave. Regardless of the effect of vegetation, it is observed that as 𝑛𝑔 increases, the distance propagated by the flood-wave decreases. The figures below show this to be true for all levels of vegetation. The reason for the presence of the streak patterns found in Figure 5-20 and other figures alike, is that aerial photography was not readily available for the entire region. Aerial photograph coverage was found only for areas affected by the Malpasset dam-break. The streak patterns are a result of the photo software used to stitch together more than one hundred aerial photographs.  64  Figure 5-20  Figure 5-21 65  Figure 5-22  Figure 5-23 66 Figure 5-20: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-21: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑣 = 0.033, πœ™β€² = 49Β°, and 𝑑50 = 1 π‘šπ‘š (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-22: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑣 = 0.067, πœ™β€² = 60Β°, and 𝑑50 = 1 π‘šπ‘š (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-23: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑣 = 0.090, πœ™β€² = 70Β°, and 𝑑50 = 1 π‘šπ‘š (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission)   67 Table 5-1 tabulates the time it takes for the dam-break flood-wave to reach the Mediterranean Sea with varied sensitivity parameters. Selecting and holding constant values of 𝑛𝑣, πœ™β€², and 𝑑50, then comparing different values of 𝑛𝑔 consistently yields the conclusion that increasing 𝑛𝑔 will lead to an increase in propagation time. Plotting 𝑑 (propagation time) versus 𝑛 (total roughness) for varying grain roughnesses (Figure 5-24) reveals that 𝑑 is a function of 𝑛 for each case of 𝑛𝑔, and that there is an approximate 3 π‘šπ‘–π‘›π‘’π‘‘π‘’ increase in 𝑑 for every 𝑛𝑔 = 0.005 increase. Table 5-1: Flood-wave propagation time after dam-break to the Mediterranean Sea on mobile- bed π’π’ˆ 𝒏𝒗 𝒏 𝝓 β€²(Β°) π’…πŸ“πŸŽ (π’Ž) 𝒕 (π’Žπ’Šπ’) 0.025 0.000 0.025 40 0.001 32 0.025 0.000 0.025 40 0.005 32 0.025 0.000 0.025 40 0.010 32 0.025 0.000 0.025 40 0.020 32 0.025 0.000 0.025 40 0.040 32 0.025 0.033 0.041 49 0.001 36 0.025 0.033 0.041 49 0.005 35 0.025 0.033 0.041 49 0.010 35 0.025 0.033 0.041 49 0.020 35 0.025 0.033 0.041 49 0.040 35 0.025 0.067 0.072 60 0.001 39 0.025 0.067 0.072 60 0.005 39 0.025 0.067 0.072 60 0.010 39 0.025 0.067 0.072 60 0.020 38 0.025 0.067 0.072 60 0.040 38 0.025 0.090 0.093 70 0.001 41 0.025 0.090 0.093 70 0.005 41 0.025 0.090 0.093 70 0.010 41 0.025 0.090 0.093 70 0.020 40 0.025 0.090 0.093 70 0.040 40 0.030 0.000 0.030 40 0.001 36 0.030 0.000 0.030 40 0.005 36 0.030 0.000 0.030 40 0.010 36 0.030 0.000 0.030 40 0.020 35 0.030 0.000 0.030 40 0.040 35 0.030 0.033 0.045 49 0.001 39 0.030 0.033 0.045 49 0.005 39 0.030 0.033 0.045 49 0.010 39 0.030 0.033 0.045 49 0.020 38 0.030 0.033 0.045 49 0.040 38 68 0.030 0.067 0.073 60 0.001 42 0.030 0.067 0.073 60 0.005 42 0.030 0.067 0.073 60 0.010 42 0.030 0.067 0.073 60 0.020 42 0.030 0.067 0.073 60 0.040 41 0.030 0.090 0.095 70 0.001 44 0.030 0.090 0.095 70 0.005 44 0.030 0.090 0.095 70 0.010 44 0.030 0.090 0.095 70 0.020 44 0.030 0.090 0.095 70 0.040 44 0.035 0.000 0.035 40 0.001 39 0.035 0.000 0.035 40 0.005 39 0.035 0.000 0.035 40 0.010 39 0.035 0.000 0.035 40 0.020 39 0.035 0.000 0.035 40 0.040 39 0.035 0.033 0.048 49 0.001 42 0.035 0.033 0.048 49 0.005 42 0.035 0.033 0.048 49 0.010 42 0.035 0.033 0.048 49 0.020 42 0.035 0.033 0.048 49 0.040 41 0.035 0.067 0.076 60 0.001 46 0.035 0.067 0.076 60 0.005 45 0.035 0.067 0.076 60 0.010 45 0.035 0.067 0.076 60 0.020 45 0.035 0.067 0.076 60 0.040 45 0.035 0.090 0.097 70 0.001 48 0.035 0.090 0.097 70 0.005 47 0.035 0.090 0.097 70 0.010 47 0.035 0.090 0.097 70 0.020 47 0.035 0.090 0.097 70 0.040 47  69  Figure 5-24: Flood-wave propagation time versus total roughness for varying grain roughnesses in mobile-bed model 5.1.3.2 FIXED-BED SIMULATIONS Figure 5-25 to Figure 5-28 show the extent that the dam-break flood-wave has propagated after 𝑑 = 30 π‘šπ‘–π‘› with assumptions of no vegetation to heavy vegetation for a fixed-bed. As the effect of vegetation increases, it can be observed that the distance travelled by the flood-wave after 𝑑 = 30 π‘šπ‘–π‘› decreases; this is due to the increase in friction experienced by the flood-wave. Regardless of the effect of vegetation, it is observed that as 𝑛𝑔 increases, the distance propagated by the flood-wave decreases. The figures below show this to be true for all levels of vegetation.   70  Figure 5-25  Figure 5-26 71  Figure 5-27  Figure 5-28 72 Figure 5-25: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑣 = 0.000 (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-26: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑣 = 0.033 (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-27: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑣 = 0.067 (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-28: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑣 = 0.090 (blue – 𝑛𝑔 = 0.025, red – 𝑛𝑔 = 0.030, green – 𝑛𝑔 = 0.035) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission)   73 Table 5-2 tabulates the time it takes for the dam-break flood-wave to reach the Mediterranean Sea with varied sensitivity parameters. Selecting and holding constant values of 𝑛𝑣, then comparing different values 𝑛𝑔 consistently yields the conclusion that increasing 𝑛𝑔 will lead to an increase in propagation time. Plotting 𝑑 (propagation time) versus 𝑛 (total roughness) for varying grain roughnesses (Figure 5-29) reveals that 𝑑 is a function of 𝑛 for each case of 𝑛𝑔, and that there is an approximate 3 π‘šπ‘–π‘›π‘’π‘‘π‘’ increase in 𝑑 for every 𝑛𝑔 = 0.005 increase. Table 5-2: Flood-wave propagation time after dam-break to the Mediterranean Sea on fixed-bed π’π’ˆ 𝒏𝒗 𝒏 𝒕 (π’Žπ’Šπ’) 0.025 0.000 0.025 33 0.025 0.033 0.041 37 0.025 0.067 0.072 40 0.025 0.090 0.093 42 0.025 0.100 0.103 43 0.030 0.000 0.030 37 0.030 0.033 0.045 40 0.030 0.067 0.073 43 0.030 0.090 0.095 45 0.030 0.100 0.104 46 0.035 0.000 0.035 40 0.035 0.033 0.048 43 0.035 0.067 0.076 46 0.035 0.090 0.097 48 0.035 0.100 0.106 49  74  Figure 5-29: Flood-wave propagation time versus total roughness for varying grain roughnesses in fixed-bed model   75 5.2 EFFECT OF VARYING VEGETATION ROUGHNESS AND FRICTION ANGLE The vegetation roughness (𝑛𝑣) and friction angle (πœ™β€²) were varied with the values in Table 4-4 for both mobile-bed and fixed-bed simulations. HWM and bed change were compared at the seven cross-sections (Figure 5-1) for both simulation types, and the 2D bed evolution at the location in Figure 5-2 was examined for only the mobile-bed cases. Flood-wave propagation times were then compared for both the mobile-bed and fixed-bed simulations. Lastly, pre- and post- dam-break steady state hydrodynamic simulations were performed to examine pre- and post-dam-break inundation. 5.2.1 CROSS-SECTIONS OF HIGH-WATER MARKS AND BED CHANGE The set of fixed-bed simulations used constant values of the following parameters: 𝑛𝑔 = 0.025 and 𝑑 = 2 β„Žπ‘œπ‘’π‘Ÿπ‘ . To test the effect of vegetation density on high water levels, the value of 𝑛𝑣 is varied among the four values of 0.000, 0.033, 0.067, and 0.090. All of the cross-sections also display the original bed elevation (before dam-break) as a basis for comparison. Results demonstrate that varying 𝑛𝑣 does have an effect on the HWM for fixed-bed simulations. As vegetation density increases, the HWM (Figure 5-30, Figure 5-32, Figure 5-34, Figure 5-36, Figure 5-38, Figure 5-40, Figure 5-42) increases in cross-sections 1, 2, and 7, and has a mixed effect in cross-sections 3, 4, 5, and 6. The set of mobile-bed simulations used constant values of the following parameters: 𝑛𝑔 = 0.025, 𝑑50 = 1 π‘šπ‘š, 𝑑𝑏 = 2 π‘š, and 𝑑 = 2 β„Žπ‘œπ‘’π‘Ÿπ‘ . To test the effect of vegetation density on high water levels, the values of 𝑛𝑣 and πœ™β€² are varied among the four pairs of values in Table 4-4 representing no vegetation to heavy vegetation. All of the cross-sections also display the original bed elevation (before dam-break) as a basis for comparison. Results demonstrate that varying vegetation density does have an effect on the HWM for mobile- bed simulations. As vegetation density increases, the HWM (Figure 5-31, Figure 5-33, Figure 5-35, Figure 5-37, Figure 5-39, Figure 5-41, Figure 5-43) decreased in cross-sections 1, 2, and 7, increased in cross-sections 4 and 5, and had a mixed effect on cross-sections 3 and 6. It is not obvious what the effect of varying vegetation density is on bed elevations.  76  Figure 5-30: HWM at cross-section 1 varying 𝑛𝑣 and πœ™β€² on a fixed-bed  Figure 5-31: HWM and bed elevation at cross-section 1 varying 𝑛𝑣 and πœ™β€² on a mobile-bed 77  Figure 5-32: HWM at cross-section 2 varying 𝑛𝑣 and πœ™β€² on a fixed-bed  Figure 5-33: HWM and bed elevation at cross-section 2 varying 𝑛𝑣 and πœ™β€² on a mobile-bed 78  Figure 5-34: HWM at cross-section 3 varying 𝑛𝑣 and πœ™β€² on a fixed-bed  Figure 5-35: HWM and bed elevation at cross-section 3 varying 𝑛𝑣 and πœ™β€² on a mobile-bed 79  Figure 5-36: HWM at cross-section 4 varying 𝑛𝑣 and πœ™β€² on a fixed-bed  Figure 5-37: HWM and bed elevation at cross-section 4 varying 𝑛𝑣 and πœ™β€² on a mobile-bed 80  Figure 5-38: HWM at cross-section 5 varying 𝑛𝑣 and πœ™β€² on a fixed-bed  Figure 5-39: HWM and bed elevation at cross-section 5 varying 𝑛𝑣 and πœ™β€² on a mobile-bed 81  Figure 5-40: HWM at cross-section 6 varying 𝑛𝑣 and πœ™β€² on a fixed-bed  Figure 5-41: HWM and bed elevation at cross-section 6 varying 𝑛𝑣 and πœ™β€² on a mobile-bed 82  Figure 5-42: HWM at cross-section 7 varying 𝑛𝑣 and πœ™β€² on a fixed-bed  Figure 5-43: HWM and bed elevation at cross-section 7 varying 𝑛𝑣 and πœ™β€² on a mobile-bed 83 5.2.2 2D BED EVOLUTION Although the effect of varying vegetation density on bed elevation was indiscernible using the previous cross-sections, the effect of increasing vegetation density is clearly demonstrated in the 2D bed evolution plots (Figure 5-44 to Figure 5-47). As vegetation density is increased, the zones of significant erosion (blue) and deposition (red) shrink, especially in regions on the flood plain. This indicates that πœπ‘£ βˆ— increases, leading to a decrease in πœπ‘” βˆ—  as vegetation density increases.    84  Figure 5-44  Figure 5-45 85  Figure 5-46  Figure 5-47 86 Figure 5-44: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-45: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.033, πœ™ β€² = 49Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-46: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.067, πœ™ β€² = 60Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-47: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.090, πœ™ β€² = 70Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission)   87 5.2.3 FLOOD-WAVE PROPAGATION TIME 5.2.3.1 MOBILE-BED SIMULATIONS Figure 5-48 to Figure 5-50 show the extent that the dam-break flood-wave has propagated after 𝑑 = 30 π‘šπ‘–π‘› with 𝑛𝑔 = 0.025, 0.030, and 0.035 respectively for a mobile-bed. As 𝑛𝑔 increases, it can be observed that the distance travelled by the flood-wave after 𝑑 = 30 π‘šπ‘–π‘› decreases; this is due to the increase in friction experienced by the flood-wave. Regardless of the effect of 𝑛𝑔, it is observed that as vegetation density increases, the distance propagated by the flood-wave decreases. The figures below show this to be true for all values of 𝑛𝑔.   88  Figure 5-48  Figure 5-49  89  Figure 5-50 Figure 5-48: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.025, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑛𝑣 = 0.000 and πœ™ β€² = 40Β°, blue – 𝑛𝑣 = 0.033 and πœ™ β€² = 49Β°, red – 𝑛𝑣 = 0.067 and πœ™ β€² = 60Β°, green – 𝑛𝑣 = 0.090 and πœ™ β€² = 70Β°) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-49: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.030, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑛𝑣 = 0.000 and πœ™ β€² = 40Β°, blue – 𝑛𝑣 = 0.033 and πœ™ β€² = 49Β°, red – 𝑛𝑣 = 0.067 and πœ™ β€² = 60Β°, green – 𝑛𝑣 = 0.090 and πœ™ β€² = 70Β°) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-50: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.035, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑛𝑣 = 0.000 and πœ™ β€² = 40Β°, blue – 𝑛𝑣 = 0.033 and πœ™ β€² = 49Β°, red – 𝑛𝑣 = 0.067 and πœ™ β€² = 60Β°, green – 𝑛𝑣 = 0.090 and πœ™ β€² = 70Β°) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission)   90 Referring to Table 5-1, it can be seen that if 𝑛𝑔 and 𝑑50 are held constant with only 𝑛𝑣 and πœ™ β€² varying, the conclusion that increasing vegetation density will increase flood-wave travel time to the Mediterranean Sea is consistently true.  5.2.3.2 FIXED-BED SIMULATIONS Figure 5-51 to Figure 5-53 show the extent that the dam-break flood-wave has propagated after 𝑑 = 30 π‘šπ‘–π‘› with 𝑛𝑔 = 0.025, 0.030, and 0.035 respectively for a fixed-bed. As 𝑛𝑔 increases, it can be observed that the distance travelled by the flood-wave after 𝑑 = 30 π‘šπ‘–π‘› decreases; this is due to the increase in friction experienced by the flood-wave. Regardless of the effect of 𝑛𝑔, it is observed that as vegetation density increases, the distance propagated by the flood-wave decreases. The figures below show this to be true for all values of 𝑛𝑔.   91  Figure 5-51  Figure 5-52 92  Figure 5-53 Figure 5-51: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑔 = 0.025 (orange – 𝑛𝑣 = 0.000, blue – 𝑛𝑣 = 0.033, red – 𝑛𝑣 = 0.067, green – 𝑛𝑣 = 0.090) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-52: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑔 = 0.030 (orange – 𝑛𝑣 = 0.000, blue – 𝑛𝑣 = 0.033, red – 𝑛𝑣 = 0.067, green – 𝑛𝑣 = 0.090) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-53: Extent of inundation 30 minutes after dam-break on a fixed-bed with 𝑛𝑔 = 0.035 (orange – 𝑛𝑣 = 0.000, blue – 𝑛𝑣 = 0.033, red – 𝑛𝑣 = 0.067, green – 𝑛𝑣 = 0.090) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission)   93 Referring to Table 5-2, it can be seen that if 𝑛𝑔 is held constant with only 𝑛𝑣 varying, the conclusion that increasing vegetation density will increase flood-wave travel time to the Mediterranean Sea is consistently true. 5.2.4 PRE-/POST-DAM-BREAK STEADY-STATE HYDRODYNAMICS To compare how the morphology of the Reyran River and its flood plain changed as a result of the propagation of a dam-break flood-wave, steady-state fixed-bed hydrodynamic simulations were run. From these simulations, it was possible to examine how zones of inundation were affected under the assumed mean annual flood of 𝑄 = 100 π‘š3/𝑠.  As a proof-of-concept trial, steady-state hydrodynamic simulations were run with parameters of 𝑛𝑔 = 0.035, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š 3/𝑠, and vegetation density varying from no vegetation (𝑛𝑣 = 0.000 and πœ™ β€² = 40Β°) to heavy vegetation (𝑛𝑣 = 0.090 and πœ™ β€² = 70Β°). Figure 5-54, Figure 5-56, Figure 5-58, and Figure 5-60 show the pre-dam-break inundated zones, and Figure 5-55, Figure 5-57, Figure 5-59, and Figure 5-61 show the post-dam-break inundated zones for the different vegetation density scenarios.  From the following figures, it is clear that zones of inundation are somewhat different. For example, in the pre-dam-break figures, the area directly west of Frejus and the river is inundated; this region is no longer inundated post-dam-break. The morphological changes caused by propagation of the dam-break flood-wave yield many alterations in zones of inundation. 94  Figure 5-54  Figure 5-55 95  Figure 5-56  Figure 5-57 96  Figure 5-58  Figure 5-59 97  Figure 5-60  Figure 5-61  98 Figure 5-54: Pre-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š 3/𝑠 (aerial photograph of Frejus [3544- 3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) Figure 5-55: Post-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.000, πœ™β€² = 40Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š 3/𝑠 (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-56: Pre-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.033, πœ™β€² = 49Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š 3/𝑠 (aerial photograph of Frejus [3544- 3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) Figure 5-57: Post-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.033, πœ™β€² = 49Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š 3/𝑠 (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-58: Pre-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.067, πœ™β€² = 60Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š 3/𝑠 (aerial photograph of Frejus [3544- 3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) Figure 5-59: Post-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.067, πœ™β€² = 60Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š 3/𝑠 (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-60: Pre-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.090, πœ™β€² = 70Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š 3/𝑠 (aerial photograph of Frejus [3544- 3644, #41 to #121] in 1955 Β© IGN, 2012, by permission) Figure 5-61: Post-dam-break inundation under steady-state fixed-bed conditions with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.090, πœ™β€² = 70Β°, 𝑑50 = 40 π‘šπ‘š, and 𝑄 = 100 π‘š 3/𝑠 (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission)   99 5.3 EFFECT OF VARYING MEAN GRAIN SIZE 5.3.1 CROSS-SECTIONS OF HIGH-WATER MARKS AND BED CHANGE The set of simulations used to produce these cross-sections has the following parameters: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, 𝑑𝑏 = 2 π‘š, and 𝑑 = 2 β„Žπ‘œπ‘’π‘Ÿπ‘ . 𝑑50 is varied among the five values in Table 4-1. All of the cross-sections also display the original bed elevation (before dam- break) as a basis for comparison. Figure 5-62 to Figure 5-68 show cross-sections 1 to 7. From the figures, it is clear that varying 𝑑50 does have an effect on the HWM. As 𝑑50 increases, the HWM decreases in cross-sections 1, 4, and 6, increases in cross-sections 3 and 7, and has a mixed effect on cross-sections 2 and 5. It is also clear that varying 𝑑50 has an impact on final bed elevations. This is exemplified in Figure 5-67 and Figure 5-68, where the increase in 𝑑50 yields increased deposition and increased erosion.   100  Figure 5-62: HWM and bed elevation at cross-section 1 varying 𝑑50 on a mobile-bed  Figure 5-63: HWM and bed elevation at cross-section 2 varying 𝑑50 on a mobile-bed 101  Figure 5-64: HWM and bed elevation at cross-section 3 varying 𝑑50 on a mobile-bed  Figure 5-65: HWM and bed elevation at cross-section 4 varying 𝑑50 on a mobile-bed 102  Figure 5-66: HWM and bed elevation at cross-section 5 varying 𝑑50 on a mobile-bed  Figure 5-67: HWM and bed elevation at cross-section 6 varying 𝑑50 on a mobile-bed 103  Figure 5-68: HWM and bed elevation at cross-section 7 varying 𝑑50 on a mobile-bed 5.3.2 2D BED EVOLUTION The selection of 𝑑50 has a significant impact on the zones of erosion (blue) and deposition (red) shown in Figure 5-69 to Figure 5-73. As 𝑑50 increases from 1 π‘šπ‘š to 40 π‘šπ‘š, the erosion and deposition zones grow. The simulations used to produce the figures are not influenced by vegetation. However, similar results are expected after the first metre of vegetation-influenced sediment is eroded away in those simulations. The reason that an increase in 𝑑50 leads to more erosion, and hence deposition, is not entirely clear. It is possibly caused by the way SISYPHE computes sediment transport using the active layer and active stratum concept (more information on this may be found in the SISYPHE manual at www.opentelemac.org).    104  Figure 5-69  Figure 5-70 105  Figure 5-71  Figure 5-72 106  Figure 5-73  107 Figure 5-69: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-70: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 5 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-71: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 10 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-72: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 20 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-73: Bed evolution of case where: 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 40 π‘šπ‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission)   108 5.3.3 FLOOD-WAVE PROPAGATION TIME Figure 5-74 and Figure 5-75 show the extent that the dam-break flood-wave has propagated after 𝑑 = 30 π‘šπ‘–π‘› with two different scenarios of 𝑛𝑔, 𝑛𝑣, and πœ™β€², but with a varying spectrum of 𝑑50. From both figures, it is clear that as 𝑑50 increases, the distance propagated by the flood- wave increases. Unlike the parameters of 𝑛𝑔 and 𝑛𝑣, flood-wave propagation distance is not as sensitive to variations in 𝑑50. Nonetheless, 𝑑50 does affect flood-wave propagation characteristics and is noteworthy when modelling dam-breaks with mobile-beds. Table 5-1 shows that for scenarios where all parameters are constant except 𝑑50, the flood-wave propagation time will vary at most by 1 or 2 minutes. This supports the conclusion that flood- wave propagation time is not very sensitive to the 𝑑50 parameter.   109  Figure 5-74  Figure 5-75   110 Figure 5-74: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, and πœ™ β€² = 40Β° (orange – 𝑑50 = 1 π‘šπ‘š, blue – 𝑑50 = 5 π‘šπ‘š, red – 𝑛𝑣 = 𝑑50 = 10 π‘šπ‘š, green – 𝑛𝑣 = 𝑑50 = 20 π‘šπ‘š, black – 𝑑50 = 40 π‘šπ‘š) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-75: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.090, and πœ™ β€² = 70Β° (orange – 𝑑50 = 1 π‘šπ‘š, blue – 𝑑50 = 5 π‘šπ‘š, red – 𝑛𝑣 = 𝑑50 = 10 π‘šπ‘š, green – 𝑛𝑣 = 𝑑50 = 20 π‘šπ‘š, black – 𝑑50 = 40 π‘šπ‘š) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission)   111 5.4 EFFECT OF VARYING DEPTH TO BEDROCK 5.4.1 CROSS-SECTIONS OF HIGH-WATER MARKS AND BED CHANGE The set of simulations used to produce these cross-sections has the following parameters: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑 = 2 β„Žπ‘œπ‘’π‘Ÿπ‘ . 𝑑𝑏 is varied among the five values in Table 4-1. All of the cross-sections also display the original bed elevation (before dam- break) as a basis for comparison. Figure 5-76 to Figure 5-82 show cross-sections 1 to 7. From the figures, it is clear that varying 𝑑𝑏 has no impact on HWM, with the exception of cross-section 3, where the variation is likely a result of extreme bed elevation differences. Varying 𝑑𝑏 should not have an impact on the development of erosion and deposition zones; it merely affects how deep the alluvial layer can erode. In regions of high velocities, hence high πœβˆ—, erosion will occur until a depth is reached where πœβˆ— < πœπ‘ βˆ—. This depth may or may not be greater than 𝑑𝑏. In the case of cross-section 3, it is clear that this depth exceeds 𝑑𝑏 = 2, 5, 10, and 15 π‘š. Thus, erosion is limited by 𝑑𝑏, resulting in varied HWMs.    112  Figure 5-76: HWM and bed elevation at cross-section 1 varying 𝑑𝑏 on a mobile-bed  Figure 5-77: HWM and bed elevation at cross-section 2 varying 𝑑𝑏 on a mobile-bed 113  Figure 5-78: HWM and bed elevation at cross-section 3 varying 𝑑𝑏 on a mobile-bed  Figure 5-79: HWM and bed elevation at cross-section 4 varying 𝑑𝑏 on a mobile-bed 114  Figure 5-80: HWM and bed elevation at cross-section 5 varying 𝑑𝑏 on a mobile-bed  Figure 5-81: HWM and bed elevation at cross-section 6 varying 𝑑𝑏 on a mobile-bed 115  Figure 5-82: HWM and bed elevation at cross-section 7 varying 𝑑𝑏 on a mobile-bed   116 5.4.2 2D BED EVOLUTION Figure 5-83 to Figure 5-89 show plots of 2D bed evolution, where 𝑛𝑔, 𝑛𝑣, πœ™β€², and 𝑑50 are fixed; only 𝑑𝑏 is varied with values of 2, 5, 10, and 15 π‘š. Figure 5-84 to Figure 5-89 are presented in pairs of differing scales so that the locations that have scoured down to bedrock can be detected.  Comparing Figure 5-83, Figure 5-84, Figure 5-86, and Figure 5-88, which have the same scale, it can be deduced that varying 𝑑𝑏 has no impact on the location or the erosion (blue) and deposition (red) zones, nor does it have an impact on their size. Further examination of Figure 5-85, Figure 5-87, and Figure 5-89 leads to the conclusion that 𝑑𝑏 merely limits how deep the bed can be eroded. Although increased erosion means increased deposition, zones with increased deposition appear to be small and inconsequential.     117  Figure 5-83  Figure 5-84 118  Figure 5-85  Figure 5-86 119  Figure 5-87  Figure 5-88 120  Figure 5-89   121 Figure 5-83: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 2 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-84: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 5 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-85: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 5 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-86: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 10 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-87: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 10 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-88: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 15 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-89: Bed evolution of case where: 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, 𝑑50 = 1 π‘šπ‘š, and 𝑑𝑏 = 15 π‘š (positive evolution = deposition, negative evolution = erosion) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission)   122 5.4.3 FLOOD-WAVE PROPAGATION TIME Figure 5-90 to Figure 5-92 show the distance that the flood-wave has propagated after 𝑑 = 30 π‘šπ‘–π‘›, holding constant all parameters other than 𝑑𝑏. It is clear that 𝑑𝑏 has a negligible effect on flood-wave propagation, since the distance travelled by the flood-wave in each case of 𝑑𝑏 is exactly the same. The notion that 𝑑𝑏 does not affect flood-wave propagation is further supported by Table 5-3, where flood-wave travel times to the Mediterranean Sea are equal for cases where all other parameters are held constant.   123  Figure 5-90  Figure 5-91 124  Figure 5-92 Figure 5-90: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.025, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑑𝑏 = 2 π‘š, blue – 𝑑𝑏 = 5 π‘š, red – 𝑑𝑏 = 10 π‘š, green – 𝑑𝑏 = 15 π‘š) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-91: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.030, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑑𝑏 = 2 π‘š, blue – 𝑑𝑏 = 5 π‘š, red – 𝑑𝑏 = 10 π‘š, green – 𝑑𝑏 = 15 π‘š) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission) Figure 5-92: Extent of inundation 30 minutes after dam-break on a mobile-bed with 𝑛𝑔 = 0.035, 𝑛𝑣 = 0.000, πœ™ β€² = 40Β°, and 𝑑50 = 1 π‘šπ‘š (orange – 𝑑𝑏 = 2 π‘š, blue – 𝑑𝑏 = 5 π‘š, red – 𝑑𝑏 = 10 π‘š, green – 𝑑𝑏 = 15 π‘š) (aerial photograph of Frejus [FR 177-150, #1 to #104] in 1959 Β© IGN, 2012, by permission)   125 Table 5-3: Flood-wave propagation time after dam-break to the Mediterranean Sea on mobile- bed with varied 𝑑𝑏 π’π’ˆ 𝒏𝒗 𝝓 β€²(Β°) π’…πŸ“πŸŽ (π’Ž) 𝒅𝒃 (π’Ž) 𝒕 (π’Žπ’Šπ’) 0.025 0.000 40 0.001 2 32 0.025 0.000 40 0.001 5 32 0.025 0.000 40 0.001 10 32 0.025 0.000 40 0.001 15 33 0.030 0.000 40 0.001 2 36 0.030 0.000 40 0.001 5 36 0.030 0.000 40 0.001 10 36 0.030 0.000 40 0.001 15 36 0.035 0.000 40 0.001 2 39 0.035 0.000 40 0.001 5 39 0.035 0.000 40 0.001 10 39 0.035 0.000 40 0.001 15 39   126 6 SUMMARY 6.1 CONCLUSIONS This thesis develops a model using the TELEMAC suite that is suitable for simulating mobile- bed dam-breaks in 2D, then tests it on the Malpasset dam-break as a case study. To develop a model capable of simulating dam-break flows over a mobile bed, a number of TELEMAC2D and SYSIPHE subroutines were created or altered. The final version of the coupled TELEMAC2D-SISYPHE dam-break model has the following capabilities and features: β€’ set unique critical shear stresses for each of 10 different sediment size classes; β€’ set unique friction coefficients on nodes inside boundaries defined by input files; β€’ temporally vary friction coefficients based on total erosion or deposition that has occurred at each computational node; β€’ compute sediment transport based on developed combination Meyer-Peter and Muller (1948) and Wilson (1966) equation; β€’ adjust computed sediment transport to account for the presence of vegetation; β€’ spatially vary and stratify sediment; and β€’ spatially define bedrock (rigid boundary) elevation. Due to a lack of available data to calibrate the mobile-bed version of the Malpasset dam-break model, it was decided that a sensitivity analysis would be performed on the parameters of grain roughness (𝑛𝑔), vegetation density (𝑛𝑣 and πœ™β€²), mean grain size (𝑑50), and depth to bedrock (𝑑𝑏) to examine its effects on inundation and flood-wave propagation characteristics (namely travel time). 6.1.1 SENSITIVITY ANALYSIS In Section 5.1, increasing 𝑛𝑔 was found to impact the inundation and flood-wave propagation in such a way that β€’ the HWM increased in some cross-sections and decreased in others, indicating a varied effect, the magnitude of which is amplified by 𝑛𝑔, on the extent of flood plain inundation; 127 β€’ erosion and deposition decreased, indicating an inverse relationship between πœβˆ— and 𝑛𝑔; and β€’ flood-wave celerity decreased, yielding an increased time required to propagate a set distance. In Section 5.2, increasing vegetation density (𝑛𝑣 and πœ™β€²) was found to impact the inundation and flood-wave propagation in such a way that β€’ the HWM increased in some cross-sections and decreased in others, indicating a varied effect, the magnitude of which is amplified by vegetation density, on the extent of flood plain inundation; this is further supported by the steady-state hydrodynamic simulations modelling a mean annual flood; β€’ erosion and deposition decreased, indicating a decrease in the πœπ‘”π‘Ÿπ‘Žπ‘–π‘› βˆ—  partition of πœβˆ—; and β€’ flood-wave celerity decreased, yielding an increased time required to propagate a set distance. In Section 5.3, increasing 𝑑50 was found to impact the inundation and flood-wave propagation in such a way that β€’ the HWM increased in some cross-sections and decreased in others, indicating a varied effect, the magnitude of which is amplified by 𝑛𝑔, on the extent of flood plain inundation; β€’ erosion and deposition increased; and β€’ flood-wave celerity increased, yielding a decreased time required to propagate a set distance. In Section 5.4, increasing 𝑑𝑏 was found to impact the inundation and flood-wave propagation in such a way that β€’ no effect was observed on the HWM, indicating that flood plain inundation is not impacted by 𝑑𝑏; β€’ only the depth of erosion increased in regions of high πœβˆ—, with no change observed in the size of erosion and deposition zones; and β€’ no effect was observed on flood-wave celerity. 128 6.1.2 THE FIXED-BED ASSUMPTION From the case studies mentioned in Section 1.2 and Section 4.1, it is clear that the fixed-bed assumption used in industry standard dam-break analyses is flawed. Models created with this assumption cannot account for morphological changes to the flow paths that occur over the course of a dam-break. However, the fixed-bed assumption is adequate in some instances, for example, the difference in flood-wave propagation time between a fixed-bed and mobile-bed simulation (Figure 5-24 and Figure 5-29) is 1.5 minutes (5%) when all other simulation parameters are held constant. If only flood-wave propagation time were of interest, a fixed-bed model would be sufficient to model the Malpasset dam-break. For other analyses, such as comparing pre- and post-dam-break inundation extents, morphologic changes induced by the propagation of a flood-wave would be more significant as discussed in Section 5.2.4. With current computing capabilities, there is no reason why industry should not adopt mobile-bed models in dam-break analyses, especially when performing inundation studies. The fixed-bed assumption is valid only when no significant impact to simulation results is expected from morphological change. 6.1.3 RESEARCH CONTRIBUTION The development of a mobile-bed dam-break model provides an initial step towards improved dam-break simulations and predictions of morphological change. Although at present this model is still primitive, a comparison of results against a fixed-bed model could identify potential planning and design deficiencies that warrant further investigation. 6.2 LIMITATIONS The following are limitations of this mobile-bed dam-break model: β€’ The secondary flow correction algorithm built into SISYPHE requires further development and is inferior to the River2D-Morphology algorithm created by Stephen Kwan. It is possible to reprogram the SISYPHE algorithm in the future. β€’ The Meyer-Peter and Muller (1948) and Wilson (1966) combination sediment transport equation does not account for debris flows, which are known to exist during dam-breaks. It was originally intended that the Hanes (1985) equation be used in place of Wilson 129 (1966), but the Hanes (1985) equation caused simulations to become highly unstable and eventually crash. It is very possible that sediment transport rates are underestimated. β€’ Infrastructure in the Malpasset model, such as buildings, was assumed to impact flow the same way that vegetation would. This is inaccurate, as buildings tend to be impermeable. Future work on this model would require a better method of accounting for the presence of infrastructure. β€’ Global values of 𝑛𝑔, 𝑛𝑣, πœ™β€², 𝑑50, and 𝑑𝑏 were used for the sensitivity analysis on the Malpasset model. However, a switch to local values would better represent the physical world and hopefully yield more realistic results. β€’ Manning’s 𝑛 was chosen to represent bed roughness. Perhaps another method could be chosen since effects of bed roughness vary with water depth, and Manning’s 𝑛 is unable to capture this. 6.3 FUTURE WORK The end result of any future work for this research would be to improve upon the created mobile- bed dam-break model. A number of suggestions for future work were outlined in the limitations section. Additional suggestions are listed below: β€’ Conduct and model a laboratory flume experiment with a variety of conditions to model performance. β€’ Simulate real-case dam-breaks that have pre- and post-dam-break topography available in order to further examine model performance and validity. β€’ Extend all of this work to create a 3D mobile-bed dam-break model.   130 REFERENCES Bagnold, R. A. (1966). "An Approach to the Sediment Transport Problem for General Physics." Rep. No. Geological Survey Professional Paper 422-I, Washington, D.C. Cao, Z., Pender, G., Wallis, S., and Carling, P. (2004). "Computational dam-break hydraulics over erodible sediment bed." J.Hydraul.Eng., 130(7), 689-703. Capart, H., Spinewine, B., Young, D. L., Zech, Y., Brooks, G. R., Leclerc, M., and Secretan, Y. (2007). "The 1996 Lake Ha! Ha! breakout flood, Quebec: Test data for geomorphic flood routing methods." Journal of Hydraulic Research, 45, 97-109. Capart, H., and Young, D. L. (1998). "Formation of a jump by the dam-break wave over a granular bed." J.Fluid Mech., 372, 165-187. Cheng, N. (2002). "Exponential formula for bedload transport." J.Hydraul.Eng., 128(10), 942- 946. Dewals, B., Archambeau, P., Erpicum, S., Mouzelard, T., and Pirotton, M. (2002). "Dam-break hazard assessment with geomorphic flow computation, using WOLF 2D hydrodynamic software." Third International Conference Computer Simulation in Risk Analysis and Hazard Mitigation, Risk Analysis III, June 19, 2002 - June 21, WITPress, Sintra, Portugal, 59-68. DHL (Delft Hydraulics Laboratory). (1982). "Initiation of Motion and Suspension, Development of Concentration Profiles in a Steady, Uniform Flow Without Initial Sediment Load." Report M1531-III. EDF (ElectricitΓ© de France). (2010). "TELEMAC modelling system and SISYPHE user manual version 6.0." ElectricitΓ© de France: Research & Development, France. Einstein, H. A. (1950). "The Bedload Function for Bedload Transportation in Open Channel Flows." Technical Bulletin no. 1026, 1-71. Engelund, F. (1965). "A Criterion for the Occurrence of Suspended Load." La Houille Blanche, (8), 7. 131 Engelund, F., and Fredsoe, J. (1976). "Sediment Transport Model for Straight Alluvial Channels." Nordic Hydrol., 7(5), 293-306. EWRI (Environmental and Water Resources Institute). (2008). "Sedimentation Engineering: Processes, Measurements, Modeling, and Practice." Rep. No. 110, American Society of Civil Engineers, USA. Ferrari, A., Fraccarollo, L., Dumbser, M., Toro, E. F., and Armanini, A. (2010). "Three- dimensional flow evolution after a dam break." J.Fluid Mech., 663, 456-477. Gilbert, G. K. (1914). "The Transportation of Debris by Running Water." U.S. Geological Survey Professional Paper 86, 263. Hanes, D. M. (1985). "GRAIN FLOWS AND BED-LOAD SEDIMENT TRANSPORT: REVIEW AND EXTENSION." Acta Mech., 63(1-4), 131-142. Hardy, R. J., Lane, S. N., Lawless, M. R., Best, J. L., Elliott, L., and Ingham, D. B. (2005). "Development and testing of a numerical code for treatment of complex river channel topography in three-dimensional CFD models with structured grids." Journal of Hydraulic Research, 43(5), 468-480. Hervouet, J. (2000). "A high resolution 2-D dam-break model using parallelization." Hydrol.Process., 14(13), 2211-2230. Hervouet, J., and Petitjean, A. (1999). "Malpasset dam-break revisited with two-dimensional computations." Journal of Hydraulic Research/De Recherches Hydrauliques, 37(6), 777- 788. Leal, J. G. A. B., Ferreira, R. M. L., and Cardoso, A. H. (2002). "Dam-Break Waves on Movable Bed." Proceedings River Flow 2002 Conference, River Flow 2002, Louvain-la-Neuve, Belgium, 981-990. Li, S., and Millar, R. G. (2011). "A two-dimensional morphodynamic model of gravel-bed river with floodplain vegetation." Earth Surf.Process.Landforms, 36(2), 190-202. 132 Liu, N., Chen, Z., Zhang, J., Lin, W., Chen, W., and Xu, W. (2010). "Draining the Tangjiashan barrier lake." J.Hydraul.Eng., 136(11), 914-923. Mays, L. (1999). "Sedimentation and Erosion Hydraulics." Hydraulic Design Handbook, McGraw-Hill, 6.1. Meland, N., and Normann, J. O. (1966). "Transport Velocities of Single Particles in Bed-Load Motion." Geografiska Annaler, 48(A). Meyer-Peter, E., and Muller, R. (1948). "Formulas for Bed-Load Transport." Proceedings of the 2nd Congress, International Association for Hydraulic Structures Research, 39-64. Newlin, B. (2007). "Dam Failure Analysis: Current methods for analysis and the implications for emergency action planning." Retrieved June 21, 2011: http://mafsm.org/pdf/2007Conf/Dam_Failure.pdf. Parker, G. (1979). "Hydraulic Geometry of Active Gravel Rivers." J.Hydraul.Eng., 105(9), 1185-1201. Quanhong, L. (2009). "Numerical Simulation of Sediment Transport and Morphological Evolution." PhD thesis, National University of Singapore, Singapore. Soares Frazao, S., Poncin, M. P., Paquier, V., Spinewine, B., and Zech, Y. (2001). "Dam-break induced bank erosion: exploratory investigation and perspectives." Proceedings of Congress of International Association for Hydraulic Research, 29, Theme C, 246-251. Soares Frazao, S., and Zech, Y. (2002). "Dam break in channels with 90 bend." J.Hydraul.Eng., 128(11), 956-968. Steffler, P. M., and Blackburn, J. (2002). "River2D: Two-dimensional depth-averaged model of river hydrodynamics and fish habitats." University of Alberta, Edmonton, AB. USACE. (1997). "Engineering and Design: Hydrologic Engineering Requirements for Reservoirs." Rep. No. EM 1110-2-1420, U.S. Army Corps of Engineers, Washington, D.C. 133 van Rijn, L. C. (1984). "Sediment Transport, Part II: Suspended Load Transport." J.Hydraul.Eng., 110(11), 1613-1641. Vasquez, J. A. (2005). "Two-dimensional finite element river morphology model." PhD thesis, University of British Columbia, Vancouver, BC. Vasquez, J. A., and Leal, J. G. A. B. (2006). "Two-dimensional dam-break simulation over movable beds with an unstructured mesh." International Conference on Fluvial Hydraulics - River Flow 2006, September 6, 2006 - September 8, Taylor and Francis/Balkema, Lisbon, Portugal, 1483-1491. Vasquez, J. A., Millar, R. G., and Steffler, P. M. (2007). "Two-dimensional finite element river morphology model." National Research Council of Canada, Ottawa, ON, 752-760. Vasquez, J. A., and Roncal, J. J. (2009). "Testing River2D and Flow-3D for sudden dam-break flow simulations." Canadian Dam Association 2009 Annual Conference, Canadian Dam Association, Whistler, BC . Wilson, K. C. (1966). "Bedload Transport at High Shear Stresses." Journal of the Hydraulics Division, ASCE, 92(HY6), 49-59. Wong, M., and Parker, G. (2006). "Reanalysis and correction of bed-load relation of Meyer-Peter and Muller using their own database."J.Hydraul.Eng., 132(11), 1159-1168. Xia, J., Lin, B., Falconer, R. A., and Wang, G. (2010). "Modelling dam-break flows over mobile beds using a 2D coupled approach." Adv.Water Resour., 33(2), 171-183. 134 APPENDIX A – SAMPLE TELEMAC2D INPUT FILE FICHIER DE GEOMETRIE = geometry.slf FICHIER FORTRAN = fortran.f FICHIER DES CONDITIONS AUX LIMITES = boundary.cli FICHIER DES RESULTATS = t2d_results.slf TITRE = 'Le barrage de MALPASSET'  SUITE DE CALCUL = NON   VARIABLES POUR LES SORTIES GRAPHIQUES =  U,V,H,S,B,F,Q,M,W,N,O,MAXZ,TMXZ,MAXV,TMXV,US NOMBRE DE TABLEAUX PRIVES = 2 BILAN DE MASSE = VRAI NOMBRE DE PAS DE TEMPS = 72000   PAS DE TEMPS = 0.1 PERIODE POUR LES SORTIES GRAPHIQUES = 50  PERIODE DE SORTIE LISTING = 10 PRECONDITIONNEMENT = 2 BANCS DECOUVRANTS = VRAI FORME DE LA CONVECTION = 14;5 OPTION DE SUPG = 0;0 MAXIMUM D'ITERATIONS POUR LE SOLVEUR = 200 SOLVEUR = 7  OPTION DU SOLVEUR = 3  PRECISION DU SOLVEUR = 0.0001 STOCKAGE DES MATRICES : 3     PRODUIT MATRICE-VECTEUR : 2 IMPLICITATION POUR LA HAUTEUR = 0.55   IMPLICITATION POUR LA VITESSE = 0.55 MASS-LUMPING SUR H = 1. CLIPPING DE H = NON  LOI DE FROTTEMENT SUR LE FOND = 4 COEFFICIENT DE FROTTEMENT : 0.       MODELE DE TURBULENCE = 1 COEFFICIENT DE DIFFUSION DES VITESSES = 1. COTE INITIALE = 0.               EQUATIONS : 'SAINT-VENANT EF' OPTION DE TRAITEMENT DES BANCS DECOUVRANTS : 1 TRAITEMENT DU SYSTEME LINEAIRE : 2 SOLVEUR : 1 PRECONDITIONNEMENT : 2 COMPATIBILITE DU GRADIENT DE SURFACE LIBRE : 0.9  FICHIER DES PARAMETRES DE SISYPHE  = sisyphe.cas COUPLAGE AVEC = 'SISYPHE' TRAITEMENT DES HAUTEURS NEGATIVES=2 CORRECTION DE CONTINUITE=OUI  &FIN   135 APPENDIX B – SAMPLE SISYPHE INPUT FILE /-------------------------------------------------------------------/ /     SISYPHE         /-------------------------------------------------------------------/  FICHIER DES CONDITIONS AUX LIMITES = boundary.cli FICHIER DE GEOMETRIE   = geometry.slf   /-------------------------------------------------------------------/ /     GENERAL OPTIONS  /-------------------------------------------------------------------/  VARIABLES POUR LES SORTIES GRAPHIQUES =  R,CHESTR,TOB,E,KS,D50 FICHIER DES RESULTATS  = sis_results.slf  /-------------------------------------------------------------------/ /     NUMERICAL OPTIONS /-------------------------------------------------------------------/  BILAN DE MASSE = OUI /STEADY CASE    = YES  /-------------------------------------------------------------------/ /     PHYSICAL OPTIONS /-------------------------------------------------------------------/  FORMULE DE TRANSPORT SOLIDE = 1 RAPPORT D'EVOLUTION CRITIQUE = 0.1 EPAISSEUR DE COUCHE ACTIVE = 1.0 NOMBRE DE CLASSES GRANULOMETRIQUES = 3 DIAMETRE MOYEN DES GRAINS = 0.001;0.001;0.001 COURANTS SECONDAIRES = OUI  VOLUMES FINIS = OUI OPTION DE TRAITEMENT DES FONDS NON ERODABLES = 4  &FIN   136 APPENDIX C – SAMPLE FORTRAN INPUT FILE C    SET SHIELDS PARAMETER (AC) FOR EACH SEDIMENT SIZE CLASS !        ************************          SUBROUTINE INIT_SEDIMENT !        ************************ !      &(NSICLA,ELAY,ZF,ZR,NPOIN,AVAIL,FRACSED_GF,AVA0,      & LGRAFED,CALWC,XMVS,XMVE,GRAV,VCE,XWC,FDM,      & CALAC,AC,SEDCO,ES,NCOUCH_TASS,CONC_VASE,      & MS_SABLE,MS_VASE,ACLADM,UNLADM,TOCE_SABLE) C !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !| AC             |<->| CRITICAL SHIELDS PARAMETER !| ACLADM         |-->| MEAN DIAMETER OF SEDIMENT !| AT0            |<->| TIME IN S !| AVAIL          |<->| VOLUME PERCENT OF EACH CLASS !| CALAC          |---| **** !| CALWC          |-->| **** !| CONC_VASE      |<->| MUD CONCENTRATION FOR EACH LAYER !| ELAY           |<->| THICKNESS OF SURFACE LAYER !| ES             |<->| LAYER THICKNESSES AS DOUBLE PRECISION !| FDM            |-->| DIAMETER DM FOR EACH CLASS  !| FRACSED_GF     |-->|(A SUPPRIMER) !| GRAV           |-->| ACCELERATION OF GRAVITY !| LGRAFED        |-->|(A SUPPRIMER) !| MS_SABLE       |<->| MASS OF SAND PER LAYER (KG/M2) !| MS_VASE        |<->| MASS OF MUD PER LAYER (KG/M2) !| NCOUCH_TASS    |-->| NUMBER OF LAYERS FOR CONSOLIDATION !| NPOIN          |-->| NUMBER OF POINTS !| NSICLA         |-->| NUMBER OF SEDIMENT CLASSES !| SEDCO          |-->| LOGICAL, SEDIMENT COHESIVE OR NOT !| UNLADM         |-->| MEAN DIAMETER OF ACTIVE STRATUM LAYER !| VCE            |-->| WATER VISCOSITY !| XMVE           |-->| FLUID DENSITY  !| XMVS           |-->| WATER DENSITY  !| XWC            |-->| SETTLING VELOCITY !| ZF             |-->| ELEVATION OF BOTTOM !| ZR             |-->| NON ERODABLE BED !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~        USE BIEF       USE INTERFACE_SISYPHE, EX_INIT_SEDIMENT => INIT_SEDIMENT !       IMPLICIT NONE       INTEGER LNG,LU 137       COMMON/INFO/LNG,LU C C+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ C       INTEGER,           INTENT(IN)     :: NSICLA,NPOIN,NCOUCH_TASS       TYPE(BIEF_OBJ),    INTENT(INOUT)  :: ELAY,ZF,ZR       TYPE(BIEF_OBJ), INTENT(INOUT)     :: MS_SABLE, MS_VASE       TYPE(BIEF_OBJ),    INTENT(INOUT)  :: ACLADM, UNLADM       LOGICAL,           INTENT(IN)     :: LGRAFED,CALWC       LOGICAL,           INTENT(IN)     :: CALAC       DOUBLE PRECISION,  INTENT(IN)     :: XMVS,XMVE,GRAV,VCE       DOUBLE PRECISION,  INTENT(INOUT)  :: AVA0(NSICLA)       DOUBLE PRECISION,  INTENT(INOUT)  :: AVAIL(NPOIN,10,NSICLA)       DOUBLE PRECISION,  INTENT(INOUT)  :: FRACSED_GF(NSICLA)       DOUBLE PRECISION,  INTENT(INOUT)  :: FDM(NSICLA),XWC(NSICLA)       DOUBLE PRECISION,  INTENT(INOUT)  :: AC(NSICLA),TOCE_SABLE C       LOGICAL,           INTENT(IN)     :: SEDCO(NSICLA) C C IF SEDCO(1) OR SEDCO(2) = YES --> CONSOLIDATION MODEL C C       DOUBLE PRECISION, INTENT(IN)    :: CONC_VASE(10)       DOUBLE PRECISION, INTENT(INOUT) :: ES(NPOIN,10) C C+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ C       INTEGER            :: I,J       DOUBLE PRECISION   :: DENS,DSTAR       LOGICAL            :: MIXTE ! !==================================================================== ==! !==================================================================== ==! C                               PROGRAM                                ! !==================================================================== ==! !==================================================================== ==! ! C  ------ BED COMPOSITION !         CALL OS('X=Y-Z   ',X=ELAY,Y=ZF,Z=ZR) ! C     ONLY ONE CLASS 138 C       IF(NSICLA.EQ.1) THEN          DO I=1,NPOIN           AVAIL(I,1,1) = 1.D0           ACLADM%R(I) = FDM(1)         ENDDO C     PURE MUD ONLY         IF(SEDCO(1)) CALL INIT_MIXTE(XMVS,NPOIN,AVAIL,NSICLA,ES,      &                               ELAY%R,NCOUCH_TASS,CONC_VASE,      &                                  MS_SABLE%R,MS_VASE%R,ZF%R,      &                                               ZR%R,AVA0) C       ELSE C C     NON-COHESIVE, MULTI-CLASSES C         IF(.NOT.SEDCO(2)) THEN           CALL INIT_AVAI C         CALL MEAN_GRAIN_SIZE C THIS PART CAN BE INTEGRATED INTO INIT_AVAI           DO J=1,NPOIN             ACLADM%R(J) = 0.D0             UNLADM%R(J) = 0.D0             DO I=1,NSICLA               IF(AVAIL(J,1,I).GT.0.D0) THEN                 ACLADM%R(J) = ACLADM%R(J) + FDM(I)*AVAIL(J,1,I)                 UNLADM%R(J) = UNLADM%R(J) + FDM(I)*AVAIL(J,2,I)               ENDIF             ENDDO             ACLADM%R(J)=MAX(ACLADM%R(J),0.D0)             UNLADM%R(J)=MAX(UNLADM%R(J),0.D0)           ENDDO         ELSE C C        MIXED (so far only 2 classes: NON COHESIVE /COHESIVE) C             MIXTE=.TRUE.                 CALL INIT_MIXTE(XMVS,NPOIN,AVAIL,NSICLA,ES,ELAY%R,      &                     NCOUCH_TASS,CONC_VASE,MS_SABLE%R,      &                     MS_VASE%R,ZF%R,ZR%R,AVA0)           DO I=1,NPOIN             ACLADM%R(I) = FDM(1)           ENDDO         ENDIF C       ENDIF 139 C       IF(LGRAFED) THEN         DO I=1, NSICLA           FRACSED_GF(I)=AVA0(I)         ENDDO       ENDIF C C C ------ SETTLING VELOCITY C       IF(.NOT.CALWC) THEN         DENS = (XMVS - XMVE) / XMVE         DO I = 1, NSICLA           CALL VITCHU_SISYPHE(XWC(I),DENS,FDM(I),GRAV,VCE)         ENDDO       ENDIF C C------ SHIELDS PARAMETER C       WRITE(*,*)       WRITE(*,*) 'INPUT SEDIMENT CLASSES AND SHIELDS PARAMETER'           WRITE(*,*) C       IF(.NOT.CALAC) THEN          DENS  = (XMVS - XMVE )/ XMVE          AC(1)=0.056*tan(40*3.141592654/180)          AC(2)=0.056*tan(40*3.141592654/180)          AC(3)=999999       ENDIF        DO I = 1, NSICLA           WRITE(*,*) 'D50 = ', FDM(I), ', AC = ', AC(I)       ENDDO         C      IF(.NOT.CALAC) THEN C        DENS  = (XMVS - XMVE )/ XMVE C        DO I = 1, NSICLA C          DSTAR = FDM(I)*(GRAV*DENS/VCE**2)**(1.D0/3.D0) C          IF (DSTAR <= 4.D0) THEN C            AC(I) = 0.24*DSTAR**(-1.0D0) C          ELSEIF (DSTAR <= 10.D0) THEN C            AC(I) = 0.14D0*DSTAR**(-0.64D0) C          ELSEIF (DSTAR <= 20.D0) THEN C            AC(I) = 0.04D0*DSTAR**(-0.1D0) C          ELSEIF (DSTAR <= 150.D0) THEN 140 C            AC(I) = 0.013D0*DSTAR**(0.29D0) C          ELSE C            AC(I) = 0.055D0 C          ENDIF   C      AC(3)=9999     C          WRITE(*,*) 'D50 = ', FDM(I), ', AC = ', AC(I)     C        ENDDO C      ENDIF           WRITE(*,*)     C pour les sΓ©diments mixtes (suspension_flux_mixte)       IF(MIXTE) TOCE_SABLE=AC(1)*FDM(1)*GRAV*(XMVS - XMVE) C C----------------------------------------------------------------------- C       RETURN       END  C    INITIALIZE FRICTION COEFFICIENT IN BOTH TELEMAC2D AND SISYPHE !        *****************          SUBROUTINE FONSTR !        ***************** !      &(H,ZF,Z,CHESTR,NGEO,NFON,NOMFON,MESH,FFON,LISTIN) ! !*********************************************************************** ! BIEF   V6P1                                   21/08/2010 !*********************************************************************** ! !brief    LOOKS FOR 'BOTTOM' IN THE GEOMETRY FILE. !+ !+            LOOKS FOR 'BOTTOM FRICTION' (COEFFICIENTS). ! !note     THE NAMES OF THE VARIABLES HAVE BEEN DIRECTLY !+         WRITTEN OUT AND ARE NOT READ FROM 'TEXTE'. !+         THIS MAKES IT POSSIBLE TO HAVE A GEOMETRY FILE !+         COMPILED IN ANOTHER LANGUAGE. ! !history  J-M HERVOUET (LNH) !+        17/08/94 !+        V5P6 !+ ! !history  N.DURAND (HRW), S.E.BOURBAN (HRW) !+        13/07/2010 141 !+        V6P0 !+   Translation of French comments within the FORTRAN sources into !+   English comments ! !history  N.DURAND (HRW), S.E.BOURBAN (HRW) !+        21/08/2010 !+        V6P0 !+   Creation of DOXYGEN tags for automated documentation and !+   cross-referencing of the FORTRAN sources ! !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !| CHESTR         |<--| FRICTION COEFFICIENT (DEPENDING ON FRICTION LAW) !| FFON           |-->| FRICTION COEFFICIENT IF CONSTANT !| H              |<--| WATER DEPTH !| LISTIN         |-->| IF YES, WILL GIVE A REPORT !| MESH           |-->| MESH STRUCTURE !| NFON           |-->| LOGICAL UNIT OF BOTTOM FILE !| NGEO           |-->| LOGICAL UNIT OF GEOMETRY FILE !| NOMFON         |-->| NAME OF BOTTOM FILE !| Z              |<--| FREE SURFACE ELEVATION !| ZF             |-->| ELEVATION OF BOTTOM !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !       USE BIEF, EX_FONSTR => FONSTR       USE DECLARATIONS_TELEMAC2D, only: NPOIN, inpoly, X, Y !       IMPLICIT NONE       INTEGER LNG,LU,I,J,N       COMMON/INFO/LNG,LU ! !+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ !       TYPE(BIEF_OBJ), INTENT(INOUT) :: H,ZF,Z,CHESTR       CHARACTER(LEN=72), INTENT(IN) :: NOMFON       TYPE(BIEF_MESH), INTENT(IN)   :: MESH       DOUBLE PRECISION, INTENT(IN)  :: FFON       LOGICAL, INTENT(IN)           :: LISTIN       INTEGER, INTENT(IN)           :: NGEO,NFON ! !+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ !       INTEGER ERR !       DOUBLE PRECISION BID       REAL, ALLOCATABLE :: W(:) ! 142       LOGICAL CALFON,CALFRO,OK,LUZF,LUH,LUZ            INTEGER NPMAX2        PARAMETER (NPMAX2=200)             INTEGER NP1       DOUBLE PRECISION X1(NPMAX2),Y1(NPMAX2)          INTEGER NP2       DOUBLE PRECISION X2(NPMAX2),Y2(NPMAX2)        INTEGER NP3       DOUBLE PRECISION X3(NPMAX2),Y3(NPMAX2)        INTEGER NP4       DOUBLE PRECISION X4(NPMAX2),Y4(NPMAX2)        INTEGER NP5       DOUBLE PRECISION X5(NPMAX2),Y5(NPMAX2)        INTEGER NP6       DOUBLE PRECISION X6(NPMAX2),Y6(NPMAX2)        INTEGER NP7       DOUBLE PRECISION X7(NPMAX2),Y7(NPMAX2)        INTEGER NP8       DOUBLE PRECISION X8(NPMAX2),Y8(NPMAX2)        INTEGER NP9       DOUBLE PRECISION X9(NPMAX2),Y9(NPMAX2)           INTEGER NP10       DOUBLE PRECISION X10(NPMAX2),Y10(NPMAX2)          INTEGER NP11       DOUBLE PRECISION X11(NPMAX2),Y11(NPMAX2)          INTEGER NP12       DOUBLE PRECISION X12(NPMAX2),Y12(NPMAX2)        INTEGER NP13       DOUBLE PRECISION X13(NPMAX2),Y13(NPMAX2)        INTEGER NP14       DOUBLE PRECISION X14(NPMAX2),Y14(NPMAX2)        INTEGER NP15       DOUBLE PRECISION X15(NPMAX2),Y15(NPMAX2)        INTEGER NP16       DOUBLE PRECISION X16(NPMAX2),Y16(NPMAX2)        INTEGER NP17       DOUBLE PRECISION X17(NPMAX2),Y17(NPMAX2)        INTEGER NP18       DOUBLE PRECISION X18(NPMAX2),Y18(NPMAX2)        INTEGER NP19       DOUBLE PRECISION X19(NPMAX2),Y19(NPMAX2)           INTEGER NP20       DOUBLE PRECISION X20(NPMAX2),Y20(NPMAX2)      143       INTEGER NP21       DOUBLE PRECISION X21(NPMAX2),Y21(NPMAX2)          INTEGER NP22       DOUBLE PRECISION X22(NPMAX2),Y22(NPMAX2)        INTEGER NP23       DOUBLE PRECISION X23(NPMAX2),Y23(NPMAX2)        INTEGER NP24       DOUBLE PRECISION X24(NPMAX2),Y24(NPMAX2)        INTEGER NP25       DOUBLE PRECISION X25(NPMAX2),Y25(NPMAX2)        INTEGER NP26       DOUBLE PRECISION X26(NPMAX2),Y26(NPMAX2)  ! !----------------------------------------------------------------------- !       ALLOCATE(W(MESH%NPOIN),STAT=ERR)       IF(ERR.NE.0) THEN         IF(LNG.EQ.1) WRITE(LU,*) 'FONSTR : MAUVAISE ALLOCATION DE W'         IF(LNG.EQ.2) WRITE(LU,*) 'FONSTR: WRONG ALLOCATION OF W'         STOP       ENDIF ! !----------------------------------------------------------------------- ! !    ASSUMES THAT THE FILE HEADER LINES HAVE ALREADY BEEN READ !    WILL START READING THE RESULT RECORDS ! !----------------------------------------------------------------------- ! !    INITIALISES !       LUH  =  .FALSE.       LUZ  =  .FALSE.       LUZF =  .FALSE.       CALFRO = .TRUE. ! !----------------------------------------------------------------------- ! !     LOOKS FOR THE FRICTION COEFFICIENT IN THE FILE !       IF(LNG.EQ.1) CALL FIND_IN_SEL(CHESTR,'FROTTEMENT      ',NGEO,W,OK,      &                              TIME=BID)       IF(LNG.EQ.2) CALL FIND_IN_SEL(CHESTR,'BOTTOM FRICTION ',NGEO,W,OK,      &                              TIME=BID) !     CASE OF A GEOMETRY FILE IN ANOTHER LANGUAGE       IF(.NOT.OK.AND.LNG.EQ.1) THEN 144         CALL FIND_IN_SEL(CHESTR,'BOTTOM FRICTION ',NGEO,W,OK,TIME=BID)       ENDIF       IF(.NOT.OK.AND.LNG.EQ.2) THEN         CALL FIND_IN_SEL(CHESTR,'FROTTEMENT      ',NGEO,W,OK,TIME=BID)       ENDIF       IF(OK) THEN         CALFRO = .FALSE.         IF(LNG.EQ.1) WRITE(LU,5)         IF(LNG.EQ.2) WRITE(LU,6) 5       FORMAT(1X,'FONSTR : COEFFICIENTS DE FROTTEMENT LUS DANS',/,      &         1X,'         LE FICHIER DE GEOMETRIE') 6       FORMAT(1X,'FONSTR : FRICTION COEFFICIENTS READ IN THE',/,      &         1X,'         GEOMETRY FILE')       ENDIF ! !     LOOKS FOR THE BOTTOM ELEVATION IN THE FILE !       IF(LNG.EQ.1) CALL FIND_IN_SEL(ZF,'FOND            ',NGEO,W,OK,      &                              TIME=BID)       IF(LNG.EQ.2) CALL FIND_IN_SEL(ZF,'BOTTOM          ',NGEO,W,OK,      &                              TIME=BID)       IF(.NOT.OK.AND.LNG.EQ.1) THEN         CALL FIND_IN_SEL(ZF,'BOTTOM          ',NGEO,W,OK,TIME=BID)       ENDIF       IF(.NOT.OK.AND.LNG.EQ.2) THEN         CALL FIND_IN_SEL(ZF,'FOND            ',NGEO,W,OK,TIME=BID)       ENDIF !     MESHES FROM BALMAT ?       IF(.NOT.OK) CALL FIND_IN_SEL(ZF,'ALTIMETRIE      ',NGEO,W,OK,      &                             TIME=BID) !     TOMAWAC IN FRENCH ?       IF(.NOT.OK) CALL FIND_IN_SEL(ZF,'COTE_DU_FOND    ',NGEO,W,OK,      &                             TIME=BID) !     TOMAWAC IN ENGLISH ?       IF(.NOT.OK) CALL FIND_IN_SEL(ZF,'BOTTOM_LEVEL    ',NGEO,W,OK,      &                             TIME=BID)       LUZF = OK !       IF(.NOT.LUZF) THEN !       LOOKS FOR WATER DEPTH AND FREE SURFACE ELEVATION         IF(LNG.EQ.1) CALL FIND_IN_SEL(H,'HAUTEUR D''EAU   ',NGEO,W,OK,      &                                TIME=BID)         IF(LNG.EQ.2) CALL FIND_IN_SEL(H,'WATER DEPTH     ',NGEO,W,OK,      &                                TIME=BID)         IF(.NOT.OK.AND.LNG.EQ.1) THEN           CALL FIND_IN_SEL(H,'WATER DEPTH     ',NGEO,W,OK,TIME=BID) 145         ENDIF         IF(.NOT.OK.AND.LNG.EQ.2) THEN           CALL FIND_IN_SEL(H,'HAUTEUR D''EAU   ',NGEO,W,OK,TIME=BID)         ENDIF         LUH = OK         IF(LNG.EQ.1) CALL FIND_IN_SEL(Z,'SURFACE LIBRE   ',NGEO,W,OK,      &                                TIME=BID)         IF(LNG.EQ.2) CALL FIND_IN_SEL(Z,'FREE SURFACE    ',NGEO,W,OK,      &                                TIME=BID)         IF(.NOT.OK.AND.LNG.EQ.1) THEN           CALL FIND_IN_SEL(Z,'FREE SURFACE    ',NGEO,W,OK,TIME=BID)         ENDIF         IF(.NOT.OK.AND.LNG.EQ.2) THEN           CALL FIND_IN_SEL(Z,'SURFACE LIBRE   ',NGEO,W,OK,TIME=BID)         ENDIF         LUZ = OK       ENDIF ! !     INITIALISES THE BOTTOM ELEVATION !       IF(LUZF) THEN !          CALFON = .FALSE. !       ELSE !          IF (LUZ.AND.LUH) THEN !             CALL OS( 'X=Y-Z   ' , ZF , Z , H , BID )             IF(LNG.EQ.1) WRITE(LU,24)             IF(LNG.EQ.2) WRITE(LU,25) 24          FORMAT(1X,'FONSTR (BIEF) : ATTENTION, FOND CALCULE AVEC',/,      &                '                PROFONDEUR ET SURFACE LIBRE',/,      &                '                DU FICHIER DE GEOMETRIE') 25          FORMAT(1X,'FONSTR (BIEF): ATTENTION, THE BOTTOM RESULTS',/,      &                '               FROM DEPTH AND SURFACE ELEVATION',      &              /,'               FOUND IN THE GEOMETRY FILE')             CALFON = .FALSE. !          ELSE !             CALFON = .TRUE. !          ENDIF !       ENDIF 146 ! !----------------------------------------------------------------------- ! ! BUILDS THE BOTTOM IF IT WAS NOT IN THE GEOMETRY FILE !       IF(NOMFON(1:1).NE.' ') THEN !       A BOTTOM FILE WAS GIVEN, (RE)COMPUTES THE BOTTOM ELEVATION         IF(LISTIN) THEN           IF(LNG.EQ.1) WRITE(LU,2223) NOMFON           IF(LNG.EQ.2) WRITE(LU,2224) NOMFON           IF(.NOT.CALFON) THEN             IF(LNG.EQ.1) WRITE(LU,2225)             IF(LNG.EQ.2) WRITE(LU,2226)           ENDIF         ENDIF 2223    FORMAT(/,1X,'FONSTR (BIEF) : FOND DANS LE FICHIER : ',A72) 2224    FORMAT(/,1X,'FONSTR (BIEF): BATHYMETRY GIVEN IN FILE : ',A72) 2225    FORMAT(  1X,'                LE FOND TROUVE DANS LE FICHIER',/,      &           1X,'                DE GEOMETRIE EST IGNORE',/) 2226    FORMAT(  1X,'               BATHYMETRY FOUND IN THE',/,      &           1X,'               GEOMETRY FILE IS IGNORED',/) !         CALL FOND(ZF%R,MESH%X%R,MESH%Y%R,MESH%NPOIN,NFON,      &            MESH%NBOR%I,MESH%KP1BOR%I,MESH%NPTFR) !       ELSEIF(CALFON) THEN         IF(LISTIN) THEN           IF(LNG.EQ.1) WRITE(LU,2227)           IF(LNG.EQ.2) WRITE(LU,2228)         ENDIF 2227    FORMAT(/,1X,'FONSTR (BIEF) : PAS DE FOND DANS LE FICHIER DE',      &         /,1X,'                GEOMETRIE ET PAS DE FICHIER DES',      &         /,1X,'                FONDS. LE FOND EST INITIALISE A'      &         /,1X,'                ZERO MAIS PEUT ENCORE ETRE MODIFIE'      &         /,1X,'                DANS CORFON.',      &         /,1X) 2228    FORMAT(/,1X,'FONSTR (BIEF): NO BATHYMETRY IN THE GEOMETRY FILE',      &         /,1X,'               AND NO BATHYMETRY FILE. THE BOTTOM',      &         /,1X,'               LEVEL IS FIXED TO ZERO BUT STILL',      &         /,1X,'               CAN BE MODIFIED IN CORFON.',      &         /,1X)         CALL OS( 'X=C     ' , ZF , ZF , ZF , 0.D0 )       ENDIF ! !----------------------------------------------------------------------- ! 147 ! COMPUTES THE BOTTOM FRICTION COEFFICIENT !       IF(CALFRO) THEN         CALL OS( 'X=C     ' , CHESTR , CHESTR , CHESTR , FFON )       ENDIF       CALL STRCHE   C C-----------------------------------------------------------------------              WRITE(*,*)       WRITE(*,*) 'SET FRICTION ACCORDING TO FOLLOWING BOUNDARIES'          WRITE(*,*)           OPEN (61,file='../BOUNDARIES/V1.xyz',status='old')        read (61,*) NP1        DO n=1, NP1           read (61,*) X1(n),Y1(n)        ENDDO        print *,'FIN LECTURE V1.xyz', NP1       CLOSE(61)         OPEN (61,file='../BOUNDARIES/V2.xyz',status='old')        read (61,*) NP2        DO n=1, NP2           read (61,*) X2(n),Y2(n)        ENDDO        print *,'FIN LECTURE V2.xyz', NP2       CLOSE(61)            OPEN (61,file='../BOUNDARIES/V3.xyz',status='old')        read (61,*) NP3        DO n=1, NP3           read (61,*) X3(n),Y3(n)        ENDDO        print *,'FIN LECTURE V3.xyz', NP3       CLOSE(61)            OPEN (61,file='../BOUNDARIES/V4.xyz',status='old')        read (61,*) NP4        DO n=1, NP4           read (61,*) X4(n),Y4(n)        ENDDO        print *,'FIN LECTURE V4.xyz', NP4       CLOSE(61)     148           OPEN (61,file='../BOUNDARIES/V5.xyz',status='old')        read (61,*) NP5        DO n=1, NP5           read (61,*) X5(n),Y5(n)        ENDDO        print *,'FIN LECTURE V5.xyz', NP5       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V6.xyz',status='old')        read (61,*) NP6        DO n=1, NP6           read (61,*) X6(n),Y6(n)        ENDDO        print *,'FIN LECTURE V6.xyz', NP6       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V7.xyz',status='old')        read (61,*) NP7       DO n=1, NP7           read (61,*) X7(n),Y7(n)        ENDDO        print *,'FIN LECTURE V7.xyz', NP7       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V8.xyz',status='old')        read (61,*) NP8       DO n=1, NP8          read (61,*) X8(n),Y8(n)        ENDDO        print *,'FIN LECTURE V8.xyz', NP8       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V9.xyz',status='old')        read (61,*) NP9        DO n=1, NP9          read (61,*) X9(n),Y9(n)        ENDDO        print *,'FIN LECTURE V9.xyz', NP9       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V10.xyz',status='old')        read (61,*) NP10       DO n=1, NP10          read (61,*) X10(n),Y10(n)        ENDDO  149       print *,'FIN LECTURE V10.xyz', NP10       CLOSE(61)        OPEN (61,file='../BOUNDARIES/V11.xyz',status='old')        read (61,*) NP11        DO n=1, NP11          read (61,*) X11(n),Y11(n)        ENDDO        print *,'FIN LECTURE V11.xyz', NP11       CLOSE(61)         OPEN (61,file='../BOUNDARIES/V12.xyz',status='old')        read (61,*) NP12        DO n=1, NP12           read (61,*) X12(n),Y12(n)        ENDDO        print *,'FIN LECTURE V12.xyz', NP12       CLOSE(61)            OPEN (61,file='../BOUNDARIES/V13.xyz',status='old')        read (61,*) NP13        DO n=1, NP13           read (61,*) X13(n),Y13(n)        ENDDO        print *,'FIN LECTURE V13.xyz', NP13       CLOSE(61)            OPEN (61,file='../BOUNDARIES/V14.xyz',status='old')        read (61,*) NP14        DO n=1, NP14           read (61,*) X14(n),Y14(n)        ENDDO        print *,'FIN LECTURE V14.xyz', NP14       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V15.xyz',status='old')        read (61,*) NP15        DO n=1, NP15           read (61,*) X15(n),Y15(n)        ENDDO        print *,'FIN LECTURE V15.xyz', NP15       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V16.xyz',status='old')        read (61,*) NP16        DO n=1, NP16  150          read (61,*) X16(n),Y16(n)        ENDDO        print *,'FIN LECTURE V16.xyz', NP16       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V17.xyz',status='old')        read (61,*) NP17       DO n=1, NP17           read (61,*) X17(n),Y17(n)        ENDDO        print *,'FIN LECTURE V17.xyz', NP17       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V18.xyz',status='old')        read (61,*) NP18       DO n=1, NP18          read (61,*) X18(n),Y18(n)        ENDDO        print *,'FIN LECTURE V18.xyz', NP18       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V19.xyz',status='old')        read (61,*) NP19        DO n=1, NP19          read (61,*) X19(n),Y19(n)        ENDDO        print *,'FIN LECTURE V19.xyz', NP19       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V20.xyz',status='old')        read (61,*) NP20       DO n=1, NP20          read (61,*) X20(n),Y20(n)        ENDDO        print *,'FIN LECTURE V20.xyz', NP20       CLOSE(61)        OPEN (61,file='../BOUNDARIES/B1.xyz',status='old')        read (61,*) NP21        DO n=1, NP21           read (61,*) X21(n),Y21(n)        ENDDO        print *,'FIN LECTURE B1.xyz', NP21       CLOSE(61)         OPEN (61,file='../BOUNDARIES/B2.xyz',status='old')  151       read (61,*) NP22        DO n=1, NP22           read (61,*) X22(n),Y22(n)        ENDDO        print *,'FIN LECTURE B2.xyz', NP22       CLOSE(61)            OPEN (61,file='../BOUNDARIES/B3.xyz',status='old')        read (61,*) NP23        DO n=1, NP23           read (61,*) X23(n),Y23(n)        ENDDO        print *,'FIN LECTURE B3.xyz', NP23       CLOSE(61)            OPEN (61,file='../BOUNDARIES/B4.xyz',status='old')        read (61,*) NP24        DO n=1, NP24           read (61,*) X24(n),Y24(n)        ENDDO        print *,'FIN LECTURE B4.xyz', NP24       CLOSE(61)               OPEN (61,file='../BOUNDARIES/B5.xyz',status='old')        read (61,*) NP25        DO n=1, NP25           read (61,*) X25(n),Y25(n)        ENDDO        print *,'FIN LECTURE B5.xyz', NP25       CLOSE(61)               OPEN (61,file='../BOUNDARIES/B6.xyz',status='old')        read (61,*) NP26        DO n=1, NP26           read (61,*) X26(n),Y26(n)        ENDDO        print *,'FIN LECTURE B6.xyz', NP26       CLOSE(61)            DO J=1,NPOIN          IF (inpoly(X(J),Y(J),X1,Y1,NP1).OR.      &       inpoly(X(J),Y(J),X2,Y2,NP2).OR.      &       inpoly(X(J),Y(J),X3,Y3,NP3).OR.      &       inpoly(X(J),Y(J),X4,Y4,NP4).OR.        &       inpoly(X(J),Y(J),X5,Y5,NP5).OR.        &       inpoly(X(J),Y(J),X6,Y6,NP6).OR.   152      &       inpoly(X(J),Y(J),X7,Y7,NP7).OR.        &       inpoly(X(J),Y(J),X8,Y8,NP8).OR.        &       inpoly(X(J),Y(J),X9,Y9,NP9).OR.        &       inpoly(X(J),Y(J),X10,Y10,NP10).OR.        &       inpoly(X(J),Y(J),X11,Y11,NP11).OR.      &       inpoly(X(J),Y(J),X12,Y12,NP12).OR.      &       inpoly(X(J),Y(J),X13,Y13,NP13).OR.      &       inpoly(X(J),Y(J),X14,Y14,NP14).OR.        &       inpoly(X(J),Y(J),X15,Y15,NP15).OR.        &       inpoly(X(J),Y(J),X16,Y16,NP16).OR.        &       inpoly(X(J),Y(J),X17,Y17,NP17).OR.        &       inpoly(X(J),Y(J),X18,Y18,NP18).OR.        &       inpoly(X(J),Y(J),X19,Y19,NP19).OR.        &       inpoly(X(J),Y(J),X20,Y20,NP20).OR.        &       inpoly(X(J),Y(J),X21,Y21,NP21).OR.      &       inpoly(X(J),Y(J),X22,Y22,NP22).OR.      &       inpoly(X(J),Y(J),X23,Y23,NP23).OR.      &       inpoly(X(J),Y(J),X24,Y24,NP24).OR.        &       inpoly(X(J),Y(J),X25,Y25,NP25).OR.        &       inpoly(X(J),Y(J),X26,Y26,NP26)) THEN                            CHESTR%R(J)=0.025+0.000          ELSE              CHESTR%R(J)=0.025          ENDIF        ENDDO !       WRITE(*,*) ! !----------------------------------------------------------------------- !       DEALLOCATE(W) ! !----------------------------------------------------------------------- !       RETURN       END  C    SPECIFY HOW FRICTION COEFFICIENT WILL VARY WITH TIME IN TELEMAC2D !        *****************          SUBROUTINE CORSTR !        ***************** !brief    CORRECTS THE FRICTION COEFFICIENT ON THE BOTTOM !+                WHEN IT IS VARIABLE IN TIME.       USE BIEF       USE DECLARATIONS_TELEMAC2D 153       USE DECLARATIONS_SISYPHE, ONLY: ESOMT,ZR        IMPLICIT NONE       INTEGER LNG,LU       COMMON/INFO/LNG,LU        INTEGER I    !-----------------------------------------------------------------------  C MAYBE THIS SHOULD ONLY BE APPLIED INTO THE FLOODPLAIN???       DO I=1,NPOIN          IF(ESOMT%R(I)<-1.0) THEN              CHESTR%R(I)=0.025          ENDIF       ENDDO            RETURN       END  C    SPECIFY HOW FRICTION COEFFICIENT WILL VARY WITH TIME IN SISYPHE !        *************************          SUBROUTINE CORSTR_SISYPHE !        ************************* ! ! !*********************************************************************** ! SISYPHE   V6P1                                   21/07/2011 !*********************************************************************** ! !brief    CORRECTS THE BOTTOM FRICTION COEFFICIENT !+               (IF VARIABLE IN TIME). !       USE BIEF       USE DECLARATIONS_SISYPHE !       IMPLICIT NONE       INTEGER LNG,LU       COMMON/INFO/LNG,LU        INTEGER I    !-----------------------------------------------------------------------  C MAYBE THIS SHOULD ONLY BE APPLIED INTO THE FLOODPLAIN??? 154       DO I=1,NPOIN          IF(ESOMT%R(I)<-1.0) THEN              CHESTR%R(I)=0.025          ENDIF       ENDDO            RETURN       END  C    BEDLOAD TRANSPORT EQUATION INCORPORATING VEGETATION EFFECTS  C    COMBINATION OF MEYER PETER MULLER AND WILSON EQUATIONS   C        ************************          SUBROUTINE BEDLOAD_MEYER  C        ************************ C      &  (TETAP, HIDING, HIDFAC, DENS, GRAV, DM, AC,      &   ACP, QSC, SLOPEFF, COEFPN) C C brief    MEYER-PETER BEDLOAD TRANSPORT FORMULATION. C~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ C| AC             |<->| CRITICAL SHIELDS PARAMETER C| ACP            |<->| MODIFIED SHIELDS PARAMETER C| COEFPN         |<->| CORRECTION OF TRANSORT FOR SLOPING BED EFFECT C| DENS           |-->| RELATIVE DENSITY C| DM             |-->| SEDIMENT GRAIN DIAMETER C| GRAV           |-->| ACCELERATION OF GRAVITY C| HIDFAC         |-->| HIDING FACTOR FORMULAS C| HIDING         |-->| HIDING FACTOR CORRECTION  C| QSC            |<->| BED LOAD TRANSPORT  C| SLOPEFF        |-->| LOGICAL, SLOPING BED EFFECT OR NOT  C| TETAP          |-->| ADIMENSIONAL SKIN FRICTION C~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ C       USE INTERFACE_SISYPHE,      &    EX_BEDLOAD_MEYER => BEDLOAD_MEYER       USE BIEF       USE DECLARATIONS_SISYPHE, only : MPM_ARAY, ESOMT       USE DECLARATIONS_TELEMAC2D, only : CHESTR, NPOIN       USE DECLARATIONS_TELEMAC2D, only : PRIVE1, PRIVE2           IMPLICIT NONE       INTEGER LNG,LU       COMMON/INFO/LNG,LU 155  C 2/ GLOBAL VARIABLES C -------------------       TYPE(BIEF_OBJ),   INTENT(IN)    :: TETAP, HIDING       INTEGER,          INTENT(IN)    :: HIDFAC, SLOPEFF       DOUBLE PRECISION, INTENT(IN)    :: DENS, GRAV, DM, AC C WORK ARRAY T1       TYPE(BIEF_OBJ),   INTENT(INOUT) :: ACP         TYPE(BIEF_OBJ),   INTENT(INOUT) :: QSC, COEFPN C N1=GRAIN ROUGHNESS C N2=VEGETATION ROUGHNESS C PRIVE1=SHEAR STRESS FOR SEDIMENT TRANSPORT  C 3/ LOCAL VARIABLES C ------------------       DOUBLE PRECISION :: C2, N1, N2, MY,WY,MX,WX       INTEGER          :: I  C=================================================================== ===C C=================================================================== ===C C                               PROGRAM                                C C=================================================================== ===C C=================================================================== ===C        CALL CPSTVC(QSC,ACP)       CALL OS('X=C     ', X=ACP, C=AC) C      WRITE(*,*) AC C **************************************** C C ADJUST SHEAR STRESS FOR SED TRANSPORT    C (_IMP_) C **************************************** C        DO I=1,NPOIN       IF(ESOMT%R(I)<-1) THEN          PRIVE1(I)=TETAP%R(I)       ELSEIF(ESOMT%R(I)>0) THEN          PRIVE1(I)=TETAP%R(I)       ELSEIF(CHESTR%R(I)<N1) THEN          PRIVE1(I)=TETAP%R(I)       ELSE          N1=0.025          N2=CHESTR%R(I)-N1          PRIVE1(I)=TETAP%R(I)*N1/(N1**2+N2**2)**0.5 156       ENDIF       PRIVE2(I)=TETAP%R(I)       ENDDO     C **************************************** C C 0 - SLOPE EFFECT: SOULBY FORMULATION     C (_IMP_) C **************************************** C       IF(SLOPEFF == 2) THEN         CALL OS('X=XY    ', X=ACP, Y=COEFPN )       ENDIF  C **************************************** C C III - BEDLOAD TRANSPORT CORRECTED        C (_IMP_) C       FOR EXTENDED GRAIN SIZE            C (_IMP_) C       WITH VARIABLE MPM_COEFFICIENT      C C **************************************** C       C2 = SQRT(GRAV*DENS*DM**3)        DO I=1,NPOIN          IF (PRIVE1(I)-ACP%R(I)>=0) THEN              IF (PRIVE1(I)<0.18) THEN C                MEYER-PETER MULLER 1948                  QSC%R(I)=8*C2*(PRIVE1(I)-ACP%R(I))**1.5 C                 WRITE(*,*) 'MPM', PRIVE1(I) C             ELSEIF (PRIVE1(I)>0.5) THEN              ELSEIF (PRIVE1(I)>0.5) THEN C                WILSON 1966                  QSC%R(I)=12*C2*(PRIVE1(I)-ACP%R(I))**1.5 C                 WRITE(*,*) 'WILSON', PRIVE1(I)              ELSE C                INTERPOLATE BETWEEN WILSON AND MPM                  MX=0.18                  MY=8*C2*(MX-ACP%R(I))**1.5                  WX=0.5                  WY=12*C2*(WX-ACP%R(I))**1.5                  QSC%R(I)=MY*(PRIVE1(I)/MX)**(LOG(WY/MY)/LOG(WX/MX)) C                 WRITE(*,*) 'OTHER', PRIVE1(I)              ENDIF          ELSE              QSC%R(I)=0          ENDIF       ENDDO        C      IF ((HIDFAC == 1) .OR. (HIDFAC == 2) ) THEN C  157 C      DO I=1,NPOIN C         IF (PRIVE1(I)-ACP%R(I) >= 0) THEN C      QSC%R(I)=MPM_ARAY%R(I)*C2*(PRIVE1(I)-ACP%R(I)*HIDING%R(I))**1.5D0    C         ELSE C      QSC%R(I)=0 C         ENDIF C      ENDDO    C    C      ELSE C C      DO I=1,NPOIN C         IF (PRIVE1(I)-ACP%R(I) >= 0) THEN C      QSC%R(I)=MPM_ARAY%R(I)*HIDING%R(I)*C2*(PRIVE1(I)-ACP%R(I))**1.5D0 C         ELSE C      QSC%R(I)=0 C         ENDIF C      ENDDO       C C      ENDIF C=================================================================== ===C C=================================================================== ===C       RETURN       END  C    SPATIAL AND STRATIFICATION OF SEDIMENT    !        *********************          SUBROUTINE INIT_COMPO !        ********************* !      &(NCOUCHES) ! !*********************************************************************** ! SISYPHE   V6P1                                   21/07/2011 !*********************************************************************** ! !brief    INITIAL FRACTION DISTRIBUTION, STRATIFICATION, !+                VARIATION IN SPACE. ! !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !| NCOUCHES       |-->| NUMBER OF LAYER FOR EACH POINT !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !       USE BIEF       USE DECLARATIONS_SISYPHE 158 !       IMPLICIT NONE       INTEGER LNG,LU       COMMON/INFO/LNG,LU ! !+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ ! !                                       NPOIN       INTEGER, INTENT (INOUT)::NCOUCHES(*) ! !+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ !       INTEGER I, J, N C-----------------------------------------------------------------------    C       INTEGER NPMAX2        PARAMETER (NPMAX2=200)             INTEGER NP1       DOUBLE PRECISION X1(NPMAX2),Y1(NPMAX2)          INTEGER NP2       DOUBLE PRECISION X2(NPMAX2),Y2(NPMAX2)        INTEGER NP3       DOUBLE PRECISION X3(NPMAX2),Y3(NPMAX2)        INTEGER NP4       DOUBLE PRECISION X4(NPMAX2),Y4(NPMAX2)        INTEGER NP5       DOUBLE PRECISION X5(NPMAX2),Y5(NPMAX2)        INTEGER NP6       DOUBLE PRECISION X6(NPMAX2),Y6(NPMAX2)        INTEGER NP7       DOUBLE PRECISION X7(NPMAX2),Y7(NPMAX2)        INTEGER NP8       DOUBLE PRECISION X8(NPMAX2),Y8(NPMAX2)        INTEGER NP9       DOUBLE PRECISION X9(NPMAX2),Y9(NPMAX2)           INTEGER NP10       DOUBLE PRECISION X10(NPMAX2),Y10(NPMAX2)          INTEGER NP11       DOUBLE PRECISION X11(NPMAX2),Y11(NPMAX2)          INTEGER NP12       DOUBLE PRECISION X12(NPMAX2),Y12(NPMAX2)        INTEGER NP13       DOUBLE PRECISION X13(NPMAX2),Y13(NPMAX2)        INTEGER NP14       DOUBLE PRECISION X14(NPMAX2),Y14(NPMAX2)  159       INTEGER NP15       DOUBLE PRECISION X15(NPMAX2),Y15(NPMAX2)        INTEGER NP16       DOUBLE PRECISION X16(NPMAX2),Y16(NPMAX2)        INTEGER NP17       DOUBLE PRECISION X17(NPMAX2),Y17(NPMAX2)        INTEGER NP18       DOUBLE PRECISION X18(NPMAX2),Y18(NPMAX2)        INTEGER NP19       DOUBLE PRECISION X19(NPMAX2),Y19(NPMAX2)           INTEGER NP20       DOUBLE PRECISION X20(NPMAX2),Y20(NPMAX2)            INTEGER NP21       DOUBLE PRECISION X21(NPMAX2),Y21(NPMAX2)          INTEGER NP22       DOUBLE PRECISION X22(NPMAX2),Y22(NPMAX2)        INTEGER NP23       DOUBLE PRECISION X23(NPMAX2),Y23(NPMAX2)        INTEGER NP24       DOUBLE PRECISION X24(NPMAX2),Y24(NPMAX2)        INTEGER NP25       DOUBLE PRECISION X25(NPMAX2),Y25(NPMAX2)        INTEGER NP26       DOUBLE PRECISION X26(NPMAX2),Y26(NPMAX2)  C C-----------------------------------------------------------------------           WRITE(*,*)       WRITE(*,*) 'SET SEDIMENT SIZES ACCORDING TO FOLLOWING BOUNDARIES'       WRITE(*,*)        OPEN (61,file='../BOUNDARIES/V1.xyz',status='old')        read (61,*) NP1        DO n=1, NP1           read (61,*) X1(n),Y1(n)        ENDDO        print *,'FIN LECTURE V1.xyz', NP1       CLOSE(61)         OPEN (61,file='../BOUNDARIES/V2.xyz',status='old')        read (61,*) NP2        DO n=1, NP2           read (61,*) X2(n),Y2(n)        ENDDO        print *,'FIN LECTURE V2.xyz', NP2       CLOSE(61)  160           OPEN (61,file='../BOUNDARIES/V3.xyz',status='old')        read (61,*) NP3        DO n=1, NP3           read (61,*) X3(n),Y3(n)        ENDDO        print *,'FIN LECTURE V3.xyz', NP3       CLOSE(61)            OPEN (61,file='../BOUNDARIES/V4.xyz',status='old')        read (61,*) NP4        DO n=1, NP4           read (61,*) X4(n),Y4(n)        ENDDO        print *,'FIN LECTURE V4.xyz', NP4       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V5.xyz',status='old')        read (61,*) NP5        DO n=1, NP5           read (61,*) X5(n),Y5(n)        ENDDO        print *,'FIN LECTURE V5.xyz', NP5       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V6.xyz',status='old')        read (61,*) NP6        DO n=1, NP6           read (61,*) X6(n),Y6(n)        ENDDO        print *,'FIN LECTURE V6.xyz', NP6       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V7.xyz',status='old')        read (61,*) NP7       DO n=1, NP7           read (61,*) X7(n),Y7(n)        ENDDO        print *,'FIN LECTURE V7.xyz', NP7       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V8.xyz',status='old')        read (61,*) NP8       DO n=1, NP8          read (61,*) X8(n),Y8(n)        ENDDO  161       print *,'FIN LECTURE V8.xyz', NP8       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V9.xyz',status='old')        read (61,*) NP9        DO n=1, NP9          read (61,*) X9(n),Y9(n)        ENDDO        print *,'FIN LECTURE V9.xyz', NP9       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V10.xyz',status='old')        read (61,*) NP10       DO n=1, NP10          read (61,*) X10(n),Y10(n)        ENDDO        print *,'FIN LECTURE V10.xyz', NP10       CLOSE(61)        OPEN (61,file='../BOUNDARIES/V11.xyz',status='old')        read (61,*) NP11        DO n=1, NP11          read (61,*) X11(n),Y11(n)        ENDDO        print *,'FIN LECTURE V11.xyz', NP11       CLOSE(61)         OPEN (61,file='../BOUNDARIES/V12.xyz',status='old')        read (61,*) NP12        DO n=1, NP12           read (61,*) X12(n),Y12(n)        ENDDO        print *,'FIN LECTURE V12.xyz', NP12       CLOSE(61)            OPEN (61,file='../BOUNDARIES/V13.xyz',status='old')        read (61,*) NP13        DO n=1, NP13           read (61,*) X13(n),Y13(n)        ENDDO        print *,'FIN LECTURE V13.xyz', NP13       CLOSE(61)            OPEN (61,file='../BOUNDARIES/V14.xyz',status='old')        read (61,*) NP14        DO n=1, NP14  162          read (61,*) X14(n),Y14(n)        ENDDO        print *,'FIN LECTURE V14.xyz', NP14       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V15.xyz',status='old')        read (61,*) NP15        DO n=1, NP15           read (61,*) X15(n),Y15(n)        ENDDO        print *,'FIN LECTURE V15.xyz', NP15       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V16.xyz',status='old')        read (61,*) NP16        DO n=1, NP16           read (61,*) X16(n),Y16(n)        ENDDO        print *,'FIN LECTURE V16.xyz', NP16       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V17.xyz',status='old')        read (61,*) NP17       DO n=1, NP17           read (61,*) X17(n),Y17(n)        ENDDO        print *,'FIN LECTURE V17.xyz', NP17       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V18.xyz',status='old')        read (61,*) NP18       DO n=1, NP18          read (61,*) X18(n),Y18(n)        ENDDO        print *,'FIN LECTURE V18.xyz', NP18       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V19.xyz',status='old')        read (61,*) NP19        DO n=1, NP19          read (61,*) X19(n),Y19(n)        ENDDO        print *,'FIN LECTURE V19.xyz', NP19       CLOSE(61)               OPEN (61,file='../BOUNDARIES/V20.xyz',status='old')  163       read (61,*) NP20       DO n=1, NP20          read (61,*) X20(n),Y20(n)        ENDDO        print *,'FIN LECTURE V20.xyz', NP20       CLOSE(61)        OPEN (61,file='../BOUNDARIES/B1.xyz',status='old')        read (61,*) NP21        DO n=1, NP21           read (61,*) X21(n),Y21(n)        ENDDO        print *,'FIN LECTURE B1.xyz', NP21       CLOSE(61)         OPEN (61,file='../BOUNDARIES/B2.xyz',status='old')        read (61,*) NP22        DO n=1, NP22           read (61,*) X22(n),Y22(n)        ENDDO        print *,'FIN LECTURE B2.xyz', NP22       CLOSE(61)            OPEN (61,file='../BOUNDARIES/B3.xyz',status='old')        read (61,*) NP23        DO n=1, NP23           read (61,*) X23(n),Y23(n)        ENDDO        print *,'FIN LECTURE B3.xyz', NP23       CLOSE(61)            OPEN (61,file='../BOUNDARIES/B4.xyz',status='old')        read (61,*) NP24        DO n=1, NP24           read (61,*) X24(n),Y24(n)        ENDDO        print *,'FIN LECTURE B4.xyz', NP24       CLOSE(61)               OPEN (61,file='../BOUNDARIES/B5.xyz',status='old')        read (61,*) NP25        DO n=1, NP25           read (61,*) X25(n),Y25(n)        ENDDO        print *,'FIN LECTURE B5.xyz', NP25       CLOSE(61)     164           OPEN (61,file='../BOUNDARIES/B6.xyz',status='old')        read (61,*) NP26        DO n=1, NP26           read (61,*) X26(n),Y26(n)        ENDDO        print *,'FIN LECTURE B6.xyz', NP26       CLOSE(61)    C     SPECIFY NUMBER OF LAYERS, AND LAYER THICKNESSES          DO J=1,NPOIN          IF (inpoly(X(J),Y(J),X1,Y1,NP1).OR.      &       inpoly(X(J),Y(J),X2,Y2,NP2).OR.      &       inpoly(X(J),Y(J),X3,Y3,NP3).OR.      &       inpoly(X(J),Y(J),X4,Y4,NP4).OR.        &       inpoly(X(J),Y(J),X5,Y5,NP5).OR.        &       inpoly(X(J),Y(J),X6,Y6,NP6).OR.        &       inpoly(X(J),Y(J),X7,Y7,NP7).OR.        &       inpoly(X(J),Y(J),X8,Y8,NP8).OR.        &       inpoly(X(J),Y(J),X9,Y9,NP9).OR.        &       inpoly(X(J),Y(J),X10,Y10,NP10).OR.        &       inpoly(X(J),Y(J),X11,Y11,NP11).OR.      &       inpoly(X(J),Y(J),X12,Y12,NP12).OR.      &       inpoly(X(J),Y(J),X13,Y13,NP13).OR.      &       inpoly(X(J),Y(J),X14,Y14,NP14).OR.        &       inpoly(X(J),Y(J),X15,Y15,NP15).OR.        &       inpoly(X(J),Y(J),X16,Y16,NP16).OR.        &       inpoly(X(J),Y(J),X17,Y17,NP17).OR.        &       inpoly(X(J),Y(J),X18,Y18,NP18).OR.        &       inpoly(X(J),Y(J),X19,Y19,NP19).OR.        &       inpoly(X(J),Y(J),X20,Y20,NP20).OR.        &       inpoly(X(J),Y(J),X21,Y21,NP21).OR.      &       inpoly(X(J),Y(J),X22,Y22,NP22).OR.      &       inpoly(X(J),Y(J),X23,Y23,NP23).OR.      &       inpoly(X(J),Y(J),X24,Y24,NP24).OR.        &       inpoly(X(J),Y(J),X25,Y25,NP25).OR.        &       inpoly(X(J),Y(J),X26,Y26,NP26)) THEN               NCOUCHES(J) = 3              ES(J,1)=1              ES(J,2)=1              ES(J,3)=98                 AVAIL(J,1,1) = 1              AVAIL(J,1,2) = 0                AVAIL(J,1,3) = 0   165              AVAIL(J,2,1) = 0              AVAIL(J,2,2) = 1                 AVAIL(J,2,3) = 0                   AVAIL(J,3,1) = 0              AVAIL(J,3,2) = 0                 AVAIL(J,3,3) = 1                ELSE                  NCOUCHES(J) = 2              ES(J,1)=2              ES(J,2)=99                AVAIL(J,1,1) = 0              AVAIL(J,1,2) = 1                AVAIL(J,1,3) = 0                AVAIL(J,2,1) = 0              AVAIL(J,2,2) = 0                 AVAIL(J,2,3) = 1                       ENDIF        ENDDO         WRITE(*,*) ! !----------------------------------------------------------------------- !       RETURN       END  C    SPATIAL DEFINITION OF BEDROCK (RIGID BOUNDARY) ELEVATION C        *****************          SUBROUTINE NOEROD C        ***************** C      * (H , ZF , ZR , Z , X , Y , NPOIN , CHOIX , NLISS ) C C*********************************************************************** C SISYPHE VERSION 5.1                             C. LENORMANT C                                                 C COPYRIGHT EDF-DTMPL-SOGREAH-LHF-GRADIENT    C*********************************************************************** C C     FONCTION  : IMPOSE LA VALEUR DE LA COTE DU FOND NON ERODABLE  ZR C C 166 C     RQ: LES METHODES DE TRAITEMENT DES FONDS NON ERODABLES PEUVENT CONDUIRE C     A ZF < ZR A CERTAINS PAS DE TEMPS, POUR PALLIER A CELA ON PEUT CHOISIR  C     CHOISIR DE LISSER LA SOLUTION OBTENUE i.e NLISS > 0.   C C     FUNCTION  : IMPOSE THE RIGID BED LEVEL  ZR C C----------------------------------------------------------------------- C                             ARGUMENTS C .________________.____.______________________________________________ C |      NOM       |MODE|                   ROLE C |________________|____|______________________________________________ C |   H            | -->| WATER DEPTH C |   ZF           | -->| BED LEVEL C |   ZR           |<-- | RIGID BED LEVEL C |   Z            | -->| FREE SURFACE  C |   X,Y          | -->| 2D COORDINATES C |   NPOIN        | -->| NUMBER OF 2D POINTS C |   CHOIX        | -->| SELECTED METHOD FOR THE TREATMENT OF RIGID BEDS C |   NLISS        |<-->| NUMBER OF SMOOTHINGS C |________________|____|______________________________________________ C MODE : -->(INPUT), <--(RESULT), <-->(MODIFIED DATA) C----------------------------------------------------------------------- C       USE BIEF C      USE DECLARATIONS_SISYPHE, ONLY : MESH,NPTFR C       IMPLICIT NONE       INTEGER LNG,LU       COMMON/INFO/LNG,LU C C+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ C       INTEGER, INTENT(IN):: NPOIN , CHOIX       INTEGER, INTENT(INOUT):: NLISS  C       DOUBLE PRECISION, INTENT(IN)::  Z(NPOIN) , ZF(NPOIN)           DOUBLE PRECISION , INTENT(IN)::  X(NPOIN) , Y(NPOIN), H(NPOIN)       DOUBLE PRECISION , INTENT(INOUT)::  ZR(NPOIN) C C+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ C       INTEGER I       INTEGER k, n       DOUBLE PRECISION C  167       DOUBLE PRECISION ZEMAX, XMAX       INTEGER NPMAX2        PARAMETER (NPMAX2=200)             INTEGER NP1       DOUBLE PRECISION X1(NPMAX2),Y1(NPMAX2)          INTEGER NP2       DOUBLE PRECISION X2(NPMAX2),Y2(NPMAX2)        INTEGER NP3       DOUBLE PRECISION X3(NPMAX2),Y3(NPMAX2)        INTEGER NP4       DOUBLE PRECISION X4(NPMAX2),Y4(NPMAX2)        INTEGER NP5       DOUBLE PRECISION X5(NPMAX2),Y5(NPMAX2)        INTEGER NP6       DOUBLE PRECISION X6(NPMAX2),Y6(NPMAX2)        INTEGER NP7       DOUBLE PRECISION X7(NPMAX2),Y7(NPMAX2)        INTEGER NP8       DOUBLE PRECISION X8(NPMAX2),Y8(NPMAX2)        INTEGER NP9       DOUBLE PRECISION X9(NPMAX2),Y9(NPMAX2)           INTEGER NP10       DOUBLE PRECISION X10(NPMAX2),Y10(NPMAX2)         C C-------------------- C RIGID BEDS POSITION C--------------------- C C     DEFAULT VALUE:       ZR=ZF-100.  C                  C    ZEMAX: EPAISSEUR MAX DU LIT              ZEMAX=100.D0       CALL OV( 'X=Y+C     ',ZR,ZF,ZF,-ZEMAX,NPOIN)                                                C      print *,'DANS NOEROD...'  C      OPEN (61,file='../BOUNDARIES/1.xyz',status='old')  C      read (61,*) NP1  C      DO n=1, NP1  C         read (61,*) X1(n),Y1(n)  C      ENDDO  C      print *,'FIN LECTURE 1.xyz', NP1 C      CLOSE(61)   168     C      DO N=1,NPOIN C         ZR(N) = ZF(N)-2.0 C      IF (inpoly(x(N),y(N),X1,Y1,NP1)) THEN C         ZR(N)= ZF(N)-0.5 C      ELSEIF (inpoly(x(N),y(N),X2,Y2,NP2)) THEN C         ZR(N)= ZF(N)-1.0 C      ENDIF  C      ENDDO C  C------------------ C SMOOTHING OPTION C------------------ C C     NLISS : NUMBER OF SMOOTHING IF  (ZF - ZR ) NEGATIVE C             DEFAULT VALUE : NLISS = 0 (NO SMOOTHING) C       NLISS = 0         C C----------------------------------------------------------------------- C       RETURN       END  C    TELEMAC2D GRAPHICAL OUTPUT !        ***************************          SUBROUTINE NOMVAR_TELEMAC2D !        *************************** !      &(TEXTE,TEXTPR,MNEMO,NPERIAF,NTRAC,NAMETRAC) ! !*********************************************************************** ! TELEMAC2D   V6P1                                   21/08/2010 !*********************************************************************** ! !brief    GIVES THE VARIABLE NAMES FOR THE RESULTS AND GEOMETRY !+                FILES (IN TEXTE) AND FOR THE PREVIOUS COMPUTATION !+                RESULTS FILE (IN TEXTPR). !+ !+                TEXTE AND TEXTPR ARE GENERALLY EQUAL EXCEPT IF THE !+                PREVIOUS COMPUTATION COMES FROM ANOTHER SOFTWARE. ! !history  J-M HERVOUET (LNHE) !+        31/08/2007 !+        V5P8 !+ 169 ! !history  N.DURAND (HRW), S.E.BOURBAN (HRW) !+        13/07/2010 !+        V6P0 !+   Translation of French comments within the FORTRAN sources into !+   English comments ! !history  N.DURAND (HRW), S.E.BOURBAN (HRW) !+        21/08/2010 !+        V6P0 !+   Creation of DOXYGEN tags for automated documentation and !+   cross-referencing of the FORTRAN sources ! !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !| MNEMO          |<--| MNEMONIC FOR 'VARIABLES FOR GRAPHIC OUTPUTS' !| NAMETRAC       |-->| NAME OF TRACERS (GIVEN BY KEYWORDS) !| NPERIAF        |-->| NUMBER OF PERIODS FOR FOURRIER ANALYSIS !| NTRAC          |-->| NUMBER OF TRACERS !| TEXTE          |<--| SEE ABOVE !| TEXTPR         |<--| SEE ABOVE !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !       IMPLICIT NONE       INTEGER LNG,LU       COMMON/INFO/LNG,LU ! !+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ !       CHARACTER(LEN=32), INTENT(INOUT) :: TEXTE(*),TEXTPR(*)       CHARACTER(LEN=8),  INTENT(INOUT) :: MNEMO(*)       INTEGER, INTENT(IN)              :: NPERIAF,NTRAC       CHARACTER(LEN=32), INTENT(IN)    :: NAMETRAC(32) ! !+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ !       CHARACTER(LEN=2) I_IN_2_LETTERS(32)       DATA I_IN_2_LETTERS /'1 ','2 ','3 ','4 ','5 ','6 ','7 ','8 ','9 ',      &                     '10','11','12','13','14','15','16','17','18',      &                     '19','20','21','22','23','24','25','26','27',      &                     '28','29','30','31','32'/       INTEGER I ! !----------------------------------------------------------------------- ! !  ENGLISH ! 170       IF(LNG.EQ.2) THEN !       TEXTE (1 ) = 'VELOCITY U      M/S             '       TEXTE (2 ) = 'VELOCITY V      M/S             '       TEXTE (3 ) = 'CELERITY        M/S             '       TEXTE (4 ) = 'WATER DEPTH     M               '       TEXTE (5 ) = 'FREE SURFACE    M               '       TEXTE (6 ) = 'BOTTOM          M               '       TEXTE (7 ) = 'FROUDE NUMBER                   '       TEXTE (8 ) = 'SCALAR FLOWRATE M2/S            '       TEXTE (9 ) = 'EX TRACER                       '       TEXTE (10) = 'TURBULENT ENERG.JOULE/KG        '       TEXTE (11) = 'DISSIPATION     WATT/KG         '       TEXTE (12) = 'VISCOSITY       M2/S            '       TEXTE (13) = 'FLOWRATE ALONG XM2/S            '       TEXTE (14) = 'FLOWRATE ALONG YM2/S            '       TEXTE (15) = 'SCALAR VELOCITY M/S             '       TEXTE (16) = 'WIND ALONG X    M/S             '       TEXTE (17) = 'WIND ALONG Y    M/S             '       TEXTE (18) = 'AIR PRESSURE    PASCAL          '       TEXTE (19) = 'BOTTOM FRICTION                 '       TEXTE (20) = 'DRIFT ALONG X   M               '       TEXTE (21) = 'DRIFT ALONG Y   M               '       TEXTE (22) = 'COURANT NUMBER                  '       TEXTE (23) = 'GRAIN SHEAR     NONDIMENSIONAL  '       TEXTE (24) = 'TOTAL SHEAR     NONDIMENSIONAL  '       TEXTE (25) = 'VARIABLE 25     UNIT   ??       '       TEXTE (26) = 'VARIABLE 26     UNIT   ??       '       TEXTE (27) = 'HIGH WATER MARK M               '       TEXTE (28) = 'HIGH WATER TIME S               '       TEXTE (29) = 'HIGHEST VELOCITYM/S             '       TEXTE (30) = 'TIME OF HIGH VELS               '       TEXTE (31) = 'FRICTION VEL.   M/S             ' ! ! TEXTPR IS USED TO READ PREVIOUS COMPUTATION FILES. ! IN GENERAL TEXTPR=TEXTE BUT YOU CAN FOLLOW UP A COMPUTATION ! FROM ANOTHER CODE WITH DIFFERENT VARIABLE NAMES, WHICH MUST ! BE GIVEN HERE: !       TEXTPR (1 ) = 'VELOCITY U      M/S             '       TEXTPR (2 ) = 'VELOCITY V      M/S             '       TEXTPR (3 ) = 'CELERITY        M/S             '       TEXTPR (4 ) = 'WATER DEPTH     M               '       TEXTPR (5 ) = 'FREE SURFACE    M               '       TEXTPR (6 ) = 'BOTTOM          M               '       TEXTPR (7 ) = 'FROUDE NUMBER                   ' 171       TEXTPR (8 ) = 'SCALAR FLOWRATE M2/S            '       TEXTPR (9 ) = 'EX TRACER                       '       TEXTPR (10) = 'TURBULENT ENERG.JOULE/KG        '       TEXTPR (11) = 'DISSIPATION     WATT/KG         '       TEXTPR (12) = 'VISCOSITY       M2/S            '       TEXTPR (13) = 'FLOWRATE ALONG XM2/S            '       TEXTPR (14) = 'FLOWRATE ALONG YM2/S            '       TEXTPR (15) = 'SCALAR VELOCITY M/S             '       TEXTPR (16) = 'WIND ALONG X    M/S             '       TEXTPR (17) = 'WIND ALONG Y    M/S             '       TEXTPR (18) = 'AIR PRESSURE    PASCAL          '       TEXTPR (19) = 'BOTTOM FRICTION                 '       TEXTPR (20) = 'DRIFT ALONG X   M               '       TEXTPR (21) = 'DRIFT ALONG Y   M               '       TEXTPR (22) = 'COURANT NUMBER                  '       TEXTPR (23) = 'GRAIN SHEAR     NONDIMENSIONAL  '       TEXTPR (24) = 'TOTAL SHEAR     NONDIMENSIONAL  '       TEXTPR (25) = 'VARIABLE 25     UNIT   ??       '       TEXTPR (26) = 'VARIABLE 26     UNIT   ??       '       TEXTPR (27) = 'HIGH WATER MARK M               '       TEXTPR (28) = 'HIGH WATER TIME S               '       TEXTPR (29) = 'HIGHEST VELOCITYM/S             '       TEXTPR (30) = 'TIME OF HIGH VELS               '       TEXTPR (31) = 'FRICTION VEL.   M/S             ' ! !----------------------------------------------------------------------- ! !  FRANCAIS OU AUTRE !       ELSE !       TEXTE (1 ) = 'VELOCITY U      M/S             '       TEXTE (2 ) = 'VELOCITY V      M/S             '       TEXTE (3 ) = 'CELERITY        M/S             '       TEXTE (4 ) = 'WATER DEPTH     M               '       TEXTE (5 ) = 'FREE SURFACE    M               '       TEXTE (6 ) = 'BOTTOM          M               '       TEXTE (7 ) = 'FROUDE NUMBER                   '       TEXTE (8 ) = 'SCALAR FLOWRATE M2/S            '       TEXTE (9 ) = 'EX TRACER                       '       TEXTE (10) = 'TURBULENT ENERG.JOULE/KG        '       TEXTE (11) = 'DISSIPATION     WATT/KG         '       TEXTE (12) = 'VISCOSITY       M2/S            '       TEXTE (13) = 'FLOWRATE ALONG XM2/S            '       TEXTE (14) = 'FLOWRATE ALONG YM2/S            '       TEXTE (15) = 'SCALAR VELOCITY M/S             ' 172       TEXTE (16) = 'WIND ALONG X    M/S             '       TEXTE (17) = 'WIND ALONG Y    M/S             '       TEXTE (18) = 'AIR PRESSURE    PASCAL          '       TEXTE (19) = 'BOTTOM FRICTION                 '       TEXTE (20) = 'DRIFT ALONG X   M               '       TEXTE (21) = 'DRIFT ALONG Y   M               '       TEXTE (22) = 'COURANT NUMBER                  '       TEXTE (23) = 'GRAIN SHEAR     NONDIMENSIONAL  '       TEXTE (24) = 'TOTAL SHEAR     NONDIMENSIONAL  '       TEXTE (25) = 'VARIABLE 25     UNIT   ??       '       TEXTE (26) = 'VARIABLE 26     UNIT   ??       '       TEXTE (27) = 'HIGH WATER MARK M               '       TEXTE (28) = 'HIGH WATER TIME S               '       TEXTE (29) = 'HIGHEST VELOCITYM/S             '       TEXTE (30) = 'TIME OF HIGH VELS               '       TEXTE (31) = 'FRICTION VEL.   M/S             ' ! ! TEXTPR IS USED TO READ PREVIOUS COMPUTATION FILES. ! IN GENERAL TEXTPR=TEXTE BUT YOU CAN FOLLOW UP A COMPUTATION ! FROM ANOTHER CODE WITH DIFFERENT VARIABLE NAMES, WHICH MUST ! BE GIVEN HERE: !       TEXTPR (1 ) = 'VELOCITY U      M/S             '       TEXTPR (2 ) = 'VELOCITY V      M/S             '       TEXTPR (3 ) = 'CELERITY        M/S             '       TEXTPR (4 ) = 'WATER DEPTH     M               '       TEXTPR (5 ) = 'FREE SURFACE    M               '       TEXTPR (6 ) = 'BOTTOM          M               '       TEXTPR (7 ) = 'FROUDE NUMBER                   '       TEXTPR (8 ) = 'SCALAR FLOWRATE M2/S            '       TEXTPR (9 ) = 'EX TRACER                       '       TEXTPR (10) = 'TURBULENT ENERG.JOULE/KG        '       TEXTPR (11) = 'DISSIPATION     WATT/KG         '       TEXTPR (12) = 'VISCOSITY       M2/S            '       TEXTPR (13) = 'FLOWRATE ALONG XM2/S            '       TEXTPR (14) = 'FLOWRATE ALONG YM2/S            '       TEXTPR (15) = 'SCALAR VELOCITY M/S             '       TEXTPR (16) = 'WIND ALONG X    M/S             '       TEXTPR (17) = 'WIND ALONG Y    M/S             '       TEXTPR (18) = 'AIR PRESSURE    PASCAL          '       TEXTPR (19) = 'BOTTOM FRICTION                 '       TEXTPR (20) = 'DRIFT ALONG X   M               '       TEXTPR (21) = 'DRIFT ALONG Y   M               '       TEXTPR (22) = 'COURANT NUMBER                  '       TEXTPR (23) = 'GRAIN SHEAR     NONDIMENSIONAL  '       TEXTPR (24) = 'TOTAL SHEAR     NONDIMENSIONAL  ' 173       TEXTPR (25) = 'VARIABLE 25     UNIT   ??       '       TEXTPR (26) = 'VARIABLE 26     UNIT   ??       '       TEXTPR (27) = 'HIGH WATER MARK M               '       TEXTPR (28) = 'HIGH WATER TIME S               '       TEXTPR (29) = 'HIGHEST VELOCITYM/S             '       TEXTPR (30) = 'TIME OF HIGH VELS               '       TEXTPR (31) = 'FRICTION VEL.   M/S             ' !       ENDIF ! !----------------------------------------------------------------------- ! !   ALIASES FOR THE VARIABLES IN THE STEERING FILE ! !     UVCHSBFQTKEDIJMXYPWAGLNORZ !     VELOCITY COMPONENT U       MNEMO(1)   = 'U       ' !     VELOCITY COMPONENT V       MNEMO(2)   = 'V       ' !     CELERITY       MNEMO(3)   = 'C       ' !     WATER DEPTH       MNEMO(4)   = 'H       ' !     FREE SURFACE ELEVATION       MNEMO(5)   = 'S       ' !     BOTTOM ELEVATION       MNEMO(6)   = 'B       ' !     FROUDE       MNEMO(7)   = 'F       ' !     FLOW RATE       MNEMO(8)   = 'Q       ' !     EX TRACER       MNEMO(9)   = '?       ' !     TURBULENT ENERGY       MNEMO(10)   = 'K       ' !     DISSIPATION       MNEMO(11)   = 'E       ' !     TURBULENT VISCOSITY       MNEMO(12)   = 'D       ' !     FLOWRATE ALONG X       MNEMO(13)   = 'I       ' !     FLOWRATE ALONG Y       MNEMO(14)   = 'J       ' !     SPEED       MNEMO(15)   = 'M       ' !     WIND COMPONENT X 174       MNEMO(16)   = 'X       ' !     WIND COMPONENT Y       MNEMO(17)   = 'Y       ' !     ATMOSPHERIC PRESSURE       MNEMO(18)   = 'P       ' !     FRICTION       MNEMO(19)   = 'W       ' !     DRIFT IN X       MNEMO(20)   = 'A       ' !     DRIFT IN Y       MNEMO(21)   = 'G       ' !     COURANT NUMBER       MNEMO(22)   = 'L       ' !     VARIABLE 23       MNEMO(23)   = 'N       ' !     VARIABLE 24       MNEMO(24)   = 'O       ' !     VARIABLE 25       MNEMO(25)   = 'R       ' !     VARIABLE 26       MNEMO(26)   = 'Z       ' !     VARIABLE 27       MNEMO(27)   = 'MAXZ    ' !     VARIABLE 28       MNEMO(28)   = 'TMXZ    ' !     VARIABLE 29       MNEMO(29)   = 'MAXV    ' !     VARIABLE 30       MNEMO(30)   = 'TMXV    ' !     VARIABLE 31       MNEMO(31)   = 'US      ' ! !----------------------------------------------------------------------- ! !     FOURIER ANALYSES !       IF(NPERIAF.GT.0) THEN         DO I=1,NPERIAF           IF(LNG.EQ.1) THEN             TEXTE(32+NTRAC+2*(I-1)) =  'AMPLI PERIODE '      &                         //I_IN_2_LETTERS(I)      &                         //'M               '             TEXTE(33+NTRAC+2*(I-1)) =  'PHASE PERIODE '      &                         //I_IN_2_LETTERS(I)      &                         //'DEGRES          '             TEXTPR(32+NTRAC+2*(I-1)) =  'AMPLI PERIODE ' 175      &                         //I_IN_2_LETTERS(I)      &                         //'M               '             TEXTPR(33+NTRAC+2*(I-1)) =  'PHASE PERIODE '      &                         //I_IN_2_LETTERS(I)      &                         //'DEGRES          '           ELSE             TEXTE(32+NTRAC+2*(I-1)) =  'AMPLI PERIOD  '      &                         //I_IN_2_LETTERS(I)      &                         //'M               '             TEXTE(33+NTRAC+2*(I-1)) =  'PHASE PERIOD  '      &                         //I_IN_2_LETTERS(I)      &                         //'DEGRES          '             TEXTPR(32+NTRAC+2*(I-1)) =  'AMPLI PERIOD  '      &                         //I_IN_2_LETTERS(I)      &                         //'M               '             TEXTPR(33+NTRAC+2*(I-1)) =  'PHASE PERIOD  '      &                         //I_IN_2_LETTERS(I)      &                         //'DEGRES          '           ENDIF           MNEMO(32+NTRAC+2*(I-1)) = 'AMPL'//I_IN_2_LETTERS(I)//'  '           MNEMO(33+NTRAC+2*(I-1)) = 'PHAS'//I_IN_2_LETTERS(I)//'  '         ENDDO       ENDIF ! !----------------------------------------------------------------------- ! !     TRACERS !       IF(NTRAC.GT.0) THEN         DO I=1,NTRAC           TEXTE(31+I)  = NAMETRAC(I)           TEXTPR(31+I) = NAMETRAC(I)           MNEMO(31+I)  = 'T'//I_IN_2_LETTERS(I)//'   '         ENDDO       ENDIF ! !----------------------------------------------------------------------- !       RETURN       END  C    SISYPHE GRAPHICAL OUTPUT !        *************************          SUBROUTINE NOMVAR_SISYPHE !        ************************* ! 176      &( TEXTE ,TEXTPR , MNEMO , NSICLA , UNIT ) ! !*********************************************************************** ! SISYPHE   V6P1                                   21/07/2011 !*********************************************************************** ! !brief    GIVES THE VARIABLE NAMES FOR THE RESULTS AND !+                GEOMETRY FILES. ! !history  E. PELTIER; C. LENORMANT; J.-M. HERVOUET !+        11/09/95 !+ !+ ! !history  M. GONZALES DE LINARES; C.VILLARET !+        2003 !+ !+ ! !history  JMH !+        03/11/2009 !+        V6P0 !+   MODIFIED AFTER JACEK JANKOWSKI DEVELOPMENTS ! !history  N.DURAND (HRW), S.E.BOURBAN (HRW) !+        13/07/2010 !+        V6P0 !+   Translation of French comments within the FORTRAN sources into !+   English comments ! !history  N.DURAND (HRW), S.E.BOURBAN (HRW) !+        21/08/2010 !+        V6P0 !+   Creation of DOXYGEN tags for automated documentation and !+   cross-referencing of the FORTRAN sources ! !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !| MNEMO          |<--| SYMBOLS TO SPECIFY THE VARIABLES FOR OUTPUT !|                |   | IN THE STEERING FILE !| NSICLA         |-->| NUMBER OF SIZE CLASSES FOR BED MATERIALS !| TEXTE          |<--| NAMES OF VARIABLES (PRINTOUT) !| TEXTPR         |<--| NAMES OF VARIABLES (INPUT) !| UNIT           |-->| LOGICAL, FILE NUMBER !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! 177       USE DECLARATIONS_SISYPHE, ONLY : MAXVAR,NSICLM,NLAYMAX,NOMBLAY,      &                                 NPRIV !       IMPLICIT NONE       INTEGER LNG,LU       COMMON/INFO/LNG,LU ! !+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ !       INTEGER, INTENT(IN)         :: NSICLA       CHARACTER*8, INTENT(INOUT)  :: MNEMO(MAXVAR)       CHARACTER*32, INTENT(INOUT) :: TEXTE(MAXVAR),TEXTPR(MAXVAR)       LOGICAL, INTENT(IN)         :: UNIT ! !+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ !       INTEGER I,J,K,ADD !       CHARACTER(LEN=32) TEXTE_AVAI(NLAYMAX*NSICLM),TEXTE_QS(NSICLM)       CHARACTER(LEN=32) TEXTE_CS(NSICLM),TEXTE_QSC(NSICLM)       CHARACTER(LEN=32) TEXTE_QSS(NSICLM),TEXTE_ES(NLAYMAX)       CHARACTER(LEN=8)  MNEMO_AVAI(NLAYMAX*NSICLM),MNEMO_QS(NSICLM)       CHARACTER(LEN=8)  MNEMO_CS(NSICLM),MNEMO_ES(NLAYMAX)       CHARACTER(LEN=8)  MNEMO_QSC(NSICLM),MNEMO_QSS(NSICLM)       CHARACTER(LEN=2)  CLA       CHARACTER(LEN=1)  LAY ! !----------------------------------------------------------------------- ! CV 3010 +1       ADD=27+MAX(4,NPRIV)+NSICLA*(NOMBLAY+4)+NOMBLAY !V      ADD=26+MAX(4,NPRIV)+NSICLA*(NOMBLAY+4)+NOMBLAY       IF(ADD.GT.MAXVAR) THEN         IF(LNG.EQ.1) THEN          WRITE(LU,*) 'NOMVAR_SISYPHE : MAXVAR DOIT VALOIR AU MOINS ',ADD         ENDIF         IF(LNG.EQ.2) THEN          WRITE(LU,*) 'NOMVAR_SISYPHE: MAXVAR SHOULD BE AT LEAST ',ADD         ENDIF         CALL PLANTE(1)         STOP       ENDIF ! !----------------------------------------------------------------------- !     2 3RD FRACTION MEANS FRACTION OF SEDIMENT OF CLASS 3 IN 2ND LAYER ! 178       IF(NOMBLAY.GT.9.OR.NSICLA.GT.99) THEN         WRITE (LU,*) 'REPROGRAM NOMVAR_SISYPHE DUE TO CONSTANT FORMATS'         CALL PLANTE(1)         STOP       ENDIF !       DO I=1,NSICLA         DO J=1,NOMBLAY           K=(I-1)*NOMBLAY+J           WRITE(LAY,'(I1)') J           IF(I.LT.10) THEN             WRITE(CLA,'(I1)') I           ELSE             WRITE(CLA,'(I2)') I           ENDIF           TEXTE_AVAI(K) = TRIM('FRAC LAY '//LAY//' CL '//CLA)           MNEMO_AVAI(K) = TRIM(LAY//'A'//CLA)         ENDDO       ENDDO !       DO J=1,NSICLA         IF(J<10) THEN           WRITE(CLA,'(I1)') J         ELSE           WRITE(CLA,'(I2)') J         ENDIF         TEXTE_QS(J)  = TRIM('QS CLASS '//CLA)         TEXTE_QSC(J) = TRIM('QS BEDLOAD CL'//CLA)         TEXTE_QSS(J) = TRIM('QS SUSP. CL'//CLA)         IF(UNIT) THEN           TEXTE_CS(J) = TRIM('CONC MAS CL'//CLA)           TEXTE_CS(J)(17:19) = 'G/L'         ELSE           TEXTE_CS(J) = TRIM('CONC VOL CL'//CLA)         ENDIF         MNEMO_QS(J)  = TRIM('QS'//CLA)         MNEMO_QSC(J) = TRIM('QSBL'//CLA)         MNEMO_QSS(J) = TRIM('QSS'//CLA)         MNEMO_CS(J)  = TRIM('CS'//CLA)       ENDDO !       DO K=1,NOMBLAY         WRITE(LAY,'(I1)') K !V        TEXTE_ES(K)(1:16)  = 'LAY. '//LAY//' THICKNESS'         TEXTE_ES(K)(1:16)  = 'LAYER'//LAY//' THICKNESS'         TEXTE_ES(K)(17:32) = 'M               ' 179         MNEMO_ES(K) = LAY//'ES     '       ENDDO ! !----------------------------------------------------------------------- !       IF(LNG.EQ.2) THEN ! !       ENGLISH VERSION !         TEXTE(01) = 'VELOCITY U      M/S             '         TEXTE(02) = 'VELOCITY V      M/S             '         TEXTE(03) = 'WATER DEPTH     M               '         TEXTE(04) = 'FREE SURFACE    M               '         TEXTE(05) = 'BOTTOM          M               '         TEXTE(06) = 'FLOWRATE Q      M3/S/M          '         TEXTE(07) = 'FLOWRATE QX     M3/S/M          '         TEXTE(08) = 'FLOWRATE QY     M3/S/M          '         TEXTE(09) = 'RIGID BED       M               '         TEXTE(10) = 'FRICTION COEFT                  '         TEXTE(11) = 'BED SHEAR STRESSN/M2        '         TEXTE(12) = 'WAVE HEIGHT HM0 M               '         TEXTE(13) = 'PEAK PERIOD TPR5S               '         TEXTE(14) = 'MEAN DIRECTION  DEG             '         TEXTE(15) = 'SOLID DISCH     M2/S            '         TEXTE(16) = 'SOLID DISCH X   M2/S            '         TEXTE(17) = 'SOLID DISCH Y   M2/S            '         TEXTE(18) = 'EVOLUTION       M               '         TEXTE(19) = 'RUGOSITE TOTALE M               '         TEXTE(20) = 'FROT. PEAU MU                   ' !V 2010         TEXTE(21) = 'MEAN DIAMETER M                 ' ! CV 2010 +1         ADD=NSICLA*(NOMBLAY+2)         TEXTE(22+ADD)='QS BEDLOAD      M2/S            '         TEXTE(23+ADD)='QS BEDLOAD X    M2/S            '         TEXTE(24+ADD)='QS BEDLOAD Y    M2/S            '         TEXTE(25+ADD)='QS SUSPENSION   M2/S            '         TEXTE(26+ADD)='QS SUSPENSION X M2/S            '         TEXTE(27+ADD)='QS SUSPENSION Y M2/S            ' !       ELSE ! !       FRENCH VERSION !         TEXTE(01) = 'VELOCITY U      M/S             '         TEXTE(02) = 'VELOCITY V      M/S             ' 180         TEXTE(03) = 'WATER DEPTH     M               '         TEXTE(04) = 'FREE SURFACE    M               '         TEXTE(05) = 'BOTTOM          M               '         TEXTE(06) = 'FLOWRATE Q      M3/S/M          '         TEXTE(07) = 'FLOWRATE QX     M3/S/M          '         TEXTE(08) = 'FLOWRATE QY     M3/S/M          '         TEXTE(09) = 'RIGID BED       M               '         TEXTE(10) = 'FRICTION COEFT                  '         TEXTE(11) = 'BED SHEAR STRESSN/M2        '         TEXTE(12) = 'WAVE HEIGHT HM0 M               '         TEXTE(13) = 'PEAK PERIOD TPR5S               '         TEXTE(14) = 'MEAN DIRECTION  DEG             '         TEXTE(15) = 'SOLID DISCH     M2/S            '         TEXTE(16) = 'SOLID DISCH X   M2/S            '         TEXTE(17) = 'SOLID DISCH Y   M2/S            '         TEXTE(18) = 'EVOLUTION       M               '         TEXTE(19) = 'RUGOSITE TOTALE M               '         TEXTE(20) = 'FROT. PEAU MU                   ' !V 2010         TEXTE(21) = 'MEAN DIAMETER M                 ' ! CV 2010 +1         ADD=NSICLA*(NOMBLAY+2)         TEXTE(22+ADD)='QS BEDLOAD      M2/S            '         TEXTE(23+ADD)='QS BEDLOAD X    M2/S            '         TEXTE(24+ADD)='QS BEDLOAD Y    M2/S            '         TEXTE(25+ADD)='QS SUSPENSION   M2/S            '         TEXTE(26+ADD)='QS SUSPENSION X M2/S            '         TEXTE(27+ADD)='QS SUSPENSION Y M2/S            ' !       ENDIF ! !     AVAIL: ALL LAYERS OF CLASS 1, THEN ALL LAYERS OF CLASS 2, ETC. !            SAME ORDER AS IN POINT_SISYPHE !       DO J=1,NOMBLAY         DO I=1,NSICLA !V 2010    +1           TEXTE(21+(I-1)*NOMBLAY+J) = TEXTE_AVAI((I-1)*NOMBLAY+J)           MNEMO(21+(I-1)*NOMBLAY+J) = MNEMO_AVAI((I-1)*NOMBLAY+J)         ENDDO       ENDDO !       DO I=1,NSICLA !V 2010    +1         TEXTE(21+I+NOMBLAY*NSICLA)     = TEXTE_QS(I)         MNEMO(21+I+NOMBLAY*NSICLA)     = MNEMO_QS(I) 181         TEXTE(21+I+(NOMBLAY+1)*NSICLA) = TEXTE_CS(I)         MNEMO(21+I+(NOMBLAY+1)*NSICLA) = MNEMO_CS(I)         TEXTE(27+I+NSICLA*(NOMBLAY+2)) = TEXTE_QSC(I)         MNEMO(27+I+NSICLA*(NOMBLAY+2)) = MNEMO_QSC(I)         TEXTE(27+I+NSICLA*(NOMBLAY+3)) = TEXTE_QSS(I)         MNEMO(27+I+NSICLA*(NOMBLAY+3)) = MNEMO_QSS(I)       ENDDO ! !V 2010    +1       DO I=1,NOMBLAY         TEXTE(27+I+NSICLA*(NOMBLAY+4)) = TEXTE_ES(I)         MNEMO(27+I+NSICLA*(NOMBLAY+4)) = MNEMO_ES(I)       ENDDO !       ADD=NSICLA*(NOMBLAY+4)+NOMBLAY       TEXTE(28+ADD)='PRIVE 1                         '       TEXTE(29+ADD)='PRIVE 2                         '       TEXTE(30+ADD)='PRIVE 3                         '       TEXTE(31+ADD)='PRIVE 4                         ' !     NPRIV MAY BE GREATER THAN 4 !     TEXTE(31+ADD)='PRIVE 5                         ' ! !V 2010 +1       DO I=1,31+NSICLA*(NOMBLAY+4)+NOMBLAY         TEXTPR(I)=TEXTE(I)       ENDDO ! !----------------------------------------------------------------------- ! !     OTHER NAMES FOR OUTPUT VARIABLES (STEERING FILE) ! !     VELOCITY U       MNEMO(1)   = 'U       ' !     VELOCITY V       MNEMO(2)   = 'V       ' !     WATER DEPTH       MNEMO(3)   = 'H       ' !     FREE SURFACE       MNEMO(4)   = 'S       ' !     BOTTOM       MNEMO(5)   = 'B       ' !     SCALAR FLOW RATE       MNEMO(6)   = 'Q       ' !     SCALAR FLOW RATE X       MNEMO(7)   = 'I       ' !     SCALAR FLOW RATE Y 182       MNEMO(8)   = 'J       ' !     RIGID BED       MNEMO(9)   = 'R       ' !     FRICTION COEFFICIENT       MNEMO(10)   = 'CHESTR  ' !     MEAN BOTTOM FRICTION       MNEMO(11)   = 'TOB     ' !     WAVE HEIGHT       MNEMO(12)   = 'W       ' !     PEAK PERIOD       MNEMO(13)   = 'X       ' !     WAVE DIRECTION       MNEMO(14)   = 'THETAW  ' !     SOLID DISCHARGE       MNEMO(15)   = 'M       ' !     SOLID DISCHARGE X       MNEMO(16)   = 'N       ' !     SOLID DISCHARGE Y       MNEMO(17)   = 'P       ' !     EVOLUTION       MNEMO(18)   = 'E       ' !     KS       MNEMO(19)   = 'KS      ' !     MU       MNEMO(20)   = 'MU      ' ! CV 2010       MNEMO(21)   = 'D50     ' ! +1       MNEMO(22+NSICLA*(NOMBLAY+2)) = 'QSBL    '       MNEMO(23+NSICLA*(NOMBLAY+2)) = 'QSBLX   '       MNEMO(24+NSICLA*(NOMBLAY+2)) = 'QSBLY   '       MNEMO(25+NSICLA*(NOMBLAY+2)) = 'QSSUSP  '       MNEMO(26+NSICLA*(NOMBLAY+2)) = 'QSSUSPX '       MNEMO(27+NSICLA*(NOMBLAY+2)) = 'QSSUSPY ' !       ADD=NSICLA*(NOMBLAY+4)+NOMBLAY       MNEMO(28+ADD) = 'A       '       MNEMO(29+ADD) = 'G       '       MNEMO(30+ADD) = 'L       '       MNEMO(31+ADD) = 'O       ' !     THE NUMBER OF PRIVATE ARRAYS IS A KEYWORD !     MNEMO(31+ADD) = '????????' ! !---------------------------- ! CV 2010: +1       ADD=NSICLA*(NOMBLAY+4)+NOMBLAY+27+MAX(NPRIV,4) 183       IF(ADD.LT.MAXVAR) THEN         DO I=ADD+1,MAXVAR           MNEMO(I) =' '           TEXTE(I) =' '           TEXTPR(I)=' '         ENDDO       ENDIF ! !----------------------------------------------------------------------- !       RETURN       END  C    ORIGINAL SUBROUTINE IN MALPASSET SIMULATION C        *****************          SUBROUTINE CONDIN C        ***************** C C*********************************************************************** C TELEMAC-2D VERSION 5.0         19/08/98  J-M HERVOUET TEL: 30 87 80 18 C C*********************************************************************** C C     FONCTION  : INITIALISATION DES GRANDEURS PHYSIQUES H, U, V ETC C C----------------------------------------------------------------------- C                             ARGUMENTS C .________________.____.______________________________________________ C |      NOM       |MODE|                   ROLE C |________________|____|______________________________________________ C |                | -- |   C |________________|____|______________________________________________ C MODE : -->(DONNEE NON MODIFIEE), <--(RESULTAT), <-->(DONNEE MODIFIEE) C*********************************************************************** C       USE BIEF       USE DECLARATIONS_TELEMAC2D C       IMPLICIT NONE       INTEGER LNG,LU       COMMON/INFO/LNG,LU C C+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ C C C+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ 184 C        INTEGER ITRAC  C C----------------------------------------------------------------------- C C   INITIALISATION DU TEMPS C       AT = 0.D0 C C----------------------------------------------------------------------- C C   INITIALISATION DES VITESSES : VITESSES NULLES C       CALL OS( 'X=C     ' , X=U , C=0.D0 )       CALL OS( 'X=C     ' , X=V , C=0.D0 ) C C----------------------------------------------------------------------- C C   INITIALISATION DE H , LA HAUTEUR D'EAU C       IF(CDTINI(1:10).EQ.'COTE NULLE') THEN         CALL OS( 'X=C     ' , H , H  , H , 0.D0 )         CALL OS( 'X=X-Y   ' , H , ZF , H , 0.D0 )       ELSEIF(CDTINI(1:14).EQ.'COTE CONSTANTE') THEN         CALL OS( 'X=C     ' , H , H  , H , COTINI )         CALL OS( 'X=X-Y   ' , H , ZF , H , 0.D0   )       ELSEIF(CDTINI(1:13).EQ.'HAUTEUR NULLE') THEN         CALL OS( 'X=C     ' , H , H  , H , 0.D0  )       ELSEIF(CDTINI(1:13).EQ.'PARTICULIERES') THEN C  ZONE A MODIFIER                                                              STOP 'CONDITIONS PARTICULIERES A PROGRAMMER'                  C  FIN DE LA ZONE A MODIFIER             ELSE         WRITE(LU,*) 'CONDIN : CONDITION INITIALE NON PREVUE : ',CDTINI         STOP       ENDIF C       CALL CORSUI(H%R,U%R,V%R,ZF%R,X,Y,NPOIN)    C C----------------------------------------------------------------------- C C   INITIALISATION DU TRACEUR C       IF(NTRAC.GT.0) THEN         DO ITRAC=1,NTRAC           CALL OS('X=C     ',X=T%ADR(ITRAC)%P,C=TRAC0(ITRAC)) 185         ENDDO       ENDIF C C----------------------------------------------------------------------- C C INITIALISATION DE LA VISCOSITE C       CALL OS( 'X=C     ' , VISC , VISC , VISC , PROPNU ) C C----------------------------------------------------------------------- C       RETURN       END  C    ORIGINAL SUBROUTINE IN MALPASSET SIMULATION   C        ***************************************************              DOUBLE PRECISION FUNCTION DISTAN(X1,Y1,X2,Y2,X3,Y3)       C        ***************************************************       C                                                                         C***********************************************************************  C PROGICIEL : TELEMAC           23/07/91                                  C                                                                        C***********************************************************************  C                                                                        C   FONCTION : CETE FONCTION CALCULE LA DISTANCE ENTRE UNE DROITE         C ET UN POINT SUR LE MAILLAGE                                            C-----------------------------------------------------------------------  C                             ARGUMENTS                                   C .________________.____.______________________________________________.  C |      NOM       |MODE|                   ROLE                       |  C |________________|____|______________________________________________| C |    X1          | -->  ABSCISSE DU PREMIER POINT SUR LA DROITE        C |    Y1          | -->| COORDONNEE DU PREMIER POINT SUR LA DROITE     C |    X2          | -->  ABSCISSE DU DEUXIEME POINT SUR LA DROITE      C |    Y2          | -->| COORDONNEE DU DEUXIEME POINT SUR LA DROITE     C |    X           | -->| ABSCISSE DU POINT POUR LEQUEL ON CHERCHE DIST1  C |    Y           | -->| COORDONNEE DU POINT POUR LEQUEL ON CHERCHE DIS  C |    DISTAN      |<-- |  DISTANCE ENTRE LA DROITE ET LE POINT          C |________________|____|_______________________________________________  C MODE : -->(DONNEE NON MODIFIEE), <--(RESULTAT), <-->(DONNEE MODIFIEE)   C***********************************************************************  C                                                                         C                                                                               IMPLICIT NONE                                                             DOUBLE PRECISION X1,X2,X3,Y1,Y2,Y3                                        DOUBLE PRECISION A1,B1,C1,DET                                       186       INTRINSIC SQRT                                                            A1=Y1-Y2                                                                  B1=-X1+X2                                                                 C1=X1*Y2-X2*Y1                                                            DET=SQRT((A1**2)+(B1**2))                                                 DISTAN=((A1*X3)+(B1*Y3)+C1)/DET                                           RETURN                                                                    END    C    ORIGINAL SUBROUTINE IN MALPASSET SIMULATION   C        *****************                                          SUBROUTINE CORSUI                                  C        *****************                                 C                                                                          C                                                                              *(H,U,V,ZF,X,Y,NPOIN)                                               C                                                                         C***********************************************************************   C PROGICIEL : TELEMAC           01/03/90    J-M HERVOUET                   C***********************************************************************  C                                                                       C  FONCTION  : FONCTION DE CORRECTION DES FONDS RELEVES                 C                                                                       C              CE SOUS-PROGRAMME UTILITAIRE NE FAIT RIEN DANS LA        C              VERSION STANDARD. IL EST A LA DISPOSITION DES               C              UTILISATEURS, POUR LISSER OU CORRIGER DES FONDS SAISIS     C              PAR EXEMPLE.                                                C                                                                         C-----------------------------------------------------------------------   C                             ARGUMENTS                                    C .________________.____.______________________________________________    C |      NOM       |MODE|                   ROLE                           C |________________|____|_______________________________________________   C |      ZF        |<-->| FOND A MODIFIER.                                 C |      X,Y,(Z)   | -->| COORDONNEES DU MAILLAGE (Z N'EST PAS EMPLOYE).   C |      NPOIN     | -->| NOMBRE DE POINTS DU MAILLAGE.                    C |________________|____|______________________________________________    C MODE : -->(DONNEE NON MODIFIEE), <--(RESULTAT), <-->(DONNEE MODIFIEE)    C-----------------------------------------------------------------------   C                                                                          C PROGRAMME APPELANT : TELMAC                                              C PROGRAMMES APPELES : RIEN EN STANDARD                                    C                                                                          C***********************************************************************   C                                                                                IMPLICIT NONE                                                        187 C                                                                                INTEGER NPOIN,I                                                 C                                                                                DOUBLE PRECISION H(*),X(*),Y(*),ZF(*),U(*),V(*)                      C                                                                                DOUBLE PRECISION DISTAN,X1,X2,Y1,Y2,HD                                     EXTERNAL DISTAN                                                      C                                                                          C-----------------------------------------------------------------------   C                                                                          C   INITIALISATION DES VARIABLES POUR LE CALCUL DE LA SITUATION DU POINT  C   X1,Y1,X2,Y2 POINT DEFINISANT LA DROITE DE LIMITE DE BARRAGE           C   X3,Y3 POINT DEFINISANT LES COORDONNEES D POINT A DROITE DE LIMITE DE  C                                                                                X1= 4701.183D0                                                             Y1= 4143.407D0                                                            X2= 4655.553D0                                                       Y2= 4392.104D0                                                     C                                                                               DO 99 I=1,NPOIN                                                            HD=DISTAN(X1,Y1,X2,Y2,X(I),Y(I))                                        IF(HD.GT.0.001D0) THEN                                                                                                                                                                  H(I) = 100.D0 - ZF(I)                                                    U(I) = 0.D0                                                               V(I) = 0.D0                                                            ENDIF                                                            C                                                                          C  ZONE DERRIERE LE BARRAGE MAIS QUI N'EST PAS DANS                       C  LA RETENUE.                                                             C                                                                                  IF((X(I)-4500.D0)**2+(Y(I)-5350.D0)**2.LT.200.D0**2) THEN                   H(I)=0.D0                                                                ENDIF                                                             C                                                                          99     CONTINUE                                                            C                                                                          C-----------------------------------------------------------------------   C                                                                                RETURN                                                                     END 

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