Calculator

This spreadsheet workbook implements the calculation for steady-state aggradation o river in response to sea level rise at a constant rate, as outlined in Chapter 2 of the e-book. The workbook does not contain embedded code. The colored boxes: Main Input Parameters indicate the parameters you must sp Input Gt,feed 12 Mt/year Mean annual bed material sediment feed rate L 400 km Reach length (downchannel distance) Lv 266.67 km Reach length (downvalley distance) dxd/dt 10 mm/year Rate of sea level rise 3 Qbf 5000 m /s Bankfull water discharge Bf D L Qtbf,feed C BMSS Su b 8 km 0.25 mm 2.5 3 1.43493228 m /s 0.0002869 760.295913 Floodplain width Grain size Fraction wash load deposited per unit bed materia Volume bed material sediment transport rate durin Volume concentration of bed material load Flood concentration of bed material load in mg/lite Upstream slope Adjust L to make sure that this parameter < 1. If b > 1 then the sediment transport drops to zero before reaching the delta. Results are given below in digital form. Plotted results are given in subsequ 2.037E-04 0.80761905 xhat 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 x km 0 20 40 60 80 100 120 140 Qtbf m3/s S etahat 1.434932 2.037E-04 0.0001214 1.376988 1.954E-04 0.0001114 1.319044 1.872E-04 0.0001019 1.2611 1.790E-04 9.273E-05 1.203157 1.708E-04 8.398E-05 1.145213 1.625E-04 7.565E-05 1.087269 1.543E-04 6.773E-05 1.029325 1.461E-04 6.022E-05 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 160 180 200 220 240 260 280 300 320 340 360 380 400 0.971381 0.913437 0.855493 0.797549 0.739605 0.681661 0.623717 0.565773 0.507829 0.449885 0.391942 0.333998 0.276054 1.379E-04 1.296E-04 1.214E-04 1.132E-04 1.050E-04 9.675E-05 8.853E-05 8.030E-05 7.208E-05 6.385E-05 5.563E-05 4.741E-05 3.918E-05 5.312E-05 4.643E-05 4.015E-05 3.429E-05 2.883E-05 2.379E-05 1.916E-05 1.494E-05 1.113E-05 7.728E-06 4.741E-06 2.165E-06 0 alculation for steady-state aggradation of a sand-bed a constant rate, as outlined in Chapter 25 The colored boxes: indicate the parameters you must specify. ual bed material sediment feed rate ngth (downchannel distance) ngth (downvalley distance) Auxiliary Input Parameters Input tform* 1.86 Channel-forming Shields n aEH 0.05 Coefficient in Engelund-H lp 0.4 Bed porosity If 0.1 Flood intermittency Cz 25 Chezy resistance coefficie W 1.5 Channel sinuosity R 1.65 Submerged specific gravit xdo 0 Water surface elevation a Dt 1000 Time interval for plotting in wash load deposited per unit bed material load deposited ed material sediment transport rate during flood time oncentration of bed material load centration of bed material load in mg/liter o make sure that this parameter < 1. en the sediment transport drops to zero before reaching the delta. rm. Plotted results are given in subsequent worksheets. hm yrs 0 hdev m Bbf m Hbf m 0 yr 48.569923 611.9452 3.76716 48.5699 44.57881 587.23427 3.92569 44.5788 40.752183 562.52334 4.09814 40.7522 37.090041 537.81241 4.28643 37.09 33.592386 513.10148 4.49287 33.5924 30.259217 488.39055 4.72019 30.2592 27.090534 463.67962 4.97175 27.0905 24.086337 438.96869 5.25162 24.0863 1000 1000 yr 58.5699 54.5788 50.7522 47.09 43.5924 40.2592 37.0905 34.0863 2000 2000 yr 68.569923 64.57881 60.752183 57.090041 53.592386 50.259217 47.090534 44.086337 3000 3000 yr 78.57 74.579 70.752 67.09 63.592 60.259 57.091 54.086 21.246626 18.571401 16.060661 13.714408 11.532641 9.51536 7.6625648 5.9742557 4.4504325 3.0910954 1.8962443 0.8658791 0 414.25776 389.54683 364.8359 340.12497 315.41404 290.70311 265.99218 241.28125 216.57032 191.85939 167.14846 142.43753 117.7266 5.56489 5.9179 6.31873 6.7778 7.3088 7.93008 8.66679 9.5544 10.6446 12.0156 13.7919 16.1846 19.5818 21.2466 18.5714 16.0607 13.7144 11.5326 9.51536 7.66256 5.97426 4.45043 3.0911 1.89624 0.86588 0 31.2466 28.5714 26.0607 23.7144 21.5326 19.5154 17.6626 15.9743 14.4504 13.0911 11.8962 10.8659 10 41.246626 38.571401 36.060661 33.714408 31.532641 29.51536 27.662565 25.974256 24.450433 23.091095 21.896244 20.865879 20 51.247 48.571 46.061 43.714 41.533 39.515 37.663 35.974 34.45 33.091 31.896 30.866 30 Channel-forming Shields number Coefficient in Engelund-Hansen bed material load relation Bed porosity Flood intermittency Chezy resistance coefficient Cf 0.0016 Channel sinuosity Submerged specific gravity of sediment Water surface elevation at t = 0 Time interval for plotting in years 4000 4000 yr 88.57 84.579 80.752 77.09 73.592 70.259 67.091 64.086 5000 6000 5000 yr 6000 yr 98.57 108.57 94.579 104.58 90.752 100.75 87.09 97.09 83.592 93.592 80.259 90.259 77.091 87.091 74.086 84.086 7000 8000 9000 10000 7000 yr 8000 yr 9000 yr 10000 yr 118.57 128.57 138.57 148.57 114.579 124.579 134.579 144.579 110.752 120.752 130.752 140.752 107.09 117.09 127.09 137.09 103.592 113.592 123.592 133.592 100.259 110.259 120.259 130.259 97.0905 107.091 117.091 127.091 94.0863 104.086 114.086 124.086 61.247 58.571 56.061 53.714 51.533 49.515 47.663 45.974 44.45 43.091 41.896 40.866 40 71.247 68.571 66.061 63.714 61.533 59.515 57.663 55.974 54.45 53.091 51.896 50.866 50 81.247 78.571 76.061 73.714 71.533 69.515 67.663 65.974 64.45 63.091 61.896 60.866 60 91.2466 88.5714 86.0607 83.7144 81.5326 79.5154 77.6626 75.9743 74.4504 73.0911 71.8962 70.8659 70 101.247 98.5714 96.0607 93.7144 91.5326 89.5154 87.6626 85.9743 84.4504 83.0911 81.8962 80.8659 80 111.247 108.571 106.061 103.714 101.533 99.5154 97.6626 95.9743 94.4504 93.0911 91.8962 90.8659 90 121.247 118.571 116.061 113.714 111.533 109.515 107.663 105.974 104.45 103.091 101.896 100.866 100 11000 11000 yr 158.57 154.579 150.752 147.09 143.592 140.259 137.091 134.086 12000 12000 yr 168.57 164.579 160.752 157.09 153.592 150.259 147.091 144.086 131.247 128.571 126.061 123.714 121.533 119.515 117.663 115.974 114.45 113.091 111.896 110.866 110 141.247 138.571 136.061 133.714 131.533 129.515 127.663 125.974 124.45 123.091 121.896 120.866 120 Long Profile of Bed Slope 2.50E-04 2.00E-04 Bed slope S 1.50E-04 1.00E-04 5.00E-05 0.00E+00 0 50 100 150 200 250 300 350 400 Streamwise distance km Long Profile of Deviatoric Bed Elevation 60 50 40 30 20 10 0 0 50 100 150 200 250 300 350 400 Deviatoric bed elevation, m Streamwise distance km Long Profiles of Bed Elevation 180 160 0 yr 1000 yr 2000 yr Bed elevation m 140 120 100 80 60 40 20 0 0 100 200 300 400 3000 yr 4000 yr 5000 yr 6000 yr 7000 yr 8000 yr 9000 yr 10000 yr 11000 yr 12000 yr Downchannel distance km Downstream Variation in Bankfull Width and Depth 700 600 25 20 500 Bbf, Hbf m 400 300 200 15 Bbf m Hbf m 10 5 100 0 0 100 200 300 400 0 Downchannel distance km Governing equations RC1/ 2 Q tbf ,f eed f Su  aEH torm Qbf f , S ˆ  (1  bx ) Su ˆ h hdev L , ˆ x x L b  (1  l p ) B f x dL If W(1  L )Q tbf ,f eed 1 1  ˆ ˆ  ˆ h  Su (1  b)  x  b x 2  2 2    h  x do  x d t  hdev ( x ) Bbf Cf  D aEH t form   Q tbf 2.5 RgD D2 , H  D Q tbf ˆ  1  bx Q tbf ,f eed , S ˆ  (1  bx ) Su ˆ x 1 2 ˆ bx  2   hdev ( x ) Q tbf RgD D 2 , H aEH ( t )2 Qbf form  D Q tbf C1/ 2 f