{ "metadata": { "name": "", "signature": "sha256:171668d82e68d45a998b65d0e49379e70937bfcb873c2c2a1cea475a2a8d329a" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 10 : EARTH AND ROCKFILL DAM" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.1 pg : 502" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "from numpy import array,float64,round\n", "\n", "\t\t\t\t\n", "#Given\n", "K = 5.E-4; \t\t\t\t#coefficient of permeability of soil\n", "Bt = 6.; \t\t\t\t#width of top of dam\n", "wb = 146.; \t\t\t\t#width of base of dam\n", "H = 20.; \t\t\t\t#heigth of dam\n", "hw = 2.; \t\t\t\t#heigth of water in reservior\n", "hs1 = 4.; \t\t\t\t#slope on upstream side\n", "hs2 = 3.; \t\t\t\t#slope on downstream side\n", "df = 30.; \t\t\t\t#length of drainage filter\n", "\n", "x = wb-df-72+72*0.3;\n", "y = 18.;\n", "s = (x**2+y**2)**0.5-x;\n", "\n", "x = array([0, 10, 20, 30, 40, 50, 60, 65.6],dtype=float64);\n", "y = (4.849*x+5.879)**0.5;\n", "y = round(y*1000)/1000;\n", "\n", "print \"x y\";\n", "for i in range(8):\n", " print \"%.2f %.2f\"%(x[i],y[i]);\n", "sf = K*s*10000;\n", "sf = round(sf*1000)/1000;\n", "print \"Seepage flow per unit length of dam = %.2fD-6 cumecs/metre length of dam.\"%(sf);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "x y\n", "0.00 2.42\n", "10.00 7.37\n", "20.00 10.14\n", "30.00 12.30\n", "40.00 14.14\n", "50.00 15.76\n", "60.00 17.23\n", "65.60 18.00\n", "Seepage flow per unit length of dam = 12.12D-6 cumecs/metre length of dam.\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.2 pg : 502" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\t\t\t\t\n", "#Given\n", "K = 3.E-3; \t\t\t\t#coefficient of permeability\n", "nd = 25.; \t\t\t\t#number of potential drops\n", "nf = 4.; \t\t\t\t#number of flow channels\n", "lf = 40.; \t\t\t\t#filter length\n", "H = 52.; \t\t\t\t#heigth of dam\n", "fb = 2.; \t\t\t\t#free board\n", "\n", "# Calculations\n", "q = K*(H-fb)*nf/(nd*100);\n", "\n", "# Results\n", "print \"Discharge per meter length of dam = %.5f cumec/metre length.\"%(q);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Discharge per meter length of dam = 0.00024 cumec/metre length.\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.3 pg : 503" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\t\t\t\t\n", "#Given\n", "x = 4.;\n", "#Given scale\n", "An = 14.4; \t\t\t\t#area of N recmath.tangle\n", "At = 6.4; \t\t\t\t#area of T recmath.tangle\n", "Au = 4.9; \t\t\t\t#area of U recmath.tangle\n", "L = 12.6; \t\t\t\t#length of arc;\n", "gamma_m = 19.; \t\t\t\t#unit weigth of soil\n", "gamma_w = 9.81; \t\t\t\t#unit weigth of water\n", "fi = 26.; \t\t\t\t#effective angle(degree)\n", "co = 19.5; \t\t\t\t#cohesion value\n", "\n", "# Calculations\n", "#consider 1m length of dam\n", "SumN = An*x**2*gamma_m;\n", "SumT = At*x**2*gamma_m;\n", "SumU = Au*x**2*gamma_w;\n", "Le = x*L;\n", "F = ((Le*co)+(SumN-SumU)*math.tan(math.radians(fi)))/SumT;\n", "F = round(F*100)/100;\n", "\n", "# Results\n", "print \"Factor of safety for slope = %.2f.\"%(F);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Factor of safety for slope = 1.41.\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.4 pg : 503" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "#check section for:\n", "#Stability of d/s slope against steady seepage\n", "#Sloughing of u/s slope against sudden drawdown\n", "#Stability of the foundation against shear\n", "#Seepage through body of dam\n", "\n", "#Given\n", "#Dimensions\n", "H = 20.; \t\t\t\t#Heigth of dam\n", "Bt = 6.; \t\t\t\t#top width of dam\n", "s1 = 4.; \t\t\t\t#u/s slope\n", "s2 = 3.; \t\t\t\t#d/s slope\n", "fb = 2.; \t\t\t\t#free board\n", "#Properties of materials of dam\n", "gamma_d = 17.27; \t\t\t\t#dry density\n", "wc = 0.15; \t\t\t\t#optimum water content\n", "gamma_s = 21.19; \t\t\t\t#saturated density\n", "gamma_w = 9.81; \t\t\t\t#unit weigth of water\n", "wavg = 19.62; \t\t\t\t#average unit weigth under seepage\n", "theta = 26.; \t\t\t\t#average angle of internal friction(degree)\n", "co = 19.13; \t\t\t\t#average cohesion\n", "K = 5.E-4; \t\t\t\t#coefficient of permeability\n", "#properties of foundation materials\n", "gamma_f = 17.27; \t\t\t\t#average unit weigth\n", "cof = 47.87; \t\t\t\t#average cohesion\n", "fi = 8.; \t\t\t\t#average angle internal friction\n", "t = 6.; \t\t\t\t#thickness of clay\n", "FOSp = 1.5; \t\t\t\t#permissible factor of safety of slope\n", "PS = 8.E-6; \t\t\t\t#permissible seepage\n", "#(a) Stability of d/s slope against steady seepage\n", "An = 302.4; \t\t\t\t#area of N diagram\n", "At = 91.2; \t\t\t\t#area of T diagram\n", "Au = 98.4; \t\t\t\t#area of U diagram\n", "Le = 60.; \t\t\t\t#length of arc\n", "SumN = An*gamma_s;\n", "SumT = At*gamma_s;\n", "SumU = Au*gamma_w;\n", "F = (Le*co)+(SumN-SumU)*math.tan(math.radians(theta))/SumT;\n", "F = round(F*100)/100;\n", "print \"Parta:\"\n", "print \"Factor of safety for slope = %.2f.\"%(F);\n", "print \"Safe\";\n", "\n", "#(b) Sloughing of u/s slope against sudden drawdown\n", "h1 = 15.;\n", "b = 80.;\n", "P = gamma_s*H**2*math.tan(math.radians(45-(theta/2)))**2/2+gamma_w*h1**2/2;\n", "sav = P/b;\n", "smax = 2*sav;\n", "Ne = (gamma_s-gamma_w)*b*H/2;\n", "R = Ne*math.tan(math.radians(theta))+co*b;\n", "fs = R/P;\n", "fs = round(fs*100)/100;\n", "print \"Partb:\"\n", "print \"Factor of safety w.r.t average shear = %.2f.\"%(fs);\n", "print \"Safe\";\n", "sr = 0.6*H*(gamma_s-gamma_w)*math.tan(math.radians(theta))+co;\n", "FS = sr/smax;\n", "FS = round(FS*100)/100;\n", "print \"Factor of safety w.r.t maximum shear = %.2f.\"%(FS);\n", "print \"Safe\";\n", "\n", "#(c) Stability of the foundation against shear\n", "h1 = 26.;\n", "h2 = 6.;\n", "gamma_m = (wavg*(h1-h2)+gamma_f*h2)/h1;\n", "l = (gamma_m*h1*math.tan(math.radians(fi))+cof)/(gamma_m*h1);\n", "fi1 = math.tan(math.radians(l));\n", "P = (h1**2-h2**2)/2*gamma_m*math.tan(math.radians(45-(fi1/2)))**2;\n", "sav = P/b;\n", "smax = 2*sav;\n", "s1 = cof+gamma_f*h2*math.tan(math.radians(fi));\n", "s2 = cof+gamma_m*h1*math.tan(math.radians(fi));\n", "as1 = (s1+s2)/2;\n", "fs = as1/sav;\n", "fs = round(fs*100)/100;\n", "print \"Partc:\"\n", "print \"Factor of safety w.r.t overall shear = %.2f.\"%(fs);\n", "print \"Safe\";\n", "\n", "gamma_av = (wavg*0.6*H+gamma_f*h2)/(0.6*H)+h2;\n", "s = cof+gamma_av*0.6*H*math.tan(math.radians(fi));\n", "fs = s/smax;\n", "fs = round(fs*100)/100;\n", "print \"Factor of safety w.r.t overall shear = %.2f.\"%(fs);\n", "print \"Unsafe\";\n", "\n", "#(d) Seepage through body of dam\n", "s = 2.; \t\t\t\t#measured\n", "q = K*s*100000/100;\n", "print \"Partd:\"\n", "print \" Seepage through body of dam = %.2fD-5 cumecs/m length of dam\"%(q);" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Parta:\n", "Factor of safety for slope = 1149.17.\n", "Safe\n", "Partb:\n", "Factor of safety w.r.t average shear = 2.16.\n", "Safe\n", "Factor of safety w.r.t maximum shear = 1.24.\n", "Safe\n", "Partc:\n", "Factor of safety w.r.t overall shear = 1.18.\n", "Safe\n", "Factor of safety w.r.t overall shear = 0.69.\n", "Unsafe\n", "Partd:\n", " Seepage through body of dam = 1.00D-5 cumecs/m length of dam\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 10.5 pg : 507" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import math \n", "from matplotlib.pylab import plot,show\n", "from numpy import zeros\n", "#design upstream impervious blanket\n", "\t\t\t\t\n", "#Given\n", "Zb = 1.2; \t\t\t\t#thickness of blanket\n", "Zf = 8; \t\t\t\t#dismath.tance of blanket from foundation\n", "kb = 0.06; \t\t\t\t#coefficient of permeability of blanket material\n", "kf = 72; \t\t\t\t#coefficient of permeability of foundation soil\n", "Hw = 10; \t\t\t\t#heigth of water in reservior\n", "Xd = 40;\n", "\n", "a = (kb/(kf*Zb*Zf))**0.5;\n", "Xo = 1.414/a;\n", "\n", "#we vary value of x\n", "x = [0, 25, 50, 75, 100, 125, 151.8, 300]\n", "Xr = zeros(8)\n", "ho = zeros(8)\n", "r = zeros(8)\n", "\n", "for i in range(8):\n", " e = math.exp(2*a*x[i]);\n", " Xr[i] = (e-1)/(a*(e+1));\n", " ho[i] = Xr[i]*Hw/(Xr[i]+Xd);\n", " r[i] = Xr[i]*100/(Xr[i]+Xd);\n", "\n", "print \"x Xr ho reduction qpercent\";\n", "for i in range(8):\n", " print \"%.2f %.2f %.2f %.2f\"%(x[i],Xr[i],ho[i],r[i]);\n", "\n", "#graph is plotted between r and x.\n", "#after around 130m length there is only slight increase in head dissipated(ho)\n", "plot(x,r)\n", "show()\n", "L = 130;\n", "print \"Thickness of blanket = %.2f m\"%(Zb);\n", "print \"Length of blanket = %i m.\"%(L);\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The history saving thread hit an unexpected error (OperationalError('disk I/O error',)).History will not be written to the database.\n", "x Xr ho reduction qpercent" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "0.00 0.00 0.00 0.00\n", "25.00 24.56 3.80 38.04\n", "50.00 46.67 5.38 53.85\n", "75.00 64.78 6.18 61.83\n", "100.00 78.50 6.62 66.24\n", "125.00 88.28 6.88 68.82\n", "151.80 95.35 7.04 70.45\n", "300.00 106.53 7.27 72.70\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "Thickness of blanket = 1.20 m\n", "Length of blanket = 130 m.\n" ] } ], "prompt_number": 1 } ], "metadata": {} } ] }