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diff --git a/Principles_Of_Foundation_Engineering/Chapter07.ipynb b/Principles_Of_Foundation_Engineering/Chapter07.ipynb new file mode 100755 index 00000000..63b3bc22 --- /dev/null +++ b/Principles_Of_Foundation_Engineering/Chapter07.ipynb @@ -0,0 +1,358 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:6111670c8f96effbf1bc0bc29859353d67e53cd5b906d2b571173d1698f7ba9c"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter07:Lateral earth pressure"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.1:Pg-319"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 7.1\n",
+ "\n",
+ "sigmao=48.0; # in KN/m^2\n",
+ "phi1=30*math.pi/180; # angle\n",
+ "phi2=36*math.pi/180; # angle\n",
+ "Ka1=(math.tan(math.pi/4.0-phi1/2))**2;\n",
+ "Ka2=(math.tan(math.pi/4.0-phi2/2))**2;\n",
+ "sigmaa1=Ka1*sigmao; # in KN/m^2\n",
+ "print round(sigmaa1,2),\"top soil pressure in kN/m**2\"\n",
+ "sigmaa2=Ka2*sigmao; # in KN/m^2\n",
+ "print round(sigmaa2,2),\"bottom soil pressure in kN/m**2\"\n",
+ "Po=1/2.0*3*16+3*12.48+1/3.0*3*(19.65-12.48)+1/2.0*3*29.43;\n",
+ "zbar=(24*(3+3/3.0)+37.44*(3/2.0)+10.76*3/3.0+44.1*3/3.0)/Po;\n",
+ "print round(zbar,2),\"resultant force acting from the bottom in m\"\n",
+ "\n",
+ "# The answers in the book are different due to approximation while here calculations are precise"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "16.0 top soil pressure in kN/m**2\n",
+ "12.46 bottom soil pressure in kN/m**2\n",
+ "1.84 resultant force acting from the bottom in m\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.2:Pg-321"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 7.2\n",
+ "\n",
+ "import math\n",
+ "c=14.36;\n",
+ "Gamma=17.4; # in KN/m^3\n",
+ "H=6; # in m\n",
+ "phi=26*math.pi/180;\n",
+ "Ka=(math.tan(math.pi/4-phi/2))**2;\n",
+ "sigma0=Gamma*H*Ka-2*c*math.sqrt(Ka);\n",
+ "Pa=1/2.0*Gamma*H**2*Ka-2*c*H*math.sqrt(Ka);\n",
+ "print round(Pa,2),\"active force before which tensile crack appeared in kN/m\"\n",
+ "zbar=(244.32-323.1)/14.46;\n",
+ "print round(zbar,2),\"the line of action on which net force is acting in m\"\n",
+ "zc=2*c/Gamma/math.sqrt(Ka);\n",
+ "print round(zc,2),\"distance where tensile crack appeared in m\"\n",
+ "Pa=1/2.0*(H-zc)*(Gamma*H*Ka-2*c*math.sqrt(Ka));\n",
+ "print round(Pa,2),\"Active force in tensile crack in kN/m\"\n",
+ "zbar=(H-zc)/3;\n",
+ "print round(zbar,2),\"the line of action on which net force is acting in m\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "14.62 active force before which tensile crack appeared in kN/m\n",
+ "-5.45 the line of action on which net force is acting in m\n",
+ "2.64 distance where tensile crack appeared in m\n",
+ "38.32 Active force in tensile crack in kN/m\n",
+ "1.12 the line of action on which net force is acting in m\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.3:Pg-322"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 7.3\n",
+ "import math\n",
+ "pi=math.pi\n",
+ "H=10.0; # in ft\n",
+ "Gamma=110.0; # in lb/ft^3\n",
+ "phi=35*math.pi/180.0; # angle\n",
+ "alpha=15*math.pi/180.0; # angle\n",
+ "theta=10*math.pi/180.0; # angle\n",
+ "zi=math.sin(math.sin(alpha)/math.sin(phi))-alpha+2*theta;\n",
+ "print round(zi*180.0/math.pi,2),\" is zi in degrees\"\n",
+ "Ka=math.cos(alpha-theta)*math.sqrt(1+(math.sin(phi))**2-2*math.sin(phi)*math.sin(zi))/((math.cos(theta))**2*(math.cos(alpha)+math.sqrt((math.sin(phi))**2+((math.sin(alpha))**2))));\n",
+ "Pa=1/2.0*Gamma*H**2*Ka;\n",
+ "print round(Pa,2),\" is rankine earth pressure in lb/ft\"\n",
+ "print \"there is slight error in answer due to rounding off error\"\n",
+ "Beta=math.tan(math.sin(phi)*math.sin(zi)/(1-math.sin(phi)*math.cos(zi)));\n",
+ "print round(Beta*180/pi,2),\" is angle in degrees\"\n",
+ "\n",
+ "# The answers in the book are different due to approximation while here calculations are precise"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "29.99 is zi in degrees\n",
+ "3078.61 is rankine earth pressure in lb/ft\n",
+ "there is slight error in answer due to rounding off error\n",
+ "36.7 is angle in degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.4:Pg-326"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 7.4\n",
+ "\n",
+ "H=4.6; # in m\n",
+ "Gamma=16.5; # in KN/m^3\n",
+ "Ka=0.297;\n",
+ "Po=1/2.0*Gamma*H**2*Ka;\n",
+ "print round(Po,2),\"coulomb active force per unit length in kN/m\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "51.85 coulomb active force per unit length in kN/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.5:Pg-331"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 7.5\n",
+ "\n",
+ "#part(a)\n",
+ "Gamma=105; # in lb/ft^3\n",
+ "H=10; #in ft\n",
+ "Kae=0.474;\n",
+ "k1=0;\n",
+ "Pae=1/2.0*Gamma*H**2*Kae*(1-k1) # in lb/ft\n",
+ "print Pae,\"active force in lb/ft\"\n",
+ "#part(b)\n",
+ "Ka=0.246;\n",
+ "Pa=1/2.0*Gamma*H**2*Ka; # in lb/ft\n",
+ "print Pa,\"active force in lb/ft\"\n",
+ "DPae=Pae-Pa;#deltaPae\n",
+ "zbar=(0.6*H*DPae+H/3*(Pa))/Pae;\n",
+ "print round(zbar,2),\"the distance of resultant force from bottom in ft\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "2488.5 active force in lb/ft\n",
+ "1291.5 active force in lb/ft\n",
+ "4.44 the distance of resultant force from bottom in ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.6:Pg-337"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 7.6\n",
+ "\n",
+ "import math\n",
+ "import numpy\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "z=[0, 4, 8, 12, 16];\n",
+ "Gamma=110; # in lb/ft^3\n",
+ "phi=36*math.pi/180;\n",
+ "H=16; # in ft\n",
+ "Sa1=numpy.zeros(5);#sigma(1)\n",
+ "Sa2=numpy.zeros(5);#sigma(2)\n",
+ "Sztr=numpy.zeros(5);#sigma(z)translation\n",
+ "print \"z(ft)\\t sigma(1)(lb/ft**2) \\t sigma(2)(lb/ft**2) \\t sigma(z)translation (lb/ft**2)\\n\"\n",
+ "for i in range(0,5):\n",
+ " Sa1[i]=Gamma*(math.tan(math.pi/4-phi*z[i]/2/H))**2*(z[i]-phi*z[i]**2/H/math.cos(phi*z[i]/H));\n",
+ " Sa2[i]=Gamma*z[i]*(math.cos(phi)/(1+math.sin(phi)))**2;\n",
+ " Sztr[i]=Sa1[i]/2.0+Sa2[i]/2.0;\n",
+ " print round(z[i],2),\"\\t \",round(Sa1[i],2),\"\\t\\t\\t \",round(Sa2[i],2),\"\\t\\t\\t \",round(Sztr[i],2),\"\\n\"\n",
+ "plt.plot(Sztr,z);\n",
+ "plt.title(\"sigma(z)translation vs z\")\n",
+ "plt.ylabel(\"z(ft)\")\n",
+ "plt.xlabel(\"sigma(z)translation (lb/ft**2)\")\n",
+ "plt.show()\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "z(ft)\t sigma(1)(lb/ft**2) \t sigma(2)(lb/ft**2) \t sigma(z)translation (lb/ft**2)\n",
+ "\n",
+ "0.0 \t 0.0 \t\t\t 0.0 \t\t\t 0.0 \n",
+ "\n",
+ "4.0 \t 269.92 \t\t\t 114.23 \t\t\t 192.07 \n",
+ "\n",
+ "8.0 \t 311.08 \t\t\t 228.46 \t\t\t 269.77 \n",
+ "\n",
+ "12.0 \t 233.53 \t\t\t 342.69 \t\t\t 288.11 \n",
+ "\n",
+ "16.0 \t 102.06 \t\t\t 456.92 \t\t\t 279.49 \n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.7:Pg-342"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 7.7\n",
+ "import math\n",
+ "Gammasat=18.86; # in KN/m^3\n",
+ "Gammaw=9.81; # in KN/m^3\n",
+ "phi1=math.pi/180*30; # angle 1\n",
+ "phi2=math.pi/180*26; # angle 2\n",
+ "Kp1=(math.tan(math.pi/4+phi1/2))**2;\n",
+ "Kp2=(math.tan(math.pi/4+phi2/2))**2;\n",
+ "#for top soil\n",
+ "c=0;\n",
+ "sigma0=31.44; # in KN/m^2\n",
+ "sigmap=sigma0*Kp1+2*c*math.sqrt(Kp1);\n",
+ "print round(sigmap,2),\"passive pressure for top layer in kN/m**2\"\n",
+ "#for z=2\n",
+ "c=10;\n",
+ "sigma0=31.44; # in KN/m^2\n",
+ "sigmap=sigma0*Kp2+2*c*math.sqrt(Kp2);\n",
+ "print round(sigmap,2),\"passive pressure for z=2m in kN/m**2\"\n",
+ "#for z=3\n",
+ "c=10;\n",
+ "sigma0=15.72*2+(Gammasat-Gammaw)*1; # in KN/m^2\n",
+ "sigmap=sigma0*Kp2+2*c*math.sqrt(Kp2); # in KN/m^2\n",
+ "print round(sigmap,2),\" is passive pressure for z=3m in kN/m**2\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "94.32 passive pressure for top layer in kN/m**2\n",
+ "112.53 passive pressure for z=2m in kN/m**2\n",
+ "135.7 is passive pressure for z=3m in kN/m**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |