Slope Stabilization - Mound Site.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Full Bank Stabilization Estimate\n",
    "\n",
    "I located the steepest bank slope at cross section 4:\n",
    "\n",
    "![Cross Section 4](files/cross_section_4.png)\n",
    "\n",
    "Estimate the slope:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bank slope: -0.7714285714285712\n"
     ]
    }
   ],
   "source": [
    "top=(13.0,41.6)\n",
    "bottom=(20.0,36.2)\n",
    "slope = (top[1]-bottom[1])/(top[0]-bottom[0])\n",
    "print(\"Bank slope:\",slope)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The channel bottom is relatively flat. I'll assume it is completely flat and use a target slope of 1:2 to find the outer edge of the re-enforced bank toe. This calculation yields:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "New bank toe:  23.799999999999997\n"
     ]
    }
   ],
   "source": [
    "target_slope = 1/2\n",
    "new_bottom_x = (top[1]-bottom[1])/target_slope + top[0]\n",
    "print(\"New bank toe: \",new_bottom_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the proposed new bank on an estimate of the current channel profile:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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a+vJQ3T7/duXm50Z7rNCIdwAAAABiCNEOAFAlWjVqpUUjF+k3HX+jhz94WL2f763vMr+L9lhlI94BAAAAiAFEOwBAlUmKT9Lj5z+umRfN1IotK5T2VJoWrl8Y7bHCQ7wDAAAAEEVEOwBAlRv+i+H6eNTHapzSWOc8f47uX3y/vLpEL+IdAAAAgCgg2gEAIqJd83Zadt0yDWs7TL9f8Htd+NKF2pW1K9pjhY94BwAAACCCiHYAgIhpkNxAfx36Vz3S7xG9ufZNpU9J1yfffxLtscqHeAcAAAAgAoh2AICIMjPd0uUWvXf1ezqQd0Bdnumi6aumR3us8iPeQdKPP0rjx0uNG0vt20tz5kgFBdGeCgAAADUB0Q4AEBVntjxTK8es1Jktz9TI10fqur9dp6y8rGiPVX7Eu1rpYKxr3VqaOFE66ywpJ0caNkxKTSXeAQAAoOKIdgCAqGler7nmj5ivsT3GaurKqTrzmTP1zY/fRHusI0O8qxWKx7o+faRPPpFef11avVp68UXiHQAAACoH0Q4AEFXxcfGa1HuS3hj+htbtWqczppyheV/Oi/ZYR454VyOVFutmzw58LVaS4uOlyy8/PN516CC9+irxDgAAAOVDtAMAxISBJw/U8tHL1aZxG10w6wKNXTBW+QX50R7ryBHvaoRwYl1xRePdjBlSVpY0dCjxDgAAAOVDtAMAxIwTm5yopdcu1agOo3Tv4nvVd0Zfbd23NdpjVQzxrlratUuaMEFq0yb8WFdcfLx0xRXS558T7wAAAFB+RDsAQExJSUjR04Oe1rODntXSTUuV9lSalm5aGu2xKo54Vy0cjHWtW0t33y2dc460alX5Yl1xxDsAAAAcCaIdACAmjewwUh9c+4FSElJ01vSz9OiHj8prQtgi3sWk0mLdnDnSL39ZOfsoLd6lpUmvvUa8AwAAwKGIdgCAmJV6TKoyRmdowEkDdOs/btVlcy5TZnZmtMeqHMS7mBCJWFfcwXi3erX0wgvSgQPSRRcR7wAAAHAooh0AIKY1Tmms1y59Tfefe79mfz5bHZ/uqNVbV0d7rMpDvIuKXbsCkS6Ssa64hARpxIif4t3+/cQ7AAAA/IRoBwCIeWamO7rdoYkPh7gAABoFSURBVAVXLtCurF3qNLWTZn42M9pjVS7iXUQUjXUTJki9e0srV0Y21hV3MN59/jnxDgAAAD8h2gEAqo1erXtpxZgVSjs2TVe8eoV+89ZvlJ2XHe2xKhfxrkqUFutefVVKTY32dAGlxbszzpDmzuWjBwAAqG0skhf1Tk9P94yMjIjtDwBQM+Xm5+quBXfp4Q8eVufjO+uVi19Ry0Ytoz1W1cjKkp55RrrvPunbb6Xu3X+qTmbRni7m7dolPfqo9L//K+3eLV14oTRuXOyEulDy8qRZs6Q//UlauzYw8/jx0uDBfPQAAKDmcHfty92nXVm7SvyzO2u3urXqpl6te0V71CpjZsvdPf2w54l2AIDqas7nczTy9ZFKik/SzKEz1ffnfaM9UtUh3pXLrl3SY48FYt2uXdUr1hVHvAMAALGswAu0N2dvqdHtYHjblbVLu7JLXpbv+SH3Ma7nON199t0R+o0ij2gHAKiRvtzxpYa+PFSrt67WhF4T9Ieef1Cc1eCrPxDvQtq9+6cz66p7rCuOeAcAAKpCfkG+MnMyy45uJQS3g8tcodtS/aT6apzSWI1TGqtRcqPCn4v/KWlZo5RGSopPitC7ER1HHO3MLEXSIknJkhIkzXb38WaWKulJSSmS8iTd6O4fh9oW0Q4AUBX25ezTDW/eoBc+fUHn/dd5euHCF9S0btNoj1W1iHeHKB7rhgwJxLoOHaI9WeUrKd5NmCANGlQrP3oAAGq9vII87c7ard3Zu0OHt1KW78neU+Y+GiY3DCu6lbS8UUojJcQlROCdqL4qEu1MUj1332tmiZIWS7pF0kRJ/+vufzez8yXd4e69Qm2LaAcAqCrurinLp+jmt2/WMfWP0eyLZ6vj8R2jPVbVq+XxrjbFuuIOxruJEwP3LSHeAQBQPeXm54aMamVFt705e0Nu32RqlNLoiKNbw+SGio+Lj9C7UTtVytdjzayuAtHuBgWi3bPu/pKZDZd0gbtfHmp9oh0AoKot+3aZhr0yTN/v/V6P9n9UY84YI6sNBaOWxbvduwPXrPvzn2tfrCsuL0+aOTNw5t1XXwXeg/HjiXcAAERKdl52mWEt1LL9uftDbj/O4sL6GmlpyxskN6jZl4+pASoU7cwsXtJySf8l6S/ufqeZnSbpH5JMUpykM919QwnrjpY0WpJatWp1xoYNh70EAIBKtWP/Do14bYTe/uptjWg/Qk8OeFL1kupFe6zIqOHxjlhXOuIdAADl5+7KyssKK7qVtjwrLyvkPhLiEsK+fltJy+on1a8d/xK6FqusM+0aS3pN0k0KhLj33H2OmV0iabS7nxtqfc60AwBESoEX6J5F92j8wvFq17yd5lwyRyc3PTnaY0VODYt3xWPd4MGBIEWsO1xJ8W7CBOmCC6rlRw8AQEjurv25+8M6o6205Tn5OSH3kRiXqCZ1mhzx2W51E+sS3RBSpd091szGS9on6Y+SGru7B697t9vdG4Zal2gHAIi0+V/P1+VzLldOfo6mD5mui067KNojRVY1j3fEuiNHvAMAVAfurr05eysU3fIK8kLuIyUhpdxnuhVdnpKQQnRDlarIjSiaScp1911mVkfSfEn3S3pQ0g3uvtDMzpH0gLufEWpbRDsAQDRs3L1Rl7xyiT769iPd1vU23XfOfUqMT4z2WJFVzeLd7t3S448HYt2PPwZi3bhxUlpatCerfvLypBdfDMS7r78m3gEAKleBFygzO7NC0a3AC0Luo25i3ZLDWnLjQ26wUFJ0a5TSSCkJKRF6N4AjU5Fo117Sc5LiFbh23cvuPtHMukt6VFKCpCxJN7r78lDbItoBAKIlJz9Ht/3jNk1eNlndW3XXS8Ne0nENjov2WJEX4/GOWFd1iHcAgJLkF+RrT/aesG+aUHz57qzdcoXuCvWT6h9RdDsY3mrdv2xFrVNpX4+tCKIdACDaZn02S6PeGKUGSQ3012F/Va/WvaI9UnTEWLzbs+enr8H++GPg5gnjxxPrqgLxDgBqlryCPO3OKjmwhRPe9mTvKXMfDZMblhrdGqeEDm8NkxsqIS4hAu8EUH0R7QAACFq9dbWGvjxUa3eu1b2979Ud3e6ovdcpiXK8I9ZFT/F4l5YW+OgHDiTeAUAk5eTnVCi67c3ZG3L7Jis9qoUR3RokNVB8XHyE3g2gdiLaAQBQRGZ2pka9MUovr35Zg08ZrOlDpqtxSuNojxU9EY53JcW6ceOkM0JeHRdVIS9PmjFDmjSJeAcARyI7Lzvsa7eVtHx/7v6Q24+3+JLDWnKxr5GWEt7qJ9VXnMVF6N0AcCSIdgAAFOPueuyjx3T7O7frhEYnaPYls5V6TGq0x4quKo53e/YErln38MPEulhzMN796U/SN98Q7wDUDu6urLysct00ofif7PzskPtIiEtQk5QmRxzd6iXWq73fCABqCaIdAAClWLppqS5+5WLtPLBT/zfg/3R16tXRHin6KjneFY91F1wQ+BossS725Ob+9LVZ4h2AWOfu2pe7r9Svl4YT3XILckPuIyk+qULRrU5CHaIbgJCIdgAAhLB131YNnzNc7657V6M6jNLj5z+ulISUaI8VfRWMd8S66qt4vDvjjMBHP2AA8Q5A5XF3ZeZkhoxuZYW3fM8PuY86CXVKDmvJhwe2ksIb/38AQFUj2gEAUIb8gnyN+9c43bv4XnU4poNmXzJbJzY5MdpjxYZyxjtiXc2Rm/vTNe+IdwCKK/AC7cneEwhrR3C22+7s3SrwgpD7qJdYr+SwFkZ0a5TcSMkJyRF6NwDgyBDtAAAI0xtfvKEr514pSXrhwhc08OSBUZ4ohpQR7/bskSZPDsS6nTuJdTUJ8Q6omfIL8guDWsiz3bJLXr4ne49cof+ZskFSg7CjW/Hw1ii5kRLjEyP0bgBAdBDtAAAoh29+/EbDXh6mld+v1P/r/v808eyJio+Lj/ZYsaNYvNvTpa8mt/2LHp77c+3caRo4MBDr0g/7vx6o7oh3QGzJzc+tUHTLzMkscx+NkhsdcXRrmNxQCXEJEXgnAKD6ItoBAFBOWXlZuumtmzR15VT1btNbs4bOUvN6zaM9VkzZszVLk0et0sPzTtFOb6KBTZZo/KREpd/QkYJTwx2Md3/6k7RuXSDQTpggnX8+Hz1QHjn5OYd+XbS08JZd8vJ9uftCbj/O4g6LboVhrZToVjS8NUhqwL+0AoAqRrQDAOAITVs5TTe+daOOqnOUXrn4FZ3Z8sxojxR1mZk/XbNu505p4Pn5Gt9ujtJn/nel3G0W1UdurvTCC4Ez74h3qI2y8rIqFN0O5B0Iuf14iy85qpUQ4kqKbvWT6ivO4iL0bgAAjgTRDgCAClj1/SoNe3mYNuzeoIf6PKSbO98sq4VFIjMzcM26hx4KxrriX4Ot4N1mUX0R71AdubsO5B04/OYIJYW37JKXZ+dnh9xHYlxi6WEtjPBWL7FerfzfGwCoTYh2AABU0K6sXbp67tV6/YvXdUm7SzT1gqlqkNwg2mNFRPFYN2BAINZ17FjKCsS7Wot4h0hyd+3L3Veh6JZbkBtyH8nxyRWKbnUS6hDdAAAhEe0AAKgE7q4Hlz6ouxbcpZOOOklzLpmjds3bRXusKlPuWFcc8a7WKh7vOnYMfPTnncdHj58UeIH25uwt8eukh4W3UqJbvueH3EedhDqhw1qI8NYopZFSElIi9G4AAGoroh0AAJVo4fqFumz2ZcrMydTTFzyty39xebRHqlQVjnXFEe9qLeJdzVbgBdqTvafs6JZd8vLd2btV4AUh91EvsV6FoltSfFKE3g0AAI4M0Q4AgEr2XeZ3unT2pVq8cbF+3fHXerjvw0pOSI72WBWSmSn95S+BWLdjRyXEuuKId7VWbq70/POBeLd+PfE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      "text/plain": [
       "<Figure size 1584x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "thickness = 0.6096# 2ft\n",
    "fig = plt.figure(figsize=(22,4))\n",
    "plt.plot([0.0,top[0],bottom[0],27.5,30,55],[top[1],top[1],bottom[1],36.1,36.7,38.25],'g',[thickness+top[0],thickness+new_bottom_x],[top[1],bottom[1]],'r')\n",
    "plt.plot([top[0],thickness+top[0]],[top[1],top[1]],'r')\n",
    "#plt.plot([0.0,top[0],bottom[0],27.5,30,55],[top[1],top[1],bottom[1],36.1,36.7,38.25],'g',[top[0],new_bottom_x],[top[1],bottom[1]],'r')\n",
    "plt.plot([bottom[0],bottom[0]+10.67/2,bottom[0]+10.67],[bottom[1],bottom[1]+2.67,bottom[1]],'b')\n",
    "#plt.plot([bottom[0]-10.67/2.,bottom[0],bottom[0]+10.67/2.],[bottom[1],bottom[1]+2.67,bottom[1]],'b-.')\n",
    "plt.legend(['existing profile','re-enforced bank'])\n",
    "plt.axis('equal')\n",
    "plt.title('Full Bank Protection');\n",
    "plt.savefig(\"moundriprap.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the fill volume per foot along the bank:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rate of fill:  349.30869967929544 cubic feet per foot\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "ft_per_m=3.2808399\n",
    "face_length=math.sqrt((top[0]-bottom[0])**2 + (top[1]-bottom[1])**2)\n",
    "face_diag = math.sqrt((top[0]-(bottom[0]+thickness))**2+(top[1]-bottom[1])**2)\n",
    "S = (face_diag+face_length+thickness)/2.0\n",
    "par_area = 2.0*math.sqrt(S*(S-thickness)*(S-face_length)*(S-face_diag))#area of parallelogram for blanket thickness\n",
    "volume_per_ft = (abs(0.5*(top[1]-bottom[1])*(top[0]-new_bottom_x))+par_area)* (ft_per_m**2)\n",
    "print(\"Rate of fill: \", volume_per_ft, \"cubic feet per foot\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Length of Bank Protection\n",
    "\n",
    "The bank profile is similar to this worst case scenario profile, both upstream and downstream roughly 150ft.\n",
    "\n",
    "![Existing bank](files/existing_bank.png)\n",
    "\n",
    "Carrying the bank protection upstream another 250 feet (to prevent the structure being flanked by a possible chute cutoff of the upstream bar) results in the following planform of the bank protection, with a length of 600ft:\n",
    "\n",
    "![New Bank](files/top_bank.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Total volume of riprap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fill volume:  7762.415548428788 cubic yards\n",
      "Cost at $50/cubic yard: $388120.78\n"
     ]
    }
   ],
   "source": [
    "volume = 600*volume_per_ft/(3**3)\n",
    "print(\"Fill volume: \",volume, \"cubic yards\")\n",
    "print(\"Cost at $50/cubic yard: ${0:.2f}\".format(volume*50.0))"
   ]
  }
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