ProjectExcalibur.ipynb

projectexcalibur.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "ProjectExcalibur.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/shenlebantongying/50b95a2a3d2e21a4064548c958677c3e/projectexcalibur.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c3Y06oTxPMdC"
      },
      "source": [
        "**How to use**\n",
        "+ **First time use -> top -> Runtime -> Restart and run all**\n",
        "+ then click the red triangle of each code block to run certain parts"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "167lR_PaoJY1"
      },
      "source": [
        "**Notes**\n",
        "\n",
        "+ To easily embed the \"algorithm\" into UI without much extra work, I put everything into a \"class\" core, and single output function -> plot().(i smiplily copy and paste the code below to assembly the final program and bingo its done :) \n",
        "\n",
        "+ There are a lot of self.x within the code. The \"self\" is a special keyword in python which means the paramater belong to the class rather than the global variable scope. (I think they can be elimated...)\n",
        "\n",
        "+ In this program, self.x means it is just a paramater or an intermediate constant which will not change during plotting or calculation after initlization.\n",
        "\n",
        "+ python's ^ \"power\" operator is double star. ($x^2$ shuold be x**2)\n",
        "\n",
        "+ scipy & numpy & matplotlib is the *de facto* scientific libries combination of python ecoosystem.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xzTRDRvlVmCW"
      },
      "source": [
        "**TODO**\n",
        "+ Validate input paramaters (some paramaters seems only possible in certain range?)\n",
        "+ units of final solution??\n",
        "+ what is \"outter radius\" b? \n",
        "+ let user directly set $q$ rather than force use $\\theta$\n",
        "+ check again if soil's cohension is always near zero( near the book's MC ceriterion part)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C-UNsdBqMD51"
      },
      "source": [
        "**Symbols Table**\n",
        "\n",
        "|symbol | in-program | meaning | other note|\n",
        "|---|---|---|---|\n",
        "|$r$|r| radius(the only variable)| |\n",
        "|$c_o$ | co | part of the Coulomb filure criterion | I dont quite understand it, around chapter 4.5(but directly calculated from $S_o$ or cohension )|\n",
        "|$\\rho$ | rho | yield point | |\n",
        "|$P_o$  | po  | Hydrostatic stress ||\n",
        "|$P_i$  | pi  | stress at $r=a$, or the deformation of the hollow cylinder finished | first paragraph of the book|\n",
        "|$\\theta'$ | theta_prime | angle of internal friction before yield | TODO: some where around chapter 3 or 4 of the book |\n",
        "|$\\theta$ | theta | angle of internal friction after yield| yield: from elastic to plastic  |\n",
        "|$q'$|q_prime|Part of coulomb filure criterion **before** yield| can be directly calculated from $\\theta'$|\n",
        "|$q$|q|Part of coulomb filure criterion **after** yield|\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ndyQmOWRJdkW"
      },
      "source": [
        "%matplotlib inline \n",
        "import numpy as np\n",
        "import scipy \n",
        "import matplotlib.pyplot as plt "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3JATJ6tMNqi2",
        "outputId": "fe580165-1603-474e-996f-6b0f61ce927b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 543
        }
      },
      "source": [
        "class core():\n",
        "  def __init__(self,a,b,pi,so,theta,material,so_p=0,theta_p=0): \n",
        "    self.a = a   # inner radius\n",
        "    self.b = b   # outter radius \n",
        "    self.pi = pi # ->NOTICE<- this might also need to distinguish between different materials\n",
        "    self.material=material\n",
        "\n",
        "    # ---> NOTE <----\n",
        "    # if material type is *soil*, the cohension will not change after the yield point\n",
        "    # only theta, q, and co are used\n",
        "\n",
        "    # if material type is *rock*, the cohension will change\n",
        "    #   when (a <  r < rho) -> plastic (after  yield) -> paramaters: q, co ,theta\n",
        "    #   when (rho< r < b  ) -> elastic (before yield) -> paramaters: q',co',theta' < notice the prime\n",
        "\n",
        "\n",
        "    # >>>> paramaters initilization <<<<\n",
        "    if self.material is \"soil\":\n",
        "      self.co    = 2*so\n",
        "      self.theta = np.radians(theta)\n",
        "      self.po = self.co\n",
        "      self.q = (1+np.sin(self.theta))/(1-np.sin(self.theta))\n",
        "\n",
        "\n",
        "    elif self.material is \"rock\":\n",
        "      self.co    = 2*so\n",
        "      self.theta = np.radians(theta)\n",
        "      self.q = (1+np.sin(self.theta))/(1-np.sin(self.theta))\n",
        "\n",
        "      self.co_p  = 2*so_p\n",
        "      self.theta_p = np.radians(theta_p)\n",
        "      self.q_p = (1+np.sin(self.theta_p))/(1-np.sin(self.theta_p))\n",
        "\n",
        "      self.po = self.co_p\n",
        "\n",
        "    # >>>> calculation of yield point & B  <<<<\n",
        "  \n",
        "    if self.material is \"soil\":\n",
        "      # equation (9.28) & (9.29)\n",
        "      self.rho =  self.a* ( 2*( self.po*(self.q-1)+self.co )/( ( self.pi*(self.q-1) + self.co)*(self.q+1) ) )**(1/(self.q-1))\n",
        "      self.B   = (self.rho**2)*(self.co+self.po*(self.q-1))/(self.q+1)\n",
        "\n",
        "    elif self.material is \"rock\":\n",
        "      # equation (9.35) & (9.36) 0> care for difference between \"primes\"\n",
        "      self.rho = self.a*(((2*self.po-self.co_p)*(1-self.q) - self.co*(1+self.q_p) )/( (self.pi*(1-self.q)-self.co)*(1+self.q_p) )  )**(1/(self.q-1))\n",
        "      self.B   = (self.rho**2)*(self.co_p+self.po*(self.q_p-1) )/(self.q_p+1 )\n",
        "\n",
        "  #=============================================================================\n",
        "\n",
        "  def radical_stress(self,r):\n",
        "    if self.a<=r and r<self.rho:\n",
        "      return self.co/(1-self.q)+(self.pi-self.co/(1-self.q))*(r/self.a)**(self.q-1)\n",
        "    elif r > self.rho:\n",
        "      return self.po - self.B/(r**2)\n",
        "    else:\n",
        "      return np.nan\n",
        "\n",
        "  def tangential_stress(self,r):\n",
        "    if self.a<=r and r<self.rho:\n",
        "      return self.co/(1-self.q)+self.q*(self.pi-self.co/(1-self.q))*(r/self.a)**(self.q-1)\n",
        "    elif r > self.rho:\n",
        "      return self.po + self.B/(r**2)\n",
        "    else:\n",
        "      return np.nan\n",
        "\n",
        "\n",
        "  #=============================================================================\n",
        "  def plot(self):\n",
        "    # plotting-related\n",
        "    # ps:code below suck, cuz matplotlib use similar api of MATLAB which have bad plotting functions.....\n",
        "    x_a_rho = np.linspace(self.a,self.rho,500)\n",
        "    x_rho_b = np.linspace(self.rho,self.b,500)\n",
        "\n",
        "    rsline=plt.plot(x_a_rho,[self.radical_stress(r)/self.pi for r in x_a_rho],\"B\",\n",
        "             x_rho_b,[self.radical_stress(r)/self.pi for r in x_rho_b],\"B\",\n",
        "             )\n",
        "    rsline[0].set_label(\"Radical stress\")\n",
        "\n",
        "    tsline=plt.plot(x_a_rho, [self.tangential_stress(r)/self.pi for r in x_a_rho],\"g\",\n",
        "             x_rho_b, [self.tangential_stress(r)/self.pi for r in x_rho_b],\"g\",\n",
        "             )\n",
        "    tsline[0].set_label(\"Tangential stress\")\n",
        "\n",
        "    \n",
        "    plt.xlabel(r'radius r (m)')\n",
        "    plt.ylabel(r'Stress')\n",
        "\n",
        "\n",
        "    # Styling the plot\n",
        "    plt.grid()\n",
        "    plt.legend()\n",
        "    plt.show()\n",
        "\n",
        "#===============================================================================\n",
        "# >>> testing code <<<\n",
        "# Reproduce fig. 9.3 a\n",
        "testCase_a = core(a=1,\n",
        "                  b=10,\n",
        "                  so=10,\n",
        "                  pi=1,\n",
        "                  theta=60,\n",
        "                  material=\"soil\")\n",
        "testCase_a.plot()\n",
        "\n",
        "# Reproduce fig. 9.3 b\n",
        "\n",
        "testCase_b = core(a=1,\n",
        "                  b=10,\n",
        "                  pi=1,\n",
        "                  so=0,\n",
        "                  so_p=10,\n",
        "                  theta_p=30,\n",
        "                  theta=30,\n",
        "                  material=\"rock\")\n",
        "testCase_b.plot()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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JCSEuLq5SvwN39upp6qzpIyKhwGBgq4hEOdcJMBxIdVcMBYUFBPiVfLdFhEYQExnDkt1L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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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xkqnkPIra1TPIWDdf3QhUwWrJf8JFEr9Syj1kZcGJE3DsmLUcP269P3my4CUn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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p737BtzzJSgl"
      },
      "source": [
        "> code below just some code sketch & backup"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zXB5CgUu1oDV",
        "outputId": "01e385a5-2e33-41ca-e66f-dfaab8c1a71e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "#===== code below just for practice python ======\n",
        "class cat():\n",
        "  def __init__(self,name):\n",
        "    self.name = name\n",
        "    self.truename = self.name\n",
        "  def p(self):\n",
        "    print(self.truename)\n",
        "\n",
        "mike=cat(\"so\")\n",
        "mike.p()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "so\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cBAk_xNz7fu7",
        "outputId": "489a918d-d6d7-485b-f630-6bebfe8b533b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        }
      },
      "source": [
        "#====== code below was draft version of the algorithm which can only calculate fig. 9.3 a\n",
        "# just put here as backup\n",
        "# Reproduce fig. 9.3 a\n",
        "# r -> radius (variable)\n",
        "# co ->  part of the Coulomb filure criterion\n",
        "# phi (Φ) -> angle of internal friction !!!!!! what?\n",
        "\n",
        "class core():\n",
        "  def __init__(self,a,b,so,pi):\n",
        "    self.a = a     # a -> inner radius\n",
        "    self.b = b     # b -> outter radius\n",
        "    self.so = so   # so -> cohension\n",
        "    self.pi = pi   # pi -> TODO!\n",
        "\n",
        "    # calculate intermediate constants\n",
        "    self.co=2*self.so #\n",
        "    self.po = self.co #\n",
        "    \n",
        "    # calculate yield point from cohension & hydrostatic stress po\n",
        "    self.rho=self.a* np.sqrt((self.co+2*self.po)/(2*self.co+4*self.pi)) \n",
        "\n",
        "  def radical_stress(self,r):\n",
        "    if self.a<=r and r<self.rho:\n",
        "      return (self.pi+(self.co/2))*(r/self.a)**2 - (self.co/2)\n",
        "    elif r >= self.rho:\n",
        "      return (self.po-0.5*(self.po+(self.co/2))*(self.rho /r)**2)\n",
        "    else:\n",
        "      return None\n",
        "\n",
        "  def tangential_stress(self,r):\n",
        "    if self.a<=r and r<self.rho:\n",
        "      return 3*(self.pi+(self.co/2))*(r/self.a)**2-(self.co/2)\n",
        "    elif r >= self.rho:\n",
        "      return self.po+0.5*(self.po+(self.co/2))*(self.rho/r)**2\n",
        "    else:\n",
        "      return None\n",
        "\n",
        "\n",
        "  def plot(self):\n",
        "    # plotting-related\n",
        "    \n",
        "    # ps:code below suck, cuz matplotlib use similar api of MATLAB which have bad plotting functions.....\n",
        "    x_r = np.linspace(self.a,self.b,100)\n",
        "\n",
        "    y_radical_stress = [self.radical_stress(r) for r in x_r]\n",
        "    plt.plot(x_r,y_radical_stress,label=\"Radial stress\")\n",
        "\n",
        "\n",
        "    y_trangential_stress = [self.tangential_stress(r) for r in x_r]\n",
        "    plt.plot(x_r,y_trangential_stress,label=\"Tangential stress\")\n",
        "\n",
        "    plt.xlabel(r'radius r (m)')\n",
        "    plt.ylabel(r'Stress')\n",
        "\n",
        "\n",
        "    # Styling the plot\n",
        "    plt.grid()\n",
        "    plt.legend()\n",
        "\n",
        "    plt.show()\n",
        "\n",
        "#===============================\n",
        "# test\n",
        "testCase = core (a=1,\n",
        "                 b=10,\n",
        "                 so=10,\n",
        "                 pi=0)\n",
        "testCase.plot()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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vIieNMV0bO8a4cePMhg0bzi4Ad6n1JEWYZVXWYhSg5VFTeykLYwxen8HjM7i9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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j8Zd57IvzTpL",
        "outputId": "86ec50b6-63bf-4f26-cfbd-8de7cf5739d3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        }
      },
      "source": [
        "plt.plot([1,2,3],[4,5,6],[4,5,6],[7,8,9])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7ff34c98f208>,\n",
              " <matplotlib.lines.Line2D at 0x7ff34c98f588>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AqKjl35SUOi9/uZLHPlhEWiXjwXO7ctHRWVSqpO3fIkFRUcs/Ld6Uz/DRc5i9Zgcnd2zE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\nCJcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BSa0CVAAzdeD",
        "outputId": "a3d63062-749e-4555-f446-0c12f6a0bc35",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 167
        }
      },
      "source": [
        "raise ValueError('A very specific bad thing happened.')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-6-bf62aa681e65>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'A very specific bad thing happened.'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m: A very specific bad thing happened."
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5c39GUFwTw-R"
      },
      "source": [
        "```\n",
        "# segiment backup\n",
        "  def radical_stress_soil (self,r):\n",
        "    if self.a<=r and r<self.rho:\n",
        "      return self.co/(1-self.q)+(self.pi-self.co/(1-self.q))*(r/self.a)**(self.q-1)\n",
        "    elif r > self.rho:\n",
        "      return self.po - self.B/(r**2)\n",
        "    else:\n",
        "      return np.nan\n",
        "\n",
        "  def radical_stress_rock (self,r):\n",
        "    if self.a<=r and r<self.rho:\n",
        "      return self.co/(1-self.q)+(self.pi-self.co/(1-self.q))*(r/self.a)**(self.q-1)\n",
        "    elif r > self.rho:\n",
        "      return self.po - self.B/(r**2)\n",
        "    else:\n",
        "      return np.nan\n",
        "```"
      ]
    }
  ]
}