notebooks/03_rupture/global_equilibrium_method.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Global equilibrium method\n",
    "\n",
    "© 2022 Exneyder A. Montoya-Araque, Daniel F. Ruiz and Universidad EAFIT.\n",
    "\n",
    "This notebook can be interactively run in [Google - Colab](https://colab.research.google.com/github/AppliedMechanics-EAFIT/EAFIT_slope_stability/blob/main/notebooks/03_rupture/global_equilibrium_method.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Required modules and initial setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from shapely.geometry import Polygon, LineString, Point\n",
    "from shapely.ops import split\n",
    "from ipywidgets import widgets as wgt\n",
    "from IPython import get_ipython\n",
    "from IPython.display import display\n",
    "\n",
    "if 'google.colab' in str(get_ipython()):\n",
    "    print('Running on CoLab. Installing the required modules...')\n",
    "    from subprocess import run\n",
    "    run('pip install ipympl', shell=True);\n",
    "    from google.colab import output\n",
    "    output.enable_custom_widget_manager()\n",
    "\n",
    "%matplotlib widget\n",
    "\n",
    "plt.style.use(\"default\")\n",
    "mpl.rcParams.update(\n",
    "    {\n",
    "        'figure.constrained_layout.use': True,\n",
    "        'interactive': False,\n",
    "        \"text.usetex\": False,  # Use mathtext, not LaTeX\n",
    "        \"font.family\": \"cmr10\",  # Use the Computer modern font\n",
    "        \"mathtext.fontset\": \"cm\",\n",
    "        \"axes.formatter.use_mathtext\": True,\n",
    "        \"axes.unicode_minus\": False,\n",
    "    }\n",
    ")\n",
    "html_setup = '<style> div.jupyter-widgets.widget-label {display: none;} </style>'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Area and centroid of a mass sliding along a circular surface\n",
    "\n",
    "### Funtions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def slope(height, inclination, hzt_dist):\n",
    "    hzt_slope = height / np.tan(np.radians(inclination))  # horizontal dist. of slope face\n",
    "    terrain_coords = ((hzt_dist, 0, -hzt_slope, -hzt_slope - hzt_dist),\n",
    "                      (0, 0, height, height))\n",
    "    return np.array(terrain_coords)\n",
    "\n",
    "def get_geometric_parameters(terrain_coords, center_x, center_y, radius):\n",
    "    slope_surf = LineString(terrain_coords.T)\n",
    "    circle = Point(center_x, center_y).buffer(radius)\n",
    "    split_circle = split(circle, slope_surf)\n",
    "    if len(split_circle.geoms)==1:\n",
    "        mass_polygon = split_circle.geoms[0]\n",
    "        surface_line = mass_polygon.exterior\n",
    "    else:\n",
    "        split_circle_0_xy = split_circle.geoms[0].exterior.xy\n",
    "        split_circle_1_xy = split_circle.geoms[1].exterior.xy\n",
    "        if max(split_circle_0_xy[1]) > max(split_circle_1_xy[1]):\n",
    "            mass_polygon = split_circle.geoms[1]\n",
    "        else:\n",
    "            mass_polygon = split_circle.geoms[0]\n",
    "        surface_line = mass_polygon.exterior.difference(slope_surf.buffer(.001))\n",
    "    return mass_polygon, surface_line\n",
    "\n",
    "\n",
    "def plot_slope(height, inclination, center_x, center_y, radius, widget=False, **kwargs):\n",
    "    hzt_slope = height / np.tan(np.radians(inclination))\n",
    "    terrain_coords = slope(height, inclination, 1e9)\n",
    "    mass_polygon, surface_line = get_geometric_parameters(\n",
    "        terrain_coords, center_x, center_y, radius)\n",
    "    hzt_dist = max(\n",
    "        max(surface_line.xy[0]), abs(min(surface_line.xy[0]))-hzt_slope, 0.5*height)\n",
    "    terrain_coords = slope(height, inclination, 1.2 * hzt_dist)\n",
    "    # Figure\n",
    "    fig, ax = plt.subplots(ncols=1, nrows=1, figsize=kwargs.get('figsize', [8, 4]))\n",
    "    # ax.plot(terrain_coords[0], terrain_coords[1], \"ok\")\n",
    "    # ax.plot(*mass_polygon.exterior.xy, ':y')\n",
    "    ax.plot(terrain_coords[0], terrain_coords[1], \"-k\")\n",
    "    ax.plot(*surface_line.xy, \"#BB5566\", ls=\"--\",\n",
    "            label=f\"Slip surface \\n$\\cdot$Area: {mass_polygon.area:.2f} m$^2$ \"\n",
    "            +f\"\\n$\\cdot$Length: {surface_line.length:.2f} m\")\n",
    "    ax.plot(center_x, center_y, color=\"black\", marker=\"x\", ls=\"\",\n",
    "        label=f\"Center: $x=${center_x:.1f} m, $y=${center_y:.1f} m\")\n",
    "    ax.plot(*mass_polygon.centroid.xy, color=\"#004488\", marker=\"o\", ls=\"\",\n",
    "            label=f\"Centroid: $x=${mass_polygon.centroid.x:.1f} m, \"\n",
    "            + f\"$y=${mass_polygon.centroid.y:.1f} m\")\n",
    "    ax.set(xlabel=\"$x$ [m]\", ylabel=\"$y$ [m]\")\n",
    "    ax.set_aspect(\"equal\", \"box\")\n",
    "    ax.spines[\"bottom\"].set_linewidth(1.5)\n",
    "    ax.spines[\"left\"].set_linewidth(1.5)\n",
    "    ax.spines[\"right\"].set_visible(False)\n",
    "    ax.spines[\"top\"].set_visible(False)\n",
    "    ax.legend(loc=\"center left\", bbox_to_anchor=(1.01, 0.5))\n",
    "    if widget:\n",
    "        display(fig)\n",
    "    else:\n",
    "        plt.show()\n",
    "        display(wgt.HTML(html_setup))\n",
    "    plt.close()\n",
    "    return\n",
    "\n",
    "# plot_slope(height=18, inclination=45, center_x=-3.5, center_y=12, radius=15)\n",
    "# plot_slope(height=8, inclination=45, center_x=-3.5, center_y=12, radius=11.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Static figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "model_id": "e588cca9bd234990bb3eb6adf72a2b80",
       "version_major": 2,
       "version_minor": 0
      },
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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=800.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4d636c84d647493d88650f2efb18641b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HTML(value='<style> div.jupyter-widgets.widget-label {display: none;} </style>')"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "height = 8  # [m]\n",
    "inclination = 45  # [°]\n",
    "center_x = -3.5  # [m]\n",
    "center_y = 12  # [m]\n",
    "radius = 15  # [m]\n",
    "plot_slope(height, inclination, center_x, center_y, radius)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interactive figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b9197bd4c032417b83bbd7c24e3be99a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(FloatSlider(value=8.0, description='Height [m]', layout=Layout(width='400px'), s…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s, l = {'description_width': '150'}, wgt.Layout(width='400px')\n",
    "controls = {\n",
    "    'height': wgt.FloatSlider(value=8, min=0.0, description=\"Height [m]\", style=s, layout=l),\n",
    "    'inclination': wgt.FloatSlider(value=45, min=0.5, max=90, description=\"Inclination [°]\", style=s, layout=l),\n",
    "    'center_x': wgt.FloatSlider(value=-3.5, min=-50, description=\"Center_𝑥 [m]\", style=s, layout=l),\n",
    "    'center_y': wgt.FloatSlider(value=12, min=0.1, description=\"Center_𝑦 [m]\", style=s, layout=l),\n",
    "    'radius': wgt.FloatSlider(value=15, min=0.1, description=\"Radius [m]\", style=s, layout=l),\n",
    "    'widget': wgt.Checkbox(value=True, description='Non-vector image (improve widget performance)', style=s, layout=l)\n",
    "}\n",
    "fig = wgt.interactive_output(plot_slope, controls)\n",
    "wgt.HBox((wgt.VBox(list(controls.values())), fig), layout=wgt.Layout(align_items='center'))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "EAFIT-env",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.13"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "ef8c03790f2d0da309ee3dc20d7c1e218681fdbff540ce14f81a0ed1380bf99b"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}