Spundwand.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "<div style=\"display: flex; align-items: center;\">\n",
        "    <img src=\"https://github.com/nagelt/Teaching_Scripts/raw/9d9e29ecca4b04eaf7397938eacbf116d37ddc93/Images/TUBAF_Logo_blau.png\" width=\"500\" height=\"auto\" height=\"auto\" style=\"margin-right: 100px;\" />\n",
        "    <div>\n",
        "        <p><strong>Prof. Dr. Thomas Nagel</strong></p>\n",
        "        <p>Chair of Soil Mechanics and Foundation Engineering<br>Geotechnical Institute<br>Technische Universität Bergakademie Freiberg.</p>\n",
        "        <p><a href=\"https://tu-freiberg.de/en/soilmechanics\">https://tu-freiberg.de/en/soilmechanics</a></p>\n",
        "    </div>\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Erddruckberechnung -- Spundwand\n",
        "\n",
        "Das folgende Beispiel ist an das Beispiel aus W. Fellin \"Geotechnik -- Lernen mit Beispielen\" angelehnt.\n",
        "\n",
        "![Rankine.png](https://raw.githubusercontent.com/nagelt/Teaching_Scripts/master/Images/Spundwand.png)\n",
        "\n",
        "**Aufgabe:** Zu untersuchen sind die Verteilungen von Erd- und Wasserdrücken im Falle des Niedrigwassers, für den davon ausgegangen wird, dass sich aufgrund der sich einstellenden Wandverschiebung auf der Bodenseite der aktive Erddruck einstellt und auf der Wasserseite der Erdwiderstand aktiviert wird.\n",
        "\n",
        "Den Wandreibungswinkel legen wir zu $\\delta_\\text{a} = 2/3\\,\\varphi$ fest. Auf der passiven Seite wird zunächst $\\delta_\\text{p} = -\\varphi/3$ angesetzt und diese Wahl später über das vertikale Kräftegleichgewicht überprüft.\n",
        "\n",
        "Sei außerdem $p_\\text{v} = 10\\,$kN/m²."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "#Some plot settings\n",
        "import plot_functions.plot_settings"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Die aktiven und passiven Erddrücke in horizontaler Richtung ergeben sich zu \n",
        "\n",
        "\\begin{align}\n",
        "    e_\\text{ah} &= \\gamma z K_\\text{agh} + p_\\text{v} K_\\text{aph} - c K_\\text{ach}\n",
        "    \\\n",
        "    e_\\text{ph} &= \\gamma z K_\\text{pgh} + p_\\text{v} K_\\text{pph} + c K_\\text{pch}\n",
        "\\end{align}\n",
        "\n",
        "Betrachten wir zunächst die aktive Seite mit den Eddruckbeiwerten:\n",
        "\n",
        "\\begin{align*}\n",
        "\tK_\\text{agh} &= \\left[\n",
        "\t\\frac{\\cos(\\varphi - \\alpha)}{\\cos \\alpha \\left( 1 + \\sqrt{\\displaystyle\\frac{\\sin(\\varphi + \\delta_\\text{a}) \\sin (\\varphi - \\beta)}{\\cos(\\alpha - \\beta) \\cos(\\alpha + \\delta_\\text{a})}} \\right)}\n",
        "\t\\right]^2\n",
        "\t\\qquad\n",
        "\tK_\\text{ag} = \\frac{K_\\text{agh}}{\\cos (\\alpha + \\delta_\\text{a})} \n",
        "    \\qquad\n",
        "    K_\\text{agv} = K_\\text{agh} \\tan (\\alpha + \\delta_\\text{a})\n",
        "    \\\n",
        "    K_\\text{aph} &= \\frac{\\cos \\alpha \\cos \\beta}{\\cos(\\alpha - \\beta)} K_\\text{agh}\n",
        "    \\\n",
        "    K_\\text{ach} &= \\frac{2\\cos(\\alpha - \\beta) \\cos\\varphi \\cos(\\alpha+\\delta_\\text{a})}{\\left[ 1 + \\sin(\\varphi + \\alpha + \\delta_\\text{a} - \\beta)\\right]\\cos\\alpha}\n",
        "\\end{align*}\n",
        "\n",
        "Dabei ergeben sich die Überlegungen zu $K_\\text{agv}$ bzw. $K_\\text{ag}$ aus den Betrachtungen des Zusammenspiels von $e_\\text{agh}$ mit $e_\\text{agv}$ und $e_\\text{ag}$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "K_agh = lambda alpha,beta,delta,phi: (np.cos(phi - alpha)/(np.cos(alpha) * \n",
        "                                                           (1 + np.sqrt(np.sin(phi+delta)*np.sin(phi-beta)/\n",
        "                                                                        (np.cos(alpha+delta)*np.cos(alpha-beta))))))**2\n",
        "\n",
        "K_aph = lambda Kagh,alpha,beta: np.cos(alpha)*np.cos(beta)/np.cos(alpha-beta)*Kagh\n",
        "\n",
        "K_ach = lambda alpha,beta,delta,phi: 2*np.cos(alpha-beta)*np.cos(phi)*np.cos(alpha+delta)/(np.cos(alpha)*(1+np.sin(phi+alpha+delta-beta)))\n",
        "\n",
        "h_in_v = lambda h,alpha,delta: h*np.tan(alpha+delta)\n",
        "h_in_t = lambda h,alpha,delta: h/np.cos(alpha+delta)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "phi = np.deg2rad(np.array([34,27]))\n",
        "delta_a = 2/3*phi\n",
        "delta_p = -1/3*phi"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "K_{agh} = 0.235 für Sa und 0.318 für saSi\n",
            "K_{aph} = 0.235 für Sa und 0.318 für saSi\n",
            "K_{ach} entfällt für Sa und beträgt 0.993 für saSi\n",
            "\n",
            "K_{ag} = 0.254 für Sa und 0.334 für saSi\n",
            "K_{ap} = 0.254 für Sa und 0.334 für saSi\n",
            "K_{ac} entfällt für Sa und beträgt 1.044 für saSi\n"
          ]
        }
      ],
      "source": [
        "res_K_agh = np.array([K_agh(0,0,delta_a[0],phi[0]),\n",
        "                      K_agh(0,0,delta_a[1],phi[1])])\n",
        "res_K_aph = np.array([K_aph(res_K_agh[0],0,0),\n",
        "                      K_aph(res_K_agh[1],0,0)])\n",
        "res_K_ach = K_ach(0,0,delta_a[1],phi[1])\n",
        "\n",
        "\n",
        "print(\"K_{agh} = %.3f für Sa und %.3f für saSi\" %(res_K_agh[0],res_K_agh[1]))\n",
        "print(\"K_{aph} = %.3f für Sa und %.3f für saSi\" %(res_K_aph[0],res_K_aph[1]))\n",
        "print(\"K_{ach} entfällt für Sa und beträgt %.3f für saSi\" %(res_K_ach))\n",
        "\n",
        "print(\"\\nK_{ag} = %.3f für Sa und %.3f für saSi\" %(h_in_t(res_K_agh[0],0,2./3*np.deg2rad(34)),h_in_t(res_K_agh[1],0,2./3*np.deg2rad(27))))\n",
        "print(\"K_{ap} = %.3f für Sa und %.3f für saSi\" %(h_in_t(res_K_aph[0],0,2./3*np.deg2rad(34)),h_in_t(res_K_aph[1],0,2./3*np.deg2rad(27))))\n",
        "print(\"K_{ac} entfällt für Sa und beträgt %.3f für saSi\" %h_in_t(res_K_ach,0,2./3*np.deg2rad(27)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Auf der passiven Seite nutzen wir:\n",
        "\n",
        "\\begin{align}\n",
        "    K_\\text{pgh} &= \\cos(\\alpha + \\delta_\\text{p}) K_\\text{pg,0} i_\\text{pg} g_\\text{pg} t_\\text{pg}\n",
        "    \\\n",
        "    K_\\text{pph} &= \\cos(\\alpha + \\delta_\\text{p}) K_\\text{pp,0} i_\\text{pp} g_\\text{pp} t_\\text{pp}\n",
        "    \\\n",
        "    K_\\text{pch} &= \\cos(\\alpha + \\delta_\\text{p}) K_\\text{pc,0} i_\\text{pc} g_\\text{pc} t_\\text{pc}\n",
        "    \\\n",
        "    &\\text{mit}\n",
        "    \\\n",
        "    K_\\text{pg,0} &= K_\\text{pp,0} = \\frac{1+\\sin\\varphi}{1-\\sin\\varphi}\n",
        "    \\\n",
        "    K_\\text{pc,0} &= 2 \\sqrt{K_\\text{pg,0}}\n",
        "\\end{align}\n",
        "\n",
        "Die Beiwerte können nach DIN4085 berechnet werden. Alternativ können die Erddruckbeiwerte aus den im Anhang gegebenen Abbildungen abgelesen werden. Damit ergibt sich ungefähr:\n",
        "\n",
        "$$\n",
        "    K_\\text{pgh} \\approx 3.4 \\qquad K_\\text{pch} \\approx 4.1\n",
        "$$\n",
        "Nun rechnen wir die Erddrücke an den Schichtgrenzen aus."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Tiefen unter GOK bergseitig in m: [ 0.   6.  10.5 19.5]\n",
            "Zugehörige Vertikaleffektivspannungen in kN/m²: [  0. 108. 153. 234.]\n"
          ]
        }
      ],
      "source": [
        "#Schichtdicken:\n",
        "dza = np.array([0,6,4.5,9])\n",
        "#maßgebliche Wichten\n",
        "gamma = np.array([18,18,10,9])\n",
        "#Vertikale Effektivspannungszuwächse:\n",
        "d_sigma_v = dza*gamma\n",
        "#Vertikale Effektivspannungen\n",
        "sigma_v=d_sigma_v.cumsum()\n",
        "print(\"Tiefen unter GOK bergseitig in m:\", dza.cumsum())\n",
        "print(\"Zugehörige Vertikaleffektivspannungen in kN/m²:\", sigma_v)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Sandschicht: Tiefen unter GOK bergseitig in m: [ 0.   6.  10.5]\n",
            "Sandschicht: Zugehörige horizontale Erddrücke in kN/m²: [ 2.3462205  27.68540184 38.24339407]\n",
            "Sandschicht: Zugehörige vertikale Erddrücke in kN/m²: [ 0.97984186 11.56213396 15.97142233]\n",
            "Schluffschicht: Tiefen unter GOK bergseitig in m: [10.5 19.5]\n",
            "Schluffschicht: Zugehörige horizontale Erddrücke in kN/m²: [31.91630531 57.64352792]\n",
            "Schluffschicht: Zugehörige vertikale Erddrücke in kN/m²: [10.37023623 18.72951758]\n"
          ]
        }
      ],
      "source": [
        "pv = 10.\n",
        "c = 20.\n",
        "e_ah_Sa = sigma_v[:3]*res_K_agh[0] + pv*res_K_aph[0]\n",
        "e_ah_Si = sigma_v[2:]*res_K_agh[1] + pv*res_K_aph[1] - c * res_K_ach\n",
        "print(\"Sandschicht: Tiefen unter GOK bergseitig in m:\", dza.cumsum()[:3])\n",
        "print(\"Sandschicht: Zugehörige horizontale Erddrücke in kN/m²:\", e_ah_Sa)\n",
        "print(\"Sandschicht: Zugehörige vertikale Erddrücke in kN/m²:\", h_in_v(e_ah_Sa,0,delta_a[0]))\n",
        "print(\"Schluffschicht: Tiefen unter GOK bergseitig in m:\", dza.cumsum()[2:])\n",
        "print(\"Schluffschicht: Zugehörige horizontale Erddrücke in kN/m²:\", e_ah_Si)\n",
        "print(\"Schluffschicht: Zugehörige vertikale Erddrücke in kN/m²:\", h_in_v(e_ah_Si,0,delta_a[1]))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Tiefen unter Sohle wasserseitig in m: [0 9]\n",
            "Zugehörige Vertikaleffektivspannungen in kN/m²: [ 0 81]\n"
          ]
        }
      ],
      "source": [
        "#Schichtdicken:\n",
        "dzp = np.array([0,9])\n",
        "#maßgebliche Wichten\n",
        "gamma = 9\n",
        "#Vertikale Effektivspannungszuwächse:\n",
        "d_sigma_vp = dzp*gamma\n",
        "#Vertikale Effektivspannungen\n",
        "sigma_vp=d_sigma_vp.cumsum()\n",
        "print(\"Tiefen unter Sohle wasserseitig in m:\", dzp.cumsum())\n",
        "print(\"Zugehörige Vertikaleffektivspannungen in kN/m²:\", sigma_vp)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Schluffschicht: Tiefen unter Sohle wasserseitig in m: [0 9]\n",
            "Schluffschicht: Zugehörige horizontale Erddrücke in kN/m²: [ 82.  357.4]\n",
            "Schluffschicht: Zugehörige vertikale Erddrücke in kN/m²: [-12.98752411 -56.60659897]\n"
          ]
        }
      ],
      "source": [
        "K_pgh = 3.4\n",
        "K_pch = 4.1\n",
        "e_ph_Si = sigma_vp*K_pgh + c * K_pch\n",
        "print(\"Schluffschicht: Tiefen unter Sohle wasserseitig in m:\", dzp.cumsum())\n",
        "print(\"Schluffschicht: Zugehörige horizontale Erddrücke in kN/m²:\", e_ph_Si)\n",
        "print(\"Schluffschicht: Zugehörige vertikale Erddrücke in kN/m²:\", h_in_v(e_ph_Si,0,delta_p[1]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Wir vernachlässigen vorerst Strömungskräfte und rechnen die hydrostatische Wasserdruckverteilung aus:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [],
      "source": [
        "z_wa = np.array([6,19.5])\n",
        "p_wa = 10*(z_wa-6)\n",
        "\n",
        "z_wp = np.array([7,19.5])\n",
        "p_wp = 10*(z_wp-7)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Wir können das Ergebnis nun darstellen."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.plot(np.append(e_ah_Sa,e_ah_Si),-np.append(dza.cumsum()[:3],dza.cumsum()[2:]),label=r'$e_\\mathrm{ah}$',color='red')\n",
        "ax.plot(-e_ph_Si,-dzp.cumsum()-10.5,label=r'$e_\\mathrm{ph}$',color='green')\n",
        "ax.plot(p_wa,-z_wa,label=r'$u$',color='blue')\n",
        "ax.plot(-p_wp,-z_wp,color='blue')\n",
        "ax.axvline(0)\n",
        "ax.set_xlabel(r'$\\sigma_h$ / kN m$^{-2}$')\n",
        "ax.set_ylabel(r'$z_\\mathrm{GOK}$ / m')\n",
        "fig.tight_layout()\n",
        "fig.legend();"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Wir überprüfen nun, ob $\\sum V \\approx 0$, um die Annahme $\\delta_\\text{p} = -\\varphi/3$ zu verifizieren. \n",
        "\n",
        "Dazu berücksichtigen wir auch das Gewicht der Spundwand mit $q_\\text{SPW} = 1.06\\,\\text{kN}\\,\\text{m}^{-2}$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Summe der bergseitigen Vertikalkräfte: 252.8 kN/m\n",
            "Summe der wasserseitigen Vertikalkräfte: -313.2 kN/m\n"
          ]
        }
      ],
      "source": [
        "q_spw = 1.06 #kN/m²\n",
        "H_spw = 21 #m\n",
        "V_spw = q_spw*H_spw\n",
        "Eav = np.trapz(h_in_v(e_ah_Sa,0,delta_a[0]),x=dza.cumsum()[:3]) + np.trapz(h_in_v(e_ah_Si,0,delta_a[1]),x=dza.cumsum()[2:])\n",
        "Epv = np.trapz(h_in_v(e_ph_Si,0,delta_p[1]),x=dzp.cumsum())\n",
        "print(\"Summe der bergseitigen Vertikalkräfte: %.1f kN/m\" %(Eav+V_spw))\n",
        "print(\"Summe der wasserseitigen Vertikalkräfte: %.1f kN/m\" %(Epv))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Wir überprüfen außerdem das horizontale Kräftegleichgewicht:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Summe der bergseitigen Horizontalkräfte: 1552.7 kN/m\n",
            "Summe der wasserseitigen Horizontalkräfte: 2758.6 kN/m\n"
          ]
        }
      ],
      "source": [
        "Eah = np.trapz(e_ah_Sa,x=dza.cumsum()[:3]) + np.trapz(e_ah_Si,x=dza.cumsum()[2:])\n",
        "P_a = np.trapz(p_wa,x=z_wa)\n",
        "Eph = np.trapz(e_ph_Si,x=dzp.cumsum())\n",
        "P_p = np.trapz(p_wp,x=z_wp)\n",
        "print(\"Summe der bergseitigen Horizontalkräfte: %.1f kN/m\" %(Eah+P_a))\n",
        "print(\"Summe der wasserseitigen Horizontalkräfte: %.1f kN/m\" %(Eph+P_p))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Wiederholen wir die Berechnung mit $\\delta_\\text{p} = 0°$ ($K_\\text{pgh} = 2.8$ und $K_\\text{pch} = \\text{3.3}$), so erhalten wir:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Schluffschicht: Tiefen unter Sohle wasserseitig in m: [0 9]\n",
            "Schluffschicht: Zugehörige horizontale Erddrücke in kN/m²: [ 66.  292.8]\n",
            "Schluffschicht: Zugehörige vertikale Erddrücke in kN/m²: [0. 0.]\n",
            "Summe der bergseitigen Vertikalkräfte: 252.8 kN/m\n",
            "Summe der wasserseitigen Vertikalkräfte: 0.0 kN/m\n",
            "Summe der bergseitigen Horizontalkräfte: 1552.7 kN/m\n",
            "Summe der wasserseitigen Horizontalkräfte: 2395.8 kN/m\n"
          ]
        }
      ],
      "source": [
        "K_pgh = 2.8\n",
        "K_pch = 3.3\n",
        "e_ph_Si = sigma_vp*K_pgh + c * K_pch\n",
        "print(\"Schluffschicht: Tiefen unter Sohle wasserseitig in m:\", dzp.cumsum())\n",
        "print(\"Schluffschicht: Zugehörige horizontale Erddrücke in kN/m²:\", e_ph_Si)\n",
        "print(\"Schluffschicht: Zugehörige vertikale Erddrücke in kN/m²:\", h_in_v(e_ph_Si,0,0))\n",
        "Eav = np.trapz(h_in_v(e_ah_Sa,0,delta_a[0]),x=dza.cumsum()[:3]) + np.trapz(h_in_v(e_ah_Si,0,delta_a[1]),x=dza.cumsum()[2:])\n",
        "Epv = np.trapz(h_in_v(e_ph_Si,0,0),x=dzp.cumsum())\n",
        "print(\"Summe der bergseitigen Vertikalkräfte: %.1f kN/m\" %(Eav+V_spw))\n",
        "print(\"Summe der wasserseitigen Vertikalkräfte: %.1f kN/m\" %(Epv))\n",
        "Eah = np.trapz(e_ah_Sa,x=dza.cumsum()[:3]) + np.trapz(e_ah_Si,x=dza.cumsum()[2:])\n",
        "P_a = np.trapz(p_wa,x=z_wa)\n",
        "Eph = np.trapz(e_ph_Si,x=dzp.cumsum())\n",
        "P_p = np.trapz(p_wp,x=z_wp)\n",
        "print(\"Summe der bergseitigen Horizontalkräfte: %.1f kN/m\" %(Eah+P_a))\n",
        "print(\"Summe der wasserseitigen Horizontalkräfte: %.1f kN/m\" %(Eph+P_p))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Weiterführende Aufgaben:\n",
        "\n",
        "* Interpretieren Sie das Ergebnis bzgl. des mobilisierten Erdwiderstands."
      ]
    }
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