{ "cells": [ { "cell_type": "markdown", "id": "7d6f0946", "metadata": {}, "source": [ "# Reliability analysis with a model\n", "\n", "In this example, we will demonstrate how to perform a reliability analysis using a model that is not a limit state function. We consider the critical head difference model developed by Sellmeijer. This model is applicable to the piping failure mechanism, which addresses backward internal erosion beneath dikes with predominantly horizontal seepage paths.\n", "\n", "In this example, the limit state function is defined outside of the model. \n", "\n", "### Define model\n", "\n", "First, let's import the necessary classes:" ] }, { "cell_type": "code", "execution_count": 1, "id": "4989b056", "metadata": {}, "outputs": [], "source": [ "from probabilistic_library import ReliabilityProject, DistributionType, ReliabilityMethod, CompareType" ] }, { "cell_type": "markdown", "id": "76d8a8db", "metadata": {}, "source": [ "The critical head difference, $H_c$, according to the Sellmeijer's model is described by the following equations:" ] }, { "cell_type": "markdown", "id": "354841e1", "metadata": {}, "source": [ "$F_{resistance}=\\eta\\cdot \\frac{\\gamma_{sub,particles}}{\\gamma_{water}}\\cdot \\tan \\theta_{sellmeijer,rev}$\n", "\n", "\n", "$F_{scale}=\\frac{d_{70.m}}{\\sqrt[3]{\\kappa\\cdot L}}\\cdot\\left(\\frac{d_{70}}{d_{70.m}}\\right)^{0.4}$ and $\\kappa = \\frac{\\nu_{water}}{g}\\cdot k$\n", "\n", "\n", "$F_{geometry}=0.91\\cdot \\left(\\frac{D}{L}\\right)^{\\frac{0.28}{\\left(\\frac{D}{L}\\right)^{2.8}-1}+0.04}$\n", "\n", "$H_c = F_{resistance} \\cdot F_{scale} \\cdot F_{geometry} \\cdot L$\n", "\n", "where:
\n", "$L$ - seepage length (m)
\n", "$D$ - thickness of upper sand layer (m)
\n", "$\\theta$ - bedding angle ($\\circ$)
\n", "$d_{70}$ - particle diameter (m)
\n", "$k$ - permeability of the upper sand layer (m/s)" ] }, { "cell_type": "code", "execution_count": 2, "id": "abd29107", "metadata": {}, "outputs": [], "source": [ "from utils.models import model_sellmeijer" ] }, { "cell_type": "markdown", "id": "8c7d0666", "metadata": {}, "source": [ "### Perform reliability analysis\n", "\n", "We create a project using the `ReliabilityProject()` class and reference Sellmeijer's model. Note that this model functions as a limit state function." ] }, { "cell_type": "code", "execution_count": 3, "id": "fa1879e9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model model_sellmeijer:\n", "Input parameters:\n", " k\n", " L\n", " d70\n", " D\n", "Output parameters:\n", " delta_h_c\n" ] } ], "source": [ "project = ReliabilityProject()\n", "project.model = model_sellmeijer\n", "\n", "project.model.print()" ] }, { "cell_type": "markdown", "id": "cde91cc9", "metadata": {}, "source": [ "We define all the input parameters of the model as log normal variables, all with variation coefficient of $0.25$:" ] }, { "cell_type": "code", "execution_count": 4, "id": "ad1ee1db", "metadata": {}, "outputs": [], "source": [ "project.variables[\"k\"].distribution = DistributionType.log_normal\n", "project.variables[\"k\"].mean = 0.000245598\n", "project.variables[\"k\"].variation = 0.25\n", "\n", "project.variables[\"L\"].distribution = DistributionType.log_normal\n", "project.variables[\"L\"].mean = 40.0\n", "project.variables[\"L\"].variation = 0.25\n", "\n", "project.variables[\"d70\"].distribution = DistributionType.log_normal\n", "project.variables[\"d70\"].mean = 0.00019\n", "project.variables[\"d70\"].variation = 0.25\n", "\n", "project.variables[\"D\"].distribution = DistributionType.log_normal\n", "project.variables[\"D\"].mean = 30.0\n", "project.variables[\"D\"].variation = 0.25" ] }, { "cell_type": "markdown", "id": "ac64e361", "metadata": {}, "source": [ "Now, we specify the limit state function as follows: failure occurs when the head difference exceeds $3.0$ meters.\n", "This can be expressed as." ] }, { "cell_type": "code", "execution_count": 5, "id": "ebbb5d6e", "metadata": {}, "outputs": [], "source": [ "project.limit_state_function.parameter = project.model.output_parameters[0]\n", "project.limit_state_function.compare_type = CompareType.greater_than\n", "project.limit_state_function.critical_value = 3.0" ] }, { "cell_type": "markdown", "id": "46cce6bf", "metadata": {}, "source": [ "We use the `crude_monte_carlo` method and define the relevant settings: `minimum_samples` and `maximum_samples`. The reliability analysis is performed using `project.run()`, and the results can be accessed from `project.design_point`." ] }, { "cell_type": "code", "execution_count": 6, "id": "71bde011", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "gallery", "reliability" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reliability:\n", " Reliability index = 1.0669\n", " Probability of failure = 0.143\n", " Convergence = 0.0547 (not converged)\n", " Model runs = 2001\n", "Alpha values:\n", " k: alpha = 0.2634, x = 0.0002\n", " L: alpha = -0.8719, x = 48.7939\n", " d70: alpha = -0.3819, x = 0.0002\n", " D: alpha = 0.157, x = 27.9284\n", "\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "project.settings.reliability_method = ReliabilityMethod.crude_monte_carlo\n", "project.settings.minimum_samples = 1000\n", "project.settings.maximum_samples = 2000\n", "\n", "project.run()\n", "\n", "project.design_point.print()\n", "project.design_point.plot_alphas()" ] } ], "metadata": { "kernelspec": { "display_name": "base", "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": "3.12.10" } }, "nbformat": 4, "nbformat_minor": 5 }