DOI: 10.4121/59968977-7d4a-4b98-be3c-dc9360b931e1.v1
title: Code underlying the PhD thesis: Structural reliability updating through proof load testing

description: This C++ code belongs to the PhD thesis of Rein de Vries titled "Structural reliability updating through proof load testing – A Bayesian methodology applied to reinforced concrete road bridges and viaducts". The data is organised following the structure of the dissertation, which can be found via the TUD repository: https://repository.tudelft.nl/<br>The dissertation followed from the PhD project "Probabilistic substantiation of proof load testing" executed at the Concrete Structures department of the Delft University of Technology (TUD) from 1 September 2020 to 1 September 2025. The project number is CS3B09, and the Directorate-General for Public Works and Water Management (Rijkswaterstaat, RWS) has financed the work. This project was a collaboration between TUD, TNO and RWS.<br>This code requires the following compiler, libraries and editor: GCC C++ 10.2 or later, 64-bit version installed in %USERPROFILE%\msys64\mingw64 Boost C++ library 1.65 or later, located in %USERPROFILE%\cpp_include (headers only) Eigen C++ library 3.4 or later, located in %USERPROFILE%\cpp_include Visual Studio Code 1.103.2 or later, with extensions: C/C++, C/C++ Themes, F5 Anything.<br>Description of files: <strong>.vscode/c_cpp_properties.json, .vscode/launch.json, .vscode/tasks.json</strong>: These are the project configuration files for Visual Studio Code. The project is set up such that when running (pressing F5) the currently displayed source file is compiled and executed. Debug and Release configurations are provided, with the executables following from the latter are significantly faster. This speed is absolutely required for the Monte Carlo simulations, which would otherwise take a lot of time. <strong>rdv/distributions.hpp, rdv/erf_inv.hpp, ...</strong>: Together, these files contain the header-only "rdv" probabilistic library that is used in the rest of the code, containing the implementation of distributions, mathematical functions, etc. <strong>chapter_2.cpp</strong>: Contains the Monte Carlo simulation procedure to produce graphs displaying the evolution of reliability over time. Importance sampling is used on variables f_y, C_0Q and θ_E to increase the accuracy and ultimately reduce the run time. The output is displayed in Figures 2.2 and 2.3. <strong>chapter_3.cpp</strong>: This code iteratively calculates the target proof load factors for CC2 and CC3 in bending and shear. These are the factors provided in data file Chapter 3 Factors CC2 and CC3.csv and are plotted in Figure 3.3. <strong>chapter_4_prior_sensitivity.cpp</strong>: Using this code, the sensitivity to various choices for the prior distribution of the resistance is explored. The distribution is changed by uncommenting the relevant rv_R_hat definition. The result of the calculation is the posterior distribution of the resistance, assuming survival of the proof load effect. The results of these calculations are displayed in Figures 4.2 and 4.3. <strong>chapter_4_time-dependent.cpp</strong>: This code is quite similar to chapter_2.cpp as it also performs a time-dependent reliability analysis. However, in this case a low-informative prior distribution is assumed for the resistance with its mean value directly calculated from the mean values of the load variables. The output of the analysis is provided in Figure 4.4. <strong>chapter_5_case_study_1.cpp</strong>: In this code the reliability analysis of case study 1, where laboratory data is used to predict the resistance, is performed. Several target load levels are used to simulate the incremental load application. For each step a Markov-chain Monte Carlo (MCMC) simulation is performed by which the reliability during and after a successful load step is calculated. The output of this code is provided in Table 5.1. <strong>chapter_5_case_study_2_sectional_analysis.cpp</strong>: Since for the second case study no laboratory data is available, a numerical simulation using Latin Hypercube Sampling (LHS) is performed. The output of this code has resulted in the data of Chapter 5 Sectional analysis.csv and is displayed in Figure 5.6. <strong>chapter_5_case_study_2_reliability_updating.cpp</strong>: This code is similar to chapter_5_case_study_1.cpp, but in this case the resistance is predicted using the numerically simulated data. The resulting reliability indices are provided in Table 5.2. <strong>chapter_6_load_correlation_decay.cpp</strong>: In this code a Monte Carlo simulation is performed to determine the decay of the correlation between load effects when the reference period increases. Gumbel distributed random variables with given initial correlation and block sizes are defined using vectors. The output is provided in Figure 6.5. <strong>chapter_6_case_study_1_bending.cpp, chapter_6_case_study_1_shear.cpp</strong>: These codes calculate transfer factors for case study 1, considering bending and shear. The flag 'correlated_Q' switches between the correlated and uncorrelated situations. Using interpolation, the target load corresponding to beta = 4 may be determined. The ratio between the load required in each configuration and the n = N case results in the transfer factors. The results for bending and shear are provided in Tables 6.3 and 6.4. <strong>chapter_6_case_study_2.cpp</strong>: Using this code, the reliability of the continuous bridge with two spans can be calculated, given two load testing strategies and two load test vehicle configurations (tipper truck and semi-low trailer). If the axle loads are set to zero, the code can also be used to calculate the in-service proven strength from one year of traffic loading. The calculated reliability indices are provided in Table 6.5.<br>LICENSE:This source code is distributed under the European Union Public Licence, version 1.2 (EUPL-1.2). You may obtain a copy of the licence at: https://joinup.ec.europa.eu/collection/eupl/eupl-text-eupl-12<br>Not intended for commercial use.