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- ItemGlobal Sensitivity Analysis of Structural Reliability Using Cliff Delta(MDPI, 2024-07-07) Kala, ZdeněkThis paper introduces innovative sensitivity indices based on Cliff's Delta for the global sensitivity analysis of structural reliability. These indices build on the Sobol' method, using binary outcomes (success or failure), but avoid the need to calculate failure probability P-f and the associated distributional assumptions of resistance R and load F. Cliff's Delta, originally used for ordinal data, evaluates the dominance of resistance over load without specific assumptions. The mathematical formulations for computing Cliff's Delta between R and F quantify structural reliability by assessing the random realizations of R > F using a double-nested-loop approach. The derived sensitivity indices, based on the squared value of Cliff's Delta delta(2)(C), exhibit properties analogous to those in the Sobol' sensitivity analysis, including first-order, second-order, and higher-order indices. This provides a framework for evaluating the contributions of input variables on structural reliability. The results demonstrate that the Cliff's Delta method provides a more accurate estimate of Pf. In one case study, the Cliff's Delta approach reduces the standard deviation of Pf estimates across various Monte Carlo run counts. This method is particularly significant for FEM applications, where repeated simulations of R or F are computationally intensive. The double-nested-loop algorithm of Cliff's Delta maximizes the extraction of information about structural reliability from these simulations. However, the high computational demand of Cliff's Delta is a disadvantage. Future research should optimize computational demands, especially for small values of P-f.
- ItemFinite element analysis of concrete slab exposed to high velocity pressure wave – simplified vs. smoothed-particle hydrodynamics (SPH) method(EDP Sciences, 2024-05-24) Jindra, Daniel; Hradil, Petr; Kala, JiříMany structures are required to sustain the structural resistance also under extreme loading conditions, for example impacts of high-velocity objects (airplane crash into nuclear power plant), impacts of projectiles (defence structures), or while exposed to high velocity pressure wave caused e.g. by explosion of various chemicals in industry, nature gas, or also conventional weapons. Numerical analyses of these phenomena are feasible while utilizing explicit approach of the finite element method (FEM), available in commercially accessible software LS-Dyna. In order to predict the behaviour of the structure properly, advanced nonlinear material models are required to be considered, which are often mathematically described by numerous input parameters. Several approaches to model the exposure to blast load exist, from simplified, where the blast wave is considered as timedependent pressure based on empirical equations, to more advanced ones, where the propagation of the pressure wave itself through the surrounding environment is being modelled Arbitrary Lagrangian Eulerian, (ALE method), or so called smoothed-particle hydrodynamics (SPH) method, which might be used to model the blast itself. In this paper, FEM analyses of a simply supported concrete slab with basalt fibre reinforced polymer (BFRP) bars exposed to close range explosion of TNT charge are presented. 3D numerical models are analysed utilizing explicit solver of LS-Dyna. Karagozian and Case (K&C) nonlinear material model for concrete is used, which is suitable when high strain rates are present in the quasi brittle materials. Two variants of the blast loads modelling are compared. The simplified empirical approach, which is less demanding on computational power, and feasible for utilization in case of simple structure geometry, and more demanding method using SPH method to model the TNT detonation and interaction with the exposed concrete slab. The results of these numerical analyses are compared with experimental data based on available literature, and properly discussed.
- ItemCalibration and verification of creep parameters for concrete(EDP Sciences, 2024-05-24) Jindra, Daniel; Hradil, Petr; Kala, JiříConcrete is a material which undergoes slow increasing deformation while subjected to persistent mechanical stress. This phenomenon is known as creep. In concrete material, creep occurs at all stress levels. Additional deformation of concrete structures at the end of their design working life caused by creep is usually two to three times of the immediate elastic deformation value, but might be even more in some cases. The value is dependent on many parameters, e.g. concrete grade, cement class, ambient environment relative humidity, geometry of the structure (drying surface of concrete in contact with air) and also the age of concrete at the time of loading. According to corresponding European standard, the effects of creep are evaluated using creep coefficient, and should be considered for verification of serviceability limit states, and if significant, also at ultimate limit states. In order to evaluate the creep effects in geometrically more complex structures, numerical finite element (FEM) analyses might be conducted. In commercially available software ANSYS, there is a library of several implicit creep equations, with several input parameters. These parameters need to be calibrated in order to match the assumptions of the creep effects over time in accordance with the corresponding European standard. In this study, calibration process of European standard concrete C35/45 parameters for selected implicit creep equation from ANSYS library is presented. The parameters are calibrated for two different ambient relative humidity (RH) levels, 78.8% and 90%, each for concrete loaded in 28 days (also 90 days for RH 78.8% and 50 days for RH 90%) after its casting, and suitable for finite element analysis of creep effects within the first year after loading of the concrete structure. The calibration process is split into two parts, analytical one conducted in table processor, where approximate estimations of suitable parameter values are determined. The second part consist of the subsequent optimization process in OptiSLang software, where the optimal parameter values are determined in order to achieve the best match between the time dependent Eurocode standard creep coefficient and the creep coefficient based on the results of one solid element uniaxial compression test in ANSYS finite element software. The obtained parameters are then verified on an analysis of a simply-supported concrete beam modelled of solid 3D finite elements. The values of selected creep equation parameters are summarized in the table, and might be used in the subsequent ongoing research.
- ItemCorrosion vs. fatigue in a high-strength steel specimen investigated via FEM(Elsevier, 2024-06-06) Malíková, Lucie; Benešová, Anna; Al Khazali, Mohammad Sami; Seitl, StanislavThe work is devoted to investigations of the stress distribution/concentration in a corroded specimen loaded via remote tensile loading. Existence of corrosion pits of various size and various mutual distance affects stress distribution in a specimen which can have influence on its lifetime. Thus, numerical simulations via finite element method were performed in order to assess the stress field near corrosion pits in specimens made of high-strength steel. The geometry of the numerical model was suggested based on the dimensions of the real specimens produced for fatigue experiments. The results obtained are discussed and mutual comparison with experimental data is intended in oncoming months.
- ItemStress relaxation of concrete beams caused by creep and shrinkage effects(EDP Sciences, 2024-05-24) Jindra, Daniel; Hradil, Petr; Kala, JiříShrinkage and creep are two important physical properties of concrete material which cause increase of the deformation of the constantly loaded structure over long period of time, the feature known as rheology. Additional deformation of concrete structures at the end of the design working period (most commonly 50 years) caused by these phenomena is circa three times larger than the value of the immediate elastic deformation (or even larger in some cases). Hence, in accordance with the corresponding European standard, these effects should be taken in account while evaluating the serviceability limit state of concrete structures, and if significant, consideration of these phenomena is also needed for the verification of the ultimate limit state. In concrete material, creep occurs at all stress levels, and is dependent on many parameters, as cement class, concrete grade, relative humidity of the environment, surface of the structure in contact with the ambient air (drying surface), and the age of concrete (after casting) at the loading moment. Shrinkage of the concrete is independent on loading. It is caused by decrease of the pore water content in the hardened concrete, and is predominantly dependent on the ambient relative humidity. Relaxation describes stress reduction at a constant material strain, usually in prestressing steel tendons. In this study, the physical experiments of multiple concrete beams over time with respect to rheological processes are described. Each experimental system consists of two C35/45 beams horizontally bounded by a prestressed steel cylinder. Decrease of these pretension forces in cylinders over time have been monitored (stress relaxation). All together time histories of two forces are documented, based on measurements conducted in interior environment of an agricultural building. The experimental time histories of the pretension forces are then compared with the results of the finite element numerical analyses conducted in ANSYS software. Creep and shrinkage effects of the concrete material have been considered based on the corresponding European standard for design of the concrete structures. The time-histories of the forces in prestressed cylinders obtained from the numerical simulations are then compared with the experimental data, and discussed. It is concluded, that the estimation of the force decrease over analysed time with the creep and shrinkage effects considered according to the corresponding European standard appears to be slightly larger than the experimentally measured decrease of the force value, hence the assumption is more conservative.