Variability Of Material Parameters Research Articles

Dynamic reliability assessment for high CFRDs incorporating ground motion and material parameter variability via GPDEM

The randomness of earthquake and material parameters significantly impacts the seismic response and dynamic reliability of geotechnical engineering structures. In this study, a dynamic reliability analysis method for high concrete face rockfill dams (CFRDs) under the influence of random factors is proposed by combining random sample generation methods with the generalized probability density evolution method (GPDEM). Firstly, the spectral representation-random function method is employed to achieve dimensionality reduction expression for intensity-frequency non-stationary ground motion. Sensitivity analysis is then used to identify the random variables of the rockfill constitutive model, and the improved generalized F-discrepancy (GF-discrepancy) method is utilized to generate random material parameters. Then, the random samples of earthquake and material parameter are introduced into the finite element calculation of CFRD, conducting a series of dynamic finite element calculations. Finally, GPDEM is used to derive probability information and dynamic reliability from the deterministic time history responses. The results indicate that random factors contribute to the variability of seismic response and dynamic reliability. Stochastic ground motion significantly affects extreme values, while variability in material parameters has a more pronounced influence on the overall process of seismic response. These findings provide valuable references for the seismic design of CFRDs.

Random field of homogeneous and multi-material structures by the smoothed finite element method and Karhunen–Loève expansion

A random field of homogeneous and multi-material structures with uncertain scenarios is addressed by constructed the generalized stochastic cell-based smoothed finite element model. Smoothed finite element method (S-FEM) is “Jacobian-free”, which is not only overcomes the limitations of “overly-stiff” and low accuracy of the standard FEM, but also demonstrates strong resistance to mesh distortion. This paper proposes an efficient non-intrusive stochastic smoothed finite element method (SS-FEM) based on cell-based smoothing domains (SD) for the stochastic analysis of elastic problems, which describe much more realistically real physical systems under uncertain scenarios. This SS-FEM starts from the Gaussian random field based on representation related to the spatial variability in material parameters based on the Karhunen-Loève (KL) expansion, and then establishes the basic formulation that considers the effects of uncertainties. A generalized solving framework based on numerical integration is further developed. The non-intrusive dimension reduction method is also adopted to obtain the statistical moments and probability density function. The proposed SS-FEM can capture the structural stochastic responses under uncertainty condition by combining gradient smoothing technology and uncertainty quantification. A number of engineering examples are compared with the solution of Monte Carlo simulation to demonstrate both the accuracy and the efficiency of the proposed method.

Effect of variability of mechanical properties on the predictive capabilities of vulnerable coronary plaques

Background and Objective:Coronary plaque rupture is a precipitating event responsible for two thirds of myocardial infarctions. Currently, the risk of plaque rupture is computed based on demographic, clinical, and image-based adverse features. However, using these features the absolute event rate per single higher-risk lesion remains low. This work studies the power of a novel framework based on biomechanical markers accounting for material uncertainty to stratify vulnerable and non-vulnerable coronary plaques. Methods:Virtual histology intravascular ultrasounds from 55 patients, 29 affected by acute coronary syndrome and 26 affected by stable angina pectoris, were included in this study. Two-dimensional vessel cross-sections for finite element modeling (10 sections per plaque) incorporating plaque structure (medial tissue, loose matrix, lipid core and calcification) were reconstructed. A Montecarlo finite element analysis was performed on each section to account for material variability on three biomechanical markers: peak plaque structural stress at diastolic and systolic pressure, and peak plaque stress difference between systolic and diastolic pressures, together with the luminal pressure. Machine learning decision tree classifiers were trained on 75% of the dataset and tested on the remaining 25% with a combination of feature selection techniques. Performance against classification trees based on geometric markers (i.e., luminal, external elastic membrane and plaque areas) was also performed. Results:Our results indicate that the plaque structural stress outperforms the classification capacity of the combined geometric markers only (0.82 vs 0.51 area under curve) when accounting for uncertainty in material parameters. Furthermore, the results suggest that the combination of the peak plaque structural stress at diastolic and systolic pressures with the maximum plaque structural stress difference between systolic and diastolic pressures together with the systolic pressure and the diastolic to systolic pressure gradient is a robust classifier for coronary plaques when the intrinsic variability in material parameters is considered (area under curve equal to [0.91–0.93]). Conclusion:In summary, our results emphasize that peak plaque structural stress in combination with the patient’s luminal pressure is a potential classifier of plaque vulnerability as it independently considers stress in all directions and incorporates total geometric and compositional features of atherosclerotic plaques.

Random dynamic response analysis of an asphalt concrete core wall dam on deep overburden with double random factors

The spatial variability of material parameters and the randomness of ground motion are factors that influence the seismic response of a dam. To obtain more reliable seismic response results, it is crucial to study the influence of various uncertain factors on the response to earthquakes. In this paper, the K-L series expansion method and LH sampling technique are combined to characterize the spatial correlation of material parameters using a Gaussian autocorrelation function. This allows for the simulation of random fields of material parameters. By improved the Clough-Penzien power spectrum model and incorporating the concept of a random function, it becomes possible to generate nonstationary random ground motion that accurately reflects the site conditions. Taking an asphalt concrete core dam on deep overburden as an example, a random dynamic response analysis was conducted, considering various random factors. Statistical analysis and distribution testing were conducted on the horizontal acceleration and vertical permanent deformation responses. The process of the evolution of the probability density of the horizontal acceleration at the top of the dam was determined using the generalized probability density evolution method. This method helps to reveal the influence of various random factors on the response of the dam body. The research results show that among the spatial variability of material parameters and the randomness of ground motions, the randomness of ground motions is the main influencing factor of the random response results of the dam body. The mean response of two random factors is significantly larger than that of a single random factor. When considering dual random factors simultaneously, the complexity of the random factors increases, resulting in statistical properties that differ from those of single random factors. Therefore, to obtain more reliable random seismic response results, it is necessary to consider both the spatial variability of material parameters and the randomness of ground motions.

On site investigations and laboratory testing on full scale elements for the characterization of an existing RC bridge

The assessment of the mechanical characteristics and of the degradation level of existing bridges is a topic of great relevance today. In this regard, the methodology proposed by the Italian “Guidelines for risk classification, safety assessment and structural health monitoring of existing bridges” represents a fundamental support in the whole evaluation process. In this paper, the first phases of an experimental and numerical research on an existing RC bridge which was scheduled for demolition are presented. This opportunity allows to carry out both on-site tests and, subsequently, laboratory tests on full-scale elements extracted from the bridge, which can be supported by Finite Element (FE) analyses of different levels of detail. In particular, in this paper a first numerical analyses have been carried out by assuming the mean values of all the material parameters in order to obtain the necessary information for the design of the experimental setup. Moreover a Montecarlo analysis has been also carried out to assess the influence of the statistic variability of material parameters on the structural response.

Stochastic free vibration analysis of FG-CNTRC plates based on a new stochastic computational scheme

Stochastic analysis can provide more accurate results compared to deterministic analysis. In this study, the spatial variability of material parameters is introduced into the free vibration analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates to achieve a higher degree of accuracy, and a new stochastic computational scheme is proposed to handle the low-level uncertainties. First-order shear deformation theory (FSDT) is employed to establish the displacement field of the plates. The Young's moduli of carbon nanotube (CNT) and matrix are regarded as one-dimensional (1D) and two-dimensional (2D) random fields, respectively, which is discretized by Karhunen-Loève (K-L) expansion. The obtained random variables are substituted into modified perturbation stochastic method (MPSM) and radial point interpolation method (RPIM) to calculate the first two order estimates of the stochastic non-dimensional natural frequencies ω¯. The sensitivity of the first to fourth ω¯ to the random fields is analyzed, and the corresponding stochastic bands are plotted. The results indicate that the presented approach can accurately solve the generalized eigenvalue problem in stochastic free vibration; ω¯ is sensitive to random fields E11CNT and Em, and insensitive to random field E22CNT; the CNT distribution mode also affects the sensitivity.

Evolutionary Optimizing Process Parameters in the Induction Hardening of Rack Bar by Response Surface Methodology and Desirability Function Approach under Industrial Conditions.

Conditions of industrial production introduce additional complexities while attempting to solve optimization problems of material technology processes. The complexity of the physics of such processes and the uncertainties arising from the natural variability of material parameters and the occurrence of disturbances make modeling based on first principles and modern computational methods difficult and even impossible. In particular, this applies to designing material processes considering their quality criteria. This paper shows the optimization of the rack bar induction hardening operation using the response surface methodology approach and the desirability function. The industrial conditions impose additional constraints on time, cost and implementation of experimental plans, so constructing empirical models is more complicated than in laboratory conditions. The empirical models of nine system responses were identified and used to construct a desirability function using expert knowledge to describe the quality requirements of the hardening operation. An analysis of the hypersurface of the desirability function is presented, and the impossibility of using classical gradient algorithms during optimization is empirically established. An evolutionary strategy in the form of a floating-point encoded genetic algorithm was used, which exhibits a non-zero probability of obtaining a global extremum and is a gradient-free method. Confirmation experiments show the improvement of the process quality using introduced measures.

An advanced method for evaluating the cracking risks of gravity dams during the construction period considering the uncertainty of thermodynamic parameters

The thermal stress field of the gravity dam is often simulated in a deterministic way at present, ignoring the effect of spatial variability of parameters, resulting in unreasonable results of the thermal stress field simulation and cracking risk analysis of the dam body. Therefore, based on the random field theory and autocorrelation function, a simulation method for the spatial variability of thermodynamic parameters is proposed in this paper. The agent risk analysis model for the cracking of a gravity dam during the construction period is constructed with the consideration of spatial variability of material parameters, and then an advanced system cracking risk evaluation method for gravity dams during the construction period considering the spatial variability of thermodynamic parameters is formed. The application of the TJ dam illustrates that the temperature control measures proposed according to the analysis results of the deterministic thermal stress field are dangerous, and considering the spatial variability of material parameters has a significant effect on the cracking risk of the dam body. This study gives a more reasonable and realistic cracking risk assessment of the dam, which can provide technical support for the formulation of temperature control measures and cracking risk control of the roller compacted concrete (RCC) gravity dam.

Dynamic Reliability Analysis of Layered Slope Considering Soil Spatial Variability Subjected to Mainshock–Aftershock Sequence

The slope instability brought on by earthquakes frequently results in significant property damage and casualties. At present, the research on displacement response of a slope under earthquake has mainly emphasized the action of the mainshock, without accounting for the impact of an aftershock, and the spatial variability of material parameters is often neglected. The spatial variability of parameters is fully accounted for in this paper, and dynamic reliability of permanent displacement (DP) of a slope produced by the mainshock–aftershock sequence (MAS) is studied. A slope reliability analysis method is proposed based on the Newmark displacement method and the generalized probability density evolution method (GPDEM) to quantify the effect of the spatial variability of materials parameters on dynamic reliability. Firstly, the parameter random field is generated based on the spectral representation method, and the randomly generated parameters are assigned to the finite element model (FEM). In addition, the random simulation method of MAS considering the correlation between aftershock and mainshock is adopted based on the Copula function to generate the MAS. Then, the DP of slopes caused by the MAS considering the spatial variability is calculated based on the Newmark method. The impacts of the coefficient of variation (COV) and aftershock on the DP of slope is analyzed by means of mean values. Finally, the effect of COV and aftershock on the reliability of DP is explained from a probabilistic point of view based on the GPDEM. The results revealed that with the increase in the COV, the mean of the DP of the slope shows a trend of increasing gradually. The DP of slope is more sensitive to the coefficient of variation of friction angle (COVF). The mean DP of the slope induced by the MAS is larger compared to the single mainshock, and the PGA has a significant impact on the DP.

An improved system identification method for hardfill dams considering the spatial variability of material parameters based on random field theory

Calibrating the finite element model plays an important role in the accurate safety evaluation of dams. Recent studies show that the material heterogeneity has important impact on the safety evaluation of hardfill dams. However, due to the complexity of material heterogeneity, only limited researches involve the system identification of dams considering the material heterogeneity. In this study, an improved system identification method considering the material parameters heterogeneity is proposed for hardfill dams based on the Hariri-Ardebili et al.’s method. The proposed improved method is composed by two main steps: firstly, identification of the correlation length based on the support vector machine (SVM) and then estimation of the spatial varied hardfill modulus based on the combination of the Karhunen-Loeve expansion (KLE) and surrogate-based optimization (SBO) algorithm. A series of numerical simulations are performed to test the proposed method. The simulation results indicate that the proposed method can improve both the accuracy and computational efficiency. In addition, the effects of the hardfill heterogeneity on the modal responses are also investigated in this study. It is observed that the variation of the natural frequencies tends to increase with the increase of correlation length.

Analysis of Dam Overtopping Failure Risks Caused by Landslide-Induced Surges Considering Spatial Variability of Material Parameters

Many of the existing reservoir dams are constructed in alpine and gorge regions, where the topography and geological conditions are complicated, bank slopes are steep, and landslides have a high potential to occur. Surges triggered by landslides in the reservoir are one of the major causes of dam overtopping failures. Many factors affect the slope stability of reservoir banks and the height of surges triggered by landslides, such as spatial variability of material properties, speed of landslides, etc. To reasonably evaluate dam overtopping risk caused by landslide-induced surges is a key technology in engineering that is urgent to be solved. Therefore, a novel risk analysis method for overtopping failures caused by waves triggered by landslides induced by bank instability considering the spatial variability of material parameters is proposed in this study. Based on the random field theory, the simulation method for the spatial variability of material parameters is proposed, and the most dangerous slip surface of the reservoir bank slope is determined with the minimum value of the safety factors. The proxy risk analysis models for both the slope instability and dam overtopping are constructed with the consideration of spatial variability of material parameters, and then the dam overtopping failure risk caused by landslide-induced surges is calculated using the Monte-Carlo sampling. The proposed models are applied to a practical engineering project. Results show that the spatial variability of material properties significantly affects the instability risk of slopes, without considering which the risks of slope instability and dam overtopping may be overestimated. This study gives a more reasonable and realistic risk assessment of dam overtopping failures, which can provide technical support for the safety evaluation and risk control of reservoir dams.

Fuzzy seismic fragility analysis of gravity dams considering spatial variability of material parameters

Due to the heterogeneity of massive concrete and unevenness of pouring process, concrete strengths in gravity dams show obvious spatial variability. In addition, since the evolution of damage states for gravity dams is a gradually transitional process, the threshold between adjacent damage states is ambiguous. A mathematical model for describing the fuzziness of damage states threshold is presented. And a methodology for fuzzy seismic fragility analysis of gravity dams considering spatial variability of material parameters is proposed by combining nonlinear dynamic analysis of dam-reservoir-foundation system, Hariri-Ardebili's damage quantification method and an approach for simulation of random field of material parameters. The seismic fragility of gravity dams was investigated to illustrate the proposed methodology. It is found that the spatial variability of concrete tensile strength leads the seismic damage of the dam to be spatially varying as well. The damage of dam body intensifies and the probability of exceeding for each damage state increases. The fuzzy seismic fragility curves are insensitive to the types of membership function (linear, mountain and polynomial). Due to the influence of frequency distribution of damage index, the effects of variation in the size of the fuzzy interval of threshold on seismic fragility curves are different. The probability of exceeding of each damage state for gravity dams obviously increases when the spatial variability of tensile strength and fuzziness of damage states threshold are considered simultaneously.

A staggered high-dimensional Proper Generalised Decomposition for coupled magneto-mechanical problems with application to MRI scanners

Manufacturing new Magnetic Resonance Imaging (MRI) scanners represents a computational challenge to industry, due to the large variability in material parameters and geometrical configurations that need to be tested during the early design phase. This process can be highly optimised through the employment of user-friendly computational metamodels constructed on the basis of Reduced Order Modelling (ROM) techniques, where high-dimensional parametric offline solutions are obtained, stored and assimilated in order to be efficiently queried in real time. This paper presents a novel Proper Generalised Decomposition (PGD) based metamodel for the analysis of electro-magneto-mechanical interactions in the context of MRI scanner design, with three distinct novelties. First, the paper derives, from scratch, a five-dimensional parametrised offline solution process, expressed in terms of (axisymmetric) cylindrical coordinates, external excitation frequency, electrical conductivity of the embedded shields and strength of the static magnetic field. Second, by exploiting the staggered nature of the coupled problem at hand, an efficient sequential PGD algorithm is derived and compared against a previously published monolithic PGD algorithm. As a third novelty, the paper draws some interesting comparisons against an alternative tailor-made ROM technique, where the electromagnetic equations are solved using a Proper Orthogonal Decomposition model. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and potential of the considered approach, especially in terms of cost reduction.

Dynamic performance of planar mechanism with joint clearance considering stochastic parameters

Due to the influence of working temperature and pressure, collision restitution coefficient, Poisson’s ratio, friction coefficient and other material parameters could range in different intervals. However, the uncertainties and variability of material parameters is usually ignored in most researches. Along with vibration and wear, joint clearance is inevitable and widely exists in mechanical devices, which also should be taken into consideration. In this paper, the kinematic and dynamic equations are developed based on continuous Lankarani-Nikravesh contact model and the modified Coulomb friction model using a typical crank-slider mechanism as the research object. The influence of stochastic parameters (obeying normal distribution) on the dynamic characteristics of crank-slider mechanism is studied. In addition, dynamic analysis of the crank-slider mechanism with cylindrical joint clearance of different sizes is carried out in MATLAB environment. Results show that parameter random uncertainty should also be involved in dynamic models.

Multilevel surrogate modeling approach for optimization problems with polymorphic uncertain parameters

The solution of optimization problems with polymorphic uncertain data requires combining stochastic and non-stochastic approaches. The concept of uncertain a priori parameters and uncertain design parameters quantified by random variables and intervals is presented in this paper. Multiple runs of the nonlinear finite element model solving the structural mechanics with varying a priori and design parameters are needed to obtain a solution by means of iterative optimization algorithms (e.g. particle swarm optimization). The combination of interval analysis and Monte Carlo simulation is required for each design to be optimized. This can only be realized by substituting the nonlinear finite element model by numerically efficient surrogate models. In this paper, a multilevel strategy for neural network based surrogate modeling is presented. The deterministic finite element simulation, the stochastic analysis as well as the interval analysis are approximated by sequentially trained artificial neural networks. The approach is verified and applied to optimize the concrete cover of a reinforced concrete structure, taking the variability of material parameters and the structural load as well as construction imprecision into account.

Numerical studies of earth structure assessment via the theory of porous media using fuzzy probability based random field material descriptions

To account for the natural variability of material parameters in multiphasic and hydro‐mechanical coupled finite element analyses of soil and earth structure applications, the use of probabilistic methods may be effective. Here, selecting the appropriate soil auto‐correlation functions for random field realizations plays an essential role. In a joint study, the general influence of auto‐correlation lengths on the results of strongly coupled models is determined. Subsequently, a polymorphic approach using fuzzy probability based random fields is used to capture the solution space for fuzzy auto‐correlation lengths. To adequately describe the behavior of the soil the theory of porous media is implemented, which uses a homogenization approach for the multiple phases on the soil microstructure. Its foundations and the differentiated methods used for the polymorphic uncertainty quantification are explained in this contribution. Based on two representative examples, the requirements and advantages of a polymorphic uncertainty model are worked out30.

Effect of material parameter variability on vibroacoustic response in wood floors

The use of wood as construction material in multi-story buildings increased in Europe during the last decades. Wood buildings are more sensitive to dynamic loading compared to conventional concrete buildings, especially in terms of vibroacoustic comfort. Furthermore, it is more difficult to predict the accurate response due to dynamic loading for wood buildings. This is due to factors such as a complex structure involving many connections which vary in their mechanical behavior and the variability in the material parameters of wood. In the study, a reduced-order finite element model correlated to measurement data is used to examine the effect of experimentally obtained variability in material parameters on the vibroacoustic response of a wooden floor. The floor is subjected to surface loading. Monte Carlo simulations are conducted and in order to execute the probabilistic analysis in an efficient manner, the use of various sampling techniques is investigated. It was concluded that the variability in material parameters of wood significantly affects the predicted low-frequency vibrations, and thereby also affects the transmission of structure-borne sound.

Spatial variability and sensitivity analysis on the compressive strength of hollow concrete block masonry wallettes

This probabilistic study investigates the effect of material uncertainties on the numerical analysis of masonry wallette axial compressive strength. Detailed micro-modeling techniques are adopted to model hollow concrete block masonry by separately describing the specific equations for material constituents (blocks and mortar) and block-mortar interfaces. A Latin hypercube sampling technique is used to generate random input variables from the empirical distribution functions of the material parameters. A quasi-static nonlinear analysis is then carried out using a Monte Carlo simulation to evaluate the effect of the spatial variability of material parameters on the compressive behavior of masonry wallettes. The results show that ignoring the spatial variability of material properties may cause a model to overestimate the probability of compression failure. Additionally, the independent and cooperative effects of the material parameters on masonry compressive strength are investigated using first order, second order, and total sensitivity indices. The numerical results indicate that block tensile strength influences masonry compressive strength the most. Several parameters for masonry compressive strength are also ranked in order of importance.

Stochastic discrete meso-scale simulations of concrete fracture: Comparison to experimental data

The paper presents a discrete meso-scale model for fracture of concrete taking into account random spatial variability of material parameters. Beams of various sizes, with notches of various depths, are simulated numerically to study the combination of energetic and statistical size effects. A substantial part of material randomness is shown to be caused by random locations of the largest aggregates. Further randomness, due to random fluctuations of material parameters, is considered and an effect of introducing a spatially auto-correlated random field is analyzed. The results of the simulations are compared with recently published experimental data on concrete beams in three-point bending. The differences in the role of randomness in beams of various sizes, with different notch depths, are demonstrated, and differences in energy dissipation are discussed.

Different methods to model the post-cracking behaviour of hooked-end steel fibre reinforced concrete

When designing an element made of steel fibre reinforced concrete (SFRC) subjected to bending, the post-cracking residual stress capacity is taken into consideration. Characterization of this residual flexural capacity is generally performed by means of standardized three-point bending tests on notched specimens (NBN EN 14651) and is further used in the constitutive model for the Mode I crack opening of SFRC, needed for design calculations. Alternative to the constitutive models proposed by Model Code 2010, a new model for the Mode I behaviour of SFRC is proposed, which allows to also consider pseudo-hardening behaviour of SFRC. This model is available in two variants: (1) a tri-linear constitutive model derived by means of inverse analysis and (2) an analytical model based on the fibre pull-out of a single fibre. A thorough discussion on the derivation and the evaluation of the models is presented. Furthermore, this work is extended into a new method to implement the fibre pull-out behaviour into 3D finite element modelling of SFRC prisms subjected to bending, taking into consideration the variability in material parameters, spatial distribution and orientation of fibres.