Three-dimensional multivariable non-Gaussian random field modeling and simulation of concrete constitutive law
Über dieses Buch
The constitutive behavior of concrete exhibits significant randomness and spatial variability, which necessitates a probabilistic description for accurate mechanical analysis. In this study, a comprehensive framework is developed for the unified representation and simulation of four key constitutive parameters (including elastic modulus, compressive strengths, peak compressive strains, and compressive shape parameters) using three-dimensional multivariate non-Gaussian random fields. The uncertainties are represented at three hierarchical levels: variable randomness (modeled via marginal distributions), inter-variable dependence (modeled via copulas), and spatial variability (captured by correlation functions). To achieve this, two novel concepts, i.e., the bridge function and the transformed correlation function, are introduced, enabling the generation of random fields that rigorously satisfy prescribed marginal distributions, cross-dependencies, and spatial correlations. For efficient simulation, the parsimonious stochastic harmonic function (SHF) is employed. Within this framework, the three-dimensional wavenumber domain is partitioned using a Voronoi tessellation scheme, enabling the spectrum-dependent random wavenumbers to be represented with a significantly reduced number of basic random variables. In addition, a starting-time phase evolution strategy is introduced to further minimize the number of random variables required for characterizing the random phases. As a result, only 28 basic random variables are sufficient to generate high-fidelity realizations of the four-variable dependent fields. The proposed approach provides a practical and computationally efficient tool for stochastic finite element analysis of concrete structures, enabling rigorous assessment of structural performance under material uncertainties.
