SIMULATION OF CONCRETE DIFFUSION-BASED DETERIORATIONS BY STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS (SPDES)

摘要

Development of modeling and simulation methods for different types of concrete deteriorations is a crucial need for concrete durability evaluation. In the case of the existing concrete structures concrete durability extension and service life prediction are quantitatively necessary from maintenance and repair management points of view. Modeling and simulation of chloride ion ingress and carbon dioxide gas diffusion in porous media of concrete are studied by many researchers. Both types of deterministic and stochastic models are introduced. In real world uncertainty is the main attribute of almost all measurements and parameters. Thus new models should be able to represent at least some of the uncertainties in the predictions. In this paper stochastic partial differential equation (SPDE) of diffusion is introduced to show a more realistic modeling scheme for concrete diffusion-based deteriorations. Diffusion SPDE provides a consistent quantitative way of relating uncertainty in input to uncertainty in output. Although it is possible to run sensitivity analysis to get some statistical results from deterministic models but the nature of diffusion is inherently stochastic. Brownian motion process (Wiener process) is used in SPDE to simulate the random nature of the diffusion in heterogeneous media or random fields like concrete. By adding a noise term to the diffusion equation stochastic model is introduced with more capabilities to describe for instance the outcome of repeated experiments which we encounter in real world conditions. It is found that the proposed model can be a good alternative method comparing to the others.