Jan Sýkora

Computational homogenization of non-stationary transport processes in masonry structures

A fully coupled transient heat and moisture transport in a masonry structure is examined in this paper. Supported by several successful applications in civil engineering the nonlinear diffusion model proposed by Kunzel (1997) [16] is adopted in the present study. A strong material heterogeneity together with a significant dependence of the model parameters on initial conditions as well as the gradients of heat and moisture fields vindicates the use of a hierarchical modeling strategy to solve the problem of this kind. Attention is limited to the classical first order homogenization in a spatial domain developed here in the framework of a two step (meso-macro) multi-scale computational scheme (FE^2 problem). Several illustrative examples are presented to investigate the influence of transient flow at the level of constituents (meso-scale) on the macroscopic response including the effect of macro-scale boundary conditions. A two-dimensional section of Charles Bridge subjected to actual climatic conditions is analyzed next to confirm the suitability of algorithmic format of FE^2 scheme for the parallel computing.

Parameter identification in a probabilistic setting

Abstract The parameters to be identified are described as random variables, the randomness reflecting the uncertainty about the true values, allowing the incorporation of new information through Bayes’s theorem. Such a description has two constituents, the measurable function or random variable, and the probability measure. One group of methods updates the measure, the other group changes the function. We connect both with methods of spectral representation of stochastic problems, and introduce a computational procedure without any sampling which works completely deterministically, and is fast and reliable. Some examples we show have highly nonlinear and non-smooth behaviour and use non-Gaussian measures.

Homogenization of coupled heat and moisture transport in masonry structures including interfaces

Homogenization of a simultaneous heat and moisture flow in a masonry wall is presented in this paper. The principle objective is to examine an impact of the assumed imperfect hydraulic contact on the resulting homogenized properties. Such a contact is characterized by a certain mismatching resistance allowing us to represent a discontinuous evolution of temperature and moisture fields across the interface, which is in general attributed to discontinuous capillary pressures caused by different pore size distributions of the adjacent porous materials. In achieving this, two particular laboratory experiments were performed to provide distributions of temperature and relative humidity in a sample of the masonry wall, which in turn served to extract the corresponding jumps and subsequently to obtain the required interface transition parameters by matching numerical predictions and experimental results. The results suggest a low importance of accounting for imperfect hydraulic contact for the derivation of macroscopic homogenized properties. On the other hand, they strongly support the need for a fully coupled multi-scale analysis due to significant dependence of the homogenized properties on actual moisture gradients and corresponding values of both macroscopic temperature and relative humidity.

Analysis of coupled heat and moisture transfer in masonry structures

Evaluation of effective or macroscopic coefficients of thermal conductivity under coupled heat and moisture transfer is presented. The paper first gives a detailed summary on the solution of a simple steady state heat conduction problem with an emphasis on various types of boundary conditions applied to the representative volume element—a periodic unit cell. Since the results essentially suggest no superiority of any type of boundary conditions, the paper proceeds with the coupled nonlinear heat and moisture problem subjecting the selected representative volume element to the prescribed macroscopically uniform heat flux. This allows for a direct use of the academic or commercially available codes. Here, the presented results are derived with the help of the SIFEL (More information available at http://mech.fsv.cvut.cz/web/?page=software) (SImple Finite Elements) system.

Uncertainty updating in the description of coupled heat and moisture transport in heterogeneous materials

To assess the durability of structures, heat and moisture transport need to be analyzed. To provide a reliable estimation of heat and moisture distribution in a certain structure, one needs to include all available information about the loading conditions and material parameters. Moreover, the information should be accompanied by a corresponding evaluation of its credibility. Here, the Bayesian inference is applied to combine different sources of information, so as to provide a more accurate estimation of heat and moisture fields [1]. The procedure is demonstrated on the probabilistic description of heterogeneous material where the uncertainties consist of a particular value of individual material characteristic and spatial fluctuations. As for the heat and moisture transfer, it is modelled in coupled setting [2].

Probabilistic approach to damage of tunnel lining due to fire

In this paper, risk is perceived as the probable damage caused by a fire in the tunnel lining. In its first part the traffic flow is described as a Markov chain of joint states consisting of a combination of trucks/buses (TB) and personal cars (PC) from adjoining lanes. The heat release rate is then taken for a measure of the fire power. The intensity λf reflecting the frequency of fires was assessed based on extensive studies carried out in Austria [1] and Italy [2, 3]. The traffic density AADT, the length of the tunnel L, the percentage of TBs, and the number of lanes are the remaining parameters characterizing the traffic flow. In the second part, a special combination of models originally proposed by Bažant and Thonguthai [4], and Kunzel & Kiessl [5] for the description of transport processes in concrete at very high temperatures creates a basis for the prediction of the thickness of the spalling zone and the volume of concrete degraded by temperatures that exceed a certain temperature level. The model was validated against a macroscopic test on concrete samples placed into the furnace.

NON-INVASIVE INVERSE PROBLEM IN CIVIL ENGINEERING

In this contribution we focus on recovery of spatial distribution of material parameters utilizing only non-invasive boundary measurements. Such methods has gained its importance as imaging techniques in medicine, geophysics or archaeology. We apply similar principles for non-stationary heat transfer in civil engineering. In oppose to standard technique which rely on external loading devices, we assume the natural fluctuation of temperature throughout day and night can provide sufficient information to recover the underlying material parameters. The inverse problem was solved by a modified regularised Gauss-Newton iterative scheme and the underlying forward problem is solved with a finite element space-time discretisation. We show a successful reconstruction of material parameters on a synthetic example with real measurements. The virtual experiment also reveals the insensitivity to practical precision of sensor measurements.

Comparison of Numerical Approaches to Bayesian Updating

This paper investigates the Bayesian process of identifying unknown model parameters given prior information and a set of noisy measurement data. There are two approaches being adopted in this research: one that uses the classical formula for measures and probability densities and one that leaves the underlying measure unchanged and updates the relevant random variable. The former is numerically tackled by a Markov chain Monte Carlo procedure based on the Metropolis-Hastings algorithm, whereas the latter is implemented via the ensemble/square root ensemble Kalman filters, as well as the functional approximation approaches in the form of the polynomial chaos based linear Bayesian filter and its corresponding square root algorithm. The study attempts to show the principal differences between full and linear Bayesian updates when a direct or a transformed version of measurements are taken into consideration. In this regard the comparison of both strategies is provided on the example of a steady state diffusion equation with nonlinear and transformed linear measurement operators.

Stochastic Model Calibration Based on Measurements from Different Experiments

The calibration of a heterogeneous material model can be formulated as a search for probabilistic description of its parameters providing the distribution of the model response corresponding to the distribution of the observed data. This contribution is focused on developing a method for identification of parameters along with their variations based on combining measurements from different types of destructive experiments.

Algorithmic Framework for Stochastic Galerkin Method

In this contribution we focus on the computational aspects for practical use of the uncertainty propagation in groundwater flow environment using stochastic finite element method based on generalized polynomial chaos (gPC), where the uncertain part is taking place only in the spatial distribution of the transport properties. In recent years, there has been a growing trend towards real world applications in computational mechanics, thus the reduction techniques have become very desirable. Our focus is on efficient Matlab implementation in terms of computational time and memory consumption without modifying the mathematical background.