Mikrostruktur-basierte Simulation des Feuchtetransports in Zement- und Sandstein

The moisture transport in capillary-porous building materials is governed by their microstructure. This thesis describes the calculation of hygric material properties from three-dimensional representations of the building materials' microstructures using finite element methods. The moisture transport processes considered comprise the water permeation, the water diffusion and the capillary absorption. Three hardened cement pastes with two different water to cement ratios, and two sandstones, a Fontainebleau and a Bentheimer sandstone serve as examples of capillary-porous materials. The basis of the calculations are microtomographic images (µCT) of the hardened cement pastes and the sandstones, as well as microstructures of the hardened cement pastes generated with the simulation software CEMHYD3D. To what extend the latter are realistic is investigated by comparing the fractal dimension and the autocorrelation function of the pore spaces of the simulated microstructures as well as their pore space distribution with the corresponding values of the µCT images. In order to simulate the different moisture transport processes the medial axis of the pore spaces of the microstructures is first extracted. Afterwards the medial axis is converted into a transportation network, consisting of cylindrical tubes, which possesses the same moisture transport properties as the original pore space. In case of permeability Bernoulli's law is applied to every tube in the transportation network. An arbitrary pressure difference of 1 bar is imposed between the inlet and the outlet surface of the network and the resulting mass flow is calculated by finite element methods. The overall mass flow results from the sum of the mass flows of the tubes traversing the outlet surface. Using Darcy's law the permeability coefficient of the porous medium is derived. The water vapor diffusion is simulated using Fick's first law for every tube as well as for the mass current density within the porous medium. Between inlet and outlet surface a water vapor concentration difference of 10% is applied and the water vapor diffusion coefficient of the hardened cement pastes and the sandstones is deduced from the resulting mass flow. Finally the capillary water absorption of the porous media is simulated analogously to the heat conduction. The individual tubes of the network are replaced by one-dimensional heat conducting elements. The temperature conduction coefficients of the elements and the boundary conditions are adjusted so that the time needed for the heat flow to traverse an element is equivalent to the time required by the water front during the capillary water uptake. The water absorption coefficients of the materials contemplated are then obtained from the amount of absorpted water at each time step of the finite element calculation. The validation of the presented model is accomplished by comparing the simulated moisture transportation coefficients with experimental values