Bulk properties, percolation clusters

The first models, describing elastic behavior of fractal structures, were used, as a rule, for simulation within the fimneworks of percolation theory [1-5], Nonhomogeneous statistical mixture of solid and liquid then only displays solid body properties (e g., not equal to zero shear modulus G), when solid component forms percolation cluster, like at gelation in pol5uner solutions. If liquid component there is replaced by vacuum, then bulk modulus. B will also be equal to zero below percolation threshold [1]. Such model gives the following relationship for elastic constants [1,3] ... 

The first models describing the elastic behaviour of fractal structures used, as a rule, simulation within the frameworks of percolation theory [21-25]. Anon-homogeneous statistical mixture of solid and liquid displays solid properties (for instance, shear modulus G not equal to zero) only, when the solid component forms a percolation cluster at gelation in polymer solutions. If the liquid component is replaced by a vacuum then the bulk modulus K. will also be equal to zero below the percolation threshold [21]. This model gives the following relationship for elastic constants [21] ... 

As a conclusion, we have shown that there is now a number of numerical evidences indicating that the hull and bulk properties for 3D percolation clusters are identical. 

When p is nonzero, there are clusters of liquidlike cells, each one of which has at least z liquidlike neighbors. It is well known that in such situations there is a critical concentration above which there exists an infinite cluster. Thus for p>p, there is an infinite, connected liquidlike cluster, and we can consider the material within it to be liquid. For pliquidlike clusters exist, which might imply a glass phase because the fluidity would be reduced. However, percolation theory tells us that just above p the infinite cluster is very stringy or ramified so that bulk liquid properties are not fully developed. 

Crete surface to the bulk of the concrete. Permeability is high (Figure 1.6) and transport processes like, e. g., capillary suction of (chloride-containing) water can take place rapidly. With decreasing porosity the capillary pore system loses its connectivity, thus transport processes are controlled by the small gel pores. As a result, water and chlorides will penetrate only a short distance into concrete. This influence of structure (geometry) on transport properties can be described with the percolation theory [8] below a critical porosity, p, the percolation threshold, the capillary pore system is not interconnected (only finite clusters are present) above p the capillary pore system is continuous (infinite clusters). The percolation theory has been used to design numerical experiments and apphed to transport processes in cement paste and mortars [9]. 

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