Multi-scale Modeling Of Microstructures And Transport Properties Of Non-spherical Particulate Cementitious Materials Via Continuum Percolation Theory

The random packing of particles is one of the most common structural modes of composite materials.Taking the cementitious composites as an example,all of them such as cement paste,mortar and concrete can be regarded as the granular composites composed of soft/hard particles with different sizes.Both the geometrical characteristic and the random packing of these particulate components have an influence on the evolution of the microstructures,which in turn may lead to the degradation of macroscopic properties of materials.The reliability and durability of concrete structures are the hot research subjects in the field of civil engineering nowadays.From the perspective of the degradation mechanism of structural performance,the erosion of water and harmful ions is one of the essential causes that triggers the deterioration of materials.The transport behaviors of various harmful agents in cementitious composites are,to some extent,dependent on the microstructures and percolation of the internal components(e.g.,pores,microcracks,ITZ,aggregates,etc.)in materials.The majority of structural models applied in the field of cementitious composites are generated by the packing of circles,spheres and ellipsoids,which may lead to the inaccuracy of the research results on the macroscopic properties due to the limitation of particle morphologies.Therefore,it is very crucial and meaningful to explore the effect of the geometrical characterization of particulate components with non-spherical shapes on the microstructures and macroscopic transport performance of concrete materials based on the random packing models of particles with more complex and diverse geometries,and then establish the quantitative relationship among the characterization of particulate components,the microstructure parameters and the macroscopic transport properties of harmful agent in cementitious composites.In this thesis,two categories of non-spherical particles with diverse morphologies(i.e.,superellipses and superellipsoids)are applied in 2D and 3D spaces,respectively.Firstly,by combining with the means of linear coordinate transformation,these 2D and 3D non-spherical particles with the random position,size,orientation and shape are generated successfully.Based on the geometrical features of superelllipses and superellipsoids,respectively,the corresponding contact detection algorithms for them are proposed by combining the concept of the geometrical potential of particles and the strategy of linear coordinate transformation then.On this basis,both 2D and 3D packing models of these soft/hard particles with different shapes,particle size distribution and volume fraction are constructed by the random packing algorithm of particles at last.Taking the hardened cement paste as the research object firstly,the structures of cement paste here are simplified to be the 2D/3D biphasic porous systems composed of homogeneous solid matrix and the randomly distributed overlapping pores with superelliptical/superellipsoidal shapes in 2D and 3D spaces,respectively.Based on these porous models and the continuum percolation theory,the effect of both the geometrical features and equivalent sizes of these granular pores on the percolation properties of porous media is investigated in detail and the relationship among the geometries of pores,the size distribution of pores,the specific number of pores and the critical percolation thresholds of these porous systems is quantified by the numerical approximation.The studies reveal that for the porous structures in this paper,the maximum percolation thresholds will be obtained when the geometrical shapes of non-spherical particles are circular and spherical in 2D and 3D spaces,respectively.With the features of these pores be sharper,the values of percolation thresholds will decrease rapidly,which means that the corresponding porous systems are more probable and easier to form a connected porous path that spans the whole structures.For the complex porous media comprising mono-sized overlapping pores of double shapes,the critical percolation thresholds are heavily dependent on the geometrical shapes of granular pores and the relative number of these pores.For the porous media comprising mono-shaped overlapping pores of double sizes,the percolation thresholds present a monotonically increasing trend with the decrease of the equivalent radii ratio of smaller pores to larger pores and the increase of the number fraction of smaller pores.And the above-mentioned rule is not sensitive to both the geometrical shapes of pores and the space dimensions of these porous systems.Afterward,by incorporating the obtained quantitative formulas of percolation thresholds into the general effective-medium approximation,the relative diffusivity of ions in 2D/3D saturated porous systems is studied theoretically by us and the effect of both the characteristics and percolation properties of the pores with various shapes and sizes on the effective diffusion is discussed and clarified.The interfacial transition zone(ITZ)can be viewed as a primary transport path of harmful agent in the concrete materials,and its features and percolation may also have an effect on the macroscopic properties.By using the method of Minkowski sum,the topological geometry of the ITZ with a constant thickness around the regular polygons,superellipses and Platonic particles are perfectly constructed in this paper.By adopting the percolation models of hard core/soft shell,the continuum percolation of ITZ around 2D and 3D multi-sized non-spherical aggregates with different shapes are studied here and the effect of all of the factors such as the aggregate types,the geometrical shapes of aggregates,the thickness of ITZ,the size distribution of aggregates and the graduation of aggregates on the critical percolation thresholds of ITZ in the models of three-phase concretes is obtained.Based on the simulated results,the corresponding quantitative formulas for the percolation thresholds of ITZ around both 2D and 3D aggregates are further derived.The research shows that the critical percolation thresholds of ITZ in the models of three-phase concrete present an increasing trend with the decrease of the thickness of ITZ,a decreasing trend with the decrease of the circularity of 2D aggregates(and the sphericitry of 3D aggregates)and an increasing trend with the increase of the equivalent diameters of aggregates(including the maximum equivalent diameters,minimum equivalent diameter and mean equivalent diameter).Essentially,the impact of the aggregate sizes on the percolation of ITZ can be attributed to one factor,i.e.,the fineness of aggregates.In short,the larger the specific surface area of aggregates in concrete is,the smaller the critical percolation threshold of ITZ will be.On the basis of a series of the results about the percolation of ITZ,a theoretically quantitative formula of the effective diffusivity that involves the percolation behavior of ITZ around non-spherical aggregates is presented by combining the generalized self-consistent model with a multi-phase percolation-based effective media model.With the help of these models,the effect of various factors such as the geometrical shapes of non-spherical aggregates,the thickness and diffusivity of ITZ,the maximum equivalent diameter,minimum equivalent diameter and graduation of aggregate on the relative diffusivity of ions in 2D and 3D three-phase concrete is explored.From the research,it can be found that for the 3D models of three-phase concrete,the extent of the impact of all these factors on the diffusivity is more significant than that in 2D case.Finally,to have a deeper insight into the relationship between the geometrical features of particles and the diffusivity of the packing systems of non-spherical particles,the transport behaviors of ionic species in both two-phase porous systems and three-phase composite systems are numerically simulated by adopting D2Q5 and D3Q7 models in the lattice Boltzmann method,respectively.The variation rules of the relative diffusivity of ions in these models on the different scales are briefly discussed and compared with the predicted curves obtained by the analytical formulas.All of these studies here expound the essence and significance of the geometrical features of the granular components in these predigested models on the different scales once again.In this study,the transport properties of fluid in the cementitious composites on different scales are theoretically explored by the subject of mathematics,physics,stereology and so on.The outcomes of this thesis can not only provide some theoretical references for the design and durability assessment of cementitious composites,but also promote the development of the theory and knowledge in other related fields.