Relationship between fractal feature and compressive strength of concrete based on MIP

Concrete is a heterogeneous, multiphase, and multilayer composite system with extremely intricate microscopic pore structure. The structural characteristics of microscopic pore of concrete are closely related to its mechanical properties and durability. The pore structure of concrete with various strength grades (C10-C150) was analyzed by Mercury intrusion porosimetry (MIP) from the aspects of pore diameter distribution, pore volume, pore specific surface area and fractal feature. The Menger sponge model was used to calculate the fractal dimension of different pore regions in each test group, and the most suitable pore fractal region was selected to establish the mathematical model between fractal dimension and compressive strength. The results showed that all fractal curves are divided into four segments according multi-fractal characteristic of concrete, namely Region I, Region II, Region III and Region IV. Region I is macropores fractal region (d = 10 μm ∼ 950 μm), representing the packing patterns of hydrated cement grains, while Region II - Region Ⅳ is micropores fractal region (d = 0.0064 μm ∼ 10 μm), reflecting mainly the microstructure of C-S-H hydrates. Region I and Region Ⅳ exhibit obvious fractal features and the fractal dimension D is between 2 and 3. However, the fractal dimension D > 3 in Region II and Region III, which are nonphysical from the point of view of surface geometry. The fractal dimension can clearly describe the internal pore characteristic, and it is a real good correlation with the most probable pore diameter and the pore specific surface area. Moreover, the mathematical model between the fractal dimension and the compressive strength both accords with the positive power exponential function in Region I and Region IV. The fractal dimension can be viewed as a comprehensive parameter of pore shape and spatial distribution of pore structure, which can more accurately represent the relationship between the microscopic pore structure features and compressive strength of concrete. In practical engineering, it serves to realize the damage detection of concrete on site.