Application of Stochastic Geometry for Evaluating Damage Level due to Cracking in Concrete Structures

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While geometrical randomness of cracks in concrete structures on micro, meso and macro levels were taken into consideration, methodologies for evaluating the damage level developed and fundamental studies to apply these methodologies for existing damaged concrete structures were carried out. Obtained results are summarized as follows:1) As a fundamental study to link crack information and damage level of concrete structures, microcracks on the surface of concrete cylinders were observed by means of microscope. Then relationships between the crack information and the stiffness reduction, and/or the velocity of ultrasonic wave were studied experimentally.2) Microcracks in concrete specimens damaged by freezing and thawing action or cyclic loading were statistically analyzed. Since the microcracks due to freeze and thawing action were so thin and densely distributed that ordinary counting methods don't work sufficiently, a new method was developed on the basis of a stochastic geometry concept. These microcracks due to freezing and thawing actions were remarkably accumulated in an early stage of the cycles and then gradually increased.3) Strain-rate calculated by the differential of the stress-strain curve showed a possibility to be treated as an index to quantify the damage level.4) Fractal analyses were carried out to analyze crack patterns observed in existing structures so as the fractal dimension to be a meso level parameter. Damage levels of existing concrete structures were qualitatively evaluated from the typical crack patterns.5) Multifractarity was examined in cracks on concrete walls. Macroscopic changing patterns of the fractality in each sub-area were also investigated by analyzing the subdivided concrete walls.