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

在考虑混凝土结构裂缝在微观、细观和宏观层面上的几何随机性的同时，发展了评估损伤程度的方法，并进行了将这些方法应用于既有损伤混凝土结构的基础研究。1)利用显微镜观察混凝土圆柱体表面的微裂缝，作为联系裂缝信息与混凝土结构损伤程度的基础性研究。2)对冻融作用或循环荷载作用下混凝土试件的微裂纹进行了统计分析。由于冻融作用产生的微裂纹细小且分布密集，常规的计算方法不能很好地解决这一问题，基于随机几何概念，提出了一种新的计算方法。这些冻融作用引起的微裂纹在循环的早期明显积累，然后逐渐增加。3)通过应力-应变曲线的微分计算的应变率显示了将其作为量化损伤程度的指标的可能性。4)对现有结构中观察到的裂纹形态进行了分维分析，将分维作为细观层次的参数。根据典型的裂缝形态，定性地评价了在役混凝土结构的损伤程度。通过对细分后的混凝土墙体的分析，研究了各个分区的分维宏观变化规律。

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.