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

在考虑混凝土结构在微观、细观和宏观层面上裂缝的几何随机性的同时，开发了评估损伤水平的方法，并开展了将这些方法应用于现有损伤混凝土结构的基础研究。所得结果总结如下：1)利用显微镜对混凝土圆柱体表面微裂缝进行观察，作为连接裂缝信息与混凝土结构损伤程度的基础性研究。然后，实验研究了裂纹信息与刚度折减和/或超声波速度的关系。2)对冻融作用和循环加载损伤的混凝土试件的微裂缝进行了统计分析。由于冻融作用引起的微裂缝薄且分布密集，普通的计数方法无法充分发挥作用，提出了一种基于随机几何概念的新方法。冻融作用引起的微裂缝在循环初期显著积累，然后逐渐增加。3)由应力-应变曲线的差值计算的应变率有可能作为量化损伤程度的指标。4)采用分形分析方法对现有结构中观察到的裂纹形态进行分析，将分形维数作为细观水平参数。从典型裂缝模式定性评价既有混凝土结构的损伤程度。5)对混凝土墙体裂缝进行多重分形分析。通过对混凝土墙体的细分分析，探讨了各分区分形的宏观变化规律。

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.