How to Decide Which Cracks Should Be Repaired First: Theoretical Explanation of Empirical Formulas

Due to stress, cracks appear in constructions: cracks appear in buildings, bridges, pavements, among other structures. In the long run, cracks need to be repaired. However, our resources are limited, so we need to decide which cracks are more dangerous. To make this decision, we need to be able to predict how different cracks will grow. There are several empirical formulas describing crack growth. In this paper, we show that by using scale invariance, we can provide a theoretical explanation for these empirical formulas. The existence of such an explanation makes us confident that the existing empirical formulas can (and should) be used in the design of the corresponding automatic decision systems.