Theory of similarity and ultrasonic testing

Application of similarity theory (dimensional analysis) to ultrasonic (UT) testing is discussed using as an illustration the example of concrete blocks. The concept of dimensional analysis makes it possible to represent a physical system via a minimal set of variables, the so-called π groups, which are the dimensionless quantities. These dimensionless parameters, characterizing the respective phenomenon, should have approximately equal values for the real object and for the model. Small concrete samples have been tested in the lab conditions using various UT probes and techniques. Two dimensionless criteria, valid and similar for the real field case and for the laboratory samples, have been introduced: total attenuations of UT waves and ratios of void size to the UT wavelength. To get total attenuations in the field conditions for thick concrete block, similar to the total attenuations measured in lab experiments on small samples, one should apply the low-frequency UT waves 60-100kHz. However, these UT waves will be able to reliably detect only the large inhomogeneities (e.g. voids), whose size is about half of the used UT wave, i.e. inhomogeneities with dimensions larger than 20-40mm.