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NIRE Annual Report
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 1999

Measurement of Crack Tip Position Using Diffracted P-Wave

Geomechanics Division
Geotechnology Department
Objectives
Measurement of engineering properties of cracks, which exist in rocks, is very important to estimate safety of rock structure such as tunnel, underground space and so on. Many methods are used for measurement of cracks and some other materials. However, it is difficult for many conventional methods to measure their properties with a high accuracy. The objective of this study is to develop new measurement methods of their properties. As the first step of this study, new measurement method of crack tip position is suggested.
Results
There are many measurement methods of crack properties, and some of them have received practical application. Many of them are using P-wave velocity to measure the crack properties. The measurements of P-wave velocity are influenced by the frequency of P-wave. In order to measure P-wave velocity with a high accuracy, high frequency P-wave is needed. However, the higher P-wave velocity is, the larger the damping of transmitted wave is. In many cases of in-situ measurement by using high frequency P-wave, the accuracy of measurements become low, for the reason that the effective transmitted distance is short and S/N ratio is low.
The measurement methods of crack tip position, which are free from frequency of P-wave, are suggested. This method uses the diffracted P-wave by the tip of a crack. (Fig. 1) The polarity of first motion of diffracted P-wave by the tip of a crack is decided by the angle of incidence, the angle of diffraction and Poisson ratio of media. (Fig. 2) The measurement of the angle of incidence and the angle of diffraction where the polarity is changed are free from the frequency of P-wave. Therefore this method is not influenced from the frequency of P-wave, and the suitable frequency for the condition of in-situ measurement can be selected.
The applicability of this theory on the change of the polarity of first motion of diffracted P-wave by the tip of a crack to in-situ measurement is studied. As the result of theoretical study and experimental study using Inada granite, it become clear that the measurement using this theory is effective to the measurement of crack tip position.
Fig.1. Two-dimensional geometry of a crack, a receiver a transmitter
Fig.1. Two-dimensional geometry of a crack, a receiver a transmitter

Fig.2. Relation ship between angle of incidence and angle of diffraction
Fig.2. Relation ship between angle of incidence and angle of diffraction
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