Keywords: chaos theory, rock analysis, hammer test, sound wave, strange attractor, fractal dimension, Lyapunov exponent.

The hammer test is used to judge the current condition of the tested objects by listening to the sound generated upon the impact of a testing hammer. In other words, the method examines the object by analyzing the reaction to the energy inputted by hammering. In recent years, attempts have been made to examine disordered structures by analyzing the recorded data in addition to analysis by an expert. The sound produced on hammering is generally a mixture of sounds originating from a variety of sources: (1) the sound generated and emitted directly to the surroundings from the point of impact, (2) the sound generated from the arbitrarily oscillating planes including the surfaces of inner fine flaws and grain boundaries that is induced by the propagated elastic waves and (3) the sound generated by the overall vibration of the rock. Therefore, it is difficult to detect the flaw structures or disorders by analyzing the collected sound data. In this study, chaos theory was applied to the classification of various tested rocks; in other words, attractor patterns and Lyapunov exponents calculated from the collected sound data were compared among rocks that had been examined by some tests.

Four rock samples, two granites and two sandstones, were prepared in order to examine different inner structures of rocks. Two granites, Westerly granite from U.S.A. and Mannami granite from Japan, exhibit different grain sizes. Two sandstones, Izumi sandstone and Kimachi sandstone both from Japan, had different porosities and grain sizes. These materials were cut into 50 mm cubic specimens for testing. Additionally, we prepared cylindrical specimens of Westerly granite having a diameter of 20 mm and length of 40 mm. Two typical experiments - a drying and wetting test and thermal test - were conducted for the rock conditions that are expected to be classified by the chaos analysis.

In each hammer test, discrete time-series sound data converted to the voltage level was measured in order to plot the attractor patterns and calculate the Lyapunov exponents. The sound produced by hammering the rocks was captured using a high resolution noise meter NL-32 manufactured by Daiichi Kagaku Co. and the captured sound data was simultaneously stored in a PC using an A/D converter NR-2000 manufactured by Keyence Corporation. In the hammer test, cubic specimens were placed on a rubber surface that was hanging in the air to enable free vibrations and cylindrical specimens were directly hanged with two threads. The impact strength was kept the same by swinging the hammer from the same height each time. The hammer used in the hammer test has an iron head and a wooden haft and weighs 187 g with a length of 384 mm, and it is a usual type of hammer for the test. All tests were conducted in a silent room where both the temperature and humidity were constantly controlled. The sound produced by hammering the rocks was recorded for approximately 37.5 ms at 12.5 &mu#mu;s intervals. During the recording, the sound was sufficiently damped and the original silent atmosphere was restored.

As a result, it is clearly revealed that under different conditions, different attractors were reconstructed and the Lyapunov exponents were also relatively different in many cases. In fact, the training data were insufficient to exactly distinguish each rock condition. However, it was verified that it should be possible to apply chaos theory to classify rock conditions.

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