Nonlinear Elastic Waves for Estimation of Rock Properties
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Nonlinear elasticity is a well-known feature that reveals in many phenomena and at different scale, depending on the material. Many independent studies have shown that the nonlinear response of geomaterials differs significantly from the response of other media. Rocks have much higher nonlinearity than most solids (typically a few orders of magnitude higher) and the nonlinear behaviour appears already at very low strain (about 10-9), for which other solids become insensitive. In addition, rocks reveal the unique phenomena such as hysteresis, discrete memory, fast and slow dynamics, and several others, that are barely detectable elsewhere. These peculiar nonlinear features are ascribed to the complex microstructure of rock – the cracks and grain contacts in particular. Similar response has only been seen for damaged solids, which confirms the impact discontinuities have on the nonlinearity. Obviously, structure is an important indicator of the materials' elasticity. However, the current understanding of the relation between reasons (sources and mechanisms) and effects (nonlinear phenomena) is not yet complete. The work presented in this thesis is focused on examining the nonlinear elastic response of rocks via a new testing method - the SURF technique. The technique was originally intended to test biological materials (e.g. tissues), and this study is one of the first approaches towards non-biological applications. The method is a type of dynamic acoustoelastic test that, in this case, uses a dual-frequency ultrasonic pulse complex. Two pulses of different frequencies (with frequency ratio of 1:7) are simultaneously and coaxially transmitted through the medium. A low-frequency (LF) pulse – called the manipulation pulse or a pump pulse – is used to modify the elastic state of the material. A high-frequency (HF) pulse – called the probe pulse – is used to detect induced changes related to wave velocity variation. The method requires a special type of acoustic transducer, which is able to generate a SURF pulse complex. Designing and manufacturing of the prototype transducer appeared to be somewhat more demanding and time-consuming than expected, thus the method in its original form could not be tested initially. Therefore, the major part of this study is based on an approach analogous to the SURF measurements, while the last part deals with the real SURF technique. In the analogous technique, variations in the ultrasonic velocities have been measured as functions of quasi-static oscillations. These oscillations are relatively fast and of small amplitude in order to reproduce, as accurate as possible, the manipulation that a material would experience due to the high amplitude acoustic pump pulse. This method allowed us to investigate the nonlinear elasticity of rocks, but also to distinguish between the nonlinear elastic and non-elastic processes activated in the rock structure under stress. It has been shown that both processes have different impact on the stresssensitivity of the wave velocities, which indicates that the processes ought to be treated separately in the rock physics models. Moreover, the impact of the non-elastic processes on the stress-sensitivity of the wave velocities is strongly dependent on the stress direction. During unloading, the impact can be ascribed to a single process (friction control shear sliding), while during loading additional processes are most likely involved (e.g. crushing at grain contacts and cracks faces). It has been concluded, upon the first experiments, that fluids (under complete saturation) have a minor impact on the nonlinear response, thus the focus of the latter studies was given to examining the effect of the rock's structure only. Tests on dry rocks indicted that the nonlinearity differs markedly between rocks of different type, but also the same rock often reveals a slightly different response depending on the structural dissimilarities and/or stress conditions. Somewhat surprisingly, the nonlinearity appeared to be insensitive to artificial fractures introduced to the core. It has been confirmed that beside structure also the sample length, external stress and manipulation strength determine the nonlinear response of the rock. The same conclusions have been drawn based on the SURF technique and the analogue quasi-static method. Further, the methods are in agreement with respect to the magnitude of the nonlinearity (a nanosecond range), whereas the deviation may be explained by the differences in the rocks' dispersion. The SURF technique seems to have a potential for in-situ characterization of the nonlinear elasticity of the rock formations.