Low-Frequency Nonlinear Elasticity: a New Tool for Probing Damage in Rocks

Abstract:

Wave propagation in rocks is typically treated as a linear elastic phenomenon; however, as strain increases, nonlinear stress-strain behavior can result. Experimental evidence for nonlinear elastic behavior in geomaterials has existed for years, but the ability to use this property as a diagnostic tool has only begun development in the last several decades. The basis of this tool is that the degree of nonlinearity in damaged material is much greater than that in intact material, resulting in signals that are highly sensitive to the presence and progression of material damage. Elastic nonlinearity can cause a propagating wave to distort, resulting in generation of harmonics, multiplication of waves of different frequencies and, under resonant conditions, shifts in resonance frequency peaks. One way to exploit these behaviors is to propagate waves of differing frequencies through a material and observe nonlinear wave mixing phenomena, a technique referred to in the literature are nonlinear wave modulation spectroscopy (NWMS). When two waves propagate colinearly through a nonlinear material, nonlinear wave mixing manifests as wave distortion, harmonic generation and the creation of sum and difference frequencies (sidebands). We present the results of a NWMS study of intact and damaged rocks at a range of conditions to highlight the strain (10^6 – 10^-5), frequency (0.001 – 10 Hz) and normal stress (0.1 – 10 MPa) dependence of nonlinear parameters in rocks. Nonlinearity increases with the presence of damage and the amplitude of strain and decreases with the application of normal stress. Analysis of various dependencies can provide insight into the mechanisms of nonlinearity and has the potential to provide methods of monitoring damage processes in the subsurface.