Determination of Frequency-Dependent Dynamic Properties of Rocks Using the Nonresonance Method

Abstract

Assessing the dynamic properties of rocks remains a foundational pursuit in the field of rock engineering, providing crucial insights into their mechanical behaviors across a spectrum of loading conditions, including static, cyclic, and dynamic scenarios. This paper expounds upon the utilization of the nonresonance (NR) torsional shear test and its implications for understanding rock responses, particularly in the context of low and medium loading rates. The NR method serves as a pivotal tool for investigating model rock materials subjected to loading conditions characterized by low frequencies and amplitudes. Renowned for its efficacy, this method allows the simultaneous determination of two critical dynamic parameters: shear modulus (G) and damping ratio (D), all at a specific loading frequency. It has been ascertained that the loading rate increased as the loading frequency and applied amplitude of loading increased. With increasing loading rate, the shear modulus consequently increased while the damping ratio decreased. It is observed that the dynamic responses of both ramp and sinusoidal loading waveforms increase concurrently with the amplitudes of the applied torque and loading frequencies. The sinusoidal waveform exhibits greater dynamicity than the ramp waveform at a certain loading rate. Furthermore, this study delves into the intricate analysis of the nonlinear viscoelastic dynamic response exhibited by rocks, utilizing the modified hyperbolic (MH) model and the Ramberg–Osgood (RO) model as analytical tools. The findings derived from curve fitting exercises unequivocally underscore the superior applicability of the Ramberg–Osgood model, particularly in characterizing modulus reduction behavior. Conversely, the modified hyperbolic model emerges as the preferred choice for comprehensive damping ratio analyses. This study enhances the comprehension of rock dynamics and responses under diverse loading conditions, contributing valuable understanding to rock engineering. Insights into loading and strain rate effects aid informed decisions and preventive measures for rock deformation and collapse risks. This research suggests vital findings regarding the response of intact model materials to various dynamic loading conditions, providing significant insights for comprehending the mechanical response of rock structures exposed to cyclic loading conditions, which have the potential to create weaknesses in rocks resulting in untimely failures. The research can be utilized to assess the response of rocks in the context of seismic incidents, specifically those characterized by shear waves at particular frequencies. This study evaluates the response of rocks during earthquakes by establishing a correlation between the amplitude of torsional shear loading and the peak ground displacement linked to seismic events. In addition to its seismic implications, this research aids in advancing accurate predictive models and instruments that assess the stability and integrity of rock formations under different loading rates—a consequence of the symbiosis between frequency and amplitude. Professionals may ensure efficient risk mitigation, make well-informed decisions, and execute preventative measures concerning rock collapse and deformation by virtue of their comprehensive awareness of the delicate relationship between loading rate and dynamic rock properties. Incorporating the findings into engineering design standards and codes can bring about substantial improvements, augmenting the overall reliability and protection of rock structures.