Abstract
In this work, the longitudinal wave propagation in stressed rock with variable cross-section is investigated analytically. Considered the stress-sensibility of dynamic elastic modulus and the viscosity of rock, a modified viscoelastic stress-strain relationship is established. Based on the continuity equation, motion equation and stress-strain relation equations, the wave propagation equation for a stressed rock with variable cross-section is obtained. The harmonic wave propagation is discussed in detail by calculating the attenuation coefficient in amplitude. The combined effects of static stress and geometry on the wave attenuation are analyzed. The results show that due to the variable static stress along the propagation path, the wave attenuation is space-dependent, and the distribution of attenuation coefficients may be remarkably different under different levels of static stress. The wave attenuation in a stressed rock with variable cross-section is also frequency-dependent, and the influence of static stress on the lower-frequency wave components is more obvious compared with that on the higher-frequency wave components. Comparing the wave attenuation among rocks with three different geometries, we conclude that the wave attenuation depends on actual normal static stress, the cross-sectional areas and the changing rates of cross-sectional area.
Highlights
Natural rock mass consists of rock blocks and discontinuous interfaces
The results show that due to the variable static stress along the propagation path, the wave attenuation is space-dependent, and the distribution of attenuation coefficients may be remarkably different under different levels of static stress
Li and Tao (2015) investigated the effects of the initial stress and initial stress gradient on the wave propagation, and the results showed that homogenous stress affects the elastic coefficients of medium while the 1D P-wave equation is unchanged in form
Summary
Natural rock mass consists of rock blocks and discontinuous interfaces (e.g., joints and fractures). The combined effects of the static stress and variable cross-section on wave propagation have been rarely reported yet. The 1-D longitudinal wave propagation equation considering the combined effects of the static stress and variable cross-section is established. To reflect the closure and opening of interior micropores and/or microcracks under the effect of static stress, the key point in the establishment of wave propagation equation is summarizing stress-dependent dynamic elastic modulus. For the physical problem shown, the static stress can alter the dynamic elastic coefficients of rock, and the wave propagation in rock is remarkably different compared with that under unstressed condition. We can see that if the dynamic modulus is a stress-independent constant and the viscosity coefficient η = 0, Eq 8 will degrade into the wave equation of an elastic bar with variable cross-section.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
