Effect of Porosity on the Prediction of Natural Frequencies of Cylindrical Rock Samples: Analytical Model and Experiments

The prediction of natural frequencies of porous rock samples is essential for investigating their dynamic behaviors. Utilizing a cylinder vibration model governed by the Lame–Navier equation, a novel analytical model was developed to accurately predict the natural frequencies of a porous cylindrical rock sample by incorporating Nur’s (or Krief’s) model. The influence of pore structural differences on natural frequencies was explored via analytical solutions and finite-element (FE) simulations, considering the ideal cylindrical and conical holes. Microcomputed tomography and digital core techniques are subsequently employed to investigate the effect of real pore distribution on natural frequencies, with extracted precise pore geometries being imported into the FE model for simulation purposes. The analytical model can overcome the limitations of conventional spring-dashpot models of rocks, and its effectiveness in determining natural frequencies was validated through resonance experiments and FE simulations. It is found that as porosity increases, there is a consistent decrease in natural frequency; however, the main factors affecting porosity are different and scale-dependent. The present research provides valuable insights into the porosity effect on natural frequencies of rock samples, thereby establishing a theoretical foundation for various engineering applications such as resonance-enhanced drilling.