Effects of porosity on seismic velocities, elastic moduli and Poisson's ratios of solid materials and rocks

The generalized mixture rule (GMR) is used to provide a unified framework for describing Young's ( E ), shear ( G ) and bulk ( K ) moduli, Lame parameter ( λ ), and P- and S-wave velocities ( V p and V s ) as a function of porosity in various isotropic materials such as metals, ceramics and rocks. The characteristic J values of the GMR for E , G , K and λ of each material are systematically different and display consistent correlations with the Poisson's ratio of the nonporous material ( ν 0 ). For the materials dominated by corner-shaped pores, the fixed point at which the effective Poisson's ratio ( ν ) remains constant is at ν 0 = 0.2, and J ( G ) > J ( E ) > J ( K ) > J ( λ ) and J ( G ) < J ( E ) < J ( K ) < J ( λ ) for materials with ν 0 > 0.2 and ν 0 < 0.2, respectively. J ( V s ) > J ( V p ) and J ( V s ) < J ( V p ) for the materials with ν 0 > 0.2 and ν 0 < 0.2, respectively. The effective ν increases, decreases and remains unchanged with increasing porosity for the materials with ν 0 < 0.2, ν 0 > 0.2 and ν 0 = 0.2, respectively. For natural rocks containing thin-disk-shaped pores parallel to mineral cleavages, grain boundaries and foliation, however, the ν fixed point decreases nonlinearly with decreasing pore aspect ratio ( α : width/length). With increasing depth or pressure, cracks with smaller α values are progressively closed, making the ν fixed point rise and finally reach to the point at ν 0 = 0.2.