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 (lambda), 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 lambda of each material are systematically different and display consistent correlations with the Poisson's ratio of the nonporous material (nu(0)). For the materials dominated by corner-shaped pores, the fixed point at which the effective Poisson's ratio (nu) remains constant is at nu(0) = 0.2, and J(G) > J(E) > J(K) > J(lambda) and J(G) < J(E) < J(K) < J(lambda) for materials with nu(0) > 0.2 and nu(0) < 0.2, respectively. J(V-s) > J(V-p) and J(V-s) < J(V-p) for the materials with nu(0) > 0.2 and nu(0) < 0.2, respectively. The effective nu increases, decreases and remains unchanged with increasing porosity for the materials with nu(0) < 0.2, nu(0) > 0.2 and nu(0) = 0.2, respectively. For natural rocks containing thin-disk-shaped pores parallel to mineral cleavages, grain boundaries and foliation, however, the nu fixed point decreases nonlinearly with decreasing pore aspect ratio (alpha: width/length). With increasing depth or pressure, cracks with smaller alpha values are progressively closed, making the nu fixed point rise and finally reach to the point at nu(0) = 0.2. (C) 2016 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B. V. All rights reserved.