Statistical distributions of wave velocities and elastic moduli in near-surface unsaturated soils

Abstract

The shear wave velocity (vs) and the compressional wave velocity (vp) are extensively used to understand the near-surface geologic structure, derive small-strain elastic moduli of soils, and perform a wide range of geophysical, geotechnical, and geo-environmental analyses. While the dependency of vs and vp on water content or degree of saturation is well recognized, the variability of wave velocity measurements and derived elastic moduli within different saturation levels remains yet to be understood. The main objective of this study is to examine the effect of degree of saturation on the statistical distribution of measured wave velocities and the derived small-strain elastic moduli in unsaturated soils. For this purpose, 360 ultrasonic laboratory tests, an extensive array, were performed on a poorly graded fine-to-medium sand over seven full wetting-drying cycles. The laboratory-measured data were used, along with a suite of statistical tests, to evaluate the statistical distribution and variability of the vp and vs measurements and the derived elastic variables--including vp/vs ratio, shear modulus (G), Young's modulus (E), Poisson’s ratio (μ), and bulk modulus (K). The results show that many of the assumptions regarding the quantification of vp and vs measurements and elastic moduli used in geophysical, geotechnical, and geo-environmental analyses may not be valid. The vp and vs data are best represented by lognormal and Weibull distributions, respectively, yet the subsequently derived elastic properties may require more than one distribution type to adequately represent the statistical behavior for different saturation regimes and relationships.