Uncertainty propagation and parameter sensitivity analyses of relative permittivity models for use in soils

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Nondestructive subsurface investigations are becoming more popular in geotechnical engineering ranging from agricultural applications to environmental remediation projects to archaeological investigations. Using electromagnetic (EM) wave transmission through soil is one such nondestructive technique. The characteristics of electromagnetic wave propagation, attenuation and reflection through a soil are governed by the soil's relative permittivity. Relative permittivity is a complex value comprised of a real component (referred to herein as dielectric constant) and an imaginary component: however, the focus of the research is concentrated on the soil's dielectric constant. Soil parameters that govern the dielectric constant are: volumetric water content, bulk density, soil texture, soil structure, soluble ions, temperature, and measurement frequency. Numerous empirical and semi-empirical relative permittivity models exist to predict a soil's dielectric constant. Three relative permittivity models for soils were selected for analysis herein; the Topp et al. (1980) model, Hendrickx et al. (2003) model and Wagner & Scheuermann (2009)/Hilhorst (1998) model (WSH model). The Topp et al. model is strictly empirical and the simplest of the three models correlating only volumetric water content to a soil's dielectric constant. The Hendrickx et al. and WSH models are theoretically derived with some empirical calibration and are inherently more complex, requiring more soil parameter inputs. Monte Carlo (MC) simulations were used to evaluate the effects of input variability propagation on the uncertainty of the predicted dielectric constant for each model. Additionally, model sensitivity to individual input parameters was analyzed for the two multivariable models (Hendrickx et al. and WSH models). The MC simulation provides a means of conducting a stochastic analysis on deterministic models. The simulation process generates random input variables for calculation in a deterministic algorithm as a function of probability densit