Model Uncertainty in Normalized Shear Modulus and Damping Relationships

Model uncertainty associated with normalized shear modulus and material damping ratio relationships developed in a previous study is discussed in terms of standard deviations in this paper. The relationships were originally developed by separating resonant column and torsional shear test results of 122 specimens into three general geologic groups (Quaternary-age soils, Tertiary-age and older soils, and residual/saprolite soils) and determining mean regressional model parameters (i.e., $\alpha$ , $k$ , ${\gamma }_{r1}$ , and $D_{\min 1}$ ) for each group. Statistical variability of the regressional parameters is quantified and expressed by standard errors of prediction. The determined uncertainty of the regressional parameters is then propagated through the recommended relationships using the point-estimate method to estimate the model uncertainty of the relationships. The point-estimate method is a simple and effective method of uncertainty propagation. For uncertainty estimation, the regressional parameters are assumed to be uncorrelated for the sake of simplicity. The influence of this assumption on the model uncertainty of normalized shear modulus and material damping ratio values, as well as the sensitivity of the model uncertainty to the uncertainty of various regressional parameters, are also discussed.