Prediction models and associated uncertainty for dynamic shear modulus and damping ratio of Beijing silty clay

Based on experimental data of normalized shear modulus and damping ratio from undisturbed silty clay within 120 m depth in the Beijing area, the Davidenkov backbone curve is used to characterize the normalized shear modulus curve, and the damping ratio is formulated as a composite function of the small-strain damping ratio and the normalized shear modulus. It is found that the key parameters A, B, γ_r describing the Davidenkov model, as well as the small-strain damping ratio, all exhibit significant depth dependence. Accordingly, depth-dependent prediction models for the normalized shear modulus and damping ratio are established. Furthermore, the first-order second-moment method is employed to systematically analyze the uncertainty in the predicted values of the normalized shear modulus resulting from the combined effects of parameters A, B, and γ_r, as well as the evolution characteristics of the uncertainty in the predicted values of the normalized shear modulus caused solely by the individual uncertainties of parameter A, B, or γ_r with depth and shear strain. Simultaneously, the uncertainty in the predicted values of the damping ratio arising from the combined uncertainties of the normalized shear modulus and the small-strain damping ratio is quantified, along with the variation patterns of the uncertainty in the predicted values of the damping ratio caused solely by the uncertainties of either the normalized shear modulus or the small-strain damping ratio with depth and shear strain. The related research can provide guidance for determining regional soil dynamic parameters and precisely quantifying their uncertainties.