Developed nonlinear dynamic constitutive relations of soils based on Davidenkov skeleton curve

Based on Davidenkov skeleton curve of the one dimensional dynamic stress-strain relation, the dynamic shear stress-strain curves were constituted by using Mashing rules. The Davidenkov skeleton curve was corrected by using sectional functions, and the upper limit of failure shear strain amplitude was used as the sectional point. The modified skeleton curve could approach the upper limit of failure shear stress when shear strain amplitude approached infinite. The equations used to calculate damping ratio were derived. The effects of fitting parameters A, B and γ 0 on the curves of dynamic shear modulus ratio and damping ratio versus shear strain amplitude(G/Gmax–γ and D–γ ) were studied systematically. Based on these studies, a new fitting method was suggested to fit the tested G/Gmax–γ and D–γ curves. It is obvious that the new fitting method is better than the current methods to fit the tested G/Gmax–γ and D–γ curves of soils in Nanjing city. The reference values of fitting parameters A, B and γ 0 are given to fit the G/Gmax–γ and D–γ curves of soils tested by free vibration column apparatus.