Modified Pyke's hysteretic model considering damping ratio

The damping ratio is a dynamic soil property that indicates the capacity of energy dissipation under cyclic loadings, and it plays an important role in dynamic response analysis of sites and soil-structure systems. Based on the dynamic shear modulus curves and damping ratio curves in the references, the accuracy of damping ratio predicted by Pyke’s model is studied, and it is found that the predicted damping ratio by Pyke’s model largely exceeds the measured damping ratio in the range of large strain amplitude. A modified Pyke’s model for accurate simulation of damping ratio of soils, named as D-Pyke model, is proposed, which combines the damping ratio-based hysteretic curve equations with the unloading-reloading rules of the original Pyke’s model. The new model assumes that the fullness of the hyperbolic hysteresis curve is determined by the shape-factor that is determined from the experimental damping ratio curves according to the shear-strain amplitude of the current hysteretic loading curve. The shear-strain amplitude of the current hysteretic loading curve is calculated from the shear-stress amplitude based on the skeleton curve of soils, and the shear-stress amplitude is determined according to Pyke’s rules. Based on the results of cyclic simple shear tests on a silty clay, it is verified that the D-Pyke model simulates the nonlinear shear modulus and damping ratio properties more reasonably than the original Pyke’s model. The D-Pyke model inherits the advantages of Pyke’s model, i.e., it simulates well the ratcheting effects of soils under cyclic loadings, and it obeys simple unloading/reloading criteria under irregular loadings. The proposed model can provide a more reasonable constitutive simulation method for the analysis of soil response under stochastic loading.