Hyperbolic Hydro-mechanical Model for Seismic Compression Prediction of Unsaturated Soils in the Funicular Regime

A semi-empirical elasto-plastic constitutive model with a hyperbolic stress-strain curve was developed with the goal of predicting the seismic compression of unsaturated sands in the funicular regime of the soil-water retention curve (SWRC) during undrained cyclic shearing. Using a flow rule derived from energy considerations, the evolution in plastic volumetric strain (seismic compression) was predicted from the plastic shear strains of the hysteretic hyperbolic stress-strain curve. The plastic volumetric strains are used to predict the changes in degree of saturation from phase relationships and changes in pore air pressure from Boyle’s and Henry’s laws. The degree of saturation was used to estimate changes in matric suction from the transient scanning paths of the SWRC. Changes in small-strain shear modulus estimated from changes in mean effective stress computed from the constant total stress and changes in pore air pressure, degree of saturation and matric suction, in turn affect the hyperbolic stress-strain curve’s shape and the evolution in plastic volumetric strain. The model was calibrated using experimental shear stress-strain backbone curves from drained cyclic simple shear tests and transient SWRC scanning path measurements from undrained cyclic simple shear tests. Then the model predictions were validated using experimental data from undrained cyclic simple shear tests on unsaturated sand specimens with different initial degrees of saturation in the funicular regime. While the model captured the coupled evolution in hydro-mechanical variables (pore air pressure, pore water pressure, matric suction, degree of saturation, volumetric strain, effective stress, shear modulus) well over the first 15 cycles of shearing, the predictions were less accurate after continued cyclic shearing up to 200 cycles. After large numbers of cycles of undrained shearing, a linear decreasing trend between seismic compression and initial degree of saturation was predicted from the model while a nonlinear increasing-decreasing trend was observed in the cyclic simple shear experiments. This discrepancy may be due to not considering post shearing reconsolidation in the model, calibration of model parameters, or experimental issues including a drift in the position of the hysteretic shear-stress strain curve. Nonetheless, the trend from the model is consistent with predictions from previously- developed empirical models in the funicular regime of the SWRC. The developments of the new mechanistic model developed in this study will play a key role in the future development of a holistic model for predicting the seismic compression across all regimes of the SWRC.