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

Abstract

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.

Modeling seismic compression of unsaturated soils in the funicular regime

“…This may indicate that the model used for the transient SWRC scanning paths may need to be refined, or that the assumption of linking the degree of saturation to the shear-induced pore water pressure generation may not be valid for higher degrees of saturation. Another interesting observation was that the initial degree of saturation had a significant effect on the evolution in the pore air pressure with the number of cycles that matched the measured values well [14]. However, after many cycles the pore air pressures approached an asymptote that was nearly the same for all specimens as shown in Fig.…”

“…An asymptotic trend is noted in all the model predictions but not always in the data. The trends in other hydromechanical variables after 15 and 200 cycles of shearing are reported by Kinikles and McCartney [14]. While the model captured the coupled evolution in hydromechanical variables (pore air pressure, pore water pressure, matric suction, degree of saturation, volumetric strain, effective stress, shear modulus) have a reasonable match after the first 15 cycles of shearing, the predictions do not match the trends in the data after 200 cycles of shearing.…”

“…The backbone curve was calibrated using the data from drained cyclic simple shear tests at different cyclic shear strain amplitudes reported by Rong and McCartney [8], and the predicted hysteresis loops match those from the experiments relatively well. [14] reinterpreted the transient SWRC scanning path data of Rong and McCartney [14], and found that the soils with different initial degrees of saturation had a similar initial value of m = 0.021 at the beginning of cyclic shearing as shown in Fig. 4(a) and Fig.…”

“…12 does not depend on the quantity of material. The derivation of this equation is given in Kinikles and McCartney [14]. As the volume of solids, initial void ratio, and initial degree of saturation are constants, the form of Eq.…”

“…Air is assumed to be an ideal gas and the temperature of the air-water-soil system is at ambient temperature conditions (e.g., T = 294 K) with no fluctuation. Kinikles and McCartney [14] incorporated volumetric definitions of the phase diagram for unsaturated soils into the Ideal Gas Law, Boyle's law and Henry's Law to derive the pore air pressure change corresponding to the accumulation of plastic volumetric strains during undrained cyclic simple shearing. This relationship was found to be a function of the initial degree of saturation and initial void ratio, as follows:…”