Deformations of sandy soils around geotechnical structures generally involve strains in the range small (0 . 01%) to medium (0 . 5%). In this strain range the soil exhibits non-linear stress-strain behaviour, which should be incorporated in any deformation analysis. In order to capture the possible variability in the non-linear behaviour of various sands, a database was constructed including the secant shear modulus degradation curves of 454 tests from the literature. By obtaining a unique S-shaped curve of shear modulus degradation, a modified hyperbolic relationship was fitted. The three curve-fitting parameters are: an elastic threshold strain ª e , up to which the elastic shear modulus is effectively constant at G 0 ; a reference strain ª r , defined as the shear strain at which the secant modulus has reduced to 0 . 5G 0 ; and a curvature parameter a, which controls the rate of modulus reduction. The two characteristic strains ª e and ª r were found to vary with sand type (i.e. uniformity coefficient), soil state (i.e. void ratio, relative density) and mean effective stress. The new empirical expression for shear modulus reduction G/G 0 is shown to make predictions that are accurate within a factor of 1 . 13 for one standard deviation of random error, as determined from 3860 data points. The initial elastic shear modulus, G 0 , should always be measured if possible, but a new empirical relation is shown to provide estimates within a factor of 1 . 6 for one standard deviation of random error, as determined from 379 tests. The new expressions for non-linear deformation are easy to apply in practice, and should be useful in the analysis of geotechnical structures under static loading.

Geosynthetic-reinforced column-supported (GRCS) embankments have been increasingly used worldwide in the past few years. Even though a number of research investigations have been completed on this topic, the behavior of GRCS embankments is not well understood. To improve the understanding of this technology, coupled mechanical and hydraulic numerical analyses were conducted in this study under both two-dimensional (2D) and three-dimensional (3D) conditions to investigate influence of various factors on the performance of GRCS embankments.The selected parameters and their ranges in this study were based on deep-mixed (DM) columns; however, a similar study can be conducted for other types of columns.2D and 3D models were developed based on elasto-plastic constitutive relationships with Mohr-Coulomb failure criteria for DM walls or columns, soft soil, firm soil, and embankment fill. Cable and geogrid elements were selected to simulate geosynthetic reinforcement in 2D and 3D models, respectively. Staged construction was modeled by building the embankment in lifts. The ground water table was assumed at the ground surface. The mechanical model was coupled with the hydraulic model to simulate the generation and dissipation of excess pore water pressure during and after the construction.iii The 2D and 3D models were calibrated using a well documented case history with long-term field measurement data and fairly detailed material information to ensure their reasonableness and adequacy. Upon completion of the model calibrations, a 2D baseline case based on a typical configuration of GRCS embankment was analyzed.A 2D parametric study was conducted by changing the parameters individually from the baseline case to investigate the influence of that factor on the performance of the embankment including post-construction settlement, post-construction differential settlement, distortion, tension in geosynthetic, effective stress, stress concentration ratio, excess pore water pressure, and degree of consolidation. The investigated factors include soft soil modulus, soft soil friction angle, soft soil permeability, DM column modulus, DM column spacing, geosynthetic tensile stiffness, and average construction rate.After the 2D study was completed, the 2D baseline case was converted into a 3D baseline case based on an area-weighted average approach assuming a square pattern of DM columns. The 3D parametric study was preformed by changing parameters individually from the 3D baseline case to investigate the influence of that specific factor on the performance of the embankment. The factors investigated are the same as those in the 2D parametric study.iv On the basis of the numerical results from the 2D and 3D studies, the influence of factors on the performance of the embankment system was rated to provide guidance for practical use.v ACKNOWLEDGEMENTS

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