Plasticity modeling of liquefaction effects under sloping ground and irregular cyclic loading conditions

• Formulation of PM4Sand model updated.
• Improved simulation of liquefaction-induced deformation of sloping ground.
• Undrained direct simple shear data for irregular cyclic loading.
• Revised dependency of dilation and plastic modulus on fabric tensor and its history.
• Calibration to lab test results or empirical correlations common in practice.

The formulation of the constitutive model PM4Sand [7] is modified to improve simulations of liquefaction-induced deformations of sloping ground subjected to uniform and irregular cyclic loading. Existing laboratory test data on the response of liquefiable sand under sloping ground conditions subjected to uniform cyclic loading are reviewed and additional experimental data from undrained cyclic direct simple shear (DSS) tests of liquefiable sand under sloping ground conditions subjected to irregular cyclic loading are presented. The previous version of the PM4Sand model (Version 2) and its limitations in modeling liquefaction effects in sloping ground with uniform and irregular cyclic loading are described. Evidence from the laboratory tests show that it is the effect of loading history on the dilation and stiffness characteristics of the response that is not properly captured by Version 2 of the model. The modifications made in Version 3 include a revised dependency of dilation and plastic modulus on the fabric tensor and its history. These modifications are introduced using irregular cyclic DSS test results to illustrate the motivations for the changes in the constitutive equations. Finally, two examples of calibration are presented: one against a specific laboratory test result for a single sand and one against an engineering correlation describing trends observed for many sands across a broader range of relative densities, confining stresses, and loading conditions. The updated formulation in Version 3 of the model is shown to better approximate liquefaction behaviors for sloping ground and irregular cyclic loading conditions.