Evaluation of undrained shear strains in multi-directional horizontal shaking

The evaluation of shear strains under multi-directional shaking is an important issue in interpreting dynamic soil behavior for both laboratory physical modeling and in situ monitoring. Shear strain components evaluated from Cartesian coordinates in undrained conditions have limitations to fully capture the coupled shear strain-pore pressure responses with an individual expression. In the present study, radial and rotational shear strain components derived from particle motions described with cylindrical polar coordinates are proposed. The proposed radial and rotational shear strains are verified with data from a bi-directional laminar shear box and a free field downhole array. Comparison results show that the proposed expressions of shear strain effectively capture the coupled strain-pore pressure responses in terms of the frequency content, amplitude variation, phase difference, and oscillation behavior. Comparison results reveal that the radial shear strain is the dominant shearing mode and the amplitude of the rotational shear strain is only 6.5-14.5% of the radial component. This provides quantitative data for the correction factor for multi-directional shaking and suggests that a simple shear system capable of inducing the radial shear strain on the vertical plane is a better approach than other shearing modes for physically modeling the behavior of soil subjected to undrained seismic loadings.