Cyclic Response of Sand under Parabolic- or Butterfly-Shaped In Situ Stress Paths

Abstract Cyclic tests are presented to investigate the behavior of sands under complex in situ loading paths. The parabolic- and butterfly-shaped stress path trajectories considered may result from simultaneous compression and shear wave loading during earthquakes. The tests were conducted on Fraser River sand using the Carleton University hollow cylinder torsional shear apparatus. The generalized loading was simulated by applying cyclic normal stresses and cyclic shear stresses to represent seismic loading in situ. In order to capture various field loading conditions realistically, the cyclic normal stress increments considered both nonreversal and reversal scenarios, while the cyclic shear stress increment followed a reversal loading pattern. The results demonstrate that the generation of excess pore water pressure and the mechanism of liquefaction triggering are significantly influenced by the imposed stress path. Sand specimens subjected to simultaneous loading with no cyclic normal stress reversal exhibited higher cyclic resistance than those subjected to stress reversal. Under coupled loading with no normal stress reversals, liquefaction manifests due to cyclic mobility regardless of the magnitude of cyclic shear stress increments and the relative magnitude between the normal and shear stress components. Tests with phase shift between applied shear stress and normal stresses produced nonsymmetric variations in the case of normal stress increments with reversal. The cyclic resistance of sand decreases with the increase in phase shift due to the greater magnitude of stress reversal. These findings indicate that liquefaction resistance is strongly influenced by the loading path shape, suggesting that typical assessments that rely solely on the cyclic stress ratio may not fully capture soil behavior under realistic, multidirectional seismic loading conditions.