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A series of undrained cyclic axial-torsional shear tests on saturated coral sand and quartz sand under linear, circular, and heart stress paths are performed. The test results show significant differences in liquefaction characteristics for coral sand and quartz sand. A unique relationship between deviatoric strain amplitude and excess pore water pressure ratio (Ru) can be established regardless of cyclic stress paths. The termed cyclic strain path is introduced to describe the generation features of strains, and different failure patterns for various cyclic stress paths can be easily identified. Moreover, the dissipative energy required to liquefaction triggering (Ea1) of coral sand is much larger than that of quartz sand. The generation patterns of dissipative energy with Ru for both sands are almost independent of cyclic stress paths, but the correlation between the cyclic stress ratio (CSR) and the number of cycles required to liquefaction triggering (Nf) is dependent on cyclic stress paths. Using the proxy of the unit cyclic stress ratio (USR) proposed by Chen et al. (2020) instead of the CSR, the correlation between USR and Nf is independent on cyclic stress paths. A remarkable finding is that, a unique correlation between USR15 and Ea1 exists for all sands considered. [ABSTRACT FROM AUTHOR]