Energy evaluation for liquefaction-induced strain of loose sands by harmonic and irregular loading tests

A series of stress-controlled undrained cyclic loading tests using a torsional simple shear apparatus are carried out on reconstituted loose sand specimens by applying harmonic and irregular shear stresses to evaluate cumulative dissipated and strain energies, ∑ΔW and ∑W, for liquefaction-induced strain before and after 100% pore-pressure buildup. The tests with harmonic stresses show that the energy ∑ΔW, which is roughly proportional to effective confining stress, is uniquely correlated with induced strains irrespective of cyclic stress amplitudes and number of cycles for liquefaction. Also found is that an almost unique correlation holds between ∑ΔW and ∑W for all the harmonic loading tests. The tests with irregular stresses also indicate an almost unique correlation of energy with induced strains up to initial liquefaction, however the wave irregularity makes the correlation more dispersive and wave-dependent for larger strains, though the induced strain may still be evaluated using the energy-dependent correlation within some uncertainty allowable for engineering purposes.