Abstract Undrained cyclic loading tests were performed under torsional shear in a hollow cylindrical apparatus on four sands of various densities, initial stress levels, gradings and origins to establish the pattern of excess pore water pressure generation with cycles leading to initial liquefaction. Two equations were derived to predict this pattern. The first is based on the method introduced by Ishibashi et al. (1977) and incorporates density and the effective stress level into the original equation. The second involves a unique relationship between the excess pore water pressure and the shear work imparted to the sand; it was also obtained independent of the shear stress amplitude when the dissipated shear work was normalized with respect to density and the effective stress level. The excess pore water pressure required to induce liquefaction was found to necessitate lower normalized shear work from finer sands. These equations can be used to assess the liquefaction potential and/or can be directly related to the amount of seismic energy dissipated in the field.