Phase-lag effect on the instantaneously-liquefied seabed depth under progressive waves: Explicit approximations.

• Instantaneous liquefaction within a non-cohesive seabed under progressive waves is analytically investigated. • Explicit solutions for the liquefied soil depth are derived to reflect the phase-lag effect. • Due to the phase-lag effect, the maximum liquefied soil depth would no longer appear exactly under the wave trough. • Instantaneous liquefaction potential is predominantly related to a combined parameter for waves and soils. Instantaneous liquefaction can be induced by the upward seepage force while waves propagating over a porous seabed. In this study, the instantaneous liquefaction within a non-cohesive seabed under progressive waves is analytically investigated and verified with the existing offshore observations. To characterize the instantaneous liquefaction potential, the vertical gradient of excess pore-pressure is employed, and the explicit solutions for the liquefied soil depth are then derived to reflect the phase-lag effect. Wave scale effect is further examined by comparative analysis of the liquefaction potential between laboratory and field conditions. It is indicated that, due to the phase-lag effect, the maximum liquefaction potential and the maximum liquefied soil depth no longer appear exactly under the wave trough; nevertheless, such phase difference relative to the wave trough wouldn't exceed π /4. Neglecting the phase-lag effects would considerably underestimate the liquefaction potential as well as the liquefaction depth. Moreover, both the liquefaction potential and the corresponding liquefied soil depth are predominantly related to the non-dimensional parameter I c for characterizing the combined influence of wave and seabed properties. [ABSTRACT FROM AUTHOR]