Liquefaction of Sensitive Soils during Earthquakes

The occurrence of liquefaction during earthquakes of a given magnitude (M) is confined within a particular distance from the earthquake source, i.e., the liquefaction limit (Rmax). We interpreted Rmax as the distance at which the energy of the seismic waves has decayed to a threshold energy required for saturated soils to liquefy, beyond which the seismic energy is too weak to cause further liquefaction. Combining an empirical relation between M and Rmax with Bath's relation between M and earthquake energy (Es) we obtain an empirical relation between Es and Rmax. The relation implies a threshold energy of 0.032 J/m3 for liquefaction and a very small effective quality factor Q. The threshold energy, when interpreted in the light of a threshold shear amplitude for liquefaction, implies an effective shear modulus ~ 0.1 - 10 MPa, which is two orders of magnitude or more smaller than the elastic shear moduli for alluvial sands estimated from shear wave velocity. The atypical shear modulus and Q show that liquefaction of sensitive soils during earthquakes may be preceded by nonlinear behaviors, with drastic degradation of shear rigidity and severe dissipation of seismic energy.