Liquefaction Limit during Earthquakes and Underground Explosions: Implications on Ground-Motion Attenuation

Abstract Liquefaction of saturated soils and sediments documented during earth-quakes shows an empirical relation log Rmax 2.05 (0.10) 0.45 M, where Rmax is the liquefaction limit in meters (i.e., the maximum distance from liquefaction site to the hypocenter) and M is the earthquake magnitude. Combining this with an em-pirical relation between M and the seismic energy of an earthquake, we obtain a relation between the liquefaction limit and the seismic energy: E A Rbmax. The prefactor corresponds to a threshold energy for liquefaction ranging from 0.004 to 0.1 J/m3; the exponent, ranging from 3.2 to 3.3, implies that the energy density of ground motion attenuates with distance according to 1/r3.2–3.3, where r is the distance from the hypocenter. The value of the threshold energy suggests a preliquefaction degradation of the shear modulus of soils by more than 3 orders of magnitude. Liquefaction documented during underground explosions is characterized by a threshold energy several orders of magnitude greater than that for liquefaction during earthquakes but shows a similar functional relation between E and Rmax as that for liquefaction during earthquakes and implies a similar attenuation relation between ground-motion energy density and distance.