Abstract:
Liquefaction of saturated soils and sediments documented during earthquakes 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 empirical relation between M and the seismic energy of an earthquake, we obtain a relation between the liquefaction limit and the seismic energy: E = A Rmaxβ. 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.
