Sinking during earthquakes: Critical acceleration criteria control drained soil liquefaction

This article focuses on liquefaction of saturated granular soils, triggered by earthquakes. Liquefaction is definedhere as the transition from a rigid state, in which the granular soil layer supports structures placed on its surface, toa fluidlike state, in which structures placed initially on the surface sink to their isostatic depth within the granularlayer.We suggest a simple theoretical model for soil liquefaction and show that buoyancy caused by the presence ofwater inside a granular medium has a dramatic influence on the stability of an intruder resting at the surface of themedium.We confirm this hypothesis by comparison with laboratory experiments and discrete-element numericalsimulations. The external excitation representing ground motion during earthquakes is simulated via horizontalsinusoidal oscillations of controlled frequency and amplitude. In the experiments, we use particles only slightlydenser than water, which as predicted theoretically increases the effect of liquefaction and allows clear depth-of-sinkingmeasurements. In the simulations, a micromechanical model simulates grains using molecular dynamicswith friction between neighbors. The effect of the fluid is captured by taking into account buoyancy effects onthe grains when they are immersed. We show that the motion of an intruder inside a granular medium is mainlydependent on the peak acceleration of the ground motion and establish a phase diagram for the conditions underwhich liquefaction happens, depending on the soil bulk density, friction properties, presence of water, and peak acceleration of the imposed large-scale soil vibrations.We establish that in liquefaction conditions, most cases relaxtoward an equilibrium position following an exponential in time.We also show that the equilibrium position itself,for most liquefaction regimes, corresponds to the isostatic equilibrium of the intruder inside a medium of effectivedensity. The characteristic time to relaxation is shown to be essentially a function of the peak ground velocity.