Frustrated fast path effect in wet granular media

The fast path effect of elastic waves in continuous random media refers to the tendency that waves seek the fastest propagation path according to Fermat's principle of least time. This results in a frequency- and travel-distance-dependent velocity shift previously analyzed in seismology. We examine how the fast path effect can be exploited to describe ultrasonic pulse transmission in pre-stressed, partially saturated granular media. In dry granular media, it is known that optimal stress and hence wave transmission is along force chains. For partially saturated granular media, a series of ultrasonic experimental observations points to the existence of multiple scattered waves propagating along force chains and choosing the fastest path. It turns out that the fastest path is tuned by saturation, and at a critical saturation, the wave velocity undergoes a transition to that of a fully saturated medium. Beyond the critical saturation, no faster path appears possible, and the velocity remains constant. To explain the transition and saturation of the velocity, we develop a model based on a weak-wavefield-fluctuation approximation for the fast path effect in continuous random media. Key to this model is the growth of the correlation length with saturation to emulate the saturation-dependent reinforcement of percolating force chains. This frustrated fast path model is of phenomenological nature only but provides an explanation of observed velocity–saturation relations.