Spatiotemporally evolving particle impact rates in sediment-generated acoustic signals

High-frequency acoustic and seismic signals generated by granular flows, such as bedload transport and debris flows, provide valuable information on sediment dynamics, yet the physical interpretation remains challenging. In dense or partially dense solid-fluid granular flows, signal generation is controlled not only by particle-bed impacts but also by frequent inter-particle collisions within the actively shearing layer. These collisions are shear-driven and evolve rapidly in time and space, with impact rates being highly sensitive to shear strain rate, time, and granular layer thickness. However, most existing particle impact rate models assume stationary conditions and neglect the spatiotemporal variability inherent in natural geophysical flows, limiting the ability to explain observed non-stationary spectral signatures. Here, we develop a new analytical framework for particle impact rate in solid-fluid two-phase granular flows based on non-equilibrium thermodynamics. The model explicitly links collision rate to shear strain rate, granular state variables, and the thickness of the basal shearing layer, allowing impact rates to evolve dynamically in time and space. Reformulating the model in the frequency domain provides a direct theoretical connection between evolving collision rates and the spectral properties of the generated acoustic and seismic signals. For saturated channel beds, we further investigate the two-way coupling between pore water pressure and particle impacts in signal generation. Particle impacts are conceptualized as transient mechanical sources that locally compact the granular skeleton, reduce pore volume, and generate excess pore pressure, which in turn feeds back on particle impacts. Analytical solutions demonstrate that the amplitude and persistence of impact-induced pore pressure perturbations are controlled by bed permeability, shear strain rate, and the thickness of the basal shear layer. An increase in pore pressure reduces effective stress and feeds back on collision dynamics, introducing an additional control on signal generation. Building on these results, we extend existing power spectral density formulations to show that temporally evolving particle impact rates modulate frequency spectra by redistributing spectral power across frequences, resulting in departures from classical spectral scaling. Pore pressure effects further modify spectral amplitudes and attenuation. The proposed framework offers new physical insights into sediment-generated signals, enabling improved interpretation of evolving particle impact rates and pore pressure related effects in bedload transport and debris flows.