Pore pressure evolution in bed sediment overridden by debris flow: A general formulation

Debris flows can grow dramatically in volume and mobility as they override bed sediment due to the reduction in bed friction resistance caused by high pore fluid pressure (PP). However, the mechanisms that control PP evolution in overridden bed sediment are still unclear. Here, a new mathematical model clarifies how diverse styles and magnitudes of PP evolution can result from regulation of the flow diffusion and shear contraction of bed sediment. Normalization of the model equations shows that the propensity for PP generation depends on timescales of PP diffusion and deformation of the bed grains. The PP of saturated bed sediment under immobile conditions is equal to the fluid pressure at the bottom of the flow due to a non-flux basal boundary. However, the PP of unsaturated bed sediment is lower than that of the overlying flow. PP diffusion from a debris flow into an unsaturated bed increases with the bed's permeability and water content. The shear deformation behavior changes from undrained to drained with increasing permeability or decreasing shear velocity of the saturated bed sediment, leading to a reduced magnitude of pore pressure. By contrast, the shear deformation transitions from drained to undrained behavior with increasing permeability and water content of unsaturated bed sediment. The entrainment rate and erosion pattern of bed sediment are closely related to the PP evolution and liquefaction ratio of the bed sediment due to Coulomb-friction shear tractions. Our models can be used to interpret the feedback of PP on the flow momentum during debris flow entrainment.