Dynamics of pothole growth as defined by field data and geometrical description

Abstract

This paper examines cylindrical pothole growth on streambeds using empirical analyses of field data and geometric constraints. Pothole depths (d) and average radii () at three localities have the relationship = kd, where k and ɛ are regression coefficients (R2 ≥ 0.72). Observed ɛ (0.57, 0.67, 0.85) translate to d increasing faster than r at all localities. The strong correlations and absence of potholes with very low or high ratios of depth/diameter suggest that small concavities act as pothole seeds and enlargement is quasi‐systematic. Exploiting the power relationship, growing potholes can be represented as deepening and radially expanding cylinders. Absolute and relative distributions of erosion can be calculated for floors and walls using this geometrical approach. Volumetrically, more substrate is eroded from pothole walls than floors during growth for ɛ > 0.5. Among sample populations, as much as 70% more material is eroded from walls than floors (ɛ = 0.85). Wall and floor surface areas differ by 1 or more orders of magnitude for observed ɛ, and as a result, erosion rates are fastest atop floors. Differences in erosion rates may reflect the efficacy of erosion phenomena. Low‐angle impacts of tools on walls presumably have low erosion efficiencies. Efficacies are presumably influenced by substrate properties, and floor and wall erosion rates are most comparable in the weakest observed strata, although substantially more material is removed from walls at this locality (ɛ = 0.85). Additional data is needed, but quantifiable relationships may exist between geometries, substrates, and erosion phenomena.