# A probabilistic model of soil detachment by shallow turbulent flow

##### Nearing, M.A.

#### Transactions of the ASAE 34(1): 81-85

#### 1991

**ISSN/ISBN: 0001-2351**

DOI: 10.13031/2013.31627

Accession: 002013532

This study presents a simple probabilistically based mathematical model for the detachment of cohesive soil particles by shallow turbulent flows. The model is based on the concept that bursting events in turbulent flows cause the detachment of soil particles when the localized shear stress associated with the bursting event exceeds the local tensile strength on the soil surface. Both the shear stresses of the turbulent bursts and the local soil resistance were described in terms of probability density functions, and the overlap of the two probability functions represents the probability that a given bursting event causes detachment of particles. The model was applied with favorable results to detachment data from the controlled laboratory experiment of Nearing et al. (1991) for two soils, each with three aggregate size distributions. The model helps to explain why neither shear stress nor streampower adequately define detachment rates by flow, and it shows mathematically that 'critical hydraulic shear stress' is a stochastic, rather than deterministic variable. The model also explains that detachment occurs when average flow stresses are orders of magnitude less than soil strengths because burst events in the turbulent flow create much greater local shear levels than the averages, and detachment occurs only for those burst events where stress exceeds the local tensile strength of the soil.