Estimating the critical shear stress for incipient particle motion of a cohesive soil slope

The critical shear stress is a vital reference indicator for soil erosion. Soil erosion will occur when soil slope suffers from a exceed shear stress, and then causing soil loss and destruction of soil structure. In this work, an equation was proposed based on the force equilibrium of a single particle to estimate the critical shear stress for incipient particle motion of a cohesive soil slope. This formula is characterized by its physical significance, and the critical shear stress for incipient slope soil motion can be easily calculated when the soil properties and the slope angle are known. Moreover, the seepage-runoff coupled model and the excess shear stress equation are introduced in this paper. Two parameters, namely the weight of rushed soil particles and the discharge of water, must be measured in the scouring tests. Through linear regression, the tested τ_c-values were obtained to validate the τ_c-values calculated by the formula derived from the critical shear stress. In addition, two other formulas were compared with the derived formulas, which considered more parameters with physical significance. Finally, the influence of all parameters on the critical shear stress was analyzed: the porosity of the soil, the specific gravity of the soil and the slope gradient had less influence on the critical shear stress; the critical shear stress was negatively influenced by the particle diameter and positively influenced by the internal friction angle of the soil.