Unified Formula for Critical Shear Stress for Erosion of Sand, Mud, and Sand–Mud Mixtures

Abstract

Research on erosion behavior of sediments usually treats sand and mud separately. However, natural soil often occurs as a sand–mud mixture. An expression for cohesive forces in sand–mud mixtures, which considers the effect of the sand component on the mud component, is first proposed. Then the balance of forces under the initial motion condition is analyzed, and a unified formula for the critical shear stresses of sand, mud, and sand–mud mixtures is derived. The formula reproduces well the way critical shear stress varies with mud content and is more accurate than other formulas that are widely used for sand–mud mixtures and pure cohesive sediments. The proposed formula also promises to be more convenient, being based on the dry bulk density of the mixture and the stable dry bulk density of the mud component. The effect of consolidation on the erosion thresholds of both sand–mud mixtures and pure muds is considered in the formula, which makes the formula capable of predicting the erosion thresholds of sediments in the process of consolidation.