Fig. 5: Constitutive relations for Soft Earth suspensions.
From: Origins of complexity in the rheology of Soft Earth suspensions
a Non-dimensionalized flow curves of the form τ⋆ = 1 + αΓn + Γ for all values of ξ. Note changes in the vicinity of yielding (inset), corresponding to the increasing envelope of rate-dependent plasticity with increasing ξ. Colors correspond to sand–clay mixtures as indicated in Fig. 3. b The exponent n in the constitutive equation increases gradually from a minimum n = 0 at ξ = 0.20 associated with brittle failure, to a maximum n = 1/2 at ξ = 1 corresponding to fully ductile failure. Increasing the attraction strength of clay did not change n. Inset: the yielding exponent β = 1/n diverges as ξ → ξc from above, where the critical relative clay fraction ξc = 0.2. This is another way to show the continuous nature of the ductile to brittle transition in Soft Earth suspensions. c The fit parameter α, the coefficient of the rate-dependent plastic term in Eq. (2), plotted against the increasing attractive/cohesive elements (χ = χ(ξ, ζ)). The prefactor α increases with both clay concentration and ionic strength, indicating that it reflects the strength of inter-particle attraction. The ⋆ denotes clay suspension with 10−3 M NaCl (upper triangle; ξ = 1.0) and ⋆⋆ denotes the sample with 10−1 M NaCl (lower triangle; ξ = 1.0). Inset represents the same plot, with the y-axis in logarithmic space. Above the dotted line (α > 1) the plastic term becomes important. Source data are provided as a Source Data file.
