Study on the Hyperbolic Constitutive Model of Sandy Clay Purple Soil with Missing Grain Group

The sandy clayey purple soil is susceptible to alterations in particle size distribution due to hydraulic erosion, such as rainfall and fluctuations in reservoir water levels. These changes can affect the soil’s strength. To elucidate the strength characteristics of sandy clayey purple soil in the influence of the absence of different particle groups, consolidated drained triaxial shear tests of saturated sandy clayey purple soil with five distinct particle groups were conducted. The fractal dimension was employed to quantify the physical properties of varying particle sizes. The relationship between the strength characteristics of purple soil with different particle groups and the fractal dimension was obtained. The results show that: (1) There is no significant change in the internal friction angle of the soil shear strength index under the missing effect of different grain groups, but the cohesion and fractal dimension show a hyperbolic relationship; the initial tangent modulus of different grain groups is affected by confining pressure and fractal dimension, and there is a quadratic function relationship between parameter n and fractal dimension. Under low confining pressure, the stress-strain relationship of different grain groups is obviously different. With the increase of confining pressure, the stress-strain characteristics tend to be consistent. (2) Based on the Duncan-Chang E-ν model, the nonlinear elastic hyperbolic constitutive model of saturated sandy clayey purple soil under the effect of different particle groups is established by fitting the cohesion-fractal dimension hyperbolic equation, and the validity of the model is verified.