Influence of the Fractal Distribution of Particle Size on the Critical State Characteristics of Calcareous Sand

Abstract

To study the influence of the fractal distribution of particle size on the critical state characteristics of calcareous sand, a type of calcareous sand from a certain reef of the South China Sea was used in this study. For comparison, standard quartz sand was also used. A series of drained shear tests on the two sands were then conducted to investigate their critical state characteristics. It was demonstrated that the fractal dimension is suitable for characterizing the particle size distribution (PSD) of calcareous sand with different fine sand content. The critical state equation of sand proposed by Li and Wang (1998) is suitable for fitting the critical state line of calcareous sand. In the plane of deviatoric stress versus the effective confining pressure (q–p′ plane) and the plane of void ratio versus (p′/pa)α, the critical state lines of calcareous sand are always above those of quartz sand. The critical state lines of calcareous sand with different fractal dimensions in the q–p′ plane are unique. However, in the e–(p′/pa)α plane, the critical state lines appear to rotate anticlockwise as the fractal dimension increases. In addition, there is an “intersection” in the e–(p′/pa)α plane. Considering the influence of the fractal distribution of particle size, an expression for the critical state line of calcareous sand in the e–(p′/pa)α plane was proposed. The related constitutive model was also revised, where a complete set of model parameters suitable for modeling calcareous sand was provided.