The particle shape of coral sand is a crucial factor that affects its accumulation characteristics. Two-dimensional particle images of coral sand with different particle sizes were obtained through optical imaging, and the basic size parameters of particles were measured by digital image processing. The particle shape parameters were created, and on this basis, the variation of shape parameters with size, the distribution characteristics, and the sensitivity of shape parameters were analyzed by mathematical statistics and the fractal theory. In addition, a comparative analysis was conducted for the particle shape and bulk density of coral sand and quartz sand with the same particle size. The results show that (1) for coral sand with particle size ranging from 0.5 to 5.0 mm, as the particle size augments, its overall profile coefficient grows, while the flatness, angularity, and roughness diminish and the particle shape deviates more from the regular circle. (2) The shape of coral sand particles exhibits good fractal characteristics, and the particle shape gets more complex as the particle size grows as evidenced by the fact that the fractal dimension enlarges. (3) All the shape parameters obey a skewed distribution. Concerning the sensitivity to the change in particle shape, the flatness occupies the first place, the overall profile coefficient and angularity come second, and the roughness ranks third, accordingly. It is suggested that flatness should be preferred as the evaluation parameter of the particle shape. (4) Compared with that of quartz sand, the particle shape of coral sand is more irregular, and the intergranular pores are larger under the same accumulation conditions, which is the primary reason why the specific gravity of coral sand is greater than that of quartz sand while the bulk density is smaller than that of quartz sand.

In this article, the dilatancy of calcareous soil is studied systematically based on triaxial consolidation drainage shear tests, and the difference in dilatancy between calcareous soil and siliceous soil is also investigated. It was found that: ① Calcareous soil experience obvious dilated deformation. Dilatancy tendency increases with increasing related density and decreases with increasing confining pressure. ② The volumetric strain rate initially increases from negative to positive. After it reaches a maximum, there is a small decrease in the volumetric strain rate, but it is still greater than zero, and the stress-strain curves are of softening type. ③ For the same condition, the dilatancy deformation of calcareous sand begins later than that of siliceous sand, and the volume compression before dilatancy is also larger for calcareous sand. ④ The critical state alone cannot accurately describe the entire deformation process of soil, and it is proposed that the phase transformation state be added to the standard method used to assess soil dilatation and contraction. ⑤ Based on the statistical analysis of experimental data, mathematical relationships were established between void ratio, relative density, and effective confining pressure of phase transformation state and critical state, respectively.