Monotonic triaxial testing and simple modeling of calcareous sand considering the effects of fractal dimension and relative density

Calcareous sand from the Nansha Islands, South China Sea, is mainly composed of coral and shell debris, and features irregular particle morphology, abundant intragranular pores, and high particle crushability, which brings considerable geotechnical challenges to marine infrastructure construction. In this study, fractal dimension (D) was employed to quantify the inherent characteristics of saturated calcareous sand (SC sand). A series of consolidated-undrained triaxial compression tests were conducted on SC sand and standard ISO sand under various relative density (Dr), confining pressure (σ3), and fractal dimension. The shear strength, stress–strain response, pore water pressure evolution, and initial tangent modulus were systematically analyzed and compared. Within the tested ranges, the peak effective principal stress difference (σ1−σ3)f of SC sand increased with increasing D, Dr, and σ3. The corresponding increases were 129.38%, 34.25%, and 14%, respectively, indicating that the variation in D produced the largest change in peak strength among the three investigated factors. The peak pore water pressure Δuf rises with increasing Dr and σ3 but declines with increasing D. Strain-softening behavior of SC sand is intensified by higher Dr and mitigated by higher D, whereas σ3 shows no obvious effect. The initial tangent modulus Ei of SC sand increases significantly with D, while that of ISO sand is nearly insensitive to D. The growth rate of (σ1-σ3)f with D for ISO sand is only 19.67%, much lower than that for SC sand. A modified Duncan-Chang model considering the coupled effects of D and Dr is established, which can well predict the pre-failure stress–strain behavior of SC sand. The outcomes provide important experimental and theoretical supports for foundation design and stability evaluation of island-reef projects, coastal structures, and offshore wind farms in the South China Sea.