Effect of Multiscale Particle Morphology on Small-Strain Shear Modulus of Irregularly Shaped Sand under Isotropic Consolidation: Triaxial Bender Element Tests on 3D-Printed Sand

The morphological origin of sand shear modulus at small strains ($G_{\max }$) remains poorly understood. This paper introduces spherical harmonic analysis to define multiscale particle morphologies of two typical natural sands: calcareous sand (CS) and Fujian sand (FS). Three distinct scale levels were taken into consideration: general form (large), local roundness (medium), and surface roughness (small). The 3D printing technique was employed to produce uniformly graded sand analogs with independent control of grain shape. Bender element tests were subsequently conducted on these analogs after isotropic consolidation in triaxial apparatus to obtain their shear wave velocities and small-strain shear moduli. The results highlight the substantial enhancement of $G_{\max }$ through irregular particle morphologies within uniformly graded sand. Notably, the general form (large scale) emerges as the primary morphological determinant of the enhanced $G_{\max }$. Parameters of Hardin’s equation—material coefficient $A$ and stress exponent $N$—are demonstrated to reflect the comprehensive $G_{\max }$ pattern and its sensitivity to confining stress, respectively. The reduction of $N$ with diminishing overall regularity indicates the weakening effect of morphological irregularity on $G_{\max }$’s sensitivity to confining stress. Remarkably, the medium-scale level yields the lowest $N$ value, emphasizing the pivotal role of local roundness as the predominant morphological factor in this effect.