Particle shape beats gradation in setting sand shear strength, AI model shows

What makes one sand stronger than another? A new study argues that the shape of the particles themselves matters more, and it backs that claim with laboratory triaxial tests and machine-learning models trained to predict the peak internal friction angle of granular mixtures.

The research, published in AI in Civil Engineering, was carried out by Zhaoyang Xu, Zhongqi Tian, Junyuan Wang, Guangyu Li and Lijun Ke. The team conducted triaxial tests on four binary mixed granular materials with contrasting morphologies: Nanhai calcareous sand, Fujian standard sand, glass beads and glass sand. Binary mixing allowed the researchers to vary the fines content, the proportion of fine particles in each mixture, while keeping the constituent materials distinct in shape and angularity.

The central result is unambiguous in the authors’ account: particle shape dominates the peak internal friction angle, while gradation plays a secondary role. Irregular particles yield systematically higher friction angles than more regular, rounded ones. In the study’s conclusions, the authors state that for binary mixed particles, peak strength and internal friction angle increase as shape parameters decrease, meaning that more irregular particles produce higher shear strength.

Perhaps the most striking finding concerns how fines content affects strength, which turns out to depend on particle shape. For angular particles such as calcareous sand and glass sand, the friction angle follows an inverted V-shaped trend, peaking at a threshold fines content. For subrounded particles such as standard sand and glass beads, the trend is V-shaped, with the friction angle reaching a minimum at the threshold. In other words, adding fines to a mixture can either strengthen or weaken it depending on how angular the grains are, and the direction of the effect reverses between the two morphological families.

Gradation also leaves its mark, but in shape-dependent ways. For subrounded particles, both the threshold strength and the corresponding fines content decrease as the size ratio increases, which the authors attribute to an intensified ball-bearing effect of fine particles. For angular particles, the opposite occurs: the threshold strength increases with size ratio, because a larger size ratio reduces porosity and enhances interparticle interlocking at the threshold state. These contrasting mechanisms underline how strongly gradation effects are conditioned by particle morphology.

To identify which shape parameters matter most, the researchers performed heatmap correlation analysis between shape descriptors and the measured friction angle. Among all shape parameters examined, the aspect ratio showed the strongest correlation with strength. The authors also report that the correlation between shape parameters and sand strength was significantly stronger than the correlation between gradation and strength, confirming shape as the dominant factor.

The second half of the study turns to prediction. The team developed XGBoost and multilayer perceptron models to estimate the peak internal friction angle from shape and particle size inputs. Both models achieved good fit with no evidence of overfitting or underfitting, which the authors say verifies the effectiveness of the selected input parameters. XGBoost, however, significantly outperformed the multilayer perceptron in both accuracy and stability, an advantage the researchers attribute to its superior handling of small-sample data and multi-feature interactions.

The authors describe XGBoost as a robust tool for predicting shear strength in granular materials.

The study is a review-type open access paper, and the authors are candid about its limits. The experimental dataset is small, and certain features were omitted, most notably particle surface roughness, which the authors plan to incorporate in future work alongside an expanded data volume. The dataset has not yet been publicly archived but is available on reasonable request. Those caveats matter: the conclusions rest on four binary mixtures tested in the laboratory, and the machine-learning results reflect that limited scope rather than a universal predictive law.

Subject of Research: Effects of particle shape and gradation on the shear strength of granular mixtures and AI-based prediction of the peak internal friction angle

Article Title: Effects of particle shape and gradation on shear strength and AI-based prediction of friction angle

Article References: Xu, Z., Tian, Z., Wang, J., Li, G., & Ke, L. (2026). Effects of particle shape and gradation on shear strength and AI-based prediction of friction angle. AI in Civil Engineering, 5(1), Article 13. https://doi.org/10.1007/s43503-026-00092-y

Image Credits: AI Generated

DOI: 10.1007/s43503-026-00092-y

Keywords: shear strength, particle shape, gradation, friction angle, triaxial test, calcareous sand, fines content, XGBoost, machine learning, geotechnical engineering, granular materials, aspect ratio