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

Abstract

Particle shape and gradation govern force chain networks and interparticle contacts in dense granular systems, thereby determining macroscopic shear strength. To investigate their influence on the peak internal friction angle (φ_d), triaxial tests were conducted on four binary mixed granular materials with contrasting morphologies, including Nanhai calcareous sand (GZS), Fujian standard sand (FS), glass beads (GB), and glass sand (GS). Ensemble learning algorithms were then employed to model φ_d from shape and gradation parameters. Results show that particle shape dominates φ_d: irregular particles yield systematically higher φ_d, whereas gradation plays a secondary role. Fine particle content (FC) induces non-monotonic effects. Angular particles (GZS, GS) exhibit an inverted V-shaped trend, with peak φ_d at a threshold FC. In contrast, subrounded particles (FS, GB) display a V-shaped trend, with minimum φ_d at the threshold FC. For subrounded particles, the threshold FC correlates strongly with the size ratio (SR). Heatmap analysis further identifies aspect ratio (AR) as the shape parameter most strongly correlated with φ_d. XGBoost and multilayer perceptron (MLP) models were developed to predict φ_d from shape and particle size inputs. Both models achieve good fit, confirming the relevance of the selected features. Due to its superior handling of small-sample data and multi-feature interactions, XGBoost significantly outperforms MLP in both accuracy and stability, offering a robust tool for predicting shear strength in granular materials.

Keywords

Binary mixed granular materials / Peak Internal Friction Angle / Shape parameter / Fine particle content / XGBoost / MLP

References

[1] Afrasiabian B, Eftekhari M. Prediction of mode I fracture toughness of rock using linear multiple regression and gene expression programming. Journal of Rock Mechanics and Geotechnical Engineering, 2022, 14(5): 1421-1432

[2] Bai XX, Zhang HY, Wang QZ, Zhao K, Others. . A nonlinear cyclic constitutive model for soils considering pore-water-soil-skeleton coupling effects and its numerical realization in 3D stress space. Chinese Journal of Geotechnical Engineering, 2023, 45(12): 2634-2640

[3] Barrett PJ. The shape of rock particles, a critical review. Sedimentology, 1980, 27: 291-303

[4] Berger KJ, Hrenya CM. Challenges of DEM: II. Wide particle size distributions. Powder Technology, 2014, 264: 627-633

[5] Chang CS, Deng Y, Yang Z. Modeling of minimum void ratio for granular soil with effect of particle size distribution. Journal of Engineering Mechanics, 2017, 143(9): Article ID: 04017060

[6] Cho GC, Dodds J, Santamarina JC. Particle shape effects on packing density, stiffness, and strength: Natural and crushed sands. Journal of Geotechnical and Geoenvironmental Engineering, 2006, 132(5): 591-602

[7] Gong J, Nie Z, Zhu Y, Liang Z, Wang X. Exploring the effects of particle shape and content of fines on the shear behavior of sand-fines mixtures via the DEM. Canadian Geotechnical Journal, 2019, 106: 161-176

[8] Han D, Xue X. Machine learning-based prediction of shear strength parameters of rock materials. Rock Mechanics and Rock Engineering, 2024, 57: 8795-8819

[9] Kenney TC, Lau D. Internal stability of granular filters. Canadian Geotechnical Journal, 1985, 22(2): 215-225

[10] Mcgeary RK. Mechanical packing of spherical particles. Journal of the American Ceramic Society, 1961, 44(10): 513-522

[11] Miao M, Liu FY, Yin Y. The effect of surface roughness and particle size on the shear characteristics of spherical particle materials. Powder Technology, 2025, 459: 121017

[12] Naeini SA, Baziar MH. Effect of fines content on steady-state strength of mixed and layered samples of a sand. Soil Dynamics and Earthquake Engineering, 2003, 24(3): 123-134

[13] Nawal M, Shekar B, Jaiswal P. Integration of sparse and continuous data sets using machine learning for core mineralogy interpretation. Leading Edge, 2023, 42(6): 421-432

[14] Ng CWW, Zhao J, Liu H. DEM simulation of the effect of particle shape and gradation on the shear behavior of sand. Computers and Geotechnics, 2018, 102: 123-135

[15] Peters JF, Berney ES. Percolation threshold of sand-clay binary mixtures. Journal of Geotechnical and Geoenvironmental Engineering, 2010, 136(2): 310-318

[16] Pham BT, Son LH, Hoang T-A, Nguyen D-M, Tien Bui D. Prediction of shear strength of soft soil using machine learning methods. CATENA, 2018, 166: 181-191

[17] Qu TM, Wang M, Feng YT. Applicability of discrete element method with spherical and clumped particles for constitutive study of granular materials. Journal of Rock Mechanics and Geotechnical Engineering, 2022, 14: 240-251

[18] Roquier G. The theoretical packing density model (TPDM): A versatile model for estimating the minimum void ratio of binary soil mixtures. Engineering Geology, 2022, 296 Article ID: 106453

[19] Shen, C. (2021). Research on prediction model of minimum void ratio for sand mixtures with discontinuous gradation considering particle shape [Master's thesis]. Yangzhou University, Yangzhou, China.https://jgxy.yzu.edu.cn/info/1074/4347.htm

[20] Shen C, Xu Z, Yin J, Wu J. Prediction model of minimum void ratio for various sizes/shapes of sandy binary mixture. Advances in Civil Engineering, 2020

[21] Shire T, O'Sullivan C, Hanley KJ. The influence of fines content and size-ratio on the micro-scale properties of dense bimodal materials. Granular Matter, 2016, 18(3): Article ID: 52

[22] Siddig O, Ibrahim AF, Elkatatny S. Estimation of rocks' failure parameters from drilling data by using artificial neural network. Scientific Reports, 2023, 13(1): Article ID: 3146

[23] Simoni A, Houlsby GT. The direct shear strength and dilatancy of sand–gravelmixtures. Geotechnical and Geological Engineering, 2006, 24(3): 523-549

[24] Thevanayagam S, Shenthan T, Mohan S, Liang J. Undrained fragility of clean sands, silty sands, and sandy silts. Journal of Geotechnical and Geoenvironmental Engineering, 2002, 128(10): 849-859

[25] Vafaei A, Choobbasti AJ, Vafaei A, Afrakoti MP, Kutanaei SS. Prediction the peak shear strength parameters of Babolsar sand using particles swarm optimization and artificial neural network methods. Transportation Infrastructure Geotechnology, 2024, 11: 470-500

[26] Vahidi-Nia F, Bayesteh H, Khodaparast M. Effect of particle size ratio and fines content on drained/undrained behavior of binary granular soil according to confining pressure and packing density: A DEM simulation. Computational Particle Mechanics, 2024, 11: 141-167

[27] Vallejo LE. Interpretation of the limits in shear strength in binary granular mixtures. Canadian Geotechnical Journal, 2001, 38(5): 1097-1104

[28] Wiacek J. Geometrical parameters of binary granular mixtures with size ratio and volume fraction: Experiments and DEM simulations. Granular Matter, 2016, 18(3): Article ID: 42

[29] Wiacek J, Parafiniuk P, Stasiak M. Effect of particle size ratio and contribution of particle size fractions on micromechanics of uniaxially compressed binary sphere mixtures. Granular Matter, 2017, 19(2): Article ID: 34

[30] Xu ZY, Xu N, Wang HB. Effects of particle shapes and sizes on the minimum void ratios of sand. Advances in Civil Engineering, 2019

[31] Yang J, Luo XD. Exploring the relationship between critical state and particle shape for granular materials. Journal of the Mechanics and Physics of Solids, 2015, 84: 196-213

[32] Yang J, Wei LM. Collapse of loose sand with the addition of fines: The role of particle shape. Géotechnique, 2012, 62(12): 1111-1125

[33] Zhang Y, Wang X, Zhang JS, et al.. Research on the Effects of Particle Shape on the Mechanical Properties of Sand. Journal of Railway Science and Engineering, 2022, 19(11): 3256-3265

[34] Zou YX, Ma G, Zhao SW, Zou Y, Zhao S, Chen S, Zhou W. Particle shape transforms the driving of shear stress in granular materials. Powder Technology, 2023, 416 Article ID: 118235

Funding

Ke Lijun(52308378)

RIGHTS & PERMISSIONS

The Author(s)