Tavares model based statistical analysis of rock fragments under impact loading

doi:10.3785/j.issn.1008-973X.2026.10.006

Journal of ZheJiang University (Engineering Science)

2026, Vol. 60

Issue (10): 2129-2140 DOI: 10.3785/j.issn.1008-973X.2026.10.006

Tavares model based statistical analysis of rock fragments under impact loading

Zhongyuan LI1(

),Tingting ZHAO1,2,3,*(

),Jinyuan HUANG1,Hao TIAN1,Zhiyong WANG1,3

1. College of Aeronautics and Astronautics, Taiyuan University of Technology, Taiyuan 030024, China
2. Zhejiang Engineering Research Center of Intelligent Urban Infrastructure, Hangzhou 310015, China
3. Shanxi Key Laboratory of Material Strength and Structural Impact, Taiyuan 030024, China

Download:

HTML

PDF(2635KB) HTML
Export: BibTeX | EndNote (RIS)

Abstract

Discrete element method (DEM) and Tavares breakage model were employed to investigate the rock fragmentation mechanism and the statistical characteristics of fragments under impact loading. Drop hammer impact crushing process of limestone specimens with different aspect ratios (1.0—2.0) and sizes (diameter 30—50 mm) was systematically simulated. Image J image processing technology was used to quantitatively analyze the fragment count, particle size distribution, and shape indices. The results showed that increasing the aspect ratio and the size significantly raised the crushing energy threshold, which led to a delay in the peak normal force, a reduction in its amplitude, and a slowdown of the overall fragmentation process. The equivalent particle size of fragments showed poor alignment with the sieve analysis curve, which indicated that the fragments commonly exhibited irregular geometric configurations such as flaky and rod-like shapes. Fragments from specimens with lower aspect ratios (1.0) and smaller sizes (diameter 30 mm) had lower roundness, more pronounced angularity, and greater surface roughness. A quantitative relationship model among geometric parameters–crushing response–fragment morphology can provide theoretical basis and regulatory pathways for the design of impact-resistant structures, the optimization of blasting parameters, and the control of particle morphology in rockfill grading.

Key words： Tavares model impact loading rock fragments discrete element method (DEM) shape index

Received: 09 June 2025 Published: 28 July 2026

CLC:

O 347.3

Fund: 国家自然科学基金资助项目（12102294）；山西省回国留学人员科研资助项目（2022-067）；城市基础设施智能化浙江省工程研究中心开放基金资助项目（IUI2023-YB-04）；先进材料与结构的冲击安全山西省科技创新领军人才团队资助项目（202204051002006）.

Corresponding Authors: Tingting ZHAO E-mail: 1448551164@qq.com;zhaotingting@tyut.edu.cn

	Service
	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	Zhongyuan LI
	Tingting ZHAO
	Jinyuan HUANG
	Hao TIAN
	Zhiyong WANG

Cite this article:

Zhongyuan LI,Tingting ZHAO,Jinyuan HUANG,Hao TIAN,Zhiyong WANG. Tavares model based statistical analysis of rock fragments under impact loading. Journal of ZheJiang University (Engineering Science), 2026, 60(10): 2129-2140.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.10.006 OR https://www.zjujournals.com/eng/Y2026/V60/I10/2129

基于Tavares模型的冲击载荷下岩石碎片统计分析

为了探究冲击载荷下岩石破碎机理及其碎片统计特性，采用离散元法（DEM）与Tavares破碎模型，系统模拟不同长径比（1.0~2.0）和尺寸（直径30~50 mm）石灰岩试样的落锤冲击破碎过程，并采用Image J图像处理技术定量统计碎片数量、粒度分布及形状指数. 研究发现，增大长径比与尺寸显著提高了破碎能阈值，导致法向力峰值延迟、幅值降低，并延缓整体破碎进程；碎片等效粒径与筛分粒径分布曲线重合度低，表明碎片普遍呈片状、棒状等非规则几何构型；低长径比（1.0）与小尺寸（直径30 mm）试样产生的碎片圆度更低、棱角更突出，表面粗糙度更大. “几何参数-破碎响应-碎片形貌”定量关联模型可为冲击防护结构设计、爆破参数优化及堆石料级配形貌控制提供理论依据与调控路径.

关键词： Tavares模型, 冲击载荷, 岩石碎片, 离散元方法(DEM), 形状指数

Fig.1 Calculation process of Tavares breakage model

Tab.1 Physical parameters of limestone and drop hammer

Tab.2 Rock-boundary contact parameters

Tab.3 Limestone Tavares breakage model parameters

Fig.2 Drop hammer test of DEM

Fig.3 Comparison of Reference [27] with simulation results

Fig.4 Impact crushing effects of samples with different aspect ratios

Fig.5 Normal force time history curves of samples with different aspect ratios

Fig.6 Cumulative distribution curves of number of fractures and quantity of fragments for samples with different aspect ratios

Tab.5 Regression fitting of statistical data of samples with different aspect ratios

Fig.7 Fragment average equivalent particle size-quantity distribution curves of samples with different aspect ratios

Fig.8 Cumulative mass distribution curves of particle size of samples with different aspect ratios

Fig.9 Image J image processing workflow

Fig.10 Particle roundness frequency distribution of samples with different aspect ratios

Fig.11 Fragment volume-area linear regression fitting of samples with different aspect ratios

Tab.4 Fragment volume-area fitting statistical data of samples with different aspect ratios

Fig.12 Impact crushing effects of samples of different sizes

Fig.13 Normal force time history curves of samples with different sizes

Fig.14 Cumulative distribution curves of number of fractures and quantity of fragments for samples with different sizes

Fig.15 Fragment average equivalent particle size-quantity distribution curves of samples with different sizes

Fig.16 Cumulative mass distribution curves of particle size of samples with different sizes

Fig.17 Frequency distribution of particle roundness of samples with different sizes

Fig.18 Fragment volume-area linear regression fitting of samples with different sizes

Tab.6 Fragment volume-area fitting statistical data of samples with different sizes

Tab.7 Regression fitting of statistical data of samples with different sizes


[1]	李洪涛, 王志强, 姚强, 等石英云母片岩动力学特性实验及爆破裂纹扩展研究[J]. 岩石力学与工程学报, 2015, 34 (10): 2125- 2141 LI Hongtao, WANG Zhiqiang, YAO Qiang, et al Study of dynamic characteristics and blasting crack propagation of quartz mica schist[J]. Chinese Journal of Rock Mechanics and Engineering, 2015, 34 (10): 2125- 2141

[2]	李晓锋, 李海波, 刘凯, 等冲击荷载作用下岩石动态力学特性及破裂特征研究[J]. 岩石力学与工程学报, 2017, 36 (10): 2393- 2405 LI Xiaofeng, LI Haibo, LIU Kai, et al Dynamic properties and fracture characteristics of rocks subject to impact loading[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36 (10): 2393- 2405

[3]	周剑, 马刚, 周伟, 等基于FDEM的岩石颗粒破碎后碎片形状的统计分析[J]. 浙江大学学报: 工学版, 2021, 55 (2): 348- 357 ZHOU Jian, MA Gang, ZHOU Wei, et al Statistical analysis of fragment shape of rock grain after crushing based on FDEM[J]. Journal of Zhejiang University: Engineering Science, 2021, 55 (2): 348- 357

[4]	CAI P, MAO X, WU Q, et al Quantifying the influence of single particle shape on crushing characteristics of recycled aggregates: Experimental and numerical insights[J]. Construction and Building Materials, 2024, 439: 137363 doi: 10.1016/j.conbuildmat.2024.137363

[5]	孙壮壮, 马刚, 周伟, 等颗粒形状对堆石颗粒破碎强度尺寸效应的影响[J]. 岩土力学, 2021, 42 (2): 430- 438 SUN Zhuangzhuang, MA Gang, ZHOU Wei, et al Influence of particle shape on size effect of crushing strength of rockfill particles[J]. Rock and Soil Mechanics, 2021, 42 (2): 430- 438

[6]	REDDISH D J, STACE L R, VANICHKOBCHINDA P, et al Numerical simulation of the dynamic impact breakage testing of rock[J]. International Journal of Rock Mechanics and Mining Sciences, 2005, 42 (2): 167- 176 doi: 10.1016/j.ijrmms.2004.06.004

[7]	LAI J, WU C, LIAO N, et al A study on the correlation between fractal dimension and particle breakage for tungsten ores under impact crushing[J]. Minerals Engineering, 2024, 218: 108980 doi: 10.1016/j.mineng.2024.108980

[8]	纪杰杰, 李洪涛, 吴发名, 等冲击荷载作用下岩石破碎分形特征[J]. 振动与冲击, 2020, 39 (13): 176- 183 JI Jiejie, LI Hongtao, WU Faming, et al Fractal characteristics of rock fragmentation under impact load[J]. Journal of Vibration and Shock, 2020, 39 (13): 176- 183

[9]	田继荣. 堆石料的颗粒形状特征及颗粒破碎特性试验研究[D]. 大连: 大连理工大学, 2017. TIAN Jirong. Experimental study on the characteristics of particle shape and particle breakage of rockfill material [D]. Dalian: Dalian University of Technology, 2017.

[10]	DOMOKOS G, KUN F, SIPOS A A, et al Universality of fragment shapes[J]. Scientific Reports, 2015, 5 (1): 9147 doi: 10.1038/srep09147

[11]	ZHENG W, HU X, TANNANT D D Shape characterization of fragmented sand grains via X-ray computed tomography imaging[J]. International Journal of Geomechanics, 2020, 20 (3): 04020003 doi: 10.1061/(ASCE)GM.1943-5622.0001599

[12]	DWIVEDI K, ATTIA S, PATHAK H, et al. XFEM fracture parameters are not unique for consistent global behavior in tensile, CT, and SENB specimen [J]. Engineering Fracture Mechanics, 2025, 325: 111351.

[13]	CHEN X Y, YU H, ZHONG Y L, et al 3D XFEM for fluid-driven fracturing of layered anisotropic rock[J]. Computer Methods in Applied Mechanics and Engineering, 2025, 441: 117963 doi: 10.1016/j.cma.2025.117963

[14]	ZHOU Y, TAN X, YANG D, et al A numerical method to consider the interaction between multiple fractures in frozen rocks based on XFEM[J]. Computers and Geotechnics, 2024, 169: 106240 doi: 10.1016/j.compgeo.2024.106240

[15]	WANG Y, NIE J Y, ZHAO S, et al A coupled FEM-DEM study on mechanical behaviors of granular soils considering particle breakage[J]. Computers and Geotechnics, 2023, 160: 105529 doi: 10.1016/j.compgeo.2023.105529

[16]	CAI W, GAO K, AI S, et al. A 2D continuous-discontinuous heat transport model considering thermal cracking for the combined finite-discrete element method (FDEM) using node binding scheme [J]. Engineering Fracture Mechanics, 2025, 326: 111365.

[17]	王辉, 钮新强, 马刚, 等干湿循环作用下堆石料宏细观力学特性的离散元模拟研究[J]. 岩土力学, 2024, 45 (S1): 665- 676 WANG Hui, NIU Xinqiang, ZHOU Wei, et al Discrete element simulation study on the macro- and meso-mechanical properties of rockfill materials under wetting-drying cycles[J]. Rock and Soil Mechanics, 2024, 45 (S1): 665- 676

[18]	JIN Z Y, LIU J Y, MA G, et al How does the largest cluster in the strong network rule granular soil mechanics? A DEM study[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2025, 49 (3): 839- 859 doi: 10.1002/nag.3903

[19]	KUANG D M, LONG Z L, OGWU I, et al A discrete element method (DEM)-based approach to simulating particle breakage[J]. Acta Geotechnica, 2022, 17 (7): 2751- 2764 doi: 10.1007/s11440-021-01406-3

[20]	BAI Q, ZHANG C, KONIETZKY H Effects of particle shape on mechanical responses of rock materials using bonded-particle model[J]. Computers and Geotechnics, 2024, 176: 106754 doi: 10.1016/j.compgeo.2024.106754

[21]	DONG Z L, CHENG Y P, TONG C X, et al DEM modelling of particle crushing of single carbonate sand using the improved bonded particle model[J]. Powder Technology, 2024, 445: 120121 doi: 10.1016/j.powtec.2024.120121

[22]	DENZEL M, PRENNER M, SIFFERLINGER N A, et al A breakage model for DEM based on a probabilistic particle replacement with voronoi fragments[J]. Minerals Engineering, 2023, 203: 108328 doi: 10.1016/j.mineng.2023.108328

[23]	BARRIOS G K P, JIMÉNEZ-HERRERA N, TAVARES L M Simulation of particle bed breakage by slow compression and impact using a DEM particle replacement model[J]. Advanced Powder Technology, 2020, 31 (7): 2749- 2758 doi: 10.1016/j.apt.2020.05.011

[24]	张鑫. 基于离散元模拟的道砟细观力学特性及颗粒破碎的研究[D]. 武汉: 武汉理工大学, 2022. ZHANG Xin. Study on the micro-mechanical behaviour of ballast and particle breakage using DEM simulations [D]. Wuhan: Wuhan University of Technology, 2022.

[25]	BAO M, WU W, TIAN G, et al Research on discrete element parameter calibration of ore particles based on Tavares breakage model in a SAG mill[J]. Particuology, 2025, 96: 44- 56 doi: 10.1016/j.partic.2024.10.017

[26]	TAVARES L M Analysis of particle fracture by repeated stressing as damage accumulation[J]. Powder Technology, 2009, 190 (3): 327- 339 doi: 10.1016/j.powtec.2008.08.011

[27]	MIAO Q, HUANG P, ZHU W Morphology of impact fragmentation distribution of single spherical and ellipsoial particles in drop weight experiments[J]. Particuo logy, 2024, 86: 137- 148

[28]	TAVARES L M, ANDRÉ F P, POTAPOV A, et al Adapting a breakage model to discrete elements using polyhedral particles[J]. Powder Technology, 2020, 362: 208- 220 doi: 10.1016/j.powtec.2019.12.007

[29]	CHEN F, MA H, LIU Z, et al An improved breakage model with a fast-cutting method for simulating the breakage of polyhedral particles[J]. Powder Technology, 2024, 432: 119125 doi: 10.1016/j.powtec.2023.119125

[30]	DE ARRUDA TINO A A, TAVARES L M Simulating breakage tests using the discrete element method with polyhedral particles[J]. Computational Particle Mechanics, 2022, 9 (4): 811- 823 doi: 10.1007/s40571-021-00448-4

[31]	ZHANG C, ZHAO Y, GAO K, et al Numerical simulation and experimental study on rock fragmentation and crack propagation characteristics with hole enlargement under impact load[J]. Rock Mechanics and Rock Engineering, 2025, 58 (3): 3015- 3037 doi: 10.1007/s00603-024-04231-8

[32]	QIN Y, LANG L, TIAN S, et al. Characteristics of impact fragmentation and energy dissipation of cylindrical rock specimens with various aspect ratios [J]. Rock Mechanics and Rock Engineering, 2025, 58: 1–22.

[33]	李增, 马林建, 吴家文, 等中低应变率下砂岩动力特性试验研究[J]. 振动工程学报, 2020, 33 (1): 120- 127 LI Zeng, MA Linjian, WU Jiawen, et al Experimental investigation of mechanical properties of sandstone subjected to medium to low strain rate loading[J]. Journal of Vibration Engineering, 2020, 33 (1): 120- 127

[34]	王军祥, 马宝龙, 李树昊, 等中应变率下石英砂岩循环冲击破坏特性研究[J]. 爆破, 2023, 40 (2): 29- 41 WANG Junxiang, MA Baolong, LI Shuhao, et al Study on cyclic impact failure characteristics of quartz sandstone under medium strain rate[J]. Blasting, 2023, 40 (2): 29- 41

[1]	Jin-wei WANG,Shi-chun CHI,Shi-hao YAN,Yu GUO,Xin-jie ZHOU. Representative elementary volume of mechanical parameter of rockfill material with laboratory scaled gradation[J]. Journal of ZheJiang University (Engineering Science), 2023, 57(7): 1418-1427.

[2]	Rui-huan CAI,Yong-zhi ZHAO. Effect of screw structure on granular mixing in a double-screw conical mixer[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(11): 2067-2075.

[3]	Bing YANG,Wen-bo MO,Jin-liang YAO. 3D palmprint recognition by using local features and deep learning[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(3): 540-545.

[4]	Lei XU,Kun LUO,Yong-zhi ZHAO,Jian-ren FAN,Ke-fa CEN. Effect of particle size on liner wear in semi-autogenous mill[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(12): 2255-2263.

Viewed

Full text

Abstract

Cited

Shared

Discussed