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浙江大学学报(工学版)  2026, Vol. 60 Issue (10): 2129-2140    DOI: 10.3785/j.issn.1008-973X.2026.10.006
工程力学     
基于Tavares模型的冲击载荷下岩石碎片统计分析
李中源1(),赵婷婷1,2,3,*(),黄锦元1,田浩1,王志勇1,3
1. 太原理工大学 航空航天学院,山西 太原 030024
2. 城市基础设施智能化浙江省工程研究中心,浙江 杭州 310015
3. 山西省材料强度与结构冲击重点实验室,山西 太原 030024
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
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摘要:

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    
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
收稿日期: 2025-06-09 出版日期: 2026-07-28
CLC:  O 347.3  
基金资助: 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).
通讯作者: 赵婷婷     E-mail: 1448551164@qq.com;zhaotingting@tyut.edu.cn
作者简介: 李中源(2003—),男,硕士生,从事脆性材料离散元仿真研究. orcid.org/0009-0004-2382-9302. E-mail:1448551164@qq.com
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引用本文:

李中源,赵婷婷,黄锦元,田浩,王志勇. 基于Tavares模型的冲击载荷下岩石碎片统计分析[J]. 浙江大学学报(工学版), 2026, 60(10): 2129-2140.

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.

链接本文:

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

图 1  Tavares破碎模型计算流程
材料ρ/(kg?m?3)E/GPa$ \nu $
石灰岩2 7051070.26
落锤7 8002060.30
表 1  石灰岩与落锤的物理参数
材料μsμke
石灰岩-石灰岩0.350.330.54
落锤-石灰岩0.340.290.35
表 2  岩石-边界接触参数
参数数值参数数值
γ5.4A/%53.3
E/(J?kg?1)7.0b0.033
d0/mm100.0Dmin/mm2.0
φ0.8Emax/E504.0
σ20.16Emin/(J?kg?1)1.0
表 3  石灰岩Tavares破碎模型参数
图 2  落锤试验DEM模型
图 3  参考文献[27]与本研究仿真结果对比
图 4  不同长径比试样的冲击破碎效果
图 5  不同长径比试样的法向力时程曲线
图 6  不同长径比试样的破碎次数及碎片数量累积分布曲线
岩样点数自由度残差平方和Pearson’s rR2
D50H502 1492 1472.360.9030.815
D50H752 7252 7239.730.9050.819
D50H1002 6872 68524.020.8640.746
表 5  不同长径比试样的回归拟合统计数据
图 7  不同长径比试样的碎片平均等效粒径-数量分布曲线
图 8  不同长径比试样的粒径累积质量分布曲线
图 9  Image J图像处理流程
图 10  不同长径比试样的颗粒圆度频率分布
图 11  不同长径比试样的碎片体积-面积线性回归拟合
岩样参数数值标准误差t
D50H50截距?0.019 429.784×10?4?19.848
斜率0.1461.500×10?397.261
D50H75截距?0.048 231.469 ×10?3?32.838
斜率0.1991.794 ×10?3111.096
D50H100截距?0.049 132.283 ×10?3?21.515
斜率0.2522.839 ×10?388.821
表 4  不同长径比试样的碎片体积-面积拟合统计数据
图 12  不同尺寸试样的冲击破碎效果
图 13  不同尺寸试样的法向力时程曲线
图 14  不同尺寸试样的破碎次数及碎片数量累积分布曲线
图 15  不同尺寸试样的碎片平均等效粒径-数量分布曲线
图 16  不同尺寸试样的粒径累积质量分布曲线
图 17  不同尺寸试样的颗粒圆度频率分布
图 18  不同尺寸试样的碎片体积-面积线性回归拟合
岩样参数数值标准误差t
D30H60截距?0.010 085.049×10?4?19.958
斜率0.0981.070×10?391.800
D40H80截距?0.053 991.688×10?3?31.987
斜率0.2242.506×10?389.509
D50H100截距?0.049 132.283×10?3?21.515
斜率0.2522.839×10?388.821
表 6  不同尺寸试样的碎片体积-面积拟合统计数据
岩样点数自由度残差平方和Pearson’s rR2
D30H601 8631 8610.440.9050.819
D40H802 6682 66612.830.8660.750
D50H1002 6872 68524.020.8640.746
表 7  不同尺寸试样的回归拟合统计数据
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