应变局部化破坏模型试验的尺寸效应数值分析

doi:10.3785/j.issn.1008-973X.2026.02.022

浙江大学学报(工学版)

2026, Vol. 60

Issue (2): 435-444 DOI: 10.3785/j.issn.1008-973X.2026.02.022

交通工程、土木工程

应变局部化破坏模型试验的尺寸效应数值分析

孙帅非1(

),王景1,缪骁1,凌道盛1,2,*(

)

1. 浙江大学建筑工程学院，浙江杭州 310058
2. 浙江大学超重力研究中心，浙江杭州 310058

Numerical analysis of scale effects in model tests of strain localization failure

Shuaifei SUN1(

),Jing WANG1,Xiao MIAO1,Daosheng LING1,2,*(

)

1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
2. Center for Hypergravity Experimental and Interdisciplinary Research, Zhejiang University, Hangzhou 310058, China

全文: PDF(2000 KB) HTML

摘要：

同质材料超重力模型试验广泛应用于应变局部化引起的岩土体破坏研究，为此进行模型缩尺对岩土体破坏过程的影响分析. 采用黏聚区域模型表征材料的应变局部化特性，基于有限单元法分析模型缩尺比对拉伸和剪切2种典型破坏模式的影响规律. 研究结果表明，应变局部化破坏超重力缩尺模型试验存在尺寸效应，试验结果高估岩土体断裂耗散能占比和承载力，断裂带扩展路径比原型相对更长. 产生尺寸效应的内在原因：由材料基本特性决定的破裂带宽度和断裂过程区长度不随模型缩尺改变，导致采用同质材料的应变局部化破坏超重力模型试验相似率无法严格满足.

关键词： 尺寸效应; 超重力模型试验; 黏聚区域模型; 有限元; 断裂过程区; 裂纹扩展路径

Abstract:

Hypergravity model tests with homogeneous materials have been widely used to study geomaterial failure induced by strain localization, and the influence of model scaling on the failure process was systematically examined. The cohesive zone model was adopted to characterize the strain localization behavior of geomaterials, and the finite element method was used to analyze the effects of scaling ratio on two typical failure modes—tensile and shear. Results indicate that a size effect exists in hypergravity model tests involving strain-localization failure: compared with the prototype, the fracture energy dissipation ratio and load capacity of geomaterials are overestimated, with a longer fracture propagation path. The fracture-band width and the length of the fracture process zone are governed by the material’s basic properties; therefore, they remain unchanged with model scaling. As a result, the similitude requirements for hypergravity model tests of strain-localization failure with homogeneous materials were not strictly satisfied.

Key words: scale effect hypergravity model test cohesive zone model finite element fracture process region crack propagation path

收稿日期: 2025-02-04 出版日期: 2026-02-03

CLC:

TU 43

基金资助: 国家自然科学基金资助项目（51988101）.

通讯作者: 凌道盛 E-mail: 22212014@zju.edu.cn;dsling@zju.edu.cn

作者简介: 孙帅非（1999—），男，硕士生，从事岩土体应变局部化破坏尺寸效应研究. orcid.org/0009-0004-7334-6587. E-mail：22212014@zju.edu.cn

	服务
	把本文推荐给朋友
	加入引用管理器
	E-mail Alert
	作者相关文章
	孙帅非
	王景
	缪骁
	凌道盛

引用本文:

孙帅非,王景,缪骁,凌道盛. 应变局部化破坏模型试验的尺寸效应数值分析[J]. 浙江大学学报(工学版), 2026, 60(2): 435-444.

Shuaifei SUN,Jing WANG,Xiao MIAO,Daosheng LING. Numerical analysis of scale effects in model tests of strain localization failure. Journal of ZheJiang University (Engineering Science), 2026, 60(2): 435-444.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2026.02.022 或 https://www.zjujournals.com/eng/CN/Y2026/V60/I2/435

图 1 黏聚区域示意图

图 2 拉伸破坏黏聚区域模型

图 3 剪切破坏黏聚区域模型

图 4 直剪模型示意图

图 5 三点弯梁模型示意图

表 1 三点弯梁黏聚区域模型参数

表 2 三点弯梁工况设置

图 6 三点弯梁破坏过程拉应力云图

图 7 三点弯梁在4种工况下的力-位移曲线

图 8 不同材质三点弯梁承载力换算值随模型高度变化曲线

图 9 不同材质三点弯梁结构强度尺寸效应随材料韧性变化曲线

图 10 不同工况的三点弯梁在最大承载力时的拉应力云图

图 11 缺口三点弯梁模型示意图

表 3 缺口三点弯梁模型工况设置

图 12 缺口三点弯梁试件裂纹扩展路径（2-2-1）

图 13 不同工况的缺口三点弯梁试件裂纹扩展路径比较

图 14 缺口三点弯梁试件承载力换算值随模型高度变化曲线

图 15 直剪试验模型

表 4 直剪试验黏聚区域模型参数

表 5 直剪试验模型工况设置

图 16 直剪试验模型破坏过程剪应力云图

图 17 直剪试验模型承载力随模型长度变化曲线

图 18 直剪试验模型断裂耗散能占比随模型长度变化曲线

图 19 异质材料缩尺试验力-位移曲线

图 20 不同工况的直剪试验模型在最大承载力时的剪应力云图

图 21 边坡模型示意图

表 6 边坡模型工况设置

图 22 不同工况边坡模型的滑裂面路径

图 23 边坡模型承载力换算值随模型高度变化曲线

1	KRAMER S L Performance-based design methodologies for geotechnical earthquake engineering[J]. Bulletin of Earthquake Engineering, 2014, 12 (3): 1049- 1070 doi: 10.1007/s10518-013-9484-x
2	陈云敏, 马鹏程, 唐耀土体的本构模型和超重力物理模拟[J]. 力学学报, 2020, 52 (4): 901- 915 CHEN Yunmin, MA Pengcheng, TANG Yao Constitutive models and hypergravity physical simulation of soils[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52 (4): 901- 915 doi: 10.6052/0459-1879-20-059
3	蒋明镜现代土力学研究的新视野: 宏微观土力学[J]. 岩土工程学报, 2019, 41 (2): 195- 254 JIANG Mingjing New paradigm for modern soil mechanics: geomechanics from micro to macro[J]. Chinese Journal of Geotechnical Engineering, 2019, 41 (2): 195- 254
4	凌道盛, 李奖, 王文军, 等人工制备土的结构性及其对应变局部化的影响[J]. 浙江大学学报: 工学版, 2019, 53 (9): 1689- 1696 LING Daosheng, LI Jiang, WANG Wenjun, et al Structure of artificial soils and its influence on strain localization[J]. Journal of Zhejiang University: Engineering Science, 2019, 53 (9): 1689- 1696 doi: 10.3785/j.issn.1008-973X.2019.09.007
5	ROSCOE K H The influence of strains in soil mechanics[J]. Géotechnique, 1970, 20 (2): 129- 170
6	RATTEZ H, SHI Y, SAC-MORANE A, et al Effect of grain size distribution on the shear band thickness evolution in sand[J]. Géotechnique, 2022, 72 (4): 350- 363 doi: 10.1680/jgeot.20.p.120
7	WANG Z Y, WANG P, YIN Z Y, et al Micromechanical investigation of the particle size effect on the shear strength of uncrushable granular materials[J]. Acta Geotechnica, 2022, 17 (10): 4277- 4296 doi: 10.1007/s11440-022-01501-z
8	BUI T Q, HU X A review of phase-field models, fundamentals and their applications to composite laminates[J]. Engineering Fracture Mechanics, 2021, 248: 107705 doi: 10.1016/j.engfracmech.2021.107705
9	WANG L, SU H, ZHOU K A phase-field model for mixed-mode cohesive fracture in fiber-reinforced composites[J]. Computer Methods in Applied Mechanics and Engineering, 2024, 421: 116753 doi: 10.1016/j.cma.2024.116753
10	周鑫, 于佳佳, 吴文杰, 等基于非局部理论的Hoek-Brown软化塑性模型[J]. 防灾减灾工程学报, 2025, 45 (1): 13- 20 ZHOU Xin, YU Jiajia, WU Wenjie, et al Hoek-brown softening plasticity model based on nonlocal theory[J]. Journal of Disaster Prevention and Mitigation Engineering, 2025, 45 (1): 13- 20 doi: 10.13409/j.cnki.jdpme.20241104002
11	姚仰平, 武孝天, 崔文杰基于岩土材料临界状态理论的有限元非局部软化算法: 以CSUH模型为例[J]. 岩石力学与工程学报, 2023, 42 (7): 1759- 1766 YAO Yangping, WU Xiaotian, CUI Wenjie A finite element nonlocal strain-softening algorithm based on the critical state theory for geomaterials: a case study with csuh model[J]. Chinese Journal of Rock Mechanics and Engineering, 2023, 42 (7): 1759- 1766 doi: 10.13722/j.cnki.jrme.2022.1124
12	CASTELLI M, ALLODI A, SCAVIA C A numerical method for the study of shear band propagation in soft rocks[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2009, 33 (13): 1561- 1587 doi: 10.1002/nag.778
13	PALMER A C, RICE J R The growth of slip surfaces in the progressive failure of over-consolidated clay[J]. Proceedings of the Royal Series A, 1973, 332: 527- 548 doi: 10.1098/rspa.1973.0040
14	喻葭临. 土中剪切带扩展机理研究和扩展过程模拟 [D]. 北京: 清华大学, 2009: 1–142. YU Jialin. Mechanism investigation and numerical simulation of evolution of shear band in soil [D]. Beijing: Tsinghua University, 2009: 1–142.
15	程靳, 赵树山. 断裂力学 [M]. 北京: 科学出版社, 2006: 9–24.
16	FLÁDR J, BÍLÝ P Specimen size effect on compressive and flexural strength of high-strength fibre-reinforced concrete containing coarse aggregate[J]. Composites Part B: Engineering, 2018, 138: 77- 86 doi: 10.1016/j.compositesb.2017.11.032
17	VU C C, WEISS J, PLÉ O, et al The potential impact of size effects on compressive strength for the estimation of the Young’s modulus of concrete[J]. Materials and Structures, 2021, 54 (5): 196 doi: 10.1617/s11527-021-01795-7
18	BAREITHER C A, BENSON C H, EDIL T B Comparison of shear strength of sand backfills measured in small-scale and large-scale direct shear tests[J]. Canadian Geotechnical Journal, 2008, 45 (9): 1224- 1236 doi: 10.1139/T08-058
19	WU P K, MATSUSHIMA K, TATSUOKA F Effects of specimen size and some other factors on the strength and deformation of granular soil in direct shear tests[J]. Geotechnical Testing Journal, 2008, 31 (1): 45- 64 doi: 10.1520/GTJ100773
20	CANTOR D, OVALLE C Sample size effects on the critical state shear strength of granular materials with varied gradation and the role of column-like local structures[J]. Géotechnique, 2025, 75 (1): 29- 40 doi: 10.1680/jgeot.23.00032
21	NING F, LIU J, ZOU D, et al Super-large-scale triaxial tests to study the effects of particle size on the monotonic stress–strain response of rockfill materials[J]. Acta Geotechnica, 2025, 20 (4): 1847- 1858 doi: 10.1007/s11440-024-02471-0
22	ZERAATI-SHAMSABADI M, SADREKARIMI A A DEM study on the effects of specimen and particle sizes on direct simple shear tests[J]. Granular Matter, 2025, 27 (2): 36 doi: 10.1007/s10035-025-01513-y
23	JIN J, JIN Q, LI M, et al Analysis of large-scale in situ shear tests of sandy gravel with cobbles[J]. International Journal of Civil Engineering, 2024, 22 (11): 2031- 2040 doi: 10.1007/s40999-024-00969-y
24	蒋明杰, 吉恩跃, 王天成, 等粗粒土抗剪强度的缩尺效应规律试验研究[J]. 岩土工程学报, 2023, 45 (4): 855- 861 JIANG Mingjie, JI Enyue, WANG Tiancheng, et al Experimental study on laws of scale effects of shear strength of coarse-grained soils[J]. Chinese Journal of Geotechnical Engineering, 2023, 45 (4): 855- 861
25	TIJSSENS M G A, VAN DER GIESSEN E, SLUYS L J Modeling of crazing using a cohesive surface methodology[J]. Mechanics of Materials, 2000, 32 (1): 19- 35 doi: 10.1016/S0167-6636(99)00044-7
26	凌道盛, 涂福彬, 卜令方基于黏聚区域模型的边坡渐进破坏过程强化有限元分析[J]. 岩土工程学报, 2012, 34 (8): 1387- 1393 LING Daosheng, TU Fubin, BU Lingfang Enhanced finite element analysis of progressive failure of slopes based on cohesive zone model[J]. Chinese Journal of Geotechnical Engineering, 2012, 34 (8): 1387- 1393
27	石天翔, 张昕, 王洋洋, 等基于强度理论的内聚力模型的有限元实现及应用[J]. 浙江大学学报: 工学版, 2023, 57 (3): 573- 582 SHI Tianxiang, ZHANG Xin, WANG Yangyang, et al Finite element implementation and application of strength theory based cohesive zone model[J]. Journal of Zhejiang University: Engineering Science, 2023, 57 (3): 573- 582 doi: 10.3785/j.issn.1008-973X.2023.03.015
28	CUSATIS G, SCHAUFFERT E A Cohesive crack analysis of size effect[J]. Engineering Fracture Mechanics, 2009, 76 (14): 2163- 2173 doi: 10.1016/j.engfracmech.2009.06.008
29	HU C, WANG L, LING D, et al Experimental and numerical investigation on the tensile fracture of compacted clay[J]. Computer Modeling in Engineering and Sciences, 2020, 123 (1): 283- 307 doi: 10.32604/cmes.2020.07842
30	凌道盛, 徐泽龙, 蔡武军, 等压实黏土梁弯曲开裂性状试验研究[J]. 岩土工程学报, 2015, 37 (7): 1165- 1172 LING Daosheng, XU Zelong, CAI Wujun, et al Experimental study on characteristics of bending cracks of compacted soil beams[J]. Chinese Journal of Geotechnical Engineering, 2015, 37 (7): 1165- 1172
31	黄煜镔, 钱觉时, 周小平基于强度尺寸效应的准脆性材料脆性指标研究[J]. 工程力学, 2006, 23 (1): 38- 42 HUANG Yubin, QIAN Jueshi, ZHOU Xiaoping Brittleness index of quasibrittle material based on size effect of strength[J]. Engineering Mechanics, 2006, 23 (1): 38- 42 doi: 10.3969/j.issn.1000-4750.2006.01.008
32	HU C, YANG Q, LING D, et al Numerical simulations of arbitrary evolving cracks in geotechnical structures using the nonlinear augmented finite element method (N-AFEM)[J]. Mechanics of Materials, 2021, 156: 103814 doi: 10.1016/j.mechmat.2021.103814
33	凌道盛, 韩超, 陈云敏, 等土结接触面黏聚区域模型及渐进累积破坏分析[J]. 岩土工程学报, 2011, 33 (9): 1405- 1411 LING Daosheng, HAN Chao, CHEN Yunmin, et al Interfacial cohesive zone model and progressive failure of soil-structure interface[J]. Chinese Journal of Geotechnical Engineering, 2011, 33 (9): 1405- 1411

[1]	郑雅华,刘红位,冯嵩. 锯齿状毛细阻滞覆盖层渗漏量的参数研究[J]. 浙江大学学报(工学版), 2025, 59(4): 730-740.
[2]	邢国华,陆勇健,苗鹏勇,陈思锦. 基于改进遗传算法的临时转播塔结构优化设计方法[J]. 浙江大学学报(工学版), 2025, 59(3): 469-479.
[3]	张中杰,周赫宸,顾晓强,陈加核,吴航. 天津某超深地铁基坑变形分析与小应变硬化参数取值[J]. 浙江大学学报(工学版), 2025, 59(12): 2593-2603.
[4]	吴洋,肖磊,王玮彦,许金鑫,杜原,杨泊莘,安琦. 电梯安全钳制动块与导轨接触应力的有限元计算方法[J]. 浙江大学学报(工学版), 2025, 59(1): 109-119.
[5]	张兴标,王涛,姚森,叶华文,王路,白伦华. 大跨度公铁两用斜拉-悬索协作体系桥断索动力响应[J]. 浙江大学学报(工学版), 2024, 58(9): 1874-1885.
[6]	罗易飞,胡彬,赵鑫,温泽峰. 缩尺车轮-环轨滚动接触与磨耗特性仿真分析[J]. 浙江大学学报(工学版), 2024, 58(6): 1275-1284.
[7]	周敉,冯昭,张鹏利,秦伟. 大流量斜拉压力输水管桥振动台模型试验研究[J]. 浙江大学学报(工学版), 2024, 58(10): 2149-2161.
[8]	金俊超,景来红,杨风威,宋志宇,尚朋阳. 脆塑性迭代逼近算法的改进[J]. 浙江大学学报(工学版), 2023, 57(9): 1706-1717.
[9]	王玲茂,赵唯坚. 基于肋尺度精细化建模的机械锚固钢筋拉拔性能模拟[J]. 浙江大学学报(工学版), 2023, 57(8): 1573-1584.
[10]	陈晓丹,吴澳,赵睿杰,徐恩翔. 磁悬浮无轴离心泵叶轮转子动力学特性[J]. 浙江大学学报(工学版), 2023, 57(8): 1680-1688.
[11]	谢国庆,王密,孔德文. 新型高强硅酸盐墙板钢框架抗震性能[J]. 浙江大学学报(工学版), 2023, 57(7): 1402-1409.
[12]	王晋伟,迟世春,闫世豪,郭宇,周新杰. 室内缩尺级配堆石料力学参数的表征单元体积[J]. 浙江大学学报(工学版), 2023, 57(7): 1418-1427.
[13]	鲍佳文,高强,唐林,赵唯坚. 钢筋套筒灌浆连接拉伸性能的精细有限元分析[J]. 浙江大学学报(工学版), 2023, 57(4): 814-823.
[14]	陈廷国,郭召迪. 具有杆间扭转约束的轴心压杆稳定性研究[J]. 浙江大学学报(工学版), 2023, 57(3): 598-605.
[15]	刘彩霞,潘亭亭,孙一帆,李帅,刘平,黄英. 用于康复训练的分段式气动软体驱动器[J]. 浙江大学学报(工学版), 2022, 56(6): 1127-1134.

Viewed

Full text

Abstract

Cited

Shared

Discussed