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

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

Journal of ZheJiang University (Engineering Science)

2026, Vol. 60

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

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

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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

Received: 04 February 2025 Published: 03 February 2026

CLC:

TU 43

Fund: 国家自然科学基金资助项目（51988101）.

Corresponding Authors: Daosheng LING E-mail: 22212014@zju.edu.cn;dsling@zju.edu.cn

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Cite this article:

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.

URL:

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

应变局部化破坏模型试验的尺寸效应数值分析

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

Fig.1 Schematic diagram of cohesive zone

Fig.2 Cohesive zone model for tensile failure

Fig.3 Cohesive zone model for shear failure

Fig.4 Schematic diagram of direct shear model

Fig.5 Schematic diagram of three-point bending beam model

Tab.1 Parameters of cohesive zone model for three-point bending beam model

Tab.2 Test conditions for three-point bending beams

Fig.6 Tensile stress contour map of three-point bending beam during failure process

Fig.7 Force-displacement curves of three-point bending beams under four test conditions

Fig.8 Converted value of load-carrying capacity versus model height for three-point bending beams of different materials

Fig.9 Scale effects on structural strength versus material toughness for three-point bending beams of different materials

Fig.10 Tensile stress contour maps at peak load for three-point bending beams in different test conditions

Fig.11 Schematic diagram of three-point bending beam model with notches

Tab.3 Test conditions for three-point bending beam model with notches

Fig.12 Crack propagation path of three-point bending beam model with notches (2-2-1)

Fig.13 Comparison of crack propagation paths for three-point bending beam model with notches in different test conditions

Fig.14 Converted value of load-carrying capacity versus model height for three-point bending beam model with notches

Fig.15 Direct shear test model

Tab.4 Parameters of cohesive zone model for direct shear test

Tab.5 Test conditions for direct shear specimens

Fig.16 Shear stress contour map of direct shear test model during failure process

Fig.17 Load-carrying capacity versus model length for direct shear test model

Fig.18 Proportion of fracture dissipation energy versus model length for direct shear test model

Fig.19 Force-displacement curve for scaled model tests using heterogeneous materials

Fig.20 Shear stress contour maps at peak load for direct shear test models in different test conditions

Fig.21 Schematic diagram of slope model

Tab.6 Test conditions for slope models

Fig.22 Slip surface path of slope model in different test conditions

Fig.23 Converted value of load-carrying capacity versus model height for slope model


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