Please wait a minute...
Journal of ZheJiang University (Engineering Science)  2026, Vol. 60 Issue (7): 1577-1585    DOI: 10.3785/j.issn.1008-973X.2026.07.019
    
Reconstruction of root system based on foundation beam approach
Yongqi MIAO1,2(),Xingyu ZHANG1,2,*(),Lu YANG3,Shitang KE1,2
1. Department of Civil and Airport Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2. Key Laboratory of Dynamic Multi-hazard Protection in Civil Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
3. Kunming Planning and Design Research Institute Co., Ltd, Kunming 650051, China
Download: HTML     PDF(2070KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

Aiming at complexity of the root architecture, low efficiency of typical numerical simulation method and difficulty of modelling large deformation, a root system reconstruction method was proposed on basis of Winkler foundation beam theory. The individual roots were simplified into horizontal or vertical cylindrical elements while preserving key root distribution characteristics. Two types of complex root system models were built: a narrow-deep model A and a wide-shallow model B, together with their simplified versions Am and Bm. The bending moment-rotation curves and the failure mechanisms before and after root system reconstruction under centrifugal conditions were compared. The initial stage of moment-rotation curves showed high consistency between original and reconstructed models. Model B and Bm exhibited similar responses under large displacement, whereas the tap root in Model Am was broken due to stress concentration, leading to 65% moment reduction. Windward lateral roots were pulled out of the soil, consistent with the field observations. The simplified model accurately reproduces the overturning resistance and effectively captures the failure mechanisms dominated by taproot fracture, providing theoretical basis for physical and numerical modelling of complex root systems.



Key wordsroot system reconstruction      hypergravity      beam on Winkler foundation approach      failure mechanism      moment-rotation curve     
Received: 18 April 2025      Published: 23 May 2026
CLC:  TU 375.4  
Fund:  江苏省自然科学基金资助项目(BK20230895);国家自然科学基金资助项目(52408541, 52321165649);中央高校基本科研业务费专项资金资助项目(NS2025021).
Corresponding Authors: Xingyu ZHANG     E-mail: miaoyongqi@nuaa.edu.cn;x.y.zhang@nuaa.edu.cn
Cite this article:

Yongqi MIAO,Xingyu ZHANG,Lu YANG,Shitang KE. Reconstruction of root system based on foundation beam approach. Journal of ZheJiang University (Engineering Science), 2026, 60(7): 1577-1585.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.07.019     OR     https://www.zjujournals.com/eng/Y2026/V60/I7/1577


基于地基梁法的植被根系重构方法

针对植被根系结构复杂、传统数值分析方法效率低且难以模拟大位移变形的问题,提出基于Winkler地基梁法的根系重构方法,将单根简化为水平或竖直圆柱体,保留关键根系分布特征. 构建窄而深(模型A)和宽而浅(模型B)2种根系的复杂模型及其简化模型(Am、Bm),对比分析超重力条件下根系重构前后的弯矩-转角曲线和破坏机理. 研究发现,初始阶段重构前后模型的弯矩-转角曲线高度吻合;在大位移阶段,模型B和Bm的响应较为相似,而模型Am主根因应力集中断裂,弯矩骤降65%;2种模型横向根拔出现象均与现场试验一致. 简化模型能准确再现根系的抗倾覆性能,可以有效捕捉由主根断裂等机制主导的破坏模式,为复杂根系物理模拟与数值建模提供理论基础.


关键词: 根系重构,  超重力,  Winkler地基梁法,  破坏机理,  弯矩-转角曲线 
Fig.1 Schematic diagram of root system (Black is marked as root of destruction in experiment)
物理量相似系数物理量相似系数
长度1/N应力1
体积1/N31/N2
密度1位移1/N
加速度N弯矩1/N3
刚度1转角1
Tab.1 Scale law
Fig.2 Schematic diagram of simplification of taproot
Fig.3 Schematic diagram of simplification of lateral roots
Fig.4 Schematic diagram of simplification of third order roots
Fig.5 Number of (a)(c) lateral roots and (b)(d) vertical roots in different regions of models A、B、Am and Bm (plan view)
Fig.6 Accumulated root volume for models A、Am、B and Bm
Fig.7 Mechanical properties of ABS material
Fig.8 Particle size distribution curve of test soil
Fig.9 Peak friction angle of test soil
Fig.10 Schematic diagram of centrifuge test setup
Fig.11 Moment-rotation curves for models A、Am、B and Bm
Fig.12 Schematic diagram of modelling of tap root overturning
Fig.13 Moment-rotation curves of taproot and single pile simulations
Fig.14 Coupling constraint of root system based on Winkler foundation beam method
[1]   周利芬, 吴红华, 李正农 树木抗风及对风环境影响的研究综述[J]. 自然灾害学报, 2015, 24 (5): 199- 206
ZHOU Lifen, WU Honghua, LI Zhengnong Review of research on trees' wind resistance and effects on wind environment[J]. Journal of Natural Disasters, 2015, 24 (5): 199- 206
doi: 10.13577/j.jnd.2015.0522
[2]   郝艳峰, 黄斌 树木气弹模型风致响应特性的风洞试验研究[J]. 空气动力学学报, 2024, 42 (9): 21- 34
HAO Yanfeng, HUANG bin Wind tunnel study on wind-induced response characteristics of an aeroelastic model tree[J]. Acta Aerodynamica Sinica, 2024, 42 (9): 21- 34
[3]   林滨强, 章德生, 简文彬, 等 风驱雨作用下植被斜坡稳定性响应研究[J]. 岩土力学, 2024, 45 (9): 2765- 2774
LIN Binqiang, ZHANG Desheng, JIAN Wenbin, et al Response of vegetated slope stability under wind-driven rainconditions[J]. Rock and Soil Mechanics, 2024, 45 (9): 2765- 2774
doi: 10.16285/j.rsm.2023.1563
[4]   RUEL J C Factors influencing windthrow in balsam fir forests: from landscape studies to individual tree studies[J]. Forest Ecology and Management, 2000, 135: 169-178
[5]   SELLIER D, FOURCAUD T Crown structure and wood properties: influence on tree sway and response to high winds[J]. American Journal of Botany, 2009, 96: 885- 896
doi: 10.3732/ajb.0800226
[6]   CANNON J, BARRETT M, PETERSON C The effect of species, size, failure mode, and fire-scarring on tree stability[J]. Forest Ecology and Management, 2015, 356: 196- 203
doi: 10.1016/j.foreco.2015.07.014
[7]   傅胤榕, 仉文岗 土体含水率与根系埋深对银杏树苗抗拉拔性能的影响[J]. 土木与环境工程学报, 2019, 41 (5): 42- 48
FU Yinrong, ZHANG Wengang Effects of soil moisture content and root depth on anti-overturning performance of Ginkgo biloba seedings[J]. Journal of Civil and Environmental Engineering, 2019, 41 (5): 42- 48
[8]   ZHANG X, KNAPPETT J A, LEUNG A K, et al Small-scale modelling of root–soil interaction of trees under lateral loads[J]. Plant and Soil, 2020, 456 (1/2): 289- 305
doi: 10.1007/s11104-020-04636-8
[9]   ZHANG X, KNAPPETT J, LEUNG A, et al Centrifuge modelling of root–soil interaction of laterally loaded trees under different loading conditions[J]. Géotechnique, 2023, 73: 289- 305
[10]   赵俊键, 梁腾, 詹良通, 等 基于渗透原理的可吸水模型根系研发与性能研究[J]. 浙江大学学报: 工学版, 2023, 57 (7): 1382- 1392
ZHAO Junjian, LIANG Teng, ZHAN Liangtong, et al Development and performance study of water uptake-able model root based on osmotic technique[J]. Journal of Zhejiang University: Engineering Science, 2023, 57 (7): 1382- 1392
[11]   张德顺, 陈一家, 张振, 等 上海14种园林树种根系结构与锚固力的相关性研究[J]. 同济大学学报: 自然科学版, 2024, 52 (12): 1883- 1891
ZHANG Deshun, CHEN Yijia, ZHANG Zhen, et al Relationship between root architecture and anchorage force of14 landscape tree species in shanghai[J]. Journal of Tongji University: Natural Science, 2024, 52 (12): 1883- 1891
[12]   BLACKWELL P, RENNOLLS K, COUTTS M A root anchorage model for shallowly rooted Sitka spruce[J]. Forestry, 1990, 63 (1): 73- 91
doi: 10.1093/forestry/63.1.73
[13]   ACHIM A, NICOLL B Modelling the anchorage of shallow-rooted trees[J]. Forestry, 2009, 82 (3): 273- 284
doi: 10.1093/forestry/cpp004
[14]   徐华, 袁海莉, 王歆宇, 等 根系形态和层次结构对根土复合体力学特性影响研究[J]. 岩土工程学报, 2022, 44 (5): 926- 935
XU Hua, YUAN Haili, WANG Xinyu, et al Influences of morphology and hierarchy of roots on mechanical characteristics of root-soil composites[J]. Chinese Journal of Geotechnical Engineering, 2022, 44 (5): 926- 935
[15]   DANJON F, BARKER D H, DREXHAGE M, et al Using three-dimensional plant root architecture in models of shallow-slope stability[J]. Annals of Botany, 2008, 101 (8): 1281- 1293
[16]   YANG M, DÉFOSSEZ P, DANJON F, et al Analyzing key factors of roots and soil contributing to tree anchorage of Pinus species[J]. Trees, 2018, 32: 703- 712
doi: 10.1007/s00468-018-1665-4
[17]   LIANG T, KNAPPETT J, DUCKETT N Modelling the seismic performance of rooted slopes from individual root–soil interaction to global slope behaviour[J]. Géotechnique, 2015, 65: 995- 1009
[18]   MEIJER G, MUIR W, KNAPPETT J, et al Analysis of coupled axial and lateral deformation of roots in soil[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2019, 43 (3): 684- 707
doi: 10.1002/nag.2880
[19]   ZHANG X, KNAPPETT J, CIANTIA M, et al Root size effects on transverse root-soil interactions[J]. Computers and Geotechnics, 2024, 165: 105860
doi: 10.1016/j.compgeo.2023.105860
[20]   CROOK M , ENNOS A The anchorage mechanics of deep rooted larch, Larix europea×L. japonica[J]. Journal of Experimental Botany, 1996, 47 (10): 1509- 1517
[21]   REESE L, VAN I. Single piles and pile groups under lateral loading [M]. Boca Raton: CRC Press, 2000: 157–163.
[1] Shuaifei SUN,Jing WANG,Xiao MIAO,Daosheng LING. Numerical analysis of scale effects in model tests of strain localization failure[J]. Journal of ZheJiang University (Engineering Science), 2026, 60(2): 435-444.
[2] Chuanxiang ZHENG,Yuchen DAI,Shuang WEI,Jiaming YAN,Wei HUANG. Experimental study on temperature control of scaled model of ultra-large geotechnical centrifuge based on helium replacement[J]. Journal of ZheJiang University (Engineering Science), 2024, 58(10): 2096-2103.
[3] You-jun XU,Yue-kui PANG,Chao ZHANG,Jia-wang KANG,Zheng-dong HUANG. Shear performance of F-type socket joint in rectangular pipe jacking tunnel[J]. Journal of ZheJiang University (Engineering Science), 2023, 57(5): 957-966.
[4] Tian-hao ZHAO,Jian-jing ZHENG,Jing-hua LING,Chang-yu SHI,Dao-sheng LING. Buoyancy and motion of objects in fluid in centrifugal hypergravity environment[J]. Journal of ZheJiang University (Engineering Science), 2023, 57(1): 81-91.
[5] Jia MENG,Jun-chao LI,Yun-min CHEN. Strain-hardening mechanism and applicability in hypergravity simulation of municipal solid waste[J]. Journal of ZheJiang University (Engineering Science), 2022, 56(4): 664-673.
[6] Xiao ZHANG,Hao YU,Zhuang LI,Yan-shun LIU,Zi-dong ZHANG,Xin-yu JI,Xiang-hui LI. Discrete element study on effect of cyclic loading strengthening on meso-destruction of granite[J]. Journal of ZheJiang University (Engineering Science), 2022, 56(11): 2303-2312.
[7] Yu ZHAO,Sheng CHANG,Jian-jing ZHENG,Dao-sheng LING,Teng LIANG. Analysis of raindrop trajectory in centrifuge-simulated hypergravity field[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(3): 491-499.
[8] ZHENG Ying-Ren, XU Gao, WANG Cheng, XIAO Jiang. Failure mechanism of tunnel and dividing line standard between shallow and deep bury[J]. Journal of ZheJiang University (Engineering Science), 2010, 44(10): 1851-1856.