|
|
|
| Fractional non-orthogonal elastoplastic constitutive model for structured clay with interparticle bonding |
| LI Xuancong1, 2, WENG Xiaolin1, 2*, ZHAO Jianchong3, YUAN Weijun4, YU Bangyou1, 2, LI Nannan1, 2 |
(1. Key Laboratory for Special Area Highway Engineering of Ministry of Education, Chang?an University, Xi?an, Shaanxi 710064, China; 2. School of Highway, Chang?an University, Xi?an, Shaanxi 710064, China; 3. CCCC First Highway Engineering
Group Co., Ltd., Beijing 100024, China; 4. Henan Jiaotou Zhongyuan Expressway Zheng-Luo Construction Co., Ltd.,
Zhengzhou, Henan 450003, China) |
|
|
|
|
Abstract Accurate prediction of shear behavior in structured soils is crucial for geotechnical engineering design and construction. Existing research indicates that the initial structure during shearing often does not completely deteriorate, preventing the critical state line from returning to that of the reconstituted state in the void ratio-stress plane. To address this characteristic, a fractional non-orthogonal elastoplastic constitutive model for structured clay with interparticle bonding has been developed. By introducing parameters that describe critical state properties and combining them with the evolution law of structural state variables, a state-dependent yield surface evolution equation is established. Utilizing fractional calculus theory, the non-orthogonal gradient is derived by directly solving the fractional derivative of the yield surface, which determines the direction of plastic flow. The sub-loading surface theory is incorporated to account for the influence of stress history while facilitating smooth transitions in stress-strain relationships. The relationship between equivalent yield stress and structural state variables is established through isotropic compression behavior, thereby constructing a comprehensive constitutive framework. In this model, the yield surface shape, fractional order, and structural state variables are interconnected, allowing for dynamic adjustments of the plastic flow direction as structural degradation occurs. The model comprises ten parameters, all of which can be determined through conventional geotechnical tests. The model?s validity is verified through parametric sensitivity analysis and comparisons with test results from Corinth marl, Wenzhou marine clay, and Osaka clay. Results demonstrate that the model effectively captures the nonlinear compression characteristics, deviatoric stress peak strength, and volumetric deformation behavior of soils. Compared to the associated flow rule, the model exhibits superior applicability in predicting the mechanical response of structured clays, particularly showing advantages in peak strength and volumetric deformation predictions.
|
|
|
|
|
|
[1] 刘建国. 地铁黄土地层中盾构隧道地表沉降控制技术研究[J]. 公路工程，2016，41(3)：141–146.(LIU Jianguo. Control technology in loess strata metro shield tunnel surface settlement[J]. Highway Engineering，2016，41(3)：141–146.(in Chinese))
[2] 邵嘉波，宋常军，徐凤银，等. 花岗岩残积土的室内外剪切特性对比[J]. 公路交通科技，2023，40(增1)：192–198.(SHAO Jiabo，SONG Changjun，XU Fengyin，et al. Shear property of granite residual soil based on laboratory and in-situ direct shear test[J]. Journal of Highway and Transportation Research and Development，2023，40(Supp.1)：192–198.(in Chinese))
[3] 柴少波，范康凯，赵 琅，等. 降雨对湿陷性黄土邻坡风电塔基桩–坡体系影响研究[J]. 公路工程，2025，50(3)：25–34.(CHAI Shaobo，FAN Kangkai，ZHAO Lang，et al. Study on the influence of rainfall on pile-slope system of wind turbine foundations adjacent to collapsible loess slopes[J]. Highway Engineering，2025，50(3)：25–34.(in Chinese))
[4] YANG J D，LI X A，LI L C，et al. Formation mechanism of metastable internal support microstructure in Malan Loess and its implications for collapsibility[J]. Engineering Geology，2025，346：107892.
[5] 朱 楠，诸葛爱军，喻志发，等. 湿地湖泊相黏土胶结结构性与各向异性本构模型[J]. 哈尔滨工业大学学报，2025，57(3)：160–170. (ZHU Nan，ZHUGE Aijun，YU Zhifa，et al. A structured and anisotropic constitutive model considering bonding for marshy-lacustrine clay[J]. Journal of Harbin Institute of Technology，2025，57(3)：160–170.(in Chinese))
[6] BALASUBRAMANIAM A S，HWANG Z M. Yielding of weathered Bangkok clay[J]. Soils and Foundations，1980，20(2)：1–15.
[7] 温 博，翁效林，侯乐乐，等. 湿陷性黄土的一维压缩模型及其应用[J]. 建筑科学与工程学报，2025，42(2)：190–200.(WEN Bo，WENG Xiaolin，HOU Lele，et al. One-dimensional compression model of collapsible loess and its application [J]. Journal of Architecture and Civil Engineering，2025，42(2)：190–200.(in Chinese))
[8] ROUAINIA M，MUIR WOOD D. A kinematic hardening constitutive model for natural clays with loss of structure[J]. Géotechnique，2000，50(2)：153–164.
[9] 李杭州，张志龙，廖红建，等. 结构性土的三维修正剑桥模型研究[J]. 岩土工程学报，2022，44(增1)：12–16.(LI Hangzhou，ZHANG Zhilong，LIAO Hongjian，et al. Three-dimensional modified Cam-clay model for structured soils[J]. Chinese Journal of Geotechnical Engineering，2022，44(Supp.1)：12–16.(in Chinese))
[10] ADACHI T，OKA F，HIRATA T，et al. Stress-strain behavior and yielding characteristics of Eastern Osaka clay[J]. Soils and Foundations，1995，35(3)：1–13.
[11] LIU W H，LI W G，SUN X L. New approach to interpret the mechanical behavior of structured soils[J]. International Journal of Geomechanics，2021，21(2)：06020040.
[12] NAVARRO V，ALONSO J，CALVO B，et al. A constitutive model for porous rock including effects of bond strength degradation and partial saturation[J]. International Journal of Rock Mechanics and Mining Sciences，2010，47(8)：1 330–1 338.
[13] OURIA A. Disturbed state concept-based constitutive model for structured soils[J]. International Journal of Geomechanics，2017，17(7)：04017008.
[14] RAHIMI M，CHAN D，NOURI A. Bounding surface constitutive model for cemented sand under monotonic loading[J]. International Journal of Geomechanics，2016，16(2)：04015049.
[15] KANG X S，LIAO H J. Bounding surface plasticity model for jointed soft rocks considering overconsolidation and structural decay[J]. Computers and Geotechnics，2019，108：295–307.
[16] YANG C，CARTER J P，SHENG D C. Description of compression behaviour of structured soils and its application[J]. Canadian Geotechnical Journal，2014，51(8)：921–933.
[17] SUEBSUK J，HORPIBULSUK S，LIU M D. A critical state model for overconsolidated structured clays[J]. Computers and Geotechnics，2011，38(5)：648–658.
[18] ZHOU C，NG C W W. A new thermo-mechanical model for structured soil[J]. Géotechnique，2018，68(12)：1 109–1 115.
[19] HASHIGUCHI K. Subloading surface model in unconventional plasticity[J]. International Journal of Solids and Structures，1989，25(8)：917–945.
[20] DAFALIAS Y F. Bounding surface plasticity. I：Mathematical foundation and hypoplasticity[J]. Journal of Engineering Mechanics，1986，112(9)：966–987.
[21] MCDOWELL G R. A family of yield loci based on micromechanics[J]. Soils and Foundations，2000，40(6)：133–137.
[22] SUEBSUK J，HORPIBULSUK S，LIU M D. Modified structured Cam Clay：A generalised critical state model for destructured，naturally structured and artificially structured clays[J]. Computers and Geotechnics，2010，37(7/8)：956–968.
[23] LIU M D，CARTER J P. A structured Cam Clay model[J]. Canadian Geotechnical Journal，2002，39(6)：1 313–1 332.
[24] NGUYEN L D，FATAHI B，KHABBAZ H. A constitutive model for cemented clays capturing cementation degradation[J]. International Journal of Plasticity，2014，56：1–18.
[25] SUMELKA W. A note on non-associated Drucker-Prager plastic flow in terms of fractional calculus [J]. Journal of Theoretical and Applied Mechanics，2014，52(2)：571–574.
[26] SUMELKA W. Application of fractional continuum mechanics to rate independent plasticity[J]. Acta Mechanica，2014，225(11)：3 247– 3 264.
[27] SUN Y F，GAO Y F，ZHU Q Z. Fractional order plasticity modelling of state-dependent behaviour of granular soils without using plastic potential[J]. International Journal of Plasticity，2018，102：53–69.
[28] LIANG J Y，LU D C，DU X L，et al. Non-orthogonal elastoplastic constitutive model for sand with dilatancy[J]. Computers and Geotechnics，2020，118：103329.
[29] LU D C，LIANG J Y，DU X L，et al. Fractional elastoplastic constitutive model for soils based on a novel 3D fractional plastic flow rule[J]. Computers and Geotechnics，2019，105：277–290.
[30] WANG G，LI Z，LIANG J，et al. A state-dependent non-orthogonal elastoplastic constitutive model for sand[J]. Computers and Geotechnics，2024，166：105960.
[31] 梁靖宇，杜修力，路德春，等. 特征应力空间中土的分数阶临界状态模型[J]. 岩土工程学报，2019，41(3)：581–587.(LIANG Jingyu，DU Xiuli，LU Dechun，et al. Fractional-order critical state model for soils in characteristic stress space[J]. Chinese Journal of Geotechnical Engineering，2019，41(3)：581–587.(in Chinese))
[32] 梁靖宇，齐吉琳，张跃东，等. 考虑温度与围压影响的冻结砂土非正交弹塑性本构模型[J]. 岩土工程学报，2024，46(9)：1 889–1 898. (LIANG Jingyu，QI Jilin，ZHANG Yuedong，et al. Non-orthogonal elastoplastic model for frozen sand incorporating effects of temperature and confining pressure[J]. Chinese Journal of Geotechnical Engineering，2024，46(9)：1 889–1 898.(in Chinese))
[33] LIANG J Y，LU D C，ZHOU X，et al. Non-orthogonal elastoplastic constitutive model with the critical state for clay[J]. Computers and Geotechnics，2019，116：103200.
[34] LI X Q，LU D C，LIN Q T，et al. A hydro-mechanical constitutive model for unsaturated soils over a wide saturation range[J]. Computers and Geotechnics，2023，159：105475.
[35] BURLAND J B. On the compressibility and shear strength of natural clays[J]. Géotechnique，1990，40(3)：329–378.
[36] BAUDET B，STALLEBRASS S. A constitutive model for structured clays[J]. Géotechnique，2004，54(4)：269–278.
[37] MENG F Y，CHEN R P，KANG X，et al. e-p curve-based structural parameter for assessing clayey soil structure disturbance[J]. Bulletin of Engineering Geology and the Environment，2020，79(8)：4 387–4 398.
[38] YAN W M，LI X S. A model for natural soil with bonds[J]. Géotechnique，2011，61(2)：95–106.
[39] XU L，GUAN X Q，LIAO H J，et al. A strain work constitutive model for structured soils[J]. Computers and Geotechnics，2025，184：107243.
[40] GARAKANI A A，HAERI S M，DESAI C S，et al. Testing and constitutive modeling of lime-stabilized collapsible loess. II：Modeling and validations[J]. International Journal of Geomechanics，2019，19(4)：04019007.
[41] ALI RAHMAN Z，TOLL D G，GALLIPOLI D. Critical state behaviour of weakly bonded soil in drained state[J]. Geomechanics and Geoengineering，2018，13(4)：233–245.
[42] NOUGUIER-LEHON C，VINCENS E，CAMBOU B. Structural changes in granular materials：The case of irregular polygonal particles[J]. International Journal of Solids and Structures，2005，42(24/25)：6 356–6 375.
[43] FEARON R E，COOP M R. Reconstitution：what makes an appropriate reference material?[J]. Géotechnique，2000，50(4)：471–477.
[44] AMOROSI A，RAMPELLO S. An experimental investigation into the mechanical behaviour of a structured stiff clay[J]. Géotechnique，2007，57(2)：153–166.
[45] CRUZ N，RODRIGUES C，VIANA DA FONSECA A. The influence of cementation in the critical state behaviour of artificial bonded soils[M]. [S. l.]：IOS Press，2011：730–737.
[46] XU L，COOP M R. Influence of structure on the behavior of a saturated clayey loess[J]. Canadian Geotechnical Journal，2016，53(6)：1 026–1 037.
[47] ANAGNOSTOPOULOS A G，KALTEZIOTIS N，TSIAMBAOS G K，et al. Geotechnical properties of the Corinth Canal marls[J]. Geotechnical and Geological Engineering，1991，9：1–26.
[48] LI W G，LIU W H，YANG L L，et al. Structural parameter of structured soils and its application in constitutive modeling[J]. International Journal of Geomechanics，2024，24(1)：04023245.
[49] LIU W H，ZHANG H Y，LI W G，et al. An advanced critical state constitutive model for overconsolidated structured soils[J]. International Journal of Geomechanics，2022，22(5)：06022004.
[50] 祝恩阳，李晓强，朱建明. 三维胶结结构性土UH模型[J]. 岩土工程学报，2018，40(12)：2 200–2 207.(ZHU Enyang，LI Xiaoqiang，ZHU Jianming. Three-dimensional UH model for structured soils considering bonding[J]. Chinese Journal of Geotechnical Engineering，2018，40(12)：2 200–2 207.(in Chinese))
[51] CHEN B，SUN D A，HU Y S. Experimental study on strength characteristics and microscopic mechanism of marine soft clays[J]. Marine Georesources and Geotechnology，2020，38(5)：570–582. |
|
|
|
2026, Vol. 45 
