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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2021, Vol. 55 Issue (8): 1444-1452    DOI: 10.3785/j.issn.1008-973X.2021.08.005
    
Egg-shaped elasto-plastic constitutive modeling for over-consolidated clay
Jia-qi JIANG1,2(),Ri-qing XU1,2,*(),Zhi-jian QIU3,Xiao-bo ZHAN4,Yue WANG4,Guang-mou CHENG3
1. Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China
2. Engineering Research Center of Urban Underground Space Development of Zhejiang Province, Hangzhou 310058, China
3. Hangzhou Metro Group Co. Ltd, Hangzhou 310020, China
4. Zhongtian Construction Group Co. Ltd, Hangzhou 310008, China
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Abstract  

An elasto-plastic constitutive model suitable for over-consolidated clay was established within the framework of egg-shaped function, to describe the strength and deformation characteristics of over-consolidated soft clay under different stress conditions. Firstly, the development of plastic strain (dilatancy or contraction) for clay under over-consolidation state was analyzed according to the test results from a series of stress path triaxial compression test. Meanwhile, the previously proposed rotational plastic potential flow rule was developed to meet the plastic deformation characteristics of over-consolidated soils by introducing the peak stress ratio and constructing approximate linear dependence between the normalized plastic potential rotational angle and the stress state parameter under dilatancy. Then the egg-shaped elasto-plastic constitutive model for over-consolidated clay was be well established by introducing a generalized plastic work hardening principle in which the equivalent hardening parameter was employed. Finally, the validity of this model was demonstrated by comparison between test data and model prediction of triaxial compression test. Results show that the proposed model can effectively reflect the stress-strain characteristics of over-consolidated clay under different loading conditions, such as softening and dilatancy.

Key words： over-consolidated soft clay      strain softening      dilatancy      egg-shaped constitutive modeling      rotational plastic potential surface      generalized hardening principle     
Received: 28 July 2020      Published: 01 September 2021
CLC:  TU 43  
Fund:  国家自然科学基金资助项目（41672264）；浙江省重点研发计划资助项目（2019C03103）
Corresponding Authors: Ri-qing XU     E-mail: jiangjiaqi@zju.edu.cn;xurq@zju.edu.cn
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Jia-qi JIANG
Ri-qing XU
Zhi-jian QIU
Xiao-bo ZHAN
Yue WANG
Guang-mou CHENG
Cite this article:

Jia-qi JIANG,Ri-qing XU,Zhi-jian QIU,Xiao-bo ZHAN,Yue WANG,Guang-mou CHENG. Egg-shaped elasto-plastic constitutive modeling for over-consolidated clay. Journal of ZheJiang University (Engineering Science), 2021, 55(8): 1444-1452.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2021.08.005     OR     https://www.zjujournals.com/eng/Y2021/V55/I8/1444


超固结土的蛋形弹塑性本构模型

为了描述超固结软土在不同应力条件下的强度变形特征，以蛋形函数为基本框架，建立并发展适用于超固结土体的弹塑性本构模型. 通过对一系列超固结土应力路径三轴压缩试验结果的分析，探讨土体在超固结状态下塑性应变的发展规律(剪胀/剪缩). 在先前提出的旋转塑性势面流动法则基础上对其进行发展与改进，引入峰值应力比，构建剪胀状态下归一化塑性势面旋转角与应力状态参数之间的近似线性关系，以满足超固结土的塑性变形特性. 结合基于等效硬化参量的广义塑性功硬化原理构建超固结软土的蛋形弹塑性本构模型. 将三轴压缩试验数据与数值预测结果进行对比以验证模型有效性，结果表明该模型可以有效反映超固结软土在不同加载条件下的应力应变特性，比如软化与剪胀.


关键词： 超固结软土,  应变软化,  剪胀,  蛋形本构模型,  旋转塑性势面,  广义硬化原理 
γw/（kN·m?3） w/% Gs wL/% wp/% Ip
18.6 42.7 2.73 45.6 24.7 20.9
Tab.1 Physical and mechanical properties of soil
试样编号 p0 / kPa OCR ?η
1-1/1-2/1-3 75 2 ?1.5（RTC）/∞（CMS）/3（CTC）
1-5/1-6 4 ∞（CMS）/3（CTC）
2-1/2-2/2-3 150 2 ?1.5（RTC）/∞（CMS）/3（CTC）
2-4/2-5/2-6 4 ?1.5（RTC）/∞（CMS）/3（CTC）
3-1/3-2/3-3 400 2 ?1.5（RTC）/∞（CMS）/3（CTC）
3-4/3-5/3-6 4 ?1.5（RTC）/∞（CMS）/3（CTC）
Tab.2 Test scheme of stress path triaxial test
Fig.1 Test results of stress path triaxial compression for over-consolidated soft soil
Fig.2  $\varepsilon _{\rm{v}}^{\rm{p}} \!\!{\text{ - }} \!\!\varepsilon _{\rm{s}}^{\rm{p}}$ relationship of triaxial tests for over-consolidated clay
Fig.3 Hvorslev envelope for over-consolidated soils
Fig.4 Schematic diagram of rotational plastic potential surface
试样1-3 试样2-3 试样3-3
${v^{\rm{p}}}$ $\gamma $ ${v^{\rm{p}}}$ $\gamma $ ${v^{\rm{p}}}$ $\gamma $
0.556 ?24.9 0.596 ?24.0 0.551 ?21.4
0.486 ?42.4 0.524 ?40.6 0.490 ?29.1
0.432 ?46.8 0.449 ?43.3 0.432 ?34.6
0.381 ?52.1 0.391 ?46.2 0.378 ?36.0
0.286 ?56.8 0.295 ?51.4 0.292 ?47.4
0.208 ?60.9 0.221 ?55.3 0.218 ?42.1
0.146 ?63.1 0.163 ?58.9 0.187 ?42.5
0.118 ?63.1 0.137 ?58.7 0.135 ?43.3
0.056 ?65.0 0.098 ?59.7 0.093 ?43.1
0.033 ?65.8 0.068 ?61.1 0.060 ?44.2
Tab.3 Calculated value of rotation angle under volume contraction
Fig.5 Relationship between normalized rotation angle and state parameter under volume contraction
试样2-1 试样2-4 试样3-1 试样3-4
${v^{\rm{p}}}$ $\gamma $ ${v^{\rm{p}}}$ $\gamma $ ${v^{\rm{p}}}$ $\gamma $ ${v^{\rm{p}}}$ $\gamma $
?0.698 2.94 ?0.656 6.19 ?0.321 20.83 ?0.531 11.28
?0.620 6.75 ?0.482 13.83 ?0.290 22.71 ?0.506 12.72
?0.525 11.24 ?0.406 17.76 ?0.276 23.60 ?0.472 14.52
?0.446 15.06 ?0.318 22.32 ?0.233 26.22 ?0.442 16.17
?0.399 17.62 ?0.278 25.00 ?0.195 28.48 ?0.395 18.73
?0.331 21.15 ?0.216 30.52 ?0.171 29.95 ?0.327 22.60
?0.262 25.00 ?0.174 37.86 ?0.141 31.82 ?0.276 25.68
?0.217 27.79 ?0.131 37.95 ?0.123 32.94 ?0.205 30.28
?0.153 32.19 ?0.094 40.40 ?0.102 34.28 ?0.105 37.29
?0.086 35.85 ?0.036 40.62 ?0.076 35.84 ?0.046 41.38
Tab.4 Calculated value of rotation angle under volume expansion
Fig.6 Relationship between normalized rotation angle and state parameter under volume expansion
Fig.7 Correspondence between equivalent hardening parameter and stress ratio
Fig.8 Relationship between equivalent hardening parameter and equivalent plastic work for over-consolidated soils
η0 $\chi / 10^{-2}$ η0 $\chi / 10^{-2}$
1.027 0.811 1.315 0.431
0.876 3.099 1.076 0.732
0.744 7.783 0.968 2.020
Tab.5 Regression results of parameter in hardening function for over-consolidated soils under different stress paths
土体类型 a b α k1 k2 k3 Mh Mc χ0 C
台州 1.08 0.49 0.67 1.15 0.75 2.1 1.26 1.33 12.5 6.83
Fujinomori 1.00 0.58 0.68 1.45 0.48 1.8 1.14 1.42 13.4（χ） ?
Tab.6 Parameters used in numerical simulation by egg-shaped constitutive model for over-consolidated clay
Fig.9 Comparison between test data and numerical results of triaxial compression test on over-consolidated Taizhou clay under different stress paths
Fig.10 Comparison between test data and model prediction of triaxial compression test on over-consolidated Fujinomori clay
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