Please wait a minute...
浙江大学学报(工学版)
浙江大学学报(工学版)  2021, Vol. 55 Issue (8): 1444-1452    DOI: 10.3785/j.issn.1008-973X.2021.08.005
土木工程、交通工程     
超固结土的蛋形弹塑性本构模型
蒋佳琪1,2(),徐日庆1,2,*(),裘志坚3,詹晓波4,汪悦4,成广谋3
1. 浙江大学 滨海和城市岩土工程研究中心，浙江 杭州 310058
2. 浙江省城市地下空间开发工程技术研究中心，浙江 杭州 310058
3. 杭州市地铁集团有限责任公司，浙江 杭州 310020
4. 中天建设集团有限公司，浙江 杭州 310008
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
 全文: PDF(1311 KB)   HTML
摘要：

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    
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
收稿日期: 2020-07-28 出版日期: 2021-09-01
CLC:  TU 43  
基金资助: 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）
通讯作者: 徐日庆     E-mail: jiangjiaqi@zju.edu.cn;xurq@zju.edu.cn
作者简介: 蒋佳琪（1990—），男，博士生，从事软土本构理论研究. orcid.org/0000-0003-3375-416X. E-mail: jiangjiaqi@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　　
蒋佳琪
徐日庆
裘志坚
詹晓波
汪悦
成广谋

引用本文:

蒋佳琪,徐日庆,裘志坚,詹晓波,汪悦,成广谋. 超固结土的蛋形弹塑性本构模型[J]. 浙江大学学报(工学版), 2021, 55(8): 1444-1452.

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.

链接本文:

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

γw/（kN·m?3） w/% Gs wL/% wp/% Ip
18.6 42.7 2.73 45.6 24.7 20.9
表 1  土体基本物理力学性质
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）
表 2  应力路径三轴试验方案
图 1  超固结软土应力路径三轴压缩试验结果
图 2  超固结土三轴试验 $\varepsilon _{\rm{v}}^{\rm{p}} \!\!{\text{ - }}\!\! \varepsilon _{\rm{s}}^{\rm{p}}$关系曲线
图 3  超固结土的伏斯列夫线
图 4  旋转塑性势面示意图
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
表 3  剪缩条件下旋转角的计算值
图 5  剪缩条件下归一化旋转角与状态参数之间的关系
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
表 4  剪胀条件下旋转角的计算值
图 6  剪胀条件下归一化旋转角与状态参数之间的关系
图 7  等效硬化参数与应力比之间的对应关系
图 8  超固结土等效硬化参数与等效塑性功的关系
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
表 5  超固结土不同应力路径下硬化函数参数回归分析结果
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） ?
表 6  超固结土蛋形本构模型计算参数
图 9  不同应力路径下超固结台州黏土三轴压缩数值结果与试验数据比较
图 10  超固结Fujinomori黏土三轴压缩预测曲线与试验点比较
1 NADARAJAH V. Stress-strain properties of lightly over- consolidated clays[D]. Cambridge: University of Cambridge, 1973.
2 姚爱敏, 王运霞 正常固结土与超固结土主要力学特性的比较[J]. 北方工业大学学报, 2007, 19 (1): 86- 90
YAO Ai-min, WANG Yun-xia Comparison of characteristics between normal consolidated soil and over consolidated soil[J]. Journal of North China University of Technology, 2007, 19 (1): 86- 90
doi: 10.3969/j.issn.1001-5477.2007.01.019
3 孙德安, 陈立文, 甄文战 平面应变条件下水土耦合超固结黏土分叉分析[J]. 浙江大学学报: 工学版, 2010, 44 (10): 1938- 1943
SUN De-an, CHEN Li-wen, ZHEN Wen-zhan Bifurcation analysis of water-soil coupled overconsolidated clay under plane strain condition[J]. Journal of Zhejiang University: Engineering Science, 2010, 44 (10): 1938- 1943
doi: 10.3785/j.issn.1008-973X.2010.10.016
4 YASUFUKU N, NAKATA Y, HYODO M, et al. Two surface model for soils induced anisotropy[M]// Advances in Engineering Plasticity and Its Applications, 1993, 315-322.
5 ZHANG Z C A thermodynamics-based theory for the thermo-poro-mechanical modeling of saturated clay[J]. International Journal of Plasticity, 2017, 92: 164- 185
doi: 10.1016/j.ijplas.2017.03.007
6 胡小荣, 董肖龙, 陈晓宇, 等 超固结饱和黏性土的弹塑性本构模型及三轴试验模拟[J]. 应用力学学报, 2018, 35 (1): 28- 35
HU Xiao-rong, DONG Xiao-long, CHEN Xiao-yu, et al The elasto-plastic constitutive model and tri-axial numerical simulation for saturated over-consolidated clay[J]. Chinese Journal of Applied Mechanics, 2018, 35 (1): 28- 35
7 QIU Z J, ELGAMAL A Three-dimensional modeling of strain-softening soil response for seismic-loading applications[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2020, 146 (7): 04020053
doi: 10.1061/(ASCE)GT.1943-5606.0002282
8 PENDER M J A model for the behaviour of over-consolidated soil[J]. Géotechnique, 1978, 28 (1): 1- 25
doi: 10.1680/geot.1978.28.1.1
9 沈珠江, 邓刚 超固结黏土的二元介质模型[J]. 岩土力学, 2003, 24 (4): 495- 499
SHEN Zhu-jiang, DENG Gang Binary-medium model for over-consolidated clays[J]. Rock and Soil Mechanics, 2003, 24 (4): 495- 499
doi: 10.3969/j.issn.1000-7598.2003.04.001
10 NAKAI T, HINOKIO M A simple elastoplastic model for normally and over consolidated soils with unified material parameters[J]. Soils and Foundations, 2004, 44 (2): 53- 70
doi: 10.3208/sandf.44.2_53
11 徐连民, 祁得庆, 高云开 用修正剑桥模型研究超固结土的变形特性[J]. 水利学报, 2008, 39 (3): 313- 317
XU Lian-min, QI De-qing, GAO Yun-kai Study on characteristics of over-consolidated soils with modified Cam clay model[J]. Journal of Hydraulic Engineering, 2008, 39 (3): 313- 317
doi: 10.3321/j.issn:0559-9350.2008.03.009
12 姚仰平, 侯伟, 周安楠 基于Hvorslev面的超固结土本构模型[J]. 中国科学: 技术科学, 2007, 37 (11): 1417- 1429
YAO Yang-ping, HOU Wei, ZHOU An-nan A over consolidated clay constitutive model based on Hvorslev envelope[J]. Scientia Sinica Technologica, 2007, 37 (11): 1417- 1429
13 姚仰平, 李自强, 侯伟, 等 基于改进伏斯列夫线的超固结土本构模型[J]. 水利学报, 2008, 39 (11): 1244- 1250
YAO Yang-ping, LI Zi-qiang, HOU Wei, et al Constitutive model of over-consolidated clay based on improved Hvorslev envelope[J]. Journal of Hydraulic Engineering, 2008, 39 (11): 1244- 1250
doi: 10.3321/j.issn:0559-9350.2008.11.013
14 YAO Y P, HOU W, ZHOU A N UH model: three-dimensional unified hardening model for overconsolidated clays[J]. Géotechnique, 2009, 59 (5): 451- 469
doi: 10.1680/geot.2007.00029
15 孔令明, 姚仰平 超固结土热黏弹塑性本构关系[J]. 岩土力学, 2015, 36 (增1): 1- 8
KONG Ling-ming, YAO Yang-ping Thermo-visco-elastoplastic constitutive relation for overconsolidated clay[J]. Rock and Soil Mechanics, 2015, 36 (增1): 1- 8
16 王秋生, 周济兵 基于广义热力学的超固结土本构模型[J]. 岩土力学, 2019, 40 (11): 4178- 4193
WANG Qiu-sheng, ZHOU Ji-bing Generalized thermo- dynamics based constitutive model for over-consolidated clays[J]. Rock and Soil Mechanics, 2019, 40 (11): 4178- 4193
17 HENKEL D J The effect of overconsolidation on the behaviour of clays during shear[J]. Géotechnique, 1956, 6 (4): 139- 150
18 SHIMIZU M Effect of overconsolidation on dilatancy of a cohesive soil[J]. Soils and Foundations, 1982, 22 (4): 121- 135
doi: 10.3208/sandf1972.22.4_121
19 HATTAB M, HICHER P Y Dilating behaviour of overconsolidated clay[J]. Soils and Foundations, 2004, 44 (4): 27- 40
doi: 10.3208/sandf.44.4_27
20 GAO Z W, ZHAO J D, YIN Z Y Dilatancy relation for overconsolidated clay[J]. International Journal of Geomechanics, 2017, 17 (5): 06016035
doi: 10.1061/(ASCE)GM.1943-5622.0000793
21 姚仰平 UH模型系列研究[J]. 岩土工程学报, 2015, 37 (2): 193- 217
YAO Yang-ping Advanced UH models for soils[J]. Chinese Journal of Geotechnical Engineering, 2015, 37 (2): 193- 217
doi: 10.11779/CJGE201502001
22 徐日庆, 蒋佳琪, 冯苏阳, 等 一种旋转塑性势面模型及非关联塑性流动法则[J]. 岩土力学, 2020, 41 (5): 1474- 1482
XU Ri-qing, JIANG Jia-qi, FENG Su-yang, et al A rotational plastic potential model and non-associated plastic flow rule[J]. Rock and Soil Mechanics, 2020, 41 (5): 1474- 1482
23 GUO R P, LI G X Elasto-plastic constitutive model for geotechnical materials with strain-softening behaviour[J]. Computers and Geosciences, 2008, 34 (1): 14- 23
doi: 10.1016/j.cageo.2007.03.012
24 任放, 盛谦, 常燕庭 岩土类工程材料的蛋形屈服函数[J]. 岩土工程学报, 1993, 15 (4): 33- 39
REN Fang, SHENG Qian, CHANG Yan-ting Egg shaped yield function for geotechnical engineering materials[J]. Chinese Journal of Geotechnical Engineering, 1993, 15 (4): 33- 39
doi: 10.3321/j.issn:1000-4548.1993.04.005
25 彭芳乐, 白晓宇, 亚辛, 等 砂土应力路径不相关的修正塑性功硬化参量与函数[J]. 岩石力学与工程学报, 2008, 27 (6): 1171- 1180
PENG Fang-le, BAI Xiao-yu, YASIN S J M, et al Modified plastic-work hardening parameter and function independent of stress path for sandy soil[J]. Chinese Journal of Rock Mechanics and Engineering, 2008, 27 (6): 1171- 1180
doi: 10.3321/j.issn:1000-6915.2008.06.010
26 MOROTO N. Shearing deformation of granular materials such as sand[R]. Hachinohe: Department of Civil Engineering, Hachinohe Institute of Technology, 1980.
27 曾军军, 卢廷浩 考虑土体结构性的弹塑性软化模型[J]. 岩土力学, 2007, 28 (6): 1901- 1904
ZENG Jun-jun, LU Ting-hao An elastoplastic softening model of structured soil[J]. Rock and Soil Mechanics, 2007, 28 (6): 1901- 1904
[1] 胡成宝, 凌道盛, 巩师林, 石吉森, 韩超, 丁志锋. 基于砂土状态和细观特征的剪切带倾角公式[J]. 浙江大学学报(工学版), 2018, 52(11): 2068-2076.
[2] 蔡袁强 陈静 王军. 循环荷载下各向异性软黏土应变-软化模型[J]. J4, 2008, 42(6): 1058-1064.
[3] 胡士兵 王金昌 朱向荣. 线性软化土体中球孔扩张问题的解析解[J]. J4, 2007, 41(9): 1503-1507.