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
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.
Fig.1Test 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.3Hvorslev envelope for over-consolidated soils
Fig.4Schematic 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.3Calculated value of rotation angle under volume contraction
Fig.5Relationship 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.4Calculated value of rotation angle under volume expansion
Fig.6Relationship between normalized rotation angle and state parameter under volume expansion
Fig.7Correspondence between equivalent hardening parameter and stress ratio
Fig.8Relationship 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.5Regression 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.6Parameters used in numerical simulation by egg-shaped constitutive model for over-consolidated clay
Fig.9Comparison between test data and numerical results of triaxial compression test on over-consolidated Taizhou clay under different stress paths
Fig.10Comparison between test data and model prediction of triaxial compression test on over-consolidated Fujinomori clay
[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
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
