适用于黏土的分数阶应力诱导剪胀方程

李海潮; 马博; 张升; 盛岱超

doi:10.6052/j.issn.1000-4750.2019.12.0777

适用于黏土的分数阶应力诱导剪胀方程

李海潮^1,,
马博^1,,
张升^{1, 2, ,},
盛岱超^3,

1.
中南大学土木工程学院，湖南，长沙 410075
2.
高速铁路建造技术国家工程实验室，湖南，长沙 410075
3.
悉尼科技大学土木与环境工程学院，澳大利亚，悉尼 NSW 2007

基金项目: 国家自然科学基金优秀青年科学基金项目(51722812)；湖湘高层次人才聚集工程项目(2018RS3016)；中南大学研究生科研创新项目(1053320170586)

详细信息

作者简介:
李海潮(1991−)，男，湖北人，博士生，主要从事土体本构关系方面的研究(E-mail: haichao821@outlook.com)

马　博(1993−)，男，湖南人，博士生，主要从事土体本构关系方面的研究(E-mail: mabo19@csu.edu.cn)

盛岱超(1965−)，男，湖南人，教授，博士，主要从事土体本构关系方面的研究(E-mail: daichao.sheng@gmail.com)

通讯作者:
张　升(1979−)，男，湖南人，教授，博士，博导，主要从事土体本构关系方面的研究 (E-mail: zhang-sheng@csu.edu.cn)

中图分类号: TU43
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出版历程
- 收稿日期: 2019-12-22
- 修回日期: 2020-07-05
- 网络出版日期: 2020-08-23
- 刊出日期: 2020-11-24

A STRESS-INDUCED FRACTIONAL DILATANCY RULE FOR CLAYS

LI Hai-chao^1,,
MA Bo^1,,
ZHANG Sheng^{1, 2, ,},
SHENG Dai-chao^3,

1.
School of Civil Engineering, Central South University, Changsha, Hunan 410075, China
2.
National Engineering Laboratory for High Speed Railway Construction, Changsha, Hunan 410075, China
3.
School of Civil & Environmental Engineering, University of Technology Sydney, Sydney NSW 2007, Australia

摘要

摘要: 建立了适用于黏性土的分数阶下加载面模型，该模型所采用的分数阶塑性流动法则能够在不引入塑性势函数的情况考虑塑性流动方向与土体物理屈服面之间的非正交特性，进而统一地描述相关联和非相关联塑性流动法则。基于该流动法则可以得到一个新的应力诱导分数阶剪胀方程以考虑超固结比对黏性土剪胀特性的影响。理论分析结果表明，在相同的应力水平下，土体剪胀量会随着超固结比增大而逐渐减小。相比较修正剑桥模型，该文模型仅额外地引入一个与土体剪胀特性相关的模型参数，并且能够对超固结黏土的应变软化和剪胀特性进行合理的描述。模型计算结果与试验结果对比分析结果表明，该文模型能够准确地描述黏性土在超固结状态下的应力-应变响应和剪胀特性。
- 分数阶微分 /
- 剪胀特性 /
- 下加载面 /
- 超固结比 /
- 连续方程
Abstract: A fractional sub-loading surface model for clays is developed in the present study. The fractional plastic flow rule adopted in the proposed model is able to account for the non-normality of the flow direction with respect to the yield locus without introducing a plastic potential. Hence, a unified description of the associated and non-associated plastic flow rules is achieved. A stress-induced fractional dilatancy rule can be conveniently derived through the fractional plastic flow rule to consider the effect of the over-consolidation ratio on the dilatancy of clays. The analysis shows that increasing the over-consolidation ratio will reduce the dilatancy under a constant loading pressure. Compared with the modified Cam-clay model, the proposed model introduces only one extra dilatancy-related parameter and can describe the strain-softening and dilatancy features of over-consolidated clays. Model predictions show good agreement with the experimental results, indicating the capability of the proposed model in describing the behavior of clays.
- fractional derivative /
- stress-dilatancy /
- sub-loading surface /
- over consolidation /
- constitutive equations

HTML全文

图 1 分数阶流动法则示意图

Figure 1. Schematic plot of fractional flow rule

下载: 全尺寸图片幻灯片

图 2 下加载面示意图

Figure 2. Schematic plot of sub-loading surface

下载: 全尺寸图片幻灯片

图 3 剪胀因子d随剪应力比 $\eta$ 和相似因子R变化规律

Figure 3. Evolution of dilatancy ratio d with shear stress ratio $\eta$ and similarity ratio R

下载: 全尺寸图片幻灯片

图 4 参数m三轴压缩排水试验模型计算结果的影响

Figure 4. Effect of parameter m on drained triaxial test model predictions

下载: 全尺寸图片幻灯片

图 5 参数m三轴压缩不排水试验模型计算结果的影响

Figure 5. Effect of parameter m on undrained triaxial test model predictions

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图 6 Black Kaolin黏土试验结果与模型计算结果对比

Figure 6. Comparison between experimental data and model predictions of Black Kaolin clay

下载: 全尺寸图片幻灯片

图 7 Fujinomori黏土试验结果与模型计算结果对比

Figure 7. Comparison between experimental data and model predictions of Fujinomori clay

下载: 全尺寸图片幻灯片

表 1 模型参数敏感性试验材料参数

Table 1 Parameters used in model sensitive analysis

参数名称	参数取值
参考临界状态孔隙比 ${e_\Gamma }$	1.23
初始孔隙比 ${e_0}$	0.83
泊松比ν	0.2
临界状态剪应力比M	0.94
压缩模量λ	0.093
回弹模量κ	0.02
剪胀特性相关模型参数m	0.0、0.3、0.6和0.9

下载: 导出CSV

表 2 模型参数敏感性试验材料参数

Table 2 Parameters used in model sensitive analysis

土体名称	参考临界状态孔隙比 ${e_\Gamma }$	泊松比ν	临界状态剪应力比M	压缩模量λ	回弹模量κ	剪胀特性相关模型参数m
Black Kaolin 黏土	1.65	0.2	0.83	0.244	0.079	0.2
Fujinomori 黏土	1.23	0.2	1.36	0.093	0.020	0.9

下载: 导出CSV

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