非饱和黄土中椭球形扩孔问题弹塑性解析

党星海; 周鹏; 钞鑫; 郭启明; 吴润霖

doi:10.21656/1000-0887.400186

非饱和黄土中椭球形扩孔问题弹塑性解析

doi: 10.21656/1000-0887.400186

党星海^1,2,
周鹏^1,2,
钞鑫²,
郭启明²,
吴润霖²

¹西部土木工程防灾减灾教育部工程研究中心, 兰州 730050;²兰州理工大学甘肃省土木工程防灾减灾重点实验室, 兰州 730050

基金项目: 国家自然科学基金（51468040）

详细信息

作者简介:
党星海（1972—），男，教授，硕士生导师(通讯作者. E-mail: 245515697@qq.com).

中图分类号: TU444
计量
- 文章访问数: 771
- HTML全文浏览量: 170
- PDF下载量: 213
- 被引次数: 0
出版历程
- 收稿日期: 2019-06-12
- 修回日期: 2020-01-07
- 刊出日期: 2020-09-01

Elastoplastic Analysis of Ellipsoidal Hole Expansion in Unsaturated Loess

¹Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou 730050, P.R.China;²Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province, Lanzhou University of Technology, Lanzhou 730050, P.R.China

Funds: The National Natural Science Foundation of China（51468040）

摘要

摘要: 在非饱和土统一强度准则中引入非饱和原状黄土黏聚力与基质吸力拟合公式，采用改变孔型系数k的方法并结合边界条件、平衡方程及应力协调方程，推导了排水与不排水条件下椭球形扩孔在ξ平面内的弹性区与塑性区应力-应变场、塑性区半径及极限扩孔压力的解析解，并利用MATLAB软件分析了基质吸力、强度准则和剪胀对解析解的影响.结果表明：不同排水条件下非饱和黄土有效应力均随孔型系数k及基质吸力的增大而增大；当参数r/r_p一定时，在排水条件下，有效应变随剪胀系数h及基质吸力的增大而增大，且后者的影响程度更大；在同等条件下，b=1时双剪应力强度准则下的有效应力-应变均大于b=0时的Mohr-Coulomb强度准则.
- 非饱和黄土 /
- 统一强度准则 /
- 椭球形扩孔 /
- 排水条件 /
- 参数分析
Abstract: In the unified strength criterion for unsaturated soils, the formulae of cohesion of unsaturated undisturbed loess and matrix suction were introduced. The method of changing hole pattern coefficient k was combined with boundary conditions, equilibrium equations and stress compatibility equations to derive stress and strain solutions under drainage and undrained conditions. Analytical solutions of the stress and strain fields, the plastic zone radii and the limit hole expansion pressure in the elastic and plastic regions around the ellipsoid hole in the plane, and the influences of the matrix suction, the strength criterion and the dilatancy on the analytical solutions were discussed with the MATLAB software. The results show that, the effective stresses of unsaturated loess under different drainage conditions will increase with hole pattern coefficient k and the matrix suction; when the parameters are constant, the effective strain under the drainage condition will increase with dilatation coefficient h and even more with the matrix suction; with the same condition, the effective stress and strain under the double shear stress strength criterion for b=1 will be larger than those under the MC strength criterion for b=0.
- unsaturated loess /
- unified strength criterion /
- ellipsoidal hole expansion /
- drainage condition /
- parameter analysis

HTML全文

参考文献(21)

[1]	VESIC A S. Expansion of cavities in infinite soil mass[J]. Journal of the Soil Mechanics and Foundations Division,1972,〖STHZ〗 98(3): 265-290.
[2]	CARTER J P, BOOKER J R, YEUNG S K. Cavity expansion in cohesive frictional soils[J]. Géotechnique,1987,36(3): 349-358.
[3]	贾尚华, 赵春风, 赵程. 砂土中柱孔扩张问题的扩孔压力与扩孔半径分析[J]. 岩石力学与工程学报, 2015,34(1): 182-188.(JIA Shanghua, ZHAO Chunfeng, ZHAO Cheng. Analysis of expanded radius and internal expanding pressure of cylindrical hole[J]. Chinese Journal of Rock Mechanics and Engineering,2015,34(1): 182-188.(in Chinese))
[4]	VRAKAS A. Relationship between small and large strain solutions for general cavity expansion problems in elasto-plastic soils[J]. Computers & Geotechnics,2016,76: 147-153.
[5]	晁明颂, 高盟, 张继严, 等. 基于能量耗散的球孔扩张理论解答[J]. 岩土力学, 2016,〖STHZ〗 37(7): 1986-1993.(CHAO Mingsong, GAO Meng, ZHANG Jiyan, et al. An analytic solution for spherical cavity expansion based on energy dissipation theory[J]. Rock and Soil Mechanics,2016,37(7): 1986-1993.(in Chinese))
[6]	CHEN S L, ABOUSLEIMAN Y N. Cavity expansion in strain hardening frictional soils under drained condition[J]. International Journal for Numerical & Analytical Methods in Geomechanics,2017, 42(1): 132-142.
[7]	梅毕祥, 杨敏, 贾尚华. 基于摩尔库伦准则考虑渗流影响的孔扩张理论[J]. 同济大学学报(自然科学版), 2017,45(3): 309-316.(MEI Bixiang, YANG Min, JIA Shanghua. Mohr-Coulomb criterion-based theoretical solutions of spherical cavity expansion considering seepage[J]. Journal of Tongji University(Natural Science),2017,45(3): 309-316.(in Chinese))
[8]	RUSSELL A R, KHALILI N. Cavity expansion in unsaturated soils[C]//Proceedings of the Third International Conference on Unsaturated Soils . Recife, Brazil, 2002: 233-238.
[9]	胡伟, 刘明振. 非饱和土中球形孔扩张的弹塑性分析[J]. 岩土工程学报, 2006,28(10): 1292-1297.(HU Wei, LIU Mingzhen. Elastic-plastic solution of expansion of sphere cavity in unsaturated soils[J]. Chinese Journal of Geotechnical Engineering,2006,28(10): 1292-1297.(in Chinese))
[10]	刘旭. 非饱和土中的柱形孔扩张问题的研究[D]. 硕士学位论文. 北京: 北京交通大学, 2017.(LIU Xu. Cylindrical cavity expansion in unsaturated soils[D]. Master Thesis. Beijing: Beijing Jiaotong University, 2017.(in Chinese))
[11]	卢国文. 黄土扩孔问题的理论解析及其在劈裂注浆中的应用研究[D]. 硕士学位论文. 兰州: 兰州理工大学, 2018.(LU Guowen. Theoretical analysis of loess hole enlargement and its application in splitting grouting[D]. Master Thesis. Lanzhou: Lanzhou University of Technology, 2018.(in Chinese))
[12]	赵明华, 何玮茜, 衡帅, 等. 基于圆孔扩张理论的筋箍碎石桩承载力计算方法研究[J]. 岩土工程学报, 2017,39(10): 1785-1792.(ZHAO Minghua, HE Weixi, HENG Shuai, et al. Calculation method of geogrid-encased stone columns’ bearing capacity based on cavity expansion theory[J]. Chinese Journal of Geotechnical Engineering,2017,39(10): 1785-1792.(in Chinese))
[13]	ZHOU H, LIU H, KONG G, et al. Analytical solution for pressure-controlled elliptical cavity expansion in elastic-perfectly plastic soil[J]. Géotechnique Letters,2014,4(2): 72-78.
[14]	ZHOU H, KONG G, LI P, et al. Flatcavity expansion: theoretical model and application to the interpretation of the flat dilatometer test[J]. Journal of Engineering Mechanics,2015,142: 04015058. DOI: 10.1061/(ASCE)EM.1943-7889.0000957.
[15]	ZHOU H, KONG G Q, LIU H L. Pressure-controlled elliptical cavity expansion under anisotropic initial stress: Elastic solution and its application[J]. Science China Technological Sciences,2016,59(7): 1100-1119.
[16]	梁恒昌. Tresca材料椭球形孔扩张问题研究[D]. 博士学位论文. 徐州: 中国矿业大学, 2010.(LIANG Hengchang. Advances in ellipsoidal cavity expansion with Tresca material[D]. PhD Thesis. Xuzhou: China University of Mining and Technology, 2010.(in Chinese))
[17]	LU N, GODT J W, WU D T. A closed form equation for effective stress in unsaturated soil[J]. Water Resources Research,2010,〖STHZ〗 46(5): W05515. DOI: 10.1029/2009WR008646.
[18]	毕银强, 张茂省, 谷天峰, 等. 非饱和黄土土水特征及其强度指标[J]. 防灾减灾工程学报, 2018,38(3): 520-527.(BI Yinqiang, ZHANG Maosheng, GU Tianfeng, et al. Soil-water characteristics and strength indexes of unsaturated loess[J]. Journal of Disaster Prevention and Mitigation Engineering,2018,38(3): 520-527.(in Chinese))
[19]	刘朋飞, 殷跃平, 李滨, 等. 非饱和黄土干湿循环土-水特征曲线试验及渗透系数预测[J]. 中国地质灾害与防治学报, 2015,〖STHZ〗 26(4): 125-129.(LIU Pengfei, YIN Yueping, LI Bin, et al. The tests of soil-water characteristics curve and permeability coefficient prediction of the wetting-drying cycles for unsaturated loess[J]. The Chinese Journal of Geological Hazard and Control,2015,26(4): 125-129.(in Chinese))
[20]	王晋伟. 陇东地区非饱和黄土土水特征曲线及强度特性试验研究[D]. 硕士学位论文. 兰州: 兰州理工大学, 2017.(WANG Jinwei. Study on the soil water characteristics curve and strength characteristics of unsaturated loess in east Gansu province[D]. Master Thesis. Lanzhou： Lanzhou University of Technology, 2017.(in Chinese))
[21]	张常光, 范文, 赵均海. 非饱和土统一强度理论及真三轴试验结果验证[J]. 岩石力学与工程学报, 2015,34(8): 1702-1711.(ZHANG Changguang, FAN Wei, ZHAO Junhai. Unified strength theory of unsaturated soils and verification with true triaxial test[J]. Chinese Journal of Rock Mechanics and Engineering,2015,34(8): 1702-1711.(in Chinese))