剪胀性砂土中球孔扩张弹塑性解

李林; 李镜培; 孙德安; 李险峰

doi:10.11779/CJGE201708012

剪胀性砂土中球孔扩张弹塑性解 English Version

李林^{1, 2},
李镜培^1,2, ,,
孙德安³,
李险峰^{1, 2}

1. 同济大学岩土及地下工程教育部重点实验室,上海 200092;
2. 同济大学地下建筑与工程系,上海 200092;
3. 上海大学土木工程系,上海 200444

基金项目: 国家自然科学基金项目（41272288）

详细信息

作者简介:
李林（1986- ）男,甘肃通渭人,博士研究生,主要从事土体力学特性和桩基承载力方面的研究工作。E-mail: lilin_sanmao@163.com。

通讯作者:
李镜培，E-mail：lijp2773@tongji.edu.cn

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出版历程
- 收稿日期: 2016-05-14
- 发布日期: 2017-08-24

Elasto-plastic solution to expansion of a spherical cavity in dilatant sand

LI Lin^{1, 2},
LI Jing-pei^1,2, ,,
SUN De-an³,
LI Xian-feng^{1, 2}

1. Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, China;
2. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China;
3. Department of Civil Engineering, Shanghai University, Shanghai 200444, China

摘要

摘要: 目前砂土中球孔弹塑性扩张解无法合理考虑砂土的峰值强度和剪胀特性,因而其解答与实际情况存在一定偏差。为得出剪胀性砂土中球孔扩张问题的合理解答,采用砂土临界状态模型考虑球孔扩张过程中砂土剪胀特性和峰值强度对球孔扩张机制的影响,基于相关联流动法则推导了球孔扩张问题的弹塑性本构张量,进而在塑性区采用大变形理论并引入辅助变量,将球孔扩张问题归结为基于拉格朗日描述的一阶偏微分方程组的初值问题。在此基础上,结合孔周弹塑性边界条件求解得出了剪胀性砂土中球孔扩张问题的严格解答。通过与基于修正剑桥模型的球孔扩张解答相对比,研究了砂土峰值强度和剪胀特性对孔周土体应力状态和位移的影响规律。结果表明,基于砂土临界状态模型的弹塑性解答不仅可以合理反映球孔扩张过程过程中剪胀性砂土的峰值强度和剪胀特性,而且可退化为非剪胀性土体中的球孔扩张解答,因而可以更加广泛地应用于静力触探、静压沉桩等岩土工程问题中。
- 峰值强度 /
- 剪胀性 /
- 球孔扩张 /
- 辅助变量 /
- 拉格朗日描述
Abstract: The current solutions to spherical cavity expansion can not properly consider the peak strength and dilatancy of the sand, and thus there is some dispency between the solution and the practical situation. To obtain a rational solution to expansion of a spherical cavity in sand, a critical state model for sand is adopted to consider the effects of the peak strength and dilatancy of the soil on the cavity expansion. Based on the cirtical mode, the elasto-plastic constitutive tensor for the problem is derived according to the associated flow rule. By employing the large deformation theory and introducing an auxiliary variable, the problem becomes an initial value problem of a set of first-order differential equations based on the Lagrangian description. Under the elastic-plastic boundary conditions, a rigorous solution is obtained by solving the governing equaitons numerically. The effects of the peak strength and dilatancy of the sand on the expansion response are studied by comparing the results between the present solution and the modified Cam-clay model-based solution. The results show that the present solution can appropriately reflect the peak strength and dilantancy of the sand during cavity expansion and be reduced to the solution for non-dilanancy soils. Hence, the present solution can be widely applied to the geotechnical problems, such as the cone penetration tests and the pile installation.
- peak strength /
- dilatant behaviour /
- spherical cavity expansion /
- auxiliary variable /
- Lagrangian description

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参考文献(28)

[1]	YU H S. Cavity expansion methods in geomechanics[M]. Amsterdam: Kluwer Academic Publishers, 2000.
[2]	.SHUTTLE D. Cylindrical cavity expansion and contraction in Tresca soil[J]. Géotechnique, 2007, 57(3): 305-308.
[3]	.RANDOLPH M F. Science and empiricism in pile foundation design[J]. Géotechnique 2003, 53(10): 847-875.
[4]	曹权, 施建勇, 雷国辉, 等. 基于波速孔压静力触探试验研究软土中单桩桩侧承载力时效性[J]. 岩石力学与工程学报, 2011, 30(7): 1482-1487. (CAO Quan, SHI Jian-yong, LEI Guo-hui, et al. Research on time-effect of shaft bearing capacity of jacked-in single pile in soft soil based on seismic piezocone penetration tests (SCPTU)[J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(7): 1482-1487. (in Chinese))
[5]	李镜培, 李林, 孙德安, 等. 饱和软土地层静压沉桩阻力理论研究[J]. 岩土工程学报, 2015, 37(8): 1454-1461. (LI Jing-pei, LI Lin, SUN De-an, TANG Jian-hua. Theoretical study on sinking resistance of jacked piles in saturated soft clay[J]. Chinese Journal of Geotechnical Engineering, 2015, 37(8): 1454-1461. (in Chinese))
[6]	VESIC A S. Expansion of cavity in infinite soil mass[J]. Journal of Soil Mechanics Foundation Division, American Socialy of Civil Engineering, 1972, 98(3): 265-289.
[7]	.CARTER J P, BOOKER J R, YEUNG S K. Cavity expansion in cohesive frictional soils[J]. Géotechnique, 1986, 36(3): 349-353.
[8]	.YU H S, HOULSBY G T. Finite cavity expansion in dilatants soils: loading analysis[J]. Géotechnique, 1991, 41(2): 173-183.
[9]	MANTARAS F M, SCHNAID F. Cylindrical cavity expansion in dilatant cohesive-frictional materials[J]. Géotechnique, 2002, 52(5): 337-348.
[10]	PALMER A C, MITCHELL R J. Plane-strain expansion of a cylindrical cavity in clay[C]// Stress-strain Behaviour of Soils: Proceedings of the Roscoe Memorial Symposium. Cambridge, 1972: 588-599.
[11]	CAO L F, TEH C I, CHANG M F. Undrained cavity expansion in modified Cam clay I: theoretical analysis[J]. Géotechnique 2001, 51(4): 323-334.
[12]	SATHANANTHAN I, INDRARATNA B, RUJIKIATKAMJORN C. Evaluation of smear zone extent surrounding mandrel driven vertical drains using the cavity expansion theory[J]. International Journal of Geomechnics, 2008, 8(6): 355-365.
[13]	LI J P, LI L, SUN D A, et al. Analysis of undrained cylindrical cavity expansion considering three-dimensional strength of soils[J]. International Journal of Geomechnics, 2016, 10.1061/(ASCE)GM. 1943-5622. 0000650, 04016017.
[14]	肖昭然, 张昭, 杜明芳. 饱和土体小孔扩张问题的弹塑性解析解[J]. 岩土力学, 2014, 25(9): 1373-1378. (XIAO Zhao-ran, ZHANG Zhao, DU Ming-fang. An elastoplastic closed-form approach of cavity expansion in saturated soil based on modified Cam clay model[J]. Rock and Soil Mechanics, 2014, 25(9): 1373-1378. (in Chinese))
[15]	刘维正, 石名磊, 徐林荣. 考虑软黏土结构性损伤的圆柱孔扩张弹塑性分析[J]. 岩土工程学报, 2015, 35(3): 487-494. (LIU Wei-zheng, SHI Ming-lei, XU Lin-rong. Elastoplastic analysis of cylindrical cavity expansion in natural sedimentary soft clay with structure damage[J]. Chinese Journal of Geotechnical Engineering, 2015, 35(3): 487-494. (in Chinese))
[16]	VINCENZO S, GHASSAN A S. Analytical solution for undrained plane strain expansion of a cylindrical cavity in modified cam clay[J]. Geomechanics and Engineering, 2012, 4(1): 19-37.
[17]	CHEN S L, ABOUSLEIMAN Y N. Exact undrained elasto-plastic solution for cylindrical cavity expansion in modified Cam clay soil[J]. Géotechnique, 2012, 62(5): 447-456.
[18]	LI L, LI J P, SUN D A. Anisotropically elasto-plastic solution to undrained cylindrical cavity expansion in K 0 -consolidated clay[J]. Computers and Geotechnics, 2016, 73: 83-90.
[19]	COLLINS I F, PENDERr M J, WANG Y. Cavity expansion in sands under drained loading conditions[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1992, 16(1): 3-23.
[20]	COLLINS I F, STIMPSON J R. Similarity solutions for drained and undrained cavity expansion in soils[J]. Géotechnique 1994, 44(1): 21-34.
[21]	COLLINS I F, YU H S. Undrained cavity expansion in critical state soils[J]. Int J Numer Anal Methods Geomech, 1996, 20(7): 489-516.
[22]	OSINOV V A, CUDMANI R. Theoretical investigations of the cavity expansion problem based on a hypoplasticity model[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2001, 25(5): 473-495.
[23]	RUSSELL A R, KHALILI N. Drained cavity expansion in sands exhibiting particle crushing[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2002, 26: 323-340.
[24]	蒋明镜, 孙渝刚. 考虑砂土颗粒破碎的圆孔扩张半解析分析[J]. 岩土工程学报, 2009, 31(11): 1645-1651. (JIANG Ming-jing, SUN Yu-gang. Semi-analytical solution to cavity expansion in crushable sands[J]. Chinese Journal of Geotechnical Engineering, 2009, 31(11): 1645-1651. (in Chinese))
[25]	姚仰平, 罗汀, 孙德安, 等. 黏土和砂土简单的三维本构模型[J]. 岩土工程学报, 2002, 24(2): 240-243. (YAO Yang-ping, LUO Ting, SUN De-an, et al. A simple 3D constitutive model for both clay and sand[J]. Chinese Journal of Geotechnical Engineering, 2002, 24(2): 2-243. (in Chinese))
[26]	YAO Y P, SUN D A, MATSUOKA H. A unified constitutive model for both clay and sand with hardening parameter independent on stress path[J]. Computers and Geotechnics, 2008, 35(2): 210-222.
[27]	SUN D A, MATSUOKA H, YAO Y P. An anisotropic hardening elastoplastic model for clays and sands and its application to FE analysis[J]. Computers and Geotechnics, 2004, 31(1): 37-46.
[28]	YAO Y P, SUN D A, LUO T. A critical state model for sands dependent on stress and density[J]. International Journal of Geomechnics, 2004, 28(4): 323-337.