非饱和土中圆柱孔扩张问题不排水解答及吸力影响效应分析

张亚国; 翟张辉; 梁发云; 李同录

doi:10.11779/CJGE202104016

非饱和土中圆柱孔扩张问题不排水解答及吸力影响效应分析 English Version

1.
长安大学建筑工程学院,陕西　西安　710061
2.
长安大学地质工程与测绘学院,陕西　西安　710054
3.
同济大学地下建筑与工程系,上海　200092

基金项目:

国家自然科学基金青年基金项目 41807242

中央高校基本科研业务费专项项目 300102281202

详细信息

作者简介:
张亚国(1984—),男,博士,副教授,主要从事土力学与基础工程的教学科研工作。E-mail: yaguozhang29@chd.edu.cn

通讯作者:
梁发云, E-mail: fyliang@tongji.edu.cn

中图分类号: TU431
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出版历程
- 收稿日期: 2020-06-07
- 网络出版日期: 2022-12-04
- 刊出日期: 2021-03-31

Critical cylindrical cavity expansion in unsaturated soil under undrained conditions incorporating suction effects

1.
School of Civil Engineering, Chang'an University, Xi’an 710061, China
2.
School of Geological Engineering and Surveying, Chang'an University, Xi'an 710054, China
3.
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China

摘要

摘要: 圆柱孔扩张理论为沉桩挤土及旁压试验分析等提供了理论基础,然而已有研究多是针对饱和土展开,在非饱和土相关工程中并不适用。基于修正剑桥临界状态模型,对非饱和土中不排水条件下的圆柱孔扩张问题进行求解。在考虑非饱和土吸力效应的情况下推导土体应力–应变关系式,并引入反映吸力与比体积之间关系的液相本构方程。在此基础上联立圆柱孔周围土单元平衡微分方程,最终将非饱和土中的圆柱孔扩张问题归结为求解一阶偏微方程组的问题。通过引入辅助变量将所有方程转至拉格朗日系下,以弹塑性边界上的应力及比体积作为初值条件对其进行求解。结果表明：当非饱和吸力增大时,圆柱孔周围土体应力和扩孔压力均随之增大,说明土体出现了吸力硬化效应；对于初始比体积较小的土体,随着塑性区内的径向位置增加,比体积和吸力会出现先增大后减小的变化特征,说明圆柱孔在不排水扩张过程中局部土体发生了剪胀。所采用的本构关系较为简洁,参数易于确定,便于在非饱和土相关的工程问题得到实际应用。
- 非饱和土 /
- 不排水条件 /
- 圆柱孔扩张 /
- 吸力 /
- 弹塑性解
Abstract: The cylindrical cavity expansion theory provides the theoretical basis for analysis of pile installation and pressuremeter tests. However, most of the studies are conducted on cavity expansion in saturated soil, and are unsuitable for solving the engineering problem in unsaturated soil. Therefore, based on the critical state soil model, the cylindrical cavity expansion in unsaturated soil under undrained conditions is solved. The stress-strain relationship is derived considering suction effects. Meanwhile, a constitutive equation for the relationship between the suction and the void volume is introduced. Combing the radial equilibrium equation, the formulation of the problem is reduced to solving a system of the first-order ordinary differential equations. Introducing an auxiliary variable, all of the differential equations are transferred to the Lagrangian description and solved by taking the values at the elasto-plastic boundary as the initial value. The results show that the soil stresses and the cavity expansion pressure increase as the suction increases, which can be regarded as the suction-stiffening effects. For the soil with low initial ratio volume, the partial volume and the suction in the plastic zone firstly increase, and then decrease, which implies that the shear dilatancy occurs during the cavity expansion. The results have a potential application in the related projects owing to the simple constitutive relation and available parameters.
- unsaturated soil /
- undrained condition /
- cylindrical cavity expansion /
- suction /
- elasto-plastic solution

HTML全文

图 1 圆柱孔扩张模型

Figure 1. Model of cylindrical cavity expansion

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图 2 扩孔压力随孔径的变化

Figure 2. Variation of cavity pressure with cavity radius

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图 3 圆孔周围土体应力及比体积的径向变化

Figure 3. Radial variation of soil stress components and void ratio in surrounding soil

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图 4 p′–q平面内的应力路径

Figure 4. Stress paths in p′–q plane

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图 5 υ₀=1.85的孔周土体应力、比体积及吸力的径向变化

Figure 5. Radial variation of soil stress, void ratio and suction in surrounding soil with u0=1.85

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图 6 υ₀=1.70的孔周土体应力、比体积及吸力的径向变化

Figure 6. Radial variation of soil stress, void ratio and suction in surrounding soil with υ₀=1.70

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图 7 υ₀=1.55的孔周土体应力、比体积及吸力的径向变化

Figure 7. Radial variation of soil stress, void ratio and suction in surrounding soil with υ₀=1.55

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图 8 e–lnp′平面内的应力路径

Figure 8. Stress paths in e-lnp′ plane

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图 9 圆孔周围吸力增量随径向位置的变化

Figure 9. Variation of suction increment with radial positions

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图 10 扩孔压力随孔径的变化

Figure 10. Variation of cavity pressure with cavity radius

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