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 引用本文: 周凤玺, 牟占霖, 杨汝贤, 张雅森. 不同排水条件下非饱和土中柱孔扩张问题的解析分析[J]. 力学学报, 2021, 53(5): 1496-1509.
Zhou Fengxi, Mu Zhanlin, Yang Ruxian, Zhang Yasen. ANALYTICAL ANALYSIS ON THE EXPANSION OF CYLINDRICAL CAVITY IN UNSATURATED SOILS UNDER DIFFERENT DRAINAGE CONDITIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1496-1509.
 Citation: Zhou Fengxi, Mu Zhanlin, Yang Ruxian, Zhang Yasen. ANALYTICAL ANALYSIS ON THE EXPANSION OF CYLINDRICAL CAVITY IN UNSATURATED SOILS UNDER DIFFERENT DRAINAGE CONDITIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1496-1509.

## ANALYTICAL ANALYSIS ON THE EXPANSION OF CYLINDRICAL CAVITY IN UNSATURATED SOILS UNDER DIFFERENT DRAINAGE CONDITIONS

• 摘要: 现有的圆柱孔扩张理论已可为诸如石油工程中井筒稳定性鉴定、 及旁压和圆锥贯入实验分析等提供理论依据, 但在非饱和地基压力注浆, 复合地基处理等实际工程问题中却鲜有应用. 基于弹塑性理论和非饱和土力学原理, 采用统一强度理论, 对非饱和土中柱形小孔扩张问题进行了解析研究. 首先将柱孔周围土体分为弹性区和塑性区, 并考虑在弹性区遵循小应变理论, 在塑性区遵循大应变理论, 同时考虑了中间主应力及粒间吸力对非饱和土体强度的影响. 其次应用有效应力表示的统一强度准则, 在本构关系、几何方程、动量平衡方程等基本方程的基础上, 结合相应的边界条件, 最终获得了不同排水条件下柱孔扩张时周围弹塑性区域内的应力场、应变场、位移场及极限扩孔压力的解析表达式. 通过数值算例和参数分析, 在与现有的饱和及非饱和土中柱孔扩张理论进行退化验证的同时, 分析了吸力、剪胀参数、中主应力效应参数及初始径向有效应力等对弹塑性区域内的应力场、应变场及位移场的影响规律, 验证了本文理论的正确性及有效性, 以期为实际工程问题提供合理的理论依据.

Abstract: The existing expansion theory of cylindrical cavity has been able to provide theoretical basis for such as the wellbore stability evaluation in petroleum engineering and side pressure and cone penetration experiment analysis. But it is rarely applied in practical engineering problems such as unsaturated foundation pressure grouting and composite foundation treatment. Based on the theory of elastoplasticity and the principle of unsaturated soil mechanics, this paper adopts the unified strength theory to analyze the problem of cylindrical cavity expansion in unsaturated soil. Firstly, the soil around the cylindrical cavity is divided into the elastic zone and plastic zone and consider following the small strain theory in the elastic zone and the large strain theory in the plastic zone, and considering the influence of intermediate principal stress and inter-grain suction on the strength of unsaturated soil. Secondly, applying the unified strength criterion expressed by effective stress, based on basic equations such as constitutive relations, geometric equations, and momentum balance equations, combined with the corresponding boundary conditions. Finally, the analytical expressions of the stress field, strain field, displacement field and limit reaming pressure in the surrounding elastic-plastic region when the cylindrical cavity expands under different drainage conditions are obtained. Through numerical examples and parameter analysis, while degenerating verification with the existing expansion theory of cylindrical cavity in saturated and unsaturated soils, the influence laws of suction, dilatancy parameters, intermediate principal stress effect parameters and initial radial effective stress on the stress field, strain field and displacement field in the elasto-plastic region are analyzed. So as to verify the correctness and effectiveness of the theory in this article, in order to provide a reasonable theoretical basis for the later practical engineering problems.

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