在计算圆孔周应力时,为了充分考虑孔在受初始应力后的形状、介质受力的各向异性以及模量的各向异性对劈裂注浆浆脉延伸方向及启劈压力的影响,首先根据弹性理论,求解了孔的变形后形状,并在此基础上,利用复变函数把椭圆孔的外部区域映射到单位圆的内部,求解椭圆孔周应力。结果表明:圆孔受初始应力后的形状为圆与余弦函数的叠加;其孔周切向应力最小的位置与圆孔相同,即在受孔内压力时最易劈裂处与圆孔一致,但需要的压力更大;经实例验证启劈压力与实际接近,可基本满足工程应用要求。本文方法可作为进一步研究的基础。
When calculating the stress around a circular hole, the influences of hole shape under initial stress, the anisotropy of medium stress and the anisotropy of modulus on the extended direction of grout vein and the splitting pressure are studied. The deformed shape of the hole is first solved according to elastic theory, and on this basis, the complex variable function is used to map the external area of the elliptical hole to the interior of the unit circle to solve the stress around the elliptical hole. The results show that the shape of a circular hole under initial stress is the superposition of a circle and a cosine function; The position of the minimum tangential stress around the hole is the same as that of the round hole, that is, the position where is most easily split under the pressure inside the hole is the same as that of the round hole, but it needs more pressure; The example verifies that the splitting pressure is quite close to the actual value, which can basically meet the engineering application. This method can be used as the basis for further research in the future.
[1] Gibson R E, Anderson W F. In-situ measurement of soil properties with the pressuremeter[J]. Civil Engineering and Public Works Review, 1961,56(658): 615-618.
[2] Vesic A S. Expansion of cavities in infinite soil mass[J].Journal of Soil Mechanics and Foundation Engineering,1972,98(1): 75-91.
[3] 龚晓南, 王启铜, 罗晓. 拉压不同模量材料的圆孔扩张问题[J]. 应用力学学报, 1994, 11(4): 127-132.
[4] 罗战友, 杨晓军, 龚晓南. 考虑材料的拉压模量不同及应变软化特性的柱形孔扩张问题[J]. 工程力学, 2004, 21(2): 40-45.
[5] 罗战友, 夏建中, 龚晓南. 不同拉压模量及软化特性材料的球形孔扩张问题的统一解[J]. 工程力学, 2006, 23(4): 22-27.
[6] 王延斌, 俞茂宏, 魏雪英, 等. 环形均布荷载作用下简支圆板的塑性极限分析[J]. 工程力学, 2002, 19(1): 84-88.
[7] 邹金峰, 徐望国, 罗强,等. 饱和土中劈裂灌浆压力研究[J]. 岩土力学, 2008, 29(7): 1802-1806.
[8] 邹金锋, 罗恒, 李亮,等. 考虑中主应力时土体劈裂灌浆力学机制的大变形分析[J]. 岩土力学, 2008, 29(9): 2515-2520.
[9] 章定文, 刘松玉, 顾沉颖. 各向异性初始应力状态下圆柱孔扩张理论弹塑性分析[J]. 岩土力学, 2009, 30(6): 1631-1634.
[10] 饶平平, 李镜培, 张常光. 考虑各向异性、剪胀和渗流的柱孔扩张问题统一解[J]. 岩土力学, 2010, 31(增2): 79-85.
[11] 饶平平, 王道远.基于广义Lade-Duncan准则的圆柱孔扩张问题分析[J]. 地下空间与工程学报, 2012, 8(5): 946-950
[12] 张淼, 邹金锋, 陈嘉祺,等. 非对称荷载作用下土体劈裂注浆压力分析[J]. 岩土力学, 2013, 34(8): 2255-2263.
[13] 武孝天, 徐永福. 超固结土中排水圆孔扩张弹塑性UH解[J]. 岩土工程学报, 2020, 42(10): 1903-1913.
[14] 李镜培, 刘耕云, 周攀. 基于相似性原理超固结土不排水扩张半解析解[J]. 岩土力学, 2022, 43(3): 582-590.
[15] 龚晓南. 油罐软黏土地基性状[D]. 杭州:浙江大学, 1984.
[16] 龚晓南. 软黏土地基各向异性初步探讨[J]. 浙江大学学报, 1986, 20(4): 98-109.
[17] 丁金粟, 孙亚平. 水力劈裂试验中击实土厚壁筒应力分析[J]. 水利学报, 1987(3): 16-23.
[18] 阮文军. 注浆扩散与浆液若干基本性能研究[J]. 岩土工程学报, 2005, 27(1): 69-73.
[19] 徐芝纶. 弹性力学简明教程[M]. 北京:高等教育出版社, 2002.
[20] 萨文.г.н. 孔附近的应力集中[M]. 盧鼎霍,译.北京:科学出版社, 1958.
[21] 张庆松, 张连震, 刘人太, 等. 基于“浆-土”界面应力耦合效应的劈裂注浆理论研究[J]. 岩土工程学报, 2016, 38(2): 323-330.
[22] Collins I F, Yu H S. Undrained cavity expansions in critical state soils[J]. International Journal for Numerical and Analytical Methods in Geomechanics,1996, 20: 489-516.
