基于广义SMP准则的球孔扩张理论解及其应用  

Theoretical solutions of spherical cavity expansion based on generalized SMP criterion and applications

作　　者：胡长明[1,2] 王志宇 梅源 郭建霞[1] 于沭 Hu Changming;Wang Zhiyu;Mei Yuan;Guo Jianxia;Yu Shu(Department of Civil Engineering,Xi’an University of Architecture&Technology,710055,Xi’an,China;Shaanxi Key Laboratory of Geotechnical and Underground Space Engineering,XAUAT,710055,Xi’an,China;China Institute of Water Resources and Hydropower Research,100038,Beijing,China;State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin,100038,Beijing,China)

机构地区：[1]西安建筑科技大学土木工程学院,西安710055 [2]陕西省岩土与地下空间工程重点实验室,西安710055 [3]中国水利水电科学研究院,北京100038 [4]流域水循环模拟与调控国家重点实验室,北京100038

出　　处：《应用力学学报》2020年第5期1948-1956,I0008,共10页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51408463,41731289,51879285);陕西省教育厅专项科研计划项目(17JK0424);西安建筑科技大学科技计划项目(RC1375)。

摘　　要：通过广义空间滑动面(广义SMP)准则,结合非相关联流动法则对球孔扩张问题进行了理论分析。利用应力不变量推导了符合黏性土中球孔扩张的屈服准则;通过弹塑性区边界条件,推导了孔周土体应力场和考虑剪胀角影响的应变场、位移场。利用体积守恒和塑性区平均体应变表达式,推导出扩孔压力p与初始孔半径a0、扩孔后半径a三者之间的理论关系式,通过该关系式给出了求解球孔扩张问题的具体方法和极限扩孔压力pu的计算式。此外,运用镜像法推导了考虑半无限空间下的压密注浆挤土竖向位移计算公式。最后通过算例分析了球孔扩张问题中应力场分布、不同剪胀角下位移场分布,以及扩孔后半径a对塑性区半径rp和扩孔压力p的影响规律。结果表明,剪胀角是球孔扩张问题中的一个重要参数,随着剪胀角增大,径向位移减小,塑性区半径和扩孔压力均增大。The expansion of spherical cavity is analyzed based on the generalized spatially mobilized plane(generalized SMP) criterion and the non-associated flow rule. A yield criterion of spherical cavity expansion in cohesive soil is obtained by using stress invariant. Then the stress field and the strain and displacement fields considering dilatancy angle are derived employing the boundary conditions of soil around the spherical cavity. The theoretical relationship formula among the expanding pressure p, initial radius a0 and expanded radius a is derived by the volume conservation and the mean volumetric stain expression in plastic zone. The solution method of the spherical cavity expansion and the expression of limit expansion pressure are obtained with the theoretical relationship. The vertical displacement formula of squeezing soil due to compaction grouting is deduced by using the image method. Finally, an example is presented to illustrate the distributions of the stress fields and the displacement fields at different dilatancy angles, and the influences of expanded radius a on the radius of plastic zone rp and the expanding pressure p are analyzed. The results show that the dilatancy angle is an important parameter in spherical cavity expansion. With the increase of dilatancy angle, the radial displacement decreases, the radius of plastic zone rp and the expanding pressure p increase.

关 键 词：广义SMP准则 球孔扩张 体积守恒 塑性区半径 扩孔压力 

分 类 号：TU431[建筑科学—岩土工程]