管状填充性椭圆形溶洞的围岩应力弹性解析分析  

Stress analysis of rocks surrounding a tubular filled elliptical karst cave with complex function of elastic mechanics

作　　者：饶军应[1,2] 傅鹤林[1] 刘运思[1] 尹泉[1] 

机构地区：[1]中南大学土木工程学院,湖南长沙410075 [2]贵州大学土木工程学院,贵州贵阳550025

出　　处：《中南大学学报（自然科学版）》2015年第7期2605-2612,共8页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(51008308;50878213);湖南省研究生科研创新项目(CX2013B078)~~

摘　　要：为分析含管状填充性椭圆溶洞的围岩应力,将实际工况简化为计及椭圆孔洞内压(q)的双向受压无限平面应力问题;以平面弹性复变方法为基础,把z平面椭圆外域保角映射到ξ平面圆外域,利用留数定理推导简化力学模型的2个复势函数φ1(ξ)和ψ1(ξ)的表达式,得到围岩任意一点应力分量(σρ,σφ,τρφ)的解析通式。随后,导出由孔洞内压产生的孔口附加应力场,讨论孔口应力随椭圆形状与围岩侧压系数λ的变化规律。研究结果表明:q产生的附加应力在孔口与x轴、y轴相交处分别有最大值、最小值;圆形孔洞无内压时,孔口应力的最大值随λ的增大而减小,最小值与λ无关。For analyzing the stresses of surrounding rock containing a tubular filled elliptical karst cave, it was simplified to solve the stresses of infinite plane containing an elliptical hole with internal pressure （q） under bi-axial compressions. According to the complex function of elastic mechanics, the outer region of elliptical hole in z plane was mapped to the outer of a unit circle in ξ plane with a conformal mapping function. After that, the complex potential functions of φ1（ξ） and ψ1（ξ） were deduced for the simplified model by applying the residue theorem, and the analytic general formula for the component of stresses （σρ,σφ,τρφ） were solved. Then, as the elliptical hole was degraded into circular, or the filled karst cave was transformed into unfilled, their stresses were both solved. Moreover, the subsidiary stress field around hole produced by internal pressure was obtained, the variation of opening stress changing with the ellipse shape and the coefficient of horizontal pressure （2） were discussed. The results show that the subsidiary stress from q gets the maximum value at the point of ellipse intersecting with x-axis, while the minimum value is at y-axis. As q=0 for circular hole, the maximum opening stress is smaller as 2 becomes greater, but the minimum value has no relationship to 2.

关 键 词：地下工程 管状填充性岩溶 椭圆孔洞 围岩应力 孔口应力 解析分析 

分 类 号：U451[建筑科学—桥梁与隧道工程]