正方形孔扩张的弹性分析  

ELASTIC ANALYSIS OF SQUARE CAVITY EXPANSION

作　　者：周航[1,2] 孔纲强[1,2] 刘汉龙[1,2] 

机构地区：[1]河海大学岩土力学与堤坝工程教育部重点实验室,江苏南京210098 [2]河海大学土木与交通学院,江苏南京210098

出　　处：《工程力学》2013年第12期183-188,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(51008116;51278170);国家自然科学基金高铁联合基金项目(U1134207)

摘　　要：圆孔扩张理论作为一种相对成熟的理论工具已经广泛的运用于岩土工程中的各类问题，但是对于一些初始孔形并非圆孔的扩孔问题，圆孔扩张理论并不适用。基于保角变换的方法将原物理平面上初始非圆形孔洞映射到像平面上的单位圆，将原物理平面上由于孔洞扩张所产生的位移边界条件转换到像平面上，利用平面复变弹性理论，得到初始非圆形孔洞孔扩张的弹性理论解。通过基于该文的方法计算圆孔扩张并且与现有的圆孔扩张的弹性解进行对比分析，验证该文解的可靠性。续而，针对初始孔形为正方形的孔洞，采用该文方法详细地分析了正方形孔扩张的力学特性。研究结果表明，该文解在退化到圆孔扩张问题后与现有的圆孔扩张弹性解完全一致；正方形孔在扩张过程中角点处出现应力集中现象，尤其在极角为30°-45°时应力急剧增加。在离孔心的距离大于4倍的a0/2（a0为初始正方形孔边长）处，其应力分布状态就接近于圆孔扩张，即孔洞非轴对称的影响只在离孔心一定的范围内，当大于这个范围时，这种影响就可以忽略不计。Cavity expansion theory is widely used in geotechnical engineering problems as a mature theory tool. However, it is not applicable to the non-circular cavity expansion problem. The initial non-circular cavity on the physical plane is mapped to a unit circle on a phase plane by a conformal mapping method, and the displacement caused by the cavity expansion on the physical plane is transformed to the phase plane. The elastic solution of non-circular cavity expansion is presented by a plane complex variable elasticity method. This solution is compared with the circular cavity expansion, and the reliability of this study is verified. Then, the mechanics characteristics of the square cavity expansion are analyzed. The results show that this study is consistent to the present cavity expansion method when this study is degenerated to a circular cavity. The stress concentration appears at the comer of the square cavity when the square cavity is in the process of expansion, especially the stress increase rapidly at the polar angle range from 30°to 45°. The stress state where the distance away from the cavity center is more than 4 times ao/2 （ao is the side length of the initial square） is close to the cavity expansion theory. The non-ax symmetric of the cavity only has an impact within a certain range from the cavity center. The impact can be ignored when the distance from the cavity center is more than a certain range.

关 键 词：岩土工程 孔扩张 复变函数 正方形孔 位移边界 

分 类 号：TU375.4[建筑科学—结构工程]