地下圆形衬砌洞室在平面P波入射下的动应力集中：三维级数解

Three-dimensional series solution for dynamic stress concentration of an underground cylindrical lined cavity subjected to incident plane P waves

利用波函数展开法,研究了地下圆形衬砌洞室在入射平面P波作用下的动应力集中问题并给出了三维级数解。研究表明:(1)衬砌刚度对环向与轴向动应力集中系数都具有重要影响,刚性衬砌、无衬砌和柔性衬砌三种情况下的动应力集中系数在空间上的分布基本相同,但刚性衬砌情况的动应力集中系数最大,无衬砌情况次之,柔性衬砌情况最小,波阵面夹角入射时1δ=45°,环向与轴向动应力集中系数最大可分别达到16.62与8.53;(2)随着入射频率的增大,环向动应力集中系数在多数情况下逐渐减小;(3)波入射角度对动应力集中系数也有很大影响,随着入射波与y轴夹角2δ的增加,环向动应力集中系数总体上逐渐减小,而轴向动应力集中系数多数情况下逐渐增大。

By using series expansion method,dynamic stress concentration of an underground cylindrical lined cavity under incident plane P waves is studied,and the three-dimensional series solution is presented.The studied results show that：（1） the rigidity of line has great effect on hoop and axial dynamic stress concentration factor,the factor distributions of cavities with rigid lining,without lining,and with flexible lining are the same,but it is the highest for a cavity with rigid lining,and it takes second place for an unlined cavity,and it is the lowest for a cavity with flexible lining;the hoop and axial dynamic stress concentration factor can be attained 16.62 and 8.53 under the angle δ1=45° which made by incident wave front within x-y plane;（2） as the incident frequency increases,the hoop dynamic stress concentration factor decreases gradually in most cases;（3） the angles of the incident waves also plays an important role in the dynamic stress concentration factor,as the incident angle δ2 with y-axis increases,the hoop dynamic stress concentration factor decreases gradually on the whole,and the axial dynamic stress concentration factor increases gradually in most cases.