地下衬砌洞室群在平面SV波入射下的动应力分析

An analytical solution for dynamic stress concentration of underground lined cavities under incident plane SV waves

采用波函数展开法给出了半空间中衬砌洞室群在平面SV波入射下动应力集中问题的一个级数解析解,在满足一定的精度要求下,对无穷级数进行截断数值计算,衬砌分为刚性衬砌、无衬砌、柔性衬砌三种,计算结果表明:洞室间距对动应力集中系数具有重要影响,当洞室之间距离较近时,洞室之间的相互作用对地下洞室群的动应力集中具有显著的放大作用,动应力集中系数可能达到单个洞室的2倍以上;衬砌刚度对动应力集中问题也具有显著的影响,其中,刚性衬砌的动应力集中系数最大,无衬砌次之,柔性衬砌最小;随着入射波频率的增大,动应力集中系数的空间分布逐渐趋于复杂化.

An analytical series solution for dynamic stress concentration of underground lined cavities under incident plane SV waves is given by wave function expansion method. The infinite series is cut and calculated under the required precision. The lining includes rigid lining, unlined cavities, flexible lining. The numerical results show that interaction between two cavities greatly amplifies the dynamic stress concentration, and the dynamic stress concentration may reach to 2 times that in single cavity case; The rigidity of lining also has great effect on the dynamic stress concentration which is highest for the rigid lining, second for unlined cavities and is lowest for the flexible lining. With the increasing of the wave frequency, the distribution of dynamic stress concentration becomes complicated.