复杂不均匀地层中地下结构波动响应频域分析

研究了不均匀岩土介质中隧洞衬砌的波动响应.比例边界有限元法被用来求解这一类问题.这种方法的优点是只需在边界上用有限元进行离散;无限介质的辐射条件自动得到满足;对一般不均匀介质的分析可不增加额外的工作量.方法的有效性得到二维无限空间中圆形孔洞在水平向SV波入射作用下波动响应的验证.计算了马蹄形隧洞衬砌周边的应力分布.不均匀的围岩介质包含几种情况:一是含两种不同特性介质的不连续界面;另一是围岩中含软弱夹层.数值结果表明:在两种不同特性介质的不连续界面附近,以及在软弱夹层附近都会出现应力集中现象.两种介质特性差别愈大,应力集中程度愈高.此外入射波的频率愈高,应力集中现象也愈明显.这些结论对于地下结构的抗震设计将具有重要参考价值.

Frequency domain analysis of dynamic response of underground structures embedded in nonuniform soil medium

Wave motion response of tunnel lining embedded in unbounded nonuniform soil medium is studied. The scaled boundary finite element method is employed to deal with this kind of problem. It has the advantages that only the boundary is discretized with finite elements, the radiation condition for unbounded medium is satisfied automatically and the general nonuniform medium can be analyzed without additional efforts. The wave scattering at the boundary of cylindrical circular cavity in 2D infinite space under horizontal incident SV waves was evaluated to validate the effectiveness of present approach. Stress distributions along the periphery of horse hoof-shaped tunnel lining were investigated. Several cases of nonuniform soil medium have been taken into consideration, i.e. the unbounded space with discontinuous interface of two media characterized with different shear modulus of elasticity and unbounded space with weak interlayer. Numerical results demonstrate that stress concentration is found in the vicinity of discontinuous interface of two soil media with different character and in the vicinity of weak interlayer. The larger the difference between the characteristic parameters of two soil media, the higher the degree of stress concentration becomes. In addition, stress concentration becomes more evident when the frequency of incident wave tends to be higher. This result has practical significance for the seismic design of underground structures.