中文摘要：

运用波函数展开法和Graf加法定理,根据衬砌群与周围介质在界面处位移和应力连续及衬砌内边界完全自由的边界条件,得到深埋圆形衬砌群对平面P波多重散射的理论解。分析P波的入射频率、衬砌间距和衬砌厚度对高、低硬度2类双衬砌内侧动应力集中因子的影响,并与单个衬砌的情况进行对比。结果表明：随着入射频率的增大,衬砌之间的相互影响越来越明显,动应力集中因子的最大值出现在两衬砌的临近区域;对于低硬度双衬砌,动应力集中因子的最大值小于单个衬砌的情况,且会随着入射频率和衬砌厚度的增大而减小,而高硬度双衬砌则正好相反。

英文摘要：

The expansion method of wave functions and Graf＇s addition theorem were adopted, the displacements and stresses were considered as continuous at the boundaries between the linings and surrounding media and the inner side of the linings were free, and theoretical solutions were obtained about the multiple scattering problem of incident plane P waves by a group of deep-buried circular linings. The influences of incident frequencies of P waves, distances and thicknesses of linings on Sa （Dynamic stress concentration factor） at the inner side of two types of twin circular linings with higher and lower hardness were analyzed, then Sd of the twin linings were compared with that of single lining. The results reveal that the interaction of the twin linings becomes more explicit when the incident frequencies of P waves increase, and the maximum Sd at inner side of the twin linings are located at their nearest boundaries. The maximum Sa at inner side of the twin linings with lower hardness are smaller than those of a single lining, and Sd would decrease when the incident frequencies of P waves and the thickness of linings increase, while the twin linings with larger hardness have opposite properties.