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基于Biot饱和多孔介质理论和非局部弹性理论,构建了非局部Biot运动方程及本构方程。利用波函数展开法及饱和土与衬砌边界连续条件和衬砌内边界自由边界条件,求解了饱和土体中圆柱形衬砌对平面波散射问题的解析解。并通过将该解退化为单相介质中及经典Biot理论下衬砌对平面P波散射稳态解,验证了计算结果的正确性。研究结果表明,衬砌内边界及外边界动应力集中因子均随非局部因子的增大而减小;隧道内边界动应力集中因子分布曲线随非局部因子的减小而扩大;当入射波频率大于0.045MHz时,饱和土中空隙尺寸及空隙动力的影响将不可忽略;非局部因子一定时,衬砌外径与内径比越大则衬砌内边界动应力集中因子越大,且当衬砌较薄时,衬砌内边界动应力集中因子可能产生负值。
Based on Biot saturated porous media theory and nonlocal elastic theory, a nonlocal Biot equation of motion and a constitutive equation are constructed. The analytic solution to the problem of plane wave scattering of cylindrical linings in saturated soils is solved by using the wave function expansion method and the continuous boundary conditions of saturated soil and lining and the free boundary conditions of lining inner boundary. The correctness of the calculation results is verified by decomposing the solution into a single-phase medium and the steady-state solution of plane P-wave scattering by the lining of classical Biot theory. The results show that the stress concentration factors on the inner boundary and the outer boundary decrease with the increase of non-local factors. The distribution of dynamic stress concentration factor in the inner boundary of tunnel increases with the decrease of non-local factor. When the incident wave frequency is more than 0.045MHz, the influence of void size and voidage in saturated soil will not be neglected. When non-local factor is fixed, the bigger the liner diameter and inner diameter ratio is, the bigger the stress concentration factor of lining is, and when the lining is thinner, Lining inner boundary dynamic stress concentration factor may produce negative values.