为探究波浪荷载作用下含衬砌深埋海底隧道的纵向瞬态渗流规律，解决现有解析模型多局限于横截面二维定水头边界、难以反映纵向复杂水力梯度的问题，针对深埋海底隧道衬砌纵向内边界为第三类（Robin）混合边界，且地表为波浪荷载周期边界的工况，利用分离变量法及三角函数正交性，推导隧道衬砌-地层系统中纵向总水头与流速的显式解析解。通过与数值结果的对比，验证解析解的正确性与适用性。分析结果表明： 1）波浪诱导的水头及流速在时间维度上呈半周期反对称分布，在空间维度上关于隧道中点横截面呈反对称分布，且在一个波浪荷载周期内经历2次完整循环（即具有“倍频”波动特征），初始时刻二者均处于峰值演变阶段。2）相对渗透系数、衬砌厚径比、波浪荷载周期及内渗流权重系数显著影响水力响应的时空分布特征，其中，相对渗透系数与内渗流权重系数不仅影响响应幅值，而且调控总水头的初始相位滞后效应； 衬砌厚径比对衬砌外边界水力响应幅值的影响显著高于内边界； 而波浪荷载周期主要调控外边界水头的空间分布幅值及内渗流边界流速的时空演化特征。
Existing analytical models for the longitudinal transient seepage field around subsea lined tunnels under wave loading are limited to two-dimensional cross-sectional analyses with constant hydraulic head boundaries and therefore fail to capture complex longitudinal hydraulic gradients. To address this limitation, an explicit analytical solution for the longitudinal total hydraulic head and flow velocity in the soil-lining system is derived using the method of separation of variables and the orthogonality of trigonometric functions, assuming a third-kind (Robin) seepage boundary at the inner lining surface of a deep tunnel and periodic wave loading at the ground surface. The feasibility and applicability of the proposed solution are verified by comparison with numerical results. The results indicate the following. (1) The wave-induced hydraulic head and flow velocity exhibit antisymmetric distributions over half a wave period in the temporal domain and about the tunnel mid-section in the spatial domain. Both variables complete two fluctuation cycles within a single wave period, exhibiting a frequency-doubling characteristic, with fluctuations initiating near the wave crest. (2) The relative permeability, lining thickness-to-radius ratio, wave period, and inner boundary seepage parameter significantly influence the spatiotemporal characteristics of the hydraulic response. Specifically, the relative permeability and inner boundary seepage parameter primarily govern the initial phase lag of the total hydraulic head. The lining thickness-to-radius ratio has a substantially greater influence on the hydraulic response amplitude at the outer lining boundary than at the inner boundary, whereas the wave period primarily controls the spatial distribution of the hydraulic head at the outer boundary and the variation in flow velocity at the inner boundary.
