Subgrade modulus is a critical parameter when analyzing the segmental lining of shield tunnels. However, prevailing analytical solutions of radial subgrade modulus (k_r) are based on predefined ideal deformation modes, either circular or oval, which are not consistent with the actual ground deformation, and the influence of the grout layer is commonly neglected. In view of this, this study presents a solution of k_r considering the actual deformation of the ground and the grout layer between linings and surrounding ground. A displacement fitting method is proposed to relate k_r to the arbitrary distribution shape of ground deformation. With this method, k_r for actual deformation consists of a series of radial subgrade moduli (k_r^m) for single deformation modes described by sine and cosine functions. Theoretical solutions of k_r^m considering the influence of the grout layer for single deformation modes are then derived based on the composed ground which is made up of the ground and the grout layer. The influence of the grout layer on k_r^m is then discussed by a parameter study. Moreover, the applicability of the proposed method is illustrated through a design case, where the calculated internal forces agree well with the data from field measurement. The influence of actual ground deformation and grout layer on k_r, internal forces, and displacement of shield tunnel is then discussed. Results show that an accurate prediction of k_r requires the consideration of the actual deformation of the lining and the influence of the grout layer.

在分析盾构隧道管片衬砌时，路基模量是一个关键参数。_{然而，目前流行的径向路基模量（kr}）解析解是基于预先定义的理想变形模式，无论是圆形还是椭圆形，与实际地基变形不一致，并且通常忽略灌浆层的影响。鉴于此，本研究提出了考虑地基实际变形以及衬砌与周围地基之间的灌浆层的k _r的解。提出了一种位移拟合方法，将k _r与地面变形的任意分布形状联系起来。_用这种方法，kr实际变形由一系列径向路基模量 ( k _r ^m ) 组成，用于由正弦和余弦函数描述的单一变形模式。然后根据地基和灌浆层组成的复合地基，推导了考虑灌浆层对单一变形模式影响的k _r ^m理论解。然后通过参数研究讨论灌浆层对k _r ^{m的影响。}此外，通过一个设计案例说明了所提出方法的适用性，其中计算的内力与现场测量的数据非常吻合。实际地基变形和灌浆层对k的影响_{然后讨论了r}、内力和盾构隧道的位移。结果表明，准确预测k _r需要考虑衬砌的实际变形和灌浆层的影响。