ABSTRACT Due to the presence of the tunnel lining, it is difficult to develop a system of linear equations for the unknowns of a shallow lined circular tunnel (SLCT) analytically based on the conformal mapping method. Besides, the traditional complex variable based series expansion (CVSE) method is limited to the problem associated with circular boundaries. To overcome the above limitations and extend the applicability of the CVSE method, a new analytical method, that is, the generalized series expansion (GSE) method for the SLCT is developed based on complex variable method. For this purpose, two generalized series for two complex potentials of the soil are introduced. Each generalized series is composed of two parts, that is, the singular and regular parts. The singular part of each generalized series is already known and singular in the lower half‐space occupied by the soil, while the regular part is unknown and analytic in the lower half‐space and it can be obtained by using Cauchy's integral theorem as well as the traction free condition along the soil surface. For simplicity, the lining of the tunnel is treated as a thin cylindrical shell. With the expressions for the above generalized series and governing equation for the tunnel lining, a system of linear equations for all the unknowns of the SLCT is derived analytically, with which the response of the SLCT and soil to arbitrary external loads is obtained.
Lu et al. (Fri,) studied this question.