###### Abstract
Although the aforementioned research has shown that the semi-rigid sidewall joints of PUTCGEs have a great influence on the mechanical behavior of the structures, there has been little research on design calculation methods considering the influence of these seam joints. It should be mentioned that, in a shield tunnel, the segment joints also have typical semi-rigid characteristics, and the mechanical properties of the joints directly determine the bearing capacity and structural stiffness of the tunnel lining. Experimental research and numerical simulations have been carried out on the mechanical properties of segment joints in terms of strength, stiffness and ductility, and a stiffness reduction model has been proposed, along with several theoretical calculation models such as the beam-spring model, the uniform stiffness model, and the hinge model, for calculating the internal force and deformation of the structure lining [24; 25; 26]. Among these models, the stiffness reduction model is the most-used method for shield lining because of its simplicity and efficiency. Its core idea is to reduce the overall stiffness by introducing an effective bending stiffness coefficient and a bending moment transfer coefficient. The effective coefficient of bending stiffness is mainly reflected in the use of a reduced stiffness of the segment for representing the overall stiffness of the homogeneous lining ring. On the other hand, due to the semi-rigid behavior of the lining joints and the staggered joint construction, moment transfer coefficients are used to adjust the bending moments of the segment sections in adjacent lining rings at the joints. [PERSON] et al. [27] carried out a finite element comparative analysis of shield tunnel linings with and without joints. Their results showed that reducing the number of joints and increasing the stiffness of joints and foundation resistance could effectively improve the effective bending stiffness coefficient. They also provided a calculation method for the effective coefficient of bending stiffness of shield tunnel structures based on the analysis results. [PERSON] et al. [28] conducted an experimental study on a staggered joint shield tunnel structure under different loading conditions. Their results showed that the embedment depth and longitudinal force had a significant impact on the bending moment transfer coefficient and that the effective bending stiffness coefficient was affected by the lateral pressure coefficient, embedment depth, longitudinal force, and lateral resistance. Since there are a lot of similarities between a shield tunnel lining and PUTCGEs in terms of structural system and loading conditions, the stiffness reduction method as used for tunnel linings could, naturally, be extended to PUTCGEs, at least in the sense of methodology. However, there has been little progress that can be found in this direction. To this end, the current study develops and extends the stiffness reduction method for a PUTCGE in which a sidewall stiffness reduction model is proposed by introducing a sidewall stiffness reduction coefficient and a bending moment adjustment coefficient while considering the influence of the joint stiffness ratio, the aspect ratio of width to height, the coefficient of subgrade reaction, and the embedment depth. In the following sections, the analysis of the sidewall stiffness reduction model is first introduced, followed by verification and comparison with the model test results.