###### Abstract  
To fully consider the effect of elastic gasket (EG) on the segmental joint rotational behavior, an improved analytical approach is proposed to simulate the joint rotations and obtain the rotational stiffnesses. By comparing the analytical results with the experimental results and numerical results, the joint compression zone should be simulated by the concrete-EG-concrete (CGC) model instead of rigid-EG-rigid (RGR) model or concrete-concrete (CC) model. Since the analytical approach with the CGC model can simulate the combined work of EG and concrete well, it is a more effective approach to obtain the joint rotational stiffnesses. According to these analytical results, the EG has a great impact on softening the joint rotations, and this leads the rotational stiffnesses of the joint with EG to be evidently smaller than those of the joint without EG. In addition, with decreasing the axial force or increasing the EG thickness, this softening effect tends to be more obvious. Therefore, the EG is a significant factor which should be fully considered during the theoretical analysis for the joint rotation behavior, or it may lead to an unreliable design for the segmental lining. shield tunnel; segmental joint; rotational behavior; elastic gasket; analytical approach; finite element model +
Footnote †: journal: Applied Mechanics and Physics Letters A  
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Footnote 1: School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China; [EMAIL_ADDRESS]  
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Footnote 2: School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, China
The segmental joint is an important factor which can evidently affect the bearing performance of the whole lining. The mechanical mechanisms of the segmental joint are commonly described by three kinds of stiffnesses, which are rotational stiffness, axial stiffness, and shear stiffness in some analytical and numerical researches [4; 5]. Since the axial stiffness and shear stiffness contribute little to the bearing performance of the segmental joint, they can be simplified or even ignored in structural analyses [6]. However, for the rotational stiffness, some numerical simulations [6] and experimental results [7] reveal that it can make a great contribution to the bearing performance of segmental joint; it is a key parameter to be considered in the structural design for the segmental lining [8]. Therefore, in recent years, an enormous amount of research effort goes into the joint rotations from the aspects of experimental test, numerical simulation, and theoretical analysis. These researches indicate that the joint rotations are very complex, and the joint rotational stiffnesses present obvious nonlinear characteristics with the influences of the complexity and diversity of segment joint types, structural dimensions, involved materials, and environmental conditions [9; 10; 11; 12]. To calculate the joint rotation stiffness accurately, some analytical approaches are proposed for the segmental joints. As presented in Figure 2, in these approaches, the stresses of the bolt and SG are commonly assumed to be concentrated forces (\(F_{b}\) and \(F_{s}\)), and the stress distribution of the joint compression zone is assumed to be some simplified shapes to calculate the resultant force (\(F_{c}\)). Then, according to the equilibrium conditions of the joint axial force and bending moment, the joint rotational stiffnesses can be calculated. Obviously, an appropriate simplification of the stress distribution shape is the key to these approaches. For the joint without EG, as presented in Figure 2a, the concrete stress distribution can be assumed to be triangular, rectangular, trapezoidal, parabola, etc. [9; 13; 14; 15; 16; 17; 18]. The above approaches are also sometimes used for the joint with EG, while the influence of the EG is ignored in these cases.