## 1 Introduction
In the case of the ground spring model, the initial earth pressure acting on the lining can be modeled by two common load models, as shown in Figure 2. Load model type 1 in Figure 2 is composed of horizontal and vertical earth pressure [15; 17; 21; 23; 24; 25; 29], which generate shear stress at the boundary between the ground and lining, while load model type 0 in Figure 2 only considers normal earth pressure [7; 15]. The normal ground spring defines ground reactions in the normal direction against the lining and usually represents only the passive side of earth pressure [15; 22; 23; 24; 25; 30]. The ground reaction curve (GRC), which can represent the ground reaction from the active side to the passive side and can include the Winkler spring model, was developed in consideration of the initial displacement of the excavation surface [31]. On the other hand, while the boundary between the ground and lining for a conventional tunnel is always regarded as full bond, for a shield tunnel the tangential ground spring stiffness, \(k_{\text{t}}\), is commonly chosen in a range between 0 and the normal ground spring stiffness, \(k_{\text{n}}\), as shown in Table 1. In the case of \(k_{\text{t}}\cong 0\), which means the tangential slip  
Figure 1: Analysis model. **(a)** Beam-spring model; **(b)** Ground spring model. between the ground and lining, the tangential spring is chosen to stabilize the computation [19; 22]. In tunnel design practice, combinations of the load model types in Figure 2 and values of \(k_{\text{t}}\) in Table 1 are in use. Furthermore, it is noted that load model type 1 contradicts the ground-lining interaction model with small \(k_{\text{t}}\), since the generated tangential stress in the case of load model type 1 is not fully transmitted onto the lining surface. Since the ground-lining interaction is one of the most crucial factors influencing the results of the analysis, the effect of the ground-lining interaction in the normal direction has been investigated intensively, but studies on the role of the ground-lining interaction in the tangential direction are few. [PERSON] and [PERSON] [PERSON]. [6] carried out parameter studies on the effect of tangential boundary condition between the ground and lining using analytical solutions without longitudinal and circumferential joints. [PERSON] et al. [27] carried out a parameter study on the effect of tangential spring stiffness, normal spring stiffness, the lateral earth pressure ratio and the overburden load using the beam-spring model with ground springs, to simulate the site measured data; that is, a specific case. Moreover, according to the literature review mentioned above, there exists a great disparity in using load models and boundary conditions in both research and practice of tunnel lining design. Therefore, this paper aims to make clear the effects of the tangential ground-lining interaction, of which the conditions come from the standards, guidelines, and recommendations on tunnel lining design, on the lining behavior and lining sectional forces, obtained through a parameter study using the beam-spring model and ground springs. This parameter study includes the initial tangential earth pressure, tangential ground spring stiffness, normal ground spring stiffness (covering a wide range between soft ground and stiff ground), and overburden load (representing deep and shallow tunnels). The results obtained contribute to our understanding on effects of tangential ground-lining interaction; thus, giving guidelines and information for practitioners regarding the tunnel lining design.