## 2 State of the Art  
The primary lining currently used to reinforce underground constructions has not changed with regard to its function since the time when the NATM principles were proposed [1; 3; 4; 5; 13]. The most important and largest construction using this method in the Czech Republic is the Blanka Tunnel Complex, which was built in 2007-2015. The primary lining of underground structures is assessed according to the limit conditions in the time interval from its implementation to the construction of the secondary (final) lining. Thus, the primary lining is dimensioned according to all critical combinations of internal forces that may occur during different phases of development. After the secondary lining is completed, its load-bearing capacity is not commonly considered. EC7 [14], which is a standard describing the methodology for designing geotechnical constructions, and does not deal with tunnel constructions in detail. This standard defines the design approaches for considering the ratio of the uncertainty in the typical input parameters for geotechnical structures in the structural-strength calculation. An integral part of tunnel construction is monitoring in real time of the behaviour of ground rock around excavation. In the case of using NATM, the primary lining is continuously monitored and based on the comparison of the prediction with the actual behaviour, and is modified in the next construction procedure (the principle of the observation method). Basic monitoring can include, for example, convergence, inclinometric and dynamometric measurements. In underground construction, there have been  
Figure 2: Factors affecting the load on the primary lining. developed progressive monitoring technologies, which make possible comprehensive control of the shape of the work geometry, such as the thickness of the primary lining (3D scanning) and a number of other modern progressive methods of stress monitoring not only in lining structures but also in rock mass around the excavation [15], that are significant for strain-stress in lining structure. The primary lining is usually designed via numerical modelling using software based on the finite-element method [10; 16; 17; 18]. Two-dimensional (2D) analyses are applied to a larger extent, as they significantly simplify the problems in constructing tunnel structures. 2D analyses cannot capture with sufficient precision the effect of spatial relocation of stress arising in the rock mass as a tunnel is driven. This phenomenon can be included in a 2D calculation with methods that only partially describe the problem. The most frequently used method is the \(\beta\)-method [19]. The \(\beta\)-method principle (sometimes also referred to as the \(\lambda\)-method) is the consideration of the spatial situation through the coefficient \(\beta\) (dimensionless; \(0<\beta<1\)), which describes the distribution of the overall mass load of the temporarily unreinforced slope and the residual load transferred by the primary lining. The aforementioned stress distribution reflects the influence of partial convergences occurring before the reinforcement mounting [5; 10; 20]. The core-softening method can be included among the other methods for determining the spatial situation within the plane. In the 2D model, the spatial effect is reflected by reducing the value of earth elastic modulus at the location of the future excavation, prior to the excavation creation and reinforcement. Thus, it is possible to rearrange the stress that can occur in a real situation before the reinforcement mounting. Three-dimensional (3D) analysis is commonly used in cases of spatially complex tunnel structures, e.g., branching, crossings and tunnel portals [21; 22]. In contrast to 2D analysis, it provides more realistic information regarding the rock mass behaviour [23]. However, this is at the expense of longer preparation of the model and greater demands regarding the comprehensiveness of the input parameters, e.g., capturing the progress of driving.