## 1 Introduction  
A major portion of current underground line construction in Central Europe is implemented partially or fully in accordance with the principles of the New Austrian Tunnelling Method (NATM). The tunnel lining based on the NATM principles is implemented with a double-shell tunnel lining consisting of a primary lining (temporary), as shown in Figure 1, and a secondary (definitive) lining [1]. The purpose of the primary lining is to temporarily secure the excavation and create suitable conditions in the rock mass for proper secondary-lining function. The primary lining allows partial release of the original stress in the rock mass in the form of radial deformations, resulting in improved utilisation of the shear strength of the massif and ensuring that the optimum load on the secondary lining is achieved. Thus, the primary lining efficiently utilises the stability potential of the rock mass. Correct application of the primary lining forms a load-bearing ring in the rock mass. It is important for the working characteristics of the primary lining to suitably respond to rheological processes occurring in the rock mass and allow certain deformations while preventing the development of critical deformations that may cause secondary impairment and loosening of the rock mass [1,2]. This interaction between the lining and the rock mass can be influenced by the following factors:* a delay between partial excavation and the installation of the primary lining, which is known as the \"time factor\";
* the stiffness of the lining and its development in time, which depend on the time-dependent parameters of the shotcrete [3; 4]. The primary lining is a unique structure in many aspects. The main structural elements of the primary lining include shotcrete, steel arch frames (rolled profiles, triangular lattice girder, etc. ), reinforcement grids and bolts. The structure made of shotcrete and steel arches differs from conventional reinforced-concrete structures with regard to its composition and loading characteristics. Another important difference is the magnitude and impact of the load over time. A conventional reinforced-concrete structure is exposed to load only after the concrete has cured, whereas the primary lining in an underground construction is exposed to load immediately after the shotcrete is applied when NATM principles are used [5]. These differences should be considered in the design and assessment of the lining. The load on the primary lining is determined by the interaction of the lining with the surrounding soil or rock mass. This interaction depends on numerous factors. Before excavation and the building of the tunnel lining, the rock mass is in an original equilibrium state of strain-stress. This equilibrium is disrupted by tunnel construction, and the strain-stress changes itself to a new equilibrium status. The purpose of the primary lining is to allow a certain amount of radial deformation in the excavation, which reduces the final load on the lining. This interaction and its input factors are presented in Figure 2, which indicate that the load on the primary lining is highly complex and affected by many factors. In a real situation involving construction of the primary lining, the factors significantly influence the interaction between the lining and the rock mass and the stress development in the primary lining [6; 7; 8]. It is generally difficult (and often impossible) to capture in detail all the factors in structural-strength calculations using numerical models, as some of the factors cannot be accurately described. Many factors must be simplified either replaced using analytical, empirical relationships or completely disregarded during design to simplify the numerical model. However, simplification of the model should not affect the fundamental behaviour of the master model.