## 2 State of the Art
The modelling result indicates the stress-deformation status of the rock mass; the effect of the tunnel's construction on the development of the synclinal valley on the surface, which is important to predict for built-up areas; and the internal forces in the primary lining [24]. The lining cross-section is then assessed by comparing the inner forces with the load-bearing capacity, which is depicted in an interaction diagram according to EC2 [25]. The primary lining construction (shotcrete and steel arch frame) results in the creation of crosswise sections in a longitudinal direction having a high degree of reinforcement where the steel arches are placed and a low degree of reinforcement between the steel arches. According to EC2 [25], the primary lining falls under the slabs, i.e., flat elements with dimensions exceeding its thickness by a factor of five, but the conditions for the maximum reinforcement distances (i.e., the considered steel arches) are not satisfied. Under such conditions, design assessment by an interaction diagram, which is for conventional reinforced-concrete structures, cannot be applied. Owing to the interaction between the primary lining and the rock environment, which is influenced by the tunnelling process, the cross-section structure, the tunnelling time advance, the reinforcement methods and the structure of the primary lining, the steel reinforcing arches are considered in numerical structural calculations [26; 27; 28]. In addition to reinforcement with steel arches, the primary lining is characterised by time-dependent properties [4; 29]. Shortly after the spraying of the shotcrete, the lining begins to cooperate structurally with the rock mass. In the time from shotcrete application to the curing of the concrete, the deformation and strength parameters that influence the interaction change. Thus, the stiffness of the primary lining depends on not only its structure, i.e., the structural components used, but also the stage of the construction when the lining is considered in the partial structural-strength calculation [10; 30; 31]. In addition to the basic tools used to describe the lining's heterogeneous structure, such as cross-section homogenisation according to a weighted average or a calculation based on reinforced concrete, numerous alternative methods are available [31; 32; 33; 34]. Fundamentally, they approximate the heterogeneous structure of the lining and replace it with the parameters of a homogenous material. For the aforementioned reason, this question is handled in the lining design via alternative methods, or the presence of steel arches is disregarded completely, and only steel wire nettings are considered in structural calculations. If the reinforcing arches are disregarded, the design based on the reinforced-concrete theory can be applied. It is unclear whether disregarding the steel arches (to be on the safe side) results in a higher load-bearing capacity of the actual primary lining. If the steel arches are disregarded in static calculations, the lining will be more rigid than necessary according to the NATM, increasing the economic costs. The aforementioned problem can be solved via the following theories or methods. * weighted average: the simplest homogenisation method employs the weighted averages of the elastic modulus of the materials used, where the relevant weight is the surface area of the materials;
* solutions based on the steel-concrete theory;
* the method of [PERSON] [34];
* the method of [PERSON] [32];
* the theory for cooperation rings [35; 36; 37], which is used in the proposed procedure. The importance of shotcrete in the implementation of underground structures according to NRTM also consists of the gradual increase of the primary lining stiffness. The technical literature presents various approaches for defining the parameters of shotcrete as variables with functions of time [29; 30; 31].