## 1 Introduction  
The copper ore deposit mined in Poland by KGHM Polska Miedz S.A. is located in Lower Silesia, between the towns of Lubin and Glogow. The Legica-Glogow Copper Belt (LGCB) comprises three underground mining plants: Lubin, Polkowice-Sieroszowice and Rudna. The copper-bearing rocks are located at a depth from approx. 370 m b.g.l. (in the Lubin-Malomice mining area) to 1385 m b.g.l. (in the Deep Glogow mining area) [1]. Road bolting is the most commonly used roof support system in the mines of the LGCB region. The selection of a roof bolt system is preceded by identifying the roof class of a mining excavation (from class 1--the worst--to class 5--the best) in accordance with the \"Instructions on determining the geomechanical parameters of roof rocks with respect to roof classes in copper mines, as required in the selection of a roof bolting system design\" [2]. Roof rocks are classified on the basis of such parameters as:  
* Roof bedding (vertical split);
* Concentration of mineralised cracks;
* Fault concentration;
* Average fault throw;* Tensile strength of the roof rock beam. A particular design of the roof bolting system is selected in accordance with the \"Regulations on the selection, construction and control of excavation support in the KGHM Polska Miedz S.A. mines\" [3]. The roofs in the headings are protected with bolts at least 1.6 m long. The distance between the bolts (the bolting mesh) is adjusted depending on the class of the roof and on the width of the heading below the roof (Table 1). Support is provided not only to the roof but also to the side walls of the heading in cases where the excavation height is greater than 4.5 m (regardless of the side wall inclination angle) or where the excavation height is not greater than 4.5 m and moving the side walls outwards by approximately 10\({}^{\circ}\) is not possible. The roof bolts have a length of at least 1.6 m and are spaced in the side walls at 1.5 \(\times\) 1.5 m. The lower row of roof bolts is situated at a distance of approximately 1.8 m from the floor [3,4]. The regulations on the selection of roof support systems for the headings and production excavations in the LGCB mines do not allow for the values of primary stresses in the rock mass at the depth of the excavations. As a result, the roof support system may be inappropriately selected and lead to problems with the stability and functionality of the excavations. This fact may be of particular importance in the case of headings (both access and preparatory excavations) which have transport or ventilation functions. Their functionality must be ensured over a time spanning from several years to over a decade. In recent years, owing to the increase in computing power, numerical methods have become a common tool in solving various problems related to rock mass mechanics. The advantage of such methods lies in their ability to analyse objects of practically any geometry, allowing for different models describing the behaviour of the material under load, spatial changes in rock mass properties, specific field of primary stresses, dynamic loads, etc. They also provide solutions to both two-dimensional and three-dimensional tasks [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. Currently, the most popular numerical calculation methods employed in solving problems related to rock mass mechanics include the finite element method (e.g., PHASE2, RS2, RS3, NASTRAN, ANSYS, MIDAS GTS NX) and the finite difference method (e.g., FLAC software). Other methods include the boundary element method (e.g., EXAMIINE) or the distinct element method (e.g., UDIEC). Numerical methods have significantly expanded research possibilities related to the analysis and evaluation of the stability of excavations in underground mines. They are frequently used, both in Poland and abroad, to solve problems related to driving excavations in underground mines in varying or difficult geological and mining conditions [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30].