This paper systematically analyzes the challenges of stabilizing tunnel excavations in zones with low overburden in urban environments, through an engineering-validated case study of the Kobilja Glava Tunnel. A combined approach involving the New Austrian Tunneling Method (NATM) and the pre-installation of steel pipe umbrellas was applied as the primary pre-support measure under complex geotechnical conditions. The design, drilling, grouting, and formation of the temporary support arch were thoroughly documented, along with the implementation of shotcrete, lattice girders, self-drilling anchors, and reinforcement meshes. A numerical analysis was performed using the PLAXIS 2D software package, encompassing the modeling of deformations, shear forces, axial forces, and bending moments, with precisely defined support parameters. Geodetic monitoring recorded maximum surface settlements of up to 70 mm at an overburden of less than 3 m, while deformations were reduced to 28 mm at an overburden of 20 m. The numerical model confirmed soil plasticization within a 3 m wide zone, with maximum displacements reaching 6.3 cm, consistent with field measurements. Calculated tensile strain and angular distortion were classified according to established building damage criteria, confirming minimal structural impact on adjacent buildings. The applied combination of the NATM and the pipe umbrella pre-support system proved to be an effective and reliable solution for controlling deformations and ensuring excavation stability under conditions of limited rock cover and dense urban development. The obtained results provide a verified framework and practical recommendations for future tunneling projects in similar geotechnical and urban conditions, aiming to enhance safety, stability, and cost-effectiveness.

The paper presents a simultaneous numerical analysis of the geometric and material nonlinearity of the beams. It describes a process of determining the bearing capacity of a stratified cross-section of a beam made of homogeneous and isotropic material in linear and nonlinear domains of material behaviour. Material nonlinearity is analysed by the variation of the cross-sectional stiffness of the beam on bending EI in the stiffness matrix of the system obtained according to the first-order theory. Geometric nonlinearity is introduced into the calculation using the geometric stiffness matrix of the system. Numerical examples present an application of the procedure for solving problems of nonlinear structure analysis. The calculation results obtained in accordance with the procedure described in the paper are compared with the results of the SCIA software package.