In this paper, we presented a methodology for efficient and accurate modeling of water losses in hydraulic tunnels under inside internal water pressure, based on multiple linear regression (MLR). The methodology encompasses all steps needed to obtain an adequate mathematical relation between total water losses and relevant measurements in the tunnel, such as reservoir water level, piezometric levels, concrete and water temperatures, size of cracks, etc. Once the data are preprocessed and input variables were chosen, correlation analysis and PCA (principal component analysis) reduction were performed in order to obtain the pool of regression functions. Through an iterative process, according to stepwise regression principles, the most adequate MLR model in terms of accuracy and complexity was chosen. The methodology presented has been validated in modeling water losses in the hydraulic tunnel under the pressure of PSHPP “Bajina Bašta” in the Republic of Serbia. The obtained results have shown significantly better accuracy compared to the results published by other authors, proving that the developed model can be used as a powerful tool in future analyses of tunnel losses and remediation planning.

For reliable stability analysis of geotechnical structures, accurate calibration of constitutive model parameters is essential. These parameters govern the simulated material response under load, and any uncertainty can lead to significant deviations in predicted behavior. Conventional parameter determination relies on experimental testing of soil samples, whereby stress–strain measurements are used to infer individual model parameters according to their constitutive definitions. However, this manual fitting process is complex and time-consuming, particularly for soils, which exhibit highly nonlinear behavior. To address these challenges, we propose an automated parameter identification procedure for constitutive models. The methodology is developed for the Modified Cam-Clay model (MCC), a widely adopted framework for simulating the mechanical response of soft clays and normally consolidated soils. The first part of this paper presents the theoretical foundations and the implicit stress integration algorithm for the MCC model, implemented within the PAK finite element software. For automated identification, the same integration scheme is translated into Python and applied at the level of single integration point. This point-wise approach is justified for homogeneous stress states, such as those encountered in standard laboratory tests (e.g., oedometer and triaxial tests). In the second part of the paper, we describe the parameter identification program, which interfaces with the Python integration routine to perform optimization against experimental data. Finally, the developed identification algorithm is verified through a comparison of parameter estimates obtained from the PAK-based finite element implementation and those produced by the automated procedure.

Tunnelling in urban conditions is often met with demanding criteria for surface settlement control, the limitation which is arising from the fact that most of the urban area is occupied by structures which are sensitive to deformations, such as buildings, roads, communal infrastructure etc. Another important necessity in any project is to deliver the project in shortest amount of time possible. Temporary occupation of public areas for construction sites and traffic congestions alleviate social pressure which further emphasizes these requirements. If planned correctly, TBM technology promises to deliver on these requirements more readily than conventional tunnelling techniques. In this paper a Case study of Belgrade's double tube traffic tunnels is presented, in which project design went through significant conceptual transition, led by the designer's idea to change the technology of excavation from conventional to TBM, as well as to adjust the project in multiple ways to accommodate for this major turn of tides. Most notable historic background of the project is presented. Geotechnical profile of tunnels and data are shown and calculations for both TBM and conventional variants are presented and discussed.

Precise control of face pressure is essential in shield TBM tunneling to limit surface settlements and ensure the stability of surrounding structures, particularly in densely built-up urban environments. This study focuses on determining the optimal shield TBM face pressure for the specific geotechnical conditions of Phase 1, Line 1 of the Belgrade Metro, along the section from Bele Vode Station to Trgovačka Station. Three-dimensional numerical models, developed using a staged construction approach, realistically simulate sequential excavation, shield advancement, and segment installation, while incorporating representative ground properties and structural characteristics. A sensitivity analysis is conducted by systematically varying face pressure values to assess their influence on the magnitude and distribution of surface settlements. The results identify an optimal face pressure range that minimizes surface settlements while maintaining excavation stability. These findings provide practical guidance for shield TBM operation in urban tunneling, contributing to more effective settlement control and improved risk mitigation in shallow urban tunnel construction.

Rock masses are inhomogeneous, fractured, anisotropic, and initially stressed in their natural state. They consist of intact rock or rock monolith and macro-damages, which include fractures, bedding planes, faults and other forms of discontinuity. It has been experimentally confirmed that with the increase of the rock mass scale, the mechanical properties of the rock mass decrease as a consequence of discontinuities. The subject of this paper is the analysis and determination of the scale effect on the damage plasticity model parameters, which describe the mechanical behaviour of the rock mass for different loads and scales. The scale effect is analysed on a constitutive model that can simulate the most complex mechanical behaviours in rock masses (elasto-plastic with damage in stiffness and strength). The analysis is based on the results of experimental tests of rock mass, which were carried out for different scales (scale of the rock mass sample in laboratory and scale of the in situ test – shear test), while the tests were performed at the same microlocation. For the considered experimental tests, appropriate finite element models (FEMs) were formed with boundary conditions that correspond to the ones from the experiments. By simulating the performed experiments with a series of FEM analyses with complex optimization algorithms, the parameters of damage plasticity model were determined for both values of the rock mass scale, proving the scale effect numerically. Based on the obtained results, analysis and discussion of the scale effect for a given rock mass were performed.

Extended One of the most important in situ experiments for determining rock mass fracture is a direct shear test. During this test, rock mass is loaded in two phases: in the first phase, a direct normal pressure is applied and consolidation is performed, and in the second phase, a shearing stress is applied, which leads to fracture in rock mass. After fracture is reached (peak shear strength), stress decreases and shear deformation increases [1]. In this paper a simulation of rock mass behavior during direct shear test using damage plasticity model [2,3,4] is presented. For this analysis, a three-dimensional FEM model of direct shear test with dimensions 130x80x60 m was formed. In the first phase of the FEM test normal stress corresponding to measured pressure during in situ test was applied, and in the second phase of the FEM test shear displacement corresponding to recorded displacement during in situ test was applied. In the first phase normal displacements are recorded based on calculations from the FEM model, and in the second phase shear stresses are recorded. The damage plasticity model [2,3,4] is defined by the following parameters: E ₀-Modulus of elasticity, v ₀ - Poisson’s ratio, f_c - uniaxial compressive strength, f_t - uniaxial tensile strength, a_c - pressure curve parameter, D_c - degradation value for maximum compressive stress, a_t - tensile curve parameter, D_t - degradation value for tensile stress, G_c - fracture energy for uniaxial pressure, G_t - fracture energy for uniaxial tension, α_p - dilatancy parameter, α - constant defining uniaxial and biaxial compressive yield stress ratio, γ - parameter for triaxial compression, l_ch - characteristic size of elements, s₀ - stiffness recovery parameter, D_cr - critical degradation value. Numerical simulation of direct shear test (consolidation phase and shear phase) was performed for the estimated parameters of damage plasticity model. For each step of normal stress loading, corresponding value of normal displacement was calculated, and for each step of shear displacement, corresponding value of shear stress was calculated. Based on the obtained results, it is shown that damage plasticity model can successfully simulate a complex stress state during direct shear test in rock mass. Over the entire range of applied shear displacements, shear stress increases until there is a fracture in the material (peak shear strength), and afterwards stress drop is recorded (residual shear strength).