Convergence-confinement Method Research Articles

Data‐Driven Tools to Evaluate Support Pressure, Radial Displacements, and Face Extrusion for Tunnels Excavated in Elastoplastic Grounds

ABSTRACTTwo‐dimensional analysis of tunnel design based on the convergence–confinement method, although commonly used in tunnel design, may not always be applied. For example, in squeezing grounds, if the support is installed very close to the tunnel face, three‐dimensional numerical modeling is required but is computationally expensive. Therefore, it is usually performed before or after tunnel excavation. A machine learning approach is presented here as an alternative to costly computations. Two surrogate models are developed based on synthetic data. The first model aims to assess the support pressure and the radial displacement at equilibrium in the lining and the radial displacement occurring close to the face at the installation distance of the support. The second model is intended to compute the extrusion of the core considering an unlined gallery. It is assumed a circular tunnel excavated in a Mohr–Coulomb elastoplastic perfectly plastic ground under an initial isotropic stress state. In particular, the bagging method is applied to neural networks to enhance the generalization capability of the models. A good performance is obtained using relatively scarce datasets. The modeling of the surrogate models is explained from the creation of the synthetic datasets to the evaluation of their performance. Their limitations are discussed. In practice, these two machine learning tools should be helpful in the field during the excavation phase.

Determination of the Ground Reaction Curve for an Elasto-Plasto-Fractured Rock Mass

Polish National Standards for underground excavation support design outline the deformational pressure model for assessing loads acting on the support systems of deep underground excavations. They distinguish two different rock mass models, highlighting the pivotal role of the critical longitudinal strain of the rock mass in appropriate model selection. A comparison between the design method given by Polish Standards and the widely recognized convergence–confinement method, consisting of a ground reaction curve (GRC), longitudinal displacement profile (LDP), and support characteristics curve (SCC), reveals the advantages of the latter in capturing the three-dimensional nature of underground excavations. The following study presents a method for establishing a GRC curve for the elasto-plasto-fractured rock mass model, featured in Polish Standards, demonstrating its applicability through analyses of a typical circular roadway under varying rock mass conditions. Practical implications are discussed, including the design of yielding steel arches as the primary support system and the calculation of safety factors for both the support system and the surrounding rock mass, considered as a natural support component. Overall, the study contributes to a deeper understanding of the actions of rock masses in the vicinity of excavations located at great depths. Furthermore, it provides practical insights for engineering applications.

Reliability analysis of tunnels considering the rock-support interaction using a metamodel-based reliability method

The convergence-confinement method (CCM) is an important approach to analysis the rock-support interaction and to design tunnel and its support. To make an effort on efficient reliability analysis of tunnels integrated with CCM, of which performance functions are mostly highly nonlinear and implicit, a hybrid intelligent algorithm combing uniform design (UD) and Gaussian process regression (GPR) is proposed. Based on the generated UD samples, GPR-parameter metamodels to predict the important parameters of CCM and GPR-probability metamodels to approximate the real performance functions are constructed consequently. Then sensitivity analysis, determination of the optimal preliminary support timing and failure probabilities calculations can be performed in conjunction with Monte Carlo simulation (MCS) based on the constructed GPR-parameter metamodels and GPR-probability metamodels. To verify the efficiency and accuracy of the proposed method, a typical circle tunnel is analyzed and good results are achieved. Finally, a practical hydraulic tunnel is analyzed using the proposed method and some beneficial conclusions are drawn.

A quantitative tunnel support design method considering the safety factor of the surrounding rock

The quantitative support design plays a vital role in tunnel design, while the conventional quantitative framework of tunnel support design through convergence-confinement method (CCM) generally focuses on the safety of the support structure element. Herein, a quantitative tunnel support design method considering the safety factor of the surrounding rock is proposed. First, the solution for the safety factor of surrounding rock element is derived under the CCM framework considering influences of the intermediate principal stress (IPS) and the dilatancy on rock-mass yielding. Second, the allowable safety factor of surrounding rock element is obtained based on the critical support line in the widely used rock quality (Q) system. Then, the framework and procedure of the quantitative tunnel support design method are outlined. Verification of the proposed method is conducted through comparisons with the analytical solution, laboratory model experiment and field monitoring data. Furthermore, a case study is employed to illustrate the proposed method, results indicate that the failure of the whole underground system is caused by the insufficient safety reserve of surrounding rock element. In general, the proposed method provides theoretical guidance for quantitative stability analysis and design optimization of tunnels.

Mechanism and prevention of “Closed Door” collapse in tunnel construction: A case study

The prevention of “closed door” collapse is crucial for tunnel construction safety and progress assurance. To address the challenge of preventing “closed door” collapse, a study was conducted based on a case of tunnel collapse. This tunnel passes through sections of fractured rock with groundwater development. The main research methods are on-site monitoring and mechanical model calculations. The research findings indicate that weak fractured rock, groundwater, initial support quality issues, long trailing distances, and extensive excavation footage all contributed to the “closed door” collapse. On-site monitoring in the fractured rock section showed the tunnel deformation is high sensitivity to construction disturbances. Even without disturbances, tunnel deformation gradually increases. This contributes about 20% of the total deformation, worsening surrounding rock damage and loosening. Additionally, the initial support exhibits cantilever arch mechanical response characteristics due to excavation of the surrounding rock on one side of its lower part. The mechanical model calculation has verified that under a cantilever arch state, the initial support lacks the bearing capacity to withstand loose load. The continuous deformation of the surrounding rock damages the collapsed body, generating loose load. Excavation of the surrounding rock beneath the initial support arch foot changed the structure from a fixed arch to a cantilever arch, ultimately leading to the joint failure of the surrounding rock-support structure system. This is the mechanism behind the collapse. By combining the convergence confinement method, the influence mechanism of factors such as excavation footage and trailing distance on the “closed door” collapse was further elucidated. Finally, according to the stability evaluation of the collapsed cavity, a strategy of “supporting first and then grouting” is adopted for collapse treatment. Drawing from the understanding of the “closed door” collapse mechanism, the following principles for collapse prevention are proposed: “small excavation footage, ensuring the quality of initial support, short trailing distance, quick support, frequent measurement.”

Analytical approach for the design of composite linings in deep tunnels considering the blasting damaged zone

Tunneling using the drilling and blasting method induces a blasting damaged zone around the tunnel, which affects the tunnel stability as well as the resulting support design. In this article, an analytical model that represents the whole-process interaction between the sequentially installed composite linings and the surrounding rock in the presence of the blasting damaged zone is proposed. First, assuming the blasting damaged zone to be a finite cylinder with decreased mechanical parameters, four ground forms according to the distribution of plastic zone are categorized and solved. Furthermore, the fictitious pressure concept is adopted to represent the three-dimensional effect of tunnel advancement, and thus, the construction process of the tunnel can be simulated. After that, the evolution patterns of the whole-process interaction between the composite linings and ground are distinguished. The critical distances and tunnel displacements between different forms in various interaction stages are identified and solved. Finally, the analytical solutions for tunnel displacement and structural responses can be obtained, based on the displacement compatibility conditions between composite linings and the ground. The analytical model is validated by numerical simulations through several typical examples, and the applicability in actual tunnel support design is verified by field monitoring results. Comparisons with an existing model and the conventional convergence-confinement method illustrate the inherent nature and advantages of the proposed model in the support system design. It is found that the blasting damage effect is significant on the tunnel responses, which should be considered in the support design. The proposed model provides a convenient feasible approach in determining the stiffness and support time of the composite linings for tunnels using the drilling and blasting method.

Mechanical characteristics and stability analysis of an innovative type of steel–concrete composite support in shallow-buried excavation tunnels

Under the influence of the principle of New Austrain Tunnelling Method (NATM), the initial support structure of shallow-buried tunnels in urban soft rock mainly adopts the forms of section steel arches or lattice girder arches combined with bolt-mesh-shotcrete. In order to solve the problems of tunnel deformation and collapse caused by untimely support or insufficient support strength during the construction process, the concept of “timely and high-strength support” was put forward, the high-strength steel pipe grid (HSPG) arch was innovatively designed, and the steel pipe grid bolt-shotcrete (SPGB) structure was established. Next, the flexural bearing performance and failure modes of the joint component and jointless component of the HSPG arch were analyzed, and the design scheme was also optimized by finite element simulation. Then, the full-scale model test of steel pipe grid concrete component (SPGC) under the pure bending load was conducted to explore the coupling bearing effect in a laboratory. In addition, relying on the underground excavation tunnel project of urban subway, the characteristic curves and stability coefficient of surrounding rock and SPGB structure were given by using the principle of convergence-confinement method. Theoretical calculations and on-sit measurements showed that SPGB structure had good adaptability in weak surrounding rock tunnel. In general, the research results were of great significance for clarifying the bearing mechanism and applicable conditions of SPGB structure, and also provided a reference for its further application in the tunnel and underground engineering.

Evaluation on the Squeezing and Design of Support system in Headrace Tunnel of Middle Modi Hydroelectic Project

Tunneling through a weak rock possess a great challenge. These challenges depends upon type of rock, excavation method, stress and deformation behavior of the rock etc. Squeezing is one of the major problem which is likely to occur during excavation of tunnel through weak rock. A reliable prediction of the extent of squeezing is essential so that a strategy can be established regarding stabilizing measures and for optimizing the support well in advance. In this paper, Middle Modi Hydroelectric Project located in the Kaski District has been taken as the case study. In this project, huge squeezing problem occurred at about chainage 1+140m At this section deformation has been recorded well over 65cm Hence, this paper basically deals with squeezing analysis using different approaches. Rock types along the headrace tunnel alignment are sheared phyllite and fractured quartzite. Mostly, intercalation of phyllite and quartzite has been found in the squeezed section Rockmass quality found in the squeezed section is extremely poor to exceptionally poor. Four main methods have been used to evaluate the squeezing phenomenon viz empirical methods such as Singh (1992) and Goel (2000), semi-empirical such as Hoek and Marinos (2000), analytical method such as (Convergence Confinement Method, 2000) and mumerical program Phase2. The main factors that control the squeezing phenomenon are the rock mass parameters and rock stresses. The uniaxial unconfined compressive strength of intact rock has been back calculated from measured deformations using phase2 program and found to be in the range of 10 to 15Mpa in the squeezed section Deformation was calculated using CCM and Compared with phase2 result. Due to excessive deformation temporary supports were provided at several locations, steel ribs are buckled and shotcrete lining is also cracked. All these have to be removed before application of final lining Finally two different approaches have been studied using phase program to address the existing problems in squeezed section of headrace tunnel ie. design of support system considering either circular shape with final lining (shotcrete and steel rib) or reshaping existing D-shaped tunnel into horseshoe shaped and providing final concrete lining.

Analysis of the interaction between bolt-reinforced rock and surface support in tunnels based on convergence-confinement method

To investigate the interaction of the bolt-reinforced rock and the surface support, an analytical model of the convergence-confinement type is proposed, considering the sequential installation of the fully grouted rockbolts and the surface support. The rock mass is assumed to be elastic-brittle-plastic material, obeying the linear Mohr-Coulomb criterion or the non-linear Hoek-Brown criterion. According to the strain states of the tunnel wall at bolt and surface support installation and the relative magnitude between the bolt length and the plastic depth during the whole process, six cases are categorized upon solving the problem. Each case is divided into three stages due to the different effects of the active rockbolts and the passive surface support. The fictitious pressure is introduced to quantify the three-dimensional (3D) effect of the tunnel face, and thus, the actual physical location along the tunnel axis of the analytical section can be considered. By using the bolt-rock strain compatibility and the rock-surface support displacement compatibility conditions, the solutions of longitudinal tunnel displacement and the reaction pressure of surface support along the tunnel axis are obtained. The proposed analytical solutions are validated by a series of 3D numerical simulations. Extensive parametric studies are conducted to examine the effect of the typical parameters of rockbolts and surface support on the tunnel displacement and the reaction pressure of the surface support under different rock conditions. The results show that the rockbolts are more effective in controlling the tunnel displacement than the surface support, which should be installed as soon as possible with a suitable length. For tunnels excavated in weak rocks or with restricted displacement control requirements, the surface support should also be installed or closed timely with a certain stiffness. The proposed method provides a convenient alternative approach for the optimization of rockbolts and surface support at the preliminary stage of tunnel design.

Determination of Supporting Time of Tunnels in the Xigeda Stratum Based on the Convergence-Confinement Method

The mechanical properties of the surrounding rock of the Xigeda stratum are easily affected by water content. In order to obtain the support characteristics of Xigeda strata, the finite difference method was used to obtain the longitudinal deformation of the surrounding rock at a certain distance from the tunnel excavation face under different water contents. Then, the longitudinal deformation profiles of a Xigeda stratum tunnel were obtained under different water content conditions. The accuracy and applicability of the results were verified through error analysis and comparison with existing research results. Based on the convergence-confinement principle, it is proposed that the best time to apply support is when the displacement increment of the surrounding rock has a sharp increase point. The support construction time under different water content conditions was obtained with the distance from the tunnel excavation face as the control index. The results show that with the increase in water content, the longitudinal deformation profile’s growth trend is steeper near the excavation surface and it is gentler when the distance from the excavation face becomes large. At a water content of 20%, the support should be applied 2.67 m behind the excavation face; at a water content of 25%, the support should be applied 1.46 m behind the excavation face. The result has a certain guiding significance for the safety of tunnel construction in the Xigeda stratum.

Calculating of the tunnel face deformations reinforced by longitudinal fiberglass dowels: From analytical method to artificial intelligence

Deformation calculation of the reinforced tunnel is always the key and difficult problem in tunnel support design. To achieve simple and rapid tunnel performance evaluation, this paper attempts to establish a novel calculation system based on the artificial intelligence, which is transitioned from an analytical method named the Convergence-Confinement Method (CCM) based on the spherical symmetry hypothesis. 200 simulations were completed by using an analytical method to describe the reinforced tunnel behavior and seven parameters were considered to calculate the tunnel face deformation. The Boruta algorithm with a random forest (RF) model was utilized to eliminate unnecessary parameters in the analytical method to build high-precision prediction model. The performance evaluation results indicated that the prediction model based the artificial intelligence has obtained excellent accuracy for estimating the deformation of the tunnel face reinforced by the longitudinal fiberglass dowels. Furthermore, the Geological Strength Index (GSI) is the most important parameter for predicting the deformations of tunnel face in the weak rock masses. Interestingly, the tentative parameter, rock type (mi), cannot be ignored when using the proposed artificial intelligence model to predict the deformations of a tunnel face reinforced by longitudinal fiberglass dowels. In general, this successful transition helps popularize the application range of analytical methods and improve the prediction accuracy for the deformations of reinforced tunnel.

Estimating support pressure with finite element and convergence-confinement method for different rock masses

Support pressure is a key factor in the stability of the excavation area during mining and tunneling. The vital thing desired in an underground engineering structure is to ensure that the structure survives safely throughout its lifetime. For this reason, choosing the right support system at the planning stage is very important for the pressure that will affect the support system must be determined with a certain convergence. This article aims to discuss the support pressures by the finite element method and convergence-confinement method and compare the results. A series of two-dimensional finite element models are established to analyze support pressure with different rock masses selected from the literature. The results reveal that since the convergence-confinement method and the finite element method have high-order relationships regarding support pressures and displacements for weak rock masses, the support pressures and the displacement values for similar conditions can be estimated with the convergence-confinement method, which is more practical than the finite element method.

Stability analysis of tunnels in expansive soil using convergence-confinement and empirical methods

The swelling pressure of the surrounding rock in tunnels within expansive soil significantly escalates construction risks and poses a threat to overall tunnel stability. Addressing this concern, this paper has formulated calculation methods suitable for analyzing the stability of tunnels in expansive soil, taking into account swelling pressure. These methods were developed based on the convergence-confinement and empirical methods. Furthermore, measurements of surrounding rock pressure and displacement were conducted in a deep-buried tunnel within the expansive paleosol of the Chinese Loess Plateau. These measurements aimed to evaluate the suitability of the derived calculation methods. The effects of both the surrounding rock swelling pressure and support parameters on key factors such as surrounding rock pressure, displacement, and safety were thoroughly analyzed. The outcomes demonstrate that the convergence-confinement method, when considering swelling pressure, is highly relevant for assessing the stability of tunnels in expansive soil characterized by structural strength and good integrity. This approach also proves effective in evaluating the stability of tunnels situated within the expansive paleosol of the Chinese Loess Plateau. Conversely, for tunnels in expansive soil with low strength and poor integrity, the application of Protodyakonov’s theory, Terzaghi theory, and the Code method, all accounting for swelling pressure, proves to be suitable for stability analysis. In expansive paleosol tunnels, as the surrounding rock swelling pressure increases from 0 kPa to 400 kPa, the safety factor of the surrounding rock pressure decreases by more than 0.17, whereas the safety factor of the surrounding rock displacement decreases by less than 0.05. Furthermore, when optimizing the parameters of steel set spacing, steel set type, and shotcrete lining thickness, it was observed that the safety factor of the surrounding rock pressure increases by more than 0.2, while the safety factor of the surrounding rock displacement experiences an increase of less than 0.15.

Effect of Constitutive Model on the Convergence-Confinement Method and Plastic Zone Radius

Effect of Constitutive Model on the Convergence-Confinement Method and Plastic Zone Radius

Analysis of interaction between tunnel support system and surrounding rock for underwater mined tunnels considering the combined effect of blasting damage and seepage pressure

When an underwater tunnel is constructed using the drill-and-blast method, the rock mass around the tunnel undergoes significant blasting damage. Quantifying the combined effect of blasting damage and seepage pressure on the support–surrounding rock interaction is critical for an underwater mined tunnel. An analytical model is proposed to analyze the entire process of support-surrounding rock interaction in an underwater mined tunnel considering the combined effect of blasting damage and seepage pressure. First, the ground reaction curves are derived considering the combined effect of blasting damage and seepage pressure. Four configurations according to the distribution of plastic zone in the damaged and undamaged zones are distinguished and solved. Subsequently, the fictitious pressure, which is introduced to quantify the spatial effect of tunnel face, is also solved. Thereafter, combining Hoek’s longitudinal displacement profile expression and the proposed ground reaction curve solution, an analytical algorithm for the support–surrounding rock interaction is proposed. The tunnel displacement and support pressure during the entire process of support–surrounding rock interaction are obtained, which are in agreement with the 3D numerical simulations and field monitoring results. Compared with the conventional convergence-confinement method, the performance and advantages of the proposed method are demonstrated. The proposed method is feasible with higher confidence for the preliminary design of underwater mined tunnel, particularly for tunnels excavated in weak zones.

Theoretical modeling of the pre-cutting system performance for the tunnel face stability in very weak rock masses

By forming continuous pre-lining around the tunnel's perimeter, pre-cutting is a recognized tunneling technique that enables full-face excavation of a tunnel even in unfavorable ground conditions. In this study, a theoretical method is put out to simulate the performance of this kind of pre-support in squeezing conditions. The loading distribution on the pre-cutting shells is determined for this purpose using the LDP of an unsupported tunnel, and the non-linear stiffness of the pre-cutting shell is then determined using the shell theory. The convergence confinement method is used to calculate how much the pre-supported tunnel isdeformed. The non-uniform loading distribution also results in the tangential and longitudinal bending moments on the pre-cutting shell. To show the effectiveness of pre-cutting shells in extremesqueezingconditions, several examples are solved. As a result, a few graphs for the preliminarydesign of a tunnel using this technique are given. The graphs show the overall tunnel displacement for various pre-cutting shells under various geological conditions. The outcomes demonstrate good agreement between FALC 3D resultsand the ones by thesuggested analytical model. A preliminary design can be made using the assessment of the proposed methodonthe loads on the pre-cutting system.

An Improved Incremental Procedure for the Ground Reaction Based on Hoek-Brown Failure Criterion in the Tunnel Convergence-Confinement Method

The purpose of this study is to introduce the Hoek–Brown nonlinear failure criterion into the convergence–confinement method (CCM), which is based on the linear failure criterion, and implant it into the ground reaction curve (GRC) in this theory. Based on consistent and rigorous theoretical analysis and according to the mechanical relationships, the principle of equilibrium, the material constitutive law, and the strain/displacement compatibility equation are used to deduce the closed-form analytical solution of the stress/displacement of the rock mass in the plastic region and to complete the simulation and interpretation of the nonlinear behavior of surrounding rock due to the advancing excavation of a circular tunnel. In this paper, confinement loss is regarded as the concept of increment in numerical analysis, and the calculation process and analysis steps of the explicit analysis method (EAM) are proposed. This method can not only realize the calculation of analytical solutions but can also be performed using simple spreadsheets. In addition, to verify the feasibility of this calculation method, this study uses published data to verify the validity of the analytical solution implemented by the incremental procedure and to study the influence of nonlinear failure criteria on the GRC, especially the mechanical behavior at the intrados of the tunnel and the distributions of tress/displacement on the cross-section of the tunnel. A comparison between the published results and the proposed solution in this study reveals consistent and favorable trends.

A quantitative analysis procedure for solving safety factor of tunnel preliminary support considering the equivalence between Hoek–Brown and Mohr–Coulomb criteria

There is a development trend from qualitative towards quantitative analysis for tunnel stability. The widely accepted convergence-confinement method (CCM) provides a quantitative framework for tunnel stability analysis, while the conventional CCM based on closed-form functions is essentially an ideal model without considering the tunnel section shape and rock weight in plastic zone. Herein, based on the CCM framework, a quantitative analysis procedure formulated through numerical simulations for more practical situations was systematically proposed to calculate the safety factor of spray-anchor support system in non-circular tunnel. Besides, similarities and differences between the most widely used Hoek-Brown (HB) and equivalent Mohr-Coulomb (EMC) criteria were considered for practical reference. The proposed method was utilized to conduct quantitative analysis of LDPs, mechanical responses of surrounding rock and safety factors for four typical tunnels, and the consistency between tunnels based on HB criterion (TBHBC) and EMC criterion (TBEMCC) was analyzed. The results indicated that the maximum radial convergence of LDP, plastic zone area, and safety factor of TBEMCC were 34.54%, 37.29%, and 47.71% lower than those of TBHBC respectively. The reasons for differences between results were revealed. The spatial effect induced by the face excavation of TBEMCC was weakened as compared to TBHBC, leading to a drop of LDP. Consequently, the safety factor was underestimated. The method systematically provided an effective tool for quantitative stability analysis and design optimization of support system for an underground excavation.

Study on progressive failure behavior and mechanical properties of tunnel arch support structures

Multi-layer composite support structure is widely applied in tunnel excavation but shows complicated failure behavior under rock pressure. Local joint broken, out-of-plane instability and arch-shotcrete interface slip widely exist and highly weaken the overall strength of support structure, which is inconsistent with the ideal assumption, leading to sever engineering disaster. Based on above situation, this paper adopts laboratory and numerical methods to investigate the bearing mechanism and failure behavior of arch joint, arch frame and arch-shotcrete composite lining. Then, a modified safety evaluation method of arch is proposed based on convergence-confinement method. The research results proved that, component strength and arch critical instability strength check are necessary in arch design. On the other hand, compared with thin-walled steel arch, the concrete-filled steel tube arch shows higher critical instability strength and better ductility, effective for controlling large deformation of soft rock. The research conclusions can provide reference for related tunnel design and construction.

JUSTIFICATION OF THE CHOICE OF THE CALCULATION MODEL OF THE ESCALATOR TUNNEL IN FLAT AND SPATIAL SETTINGS

Purpose. To perform an analysis of analytical and numerical methods of mathematical modeling of an escalator tunnel. To identify the main characteristics and differences of methods based on flat or spatial settings. To justify the choice of the calculation model of the escalator tunnel and its setting. To justify the choice of the calculation model of the escalator tunnel and its construction. Methodology. To achieve the goal, a number of analytical methods based on a flat (2D) setting (Gap method, Volume loss control method, Convergence-confinement method) were analyzed. Approaches in numerical methods, in particular in the method of finite elements, which have successfully applied flat setting, are considered. The spatial (3D) setting in the finite element method is also analyzed. Analysis of a numerical experiment based on 3D models shows that the three-dimensional structure forces interpretation decisions that are not taken into account in the cross-section, that is, in the two-dimensional model. Findings. Finite-element models of the escalator tunnel were developed in flat and spatial settings, and the 2D model with a thickness of 1 m repeated the conditions of the 3D model in its middle part. The obtained parameters of the stress-strain state were subjected to comparative analysis. It was found that the values of the norms of horizontal and vertical stresses in the fragment of the 3D model (middle) and in the 2D model differ by 3.2 and 7.2 %, respectively. Originality. Based on the results of the justification of the choice of the calculation model of the escalator tunnel, it was proved that the use of 2D models is adequate for the system of interaction of the escalator tunnel with the surrounding massif. This statement is evidenced by the almost identical distribution of stresses and strains in finite-element models in flat and spatial settings. Practical value. In the course of research, it has been proven that the flat finite-element model of the escalator tunnel is adequate for the given task, provided that it is used in several characteristic sections of the escalator tunnel, that is, the creation of a number of models in 2D, which allows considering its position along the length of the calculated tunnel.